Model, optimize, and analyze complex energy systems with a powerful Python framework designed for flexibility and performance.
-
- 🚀 Getting Started
- New to FlixOpt? Start here with installation and your first model
-
-
-
- 💡 Examples Gallery
- Explore real-world examples from simple to complex systems
-
-
-
- 📚 API Reference
- Detailed documentation of all classes, methods, and parameters
-
-
-
- 📖 Recipes
- Common patterns and best practices for modeling energy systems
-
-
-
- ∫ Mathematical Notation
- Understand the mathematical formulations behind the framework
-
-
-
- 🛣️ Roadmap
- See what's coming next and contribute to the future of FlixOpt
-
+
+
+- :rocket: **[Getting Started](home/installation/)**
+
+ ---
+
+ New to FlixOpt? Start here with installation and your first model
+
+- :bulb: **[Examples Gallery](examples/)**
+
+ ---
+
+ Explore real-world examples from simple to complex systems
+
+- :books: **[API Reference](api-reference/)**
+
+ ---
+
+ Detailed documentation of all classes, methods and parameters
+
+- :book: **[Recipes](user-guide/recipes/)**
+
+ ---
+
+ Common patterns and best practices for modeling energy systems
+
+- :material-math-integral: **[Mathematical Notation](user-guide/mathematical-notation/)**
+
+ ---
+
+ Understand the mathematical formulations behind the framework
+
+- :material-road: **[Roadmap](roadmap/)**
+
+ ---
+
+ See what's coming next and contribute to the future of FlixOpt
+
## 🏗️ Framework Architecture
@@ -77,43 +82,31 @@ hide:
## :material-account-group: Community & Support
-
-
-
-
-:fontawesome-brands-github:{ .feature-icon }
+
-### GitHub
+- :fontawesome-brands-github: **GitHub**
-Report issues, request features, and contribute to the codebase
+ ---
-[Visit Repository →](https://github.com/flixOpt/flixopt){target="_blank" rel="noopener noreferrer"}
+ Report issues, request features, and contribute to the codebase
-
-
-
+ [Visit Repository →](https://github.com/flixOpt/flixopt){target="_blank" rel="noopener noreferrer"}
-:material-forum:{ .feature-icon }
+- :material-forum: **Discussions**
-### Discussions
+ ---
-Ask questions and share your projects with the community
+ Ask questions and share your projects with the community
-[Join Discussion →](https://github.com/flixOpt/flixopt/discussions){target="_blank" rel="noopener noreferrer"}
-
-
+ [Join Discussion →](https://github.com/flixOpt/flixopt/discussions){target="_blank" rel="noopener noreferrer"}
-
+- :material-book-open-page-variant: **Contributing**
-:material-book-open-page-variant:{ .feature-icon }
+ ---
-### Contributing
+ Help improve FlixOpt by contributing code, docs, or examples
-Help improve FlixOpt by contributing code, docs, or examples
-
-[Learn How →](contribute/){target="_blank" rel="noopener noreferrer"}
-
-
+ [Learn How →](contribute/){target="_blank" rel="noopener noreferrer"}
@@ -132,7 +125,7 @@ Help improve FlixOpt by contributing code, docs, or examples
Ready to optimize your energy system?
- ▶️ Start Building
+ ▶️ Start Building
diff --git a/docs/javascripts/plotly-instant.js b/docs/javascripts/plotly-instant.js
new file mode 100644
index 000000000..c6dd2766c
--- /dev/null
+++ b/docs/javascripts/plotly-instant.js
@@ -0,0 +1,30 @@
+// Re-initialize Plotly charts on MkDocs Material instant navigation
+document.addEventListener('DOMContentLoaded', function() {
+ initPlotlyCharts();
+});
+
+// Hook into Material's instant navigation
+if (typeof document$ !== 'undefined') {
+ document$.subscribe(function() {
+ initPlotlyCharts();
+ });
+}
+
+function initPlotlyCharts() {
+ const charts = document.querySelectorAll('div.mkdocs-plotly');
+ charts.forEach(function(chart) {
+ // Skip if already initialized (has children)
+ if (chart.children.length > 0) return;
+
+ try {
+ const plotData = JSON.parse(chart.textContent);
+ chart.textContent = '';
+ const data = plotData.data || [];
+ const layout = plotData.layout || {};
+ const config = plotData.config || {responsive: true};
+ Plotly.newPlot(chart, data, layout, config);
+ } catch (e) {
+ console.error('Failed to initialize Plotly chart:', e);
+ }
+ });
+}
diff --git a/docs/roadmap.md b/docs/roadmap.md
index fbad1043c..13233f014 100644
--- a/docs/roadmap.md
+++ b/docs/roadmap.md
@@ -18,7 +18,7 @@ We believe optimization modeling should be **approachable for beginners** yet **
## 🔮 Medium-term (6-12 months)
- **Modeling to Generate Alternatives (MGA)** - Built-in support for exploring near-optimal solution spaces to produce more robust, diverse solutions under uncertainty. See [PyPSA](https://docs.pypsa.org/latest/user-guide/optimization/modelling-to-generate-alternatives/) and [Calliope](https://calliope.readthedocs.io/en/latest/examples/modes/) for reference implementations
-- **Advanced stochastic optimization** - Build sophisticated new `Calculation` classes to perform different stochastic optimization approaches, like PyPSA's [two-stage stochastic programming and risk preferences with Conditional Value-at-Risk (CVaR)](https://docs.pypsa.org/latest/user-guide/optimization/stochastic/)
+- **Advanced stochastic optimization** - Build sophisticated new `Optimization` classes to perform different stochastic optimization approaches, like PyPSA's [two-stage stochastic programming and risk preferences with Conditional Value-at-Risk (CVaR)](https://docs.pypsa.org/latest/user-guide/optimization/stochastic/)
- **Enhanced component library** - More pre-built, domain-specific components (sector coupling, hydrogen systems, thermal networks, demand-side management)
## 🌟 Long-term (12+ months)
diff --git a/docs/stylesheets/extra.css b/docs/stylesheets/extra.css
index 2992267b6..78946b9ad 100644
--- a/docs/stylesheets/extra.css
+++ b/docs/stylesheets/extra.css
@@ -505,12 +505,16 @@
Home Page Inline Styles (moved from docs/index.md)
========================================================================= */
+/* Center home page content when navigation is hidden */
+/* Remove this rule as it conflicts with TOC layout */
+
.hero-section {
text-align: center;
padding: 4rem 2rem 3rem 2rem;
background: linear-gradient(135deg, rgba(0, 150, 136, 0.1) 0%, rgba(0, 121, 107, 0.1) 100%);
border-radius: 1rem;
- margin-bottom: 3rem;
+ margin: 0 auto 3rem auto;
+ max-width: 1200px;
}
.hero-section h1 {
@@ -558,47 +562,6 @@
margin-top: 2rem;
}
-.feature-grid {
- display: grid;
- grid-template-columns: repeat(auto-fit, minmax(280px, 1fr));
- gap: 2rem;
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- padding: 2rem;
- border-radius: 0.75rem;
- background: var(--md-code-bg-color);
- border: 1px solid var(--md-default-fg-color--lightest);
- transition: all 0.3s ease;
- text-align: center;
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-
-.feature-card:hover {
- transform: translateY(-4px);
- box-shadow: 0 8px 16px rgba(0, 0, 0, 0.1);
- border-color: var(--md-primary-fg-color);
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-.feature-icon {
- font-size: 3rem;
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- display: block;
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- margin-top: 0;
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- color: var(--md-default-fg-color--light);
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-
.stats-banner {
display: flex;
justify-content: space-around;
@@ -631,45 +594,14 @@
}
.architecture-section {
- margin: 4rem 0;
+ margin: 4rem auto;
padding: 2rem;
background: var(--md-code-bg-color);
border-radius: 0.75rem;
+ max-width: 1200px;
}
-.quick-links {
- display: grid;
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- gap: 1.5rem;
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-.quick-link-card:hover {
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- margin: 0;
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@media screen and (max-width: 768px) {
.hero-section h1 {
@@ -685,10 +617,6 @@
align-items: stretch;
}
- .feature-grid {
- grid-template-columns: 1fr;
- }
-
.stats-banner {
flex-direction: column;
}
@@ -839,27 +767,26 @@ button:focus-visible {
Footer Alignment Fix
========================================================================= */
-/* Align footer with content width */
-.md-footer-meta__inner,
-.md-footer__inner {
- max-width: 1300px;
- margin: 0 auto;
- padding-left: 1.2rem;
- padding-right: 1.2rem;
+/* Hide the social media footer section */
+.md-footer-meta {
+ display: none;
+}
+
+/* Footer navigation content matches page width */
+.md-footer .md-grid {
+ max-width: 1300px !important;
+ padding-left: 1.2rem !important;
+ padding-right: 1.2rem !important;
}
@media screen and (min-width: 76.25em) {
- .md-footer-meta__inner,
- .md-footer__inner {
- padding-left: 1rem;
- padding-right: 1rem;
+ .md-footer .md-grid {
+ padding-left: 1rem !important;
}
}
@media screen and (min-width: 100em) {
- .md-footer-meta__inner,
- .md-footer__inner {
- padding-left: 2rem;
- padding-right: 2rem;
+ .md-footer .md-grid {
+ padding-left: 2rem !important;
}
}
diff --git a/docs/user-guide/building-models/index.md b/docs/user-guide/building-models/index.md
new file mode 100644
index 000000000..27808ea56
--- /dev/null
+++ b/docs/user-guide/building-models/index.md
@@ -0,0 +1,20 @@
+# Building Models
+
+!!! note "Under Development"
+ This section is being expanded with detailed tutorials.
+
+Learn how to construct FlowSystem models step by step:
+
+- Defining time horizons and dimensions
+- Creating buses and flows
+- Adding components (Sources, Sinks, Converters, Storage)
+- Configuring effects and objectives
+- Using advanced features (Investment, On/Off, Piecewise)
+
+## Getting Started
+
+For now, see:
+
+- **[Core Concepts](../core-concepts.md)** - Understand the fundamental building blocks
+- **[Examples](../../examples/index.md)** - Working code you can learn from
+- **[Mathematical Notation](../mathematical-notation/index.md)** - Detailed specifications of each element
diff --git a/docs/user-guide/core-concepts.md b/docs/user-guide/core-concepts.md
index d63f10f27..3bccb554c 100644
--- a/docs/user-guide/core-concepts.md
+++ b/docs/user-guide/core-concepts.md
@@ -1,155 +1,196 @@
-# Core concepts of flixopt
+# Core Concepts
-FlixOpt is built around a set of core concepts that work together to represent and optimize **any system involving flows and conversions** - whether that's energy systems, material flows, supply chains, water networks, or production processes.
+This page introduces the fundamental concepts of flixOpt through practical scenarios. Understanding these concepts will help you model any system involving flows and conversions.
-This page provides a high-level overview of these concepts and how they interact.
+## The Big Picture
-## Main building blocks
+Imagine you're managing a district heating system. You have:
-### FlowSystem
+- A **gas boiler** that burns natural gas to produce heat
+- A **heat pump** that uses electricity to extract heat from the environment
+- A **thermal storage tank** to buffer heat production and demand
+- **Buildings** that need heat throughout the day
+- Access to the **gas grid** and **electricity grid**
-The [`FlowSystem`][flixopt.flow_system.FlowSystem] is the central organizing unit in FlixOpt.
-Every FlixOpt model starts with creating a FlowSystem. It:
+Your goal: **minimize total operating costs** while meeting all heat demands.
-- Defines the timesteps for the optimization
-- Contains and connects [components](#components), [buses](#buses), and [flows](#flows)
-- Manages the [effects](#effects) (objectives and constraints)
+This is exactly the kind of problem flixOpt solves. Let's see how each concept maps to this scenario.
-FlowSystem provides two ways to access elements:
+## Buses: Where Things Connect
-- **Dict-like interface**: Access any element by label: `flow_system['Boiler']`, `'Boiler' in flow_system`, `flow_system.keys()`
-- **Direct containers**: Access type-specific containers: `flow_system.components`, `flow_system.buses`, `flow_system.effects`, `flow_system.flows`
+A [`Bus`][flixopt.elements.Bus] is a connection point where energy or material flows meet. Think of it as a junction or hub.
-Element labels must be unique across all types. See the [`FlowSystem` API reference][flixopt.flow_system.FlowSystem] for detailed examples and usage patterns.
+!!! example "In our heating system"
+ - **Heat Bus** — where heat from the boiler, heat pump, and storage meets the building demand
+ - **Gas Bus** — connection to the gas grid
+ - **Electricity Bus** — connection to the power grid
-### Flows
+**The key rule:** At every bus, **inputs must equal outputs** at each timestep.
-[`Flow`][flixopt.elements.Flow] objects represent the movement of energy or material between a [Bus](#buses) and a [Component](#components) in a predefined direction.
+$$\sum inputs = \sum outputs$$
-- Have a `size` which, generally speaking, defines how much energy or material can be moved. Usually measured in MW, kW, m³/h, etc.
-- Have a `flow_rate`, which defines how fast energy or material is transported. Usually measured in MW, kW, m³/h, etc.
-- Have constraints to limit the flow-rate (min/max, total flow hours, active/inactive status etc.)
-- Can have fixed profiles (for demands or renewable generation)
-- Can have [Effects](#effects) associated by their use (costs, emissions, labour, ...)
+This balance constraint is what makes your model physically meaningful — energy can't appear or disappear.
-#### Flow Hours
-While the **Flow Rate** defines the rate in which energy or material is transported, the **Flow Hours** define the amount of energy or material that is transported.
-Its defined by the flow_rate times the duration of the timestep in hours.
+## Flows: What Moves Between Elements
-Examples:
+A [`Flow`][flixopt.elements.Flow] represents the movement of energy or material. Every flow connects a component to a bus, with a defined direction.
-| Flow Rate | Timestep | Flow Hours |
-|-----------|----------|------------|
-| 10 (MW) | 1 hour | 10 (MWh) |
-| 10 (MW) | 6 minutes | 0.1 (MWh) |
-| 10 (kg/h) | 1 hour | 10 (kg) |
+!!! example "In our heating system"
+ - Heat flowing **from** the boiler **to** the Heat Bus
+ - Gas flowing **from** the Gas Bus **to** the boiler
+ - Heat flowing **from** the Heat Bus **to** the buildings
-### Buses
+Flows have:
-[`Bus`][flixopt.elements.Bus] objects represent nodes or connection points in a FlowSystem. They:
+- A **size** (capacity) — *"This boiler can deliver up to 500 kW"*
+- A **flow rate** — *"Right now it's running at 300 kW"*
-- Balance incoming and outgoing flows
-- Can represent physical networks like heat, electricity, or gas
-- Handle infeasible balances gently by allowing the balance to be closed in return for a big Penalty (optional)
+## Components: The Equipment
-### Components
+[`Components`][flixopt.elements.Component] are the physical (or logical) elements that transform, store, or transfer flows.
-[`Component`][flixopt.elements.Component] objects usually represent physical entities in your system that interact with [`Flows`][flixopt.elements.Flow]. The generic component types work across all domains:
+### Converters — Transform One Thing Into Another
-- [`LinearConverters`][flixopt.components.LinearConverter] - Converts input flows to output flows with (piecewise) linear relationships
- - *Energy: boilers, heat pumps, turbines*
- - *Manufacturing: assembly lines, processing equipment*
- - *Chemistry: reactors, separators*
-- [`Storages`][flixopt.components.Storage] - Stores energy or material over time
- - *Energy: batteries, thermal storage, gas storage*
- - *Logistics: warehouses, buffer inventory*
- - *Water: reservoirs, tanks*
-- [`Sources`][flixopt.components.Source] / [`Sinks`][flixopt.components.Sink] / [`SourceAndSinks`][flixopt.components.SourceAndSink] - Produce or consume flows
- - *Energy: demands, renewable generation*
- - *Manufacturing: raw material supply, product demand*
- - *Supply chain: suppliers, customers*
-- [`Transmissions`][flixopt.components.Transmission] - Moves flows between locations with possible losses
- - *Energy: pipelines, power lines*
- - *Logistics: transport routes*
- - *Water: distribution networks*
+A [`LinearConverter`][flixopt.components.LinearConverter] takes inputs and produces outputs with a defined efficiency.
-**Pre-built specialized components** for energy systems include [`Boilers`][flixopt.linear_converters.Boiler], [`HeatPumps`][flixopt.linear_converters.HeatPump], [`CHPs`][flixopt.linear_converters.CHP], etc. These can serve as blueprints for custom domain-specific components.
+!!! example "In our heating system"
+ - **Gas Boiler**: Gas → Heat (η = 90%)
+ - **Heat Pump**: Electricity → Heat (COP = 3.5)
-### Effects
+The conversion relationship:
-[`Effect`][flixopt.effects.Effect] objects represent impacts or metrics related to your system. While commonly used to allocate costs, they're completely flexible:
+$$output = \eta \cdot input$$
-**Energy systems:**
-- Costs (investment, operation)
-- Emissions (CO₂, NOx, etc.)
-- Primary energy consumption
+### Storages — Save for Later
-**Other domains:**
-- Production time, labor hours (manufacturing)
-- Water consumption, wastewater (process industries)
-- Transport distance, vehicle utilization (logistics)
-- Space consumption
-- Any custom metric relevant to your domain
+A [`Storage`][flixopt.components.Storage] accumulates and releases energy or material over time.
-These can be freely defined and crosslink to each other (`CO₂` ──[specific CO₂-costs]─→ `Costs`).
-One effect is designated as the **optimization objective** (typically Costs), while others can be constrained.
-This approach allows for multi-criteria optimization using both:
+!!! example "In our heating system"
+ - **Thermal Tank**: Store excess heat during cheap hours, use it during expensive hours
- - **Weighted Sum Method**: Optimize a theoretical Effect which other Effects crosslink to
- - **ε-constraint method**: Constrain effects to specific limits
+The storage tracks its state over time:
-### Optimization
+$$charge(t+1) = charge(t) + charging - discharging$$
-A [`FlowSystem`][flixopt.flow_system.FlowSystem] can be converted to a Model and optimized by creating an [`Optimization`][flixopt.optimization.Optimization] from it.
+### Sources & Sinks — System Boundaries
-FlixOpt offers different optimization modes:
+[`Sources`][flixopt.components.Source] and [`Sinks`][flixopt.components.Sink] connect your system to the outside world.
-- [`Optimization`][flixopt.optimization.Optimization] - Solves the entire problem at once
-- [`SegmentedOptimization`][flixopt.optimization.SegmentedOptimization] - Solves the problem in segments (with optional overlap), improving performance for large problems
-- [`ClusteredOptimization`][flixopt.optimization.ClusteredOptimization] - Uses typical periods to reduce computational requirements
+!!! example "In our heating system"
+ - **Gas Source**: Buy gas from the grid at market prices
+ - **Electricity Source**: Buy power at time-varying prices
+ - **Heat Sink**: The building demand that must be met
-### Results
+## Effects: What You're Tracking
-The results of an optimization are stored in a [`Results`][flixopt.results.Results] object.
-This object contains the solutions of the optimization as well as all information about the [`Optimization`][flixopt.optimization.Optimization] and the [`FlowSystem`][flixopt.flow_system.FlowSystem] it was created from.
-The solution is stored as an `xarray.Dataset`, but can be accessed through their associated Component, Bus or Effect.
+An [`Effect`][flixopt.effects.Effect] represents any metric you want to track or optimize. One effect is your **objective** (what you minimize or maximize), others can be **constraints**.
-This [`Results`][flixopt.results.Results] object can be saved to file and reloaded from file, allowing you to analyze the results anytime after the solve.
+!!! example "In our heating system"
+ - **Costs** (objective) — minimize total operating costs
+ - **CO₂ Emissions** (constraint) — stay below 1000 tonnes/year
+ - **Gas Consumption** (tracking) — report total gas used
-## How These Concepts Work Together
+Effects can be linked: *"Each kg of CO₂ costs €80 in emissions trading"* — this creates a connection from the CO₂ effect to the Costs effect.
-The process of working with FlixOpt can be divided into 3 steps:
+## FlowSystem: Putting It All Together
-1. Create a [`FlowSystem`][flixopt.flow_system.FlowSystem], containing all the elements and data of your system
- - Define the time horizon of your system (and optionally your periods and scenarios, see [Dimensions](mathematical-notation/dimensions.md)))
- - Add [`Effects`][flixopt.effects.Effect] to represent costs, emissions, etc.
- - Add [`Buses`][flixopt.elements.Bus] as connection points in your system and [`Sinks`][flixopt.components.Sink] & [`Sources`][flixopt.components.Source] as connections to the outer world (markets, power grid, ...)
- - Add [`Components`][flixopt.components] like [`Boilers`][flixopt.linear_converters.Boiler], [`HeatPumps`][flixopt.linear_converters.HeatPump], [`CHPs`][flixopt.linear_converters.CHP], etc.
- - Add
- - [`FlowSystems`][flixopt.flow_system.FlowSystem] can also be loaded from a netCDF file*
-2. Translate the model to a mathematical optimization problem
- - Create an [`Optimization`][flixopt.optimization.Optimization] from your FlowSystem and choose a Solver
- - ...The Optimization is translated internally to a mathematical optimization problem...
- - ...and solved by the chosen solver.
-3. Analyze the results
- - The results are stored in a [`Results`][flixopt.results.Results] object
- - This object can be saved to file and reloaded from file, retaining all information about the optimization
- - As it contains the used [`FlowSystem`][flixopt.flow_system.FlowSystem], it fully documents all assumptions taken to create the results.
+The [`FlowSystem`][flixopt.flow_system.FlowSystem] is your complete model. It contains all buses, components, flows, and effects, plus the **time definition** for your optimization.
+
+```python
+import flixopt as fx
+
+# Define timesteps (e.g., hourly for one week)
+timesteps = pd.date_range('2024-01-01', periods=168, freq='h')
+
+# Create the system
+flow_system = fx.FlowSystem(timesteps)
+
+# Add elements
+flow_system.add_elements(heat_bus, gas_bus, electricity_bus)
+flow_system.add_elements(boiler, heat_pump, storage)
+flow_system.add_elements(costs_effect, co2_effect)
+```
+
+## The Workflow: Model → Optimize → Analyze
+
+Working with flixOpt follows three steps:
+
+```mermaid
+graph LR
+ A[1. Build FlowSystem] --> B[2. Run Optimization]
+ B --> C[3. Analyze Results]
+```
+
+### 1. Build Your Model
+
+Define your system structure, parameters, and time series data.
+
+### 2. Run the Optimization
+
+Create an [`Optimization`][flixopt.optimization.Optimization] and solve it:
+
+```python
+optimization = fx.Optimization('my_model', flow_system)
+results = optimization.solve(fx.solvers.HighsSolver())
+```
+
+### 3. Analyze Results
+
+The [`Results`][flixopt.results.Results] object contains all solution data:
+
+```python
+# Access component results
+boiler_output = results['Boiler'].node_balance()
+
+# Get total costs
+total_costs = results.solution['Costs']
+```
Conceptual Usage and IO operations of FlixOpt
-## Advanced Usage
-As flixopt is build on [linopy](https://github.com/PyPSA/linopy), any model created with FlixOpt can be extended or modified using the great [linopy API](https://linopy.readthedocs.io/en/latest/api.html).
-This allows to adjust your model to very specific requirements without loosing the convenience of FlixOpt.
-
-
-
-
-
-
-
-
-
+## Quick Reference
+
+| Concept | What It Represents | Real-World Example |
+|---------|-------------------|-------------------|
+| **Bus** | Connection point | Heat network, electrical grid |
+| **Flow** | Energy/material movement | Heat delivery, gas consumption |
+| **LinearConverter** | Transformation equipment | Boiler, heat pump, turbine |
+| **Storage** | Time-shifting capability | Battery, thermal tank, warehouse |
+| **Source/Sink** | System boundary | Grid connection, demand |
+| **Effect** | Metric to track/optimize | Costs, emissions, energy use |
+| **FlowSystem** | Complete model | Your entire system |
+
+## Beyond Energy Systems
+
+While our example used a heating system, flixOpt works for any flow-based optimization:
+
+| Domain | Buses | Components | Effects |
+|--------|-------|------------|---------|
+| **District Heating** | Heat, Gas, Electricity | Boilers, CHPs, Heat Pumps | Costs, CO₂ |
+| **Manufacturing** | Raw Materials, Products | Machines, Assembly Lines | Costs, Time, Labor |
+| **Supply Chain** | Warehouses, Locations | Transport, Storage | Costs, Distance |
+| **Water Networks** | Reservoirs, Treatment | Pumps, Pipes | Costs, Energy |
+
+## Next Steps
+
+- **[Building Models](building-models/index.md)** — Step-by-step guide to constructing models
+- **[Examples](../examples/index.md)** — Working code for common scenarios
+- **[Mathematical Notation](mathematical-notation/index.md)** — Detailed constraint formulations
+
+## Advanced: Extending with linopy
+
+flixOpt is built on [linopy](https://github.com/PyPSA/linopy). You can access and extend the underlying optimization model for custom constraints:
+
+```python
+# Access the linopy model after building
+optimization.do_modeling()
+model = optimization.model
+
+# Add custom constraints using linopy API
+model.add_constraints(...)
+```
+
+This allows advanced users to add domain-specific constraints while keeping flixOpt's convenience for standard modeling.
diff --git a/docs/user-guide/faq.md b/docs/user-guide/faq.md
new file mode 100644
index 000000000..63994180d
--- /dev/null
+++ b/docs/user-guide/faq.md
@@ -0,0 +1,34 @@
+# Frequently Asked Questions
+
+## What is flixOpt?
+
+flixOpt is a Python framework for modeling and optimizing energy and material flow systems. It handles both operational optimization (dispatch) and investment optimization (capacity expansion).
+
+## Which solvers does flixOpt support?
+
+- **HiGHS** (default, included)
+- **Gurobi** (commercial, academic licenses available)
+
+## How do I install flixOpt?
+
+```bash
+pip install flixopt
+```
+
+For full features:
+```bash
+pip install "flixopt[full]"
+```
+
+## Do I need to install a solver separately?
+
+No. HiGHS is included and works out of the box.
+
+## Can I add custom constraints?
+
+Yes. You can add custom constraints directly to the optimization model using linopy.
+
+## Where can I get help?
+
+- Check [Troubleshooting](troubleshooting.md)
+- Open an [issue on GitHub](https://github.com/flixOpt/flixopt/issues)
diff --git a/docs/user-guide/index.md b/docs/user-guide/index.md
new file mode 100644
index 000000000..bfb288ea4
--- /dev/null
+++ b/docs/user-guide/index.md
@@ -0,0 +1,83 @@
+# User Guide
+
+Welcome to the flixOpt User Guide! This guide will help you master energy and material flow optimization with flixOpt.
+
+## What is flixOpt?
+
+flixOpt is a comprehensive framework for modeling and optimizing energy and material flow systems. It supports:
+
+- **Operational Optimization** - Dispatch optimization with fixed capacities
+- **Investment Optimization** - Capacity expansion planning with binary or continuous sizing
+- **Multi-Period Planning** - Sequential investment decisions across multiple periods
+- **Scenario Analysis** - Stochastic modeling with weighted scenarios
+
+## Key Features
+
+
+
+- :material-puzzle: **Flexible Components**
+
+ ---
+
+ Flow, Bus, Storage, LinearConverter - build any system topology
+
+- :material-cog: **Advanced Modeling**
+
+ ---
+
+ Investment decisions, On/Off states, Piecewise linearization
+
+- :material-calculator: **Multiple Solvers**
+
+ ---
+
+ HiGHS (default), Gurobi, CPLEX - choose what fits your needs
+
+- :material-chart-line: **Built-in Analysis**
+
+ ---
+
+ Plotting, export, and result exploration tools
+
+
+
+## Learning Path
+
+This guide follows a sequential learning path:
+
+| Step | Section | What You'll Learn |
+|------|---------|-------------------|
+| 1 | [Core Concepts](core-concepts.md) | Fundamental building blocks: FlowSystem, Bus, Flow, Components, Effects |
+| 2 | [Building Models](building-models/index.md) | How to construct models step by step |
+| 3 | [Running Optimizations](optimization/index.md) | Solver configuration and execution |
+| 4 | [Analyzing Results](results/index.md) | Extracting and visualizing outcomes |
+| 5 | [Mathematical Notation](mathematical-notation/index.md) | Deep dive into the math behind each element |
+| 6 | [Recipes](recipes/index.md) | Common patterns and solutions |
+
+## Quick Links
+
+### Getting Started
+
+- [Quick Start](../home/quick-start.md) - Build your first model in 5 minutes
+- [Minimal Example](../examples/00-Minimal Example.md) - Simplest possible model
+- [Core Concepts](core-concepts.md) - Understand the fundamentals
+
+### Reference
+
+- [Mathematical Notation](mathematical-notation/index.md) - Detailed specifications
+- [API Reference](../api-reference/index.md) - Complete class documentation
+- [Examples](../examples/index.md) - Working code to learn from
+
+### Help
+
+- [FAQ](faq.md) - Frequently asked questions
+- [Troubleshooting](troubleshooting.md) - Common issues and solutions
+- [Community](support.md) - Get help from the community
+
+## Use Cases
+
+flixOpt handles any flow-based optimization problem:
+
+**Energy Systems**: Power dispatch, CHP optimization, renewable integration, battery storage, district heating
+
+**Industrial Applications**: Process optimization, multi-commodity networks, supply chains, resource allocation
diff --git a/docs/user-guide/mathematical-notation/dimensions.md b/docs/user-guide/mathematical-notation/dimensions.md
deleted file mode 100644
index 2a526e19d..000000000
--- a/docs/user-guide/mathematical-notation/dimensions.md
+++ /dev/null
@@ -1,316 +0,0 @@
-# Dimensions
-
-FlixOpt's `FlowSystem` supports multiple dimensions for modeling optimization problems. Understanding these dimensions is crucial for interpreting the mathematical formulations presented in this documentation.
-
-## The Three Dimensions
-
-FlixOpt models can have up to three dimensions:
-
-1. **Time (`time`)** - **MANDATORY**
- - Represents the temporal evolution of the system
- - Defined via `pd.DatetimeIndex`
- - Must contain at least 2 timesteps
- - All optimization variables and constraints evolve over time
-2. **Period (`period`)** - **OPTIONAL**
- - Represents independent planning periods (e.g., years 2020, 2021, 2022)
- - Defined via `pd.Index` with integer values
- - Used for multi-period optimization such as investment planning across years
- - Each period is independent with its own time series
-3. **Scenario (`scenario`)** - **OPTIONAL**
- - Represents alternative futures or uncertainty realizations (e.g., "Base Case", "High Demand")
- - Defined via `pd.Index` with any labels
- - Scenarios within the same period share the same time dimension
- - Used for stochastic optimization or scenario comparison
-
----
-
-## Dimensional Structure
-
-**Coordinate System:**
-
-```python
-FlowSystemDimensions = Literal['time', 'period', 'scenario']
-
-coords = {
- 'time': pd.DatetimeIndex, # Always present
- 'period': pd.Index | None, # Optional
- 'scenario': pd.Index | None # Optional
-}
-```
-
-**Example:**
-```python
-import pandas as pd
-import numpy as np
-import flixopt as fx
-
-timesteps = pd.date_range('2020-01-01', periods=24, freq='h')
-scenarios = pd.Index(['Base Case', 'High Demand'])
-periods = pd.Index([2020, 2021, 2022])
-
-flow_system = fx.FlowSystem(
- timesteps=timesteps,
- periods=periods,
- scenarios=scenarios,
- scenario_weights=np.array([0.5, 0.5]) # Scenario weights
-)
-```
-
-This creates a system with:
-- 24 time steps per scenario per period
-- 2 scenarios with equal weights (0.5 each)
-- 3 periods (years)
-- **Total decision space:** 24 × 2 × 3 = 144 time-scenario-period combinations
-
----
-
-## Independence of Formulations
-
-**All mathematical formulations in this documentation are independent of whether periods or scenarios are present.**
-
-The equations shown throughout this documentation (for [Flow](elements/Flow.md), [Storage](elements/Storage.md), [Bus](elements/Bus.md), etc.) are written with only the time index $\text{t}_i$. When periods and/or scenarios are added, **the same equations apply** - they are simply expanded to additional dimensions.
-
-### How Dimensions Expand Formulations
-
-**Flow rate bounds** (from [Flow](elements/Flow.md)):
-
-$$
-\text{P} \cdot \text{p}^{\text{L}}_{\text{rel}}(\text{t}_{i}) \leq p(\text{t}_{i}) \leq \text{P} \cdot \text{p}^{\text{U}}_{\text{rel}}(\text{t}_{i})
-$$
-
-This equation remains valid regardless of dimensions:
-
-| Dimensions Present | Variable Indexing | Interpretation |
-|-------------------|-------------------|----------------|
-| Time only | $p(\text{t}_i)$ | Flow rate at time $\text{t}_i$ |
-| Time + Scenario | $p(\text{t}_i, s)$ | Flow rate at time $\text{t}_i$ in scenario $s$ |
-| Time + Period | $p(\text{t}_i, y)$ | Flow rate at time $\text{t}_i$ in period $y$ |
-| Time + Period + Scenario | $p(\text{t}_i, y, s)$ | Flow rate at time $\text{t}_i$ in period $y$, scenario $s$ |
-
-**The mathematical relationship remains identical** - only the indexing expands.
-
----
-
-## Independence Between Scenarios and Periods
-
-**There is no interconnection between scenarios and periods, except for shared investment decisions within a period.**
-
-### Scenario Independence
-
-Scenarios within a period are **operationally independent**:
-
-- Each scenario has its own operational variables: $p(\text{t}_i, s_1)$ and $p(\text{t}_i, s_2)$ are independent
-- Scenarios cannot exchange energy, information, or resources
-- Storage states are separate: $c(\text{t}_i, s_1) \neq c(\text{t}_i, s_2)$
-- Binary states (active/inactive) are independent: $s(\text{t}_i, s_1)$ vs $s(\text{t}_i, s_2)$
-
-Scenarios are connected **only through the objective function** via weights:
-
-$$
-\min \quad \sum_{s \in \mathcal{S}} w_s \cdot \text{Objective}_s
-$$
-
-Where:
-- $\mathcal{S}$ is the set of scenarios
-- $w_s$ is the weight for scenario $s$
-- The optimizer balances performance across scenarios according to their weights
-- **Both the objective effect and Penalty effect are weighted by $w_s$** (see [Penalty weighting](effects-penalty-objective.md#penalty))
-
-### Period Independence
-
-Periods are **completely independent** optimization problems:
-
-- Each period has separate operational variables
-- Each period has separate investment decisions
-- No temporal coupling between periods (e.g., storage state at end of period $y$ does not affect period $y+1$)
-- Periods cannot exchange resources or information
-
-Periods are connected **only through weighted aggregation** in the objective:
-
-$$
-\min \quad \sum_{y \in \mathcal{Y}} w_y \cdot \text{Objective}_y
-$$
-
-Where **both the objective effect and Penalty effect are weighted by $w_y$** (see [Penalty weighting](effects-penalty-objective.md#penalty))
-
-### Shared Periodic Decisions: The Exception
-
-**Investment decisions (sizes) can be shared across all scenarios:**
-
-By default, sizes (e.g., Storage capacity, Thermal power, ...) are **scenario-independent** but **flow_rates are scenario-specific**.
-
-**Example - Flow with investment:**
-
-$$
-v_\text{invest}(y) = s_\text{invest}(y) \cdot \text{size}_\text{fixed} \quad \text{(one decision per period)}
-$$
-
-$$
-p(\text{t}_i, y, s) \leq v_\text{invest}(y) \cdot \text{rel}_\text{upper} \quad \forall s \in \mathcal{S} \quad \text{(same capacity for all scenarios)}
-$$
-
-**Interpretation:**
-- "We decide once in period $y$ how much capacity to build" (periodic decision)
-- "This capacity is then operated differently in each scenario $s$ within period $y$" (temporal decisions)
-- "Periodic effects (investment) are incurred once per period, temporal effects (operational) are weighted across scenarios"
-
-This reflects real-world investment under uncertainty: you build capacity once (periodic/investment decision), but it operates under different conditions (temporal/operational decisions per scenario).
-
-**Mathematical Flexibility:**
-
-Variables can be either scenario-independent or scenario-specific:
-
-| Variable Type | Scenario-Independent | Scenario-Specific |
-|---------------|---------------------|-------------------|
-| **Sizes** (e.g., $\text{P}$) | $\text{P}(y)$ - Single value per period | $\text{P}(y, s)$ - Different per scenario |
-| **Flow rates** (e.g., $p(\text{t}_i)$) | $p(\text{t}_i, y)$ - Same across scenarios | $p(\text{t}_i, y, s)$ - Different per scenario |
-
-**Use Cases:**
-
-*Investment problems (with InvestParameters):*
-- **Sizes shared** (default): Investment under uncertainty - build capacity that performs well across all scenarios
-- **Sizes vary**: Scenario-specific capacity planning where different investments can be made for each future
-- **Selected sizes shared**: Mix of shared critical infrastructure and scenario-specific optional/flexible capacity
-
-*Dispatch problems (fixed sizes, no investments):*
-- **Flow rates shared**: Robust dispatch - find a single operational strategy that works across all forecast scenarios (e.g., day-ahead unit commitment under demand/weather uncertainty)
-- **Flow rates vary** (default): Scenario-adaptive dispatch - optimize operations for each scenario's specific conditions (demand, weather, prices)
-
-For implementation details on controlling scenario independence, see the [`FlowSystem`][flixopt.flow_system.FlowSystem] API reference.
-
----
-
-## Dimensional Impact on Objective Function
-
-The objective function aggregates effects across all dimensions with weights:
-
-### Time Only
-$$
-\min \quad \sum_{\text{t}_i \in \mathcal{T}} \sum_{e \in \mathcal{E}} s_{e}(\text{t}_i)
-$$
-
-### Time + Scenario
-$$
-\min \quad \sum_{s \in \mathcal{S}} w_s \cdot \left( \sum_{\text{t}_i \in \mathcal{T}} \sum_{e \in \mathcal{E}} s_{e}(\text{t}_i, s) \right)
-$$
-
-### Time + Period
-$$
-\min \quad \sum_{y \in \mathcal{Y}} w_y \cdot \left( \sum_{\text{t}_i \in \mathcal{T}} \sum_{e \in \mathcal{E}} s_{e}(\text{t}_i, y) \right)
-$$
-
-### Time + Period + Scenario (Full Multi-Dimensional)
-$$
-\min \quad \sum_{y \in \mathcal{Y}} \sum_{s \in \mathcal{S}} w_{y,s} \cdot \left( \sum_{\text{t}_i \in \mathcal{T}} \sum_{e \in \mathcal{E}} s_{e}(\text{t}_i, y, s) \right)
-$$
-
-Where:
-- $\mathcal{T}$ is the set of time steps
-- $\mathcal{E}$ is the set of effects (including the Penalty effect $E_\Phi$)
-- $\mathcal{S}$ is the set of scenarios
-- $\mathcal{Y}$ is the set of periods
-- $s_{e}(\cdots)$ are the effect contributions (costs, emissions, etc.)
-- $w_s, w_y, w_{y,s}$ are the dimension weights
-- **Penalty effect is weighted identically to other effects**
-
-**See [Effects, Penalty & Objective](effects-penalty-objective.md) for complete formulations including:**
-- How temporal and periodic effects expand with dimensions
-- Detailed objective function for each dimensional case
-- Periodic (investment) vs temporal (operational) effect handling
-- Explicit Penalty weighting formulations
-
----
-
-## Weights
-
-Weights determine the relative importance of scenarios and periods in the objective function.
-
-### Scenario Weights
-
-You provide scenario weights explicitly via the `scenario_weights` parameter:
-
-```python
-flow_system = fx.FlowSystem(
- timesteps=timesteps,
- scenarios=scenarios,
- scenario_weights=np.array([0.3, 0.7]) # Scenario probabilities
-)
-```
-
-**Default:** If not specified, all scenarios have equal weight (normalized to sum to 1).
-
-### Period Weights
-
-Period weights are **automatically computed** from the period index (similar to how `hours_per_timestep` is computed from the time index):
-
-```python
-# Period weights are computed from the differences between period values
-periods = pd.Index([2020, 2025, 2030, 2035])
-# → period_weights = [5, 5, 5, 5] (representing 5-year intervals)
-
-flow_system = fx.FlowSystem(
- timesteps=timesteps,
- periods=periods,
- # No need to specify period weights - they're computed automatically
-)
-```
-
-**How period weights are computed:**
-- For periods `[2020, 2025, 2030, 2035]`, the weights are `[5, 5, 5, 5]` (the interval sizes)
-- This ensures that when you use `.sel()` to select a subset of periods, the weights are correctly recalculated
-- You can specify `weight_of_last_period` if the last period weight cannot be inferred from the index
-
-### Combined Weights
-
-When both periods and scenarios are present, the combined `weights` array (accessible via `flow_system.model.objective_weights`) is computed as:
-
-$$
-w_{y,s} = w_y \times \frac{w_s}{\sum_{s \in \mathcal{S}} w_s}
-$$
-
-Where:
-- $w_y$ are the period weights (computed from period index)
-- $w_s$ are the scenario weights (user-specified)
-- $\mathcal{S}$ is the set of all scenarios
-- The scenario weights are normalized to sum to 1 before multiplication
-
-**Example:**
-```python
-periods = pd.Index([2020, 2030, 2040]) # → period_weights = [10, 10, 10]
-scenarios = pd.Index(['Base', 'High'])
-scenario_weights = np.array([0.6, 0.4])
-
-flow_system = fx.FlowSystem(
- timesteps=timesteps,
- periods=periods,
- scenarios=scenarios,
- scenario_weights=scenario_weights
-)
-
-# Combined weights shape: (3 periods, 2 scenarios)
-# [[6.0, 4.0], # 2020: 10 × [0.6, 0.4]
-# [6.0, 4.0], # 2030: 10 × [0.6, 0.4]
-# [6.0, 4.0]] # 2040: 10 × [0.6, 0.4]
-```
-
-**Normalization:** Set `normalize_weights=False` in `Optimization` to turn off the normalization.
-
----
-
-## Summary Table
-
-| Dimension | Required? | Independence | Typical Use Case |
-|-----------|-----------|--------------|------------------|
-| **time** | ✅ Yes | Variables evolve over time via constraints (e.g., storage balance) | All optimization problems |
-| **scenario** | ❌ No | Fully independent operations; shared investments within period | Uncertainty modeling, risk assessment |
-| **period** | ❌ No | Fully independent; no coupling between periods | Multi-year planning, long-term investment |
-
-**Key Principle:** All constraints and formulations operate **within** each (period, scenario) combination independently. Only the objective function couples them via weighted aggregation.
-
----
-
-## See Also
-
-- [Effects, Penalty & Objective](effects-penalty-objective.md) - How dimensions affect the objective function
-- [InvestParameters](features/InvestParameters.md) - Investment decisions across scenarios
-- [FlowSystem API][flixopt.flow_system.FlowSystem] - Creating multi-dimensional systems
diff --git a/docs/user-guide/mathematical-notation/effects-and-dimensions.md b/docs/user-guide/mathematical-notation/effects-and-dimensions.md
new file mode 100644
index 000000000..011fc810e
--- /dev/null
+++ b/docs/user-guide/mathematical-notation/effects-and-dimensions.md
@@ -0,0 +1,415 @@
+# Effects & Dimensions
+
+Effects track metrics (costs, CO₂, energy). Dimensions define the structure over which effects aggregate.
+
+## Defining Effects
+
+```python
+costs = fx.Effect(label='costs', unit='€', is_objective=True)
+co2 = fx.Effect(label='co2', unit='kg')
+
+flow_system.add_elements(costs, co2)
+```
+
+One effect is the **objective** (minimized). Others are tracked or constrained.
+
+---
+
+## Effect Types
+
+=== "Temporal"
+
+ Accumulated over timesteps — operational costs, emissions, energy:
+
+ - Per flow hour: $E(t) = p(t) \cdot c \cdot \Delta t$
+ - Per event (startup): $E(t) = s^{start}(t) \cdot c$
+
+ ```python
+ fx.Flow(..., effects_per_flow_hour={'costs': 50}) # €50/MWh
+ ```
+
+=== "Periodic"
+
+ Time-independent — investment costs, fixed fees:
+
+ $E_{per} = P \cdot c_{inv}$
+
+ ```python
+ fx.InvestParameters(effects_of_investment_per_size={'costs': 200}) # €200/kW
+ ```
+
+=== "Total"
+
+ Sum of periodic and temporal components.
+
+---
+
+## Where Effects Are Contributed
+
+=== "Flow"
+
+ ```python
+ fx.Flow(
+ effects_per_flow_hour={'costs': 50, 'co2': 0.2}, # Per MWh
+ )
+ ```
+
+=== "Status"
+
+ ```python
+ fx.StatusParameters(
+ effects_per_startup={'costs': 1000}, # Per startup event
+ effects_per_active_hour={'costs': 10}, # Per hour while running
+ )
+ ```
+
+=== "Investment"
+
+ ```python
+ fx.InvestParameters(
+ effects_of_investment={'costs': 50000}, # Fixed if investing
+ effects_of_investment_per_size={'costs': 800}, # Per kW installed
+ effects_of_retirement={'costs': 10000}, # If NOT investing
+ )
+ ```
+
+=== "Bus"
+
+ ```python
+ fx.Bus(
+ excess_penalty_per_flow_hour=1e6, # Penalty for excess
+ shortage_penalty_per_flow_hour=1e6, # Penalty for shortage
+ )
+ ```
+
+---
+
+## Dimensions
+
+The model operates across three dimensions:
+
+=== "Timesteps"
+
+ The basic time resolution — always required:
+
+ ```python
+ flow_system = fx.FlowSystem(
+ timesteps=pd.date_range('2024-01-01', periods=8760, freq='h'),
+ )
+ ```
+
+ All variables and constraints are indexed by time. Temporal effects sum over timesteps.
+
+=== "Scenarios"
+
+ Represent uncertainty (weather, prices). Operations vary per scenario, investments are shared:
+
+ ```python
+ flow_system = fx.FlowSystem(
+ timesteps=pd.date_range('2024-01-01', periods=8760, freq='h'),
+ scenarios=pd.Index(['sunny_year', 'cloudy_year']),
+ scenario_weights=[0.7, 0.3],
+ )
+ ```
+
+ Scenarios are independent — no energy or information exchange between them.
+
+=== "Periods"
+
+ Sequential time blocks (years) for multi-period planning:
+
+ ```python
+ flow_system = fx.FlowSystem(
+ timesteps=pd.date_range('2024-01-01', periods=8760, freq='h'),
+ periods=pd.Index([2025, 2030]),
+ )
+ ```
+
+ Periods are independent — each has its own investment decisions.
+
+---
+
+## Objective Function
+
+The objective aggregates effects across all dimensions with weights:
+
+=== "Basic"
+
+ Single period, no scenarios:
+
+ $$\min \quad E_{per} + \sum_t E_{temp}(t)$$
+
+=== "With Scenarios"
+
+ Investment decided once, operations weighted by probability:
+
+ $$\min \quad E_{per} + \sum_s w_s \cdot \sum_t E_{temp}(t, s)$$
+
+ - $w_s$ — scenario weight (probability)
+
+=== "With Periods"
+
+ Multi-year planning with discounting:
+
+ $$\min \quad \sum_y w_y \cdot \left( E_{per}(y) + \sum_t E_{temp}(t, y) \right)$$
+
+ - $w_y$ — period weight (duration or discount factor)
+
+=== "Full"
+
+ Periods × Scenarios:
+
+ $$\min \quad \sum_y w_y \cdot \left( E_{per}(y) + \sum_s w_s \cdot \sum_t E_{temp}(t, y, s) \right)$$
+
+The penalty effect is always included: $\min \quad E_{objective} + E_{penalty}$
+
+---
+
+## Weights
+
+=== "Scenario Weights"
+
+ Provided explicitly — typically probabilities:
+
+ ```python
+ scenario_weights=[0.6, 0.4]
+ ```
+
+ Default: equal weights, normalized to sum to 1.
+
+=== "Period Weights"
+
+ Computed automatically from period index (interval sizes):
+
+ ```python
+ periods = pd.Index([2020, 2025, 2030])
+ # → weights: [5, 5, 5] (5-year intervals)
+ ```
+
+=== "Combined"
+
+ When both present:
+
+ $w_{y,s} = w_y \cdot w_s$
+
+---
+
+## Constraints on Effects
+
+=== "Total Limit"
+
+ Bound on aggregated effect (temporal + periodic) per period:
+
+ ```python
+ fx.Effect(label='co2', unit='kg', maximum_total=100_000)
+ ```
+
+=== "Per-Timestep Limit"
+
+ Bound at each timestep:
+
+ ```python
+ fx.Effect(label='peak', unit='kW', maximum_per_hour=500)
+ ```
+
+=== "Periodic Limit"
+
+ Bound on periodic component only:
+
+ ```python
+ fx.Effect(label='capex', unit='€', maximum_periodic=1_000_000)
+ ```
+
+=== "Temporal Limit"
+
+ Bound on temporal component only:
+
+ ```python
+ fx.Effect(label='opex', unit='€', maximum_temporal=500_000)
+ ```
+
+=== "Over All Periods"
+
+ Bound across all periods (weighted sum):
+
+ ```python
+ fx.Effect(label='co2', unit='kg', maximum_over_periods=1_000_000)
+ ```
+
+---
+
+## Cross-Effects
+
+Effects can contribute to each other (e.g., carbon pricing):
+
+```python
+co2 = fx.Effect(label='co2', unit='kg')
+
+costs = fx.Effect(
+ label='costs', unit='€', is_objective=True,
+ share_from_temporal={'co2': 0.08}, # €80/tonne
+)
+```
+
+---
+
+## Penalty Effect
+
+A built-in `Penalty` effect enables soft constraints and prevents infeasibility:
+
+```python
+fx.StatusParameters(effects_per_startup={'Penalty': 1})
+fx.Bus(label='heat', excess_penalty_per_flow_hour=1e5)
+```
+
+Penalty is weighted identically to the objective effect across all dimensions.
+
+---
+
+## Shared vs Independent Decisions
+
+=== "Investments (Sizes)"
+
+ By default, investment decisions are **shared across scenarios** within a period:
+
+ - Build capacity once → operate differently per scenario
+ - Reflects real-world investment under uncertainty
+
+ $$P(y) \quad \text{(one decision per period, used in all scenarios)}$$
+
+=== "Operations (Flows)"
+
+ By default, operational decisions are **independent per scenario**:
+
+ $$p(t, y, s) \quad \text{(different for each scenario)}$$
+
+---
+
+## Use Cases
+
+=== "Carbon Budget"
+
+ Limit total CO₂ emissions across all years:
+
+ ```python
+ co2 = fx.Effect(
+ label='co2', unit='kg',
+ maximum_over_periods=1_000_000, # 1000 tonnes total
+ )
+
+ # Contribute emissions from gas consumption
+ gas_flow = fx.Flow(
+ label='gas', bus=gas_bus,
+ effects_per_flow_hour={'co2': 0.2}, # 0.2 kg/kWh
+ )
+ ```
+
+=== "Investment Budget"
+
+ Cap annual investment spending:
+
+ ```python
+ capex = fx.Effect(
+ label='capex', unit='€',
+ maximum_periodic=5_000_000, # €5M per period
+ )
+
+ battery = fx.Storage(
+ ...,
+ capacity=fx.InvestParameters(
+ effects_of_investment_per_size={'capex': 600}, # €600/kWh
+ ),
+ )
+ ```
+
+=== "Peak Demand Charge"
+
+ Track and limit peak power:
+
+ ```python
+ peak = fx.Effect(
+ label='peak', unit='kW',
+ maximum_per_hour=1000, # Grid connection limit
+ )
+
+ grid_import = fx.Flow(
+ label='import', bus=elec_bus,
+ effects_per_flow_hour={'peak': 1}, # Track instantaneous power
+ )
+ ```
+
+=== "Carbon Pricing"
+
+ Add CO₂ cost to objective automatically:
+
+ ```python
+ co2 = fx.Effect(label='co2', unit='kg')
+
+ costs = fx.Effect(
+ label='costs', unit='€', is_objective=True,
+ share_from_temporal={'co2': 0.08}, # €80/tonne carbon price
+ )
+
+ # Now any CO₂ contribution automatically adds to costs
+ ```
+
+=== "Land Use Constraint"
+
+ Limit total land area for installations:
+
+ ```python
+ land = fx.Effect(
+ label='land', unit='m²',
+ maximum_periodic=50_000, # 5 hectares max
+ )
+
+ pv = fx.Source(
+ ...,
+ output=fx.Flow(
+ ...,
+ invest_parameters=fx.InvestParameters(
+ effects_of_investment_per_size={'land': 5}, # 5 m²/kWp
+ ),
+ ),
+ )
+ ```
+
+=== "Multi-Criteria Optimization"
+
+ Track multiple objectives, optimize one:
+
+ ```python
+ costs = fx.Effect(label='costs', unit='€', is_objective=True)
+ co2 = fx.Effect(label='co2', unit='kg')
+ primary_energy = fx.Effect(label='PE', unit='kWh')
+
+ # All are tracked, costs is minimized
+ # Use maximum_total on co2 for ε-constraint method
+ ```
+
+---
+
+## Reference
+
+| Symbol | Type | Description |
+|--------|------|-------------|
+| $E_{temp}(t)$ | $\mathbb{R}$ | Temporal effect at timestep $t$ |
+| $E_{per}$ | $\mathbb{R}$ | Periodic effect (per period) |
+| $E$ | $\mathbb{R}$ | Total effect ($E_{per} + \sum_t E_{temp}(t)$) |
+| $w_s$ | $\mathbb{R}_{\geq 0}$ | Scenario weight (probability) |
+| $w_y$ | $\mathbb{R}_{> 0}$ | Period weight (duration/discount) |
+| $p(t)$ | $\mathbb{R}_{\geq 0}$ | Flow rate at timestep $t$ |
+| $s^{start}(t)$ | $\{0, 1\}$ | Startup indicator |
+| $P$ | $\mathbb{R}_{\geq 0}$ | Investment size |
+| $c$ | $\mathbb{R}$ | Effect coefficient |
+| $\Delta t$ | $\mathbb{R}_{> 0}$ | Timestep duration (hours) |
+
+| Constraint | Python | Scope |
+|-----------|--------|-------|
+| Total limit | `maximum_total` | Per period |
+| Timestep limit | `maximum_per_hour` | Each timestep |
+| Periodic limit | `maximum_periodic` | Per period (periodic only) |
+| Temporal limit | `maximum_temporal` | Per period (temporal only) |
+| Global limit | `maximum_over_periods` | Across all periods |
+
+**Classes:** [`Effect`][flixopt.effects.Effect], [`EffectCollection`][flixopt.effects.EffectCollection]
diff --git a/docs/user-guide/mathematical-notation/effects-penalty-objective.md b/docs/user-guide/mathematical-notation/effects-penalty-objective.md
deleted file mode 100644
index fd8a97a1d..000000000
--- a/docs/user-guide/mathematical-notation/effects-penalty-objective.md
+++ /dev/null
@@ -1,337 +0,0 @@
-# Effects, Penalty & Objective
-
-## Effects
-
-[`Effects`][flixopt.effects.Effect] are used to quantify system-wide impacts like costs, emissions, or resource consumption. These arise from **shares** contributed by **Elements** such as [Flows](elements/Flow.md), [Storage](elements/Storage.md), and other components.
-
-**Example:**
-
-[`Flows`][flixopt.elements.Flow] have an attribute `effects_per_flow_hour` that defines the effect contribution per flow-hour:
-
-- Costs (€/kWh)
-- Emissions (kg CO₂/kWh)
-- Primary energy consumption (kWh_primary/kWh)
-
-Effects are categorized into two domains:
-
-1. **Temporal effects** - Time-dependent contributions (e.g., operational costs, hourly emissions)
-2. **Periodic effects** - Time-independent contributions (e.g., investment costs, fixed annual fees)
-
-### Multi-Dimensional Effects
-
-**The formulations below are written with time index $\text{t}_i$ only, but automatically expand when periods and/or scenarios are present.**
-
-When the FlowSystem has additional dimensions (see [Dimensions](dimensions.md)):
-
-- **Temporal effects** are indexed by all present dimensions: $E_{e,\text{temp}}(\text{t}_i, y, s)$
-- **Periodic effects** are indexed by period only (scenario-independent within a period): $E_{e,\text{per}}(y)$
-- Effects are aggregated with dimension weights in the objective function
-
-For complete details on how dimensions affect effects and the objective, see [Dimensions](dimensions.md).
-
----
-
-## Effect Formulation
-
-### Shares from Elements
-
-Each element $l$ contributes shares to effect $e$ in both temporal and periodic domains:
-
-**Periodic shares** (time-independent):
-$$ \label{eq:Share_periodic}
-s_{l \rightarrow e, \text{per}} = \sum_{v \in \mathcal{V}_{l, \text{per}}} v \cdot \text{a}_{v \rightarrow e}
-$$
-
-**Temporal shares** (time-dependent):
-$$ \label{eq:Share_temporal}
-s_{l \rightarrow e, \text{temp}}(\text{t}_i) = \sum_{v \in \mathcal{V}_{l,\text{temp}}} v(\text{t}_i) \cdot \text{a}_{v \rightarrow e}(\text{t}_i)
-$$
-
-Where:
-
-- $\text{t}_i$ is the time step
-- $\mathcal{V}_l$ is the set of all optimization variables of element $l$
-- $\mathcal{V}_{l, \text{per}}$ is the subset of periodic (investment-related) variables
-- $\mathcal{V}_{l, \text{temp}}$ is the subset of temporal (operational) variables
-- $v$ is an optimization variable
-- $v(\text{t}_i)$ is the variable value at timestep $\text{t}_i$
-- $\text{a}_{v \rightarrow e}$ is the effect factor (e.g., €/kW for investment, €/kWh for operation)
-- $s_{l \rightarrow e, \text{per}}$ is the periodic share of element $l$ to effect $e$
-- $s_{l \rightarrow e, \text{temp}}(\text{t}_i)$ is the temporal share of element $l$ to effect $e$
-
-**Examples:**
-- **Periodic share**: Investment cost = $\text{size} \cdot \text{specific\_cost}$ (€/kW)
-- **Temporal share**: Operational cost = $\text{flow\_rate}(\text{t}_i) \cdot \text{price}(\text{t}_i)$ (€/kWh)
-
----
-
-### Cross-Effect Contributions
-
-Effects can contribute shares to other effects, enabling relationships like carbon pricing or resource accounting.
-
-An effect $x$ can contribute to another effect $e \in \mathcal{E}\backslash x$ via conversion factors:
-
-**Example:** CO₂ emissions (kg) → Monetary costs (€)
-- Effect $x$: "CO₂ emissions" (unit: kg)
-- Effect $e$: "costs" (unit: €)
-- Factor $\text{r}_{x \rightarrow e}$: CO₂ price (€/kg)
-
-**Note:** Circular references must be avoided.
-
-### Total Effect Calculation
-
-**Periodic effects** aggregate element shares and cross-effect contributions:
-
-$$ \label{eq:Effect_periodic}
-E_{e, \text{per}} =
-\sum_{l \in \mathcal{L}} s_{l \rightarrow e,\text{per}} +
-\sum_{x \in \mathcal{E}\backslash e} E_{x, \text{per}} \cdot \text{r}_{x \rightarrow e,\text{per}}
-$$
-
-**Temporal effects** at each timestep:
-
-$$ \label{eq:Effect_temporal}
-E_{e, \text{temp}}(\text{t}_{i}) =
-\sum_{l \in \mathcal{L}} s_{l \rightarrow e, \text{temp}}(\text{t}_i) +
-\sum_{x \in \mathcal{E}\backslash e} E_{x, \text{temp}}(\text{t}_i) \cdot \text{r}_{x \rightarrow {e},\text{temp}}(\text{t}_i)
-$$
-
-**Total temporal effects** (sum over all timesteps):
-
-$$\label{eq:Effect_temporal_total}
-E_{e,\text{temp},\text{tot}} = \sum_{i=1}^n E_{e,\text{temp}}(\text{t}_{i})
-$$
-
-**Total effect** (combining both domains):
-
-$$ \label{eq:Effect_Total}
-E_{e} = E_{e,\text{per}} + E_{e,\text{temp},\text{tot}}
-$$
-
-Where:
-
-- $\mathcal{L}$ is the set of all elements in the FlowSystem
-- $\mathcal{E}$ is the set of all effects
-- $\text{r}_{x \rightarrow e, \text{per}}$ is the periodic conversion factor from effect $x$ to effect $e$
-- $\text{r}_{x \rightarrow e, \text{temp}}(\text{t}_i)$ is the temporal conversion factor
-
----
-
-### Constraining Effects
-
-Effects can be bounded to enforce limits on costs, emissions, or other impacts:
-
-**Total bounds** (apply to $E_{e,\text{per}}$, $E_{e,\text{temp},\text{tot}}$, or $E_e$):
-
-$$ \label{eq:Bounds_Total}
-E^\text{L} \leq E \leq E^\text{U}
-$$
-
-**Temporal bounds per timestep:**
-
-$$ \label{eq:Bounds_Timestep}
-E_{e,\text{temp}}^\text{L}(\text{t}_i) \leq E_{e,\text{temp}}(\text{t}_i) \leq E_{e,\text{temp}}^\text{U}(\text{t}_i)
-$$
-
-**Implementation:** See [`Effect`][flixopt.effects.Effect] parameters:
-- `minimum_temporal`, `maximum_temporal` - Total temporal bounds
-- `minimum_per_hour`, `maximum_per_hour` - Hourly temporal bounds
-- `minimum_periodic`, `maximum_periodic` - Periodic bounds
-- `minimum_total`, `maximum_total` - Combined total bounds
-
----
-
-## Penalty
-
-Every FlixOpt model includes a special **Penalty Effect** $E_\Phi$ to:
-
-- Prevent infeasible problems
-- Allow introducing a bias without influencing effects, simplifying results analysis
-
-**Key Feature:** Penalty is implemented as a standard Effect (labeled `Penalty`), so you can **add penalty contributions anywhere effects are used**:
-
-```python
-import flixopt as fx
-
-# Add penalty contributions just like any other effect
-on_off = fx.OnOffParameters(
- effects_per_switch_on={'Penalty': 1} # Add bias against switching on this component, without adding costs
-)
-```
-
-**Optionally Define Custom Penalty:**
-Users can define their own Penalty effect with custom properties (unit, constraints, etc.):
-
-```python
-# Define custom penalty effect (must use fx.PENALTY_EFFECT_LABEL)
-custom_penalty = fx.Effect(
- fx.PENALTY_EFFECT_LABEL, # Always use this constant: 'Penalty'
- unit='€',
- description='Penalty costs for constraint violations',
- maximum_total=1e6, # Limit total penalty for debugging
-)
-flow_system.add_elements(custom_penalty)
-```
-
-If not user-defined, the Penalty effect is automatically created during modeling with default settings.
-
-**Periodic penalty shares** (time-independent):
-$$ \label{eq:Penalty_periodic}
-E_{\Phi, \text{per}} = \sum_{l \in \mathcal{L}} s_{l \rightarrow \Phi,\text{per}}
-$$
-
-**Temporal penalty shares** (time-dependent):
-$$ \label{eq:Penalty_temporal}
-E_{\Phi, \text{temp}}(\text{t}_{i}) = \sum_{l \in \mathcal{L}} s_{l \rightarrow \Phi, \text{temp}}(\text{t}_i)
-$$
-
-**Total penalty** (combining both domains):
-$$ \label{eq:Penalty_total}
-E_{\Phi} = E_{\Phi,\text{per}} + \sum_{\text{t}_i \in \mathcal{T}} E_{\Phi, \text{temp}}(\text{t}_{i})
-$$
-
-Where:
-
-- $\mathcal{L}$ is the set of all elements
-- $\mathcal{T}$ is the set of all timesteps
-- $s_{l \rightarrow \Phi, \text{per}}$ is the periodic penalty share from element $l$
-- $s_{l \rightarrow \Phi, \text{temp}}(\text{t}_i)$ is the temporal penalty share from element $l$ at timestep $\text{t}_i$
-
-**Primary usage:** Penalties occur in [Buses](elements/Bus.md) via the `imbalance_penalty_per_flow_hour` parameter, which allows nodal imbalances at a high cost, and in time series aggregation to allow period flexibility.
-
-**Key properties:**
-- Penalty shares are added via `add_share_to_effects(name, expressions={fx.PENALTY_EFFECT_LABEL: ...}, target='temporal'/'periodic')`
-- Like other effects, penalty can be constrained (e.g., `maximum_total` for debugging)
-- Results include breakdown: temporal, periodic, and total penalty contributions
-- Penalty is always added to the objective function (cannot be disabled)
-- Access via `flow_system.effects.penalty_effect` or `flow_system.effects[fx.PENALTY_EFFECT_LABEL]`
-- **Scenario weighting**: Penalty is weighted identically to the objective effect—see [Time + Scenario](#time--scenario) for details
-
----
-
-## Objective Function
-
-The optimization objective minimizes the chosen effect plus the penalty effect:
-
-$$ \label{eq:Objective}
-\min \left( E_{\Omega} + E_{\Phi} \right)
-$$
-
-Where:
-
-- $E_{\Omega}$ is the chosen **objective effect** (see $\eqref{eq:Effect_Total}$)
-- $E_{\Phi}$ is the [penalty effect](#penalty) (see $\eqref{eq:Penalty_total}$)
-
-One effect must be designated as the objective via `is_objective=True`. The penalty effect is automatically created and always added to the objective.
-
-### Multi-Criteria Optimization
-
-This formulation supports multiple optimization approaches:
-
-**1. Weighted Sum Method**
-- The objective effect can incorporate other effects via cross-effect factors
-- Example: Minimize costs while including carbon pricing: $\text{CO}_2 \rightarrow \text{costs}$
-
-**2. ε-Constraint Method**
-- Optimize one effect while constraining others
-- Example: Minimize costs subject to $\text{CO}_2 \leq 1000$ kg
-
----
-
-## Objective with Multiple Dimensions
-
-When the FlowSystem includes **periods** and/or **scenarios** (see [Dimensions](dimensions.md)), the objective aggregates effects across all dimensions using weights.
-
-### Time Only (Base Case)
-
-$$
-\min \quad E_{\Omega} + E_{\Phi} = \sum_{\text{t}_i \in \mathcal{T}} E_{\Omega,\text{temp}}(\text{t}_i) + E_{\Omega,\text{per}} + E_{\Phi,\text{per}} + \sum_{\text{t}_i \in \mathcal{T}} E_{\Phi,\text{temp}}(\text{t}_i)
-$$
-
-Where:
-- Temporal effects sum over time: $\sum_{\text{t}_i} E_{\Omega,\text{temp}}(\text{t}_i)$ and $\sum_{\text{t}_i} E_{\Phi,\text{temp}}(\text{t}_i)$
-- Periodic effects are constant: $E_{\Omega,\text{per}}$ and $E_{\Phi,\text{per}}$
-
----
-
-### Time + Scenario
-
-$$
-\min \quad \sum_{s \in \mathcal{S}} w_s \cdot \left( E_{\Omega}(s) + E_{\Phi}(s) \right)
-$$
-
-Where:
-
-- $\mathcal{S}$ is the set of scenarios
-- $w_s$ is the weight for scenario $s$ (typically scenario probability)
-- Periodic effects are **shared across scenarios**: $E_{\Omega,\text{per}}$ and $E_{\Phi,\text{per}}$ (same for all $s$)
-- Temporal effects are **scenario-specific**: $E_{\Omega,\text{temp}}(s) = \sum_{\text{t}_i} E_{\Omega,\text{temp}}(\text{t}_i, s)$ and $E_{\Phi,\text{temp}}(s) = \sum_{\text{t}_i} E_{\Phi,\text{temp}}(\text{t}_i, s)$
-
-**Interpretation:**
-- Investment decisions (periodic) made once, used across all scenarios
-- Operations (temporal) differ by scenario
-- Objective balances expected value across scenarios
-- **Both $E_{\Omega}$ (objective effect) and $E_{\Phi}$ (penalty) are weighted identically by $w_s$**
-
----
-
-### Time + Period
-
-$$
-\min \quad \sum_{y \in \mathcal{Y}} w_y \cdot \left( E_{\Omega}(y) + E_{\Phi}(y) \right)
-$$
-
-Where:
-
-- $\mathcal{Y}$ is the set of periods (e.g., years)
-- $w_y$ is the weight for period $y$ (typically annual discount factor)
-- Each period $y$ has **independent** periodic and temporal effects (including penalty)
-- Each period $y$ has **independent** investment and operational decisions
-- **Both $E_{\Omega}$ (objective effect) and $E_{\Phi}$ (penalty) are weighted identically by $w_y$**
-
----
-
-### Time + Period + Scenario (Full Multi-Dimensional)
-
-$$
-\min \quad \sum_{y \in \mathcal{Y}} \left[ w_y \cdot \left( E_{\Omega,\text{per}}(y) + E_{\Phi,\text{per}}(y) \right) + \sum_{s \in \mathcal{S}} w_{y,s} \cdot \left( E_{\Omega,\text{temp}}(y,s) + E_{\Phi,\text{temp}}(y,s) \right) \right]
-$$
-
-Where:
-
-- $\mathcal{S}$ is the set of scenarios
-- $\mathcal{Y}$ is the set of periods
-- $w_y$ is the period weight (for periodic effects)
-- $w_{y,s}$ is the combined period-scenario weight (for temporal effects)
-- **Periodic effects** $E_{\Omega,\text{per}}(y)$ and $E_{\Phi,\text{per}}(y)$ are period-specific but **scenario-independent**
-- **Temporal effects** $E_{\Omega,\text{temp}}(y,s) = \sum_{\text{t}_i} E_{\Omega,\text{temp}}(\text{t}_i, y, s)$ and $E_{\Phi,\text{temp}}(y,s) = \sum_{\text{t}_i} E_{\Phi,\text{temp}}(\text{t}_i, y, s)$ are **fully indexed**
-
-**Key Principle:**
-- Scenarios and periods are **operationally independent** (no energy/resource exchange)
-- Coupled **only through the weighted objective function**
-- **Periodic effects within a period are shared across all scenarios** (investment made once per period)
-- **Temporal effects are independent per scenario** (different operations under different conditions)
-- **Both $E_{\Omega}$ (objective effect) and $E_{\Phi}$ (penalty) use identical weighting** ($w_y$ for periodic, $w_{y,s}$ for temporal)
-
----
-
-## Summary
-
-| Concept | Formulation | Time Dependency | Dimension Indexing |
-|---------|-------------|-----------------|-------------------|
-| **Temporal share** | $s_{l \rightarrow e, \text{temp}}(\text{t}_i)$ | Time-dependent | $(t, y, s)$ when present |
-| **Periodic share** | $s_{l \rightarrow e, \text{per}}$ | Time-independent | $(y)$ when periods present |
-| **Total temporal effect** | $E_{e,\text{temp},\text{tot}} = \sum_{\text{t}_i} E_{e,\text{temp}}(\text{t}_i)$ | Sum over time | Depends on dimensions |
-| **Total periodic effect** | $E_{e,\text{per}}$ | Constant | $(y)$ when periods present |
-| **Total effect** | $E_e = E_{e,\text{per}} + E_{e,\text{temp},\text{tot}}$ | Combined | Depends on dimensions |
-| **Penalty effect** | $E_\Phi = E_{\Phi,\text{per}} + E_{\Phi,\text{temp},\text{tot}}$ | Combined (same as effects) | **Weighted identically to objective effect** |
-| **Objective** | $\min(E_{\Omega} + E_{\Phi})$ | With weights when multi-dimensional | See formulations above |
-
----
-
-## See Also
-
-- [Dimensions](dimensions.md) - Complete explanation of multi-dimensional modeling
-- [Flow](elements/Flow.md) - Temporal effect contributions via `effects_per_flow_hour`
-- [InvestParameters](features/InvestParameters.md) - Periodic effect contributions via investment
-- [Effect API][flixopt.effects.Effect] - Implementation details and parameters
diff --git a/docs/user-guide/mathematical-notation/elements/Bus.md b/docs/user-guide/mathematical-notation/elements/Bus.md
index 5028e8ef7..464381fe8 100644
--- a/docs/user-guide/mathematical-notation/elements/Bus.md
+++ b/docs/user-guide/mathematical-notation/elements/Bus.md
@@ -1,49 +1,52 @@
-A Bus is a simple nodal balance between its incoming and outgoing flow rates.
+# Bus
-$$ \label{eq:bus_balance}
- \sum_{f_\text{in} \in \mathcal{F}_\text{in}} p_{f_\text{in}}(\text{t}_i) =
- \sum_{f_\text{out} \in \mathcal{F}_\text{out}} p_{f_\text{out}}(\text{t}_i)
-$$
-
-Optionally, a Bus can have an `imbalance_penalty_per_flow_hour` parameter, which allows to penalize the balance for missing or excess flow-rates.
-This is useful as it handles a possible infeasibility gently.
+A Bus is where flows meet and must balance — inputs equal outputs at every timestep.
-This changes the balance to
+## Basic: Balance Equation
-$$ \label{eq:bus_balance-excess}
- \sum_{f_\text{in} \in \mathcal{F}_\text{in}} p_{f_ \text{in}}(\text{t}_i) + \phi_\text{in}(\text{t}_i) =
- \sum_{f_\text{out} \in \mathcal{F}_\text{out}} p_{f_\text{out}}(\text{t}_i) + \phi_\text{out}(\text{t}_i)
$$
-
-The penalty term is defined as
-
-$$ \label{eq:bus_penalty}
- s_{b \rightarrow \Phi}(\text{t}_i) =
- \text a_{b \rightarrow \Phi}(\text{t}_i) \cdot \Delta \text{t}_i
- \cdot [ \phi_\text{in}(\text{t}_i) + \phi_\text{out}(\text{t}_i) ]
+\sum_{in} p(t) = \sum_{out} p(t)
$$
-With:
+```python
+heat_bus = fx.Bus(label='heat')
+# All flows connected to this bus must balance
+```
-- $\mathcal{F}_\text{in}$ and $\mathcal{F}_\text{out}$ being the set of all incoming and outgoing flows
-- $p_{f_\text{in}}(\text{t}_i)$ and $p_{f_\text{out}}(\text{t}_i)$ being the flow-rate at time $\text{t}_i$ for flow $f_\text{in}$ and $f_\text{out}$, respectively
-- $\phi_\text{in}(\text{t}_i)$ and $\phi_\text{out}(\text{t}_i)$ being the virtual supply and virtual demand at time $\text{t}_i$, respectively
-- $\text{t}_i$ being the time step
-- $s_{b \rightarrow \Phi}(\text{t}_i)$ being the penalty term
-- $\text a_{b \rightarrow \Phi}(\text{t}_i)$ being the penalty coefficient (`imbalance_penalty_per_flow_hour`)
+If balance can't be achieved → model is **infeasible**.
---
-## Implementation
+## With Imbalance Penalty
+
+Allow imbalance for debugging or soft constraints:
-**Python Class:** [`Bus`][flixopt.elements.Bus]
+$$
+\sum_{in} p(t) + \phi_{in}(t) = \sum_{out} p(t) + \phi_{out}(t)
+$$
+
+The slack variables $\phi$ are penalized: $(\phi_{in} + \phi_{out}) \cdot \Delta t \cdot c_\phi$
-See the API documentation for implementation details and usage examples.
+```python
+heat_bus = fx.Bus(
+ label='heat',
+ imbalance_penalty_per_flow_hour=1e5 # High penalty for imbalance
+)
+```
+
+!!! tip "Debugging"
+ If you see a `virtual_demand` or `virtual_supply` and its non zero in results → your system couldn't meet demand. Check capacities and connections.
---
-## See Also
+## Reference
+
+| Symbol | Type | Description |
+|--------|------|-------------|
+| $p(t)$ | $\mathbb{R}_{\geq 0}$ | Flow rate of connected flows |
+| $\phi_{in}(t)$ | $\mathbb{R}_{\geq 0}$ | Slack: virtual supply (covers shortages) |
+| $\phi_{out}(t)$ | $\mathbb{R}_{\geq 0}$ | Slack: virtual demand (absorbs surplus) |
+| $c_\phi$ | $\mathbb{R}_{\geq 0}$ | Penalty factor (`imbalance_penalty_per_flow_hour`) |
+| $\Delta t$ | $\mathbb{R}_{> 0}$ | Timestep duration (hours) |
-- [Flow](../elements/Flow.md) - Definition of flow rates in the balance
-- [Effects, Penalty & Objective](../effects-penalty-objective.md) - How penalties are included in the objective function
-- [Modeling Patterns](../modeling-patterns/index.md) - Mathematical building blocks
+**Classes:** [`Bus`][flixopt.elements.Bus], [`BusModel`][flixopt.elements.BusModel]
diff --git a/docs/user-guide/mathematical-notation/elements/Flow.md b/docs/user-guide/mathematical-notation/elements/Flow.md
index 2cc2e3b6a..4f5f9dcf3 100644
--- a/docs/user-guide/mathematical-notation/elements/Flow.md
+++ b/docs/user-guide/mathematical-notation/elements/Flow.md
@@ -1,65 +1,131 @@
# Flow
-The flow_rate is the main optimization variable of the Flow. It's limited by the size of the Flow and relative bounds \eqref{eq:flow_rate}.
+A Flow is the primary optimization variable — the solver decides how much flows at each timestep.
-$$ \label{eq:flow_rate}
- \text P \cdot \text p^{\text{L}}_{\text{rel}}(\text{t}_{i})
- \leq p(\text{t}_{i}) \leq
- \text P \cdot \text p^{\text{U}}_{\text{rel}}(\text{t}_{i})
-$$
-
-With:
+## Basic: Bounded Flow Rate
-- $\text P$ being the size of the Flow
-- $p(\text{t}_{i})$ being the flow-rate at time $\text{t}_{i}$
-- $\text p^{\text{L}}_{\text{rel}}(\text{t}_{i})$ being the relative lower bound (typically 0)
-- $\text p^{\text{U}}_{\text{rel}}(\text{t}_{i})$ being the relative upper bound (typically 1)
-
-With $\text p^{\text{L}}_{\text{rel}}(\text{t}_{i}) = 0$ and $\text p^{\text{U}}_{\text{rel}}(\text{t}_{i}) = 1$,
-equation \eqref{eq:flow_rate} simplifies to
+Every flow has a **size** $P$ (capacity) and a **flow rate** $p(t)$ (what the solver optimizes):
$$
- 0 \leq p(\text{t}_{i}) \leq \text P
+P \cdot p_{rel}^{min} \leq p(t) \leq P \cdot p_{rel}^{max}
$$
+```python
+# 100 kW boiler, minimum 30% when running
+heat = fx.Flow(label='heat', bus=heat_bus, size=100, relative_minimum=0.3)
+# → 30 ≤ p(t) ≤ 100
+```
-This mathematical formulation can be extended by using [StatusParameters](../features/StatusParameters.md)
-to define the active/inactive state of the Flow, or by using [InvestParameters](../features/InvestParameters.md)
-to change the size of the Flow from a constant to an optimization variable.
+!!! warning "Cannot be zero"
+ With `relative_minimum > 0`, the flow cannot be zero. Use `status_parameters` to allow shutdown.
---
-## Mathematical Patterns Used
+## Adding Features
+
+=== "Status"
+
+ Allow the flow to be zero with `status_parameters`:
+
+ $s(t) \cdot P \cdot p_{rel}^{min} \leq p(t) \leq s(t) \cdot P \cdot p_{rel}^{max}$
+
+ Where $s(t) \in \{0, 1\}$: inactive or active.
+
+ ```python
+ generator = fx.Flow(
+ label='power', bus=elec_bus, size=50,
+ relative_minimum=0.4,
+ status_parameters=fx.StatusParameters(
+ effects_per_startup={'costs': 500},
+ min_uptime=2,
+ ),
+ )
+ ```
+
+ See [StatusParameters](../features/StatusParameters.md).
+
+=== "Variable Size"
+
+ Optimize the capacity with `InvestParameters`:
+
+ $P^{min} \leq P \leq P^{max}$
+
+ ```python
+ battery = fx.Flow(
+ label='power', bus=elec_bus,
+ size=fx.InvestParameters(
+ minimum_size=0,
+ maximum_size=1000,
+ specific_effects={'costs': 100_000},
+ ),
+ )
+ ```
-Flow formulation uses the following modeling patterns:
+ See [InvestParameters](../features/InvestParameters.md).
-- **[Scaled Bounds](../modeling-patterns/bounds-and-states.md#scaled-bounds)** - Basic flow rate bounds (equation $\eqref{eq:flow_rate}$)
-- **[Scaled Bounds with State](../modeling-patterns/bounds-and-states.md#scaled-bounds-with-state)** - When combined with [StatusParameters](../features/StatusParameters.md)
-- **[Bounds with State](../modeling-patterns/bounds-and-states.md#bounds-with-state)** - Investment decisions with [InvestParameters](../features/InvestParameters.md)
+=== "Flow Effects"
+
+ Add effects per energy (flow hours) moved:
+
+ ```python
+ gas = fx.Flow(
+ label='gas', bus=gas_bus, size=150,
+ effects_per_flow_hour={'costs': 50}, # €50/MWh
+ )
+ ```
+
+ Flow hours: $h(t) = p(t) \cdot \Delta t$
+
+
+=== "Fixed Profile"
+
+ Lock the flow to a time series (demands, renewables):
+
+ $p(t) = P \cdot \pi(t)$
+
+ ```python
+ demand = fx.Flow(
+ label='demand', bus=heat_bus, size=100,
+ fixed_relative_profile=[0.5, 0.8, 1.0, 0.6] # π(t)
+ )
+ ```
---
-## Implementation
+## Optional Constraints
+
+=== "Load Factor"
+
+ Constrain average utilization:
-**Python Class:** [`Flow`][flixopt.elements.Flow]
+ $\lambda_{min} \leq \frac{\sum_t p(t)}{P \cdot n_t} \leq \lambda_{max}$
-**Key Parameters:**
+ ```python
+ fx.Flow(..., load_factor_min=0.5, load_factor_max=0.9)
+ ```
-- `size`: Flow size $\text{P}$ (can be fixed or variable with InvestParameters)
-- `relative_minimum`, `relative_maximum`: Relative bounds $\text{p}^{\text{L}}_{\text{rel}}, \text{p}^{\text{U}}_{\text{rel}}$
-- `effects_per_flow_hour`: Operational effects (costs, emissions, etc.)
-- `invest_parameters`: Optional investment modeling (see [InvestParameters](../features/InvestParameters.md))
-- `status_parameters`: Optional active/inactive operation (see [StatusParameters](../features/StatusParameters.md))
+=== "Flow Hours"
-See the [`Flow`][flixopt.elements.Flow] API documentation for complete parameter list and usage examples.
+ Constrain total energy:
+
+ $h_{min} \leq \sum_t p(t) \cdot \Delta t \leq h_{max}$
+
+ ```python
+ fx.Flow(..., flow_hours_min=1000, flow_hours_max=5000)
+ ```
---
-## See Also
+## Reference
+
+| Symbol | Type | Description |
+|--------|------|-------------|
+| $p(t)$ | $\mathbb{R}_{\geq 0}$ | Flow rate at timestep $t$ |
+| $P$ | $\mathbb{R}_{\geq 0}$ | Size (capacity) — fixed or optimized |
+| $s(t)$ | $\{0, 1\}$ | Binary status (with `status_parameters`) |
+| $p_{rel}^{min}$ | $\mathbb{R}_{\geq 0}$ | Minimum relative flow (`relative_minimum`) |
+| $p_{rel}^{max}$ | $\mathbb{R}_{\geq 0}$ | Maximum relative flow (`relative_maximum`) |
+| $\pi(t)$ | $\mathbb{R}_{\geq 0}$ | Fixed profile (`fixed_relative_profile`) |
+| $\Delta t$ | $\mathbb{R}_{> 0}$ | Timestep duration (hours) |
-- [StatusParameters](../features/StatusParameters.md) - Binary active/inactive operation
-- [InvestParameters](../features/InvestParameters.md) - Variable flow sizing
-- [Bus](../elements/Bus.md) - Flow balance constraints
-- [LinearConverter](../elements/LinearConverter.md) - Flow ratio constraints
-- [Storage](../elements/Storage.md) - Flow integration over time
-- [Modeling Patterns](../modeling-patterns/index.md) - Mathematical building blocks
+**Classes:** [`Flow`][flixopt.elements.Flow], [`FlowModel`][flixopt.elements.FlowModel]
diff --git a/docs/user-guide/mathematical-notation/elements/LinearConverter.md b/docs/user-guide/mathematical-notation/elements/LinearConverter.md
index b007aa7f5..915537d60 100644
--- a/docs/user-guide/mathematical-notation/elements/LinearConverter.md
+++ b/docs/user-guide/mathematical-notation/elements/LinearConverter.md
@@ -1,50 +1,151 @@
-[`LinearConverters`][flixopt.components.LinearConverter] define a ratio between incoming and outgoing [Flows](../elements/Flow.md).
+# LinearConverter
-$$ \label{eq:Linear-Transformer-Ratio}
- \sum_{f_{\text{in}} \in \mathcal F_{in}} \text a_{f_{\text{in}}}(\text{t}_i) \cdot p_{f_\text{in}}(\text{t}_i) = \sum_{f_{\text{out}} \in \mathcal F_{out}} \text b_{f_\text{out}}(\text{t}_i) \cdot p_{f_\text{out}}(\text{t}_i)
+A LinearConverter transforms inputs into outputs with fixed ratios.
+
+## Basic: Conversion Equation
+
+$$
+\sum_{in} a_f \cdot p_f(t) = \sum_{out} b_f \cdot p_f(t)
$$
-With:
+=== "Boiler (η = 90%)"
+
+ $0.9 \cdot p_{gas}(t) = p_{heat}(t)$
+
+ ```python
+ boiler = fx.LinearConverter(
+ label='boiler',
+ inputs=[fx.Flow(label='gas', bus=gas_bus, size=111)],
+ outputs=[fx.Flow(label='heat', bus=heat_bus, size=100)],
+ conversion_factors=[{'gas': 0.9, 'heat': 1}],
+ )
+ ```
+
+=== "Heat Pump (COP = 3.5)"
+
+ $3.5 \cdot p_{el}(t) = p_{heat}(t)$
+
+ ```python
+ hp = fx.LinearConverter(
+ label='hp',
+ inputs=[fx.Flow(label='el', bus=elec_bus, size=100)],
+ outputs=[fx.Flow(label='heat', bus=heat_bus, size=350)],
+ conversion_factors=[{'el': 3.5, 'heat': 1}],
+ )
+ ```
+
+=== "CHP (35% el, 50% th)"
+
+ Two constraints linking fuel to outputs:
+
+ ```python
+ chp = fx.LinearConverter(
+ label='chp',
+ inputs=[fx.Flow(label='fuel', bus=gas_bus, size=100)],
+ outputs=[
+ fx.Flow(label='el', bus=elec_bus, size=35),
+ fx.Flow(label='heat', bus=heat_bus, size=50),
+ ],
+ conversion_factors=[
+ {'fuel': 0.35, 'el': 1},
+ {'fuel': 0.50, 'heat': 1},
+ ],
+ )
+ ```
-- $\mathcal F_{in}$ and $\mathcal F_{out}$ being the set of all incoming and outgoing flows
-- $p_{f_\text{in}}(\text{t}_i)$ and $p_{f_\text{out}}(\text{t}_i)$ being the flow-rate at time $\text{t}_i$ for flow $f_\text{in}$ and $f_\text{out}$, respectively
-- $\text a_{f_\text{in}}(\text{t}_i)$ and $\text b_{f_\text{out}}(\text{t}_i)$ being the ratio of the flow-rate at time $\text{t}_i$ for flow $f_\text{in}$ and $f_\text{out}$, respectively
+---
-With one incoming **Flow** and one outgoing **Flow**, this can be simplified to:
+## Time-Varying Efficiency
-$$ \label{eq:Linear-Transformer-Ratio-simple}
- \text a(\text{t}_i) \cdot p_{f_\text{in}}(\text{t}_i) = p_{f_\text{out}}(\text{t}_i)
-$$
+Pass a list for time-dependent conversion:
+
+```python
+cop = np.array([3.0, 3.2, 3.5, 4.0, 3.8, ...]) # Varies with ambient temperature
-where $\text a$ can be interpreted as the conversion efficiency of the **LinearConverter**.
+hp = fx.LinearConverter(
+ ...,
+ conversion_factors=[{'el': cop, 'heat': 1}],
+)
+```
-#### Piecewise Conversion factors
-The conversion efficiency can be defined as a piecewise linear approximation. See [Piecewise](../features/Piecewise.md) for more details.
+---
+
+## Convenience Classes
+
+```python
+# Boiler
+boiler = fx.linear_converters.Boiler(
+ label='boiler', eta=0.9,
+ Q_th=fx.Flow(label='heat', bus=heat_bus, size=100),
+ Q_fu=fx.Flow(label='fuel', bus=gas_bus),
+)
+
+# Heat Pump
+hp = fx.linear_converters.HeatPump(
+ label='hp', COP=3.5,
+ P_el=fx.Flow(label='el', bus=elec_bus, size=100),
+ Q_th=fx.Flow(label='heat', bus=heat_bus),
+)
+
+# CHP
+chp = fx.linear_converters.CHP(
+ label='chp', eta_el=0.35, eta_th=0.50,
+ P_el=fx.Flow(...), Q_th=fx.Flow(...), Q_fu=fx.Flow(...),
+)
+```
---
-## Implementation
+## Adding Features
+
+=== "Status"
-**Python Class:** [`LinearConverter`][flixopt.components.LinearConverter]
+ A component is active when any of its flows is non-zero. Add startup costs, minimum run times:
-**Specialized Linear Converters:**
+ ```python
+ gen = fx.LinearConverter(
+ ...,
+ status_parameters=fx.StatusParameters(
+ effects_per_startup={'costs': 1000},
+ min_uptime=4,
+ ),
+ )
+ ```
-FlixOpt provides specialized linear converter classes for common applications:
+ See [StatusParameters](../features/StatusParameters.md).
-- **[`HeatPump`][flixopt.linear_converters.HeatPump]** - Coefficient of Performance (COP) based conversion
-- **[`Power2Heat`][flixopt.linear_converters.Power2Heat]** - Electric heating with efficiency ≤ 1
-- **[`CHP`][flixopt.linear_converters.CHP]** - Combined heat and power generation
-- **[`Boiler`][flixopt.linear_converters.Boiler]** - Fuel to heat conversion
+=== "Piecewise Conversion"
-These classes handle the mathematical formulation automatically based on physical relationships.
+ For variable efficiency — all flows change together based on operating point:
-See the API documentation for implementation details and usage examples.
+ ```python
+ chp = fx.LinearConverter(
+ label='CHP',
+ inputs=[fx.Flow('fuel', bus=gas_bus)],
+ outputs=[
+ fx.Flow('el', bus=elec_bus, size=60),
+ fx.Flow('heat', bus=heat_bus),
+ ],
+ piecewise_conversion=fx.PiecewiseConversion({
+ 'el': fx.Piecewise([fx.Piece(5, 30), fx.Piece(40, 60)]),
+ 'heat': fx.Piecewise([fx.Piece(6, 35), fx.Piece(45, 100)]),
+ 'fuel': fx.Piecewise([fx.Piece(12, 70), fx.Piece(90, 200)]),
+ }),
+ )
+ ```
+
+ See [Piecewise](../features/Piecewise.md).
---
-## See Also
+## Reference
+
+The converter creates **constraints** linking flows, not new variables.
+
+| Symbol | Type | Description |
+|--------|------|-------------|
+| $p_f(t)$ | $\mathbb{R}_{\geq 0}$ | Flow rate of flow $f$ at timestep $t$ |
+| $a_f$ | $\mathbb{R}$ | Conversion factor for input flow $f$ |
+| $b_f$ | $\mathbb{R}$ | Conversion factor for output flow $f$ |
-- [Flow](../elements/Flow.md) - Definition of flow rates
-- [Piecewise](../features/Piecewise.md) - Non-linear conversion efficiency modeling
-- [InvestParameters](../features/InvestParameters.md) - Variable converter sizing
-- [Modeling Patterns](../modeling-patterns/index.md) - Mathematical building blocks
+**Classes:** [`LinearConverter`][flixopt.components.LinearConverter], [`LinearConverterModel`][flixopt.components.LinearConverterModel]
diff --git a/docs/user-guide/mathematical-notation/elements/Storage.md b/docs/user-guide/mathematical-notation/elements/Storage.md
index 9ecd4d570..808fefaed 100644
--- a/docs/user-guide/mathematical-notation/elements/Storage.md
+++ b/docs/user-guide/mathematical-notation/elements/Storage.md
@@ -1,81 +1,120 @@
-# Storages
-**Storages** have one incoming and one outgoing **[Flow](../elements/Flow.md)** with a charging and discharging efficiency.
-A storage has a state of charge $c(\text{t}_i)$ which is limited by its `size` $\text C$ and relative bounds $\eqref{eq:Storage_Bounds}$.
-
-$$ \label{eq:Storage_Bounds}
- \text C \cdot \text c^{\text{L}}_{\text{rel}}(\text t_{i})
- \leq c(\text{t}_i) \leq
- \text C \cdot \text c^{\text{U}}_{\text{rel}}(\text t_{i})
-$$
+# Storage
-Where:
+A Storage accumulates energy over time — charge now, discharge later.
-- $\text C$ is the size of the storage
-- $c(\text{t}_i)$ is the state of charge at time $\text{t}_i$
-- $\text c^{\text{L}}_{\text{rel}}(\text t_{i})$ is the relative lower bound (typically 0)
-- $\text c^{\text{U}}_{\text{rel}}(\text t_{i})$ is the relative upper bound (typically 1)
+## Basic: Charge Dynamics
-With $\text c^{\text{L}}_{\text{rel}}(\text t_{i}) = 0$ and $\text c^{\text{U}}_{\text{rel}}(\text t_{i}) = 1$,
-Equation $\eqref{eq:Storage_Bounds}$ simplifies to
+$$
+c(t+1) = c(t) \cdot (1 - \dot{c}_{loss})^{\Delta t} + p_{in}(t) \cdot \Delta t \cdot \eta_{in} - p_{out}(t) \cdot \Delta t / \eta_{out}
+$$
-$$ 0 \leq c(\text t_{i}) \leq \text C $$
+```python
+battery = fx.Storage(
+ label='battery',
+ charging=fx.Flow(label='charge', bus=elec_bus, size=50),
+ discharging=fx.Flow(label='discharge', bus=elec_bus, size=50),
+ capacity_in_flow_hours=200, # 200 kWh
+ eta_charge=0.95,
+ eta_discharge=0.95,
+)
+# Round-trip efficiency: 95% × 95% = 90.25%
+```
-The state of charge $c(\text{t}_i)$ decreases by a fraction of the prior state of charge. The belonging parameter
-$ \dot{ \text c}_\text{rel, loss}(\text{t}_i)$ expresses the "loss fraction per hour". The storage balance from $\text{t}_i$ to $\text t_{i+1}$ is
+---
+
+## Charge State Bounds
$$
-\begin{align*}
- c(\text{t}_{i+1}) &= c(\text{t}_{i}) \cdot (1-\dot{\text{c}}_\text{rel,loss}(\text{t}_i))^{\Delta \text{t}_{i}} \\
- &\quad + p_{f_\text{in}}(\text{t}_i) \cdot \Delta \text{t}_i \cdot \eta_\text{in}(\text{t}_i) \\
- &\quad - p_{f_\text{out}}(\text{t}_i) \cdot \Delta \text{t}_i \cdot \eta_\text{out}(\text{t}_i)
- \tag{3}
-\end{align*}
+C \cdot c_{rel}^{min} \leq c(t) \leq C \cdot c_{rel}^{max}
$$
-Where:
-
-- $c(\text{t}_{i+1})$ is the state of charge at time $\text{t}_{i+1}$
-- $c(\text{t}_{i})$ is the state of charge at time $\text{t}_{i}$
-- $\dot{\text{c}}_\text{rel,loss}(\text{t}_i)$ is the relative loss rate (self-discharge) per hour
-- $\Delta \text{t}_{i}$ is the time step duration in hours
-- $p_{f_\text{in}}(\text{t}_i)$ is the input flow rate at time $\text{t}_i$
-- $\eta_\text{in}(\text{t}_i)$ is the charging efficiency at time $\text{t}_i$
-- $p_{f_\text{out}}(\text{t}_i)$ is the output flow rate at time $\text{t}_i$
-- $\eta_\text{out}(\text{t}_i)$ is the discharging efficiency at time $\text{t}_i$
+```python
+fx.Storage(...,
+ relative_minimum_charge_state=0.2, # Min 20% SOC
+ relative_maximum_charge_state=0.8, # Max 80% SOC
+)
+```
---
-## Mathematical Patterns Used
+## Initial & Final Conditions
+
+=== "Fixed Start"
-Storage formulation uses the following modeling patterns:
+ ```python
+ fx.Storage(..., initial_charge_state=100) # Start at 100 kWh
+ ```
-- **[Basic Bounds](../modeling-patterns/bounds-and-states.md#basic-bounds)** - For charge state bounds (equation $\eqref{eq:Storage_Bounds}$)
-- **[Scaled Bounds](../modeling-patterns/bounds-and-states.md#scaled-bounds)** - For flow rate bounds relative to storage size
+=== "Cyclic"
-When combined with investment parameters, storage can use:
+ Must end where it started (prevents "cheating"):
-- **[Bounds with State](../modeling-patterns/bounds-and-states.md#bounds-with-state)** - Investment decisions (see [InvestParameters](../features/InvestParameters.md))
+ ```python
+ fx.Storage(..., initial_charge_state='equals_final')
+ ```
+
+=== "Final Bounds"
+
+ ```python
+ fx.Storage(...,
+ minimal_final_charge_state=50,
+ maximal_final_charge_state=150,
+ )
+ ```
---
-## Implementation
+## Adding Features
-**Python Class:** [`Storage`][flixopt.components.Storage]
+=== "Self-Discharge"
-**Key Parameters:**
+ ```python
+ tank = fx.Storage(...,
+ relative_loss_per_hour=0.02, # 2%/hour loss
+ )
+ ```
-- `capacity_in_flow_hours`: Storage capacity $\text{C}$
-- `relative_loss_per_hour`: Self-discharge rate $\dot{\text{c}}_\text{rel,loss}$
-- `initial_charge_state`: Initial charge $c(\text{t}_0)$
-- `minimal_final_charge_state`, `maximal_final_charge_state`: Final charge bounds $c(\text{t}_\text{end})$ (optional)
-- `eta_charge`, `eta_discharge`: Charging/discharging efficiencies $\eta_\text{in}, \eta_\text{out}$
+=== "Variable Capacity"
-See the [`Storage`][flixopt.components.Storage] API documentation for complete parameter list and usage examples.
+ Optimize storage size:
----
+ ```python
+ battery = fx.Storage(...,
+ capacity_in_flow_hours=fx.InvestParameters(
+ minimum_size=0,
+ maximum_size=1000,
+ specific_effects={'costs': 200}, # €/kWh
+ ),
+ )
+ ```
+
+=== "Asymmetric Power"
-## See Also
+ Different charge/discharge rates:
+
+ ```python
+ fx.Storage(
+ charging=fx.Flow(..., size=100), # 100 MW pump
+ discharging=fx.Flow(..., size=120), # 120 MW turbine
+ ...
+ )
+ ```
+
+---
-- [Flow](../elements/Flow.md) - Input and output flow definitions
-- [InvestParameters](../features/InvestParameters.md) - Variable storage sizing
-- [Modeling Patterns](../modeling-patterns/index.md) - Mathematical building blocks
+## Reference
+
+| Symbol | Type | Description |
+|--------|------|-------------|
+| $c(t)$ | $\mathbb{R}_{\geq 0}$ | Charge state at timestep $t$ |
+| $C$ | $\mathbb{R}_{\geq 0}$ | Capacity (`capacity_in_flow_hours`) |
+| $p_{in}(t)$ | $\mathbb{R}_{\geq 0}$ | Charging power (from `charging` flow) |
+| $p_{out}(t)$ | $\mathbb{R}_{\geq 0}$ | Discharging power (from `discharging` flow) |
+| $\eta_{in}$ | $\mathbb{R}_{\geq 0}$ | Charge efficiency (`eta_charge`) |
+| $\eta_{out}$ | $\mathbb{R}_{\geq 0}$ | Discharge efficiency (`eta_discharge`) |
+| $\dot{c}_{loss}$ | $\mathbb{R}_{\geq 0}$ | Self-discharge rate (`relative_loss_per_hour`) |
+| $c_{rel}^{min}$ | $\mathbb{R}_{\geq 0}$ | Min charge state (`relative_minimum_charge_state`) |
+| $c_{rel}^{max}$ | $\mathbb{R}_{\geq 0}$ | Max charge state (`relative_maximum_charge_state`) |
+| $\Delta t$ | $\mathbb{R}_{> 0}$ | Timestep duration (hours) |
+
+**Classes:** [`Storage`][flixopt.components.Storage], [`StorageModel`][flixopt.components.StorageModel]
diff --git a/docs/user-guide/mathematical-notation/features/InvestParameters.md b/docs/user-guide/mathematical-notation/features/InvestParameters.md
index d998039c0..b6e1afe6b 100644
--- a/docs/user-guide/mathematical-notation/features/InvestParameters.md
+++ b/docs/user-guide/mathematical-notation/features/InvestParameters.md
@@ -1,310 +1,143 @@
# InvestParameters
-[`InvestParameters`][flixopt.interface.InvestParameters] model investment decisions in optimization problems, enabling both binary (invest/don't invest) and continuous sizing choices with comprehensive cost modeling.
+InvestParameters make capacity a decision variable — should we build this? How big?
-## Investment Decision Types
+## Basic: Size as Variable
-FlixOpt supports two main types of investment decisions:
-
-### Binary Investment
-
-Fixed-size investment creating a yes/no decision (e.g., install a 100 kW generator):
-
-$$\label{eq:invest_binary}
-v_\text{invest} = s_\text{invest} \cdot \text{size}_\text{fixed}
-$$
-
-With:
-
-- $v_\text{invest}$ being the resulting investment size
-- $s_\text{invest} \in \{0, 1\}$ being the binary investment decision
-- $\text{size}_\text{fixed}$ being the predefined component size
-
-**Behavior:**
-- $s_\text{invest} = 0$: no investment ($v_\text{invest} = 0$)
-- $s_\text{invest} = 1$: invest at fixed size ($v_\text{invest} = \text{size}_\text{fixed}$)
-
----
-
-### Continuous Sizing
-
-Variable-size investment with bounds (e.g., battery capacity from 10-1000 kWh):
-
-$$\label{eq:invest_continuous}
-s_\text{invest} \cdot \text{size}_\text{min} \leq v_\text{invest} \leq s_\text{invest} \cdot \text{size}_\text{max}
-$$
-
-With:
-
-- $v_\text{invest}$ being the investment size variable (continuous)
-- $s_\text{invest} \in \{0, 1\}$ being the binary investment decision
-- $\text{size}_\text{min}$ being the minimum investment size (if investing)
-- $\text{size}_\text{max}$ being the maximum investment size
-
-**Behavior:**
-- $s_\text{invest} = 0$: no investment ($v_\text{invest} = 0$)
-- $s_\text{invest} = 1$: invest with size in $[\text{size}_\text{min}, \text{size}_\text{max}]$
-
-This uses the **bounds with state** pattern described in [Bounds and States](../modeling-patterns/bounds-and-states.md#bounds-with-state).
-
----
-
-### Optional vs. Mandatory Investment
-
-The `mandatory` parameter controls whether investment is required:
-
-**Optional Investment** (`mandatory=False`, default):
-$$\label{eq:invest_optional}
-s_\text{invest} \in \{0, 1\}
-$$
-
-The optimization can freely choose to invest or not.
-
-**Mandatory Investment** (`mandatory=True`):
-$$\label{eq:invest_mandatory}
-s_\text{invest} = 1
-$$
-
-The investment must occur (useful for mandatory upgrades or replacements).
-
----
-
-## Effect Modeling
-
-Investment effects (costs, emissions, etc.) are modeled using three components:
-
-### Fixed Effects
-
-One-time effects incurred if investment is made, independent of size:
-
-$$\label{eq:invest_fixed_effects}
-E_{e,\text{fix}} = s_\text{invest} \cdot \text{fix}_e
$$
-
-With:
-
-- $E_{e,\text{fix}}$ being the fixed contribution to effect $e$
-- $\text{fix}_e$ being the fixed effect value (e.g., fixed installation cost)
-
-**Examples:**
-- Fixed installation costs (permits, grid connection)
-- One-time environmental impacts (land preparation)
-- Fixed labor or administrative costs
-
----
-
-### Specific Effects
-
-Effects proportional to investment size (per-unit costs):
-
-$$\label{eq:invest_specific_effects}
-E_{e,\text{spec}} = v_\text{invest} \cdot \text{spec}_e
+P^{min} \leq P \leq P^{max}
$$
-With:
-
-- $E_{e,\text{spec}}$ being the size-dependent contribution to effect $e$
-- $\text{spec}_e$ being the specific effect value per unit size (e.g., €/kW)
-
-**Examples:**
-- Equipment costs (€/kW)
-- Material requirements (kg steel/kW)
-- Recurring costs (€/kW/year maintenance)
-
----
-
-### Piecewise Effects
-
-Non-linear effect relationships using piecewise linear approximations:
-
-$$\label{eq:invest_piecewise_effects}
-E_{e,\text{pw}} = \sum_{k=1}^{K} \lambda_k \cdot r_{e,k}
-$$
-
-Subject to:
-$$
-v_\text{invest} = \sum_{k=1}^{K} \lambda_k \cdot v_k
-$$
-
-With:
-
-- $E_{e,\text{pw}}$ being the piecewise contribution to effect $e$
-- $\lambda_k$ being the piecewise lambda variables (see [Piecewise](../features/Piecewise.md))
-- $r_{e,k}$ being the effect rate at piece $k$
-- $v_k$ being the size points defining the pieces
-
-**Use cases:**
-- Economies of scale (bulk discounts)
-- Technology learning curves
-- Threshold effects (capacity tiers with different costs)
-
-See [Piecewise](../features/Piecewise.md) for detailed mathematical formulation.
+```python
+battery = fx.Storage(
+ ...,
+ capacity_in_flow_hours=fx.InvestParameters(
+ minimum_size=10,
+ maximum_size=1000,
+ specific_effects={'costs': 600}, # €600/kWh
+ ),
+)
+```
---
-### Retirement Effects
-
-Effects incurred if investment is NOT made (when retiring/not replacing existing equipment):
+## Investment Modes
-$$\label{eq:invest_retirement_effects}
-E_{e,\text{retirement}} = (1 - s_\text{invest}) \cdot \text{retirement}_e
-$$
+By default, investment is **optional** — the optimizer can choose $P = 0$ (don't invest).
-With:
+=== "Continuous"
-- $E_{e,\text{retirement}}$ being the retirement contribution to effect $e$
-- $\text{retirement}_e$ being the retirement effect value
+ Choose size within range (or zero):
-**Behavior:**
-- $s_\text{invest} = 0$: retirement effects are incurred
-- $s_\text{invest} = 1$: no retirement effects
+ ```python
+ fx.InvestParameters(
+ minimum_size=10,
+ maximum_size=1000,
+ )
+ # → P = 0 OR 10 ≤ P ≤ 1000
+ ```
-**Examples:**
-- Demolition or disposal costs
-- Decommissioning expenses
-- Contractual penalties for not investing
-- Opportunity costs or lost revenues
+=== "Binary"
----
+ Fixed size or nothing:
-### Total Investment Effects
+ ```python
+ fx.InvestParameters(
+ fixed_size=100, # 100 kW or 0
+ )
+ # → P ∈ {0, 100}
+ ```
-The total contribution to effect $e$ from an investment is:
+=== "Mandatory"
-$$\label{eq:invest_total_effects}
-E_{e,\text{invest}} = E_{e,\text{fix}} + E_{e,\text{spec}} + E_{e,\text{pw}} + E_{e,\text{retirement}}
-$$
+ Force investment with `mandatory=True` — zero not allowed:
-Effects integrate into the overall system effects as described in [Effects, Penalty & Objective](../effects-penalty-objective.md).
+ ```python
+ fx.InvestParameters(
+ minimum_size=50,
+ maximum_size=200,
+ mandatory=True,
+ )
+ # → 50 ≤ P ≤ 200 (no zero option)
+ ```
---
-## Integration with Components
+## Investment Effects
-Investment parameters modify component sizing:
+=== "Per-Size Cost"
-### Without Investment
-Component size is a fixed parameter:
-$$
-\text{size} = \text{size}_\text{nominal}
-$$
+ Cost proportional to capacity (€/kW):
-### With Investment
-Component size becomes a variable:
-$$
-\text{size} = v_\text{invest}
-$$
+ $E = P \cdot c_{spec}$
-This size variable then appears in component constraints. For example, flow rate bounds become:
+ ```python
+ fx.InvestParameters(
+ specific_effects={'costs': 1200}, # €1200/kW
+ )
+ ```
-$$
-v_\text{invest} \cdot \text{rel}_\text{lower} \leq p(t) \leq v_\text{invest} \cdot \text{rel}_\text{upper}
-$$
+=== "Fixed Cost"
-Using the **scaled bounds** pattern from [Bounds and States](../modeling-patterns/bounds-and-states.md#scaled-bounds).
+ One-time cost if investing:
----
+ $E = s_{inv} \cdot c_{fix}$
-## Cost Annualization
+ ```python
+ fx.InvestParameters(
+ effects_of_investment={'costs': 25000}, # €25k
+ )
+ ```
-**Important:** All investment cost values must be properly weighted to match the optimization model's time horizon.
+=== "Retirement Cost"
-For long-term investments, costs should be annualized:
+ Cost if NOT investing:
-$$\label{eq:annualization}
-\text{cost}_\text{annual} = \frac{\text{cost}_\text{capital} \cdot r}{1 - (1 + r)^{-n}}
-$$
-
-With:
-
-- $\text{cost}_\text{capital}$ being the upfront investment cost
-- $r$ being the discount rate
-- $n$ being the equipment lifetime in years
-
-**Example:** €1,000,000 equipment with 20-year life and 5% discount rate
-$$
-\text{cost}_\text{annual} = \frac{1{,}000{,}000 \cdot 0.05}{1 - (1.05)^{-20}} \approx €80{,}243/\text{year}
-$$
+ $E = (1 - s_{inv}) \cdot c_{ret}$
----
-
-## Implementation
+ ```python
+ fx.InvestParameters(
+ effects_of_retirement={'costs': 8000}, # Demolition
+ )
+ ```
-**Python Class:** [`InvestParameters`][flixopt.interface.InvestParameters]
+=== "Piecewise Cost"
-**Key Parameters:**
+ Non-linear cost curves (e.g., economies of scale):
-- `fixed_size`: For binary investments (mutually exclusive with continuous sizing)
-- `minimum_size`, `maximum_size`: For continuous sizing
-- `mandatory`: Whether investment is required (default: `False`)
-- `effects_of_investment`: Fixed effects incurred when investing (replaces deprecated `fix_effects`)
-- `effects_of_investment_per_size`: Per-unit effects proportional to size (replaces deprecated `specific_effects`)
-- `piecewise_effects_of_investment`: Non-linear effect modeling (replaces deprecated `piecewise_effects`)
-- `effects_of_retirement`: Effects for not investing (replaces deprecated `divest_effects`)
+ $E = f_{piecewise}(P)$
-See the [`InvestParameters`][flixopt.interface.InvestParameters] API documentation for complete parameter list and usage examples.
+ ```python
+ fx.InvestParameters(
+ piecewise_effects_of_investment=fx.PiecewiseEffects(
+ piecewise_origin=fx.Piecewise([
+ fx.Piece(0, 100),
+ fx.Piece(100, 500),
+ ]),
+ piecewise_shares={
+ 'costs': fx.Piecewise([
+ fx.Piece(0, 80_000), # €800/kW for 0-100
+ fx.Piece(80_000, 280_000), # €500/kW for 100-500
+ ])
+ },
+ ),
+ )
+ ```
-**Used in:**
-- [`Flow`][flixopt.elements.Flow] - Flexible capacity decisions
-- [`Storage`][flixopt.components.Storage] - Storage sizing optimization
-- [`LinearConverter`][flixopt.components.LinearConverter] - Converter capacity planning
-- All components supporting investment decisions
+ See [Piecewise](Piecewise.md) for details on the formulation.
---
-## Examples
+## Reference
-### Binary Investment (Solar Panels)
-```python
-solar_investment = InvestParameters(
- fixed_size=100, # 100 kW system
- mandatory=False, # Optional investment (default)
- effects_of_investment={'cost': 25000}, # Installation costs
- effects_of_investment_per_size={'cost': 1200}, # €1200/kW
-)
-```
+| Symbol | Type | Description |
+|--------|------|-------------|
+| $P$ | $\mathbb{R}_{\geq 0}$ | Investment size (capacity) |
+| $s_{inv}$ | $\{0, 1\}$ | Binary investment decision (0=no, 1=yes) |
+| $P^{min}$ | $\mathbb{R}_{\geq 0}$ | Minimum size (`minimum_size`) |
+| $P^{max}$ | $\mathbb{R}_{\geq 0}$ | Maximum size (`maximum_size`) |
+| $c_{spec}$ | $\mathbb{R}$ | Per-size effect (`effects_of_investment_per_size`) |
+| $c_{fix}$ | $\mathbb{R}$ | Fixed effect (`effects_of_investment`) |
+| $c_{ret}$ | $\mathbb{R}$ | Retirement effect (`effects_of_retirement`) |
-### Continuous Sizing (Battery)
-```python
-battery_investment = InvestParameters(
- minimum_size=10, # kWh
- maximum_size=1000,
- mandatory=False, # Optional investment (default)
- effects_of_investment={'cost': 5000}, # Grid connection
- effects_of_investment_per_size={'cost': 600}, # €600/kWh
-)
-```
-
-### With Retirement Costs (Replacement)
-```python
-boiler_replacement = InvestParameters(
- minimum_size=50, # kW
- maximum_size=200,
- mandatory=False, # Optional investment (default)
- effects_of_investment={'cost': 15000},
- effects_of_investment_per_size={'cost': 400},
- effects_of_retirement={'cost': 8000}, # Demolition if not replaced
-)
-```
-
-### Economies of Scale (Piecewise)
-```python
-battery_investment = InvestParameters(
- minimum_size=10,
- maximum_size=1000,
- piecewise_effects_of_investment=PiecewiseEffects(
- piecewise_origin=Piecewise([
- Piece(0, 100), # Small
- Piece(100, 500), # Medium
- Piece(500, 1000), # Large
- ]),
- piecewise_shares={
- 'cost': Piecewise([
- Piece(800, 750), # €800-750/kWh
- Piece(750, 600), # €750-600/kWh
- Piece(600, 500), # €600-500/kWh (bulk discount)
- ])
- },
- ),
-)
-```
+**Classes:** [`InvestParameters`][flixopt.interface.InvestParameters], [`InvestmentModel`][flixopt.features.InvestmentModel]
diff --git a/docs/user-guide/mathematical-notation/features/OnOffParameters.md b/docs/user-guide/mathematical-notation/features/OnOffParameters.md
deleted file mode 100644
index e69de29bb..000000000
diff --git a/docs/user-guide/mathematical-notation/features/Piecewise.md b/docs/user-guide/mathematical-notation/features/Piecewise.md
index 688ac8cea..da6405b52 100644
--- a/docs/user-guide/mathematical-notation/features/Piecewise.md
+++ b/docs/user-guide/mathematical-notation/features/Piecewise.md
@@ -1,49 +1,155 @@
# Piecewise
-A Piecewise is a collection of [`Pieces`][flixopt.interface.Piece], which each define a valid range for a variable $v$
+Piecewise linearization approximates non-linear relationships using connected linear segments.
+
+## Mathematical Formulation
+
+A piecewise linear function with $n$ segments uses per-segment interpolation:
-$$ \label{eq:active_piece}
- \beta_\text{k} = \lambda_\text{0, k} + \lambda_\text{1, k}
$$
+x = \sum_{i=1}^{n} \left( \lambda_i^0 \cdot x_i^{start} + \lambda_i^1 \cdot x_i^{end} \right)
+$$
+
+Each segment $i$ has:
-$$ \label{eq:piece}
- v_\text{k} = \lambda_\text{0, k} * \text{v}_{\text{start,k}} + \lambda_\text{1,k} * \text{v}_{\text{end,k}}
+- $s_i \in \{0, 1\}$ — binary indicating if segment is active
+- $\lambda_i^0, \lambda_i^1 \geq 0$ — interpolation weights for segment endpoints
+
+Constraints ensure valid interpolation:
+
+$$
+\lambda_i^0 + \lambda_i^1 = s_i \quad \forall i
$$
-$$ \label{eq:piecewise_in_pieces}
-\sum_{k=1}^k \beta_{k} = 1
+$$
+\sum_{i=1}^{n} s_i \leq 1
$$
-With:
+When segment $i$ is active ($s_i = 1$), the lambdas interpolate between $x_i^{start}$ and $x_i^{end}$. When inactive ($s_i = 0$), both lambdas are zero.
-- $v$: The variable to be defined by the Piecewise
-- $\text{v}_{\text{start,k}}$: the start point of the piece for variable $v$
-- $\text{v}_{\text{end,k}}$: the end point of the piece for variable $v$
-- $\beta_\text{k} \in \{0, 1\}$: defining wether the Piece $k$ is active
-- $\lambda_\text{0,k} \in [0, 1]$: A variable defining the fraction of $\text{v}_{\text{start,k}}$ that is active
-- $\lambda_\text{1,k} \in [0, 1]$: A variable defining the fraction of $\text{v}_{\text{end,k}}$ that is active
+!!! note "Implementation Note"
+ This formulation is an explicit binary reformulation of SOS2 (Special Ordered Set Type 2) constraints. It produces identical results but uses more variables. We will migrate to native SOS2 constraints once [linopy](https://github.com/PyPSA/linopy) supports them.
-Which can also be described as $v \in 0 \cup [\text{v}_\text{start}, \text{v}_\text{end}]$.
+---
-Instead of \eqref{eq:piecewise_in_pieces}, the following constraint is used to also allow all variables to be zero:
+## Building Blocks
-$$ \label{eq:piecewise_in_pieces_zero}
-\sum_{k=1}^k \beta_{k} = \beta_\text{zero}
-$$
+=== "Piece"
+
+ A linear segment from start to end value:
+
+ ```python
+ fx.Piece(start=10, end=50) # Linear from 10 to 50
+ ```
+
+ Values can be time-varying:
+
+ ```python
+ fx.Piece(
+ start=np.linspace(5, 6, n_timesteps),
+ end=np.linspace(30, 35, n_timesteps)
+ )
+ ```
+
+=== "Piecewise"
+
+ Multiple segments forming a piecewise linear function:
+
+ ```python
+ fx.Piecewise([
+ fx.Piece(0, 30), # Segment 1: 0 → 30
+ fx.Piece(30, 60), # Segment 2: 30 → 60
+ ])
+ ```
+
+=== "PiecewiseConversion"
+
+ Synchronizes multiple flows — all interpolate at the same relative position:
+
+ ```python
+ fx.PiecewiseConversion({
+ 'input_flow': fx.Piecewise([...]),
+ 'output_flow': fx.Piecewise([...]),
+ })
+ ```
+
+ All piecewise functions must have the same number of segments.
+
+=== "PiecewiseEffects"
+
+ Maps a size/capacity variable to effects (costs, emissions):
+
+ ```python
+ fx.PiecewiseEffects(
+ piecewise_origin=fx.Piecewise([...]), # Size segments
+ piecewise_shares={'costs': fx.Piecewise([...])}, # Effect segments
+ )
+ ```
+
+---
+
+## Usage
+
+=== "Variable Efficiency"
-With:
+ Converter efficiency that varies with load:
-- $\beta_\text{zero} \in \{0, 1\}$.
+ ```python
+ chp = fx.LinearConverter(
+ ...,
+ piecewise_conversion=fx.PiecewiseConversion({
+ 'el': fx.Piecewise([fx.Piece(5, 30), fx.Piece(40, 60)]),
+ 'heat': fx.Piecewise([fx.Piece(6, 35), fx.Piece(45, 100)]),
+ 'fuel': fx.Piecewise([fx.Piece(12, 70), fx.Piece(90, 200)]),
+ }),
+ )
+ ```
-Which can also be described as $v \in \{0\} \cup [\text{v}_{\text{start_k}}, \text{v}_{\text{end_k}}]$
+=== "Economies of Scale"
+ Investment cost per unit decreases with size:
-## Combining multiple Piecewises
+ ```python
+ fx.InvestParameters(
+ piecewise_effects_of_investment=fx.PiecewiseEffects(
+ piecewise_origin=fx.Piecewise([
+ fx.Piece(0, 100),
+ fx.Piece(100, 500),
+ ]),
+ piecewise_shares={
+ 'costs': fx.Piecewise([
+ fx.Piece(0, 80_000),
+ fx.Piece(80_000, 280_000),
+ ])
+ },
+ ),
+ )
+ ```
-Piecewise allows representing non-linear relationships.
-This is a powerful technique in linear optimization to model non-linear behaviors while maintaining the problem's linearity.
+=== "Forbidden Operating Region"
-Therefore, each Piecewise must have the same number of Pieces $k$.
+ Equipment cannot operate in certain ranges:
-The variables described in [Piecewise](#piecewise) are created for each Piece, but nor for each Piecewise.
-Rather, \eqref{eq:piece} is the only constraint that is created for each Piecewise, using the start and endpoints $\text{v}_{\text{start,k}}$ and $\text{v}_{\text{end,k}}$ of each Piece for the corresponding variable $v$
+ ```python
+ fx.PiecewiseConversion({
+ 'fuel': fx.Piecewise([fx.Piece(0, 0), fx.Piece(40, 100)]),
+ 'power': fx.Piecewise([fx.Piece(0, 0), fx.Piece(35, 95)]),
+ })
+ # Either off (0,0) or operating above 40%
+ ```
+
+---
+
+## Reference
+
+| Symbol | Type | Description |
+|--------|------|-------------|
+| $x$ | $\mathbb{R}$ | Interpolated variable value |
+| $s_i$ | $\{0, 1\}$ | Binary: segment $i$ is active |
+| $\lambda_i^0$ | $[0, 1]$ | Interpolation weight for segment start |
+| $\lambda_i^1$ | $[0, 1]$ | Interpolation weight for segment end |
+| $x_i^{start}$ | $\mathbb{R}$ | Start value of segment $i$ |
+| $x_i^{end}$ | $\mathbb{R}$ | End value of segment $i$ |
+| $n$ | $\mathbb{Z}_{> 0}$ | Number of segments |
+
+**Classes:** [`Piecewise`][flixopt.interface.Piecewise], [`Piece`][flixopt.interface.Piece], [`PiecewiseConversion`][flixopt.interface.PiecewiseConversion], [`PiecewiseEffects`][flixopt.interface.PiecewiseEffects]
diff --git a/docs/user-guide/mathematical-notation/features/StatusParameters.md b/docs/user-guide/mathematical-notation/features/StatusParameters.md
index 2ec34e3df..7b4c08f72 100644
--- a/docs/user-guide/mathematical-notation/features/StatusParameters.md
+++ b/docs/user-guide/mathematical-notation/features/StatusParameters.md
@@ -1,317 +1,114 @@
# StatusParameters
-[`StatusParameters`][flixopt.interface.StatusParameters] model equipment that operates in discrete active/inactive states rather than continuous operation. This captures realistic operational constraints including startup costs, minimum run times, cycling limitations, and maintenance scheduling.
+StatusParameters add on/off behavior to flows — startup costs, minimum run times, cycling limits.
-## Binary State Variable
+## Basic: Binary Status
-Equipment operation is modeled using a binary state variable:
+A status variable $s(t) \in \{0, 1\}$ controls whether equipment is active:
-$$\label{eq:status_state}
-s(t) \in \{0, 1\} \quad \forall t
-$$
-
-With:
-
-- $s(t) = 1$: equipment is operating (active state)
-- $s(t) = 0$: equipment is shutdown (inactive state)
-
-This state variable controls the equipment's operational constraints and modifies flow bounds using the **bounds with state** pattern from [Bounds and States](../modeling-patterns/bounds-and-states.md#bounds-with-state).
-
----
-
-## State Transitions and Switching
-
-State transitions are tracked using switch variables (see [State Transitions](../modeling-patterns/state-transitions.md#binary-state-transitions)):
-
-$$\label{eq:status_transitions}
-s^\text{startup}(t) - s^\text{shutdown}(t) = s(t) - s(t-1) \quad \forall t > 0
-$$
-
-$$\label{eq:status_switch_exclusivity}
-s^\text{startup}(t) + s^\text{shutdown}(t) \leq 1 \quad \forall t
-$$
-
-With:
-
-- $s^\text{startup}(t) \in \{0, 1\}$: equals 1 when switching from inactive to active (startup)
-- $s^\text{shutdown}(t) \in \{0, 1\}$: equals 1 when switching from active to inactive (shutdown)
-
-**Behavior:**
-- Inactive → Active: $s^\text{startup}(t) = 1, s^\text{shutdown}(t) = 0$
-- Active → Inactive: $s^\text{startup}(t) = 0, s^\text{shutdown}(t) = 1$
-- No change: $s^\text{startup}(t) = 0, s^\text{shutdown}(t) = 0$
-
----
-
-## Effects and Costs
-
-### Startup Effects
-
-Effects incurred when equipment starts up:
-
-$$\label{eq:status_switch_effects}
-E_{e,\text{switch}} = \sum_{t} s^\text{startup}(t) \cdot \text{effect}_{e,\text{switch}}
-$$
-
-With:
-
-- $\text{effect}_{e,\text{switch}}$ being the effect value per startup event
-
-**Examples:**
-- Startup fuel consumption
-- Wear and tear costs
-- Labor costs for startup procedures
-- Inrush power demands
-
----
-
-### Running Effects
-
-Effects incurred while equipment is operating:
-
-$$\label{eq:status_running_effects}
-E_{e,\text{run}} = \sum_{t} s(t) \cdot \Delta t \cdot \text{effect}_{e,\text{run}}
-$$
-
-With:
-
-- $\text{effect}_{e,\text{run}}$ being the effect rate per operating hour
-- $\Delta t$ being the time step duration
-
-**Examples:**
-- Fixed operating and maintenance costs
-- Auxiliary power consumption
-- Consumable materials
-- Emissions while running
-
----
-
-## Operating Hour Constraints
-
-### Total Operating Hours
-
-Bounds on total operating time across the planning horizon:
-
-$$\label{eq:status_total_hours}
-h_\text{min} \leq \sum_{t} s(t) \cdot \Delta t \leq h_\text{max}
-$$
-
-With:
-
-- $h_\text{min}$ being the minimum total operating hours
-- $h_\text{max}$ being the maximum total operating hours
-
-**Use cases:**
-- Minimum runtime requirements (contracts, maintenance)
-- Maximum runtime limits (fuel availability, permits, equipment life)
-
----
-
-### Consecutive Operating Hours
-
-**Minimum Consecutive Uptime:**
-
-Enforces minimum runtime once started using duration tracking (see [Duration Tracking](../modeling-patterns/duration-tracking.md#minimum-duration-constraints)):
-
-$$\label{eq:status_min_uptime}
-d^\text{uptime}(t) \geq (s(t-1) - s(t)) \cdot h^\text{uptime}_\text{min} \quad \forall t > 0
-$$
-
-With:
-
-- $d^\text{uptime}(t)$ being the consecutive uptime duration at time $t$
-- $h^\text{uptime}_\text{min}$ being the minimum required uptime
-
-**Behavior:**
-- When shutting down at time $t$: enforces equipment was on for at least $h^\text{uptime}_\text{min}$ prior to the switch
-- Prevents short cycling and frequent startups
-
-**Maximum Consecutive Uptime:**
-
-Limits continuous operation before requiring shutdown:
-
-$$\label{eq:status_max_uptime}
-d^\text{uptime}(t) \leq h^\text{uptime}_\text{max} \quad \forall t
-$$
-
-**Use cases:**
-- Mandatory maintenance intervals
-- Process batch time limits
-- Thermal cycling requirements
-
----
-
-### Consecutive Shutdown Hours
-
-**Minimum Consecutive Downtime:**
-
-Enforces minimum shutdown duration before restarting:
-
-$$\label{eq:status_min_downtime}
-d^\text{downtime}(t) \geq (s(t) - s(t-1)) \cdot h^\text{downtime}_\text{min} \quad \forall t > 0
-$$
-
-With:
-
-- $d^\text{downtime}(t)$ being the consecutive downtime duration at time $t$
-- $h^\text{downtime}_\text{min}$ being the minimum required downtime
-
-**Use cases:**
-- Cooling periods
-- Maintenance requirements
-- Process stabilization
-
-**Maximum Consecutive Downtime:**
-
-Limits shutdown duration before mandatory restart:
-
-$$\label{eq:status_max_downtime}
-d^\text{downtime}(t) \leq h^\text{downtime}_\text{max} \quad \forall t
-$$
+```python
+generator = fx.Flow(
+ label='power', bus=elec_bus, size=100,
+ relative_minimum=0.4, # 40% min when ON
+ status_parameters=fx.StatusParameters(
+ effects_per_startup={'costs': 25000}, # €25k per startup
+ ),
+)
+```
-**Use cases:**
-- Equipment preservation requirements
-- Process stability needs
-- Contractual minimum activity levels
+When $s(t) = 0$: flow is zero. When $s(t) = 1$: flow bounds apply.
---
-## Cycling Limits
+## Startup Tracking
-Maximum number of startups across the planning horizon:
+Detect transitions: $s^{start}(t) - s^{stop}(t) = s(t) - s(t-1)$
-$$\label{eq:status_max_switches}
-\sum_{t} s^\text{startup}(t) \leq n_\text{max}
-$$
+=== "Startup Costs"
-With:
+ ```python
+ fx.StatusParameters(
+ effects_per_startup={'costs': 25000},
+ )
+ ```
-- $n_\text{max}$ being the maximum allowed number of startups
+=== "Running Costs"
-**Use cases:**
-- Preventing excessive equipment wear
-- Grid stability requirements
-- Operational complexity limits
-- Maintenance budget constraints
+ ```python
+ fx.StatusParameters(
+ effects_per_active_hour={'costs': 100}, # €/h while on
+ )
+ ```
----
-
-## Integration with Flow Bounds
-
-StatusParameters modify flow rate bounds by coupling them to the active/inactive state.
-
-**Without StatusParameters** (continuous operation):
-$$
-P \cdot \text{rel}_\text{lower} \leq p(t) \leq P \cdot \text{rel}_\text{upper}
-$$
-
-**With StatusParameters** (binary operation):
-$$
-s(t) \cdot P \cdot \max(\varepsilon, \text{rel}_\text{lower}) \leq p(t) \leq s(t) \cdot P \cdot \text{rel}_\text{upper}
-$$
-
-Using the **bounds with state** pattern from [Bounds and States](../modeling-patterns/bounds-and-states.md#bounds-with-state).
+=== "Startup Limit"
-**Behavior:**
-- When $s(t) = 0$: flow is forced to zero
-- When $s(t) = 1$: flow follows normal bounds
+ ```python
+ fx.StatusParameters(
+ startup_limit=20, # Max 20 starts per period
+ )
+ ```
---
-## Complete Formulation Summary
+## Duration Constraints
-For equipment with StatusParameters, the complete constraint system includes:
+=== "Min Uptime"
-1. **State variable:** $s(t) \in \{0, 1\}$
-2. **Switch tracking:** $s^\text{startup}(t) - s^\text{shutdown}(t) = s(t) - s(t-1)$
-3. **Switch exclusivity:** $s^\text{startup}(t) + s^\text{shutdown}(t) \leq 1$
-4. **Duration tracking:**
+ Once on, must stay on for minimum duration:
- - On-duration: $d^\text{uptime}(t)$ following duration tracking pattern
- - Off-duration: $d^\text{downtime}(t)$ following duration tracking pattern
-5. **Minimum uptime:** $d^\text{uptime}(t) \geq (s(t-1) - s(t)) \cdot h^\text{uptime}_\text{min}$
-6. **Maximum uptime:** $d^\text{uptime}(t) \leq h^\text{uptime}_\text{max}$
-7. **Minimum downtime:** $d^\text{downtime}(t) \geq (s(t) - s(t-1)) \cdot h^\text{downtime}_\text{min}$
-8. **Maximum downtime:** $d^\text{downtime}(t) \leq h^\text{downtime}_\text{max}$
-9. **Total hours:** $h_\text{min} \leq \sum_t s(t) \cdot \Delta t \leq h_\text{max}$
-10. **Cycling limit:** $\sum_t s^\text{startup}(t) \leq n_\text{max}$
-11. **Flow bounds:** $s(t) \cdot P \cdot \max(\varepsilon, \text{rel}_\text{lower}) \leq p(t) \leq s(t) \cdot P \cdot \text{rel}_\text{upper}$
+ $s^{start}(t) = 1 \Rightarrow \sum_{j=t}^{t+k} s(j) \geq T_{up}^{min}$
----
-
-## Implementation
+ ```python
+ fx.StatusParameters(min_uptime=8) # 8 hours minimum
+ ```
-**Python Class:** [`StatusParameters`][flixopt.interface.StatusParameters]
+=== "Min Downtime"
-**Key Parameters:**
+ Once off, must stay off for minimum duration:
-- `effects_per_startup`: Costs per startup event
-- `effects_per_active_hour`: Costs per hour of operation
-- `active_hours_min`, `active_hours_max`: Total runtime bounds
-- `min_uptime`, `max_uptime`: Consecutive runtime bounds
-- `min_downtime`, `max_downtime`: Consecutive shutdown bounds
-- `startup_limit`: Maximum number of startups
-- `force_startup_tracking`: Create switch variables even without limits (for tracking)
+ $s^{stop}(t) = 1 \Rightarrow \sum_{j=t}^{t+k} (1 - s(j)) \geq T_{down}^{min}$
-See the [`StatusParameters`][flixopt.interface.StatusParameters] API documentation for complete parameter list and usage examples.
+ ```python
+ fx.StatusParameters(min_downtime=4) # 4 hours cooling
+ ```
-**Mathematical Patterns Used:**
-- [State Transitions](../modeling-patterns/state-transitions.md#binary-state-transitions) - Switch tracking
-- [Duration Tracking](../modeling-patterns/duration-tracking.md) - Consecutive time constraints
-- [Bounds with State](../modeling-patterns/bounds-and-states.md#bounds-with-state) - Flow control
+=== "Max Uptime"
-**Used in:**
-- [`Flow`][flixopt.elements.Flow] - Active/inactive operation for flows
-- All components supporting discrete operational states
+ Force shutdown after limit:
----
+ $\sum_{j=t-k}^{t} s(j) \leq T_{up}^{max}$
-## Examples
+ ```python
+ fx.StatusParameters(max_uptime=18) # Max 18h continuous
+ ```
-### Power Plant with Startup Costs
-```python
-power_plant = StatusParameters(
- effects_per_startup={'startup_cost': 25000}, # €25k per startup
- effects_per_active_hour={'fixed_om': 125}, # €125/hour while running
- min_uptime=8, # Minimum 8-hour run
- min_downtime=4, # 4-hour cooling period
- active_hours_max=6000, # Annual limit
-)
-```
+=== "Total Hours"
-### Batch Process with Cycling Limits
-```python
-batch_reactor = StatusParameters(
- effects_per_startup={'setup_cost': 1500},
- min_uptime=12, # 12-hour minimum batch
- max_uptime=24, # 24-hour maximum batch
- min_downtime=6, # Cleaning time
- startup_limit=200, # Max 200 batches
-)
-```
+ Limit total operating hours per period:
-### HVAC with Cycle Prevention
-```python
-hvac = StatusParameters(
- effects_per_startup={'compressor_wear': 0.5},
- min_uptime=1, # Prevent short cycling
- min_downtime=0.5, # 30-min minimum off
- startup_limit=2000, # Limit compressor starts
-)
-```
+ $H^{min} \leq \sum_t s(t) \cdot \Delta t \leq H^{max}$
-### Backup Generator with Testing Requirements
-```python
-backup_gen = StatusParameters(
- effects_per_startup={'fuel_priming': 50}, # L diesel
- min_uptime=0.5, # 30-min test duration
- max_downtime=720, # Test every 30 days
- active_hours_min=26, # Weekly testing requirement
-)
-```
+ ```python
+ fx.StatusParameters(
+ active_hours_min=2000,
+ active_hours_max=5000,
+ )
+ ```
---
-## Notes
-
-**Time Series Boundary:** The final time period constraints for min_uptime/max and min_downtime/max are not enforced at the end of the planning horizon. This allows optimization to end with ongoing campaigns that may be shorter/longer than specified, as they extend beyond the modeled period.
+## Reference
+
+| Symbol | Type | Description |
+|--------|------|-------------|
+| $s(t)$ | $\{0, 1\}$ | Binary status (0=off, 1=on) |
+| $s^{start}(t)$ | $\{0, 1\}$ | Startup indicator |
+| $s^{stop}(t)$ | $\{0, 1\}$ | Shutdown indicator |
+| $T_{up}^{min}$ | $\mathbb{R}_{\geq 0}$ | Min uptime in hours (`min_uptime`) |
+| $T_{up}^{max}$ | $\mathbb{R}_{\geq 0}$ | Max uptime in hours (`max_uptime`) |
+| $T_{down}^{min}$ | $\mathbb{R}_{\geq 0}$ | Min downtime in hours (`min_downtime`) |
+| $H^{min}$ | $\mathbb{R}_{\geq 0}$ | Min total active hours (`active_hours_min`) |
+| $H^{max}$ | $\mathbb{R}_{\geq 0}$ | Max total active hours (`active_hours_max`) |
+| $\Delta t$ | $\mathbb{R}_{> 0}$ | Timestep duration (hours) |
+
+**Classes:** [`StatusParameters`][flixopt.interface.StatusParameters], [`StatusModel`][flixopt.features.StatusModel]
diff --git a/docs/user-guide/mathematical-notation/index.md b/docs/user-guide/mathematical-notation/index.md
index 4512820f3..95e21db5e 100644
--- a/docs/user-guide/mathematical-notation/index.md
+++ b/docs/user-guide/mathematical-notation/index.md
@@ -1,123 +1,107 @@
-
# Mathematical Notation
-This section provides the **mathematical formulations** underlying FlixOpt's optimization models. It is intended as **reference documentation** for users who want to understand the mathematical details behind the high-level FlixOpt API described in the [FlixOpt Concepts](../core-concepts.md) guide.
-
-**For typical usage**, refer to the [FlixOpt Concepts](../core-concepts.md) guide, [Examples](../../examples/index.md), and [API Reference](../../api-reference/index.md) - you don't need to understand these mathematical formulations to use FlixOpt effectively.
-
----
-
-## Naming Conventions
-
-FlixOpt uses the following naming conventions:
-
-- All optimization variables are denoted by italic letters (e.g., $x$, $y$, $z$)
-- All parameters and constants are denoted by non italic small letters (e.g., $\text{a}$, $\text{b}$, $\text{c}$)
-- All Sets are denoted by greek capital letters (e.g., $\mathcal{F}$, $\mathcal{E}$)
-- All units of a set are denoted by greek small letters (e.g., $\mathcal{f}$, $\mathcal{e}$)
-- The letter $i$ is used to denote an index (e.g., $i=1,\dots,\text n$)
-- All time steps are denoted by the letter $\text{t}$ (e.g., $\text{t}_0$, $\text{t}_1$, $\text{t}_i$)
+This section provides the detailed mathematical formulations behind flixOpt. It expands on the concepts introduced in [Core Concepts](../core-concepts.md) with precise equations, variables, and constraints.
-## Dimensions and Time Steps
+!!! tip "When to read this"
+ You don't need this section to use flixOpt effectively. It's here for:
-FlixOpt supports multi-dimensional optimization with up to three dimensions: **time** (mandatory), **period** (optional), and **scenario** (optional).
+ - Understanding exactly what the solver is optimizing
+ - Debugging unexpected model behavior
+ - Extending flixOpt with custom constraints
+ - Academic work requiring formal notation
-**All mathematical formulations in this documentation are independent of whether periods or scenarios are present.** The equations shown are written with time index $\text{t}_i$ only, but automatically expand to additional dimensions when periods/scenarios are added.
+## Structure
-For complete details on dimensions, their relationships, and influence on formulations, see **[Dimensions](dimensions.md)**.
+The documentation follows the same structure as Core Concepts:
-### Time Steps
+| Core Concept | Mathematical Details |
+|--------------|---------------------|
+| **Buses** — where things connect | [Bus](elements/Bus.md) — balance equations, penalty terms |
+| **Flows** — what moves | [Flow](elements/Flow.md) — capacity bounds, load factors, profiles |
+| **Converters** — transform things | [LinearConverter](elements/LinearConverter.md) — conversion ratios |
+| **Storages** — save for later | [Storage](elements/Storage.md) — charge dynamics, efficiency losses |
+| **Effects** — what you track | [Effects & Dimensions](effects-and-dimensions.md) — objectives, costs, scenarios, periods |
-Time steps are defined as a sequence of discrete time steps $\text{t}_i \in \mathcal{T} \quad \text{for} \quad i \in \{1, 2, \dots, \text{n}\}$ (left-aligned in its timespan).
-From this sequence, the corresponding time intervals $\Delta \text{t}_i \in \Delta \mathcal{T}$ are derived as
+## Notation Conventions
-$$\Delta \text{t}_i = \text{t}_{i+1} - \text{t}_i \quad \text{for} \quad i \in \{1, 2, \dots, \text{n}-1\}$$
+### Variables (What the optimizer decides)
-The final time interval $\Delta \text{t}_\text n$ defaults to $\Delta \text{t}_\text n = \Delta \text{t}_{\text n-1}$, but is of course customizable.
-Non-equidistant time steps are also supported.
+Optimization variables are shown in *italic*:
----
+| Symbol | Meaning | Example |
+|--------|---------|---------|
+| $p(t)$ | Flow rate at time $t$ | Heat output of a boiler |
+| $c(t)$ | Charge state at time $t$ | Energy stored in a battery |
+| $P$ | Size/capacity (when optimized) | Installed capacity of a heat pump |
+| $s(t)$ | Binary on/off state | Whether a generator is running |
-## Documentation Structure
+### Parameters (What you provide)
-This reference is organized to match the FlixOpt API structure:
+Parameters and constants are shown in upright text:
-### Elements
-Mathematical formulations for core FlixOpt elements (corresponding to [`flixopt.elements`][flixopt.elements]):
+| Symbol | Meaning | Example |
+|--------|---------|---------|
+| $\eta$ | Efficiency | Boiler thermal efficiency (0.9) |
+| $\Delta t$ | Timestep duration | 1 hour |
+| $p_{min}$, $p_{max}$ | Flow bounds | Min/max operating power |
-- [Flow](elements/Flow.md) - Flow rate constraints and bounds
-- [Bus](elements/Bus.md) - Nodal balance equations
-- [Storage](elements/Storage.md) - Storage balance and charge state evolution
-- [LinearConverter](elements/LinearConverter.md) - Linear conversion relationships
+### Sets and Indices
-**User API:** When you create a `Flow`, `Bus`, `Storage`, or `LinearConverter` in your FlixOpt model, these mathematical formulations are automatically applied.
+| Symbol | Meaning |
+|--------|---------|
+| $t \in \mathcal{T}$ | Time steps |
+| $f \in \mathcal{F}$ | Flows |
+| $e \in \mathcal{E}$ | Effects |
-### Features
-Mathematical formulations for optional features (corresponding to parameters in FlixOpt classes):
+## The Optimization Problem
-- [InvestParameters](features/InvestParameters.md) - Investment decision modeling
-- [StatusParameters](features/StatusParameters.md) - Binary active/inactive operation
-- [Piecewise](features/Piecewise.md) - Piecewise linear approximations
+At its core, flixOpt solves:
-**User API:** When you pass `invest_parameters` or `status_parameters` to a `Flow` or component, these formulations are applied.
+$$
+\min \quad objective + penalty
+$$
-### System-Level
-- [Effects, Penalty & Objective](effects-penalty-objective.md) - Cost allocation and objective function
+**Subject to:**
-**User API:** When you create [`Effect`][flixopt.effects.Effect] objects and set `effects_per_flow_hour`, these formulations govern how costs are calculated.
+- Balance constraints at each bus
+- Capacity bounds on each flow
+- Storage dynamics over time
+- Conversion relationships in converters
+- Any additional effect constraints
-### Modeling Patterns (Advanced)
-**Internal implementation details** - These low-level patterns are used internally by Elements and Features. They are documented here for:
+The following pages detail each of these components.
-- Developers extending FlixOpt
-- Advanced users debugging models or understanding solver behavior
-- Researchers comparing mathematical formulations
+## Quick Example
-**Normal users do not need to read this section** - the patterns are automatically applied when you use Elements and Features:
+Consider a simple system: a gas boiler connected to a heat bus serving a demand.
-- [Bounds and States](modeling-patterns/bounds-and-states.md) - Variable bounding patterns
-- [Duration Tracking](modeling-patterns/duration-tracking.md) - Consecutive time period tracking
-- [State Transitions](modeling-patterns/state-transitions.md) - State change modeling
+**Variables:**
----
+- $p_{gas}(t)$ — gas consumption at each timestep
+- $p_{heat}(t)$ — heat production at each timestep
-## Quick Reference
+**Constraints:**
-### Components Cross-Reference
+1. **Conversion** (boiler efficiency 90%):
+ $$p_{heat}(t) = 0.9 \cdot p_{gas}(t)$$
-| Concept | Documentation | Python Class |
-|---------|---------------|--------------|
-| **Flow rate bounds** | [Flow](elements/Flow.md) | [`Flow`][flixopt.elements.Flow] |
-| **Bus balance** | [Bus](elements/Bus.md) | [`Bus`][flixopt.elements.Bus] |
-| **Storage balance** | [Storage](elements/Storage.md) | [`Storage`][flixopt.components.Storage] |
-| **Linear conversion** | [LinearConverter](elements/LinearConverter.md) | [`LinearConverter`][flixopt.components.LinearConverter] |
+2. **Capacity bounds** (boiler max 100 kW):
+ $$0 \leq p_{heat}(t) \leq 100$$
-### Features Cross-Reference
+3. **Balance** (meet demand):
+ $$p_{heat}(t) = demand(t)$$
-| Concept | Documentation | Python Class |
-|---------|---------------|--------------|
-| **Binary investment** | [InvestParameters](features/InvestParameters.md) | [`InvestParameters`][flixopt.interface.InvestParameters] |
-| **On/off operation** | [StatusParameters](features/StatusParameters.md) | [`StatusParameters`][flixopt.interface.StatusParameters] |
-| **Piecewise segments** | [Piecewise](features/Piecewise.md) | [`Piecewise`][flixopt.interface.Piecewise] |
+**Objective** (minimize gas cost at €50/MWh):
+$$\min \sum_t p_{gas}(t) \cdot \Delta t \cdot 50$$
-### Modeling Patterns Cross-Reference
+This simple example shows how the concepts combine. Real models have many more components, but the principles remain the same.
-| Pattern | Documentation | Implementation |
-|---------|---------------|----------------|
-| **Basic bounds** | [bounds-and-states](modeling-patterns/bounds-and-states.md#basic-bounds) | [`BoundingPatterns.basic_bounds()`][flixopt.modeling.BoundingPatterns.basic_bounds] |
-| **Bounds with state** | [bounds-and-states](modeling-patterns/bounds-and-states.md#bounds-with-state) | [`BoundingPatterns.bounds_with_state()`][flixopt.modeling.BoundingPatterns.bounds_with_state] |
-| **Scaled bounds** | [bounds-and-states](modeling-patterns/bounds-and-states.md#scaled-bounds) | [`BoundingPatterns.scaled_bounds()`][flixopt.modeling.BoundingPatterns.scaled_bounds] |
-| **Duration tracking** | [duration-tracking](modeling-patterns/duration-tracking.md) | [`ModelingPrimitives.consecutive_duration_tracking()`][flixopt.modeling.ModelingPrimitives.consecutive_duration_tracking] |
-| **State transitions** | [state-transitions](modeling-patterns/state-transitions.md) | [`BoundingPatterns.state_transition_bounds()`][flixopt.modeling.BoundingPatterns.state_transition_bounds] |
+## Next Steps
-### Python Class Lookup
+Start with the element that's most relevant to your question:
-| Class | Documentation | API Reference |
-|-------|---------------|---------------|
-| `Flow` | [Flow](elements/Flow.md) | [`Flow`][flixopt.elements.Flow] |
-| `Bus` | [Bus](elements/Bus.md) | [`Bus`][flixopt.elements.Bus] |
-| `Storage` | [Storage](elements/Storage.md) | [`Storage`][flixopt.components.Storage] |
-| `LinearConverter` | [LinearConverter](elements/LinearConverter.md) | [`LinearConverter`][flixopt.components.LinearConverter] |
-| `InvestParameters` | [InvestParameters](features/InvestParameters.md) | [`InvestParameters`][flixopt.interface.InvestParameters] |
-| `StatusParameters` | [StatusParameters](features/StatusParameters.md) | [`StatusParameters`][flixopt.interface.StatusParameters] |
-| `Piecewise` | [Piecewise](features/Piecewise.md) | [`Piecewise`][flixopt.interface.Piecewise] |
+- **Why isn't my demand being met?** → [Bus](elements/Bus.md) (balance constraints)
+- **Why is my component not running?** → [Flow](elements/Flow.md) (capacity bounds)
+- **How does storage charge/discharge?** → [Storage](elements/Storage.md) (charge dynamics)
+- **How are efficiencies handled?** → [LinearConverter](elements/LinearConverter.md) (conversion)
+- **How are costs calculated?** → [Effects & Dimensions](effects-and-dimensions.md)
diff --git a/docs/user-guide/mathematical-notation/modeling-patterns/bounds-and-states.md b/docs/user-guide/mathematical-notation/modeling-patterns/bounds-and-states.md
deleted file mode 100644
index 18235e50d..000000000
--- a/docs/user-guide/mathematical-notation/modeling-patterns/bounds-and-states.md
+++ /dev/null
@@ -1,171 +0,0 @@
-# Bounds and States
-
-This document describes the mathematical formulations for variable bounding patterns used throughout FlixOpt. These patterns define how optimization variables are constrained, both with and without state control.
-
-## Basic Bounds
-
-The simplest bounding pattern constrains a variable between lower and upper bounds.
-
-$$\label{eq:basic_bounds}
-\text{lower} \leq v \leq \text{upper}
-$$
-
-With:
-
-- $v$ being the optimization variable
-- $\text{lower}$ being the lower bound (constant or time-dependent)
-- $\text{upper}$ being the upper bound (constant or time-dependent)
-
-**Implementation:** [`BoundingPatterns.basic_bounds()`][flixopt.modeling.BoundingPatterns.basic_bounds]
-
-**Used in:**
-- Storage charge state bounds (see [Storage](../elements/Storage.md))
-- Flow rate absolute bounds
-
----
-
-## Bounds with State
-
-When a variable should only be non-zero if a binary state variable is active (e.g., active/inactive operation, investment decisions), the bounds are controlled by the state:
-
-$$\label{eq:bounds_with_state}
-s \cdot \max(\varepsilon, \text{lower}) \leq v \leq s \cdot \text{upper}
-$$
-
-With:
-
-- $v$ being the optimization variable
-- $s \in \{0, 1\}$ being the binary state variable
-- $\text{lower}$ being the lower bound when active
-- $\text{upper}$ being the upper bound when active
-- $\varepsilon$ being a small positive number to ensure numerical stability
-
-**Behavior:**
-- When $s = 0$: variable is forced to zero ($0 \leq v \leq 0$)
-- When $s = 1$: variable can take values in $[\text{lower}, \text{upper}]$
-
-**Implementation:** [`BoundingPatterns.bounds_with_state()`][flixopt.modeling.BoundingPatterns.bounds_with_state]
-
-**Used in:**
-- Flow rates with active/inactive operation (see [StatusParameters](../features/StatusParameters.md))
-- Investment size decisions (see [InvestParameters](../features/InvestParameters.md))
-
----
-
-## Scaled Bounds
-
-When a variable's bounds depend on another variable (e.g., flow rate scaled by component size), scaled bounds are used:
-
-$$\label{eq:scaled_bounds}
-v_\text{scale} \cdot \text{rel}_\text{lower} \leq v \leq v_\text{scale} \cdot \text{rel}_\text{upper}
-$$
-
-With:
-
-- $v$ being the optimization variable (e.g., flow rate)
-- $v_\text{scale}$ being the scaling variable (e.g., component size)
-- $\text{rel}_\text{lower}$ being the relative lower bound factor (typically 0)
-- $\text{rel}_\text{upper}$ being the relative upper bound factor (typically 1)
-
-**Example:** Flow rate bounds
-- If $v_\text{scale} = P$ (flow size) and $\text{rel}_\text{upper} = 1$
-- Then: $0 \leq p(t_i) \leq P$ (see [Flow](../elements/Flow.md))
-
-**Implementation:** [`BoundingPatterns.scaled_bounds()`][flixopt.modeling.BoundingPatterns.scaled_bounds]
-
-**Used in:**
-- Flow rate constraints (see [Flow](../elements/Flow.md) equation 1)
-- Storage charge state constraints (see [Storage](../elements/Storage.md) equation 1)
-
----
-
-## Scaled Bounds with State
-
-Combining scaled bounds with binary state control requires a Big-M formulation to handle both the scaling and the active/inactive behavior:
-
-$$\label{eq:scaled_bounds_with_state_1}
-(s - 1) \cdot M_\text{misc} + v_\text{scale} \cdot \text{rel}_\text{lower} \leq v \leq v_\text{scale} \cdot \text{rel}_\text{upper}
-$$
-
-$$\label{eq:scaled_bounds_with_state_2}
-s \cdot M_\text{lower} \leq v \leq s \cdot M_\text{upper}
-$$
-
-With:
-
-- $v$ being the optimization variable
-- $v_\text{scale}$ being the scaling variable
-- $s \in \{0, 1\}$ being the binary state variable
-- $\text{rel}_\text{lower}$ being the relative lower bound factor
-- $\text{rel}_\text{upper}$ being the relative upper bound factor
-- $M_\text{misc} = v_\text{scale,max} \cdot \text{rel}_\text{lower}$
-- $M_\text{upper} = v_\text{scale,max} \cdot \text{rel}_\text{upper}$
-- $M_\text{lower} = \max(\varepsilon, v_\text{scale,min} \cdot \text{rel}_\text{lower})$
-
-Where $v_\text{scale,max}$ and $v_\text{scale,min}$ are the maximum and minimum possible values of the scaling variable.
-
-**Behavior:**
-- When $s = 0$: variable is forced to zero
-- When $s = 1$: variable follows scaled bounds $v_\text{scale} \cdot \text{rel}_\text{lower} \leq v \leq v_\text{scale} \cdot \text{rel}_\text{upper}$
-
-**Implementation:** [`BoundingPatterns.scaled_bounds_with_state()`][flixopt.modeling.BoundingPatterns.scaled_bounds_with_state]
-
-**Used in:**
-- Flow rates with active/inactive operation and investment sizing
-- Components combining [StatusParameters](../features/StatusParameters.md) and [InvestParameters](../features/InvestParameters.md)
-
----
-
-## Expression Tracking
-
-Sometimes it's necessary to create an auxiliary variable that equals an expression:
-
-$$\label{eq:expression_tracking}
-v_\text{tracker} = \text{expression}
-$$
-
-With optional bounds:
-
-$$\label{eq:expression_tracking_bounds}
-\text{lower} \leq v_\text{tracker} \leq \text{upper}
-$$
-
-With:
-
-- $v_\text{tracker}$ being the auxiliary tracking variable
-- $\text{expression}$ being a linear expression of other variables
-- $\text{lower}, \text{upper}$ being optional bounds on the tracker
-
-**Use cases:**
-- Creating named variables for complex expressions
-- Bounding intermediate results
-- Simplifying constraint formulations
-
-**Implementation:** [`ModelingPrimitives.expression_tracking_variable()`][flixopt.modeling.ModelingPrimitives.expression_tracking_variable]
-
----
-
-## Mutual Exclusivity
-
-When multiple binary variables should not be active simultaneously (at most one can be 1):
-
-$$\label{eq:mutual_exclusivity}
-\sum_{i} s_i(t) \leq \text{tolerance} \quad \forall t
-$$
-
-With:
-
-- $s_i(t) \in \{0, 1\}$ being binary state variables
-- $\text{tolerance}$ being the maximum number of simultaneously active states (typically 1)
-- $t$ being the time index
-
-**Use cases:**
-- Ensuring only one operating mode is active
-- Mutual exclusion of operation and maintenance states
-- Enforcing single-choice decisions
-
-**Implementation:** [`ModelingPrimitives.mutual_exclusivity_constraint()`][flixopt.modeling.ModelingPrimitives.mutual_exclusivity_constraint]
-
-**Used in:**
-- Operating mode selection
-- Piecewise linear function segments (see [Piecewise](../features/Piecewise.md))
diff --git a/docs/user-guide/mathematical-notation/modeling-patterns/duration-tracking.md b/docs/user-guide/mathematical-notation/modeling-patterns/duration-tracking.md
deleted file mode 100644
index 2d6f46ed1..000000000
--- a/docs/user-guide/mathematical-notation/modeling-patterns/duration-tracking.md
+++ /dev/null
@@ -1,164 +0,0 @@
-# Duration Tracking
-
-Duration tracking allows monitoring how long a binary state has been consecutively active. This is essential for modeling minimum run times, ramp-up periods, and similar time-dependent constraints.
-
-## Consecutive Duration Tracking
-
-For a binary state variable $s(t) \in \{0, 1\}$, the consecutive duration $d(t)$ tracks how long the state has been continuously active.
-
-### Duration Upper Bound
-
-The duration cannot exceed zero when the state is inactive:
-
-$$\label{eq:duration_upper}
-d(t) \leq s(t) \cdot M \quad \forall t
-$$
-
-With:
-
-- $d(t)$ being the duration variable (continuous, non-negative)
-- $s(t) \in \{0, 1\}$ being the binary state variable
-- $M$ being a sufficiently large constant (big-M)
-
-**Behavior:**
-- When $s(t) = 0$: forces $d(t) \leq 0$, thus $d(t) = 0$
-- When $s(t) = 1$: allows $d(t)$ to be positive
-
----
-
-### Duration Accumulation
-
-While the state is active, the duration increases by the time step size:
-
-$$\label{eq:duration_accumulation_upper}
-d(t+1) \leq d(t) + \Delta d(t) \quad \forall t
-$$
-
-$$\label{eq:duration_accumulation_lower}
-d(t+1) \geq d(t) + \Delta d(t) + (s(t+1) - 1) \cdot M \quad \forall t
-$$
-
-With:
-
-- $\Delta d(t)$ being the duration increment for time step $t$ (typically $\Delta t_i$ from the time series)
-- $M$ being a sufficiently large constant
-
-**Behavior:**
-- When $s(t+1) = 1$: both inequalities enforce $d(t+1) = d(t) + \Delta d(t)$
-- When $s(t+1) = 0$: only the upper bound applies, and $d(t+1) = 0$ (from equation $\eqref{eq:duration_upper}$)
-
----
-
-### Initial Duration
-
-The duration at the first time step depends on both the state and any previous duration:
-
-$$\label{eq:duration_initial}
-d(0) = (\Delta d(0) + d_\text{prev}) \cdot s(0)
-$$
-
-With:
-
-- $d_\text{prev}$ being the duration from before the optimization period
-- $\Delta d(0)$ being the duration increment for the first time step
-
-**Behavior:**
-- When $s(0) = 1$: duration continues from previous period
-- When $s(0) = 0$: duration resets to zero
-
----
-
-### Complete Formulation
-
-Combining all constraints:
-
-$$
-\begin{align}
-d(t) &\leq s(t) \cdot M && \forall t \label{eq:duration_complete_1} \\
-d(t+1) &\leq d(t) + \Delta d(t) && \forall t \label{eq:duration_complete_2} \\
-d(t+1) &\geq d(t) + \Delta d(t) + (s(t+1) - 1) \cdot M && \forall t \label{eq:duration_complete_3} \\
-d(0) &= (\Delta d(0) + d_\text{prev}) \cdot s(0) && \label{eq:duration_complete_4}
-\end{align}
-$$
-
----
-
-## Minimum Duration Constraints
-
-To enforce a minimum consecutive duration (e.g., minimum run time), an additional constraint links the duration to state changes:
-
-$$\label{eq:minimum_duration}
-d(t) \geq (s(t-1) - s(t)) \cdot d_\text{min}(t-1) \quad \forall t > 0
-$$
-
-With:
-
-- $d_\text{min}(t)$ being the required minimum duration at time $t$
-
-**Behavior:**
-- When shutting down ($s(t-1) = 1, s(t) = 0$): enforces $d(t-1) \geq d_\text{min}(t-1)$
-- This ensures the state was active for at least $d_\text{min}$ before turning off
-- When state is constant or turning on: constraint is non-binding
-
----
-
-## Implementation
-
-**Function:** [`ModelingPrimitives.consecutive_duration_tracking()`][flixopt.modeling.ModelingPrimitives.consecutive_duration_tracking]
-
-See the API documentation for complete parameter list and usage details.
-
----
-
-## Use Cases
-
-### Minimum Run Time
-
-Ensuring equipment runs for a minimum duration once started:
-
-```python
-# State: 1 when running, 0 when off
-# Require at least 2 hours of operation
-duration = modeling.consecutive_duration_tracking(
- state=on_state,
- duration_per_step=time_step_hours,
- minimum_duration=2.0
-)
-```
-
-### Ramp-Up Tracking
-
-Tracking time since startup for gradual ramp-up constraints:
-
-```python
-# Track startup duration
-startup_duration = modeling.consecutive_duration_tracking(
- state=on_state,
- duration_per_step=time_step_hours
-)
-# Constrain output based on startup duration
-# (additional constraints would link output to startup_duration)
-```
-
-### Cooldown Requirements
-
-Tracking time in a state before allowing transitions:
-
-```python
-# Track maintenance duration
-maintenance_duration = modeling.consecutive_duration_tracking(
- state=maintenance_state,
- duration_per_step=time_step_hours,
- minimum_duration=scheduled_maintenance_hours
-)
-```
-
----
-
-## Used In
-
-This pattern is used in:
-
-- [`StatusParameters`](../features/StatusParameters.md) - Minimum active/inactive times
-- Operating mode constraints with minimum durations
-- Startup/shutdown sequence modeling
diff --git a/docs/user-guide/mathematical-notation/modeling-patterns/index.md b/docs/user-guide/mathematical-notation/modeling-patterns/index.md
deleted file mode 100644
index ab347eb39..000000000
--- a/docs/user-guide/mathematical-notation/modeling-patterns/index.md
+++ /dev/null
@@ -1,54 +0,0 @@
-# Modeling Patterns
-
-This section documents the fundamental mathematical patterns used throughout FlixOpt for constructing optimization models. These patterns are implemented in `flixopt.modeling` and provide reusable building blocks for creating constraints.
-
-## Overview
-
-The modeling patterns are organized into three categories:
-
-1. **[Bounds and States](bounds-and-states.md)** - Variable bounding with optional state control
-2. **[Duration Tracking](duration-tracking.md)** - Tracking consecutive durations of states
-3. **[State Transitions](state-transitions.md)** - Modeling state changes and transitions
-
-## Pattern Categories
-
-### Bounding Patterns
-
-These patterns define how optimization variables are constrained within bounds:
-
-- **Basic Bounds** - Simple upper and lower bounds on variables
-- **Bounds with State** - Binary-controlled bounds (active/inactive states)
-- **Scaled Bounds** - Bounds dependent on another variable (e.g., size)
-- **Scaled Bounds with State** - Combination of scaling and binary control
-
-### Tracking Patterns
-
-These patterns track properties over time:
-
-- **Expression Tracking** - Creating auxiliary variables that track expressions
-- **Consecutive Duration Tracking** - Tracking how long a state has been active
-- **Mutual Exclusivity** - Ensuring only one of multiple options is active
-
-### Transition Patterns
-
-These patterns model changes between states:
-
-- **State Transitions** - Tracking switches between binary states (on→off, off→on)
-- **Continuous Transitions** - Linking continuous variable changes to switches
-- **Level Changes with Binaries** - Controlled increases/decreases in levels
-
-## Usage in Components
-
-These patterns are used throughout FlixOpt components:
-
-- [`Flow`][flixopt.elements.Flow] uses **scaled bounds with state** for flow rate constraints
-- [`Storage`][flixopt.components.Storage] uses **basic bounds** for charge state
-- [`StatusParameters`](../features/StatusParameters.md) uses **state transitions** for startup/shutdown
-- [`InvestParameters`](../features/InvestParameters.md) uses **bounds with state** for investment decisions
-
-## Implementation
-
-All patterns are implemented in [`flixopt.modeling`][flixopt.modeling] module:
-
-- [`ModelingPrimitives`][flixopt.modeling.ModelingPrimitives] - Core constraint patterns
-- [`BoundingPatterns`][flixopt.modeling.BoundingPatterns] - Specialized bounding patterns
diff --git a/docs/user-guide/mathematical-notation/modeling-patterns/state-transitions.md b/docs/user-guide/mathematical-notation/modeling-patterns/state-transitions.md
deleted file mode 100644
index cf6cfe736..000000000
--- a/docs/user-guide/mathematical-notation/modeling-patterns/state-transitions.md
+++ /dev/null
@@ -1,235 +0,0 @@
-# State Transitions
-
-State transition patterns model changes between discrete states and link them to continuous variables. These patterns are essential for modeling startup/shutdown events, switching behavior, and controlled changes in system operation.
-
-## Binary State Transitions
-
-For a binary state variable $s(t) \in \{0, 1\}$, state transitions track when the state switches on or off.
-
-### Switch Variables
-
-Two binary variables track the transitions:
-
-- $s^\text{on}(t) \in \{0, 1\}$: equals 1 when switching from off to on
-- $s^\text{off}(t) \in \{0, 1\}$: equals 1 when switching from on to off
-
-### Transition Tracking
-
-The state change equals the difference between switch-on and switch-off:
-
-$$\label{eq:state_transition}
-s^\text{on}(t) - s^\text{off}(t) = s(t) - s(t-1) \quad \forall t > 0
-$$
-
-$$\label{eq:state_transition_initial}
-s^\text{on}(0) - s^\text{off}(0) = s(0) - s_\text{prev}
-$$
-
-With:
-
-- $s(t)$ being the binary state variable
-- $s_\text{prev}$ being the state before the optimization period
-- $s^\text{on}(t), s^\text{off}(t)$ being the switch variables
-
-**Behavior:**
-- Off → On ($s(t-1)=0, s(t)=1$): $s^\text{on}(t)=1, s^\text{off}(t)=0$
-- On → Off ($s(t-1)=1, s(t)=0$): $s^\text{on}(t)=0, s^\text{off}(t)=1$
-- No change: $s^\text{on}(t)=0, s^\text{off}(t)=0$
-
----
-
-### Mutual Exclusivity of Switches
-
-A state cannot switch on and off simultaneously:
-
-$$\label{eq:switch_exclusivity}
-s^\text{on}(t) + s^\text{off}(t) \leq 1 \quad \forall t
-$$
-
-This ensures:
-
-- At most one switch event per time step
-- No simultaneous active/inactive switching
-
----
-
-### Complete State Transition Formulation
-
-$$
-\begin{align}
-s^\text{on}(t) - s^\text{off}(t) &= s(t) - s(t-1) && \forall t > 0 \label{eq:transition_complete_1} \\
-s^\text{on}(0) - s^\text{off}(0) &= s(0) - s_\text{prev} && \label{eq:transition_complete_2} \\
-s^\text{on}(t) + s^\text{off}(t) &\leq 1 && \forall t \label{eq:transition_complete_3} \\
-s^\text{on}(t), s^\text{off}(t) &\in \{0, 1\} && \forall t \label{eq:transition_complete_4}
-\end{align}
-$$
-
-**Implementation:** [`BoundingPatterns.state_transition_bounds()`][flixopt.modeling.BoundingPatterns.state_transition_bounds]
-
----
-
-## Continuous Transitions
-
-When a continuous variable should only change when certain switch events occur, continuous transition bounds link the variable changes to binary switches.
-
-### Change Bounds with Switches
-
-$$\label{eq:continuous_transition}
--\Delta v^\text{max} \cdot (s^\text{on}(t) + s^\text{off}(t)) \leq v(t) - v(t-1) \leq \Delta v^\text{max} \cdot (s^\text{on}(t) + s^\text{off}(t)) \quad \forall t > 0
-$$
-
-$$\label{eq:continuous_transition_initial}
--\Delta v^\text{max} \cdot (s^\text{on}(0) + s^\text{off}(0)) \leq v(0) - v_\text{prev} \leq \Delta v^\text{max} \cdot (s^\text{on}(0) + s^\text{off}(0))
-$$
-
-With:
-
-- $v(t)$ being the continuous variable
-- $v_\text{prev}$ being the value before the optimization period
-- $\Delta v^\text{max}$ being the maximum allowed change
-- $s^\text{on}(t), s^\text{off}(t) \in \{0, 1\}$ being switch binary variables
-
-**Behavior:**
-- When $s^\text{on}(t) = 0$ and $s^\text{off}(t) = 0$: forces $v(t) = v(t-1)$ (no change)
-- When $s^\text{on}(t) = 1$ or $s^\text{off}(t) = 1$: allows change up to $\pm \Delta v^\text{max}$
-
-**Implementation:** [`BoundingPatterns.continuous_transition_bounds()`][flixopt.modeling.BoundingPatterns.continuous_transition_bounds]
-
----
-
-## Level Changes with Binaries
-
-This pattern models a level variable that can increase or decrease, with changes controlled by binary variables. This is useful for inventory management, capacity adjustments, or gradual state changes.
-
-### Level Evolution
-
-The level evolves based on increases and decreases:
-
-$$\label{eq:level_initial}
-\ell(0) = \ell_\text{init} + \ell^\text{inc}(0) - \ell^\text{dec}(0)
-$$
-
-$$\label{eq:level_evolution}
-\ell(t) = \ell(t-1) + \ell^\text{inc}(t) - \ell^\text{dec}(t) \quad \forall t > 0
-$$
-
-With:
-
-- $\ell(t)$ being the level variable
-- $\ell_\text{init}$ being the initial level
-- $\ell^\text{inc}(t)$ being the increase in level at time $t$ (non-negative)
-- $\ell^\text{dec}(t)$ being the decrease in level at time $t$ (non-negative)
-
----
-
-### Change Bounds with Binary Control
-
-Changes are bounded and controlled by binary variables:
-
-$$\label{eq:increase_bound}
-\ell^\text{inc}(t) \leq \Delta \ell^\text{max} \cdot b^\text{inc}(t) \quad \forall t
-$$
-
-$$\label{eq:decrease_bound}
-\ell^\text{dec}(t) \leq \Delta \ell^\text{max} \cdot b^\text{dec}(t) \quad \forall t
-$$
-
-With:
-
-- $\Delta \ell^\text{max}$ being the maximum change per time step
-- $b^\text{inc}(t), b^\text{dec}(t) \in \{0, 1\}$ being binary control variables
-
----
-
-### Mutual Exclusivity of Changes
-
-Simultaneous increase and decrease are prevented:
-
-$$\label{eq:change_exclusivity}
-b^\text{inc}(t) + b^\text{dec}(t) \leq 1 \quad \forall t
-$$
-
-This ensures:
-
-- Level can only increase OR decrease (or stay constant) in each time step
-- No simultaneous contradictory changes
-
----
-
-### Complete Level Change Formulation
-
-$$
-\begin{align}
-\ell(0) &= \ell_\text{init} + \ell^\text{inc}(0) - \ell^\text{dec}(0) && \label{eq:level_complete_1} \\
-\ell(t) &= \ell(t-1) + \ell^\text{inc}(t) - \ell^\text{dec}(t) && \forall t > 0 \label{eq:level_complete_2} \\
-\ell^\text{inc}(t) &\leq \Delta \ell^\text{max} \cdot b^\text{inc}(t) && \forall t \label{eq:level_complete_3} \\
-\ell^\text{dec}(t) &\leq \Delta \ell^\text{max} \cdot b^\text{dec}(t) && \forall t \label{eq:level_complete_4} \\
-b^\text{inc}(t) + b^\text{dec}(t) &\leq 1 && \forall t \label{eq:level_complete_5} \\
-b^\text{inc}(t), b^\text{dec}(t) &\in \{0, 1\} && \forall t \label{eq:level_complete_6}
-\end{align}
-$$
-
-**Implementation:** [`BoundingPatterns.link_changes_to_level_with_binaries()`][flixopt.modeling.BoundingPatterns.link_changes_to_level_with_binaries]
-
----
-
-## Use Cases
-
-### Startup/Shutdown Costs
-
-Track startup and shutdown events to apply costs:
-
-```python
-# Create switch variables
-startup, shutdown = modeling.state_transition_bounds(
- state=on_state,
- previous_state=previous_on_state
-)
-
-# Apply costs to switches
-startup_cost = startup * startup_cost_per_event
-shutdown_cost = shutdown * shutdown_cost_per_event
-```
-
-### Limited Switching
-
-Restrict the number of state changes:
-
-```python
-# Track all switches
-startup, shutdown = modeling.state_transition_bounds(
- state=on_state
-)
-
-# Limit total switches
-model.add_constraint(
- (startup + shutdown).sum() <= max_switches
-)
-```
-
-### Gradual Capacity Changes
-
-Model systems where capacity can be incrementally adjusted:
-
-```python
-# Level represents installed capacity
-level_var, increase, decrease, inc_binary, dec_binary = \
- modeling.link_changes_to_level_with_binaries(
- initial_level=current_capacity,
- max_change=max_capacity_change_per_period
- )
-
-# Constrain total increases
-model.add_constraint(increase.sum() <= max_total_expansion)
-```
-
----
-
-## Used In
-
-These patterns are used in:
-
-- [`StatusParameters`](../features/StatusParameters.md) - Startup/shutdown tracking and costs
-- Operating mode switching with transition costs
-- Investment planning with staged capacity additions
-- Inventory management with controlled stock changes
diff --git a/docs/user-guide/mathematical-notation/others.md b/docs/user-guide/mathematical-notation/others.md
deleted file mode 100644
index bdc602308..000000000
--- a/docs/user-guide/mathematical-notation/others.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Work in Progress
-
-This is a work in progress.
diff --git a/docs/user-guide/optimization/index.md b/docs/user-guide/optimization/index.md
new file mode 100644
index 000000000..7010acfc5
--- /dev/null
+++ b/docs/user-guide/optimization/index.md
@@ -0,0 +1,195 @@
+# Running Optimizations
+
+This section covers how to run optimizations in flixOpt, including different optimization modes and solver configuration.
+
+## Optimization Modes
+
+flixOpt provides three optimization modes to handle different problem sizes and requirements:
+
+### Optimization (Full)
+
+[`Optimization`][flixopt.optimization.Optimization] solves the entire problem at once.
+
+```python
+import flixopt as fx
+
+optimization = fx.Optimization('my_model', flow_system)
+optimization.solve(fx.solvers.HighsSolver())
+```
+
+**Best for:**
+
+- Small to medium problems
+- When you need the globally optimal solution
+- Problems without time-coupling simplifications
+
+### SegmentedOptimization
+
+[`SegmentedOptimization`][flixopt.optimization.SegmentedOptimization] splits the time horizon into segments and solves them sequentially.
+
+```python
+optimization = fx.SegmentedOptimization(
+ 'segmented_model',
+ flow_system,
+ segment_length=24, # Hours per segment
+ overlap_length=4 # Hours of overlap between segments
+)
+optimization.solve(fx.solvers.HighsSolver())
+```
+
+**Best for:**
+
+- Large problems that don't fit in memory
+- Long time horizons (weeks, months)
+- Problems where decisions are mostly local in time
+
+**Trade-offs:**
+
+- Faster solve times
+- May miss globally optimal solutions
+- Overlap helps maintain solution quality at segment boundaries
+
+### ClusteredOptimization
+
+[`ClusteredOptimization`][flixopt.optimization.ClusteredOptimization] uses time series aggregation to reduce problem size by identifying representative periods.
+
+```python
+clustering_params = fx.ClusteringParameters(
+ n_periods=8, # Number of typical periods
+ hours_per_period=24 # Hours per typical period
+)
+
+optimization = fx.ClusteredOptimization(
+ 'clustered_model',
+ flow_system,
+ clustering_params
+)
+optimization.solve(fx.solvers.HighsSolver())
+```
+
+**Best for:**
+
+- Investment planning problems
+- Year-long optimizations
+- When computational speed is critical
+
+**Trade-offs:**
+
+- Much faster solve times
+- Approximates the full problem
+- Best when patterns repeat (e.g., typical days)
+
+## Choosing an Optimization Mode
+
+| Mode | Problem Size | Solve Time | Solution Quality |
+|------|-------------|------------|------------------|
+| `Optimization` | Small-Medium | Slow | Optimal |
+| `SegmentedOptimization` | Large | Medium | Near-optimal |
+| `ClusteredOptimization` | Very Large | Fast | Approximate |
+
+## Solver Configuration
+
+### Available Solvers
+
+| Solver | Type | Speed | License |
+|--------|------|-------|---------|
+| **HiGHS** | Open-source | Fast | Free |
+| **Gurobi** | Commercial | Fastest | Academic/Commercial |
+| **CPLEX** | Commercial | Fastest | Academic/Commercial |
+| **GLPK** | Open-source | Slower | Free |
+
+**Recommendation:** Start with HiGHS (included by default). Use Gurobi/CPLEX for large models or when speed matters.
+
+### Solver Options
+
+```python
+# Basic usage with defaults
+optimization.solve(fx.solvers.HighsSolver())
+
+# With custom options
+optimization.solve(
+ fx.solvers.GurobiSolver(
+ time_limit_seconds=3600,
+ mip_gap=0.01,
+ extra_options={
+ 'Threads': 4,
+ 'Presolve': 2
+ }
+ )
+)
+```
+
+Common solver parameters:
+
+- `time_limit_seconds` - Maximum solve time
+- `mip_gap` - Acceptable optimality gap (0.01 = 1%)
+- `log_to_console` - Show solver output
+
+## Performance Tips
+
+### Model Size Reduction
+
+- Use longer timesteps where acceptable
+- Use `ClusteredOptimization` for long horizons
+- Remove unnecessary components
+- Simplify constraint formulations
+
+### Solver Tuning
+
+- Enable presolve and cuts
+- Adjust optimality tolerances for faster (approximate) solutions
+- Use parallel threads when available
+
+### Problem Formulation
+
+- Avoid unnecessary binary variables
+- Use continuous investment sizes when possible
+- Tighten variable bounds
+- Remove redundant constraints
+
+## Debugging
+
+### Infeasibility
+
+If your model has no feasible solution:
+
+1. **Enable excess penalties on buses** to allow balance violations:
+ ```python
+ # Allow imbalance with high penalty cost (default is 1e5)
+ heat_bus = fx.Bus('Heat', excess_penalty_per_flow_hour=1e5)
+
+ # Or disable penalty to enforce strict balance
+ electricity_bus = fx.Bus('Electricity', excess_penalty_per_flow_hour=None)
+ ```
+ When `excess_penalty_per_flow_hour` is set, the optimization can violate bus balance constraints by paying a penalty, helping identify which constraints cause infeasibility.
+
+2. **Use Gurobi for infeasibility analysis** - When using GurobiSolver and the model is infeasible, flixOpt automatically extracts and logs the Irreducible Inconsistent Subsystem (IIS):
+ ```python
+ # Gurobi provides detailed infeasibility analysis
+ optimization.solve(fx.solvers.GurobiSolver())
+ # If infeasible, check the model documentation file for IIS details
+ ```
+ The infeasible constraints are saved to the model documentation file in the results folder.
+
+3. Check balance constraints - can supply meet demand?
+4. Verify capacity limits are consistent
+5. Review storage state requirements
+6. Simplify model to isolate the issue
+
+See [Troubleshooting](../troubleshooting.md) for more details.
+
+### Unexpected Results
+
+If solutions don't match expectations:
+
+1. Verify input data (units, scales)
+2. Enable logging: `fx.CONFIG.exploring()`
+3. Visualize intermediate results
+4. Start with a simpler model
+5. Check constraint formulations
+
+## Next Steps
+
+- See [Examples](../../examples/03-Optimization Modes.md) for working code
+- Learn about [Mathematical Notation](../mathematical-notation/index.md)
+- Explore [Recipes](../recipes/index.md) for common patterns
diff --git a/docs/user-guide/results/index.md b/docs/user-guide/results/index.md
new file mode 100644
index 000000000..92656010d
--- /dev/null
+++ b/docs/user-guide/results/index.md
@@ -0,0 +1,18 @@
+# Analyzing Results
+
+!!! note "Under Development"
+ This section is being expanded with detailed tutorials.
+
+Learn how to work with optimization results:
+
+- Accessing solution data
+- Plotting flows and states
+- Exporting to various formats
+- Comparing scenarios and periods
+
+## Getting Started
+
+For now, see:
+
+- **[Examples](../../examples/index.md)** - Result analysis patterns in working code
+- **[API Reference](../../api-reference/results.md)** - Results class documentation
diff --git a/docs/user-guide/support.md b/docs/user-guide/support.md
new file mode 100644
index 000000000..5f26cdd24
--- /dev/null
+++ b/docs/user-guide/support.md
@@ -0,0 +1,23 @@
+# Support
+
+## Getting Help
+
+**[GitHub Issues](https://github.com/flixOpt/flixopt/issues)** — Report bugs or ask questions
+
+When opening an issue, include:
+
+- Minimal reproducible example
+- flixOpt version: `python -c "import flixopt; print(flixopt.__version__)"`
+- Python version and OS
+- Full error message
+
+## Resources
+
+- [FAQ](faq.md) — Common questions
+- [Troubleshooting](troubleshooting.md) — Common issues
+- [Examples](../examples/index.md) — Working code
+- [API Reference](../api-reference/index.md) — Technical docs
+
+## Contributing
+
+See our [Contributing Guide](../contribute.md) for how to help improve flixOpt.
diff --git a/docs/user-guide/troubleshooting.md b/docs/user-guide/troubleshooting.md
new file mode 100644
index 000000000..2c89be8dc
--- /dev/null
+++ b/docs/user-guide/troubleshooting.md
@@ -0,0 +1,61 @@
+# Troubleshooting
+
+## Infeasible Model
+
+**Problem:** Solver reports the model is infeasible.
+
+**Solutions:**
+
+1. Check that supply can meet demand at all timesteps
+2. Verify capacity limits are sufficient
+3. Review storage initial/final states
+
+## Unbounded Model
+
+**Problem:** Solver reports the model is unbounded.
+
+**Solutions:**
+
+1. Add upper bounds to all flows
+2. Ensure investment parameters have maximum sizes
+3. Verify effect coefficients have correct signs
+
+## Unexpected Results
+
+**Debugging Steps:**
+
+1. Enable logging:
+ ```python
+ from flixopt import CONFIG
+ CONFIG.exploring()
+ ```
+
+2. Start with a minimal model and add complexity incrementally
+
+3. Check units are consistent
+
+4. Visualize results to verify energy balances
+
+## Slow Solve Times
+
+**Solutions:**
+
+1. Use longer timesteps or aggregate time periods
+2. Use Gurobi instead of HiGHS for large models
+3. Set solver options:
+ ```python
+ solver = fx.solvers.GurobiSolver(
+ time_limit_seconds=3600,
+ mip_gap=0.01
+ )
+ ```
+
+## Getting Help
+
+If you're stuck:
+
+1. Search [GitHub Issues](https://github.com/flixOpt/flixopt/issues)
+2. Open a new issue with:
+ - Minimal reproducible example
+ - flixopt and Python version
+ - Full error message
diff --git a/flixopt/components.py b/flixopt/components.py
index 2d04586cc..0cfed39eb 100644
--- a/flixopt/components.py
+++ b/flixopt/components.py
@@ -41,8 +41,7 @@ class LinearConverter(Component):
behavior approximated through piecewise linear segments.
Mathematical Formulation:
- See the complete mathematical model in the documentation:
- [LinearConverter](../user-guide/mathematical-notation/elements/LinearConverter.md)
+ See
Args:
label: The label of the Element. Used to identify it in the FlowSystem.
@@ -260,18 +259,7 @@ class Storage(Component):
and investment-optimized storage systems with comprehensive techno-economic modeling.
Mathematical Formulation:
- See the complete mathematical model in the documentation:
- [Storage](../user-guide/mathematical-notation/elements/Storage.md)
-
- - Equation (1): Charge state bounds
- - Equation (3): Storage balance (charge state evolution)
-
- Variable Mapping:
- - ``capacity_in_flow_hours`` → C (storage capacity)
- - ``charge_state`` → c(t_i) (state of charge at time t_i)
- - ``relative_loss_per_hour`` → ċ_rel,loss (self-discharge rate)
- - ``eta_charge`` → η_in (charging efficiency)
- - ``eta_discharge`` → η_out (discharging efficiency)
+ See
Args:
label: Element identifier used in the FlowSystem.
@@ -779,6 +767,16 @@ def create_transmission_equation(self, name: str, in_flow: Flow, out_flow: Flow)
class LinearConverterModel(ComponentModel):
+ """Mathematical model implementation for LinearConverter components.
+
+ Creates optimization constraints for linear conversion relationships between
+ input and output flows, supporting both simple conversion factors and piecewise
+ non-linear approximations.
+
+ Mathematical Formulation:
+ See
+ """
+
element: LinearConverter
def __init__(self, model: FlowSystemModel, element: LinearConverter):
@@ -827,7 +825,14 @@ def _do_modeling(self):
class StorageModel(ComponentModel):
- """Submodel of Storage"""
+ """Mathematical model implementation for Storage components.
+
+ Creates optimization variables and constraints for charge state tracking,
+ storage balance equations, and optional investment sizing.
+
+ Mathematical Formulation:
+ See
+ """
element: Storage
diff --git a/flixopt/effects.py b/flixopt/effects.py
index 9df7c2ce5..5dd53258f 100644
--- a/flixopt/effects.py
+++ b/flixopt/effects.py
@@ -32,16 +32,15 @@
@register_class_for_io
class Effect(Element):
- """
- Represents system-wide impacts like costs, emissions, resource consumption, or other effects.
+ """Represents system-wide impacts like costs, emissions, or resource consumption.
- Effects capture the broader impacts of system operation and investment decisions beyond
- the primary energy/material flows. Each Effect accumulates contributions from Components,
- Flows, and other system elements. One Effect is typically chosen as the optimization
- objective, while others can serve as constraints or tracking metrics.
+ Effects quantify impacts aggregating contributions from Elements across the FlowSystem.
+ One Effect serves as the optimization objective, while others can be constrained or tracked.
+ Supports operational and investment contributions, cross-effect relationships (e.g., carbon
+ pricing), and flexible constraint formulation.
- Effects support comprehensive modeling including operational and investment contributions,
- cross-effect relationships (e.g., carbon pricing), and flexible constraint formulation.
+ Mathematical Formulation:
+ See
Args:
label: The label of the Element. Used to identify it in the FlowSystem.
@@ -302,6 +301,16 @@ def _plausibility_checks(self) -> None:
class EffectModel(ElementModel):
+ """Mathematical model implementation for Effects.
+
+ Creates optimization variables and constraints for effect aggregation,
+ including periodic and temporal tracking, cross-effect contributions,
+ and effect bounds.
+
+ Mathematical Formulation:
+ See
+ """
+
element: Effect # Type hint
def __init__(self, model: FlowSystemModel, element: Effect):
diff --git a/flixopt/elements.py b/flixopt/elements.py
index 9ca938b62..74ed7bde4 100644
--- a/flixopt/elements.py
+++ b/flixopt/elements.py
@@ -190,8 +190,7 @@ class Bus(Element):
or material flows between different Components.
Mathematical Formulation:
- See the complete mathematical model in the documentation:
- [Bus](../user-guide/mathematical-notation/elements/Bus.md)
+ See
Args:
label: The label of the Element. Used to identify it in the FlowSystem.
@@ -331,8 +330,7 @@ class Flow(Element):
- **StatusParameters**: Used for `status_parameters` when flow has discrete states
Mathematical Formulation:
- See the complete mathematical model in the documentation:
- [Flow](../user-guide/mathematical-notation/elements/Flow.md)
+ See
Args:
label: Unique flow identifier within its component.
@@ -595,6 +593,15 @@ def _format_invest_params(self, params: InvestParameters) -> str:
class FlowModel(ElementModel):
+ """Mathematical model implementation for Flow elements.
+
+ Creates optimization variables and constraints for flow rate bounds,
+ flow-hours tracking, and load factors.
+
+ Mathematical Formulation:
+ See
+ """
+
element: Flow # Type hint
def __init__(self, model: FlowSystemModel, element: Flow):
@@ -858,6 +865,15 @@ def previous_status(self) -> xr.DataArray | None:
class BusModel(ElementModel):
+ """Mathematical model implementation for Bus elements.
+
+ Creates optimization variables and constraints for nodal balance equations,
+ and optional excess/deficit variables with penalty costs.
+
+ Mathematical Formulation:
+ See
+ """
+
element: Bus # Type hint
def __init__(self, model: FlowSystemModel, element: Bus):
diff --git a/flixopt/features.py b/flixopt/features.py
index 653a2fb92..cd9e07151 100644
--- a/flixopt/features.py
+++ b/flixopt/features.py
@@ -24,16 +24,19 @@
class InvestmentModel(Submodel):
- """
- This feature model is used to model the investment of a variable.
- It applies the corresponding bounds to the variable and the active/inactive state of the variable.
+ """Mathematical model implementation for investment decisions.
+
+ Creates optimization variables and constraints for investment sizing decisions,
+ supporting both binary and continuous sizing with comprehensive effect modeling.
+
+ Mathematical Formulation:
+ See
Args:
model: The optimization model instance
label_of_element: The label of the parent (Element). Used to construct the full label of the model.
parameters: The parameters of the feature model.
label_of_model: The label of the model. This is needed to construct the full label of the model.
-
"""
parameters: InvestParameters
@@ -147,7 +150,14 @@ def invested(self) -> linopy.Variable | None:
class StatusModel(Submodel):
- """Status model for equipment with binary active/inactive states"""
+ """Mathematical model implementation for binary status.
+
+ Creates optimization variables and constraints for binary status modeling,
+ state transitions, duration tracking, and operational effects.
+
+ Mathematical Formulation:
+ See
+ """
def __init__(
self,
@@ -385,6 +395,15 @@ def _do_modeling(self):
class PiecewiseModel(Submodel):
+ """Mathematical model implementation for piecewise linear approximations.
+
+ Creates optimization variables and constraints for piecewise linear relationships,
+ including lambda variables, piece activation binaries, and coupling constraints.
+
+ Mathematical Formulation:
+ See
+ """
+
def __init__(
self,
model: FlowSystemModel,
diff --git a/flixopt/interface.py b/flixopt/interface.py
index 30db4876f..7995d5e78 100644
--- a/flixopt/interface.py
+++ b/flixopt/interface.py
@@ -82,8 +82,14 @@ def transform_data(self, name_prefix: str = '') -> None:
@register_class_for_io
class Piecewise(Interface):
- """
- Define a Piecewise, consisting of a list of Pieces.
+ """Define piecewise linear approximations for modeling non-linear relationships.
+
+ Enables modeling of non-linear relationships through piecewise linear segments
+ while maintaining problem linearity. Consists of a collection of Pieces that
+ define valid ranges for variables.
+
+ Mathematical Formulation:
+ See
Args:
pieces: list of Piece objects defining the linear segments. The arrangement
@@ -706,8 +712,7 @@ class InvestParameters(Interface):
- **Divestment Effects**: Penalties for not investing (demolition, opportunity costs)
Mathematical Formulation:
- See the complete mathematical model in the documentation:
- [InvestParameters](../user-guide/mathematical-notation/features/InvestParameters.md)
+ See
Args:
fixed_size: Creates binary decision at this exact size. None allows continuous sizing.
@@ -1028,8 +1033,7 @@ class StatusParameters(Interface):
- **Process Equipment**: Compressors, pumps with operational constraints
Mathematical Formulation:
- See the complete mathematical model in the documentation:
- [StatusParameters](../user-guide/mathematical-notation/features/StatusParameters.md)
+ See
Args:
effects_per_startup: Costs or impacts incurred for each transition from
diff --git a/mkdocs.yml b/mkdocs.yml
index 7e86d9720..8fb6765ae 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -7,37 +7,60 @@ site_description: Energy and Material Flow Optimization Framework
site_url: https://flixopt.github.io/flixopt/
repo_url: https://github.com/flixOpt/flixopt
repo_name: flixOpt/flixopt
+edit_uri: edit/main/docs/
nav:
- - Home: index.md
+ - Home:
+ - Home: index.md
+ - Getting Started:
+ - Installation: home/installation.md
+ - Quick Start: home/quick-start.md
+ - About:
+ - Users: home/users.md
+ - Citing: home/citing.md
+ - License: home/license.md
+
- User Guide:
- - Getting Started: getting-started.md
+ - Overview: user-guide/index.md
- Core Concepts: user-guide/core-concepts.md
- - Migration to v3.0.0: user-guide/migration-guide-v3.md
+ - Building Models: user-guide/building-models/index.md
+ - Running Optimizations: user-guide/optimization/index.md
+ - Analyzing Results: user-guide/results/index.md
- Mathematical Notation:
- Overview: user-guide/mathematical-notation/index.md
- - Dimensions: user-guide/mathematical-notation/dimensions.md
- - Elements:
- - Flow: user-guide/mathematical-notation/elements/Flow.md
- - Bus: user-guide/mathematical-notation/elements/Bus.md
- - Storage: user-guide/mathematical-notation/elements/Storage.md
- - LinearConverter: user-guide/mathematical-notation/elements/LinearConverter.md
- - Features:
- - InvestParameters: user-guide/mathematical-notation/features/InvestParameters.md
- - StatusParameters: user-guide/mathematical-notation/features/StatusParameters.md
- - Piecewise: user-guide/mathematical-notation/features/Piecewise.md
- - Effects, Penalty & Objective: user-guide/mathematical-notation/effects-penalty-objective.md
- - Modeling Patterns:
- - Overview: user-guide/mathematical-notation/modeling-patterns/index.md
- - Bounds and States: user-guide/mathematical-notation/modeling-patterns/bounds-and-states.md
- - Duration Tracking: user-guide/mathematical-notation/modeling-patterns/duration-tracking.md
- - State Transitions: user-guide/mathematical-notation/modeling-patterns/state-transitions.md
+ - Bus: user-guide/mathematical-notation/elements/Bus.md
+ - Flow: user-guide/mathematical-notation/elements/Flow.md
+ - LinearConverter: user-guide/mathematical-notation/elements/LinearConverter.md
+ - Storage: user-guide/mathematical-notation/elements/Storage.md
+ - Effects & Dimensions: user-guide/mathematical-notation/effects-and-dimensions.md
+ - Investment: user-guide/mathematical-notation/features/InvestParameters.md
+ - Status: user-guide/mathematical-notation/features/StatusParameters.md
+ - Piecewise: user-guide/mathematical-notation/features/Piecewise.md
- Recipes: user-guide/recipes/index.md
- - Roadmap: roadmap.md
- - Examples: examples/
- - Contribute: contribute.md
+ - Support:
+ - FAQ: user-guide/faq.md
+ - Troubleshooting: user-guide/troubleshooting.md
+ - Community: user-guide/support.md
+ - Migration & Updates:
+ - Migration Guide v3: user-guide/migration-guide-v3.md
+ - Release Notes: changelog.md
+ - Roadmap: roadmap.md
+
+ - Examples:
+ - Overview: examples/index.md
+ - Basic Examples:
+ - examples/00-Minimal Example.md
+ - examples/01-Basic Example.md
+ - Operational Optimization:
+ - examples/02-Complex Example.md
+ - examples/03-Optimization Modes.md
+ - Planning & Investment:
+ - examples/04-Scenarios.md
+ - examples/05-Two-stage-optimization.md
+
- API Reference: api-reference/
- - Release Notes: changelog/
+
+ - Contributing: contribute.md
theme:
name: material
@@ -128,7 +151,7 @@ markdown_extensions:
- toc:
permalink: true
permalink_title: Anchor link to this section
- toc_depth: 2
+ toc_depth: 3
title: On this page
# Code blocks
@@ -147,6 +170,9 @@ markdown_extensions:
- name: mermaid
class: mermaid
format: !!python/name:pymdownx.superfences.fence_code_format
+ - name: plotly
+ class: mkdocs-plotly
+ format: !!python/name:mkdocs_plotly_plugin.fences.fence_plotly
# Enhanced content
- pymdownx.details
@@ -185,6 +211,8 @@ plugins:
- search:
separator: '[\s\u200b\-_,:!=\[\]()"`/]+|\.(?!\d)|&[lg]t;|(?!\b)(?=[A-Z][a-z])'
+ - plotly
+
- table-reader
- include-markdown
@@ -310,6 +338,7 @@ extra_css:
extra_javascript:
- javascripts/mathjax.js
+ - javascripts/plotly-instant.js
- https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
- https://polyfill.io/v3/polyfill.min.js?features=es6
diff --git a/pyproject.toml b/pyproject.toml
index 258b0ab7f..206283767 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -104,6 +104,7 @@ docs = [
"mkdocs-gen-files==0.5.0",
"mkdocs-include-markdown-plugin==7.2.0",
"mkdocs-literate-nav==0.6.2",
+ "mkdocs-plotly-plugin==0.1.3",
"markdown-include==0.8.1",
"pymdown-extensions==10.16.1",
"pygments==2.19.2",
diff --git a/scripts/extract_changelog.py b/scripts/extract_changelog.py
deleted file mode 100644
index 44790fec6..000000000
--- a/scripts/extract_changelog.py
+++ /dev/null
@@ -1,151 +0,0 @@
-#!/usr/bin/env python3
-"""
-Extract individual releases from CHANGELOG.md to docs/changelog/
-Simple script to create one file per release.
-"""
-
-import re
-from pathlib import Path
-
-from packaging.version import InvalidVersion, Version
-from packaging.version import parse as parse_version
-
-
-def extract_releases():
- """Extract releases from CHANGELOG.md and save to individual files."""
-
- changelog_path = Path('CHANGELOG.md')
- output_dir = Path('docs/changelog')
-
- if not changelog_path.exists():
- print('❌ CHANGELOG.md not found')
- return
-
- # Create output directory
- output_dir.mkdir(parents=True, exist_ok=True)
-
- # Read changelog
- with open(changelog_path, encoding='utf-8') as f:
- content = f.read()
-
- # Remove template section (HTML comments)
- content = re.sub(r'', '', content, flags=re.DOTALL)
-
- # Split by release headers
- sections = re.split(r'^## \[', content, flags=re.MULTILINE)
-
- releases = []
- for section in sections[1:]: # Skip first empty section
- # Extract version and date from start of section
- match = re.match(r'([^\]]+)\] - ([^\n]+)\n(.*)', section, re.DOTALL)
- if match:
- version, date, release_content = match.groups()
- releases.append((version, date.strip(), release_content.strip()))
-
- print(f'🔍 Found {len(releases)} releases')
-
- # Sort releases by version (oldest first) to keep existing file prefixes stable.
- def version_key(release):
- try:
- return parse_version(release[0])
- except InvalidVersion:
- return parse_version('0.0.0') # fallback for invalid versions
-
- releases.sort(key=version_key, reverse=False)
-
- # Show what we captured for debugging
- if releases:
- print(f'🔧 First release content length: {len(releases[0][2])}')
-
- for i, (version_str, date, release_content) in enumerate(releases):
- # Clean up version for filename with numeric prefix (newest first)
- index = 99999 - i # Newest first, while keeping the same file names for old releases
- prefix = f'{index:05d}' # Zero-padded 5-digit number
- filename = f'{prefix}-v{version_str.replace(" ", "-")}.md'
- filepath = output_dir / filename
-
- # Clean up content - remove trailing --- separators and emojis from headers
- cleaned_content = re.sub(r'\s*---\s*$', '', release_content.strip())
-
- # Generate navigation links
- nav_links = []
-
- # Previous version (older release)
- if i > 0:
- prev_index = 99999 - (i - 1)
- prev_version = releases[i - 1][0]
- prev_filename = f'{prev_index:05d}-v{prev_version.replace(" ", "-")}.md'
- nav_links.append(f'← [Previous: {prev_version}]({prev_filename})')
-
- # Next version (newer release)
- if i < len(releases) - 1:
- next_index = 99999 - (i + 1)
- next_version = releases[i + 1][0]
- next_filename = f'{next_index:05d}-v{next_version.replace(" ", "-")}.md'
- nav_links.append(f'[Next: {next_version}]({next_filename}) →')
-
- # Always add link back to index
- nav_links.append('[📋 All Releases](index.md)')
- # Add GitHub tag link only for valid PEP 440 versions (skip e.g. "Unreleased")
- ver_obj = parse_version(version_str)
- if isinstance(ver_obj, Version):
- nav_links.append(f'[🏷️ GitHub Release](https://github.com/flixOpt/flixopt/releases/tag/v{version_str})')
- # Create content with navigation
- content_lines = [
- f'# {version_str} - {date.strip()}',
- '',
- ' | '.join(nav_links),
- '',
- '---',
- '',
- cleaned_content,
- '',
- '---',
- '',
- ' | '.join(nav_links),
- ]
-
- # Write file
- with open(filepath, 'w', encoding='utf-8') as f:
- f.write('\n'.join(content_lines))
-
- print(f'✅ Created {filename}')
-
- print(f'🎉 Extracted {len(releases)} releases to docs/changelog/')
-
-
-def extract_index():
- changelog_path = Path('CHANGELOG.md')
- output_dir = Path('docs/changelog')
- index_path = output_dir / 'index.md'
-
- if not changelog_path.exists():
- print('❌ CHANGELOG.md not found')
- return
-
- # Create output directory
- output_dir.mkdir(parents=True, exist_ok=True)
-
- # Read changelog
- with open(changelog_path, encoding='utf-8') as f:
- content = f.read()
-
- intro_match = re.search(r'# Changelog\s+([\s\S]*?)(?= minimizing costs
@@ -109,13 +114,14 @@
# Plotting through statistics accessor - returns PlotResult with .data and .figure
flow_system.statistics.plot.balance('Fernwärme')
flow_system.statistics.plot.balance('Storage')
- flow_system.statistics.plot.heatmap('CHP(Q_th)|flow_rate')
- flow_system.statistics.plot.heatmap('Storage|charge_state')
+ flow_system.statistics.plot.heatmap('CHP(Q_th)')
+ flow_system.statistics.plot.heatmap('Storage')
+ flow_system.statistics.plot.heatmap('Storage')
# Access data as xarray Datasets
print(flow_system.statistics.flow_rates)
print(flow_system.statistics.charge_states)
# Duration curve and effects analysis
- flow_system.statistics.plot.duration_curve('Boiler(Q_th)|flow_rate')
+ flow_system.statistics.plot.duration_curve('Boiler(Q_th)')
print(flow_system.statistics.temporal_effects)
diff --git a/examples/02_Complex/complex_example.py b/examples/02_Complex/complex_example.py
index f1b524a2b..3f38ff954 100644
--- a/examples/02_Complex/complex_example.py
+++ b/examples/02_Complex/complex_example.py
@@ -32,10 +32,11 @@
# --- Define Energy Buses ---
# Represent node balances (inputs=outputs) for the different energy carriers (electricity, heat, gas) in the system
+ # Carriers provide automatic color assignment in plots (yellow for electricity, red for heat, blue for gas)
flow_system.add_elements(
- fx.Bus('Strom', imbalance_penalty_per_flow_hour=imbalance_penalty),
- fx.Bus('Fernwärme', imbalance_penalty_per_flow_hour=imbalance_penalty),
- fx.Bus('Gas', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Strom', carrier='electricity', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Fernwärme', carrier='heat', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Gas', carrier='gas', imbalance_penalty_per_flow_hour=imbalance_penalty),
)
# --- Define Effects ---
@@ -200,7 +201,7 @@
flow_system.to_netcdf('results/complex_example.nc')
# Plot results using the statistics accessor
- flow_system.statistics.plot.heatmap('BHKW2(Q_th)|flow_rate')
+ flow_system.statistics.plot.heatmap('BHKW2(Q_th)') # Flow label - auto-resolves to flow_rate
flow_system.statistics.plot.balance('BHKW2')
- flow_system.statistics.plot.heatmap('Speicher|charge_state')
+ flow_system.statistics.plot.heatmap('Speicher') # Storage label - auto-resolves to charge_state
flow_system.statistics.plot.balance('Fernwärme')
diff --git a/examples/03_Optimization_modes/example_optimization_modes.py b/examples/03_Optimization_modes/example_optimization_modes.py
index 3dcd8bd1c..1f9968357 100644
--- a/examples/03_Optimization_modes/example_optimization_modes.py
+++ b/examples/03_Optimization_modes/example_optimization_modes.py
@@ -69,10 +69,10 @@ def get_solutions(optimizations: list, variable: str) -> xr.Dataset:
flow_system = fx.FlowSystem(timesteps)
flow_system.add_elements(
- fx.Bus('Strom', imbalance_penalty_per_flow_hour=imbalance_penalty),
- fx.Bus('Fernwärme', imbalance_penalty_per_flow_hour=imbalance_penalty),
- fx.Bus('Gas', imbalance_penalty_per_flow_hour=imbalance_penalty),
- fx.Bus('Kohle', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Strom', carrier='electricity', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Fernwärme', carrier='heat', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Gas', carrier='gas', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Kohle', carrier='fuel', imbalance_penalty_per_flow_hour=imbalance_penalty),
)
# Effects
diff --git a/examples/04_Scenarios/scenario_example.py b/examples/04_Scenarios/scenario_example.py
index e3c6f5fd3..820336e93 100644
--- a/examples/04_Scenarios/scenario_example.py
+++ b/examples/04_Scenarios/scenario_example.py
@@ -89,7 +89,12 @@
# --- Define Energy Buses ---
# These represent nodes, where the used medias are balanced (electricity, heat, and gas)
- flow_system.add_elements(fx.Bus(label='Strom'), fx.Bus(label='Fernwärme'), fx.Bus(label='Gas'))
+ # Carriers provide automatic color assignment in plots (yellow for electricity, red for heat, blue for gas)
+ flow_system.add_elements(
+ fx.Bus(label='Strom', carrier='electricity'),
+ fx.Bus(label='Fernwärme', carrier='heat'),
+ fx.Bus(label='Gas', carrier='gas'),
+ )
# --- Define Effects (Objective and CO2 Emissions) ---
# Cost effect: used as the optimization objective --> minimizing costs
@@ -199,10 +204,10 @@
# --- Analyze Results ---
# Plotting through statistics accessor - returns PlotResult with .data and .figure
- flow_system.statistics.plot.heatmap('CHP(Q_th)|flow_rate')
+ flow_system.statistics.plot.heatmap('CHP(Q_th)') # Flow label - auto-resolves to flow_rate
flow_system.statistics.plot.balance('Fernwärme')
flow_system.statistics.plot.balance('Storage')
- flow_system.statistics.plot.heatmap('Storage|charge_state')
+ flow_system.statistics.plot.heatmap('Storage') # Storage label - auto-resolves to charge_state
# Access data as xarray Datasets
print(flow_system.statistics.flow_rates)
diff --git a/examples/05_Two-stage-optimization/two_stage_optimization.py b/examples/05_Two-stage-optimization/two_stage_optimization.py
index 8dea1713b..bf7f13a39 100644
--- a/examples/05_Two-stage-optimization/two_stage_optimization.py
+++ b/examples/05_Two-stage-optimization/two_stage_optimization.py
@@ -37,11 +37,12 @@
gas_price = filtered_data['Gaspr.€/MWh'].to_numpy()
flow_system = fx.FlowSystem(timesteps)
+ # Carriers provide automatic color assignment in plots
flow_system.add_elements(
- fx.Bus('Strom'),
- fx.Bus('Fernwärme'),
- fx.Bus('Gas'),
- fx.Bus('Kohle'),
+ fx.Bus('Strom', carrier='electricity'),
+ fx.Bus('Fernwärme', carrier='heat'),
+ fx.Bus('Gas', carrier='gas'),
+ fx.Bus('Kohle', carrier='fuel'),
fx.Effect('costs', '€', 'Kosten', is_standard=True, is_objective=True),
fx.Effect('CO2', 'kg', 'CO2_e-Emissionen'),
fx.Effect('PE', 'kWh_PE', 'Primärenergie'),
diff --git a/flixopt/__init__.py b/flixopt/__init__.py
index 8874811b3..3c4edf7e8 100644
--- a/flixopt/__init__.py
+++ b/flixopt/__init__.py
@@ -14,6 +14,7 @@
# Import commonly used classes and functions
from . import linear_converters, plotting, results, solvers
+from .carrier import Carrier, CarrierContainer
from .clustering import ClusteringParameters
from .components import (
LinearConverter,
@@ -34,6 +35,8 @@
__all__ = [
'TimeSeriesData',
'CONFIG',
+ 'Carrier',
+ 'CarrierContainer',
'Flow',
'Bus',
'Effect',
diff --git a/flixopt/carrier.py b/flixopt/carrier.py
new file mode 100644
index 000000000..8a663eca9
--- /dev/null
+++ b/flixopt/carrier.py
@@ -0,0 +1,159 @@
+"""Carrier class for energy/material type definitions.
+
+Carriers represent types of energy or materials that flow through buses,
+such as electricity, heat, gas, or water. They provide consistent styling
+and metadata across visualizations.
+"""
+
+from __future__ import annotations
+
+from .structure import ContainerMixin, Interface, register_class_for_io
+
+
+@register_class_for_io
+class Carrier(Interface):
+ """Definition of an energy or material carrier type.
+
+ Carriers represent the type of energy or material flowing through a Bus.
+ They provide consistent color, unit, and description across all visualizations
+ and can be shared between multiple buses of the same type.
+
+ Inherits from Interface to provide serialization capabilities.
+
+ Args:
+ name: Identifier for the carrier (e.g., 'electricity', 'heat', 'gas').
+ color: Hex color string for visualizations (e.g., '#FFD700').
+ unit: Unit string for display (e.g., 'kW', 'kW_th', 'm³/h').
+ description: Optional human-readable description.
+
+ Examples:
+ Creating custom carriers:
+
+ ```python
+ import flixopt as fx
+
+ # Define custom carriers
+ electricity = fx.Carrier('electricity', '#FFD700', 'kW', 'Electrical power')
+ district_heat = fx.Carrier('district_heat', '#FF6B6B', 'kW_th', 'District heating')
+ hydrogen = fx.Carrier('hydrogen', '#00CED1', 'kg/h', 'Hydrogen fuel')
+
+ # Register with FlowSystem
+ flow_system.add_carrier(electricity)
+ flow_system.add_carrier(district_heat)
+
+ # Use with buses (just reference by name)
+ elec_bus = fx.Bus('MainGrid', carrier='electricity')
+ heat_bus = fx.Bus('HeatingNetwork', carrier='district_heat')
+ ```
+
+ Using predefined carriers from CONFIG:
+
+ ```python
+ # Access built-in carriers
+ elec = fx.CONFIG.Carriers.electricity
+ heat = fx.CONFIG.Carriers.heat
+
+ # Use directly
+ bus = fx.Bus('Grid', carrier='electricity')
+ ```
+
+ Adding custom carriers to CONFIG:
+
+ ```python
+ # Add a new carrier globally
+ fx.CONFIG.Carriers.add(fx.Carrier('biogas', '#228B22', 'kW', 'Biogas'))
+
+ # Now available as
+ fx.CONFIG.Carriers.biogas
+ ```
+
+ Note:
+ Carriers are compared by name for equality, allowing flexible usage
+ patterns where the same carrier type can be referenced by name string
+ or Carrier object interchangeably.
+ """
+
+ def __init__(
+ self,
+ name: str,
+ color: str = '',
+ unit: str = '',
+ description: str = '',
+ ) -> None:
+ """Initialize a Carrier.
+
+ Args:
+ name: Identifier for the carrier (normalized to lowercase).
+ color: Hex color string for visualizations.
+ unit: Unit string for display.
+ description: Optional human-readable description.
+ """
+ self.name = name.lower()
+ self.color = color
+ self.unit = unit
+ self.description = description
+
+ def transform_data(self, name_prefix: str = '') -> None:
+ """Transform data to match FlowSystem dimensions.
+
+ Carriers don't have time-series data, so this is a no-op.
+
+ Args:
+ name_prefix: Ignored for Carrier.
+ """
+ pass # Carriers have no data to transform
+
+ @property
+ def label(self) -> str:
+ """Label for container keying (alias for name)."""
+ return self.name
+
+ def __hash__(self):
+ return hash(self.name)
+
+ def __eq__(self, other):
+ if isinstance(other, Carrier):
+ return self.name == other.name
+ if isinstance(other, str):
+ return self.name == other.lower()
+ return False
+
+ def __repr__(self):
+ return f"Carrier('{self.name}', color='{self.color}', unit='{self.unit}')"
+
+ def __str__(self):
+ return self.name
+
+
+class CarrierContainer(ContainerMixin['Carrier']):
+ """Container for Carrier objects.
+
+ Uses carrier.name for keying. Provides dict-like access to carriers
+ registered with a FlowSystem.
+
+ Examples:
+ ```python
+ # Access via FlowSystem
+ carriers = flow_system.carriers
+
+ # Dict-like access
+ elec = carriers['electricity']
+ 'heat' in carriers # True/False
+
+ # Iteration
+ for name in carriers:
+ print(name)
+ ```
+ """
+
+ def __init__(self, carriers: list[Carrier] | dict[str, Carrier] | None = None):
+ """Initialize a CarrierContainer.
+
+ Args:
+ carriers: Initial carriers to add.
+ """
+ super().__init__(elements=carriers, element_type_name='carriers')
+
+ def _get_label(self, carrier: Carrier) -> str:
+ """Extract name from Carrier for keying."""
+ return carrier.name
diff --git a/flixopt/config.py b/flixopt/config.py
index 043142cbe..4d4571dcd 100644
--- a/flixopt/config.py
+++ b/flixopt/config.py
@@ -575,6 +575,36 @@ class Plotting:
default_sequential_colorscale: str = _DEFAULTS['plotting']['default_sequential_colorscale']
default_qualitative_colorscale: str = _DEFAULTS['plotting']['default_qualitative_colorscale']
+ class Carriers:
+ """Default carrier definitions for common energy types.
+
+ Provides convenient defaults for carriers. Colors are from D3/Plotly palettes.
+
+ Predefined: electricity, heat, gas, hydrogen, fuel, biomass
+
+ Examples:
+ ```python
+ import flixopt as fx
+
+ # Access predefined carriers
+ fx.CONFIG.Carriers.electricity # Carrier with color '#FECB52'
+ fx.CONFIG.Carriers.heat.color # '#D62728'
+
+ # Use with buses
+ bus = fx.Bus('Grid', carrier='electricity')
+ ```
+ """
+
+ from .carrier import Carrier
+
+ # Default carriers - colors from D3/Plotly palettes
+ electricity: Carrier = Carrier('electricity', '#FECB52') # Yellow
+ heat: Carrier = Carrier('heat', '#D62728') # Red
+ gas: Carrier = Carrier('gas', '#1F77B4') # Blue
+ hydrogen: Carrier = Carrier('hydrogen', '#9467BD') # Purple
+ fuel: Carrier = Carrier('fuel', '#8C564B') # Brown
+ biomass: Carrier = Carrier('biomass', '#2CA02C') # Green
+
config_name: str = _DEFAULTS['config_name']
@classmethod
@@ -601,6 +631,16 @@ def reset(cls) -> None:
for key, value in _DEFAULTS['plotting'].items():
setattr(cls.Plotting, key, value)
+ # Reset Carriers to defaults
+ from .carrier import Carrier
+
+ cls.Carriers.electricity = Carrier('electricity', '#FECB52')
+ cls.Carriers.heat = Carrier('heat', '#D62728')
+ cls.Carriers.gas = Carrier('gas', '#1F77B4')
+ cls.Carriers.hydrogen = Carrier('hydrogen', '#9467BD')
+ cls.Carriers.fuel = Carrier('fuel', '#8C564B')
+ cls.Carriers.biomass = Carrier('biomass', '#2CA02C')
+
cls.config_name = _DEFAULTS['config_name']
# Reset logging to default (silent)
diff --git a/flixopt/elements.py b/flixopt/elements.py
index 74ed7bde4..d2ebf7ac0 100644
--- a/flixopt/elements.py
+++ b/flixopt/elements.py
@@ -93,8 +93,9 @@ def __init__(
status_parameters: StatusParameters | None = None,
prevent_simultaneous_flows: list[Flow] | None = None,
meta_data: dict | None = None,
+ color: str | None = None,
):
- super().__init__(label, meta_data=meta_data)
+ super().__init__(label, meta_data=meta_data, color=color)
self.inputs: list[Flow] = inputs or []
self.outputs: list[Flow] = outputs or []
self.status_parameters = status_parameters
@@ -194,6 +195,9 @@ class Bus(Element):
Args:
label: The label of the Element. Used to identify it in the FlowSystem.
+ carrier: Name of the energy/material carrier type (e.g., 'electricity', 'heat', 'gas').
+ Carriers are registered via ``flow_system.add_carrier()`` or available as
+ predefined defaults in CONFIG.Carriers. Used for automatic color assignment in plots.
imbalance_penalty_per_flow_hour: Penalty costs for bus balance violations.
When None (default), no imbalance is allowed (hard constraint). When set to a
value > 0, allows bus imbalances at penalty cost.
@@ -201,30 +205,30 @@ class Bus(Element):
in results. Only use Python native types.
Examples:
- Electrical bus with strict balance:
+ Using predefined carrier names:
```python
- electricity_bus = Bus(
- label='main_electrical_bus',
- imbalance_penalty_per_flow_hour=None, # No imbalance allowed
- )
+ electricity_bus = Bus(label='main_grid', carrier='electricity')
+ heat_bus = Bus(label='district_heating', carrier='heat')
```
- Heat network with penalty for imbalances:
+ Registering custom carriers on FlowSystem:
```python
- heat_network = Bus(
- label='district_heating_network',
- imbalance_penalty_per_flow_hour=1000, # €1000/MWh penalty for imbalance
- )
+ import flixopt as fx
+
+ fs = fx.FlowSystem(timesteps)
+ fs.add_carrier(fx.Carrier('biogas', '#228B22', 'kW'))
+ biogas_bus = fx.Bus(label='biogas_network', carrier='biogas')
```
- Material flow with time-varying penalties:
+ Heat network with penalty for imbalances:
```python
- material_hub = Bus(
- label='material_processing_hub',
- imbalance_penalty_per_flow_hour=waste_disposal_costs, # Time series
+ heat_bus = Bus(
+ label='district_heating',
+ carrier='heat',
+ imbalance_penalty_per_flow_hour=1000,
)
```
@@ -245,6 +249,7 @@ class Bus(Element):
def __init__(
self,
label: str,
+ carrier: str | None = None,
imbalance_penalty_per_flow_hour: Numeric_TPS | None = None,
meta_data: dict | None = None,
**kwargs,
@@ -254,6 +259,7 @@ def __init__(
kwargs, 'excess_penalty_per_flow_hour', 'imbalance_penalty_per_flow_hour', imbalance_penalty_per_flow_hour
)
self._validate_kwargs(kwargs)
+ self.carrier = carrier.lower() if carrier else None # Store as lowercase string
self.imbalance_penalty_per_flow_hour = imbalance_penalty_per_flow_hour
self.inputs: list[Flow] = []
self.outputs: list[Flow] = []
diff --git a/flixopt/flow_system.py b/flixopt/flow_system.py
index 5fda024f7..ee1a10261 100644
--- a/flixopt/flow_system.py
+++ b/flixopt/flow_system.py
@@ -4,6 +4,7 @@
from __future__ import annotations
+import json
import logging
import pathlib
import warnings
@@ -39,6 +40,8 @@
from .solvers import _Solver
from .types import Effect_TPS, Numeric_S, Numeric_TPS, NumericOrBool
+from .carrier import Carrier, CarrierContainer
+
logger = logging.getLogger('flixopt')
@@ -217,6 +220,9 @@ def __init__(
# Statistics accessor cache - lazily initialized, invalidated on new solution
self._statistics: StatisticsAccessor | None = None
+ # Carrier container - local carriers override CONFIG.Carriers
+ self._carriers: CarrierContainer = CarrierContainer()
+
# Use properties to validate and store scenario dimension settings
self.scenario_independent_sizes = scenario_independent_sizes
self.scenario_independent_flow_rates = scenario_independent_flow_rates
@@ -578,6 +584,14 @@ def to_dataset(self) -> xr.Dataset:
else:
ds.attrs['has_solution'] = False
+ # Include carriers if any are registered
+ if self._carriers:
+ carriers_structure = {}
+ for name, carrier in self._carriers.items():
+ carrier_ref, _ = carrier._create_reference_structure()
+ carriers_structure[name] = carrier_ref
+ ds.attrs['carriers'] = json.dumps(carriers_structure)
+
return ds
@classmethod
@@ -661,6 +675,13 @@ def from_dataset(cls, ds: xr.Dataset) -> FlowSystem:
solution_ds = solution_ds.rename({'solution_time': 'time'})
flow_system.solution = solution_ds
+ # Restore carriers if present
+ if 'carriers' in reference_structure:
+ carriers_structure = json.loads(reference_structure['carriers'])
+ for carrier_data in carriers_structure.values():
+ carrier = cls._resolve_reference_structure(carrier_data, {})
+ flow_system._carriers.add(carrier)
+
return flow_system
def to_netcdf(self, path: str | pathlib.Path, compression: int = 0, overwrite: bool = True):
@@ -813,6 +834,8 @@ def connect_and_transform(self):
return
self._connect_network()
+ self._register_missing_carriers()
+ self._assign_element_colors()
for element in chain(self.components.values(), self.effects.values(), self.buses.values()):
element.transform_data()
@@ -821,6 +844,40 @@ def connect_and_transform(self):
self._connected_and_transformed = True
+ def _register_missing_carriers(self) -> None:
+ """Auto-register carriers from CONFIG for buses that reference unregistered carriers."""
+ for bus in self.buses.values():
+ if bus.carrier and bus.carrier not in self._carriers:
+ # Try to get from CONFIG defaults
+ default_carrier = getattr(CONFIG.Carriers, bus.carrier, None)
+ if default_carrier is not None:
+ self._carriers[bus.carrier] = default_carrier
+ logger.debug(f"Auto-registered carrier '{bus.carrier}' from CONFIG")
+
+ def _assign_element_colors(self) -> None:
+ """Auto-assign colors to elements that don't have explicit colors set.
+
+ Components and buses without explicit colors are assigned colors from the
+ default qualitative colorscale. This ensures zero-config color support
+ while still allowing users to override with explicit colors.
+ """
+ from .color_processing import process_colors
+
+ # Collect elements without colors (components only - buses use carrier colors)
+ elements_without_colors = [comp.label for comp in self.components.values() if comp.color is None]
+
+ if not elements_without_colors:
+ return
+
+ # Generate colors from the default colorscale
+ colorscale = CONFIG.Plotting.default_qualitative_colorscale
+ color_mapping = process_colors(colorscale, elements_without_colors)
+
+ # Assign colors to elements
+ for label, color in color_mapping.items():
+ self.components[label].color = color
+ logger.debug(f"Auto-assigned color '{color}' to component '{label}'")
+
def add_elements(self, *elements: Element) -> None:
"""
Add Components(Storages, Boilers, Heatpumps, ...), Buses or Effects to the FlowSystem
@@ -859,6 +916,84 @@ def add_elements(self, *elements: Element) -> None:
element_type = type(new_element).__name__
logger.info(f'Registered new {element_type}: {new_element.label_full}')
+ def add_carriers(self, *carriers: Carrier) -> None:
+ """Register a custom carrier for this FlowSystem.
+
+ Custom carriers registered on the FlowSystem take precedence over
+ CONFIG.Carriers defaults when resolving colors and units for buses.
+
+ Args:
+ carrier: A Carrier object defining the carrier properties.
+
+ Examples:
+ ```python
+ import flixopt as fx
+
+ fs = fx.FlowSystem(timesteps)
+
+ # Define and register custom carriers
+ biogas = fx.Carrier('biogas', '#228B22', 'kW', 'Biogas fuel')
+ fs.add_carrier(biogas)
+
+ # Now buses can reference this carrier by name
+ bus = fx.Bus('BioGasNetwork', carrier='biogas')
+ fs.add_elements(bus)
+
+ # The carrier color will be used in plots automatically
+ ```
+ """
+ if self.connected_and_transformed:
+ warnings.warn(
+ 'You are adding a carrier to an already connected FlowSystem. This is not recommended (But it works).',
+ stacklevel=2,
+ )
+ self._connected_and_transformed = False
+
+ for carrier in list(carriers):
+ if not isinstance(carrier, Carrier):
+ raise TypeError(f'Expected Carrier object, got {type(carrier)}')
+ self._carriers.add(carrier)
+ logger.debug(f'Adding carrier {carrier} to FlowSystem')
+
+ def get_carrier(self, label: str) -> Carrier | None:
+ """Get the carrier for a bus or flow.
+
+ Args:
+ label: Bus label (e.g., 'Fernwärme') or flow label (e.g., 'Boiler(Q_th)').
+
+ Returns:
+ Carrier or None if not found.
+
+ Note:
+ To access a carrier directly by name, use ``flow_system.carriers['electricity']``.
+
+ Raises:
+ RuntimeError: If FlowSystem is not connected_and_transformed.
+ """
+ if not self.connected_and_transformed:
+ raise RuntimeError(
+ 'FlowSystem is not connected_and_transformed. Call FlowSystem.connect_and_transform() first.'
+ )
+
+ # Try as bus label
+ bus = self.buses.get(label)
+ if bus and bus.carrier:
+ return self._carriers.get(bus.carrier.lower())
+
+ # Try as flow label
+ flow = self.flows.get(label)
+ if flow and flow.bus:
+ bus = self.buses.get(flow.bus)
+ if bus and bus.carrier:
+ return self._carriers.get(bus.carrier.lower())
+
+ return None
+
+ @property
+ def carriers(self) -> CarrierContainer:
+ """Carriers registered on this FlowSystem."""
+ return self._carriers
+
def create_model(self, normalize_weights: bool = True) -> FlowSystemModel:
"""
Create a linopy model from the FlowSystem.
diff --git a/flixopt/statistics_accessor.py b/flixopt/statistics_accessor.py
index 9f6bb01be..2927c42a6 100644
--- a/flixopt/statistics_accessor.py
+++ b/flixopt/statistics_accessor.py
@@ -738,6 +738,77 @@ def __init__(self, statistics: StatisticsAccessor) -> None:
self._stats = statistics
self._fs = statistics._fs
+ def _get_color_map_for_balance(self, node: str, flow_labels: list[str]) -> dict[str, str]:
+ """Build color map for balance plot.
+
+ - Bus balance: colors from component.color
+ - Component balance: colors from flow's carrier
+
+ Raises:
+ RuntimeError: If FlowSystem is not connected_and_transformed.
+ """
+ if not self._fs.connected_and_transformed:
+ raise RuntimeError(
+ 'FlowSystem is not connected_and_transformed. Call FlowSystem.connect_and_transform() first.'
+ )
+
+ is_bus = node in self._fs.buses
+ color_map = {}
+ uncolored = []
+
+ for label in flow_labels:
+ if is_bus:
+ color = self._fs.components[self._fs.flows[label].component].color
+ else:
+ carrier = self._fs.get_carrier(label) # get_carrier accepts flow labels
+ color = carrier.color if carrier else None
+
+ if color:
+ color_map[label] = color
+ else:
+ uncolored.append(label)
+
+ if uncolored:
+ color_map.update(process_colors(CONFIG.Plotting.default_qualitative_colorscale, uncolored))
+
+ return color_map
+
+ def _resolve_variable_names(self, variables: list[str], solution: xr.Dataset) -> list[str]:
+ """Resolve flow labels to variable names with fallback.
+
+ For each variable:
+ 1. First check if it exists in the dataset as-is
+ 2. If not found and doesn't contain '|', try adding '|flow_rate' suffix
+ 3. If still not found, try '|charge_state' suffix (for storages)
+
+ Args:
+ variables: List of flow labels or variable names.
+ solution: The solution dataset to check variable existence.
+
+ Returns:
+ List of resolved variable names.
+ """
+ resolved = []
+ for var in variables:
+ if var in solution:
+ # Variable exists as-is, use it directly
+ resolved.append(var)
+ elif '|' not in var:
+ # Not found and no '|', try common suffixes
+ flow_rate_var = f'{var}|flow_rate'
+ charge_state_var = f'{var}|charge_state'
+ if flow_rate_var in solution:
+ resolved.append(flow_rate_var)
+ elif charge_state_var in solution:
+ resolved.append(charge_state_var)
+ else:
+ # Let it fail with the original name for clear error message
+ resolved.append(var)
+ else:
+ # Contains '|' but not in solution - let it fail with original name
+ resolved.append(var)
+ return resolved
+
def balance(
self,
node: str,
@@ -801,6 +872,10 @@ def balance(
ds = _apply_selection(ds, select)
actual_facet_col, actual_facet_row = _resolve_facets(ds, facet_col, facet_row)
+ # Build color map from Element.color attributes if no colors specified
+ if colors is None:
+ colors = self._get_color_map_for_balance(node, list(ds.data_vars))
+
fig = _create_stacked_bar(
ds,
colors=colors,
@@ -836,7 +911,9 @@ def heatmap(
reshaping is skipped and variables are shown on the y-axis with time on x-axis.
Args:
- variables: Variable name(s) from solution.
+ variables: Flow label(s) or variable name(s). Flow labels like 'Boiler(Q_th)'
+ are automatically resolved to 'Boiler(Q_th)|flow_rate'. Full variable
+ names like 'Storage|charge_state' are used as-is.
select: xarray-style selection, e.g. {'scenario': 'Base Case'}.
reshape: Time reshape frequencies as (outer, inner), e.g. ('D', 'h') for
days × hours. Set to None to disable reshaping.
@@ -856,7 +933,10 @@ def heatmap(
if isinstance(variables, str):
variables = [variables]
- ds = solution[variables]
+ # Resolve flow labels to variable names
+ resolved_variables = self._resolve_variable_names(variables, solution)
+
+ ds = solution[resolved_variables]
ds = _apply_selection(ds, select)
# Stack variables into single DataArray
@@ -972,8 +1052,8 @@ def flows(
for flow in self._fs.flows.values():
# Get bus label (could be string or Bus object)
- bus_label = flow.bus if isinstance(flow.bus, str) else flow.bus.label
- comp_label = flow.component.label if hasattr(flow.component, 'label') else str(flow.component)
+ bus_label = flow.bus
+ comp_label = flow.component.label_full
# start/end filtering based on flow direction
if flow.is_input_in_component:
@@ -1075,8 +1155,8 @@ def sankey(
# Determine source/target based on flow direction
# is_input_in_component: True means bus -> component, False means component -> bus
- bus_label = flow.bus if isinstance(flow.bus, str) else flow.bus.label
- comp_label = flow.component.label if hasattr(flow.component, 'label') else str(flow.component)
+ bus_label = flow.bus
+ comp_label = flow.component.label_full
if flow.is_input_in_component:
source = bus_label
@@ -1203,8 +1283,10 @@ def duration_curve(
"""Plot load duration curves (sorted time series).
Args:
- variables: Flow label(s) to plot (e.g., 'Boiler(Q_th)').
- Uses flow_rates from statistics.
+ variables: Flow label(s) or variable name(s). Flow labels like 'Boiler(Q_th)'
+ are looked up in flow_rates. Full variable names like 'Boiler(Q_th)|flow_rate'
+ are stripped to their flow label. Other variables (e.g., 'Storage|charge_state')
+ are looked up in the solution directly.
select: xarray-style selection.
normalize: If True, normalize x-axis to 0-100%.
colors: Color specification (colorscale name, color list, or label-to-color dict).
@@ -1215,13 +1297,36 @@ def duration_curve(
Returns:
PlotResult with sorted duration curve data.
"""
- self._stats._require_solution()
+ solution = self._stats._require_solution()
if isinstance(variables, str):
variables = [variables]
- # Use flow_rates from statistics (already has clean labels without |flow_rate suffix)
- ds = self._stats.flow_rates[variables]
+ # Normalize variable names: strip |flow_rate suffix for flow_rates lookup
+ flow_rates = self._stats.flow_rates
+ normalized_vars = []
+ for var in variables:
+ # Strip |flow_rate suffix if present
+ if var.endswith('|flow_rate'):
+ var = var[: -len('|flow_rate')]
+ normalized_vars.append(var)
+
+ # Try to get from flow_rates first, fall back to solution for non-flow variables
+ ds_parts = []
+ for var in normalized_vars:
+ if var in flow_rates:
+ ds_parts.append(flow_rates[[var]])
+ elif var in solution:
+ ds_parts.append(solution[[var]])
+ else:
+ # Try with |flow_rate suffix as last resort
+ flow_rate_var = f'{var}|flow_rate'
+ if flow_rate_var in solution:
+ ds_parts.append(solution[[flow_rate_var]].rename({flow_rate_var: var}))
+ else:
+ raise KeyError(f"Variable '{var}' not found in flow_rates or solution")
+
+ ds = xr.merge(ds_parts)
ds = _apply_selection(ds, select)
if 'time' not in ds.dims:
diff --git a/flixopt/structure.py b/flixopt/structure.py
index 8bec197bc..d00066683 100644
--- a/flixopt/structure.py
+++ b/flixopt/structure.py
@@ -1015,6 +1015,7 @@ def __init__(
self,
label: str,
meta_data: dict | None = None,
+ color: str | None = None,
_variable_names: list[str] | None = None,
_constraint_names: list[str] | None = None,
):
@@ -1022,11 +1023,13 @@ def __init__(
Args:
label: The label of the element
meta_data: used to store more information about the Element. Is not used internally, but saved in the results. Only use python native types.
+ color: Optional color for visualizations (e.g., '#FF6B6B'). If not provided, a color will be automatically assigned during FlowSystem.connect_and_transform().
_variable_names: Internal. Variable names for this element (populated after modeling).
_constraint_names: Internal. Constraint names for this element (populated after modeling).
"""
self.label = Element._valid_label(label)
self.meta_data = meta_data if meta_data is not None else {}
+ self.color = color
self.submodel = None
self._flow_system: FlowSystem | None = None
# Variable/constraint names - populated after modeling, serialized for results
@@ -1127,16 +1130,20 @@ def __init__(
elements: list[T] | dict[str, T] | None = None,
element_type_name: str = 'elements',
truncate_repr: int | None = None,
+ item_name: str | None = None,
):
"""
Args:
elements: Initial elements to add (list or dict)
element_type_name: Name for display (e.g., 'components', 'buses')
truncate_repr: Maximum number of items to show in repr. If None, show all items. Default: None
+ item_name: Singular name for error messages (e.g., 'Component', 'Carrier').
+ If None, inferred from first added item's class name.
"""
super().__init__()
self._element_type_name = element_type_name
self._truncate_repr = truncate_repr
+ self._item_name = item_name
if elements is not None:
if isinstance(elements, dict):
@@ -1158,13 +1165,28 @@ def _get_label(self, element: T) -> str:
"""
raise NotImplementedError('Subclasses must implement _get_label()')
+ def _get_item_name(self) -> str:
+ """Get the singular item name for error messages.
+
+ Returns the explicitly set item_name, or infers from the first item's class name.
+ Falls back to 'Item' if container is empty and no name was set.
+ """
+ if self._item_name is not None:
+ return self._item_name
+ # Infer from first item's class name
+ if self:
+ first_item = next(iter(self.values()))
+ return first_item.__class__.__name__
+ return 'Item'
+
def add(self, element: T) -> None:
"""Add an element to the container."""
label = self._get_label(element)
if label in self:
+ item_name = element.__class__.__name__
raise ValueError(
- f'Element with label "{label}" already exists in {self._element_type_name}. '
- f'Each element must have a unique label.'
+ f'{item_name} with label "{label}" already exists in {self._element_type_name}. '
+ f'Each {item_name.lower()} must have a unique label.'
)
self[label] = element
@@ -1195,8 +1217,9 @@ def __getitem__(self, label: str) -> T:
return super().__getitem__(label)
except KeyError:
# Provide helpful error with close matches suggestions
+ item_name = self._get_item_name()
suggestions = get_close_matches(label, self.keys(), n=3, cutoff=0.6)
- error_msg = f'Element "{label}" not found in {self._element_type_name}.'
+ error_msg = f'{item_name} "{label}" not found in {self._element_type_name}.'
if suggestions:
error_msg += f' Did you mean: {", ".join(suggestions)}?'
else:
From 0d8aaff84f8f7e1e7d4e764ebc62e1c109073759 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Mon, 8 Dec 2025 14:36:17 +0100
Subject: [PATCH 18/49] Add transform accessor and move sel, isel and resample
to this accessor (#510)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
* Add planning doc
* Finalize planning
* Add plotting acessor
* Add plotting acessor
* Add tests
* Improve
* Improve
* Update docs
* Updated the plotting API so that .data always returns xarray DataArray or Dataset instead of pandas DataFrame.
* All .data now returns xr.Dataset consistently.
* Fixed Inconsistencies and Unused Parameters
* New Plot Accessors
results.plot.variable(pattern)
Plots the same variable type across multiple elements for easy comparison.
# All binary operation states across all components
results.plot.variable('on')
# All flow_rates, filtered to Boiler-related elements
results.plot.variable('flow_rate', include='Boiler')
# All storage charge states
results.plot.variable('charge_state')
# With aggregation
results.plot.variable('flow_rate', aggregate='sum')
Key features:
- Searches all elements for variables matching the pattern
- Filter with include/exclude on element names
- Supports aggregation, faceting, and animation
- Returns Dataset with element names as variables
results.plot.duration_curve(variables)
Plots load duration curves (sorted time series) showing utilization patterns.
# Single variable
results.plot.duration_curve('Boiler(Q_th)|flow_rate')
# Multiple variables
results.plot.duration_curve(['CHP|on', 'Boiler|on'])
# Normalized x-axis (0-100%)
results.plot.duration_curve('demand', normalize=True)
Key features:
- Sorts values from highest to lowest
- Shows how often each power level is reached
- normalize=True shows percentage of time on x-axis
- Returns Dataset with duration_hours or duration_pct dimension
* Fix duration curve
* Fix duration curve
* Fix duration curve
* Fix duration curve
* xr.apply_ufunc to sort along the time axis while preserving all other dimensions automatically
* ⏺ The example runs successfully. Now let me summarize the fixes:
Summary of Fixes
I addressed the actionable code review comments from CodeRabbitAI:
1. Documentation Issue - reshape parameter name ✓ (No fix needed)
The CodeRabbitAI comment was incorrect. The public API parameter in PlotAccessor.heatmap() is correctly named reshape (line 335). The reshape_time parameter exists in the lower-level heatmap_with_plotly function, but the documentation correctly shows the public API parameter.
2. Fixed simple_example.py (lines 129-130)
Problem: The example called balance() and duration_curve() without required arguments, which would cause TypeError at runtime.
Fix: Added the required arguments:
- optimization.results.plot.balance('Fernwärme') - specifying the bus to plot
- optimization.results.plot.duration_curve('Boiler(Q_th)|flow_rate') - specifying the variable to plot
3. Fixed variable collision in plot_accessors.py (lines 985-988)
Problem: When building the Dataset in the variable() method, using element names as keys could cause collisions if multiple variables from the same element matched the pattern (e.g., 'Boiler|flow_rate' and 'Boiler|flow_rate_max' would both map to 'Boiler', with the latter silently overwriting the former).
Fix: Changed to use the full variable names as keys instead of just element names:
ds = xr.Dataset({var_name: self._results.solution[var_name] for var_name in filtered_vars})
All tests pass (40 passed, 1 skipped) and the example runs successfully.
* make variable names public in results
* Fix sankey
* Fix effects()
* Fix effects
* Remove bargaps
* made faceting consistent across all plot methods:
| Method | facet_col | facet_row |
|------------------|-------------------------------------------|-----------------------------|
| balance() | 'scenario' | 'period' |
| heatmap() | 'scenario' | 'period' |
| storage() | 'scenario' | 'period' |
| flows() | 'scenario' | 'period' |
| effects() | 'scenario' | 'period' |
| variable() | 'scenario' | 'period' |
| duration_curve() | 'scenario' | 'period' (already had this) |
| compare() | N/A (uses its own mode='overlay'/'facet') | |
| sankey() | N/A (aggregates to single diagram) | |
Removed animate_by parameter from all methods
* Update storage method
* Remove mode parameter for simpli
| Method | Default mode |
|------------------|---------------------------------------------------|
| balance() | stacked_bar |
| storage() | stacked_bar (flows) + line (charge state overlay) |
| flows() | line |
| variable() | line |
| duration_curve() | line |
| effects() | bar |
* Make plotting_accessors.py more self contained
* Use faster to_long()
* Add 0-dim case
* sankey diagram now properly handles scenarios and periods:
Changes made:
1. Period aggregation with weights: Uses period_weights from flow_system to properly weight periods by their duration
2. Scenario aggregation with weights: Uses normalized scenario_weights to compute a weighted average across scenarios
3. Selection support: Users can filter specific scenarios/periods via select parameter before aggregation
Weighting logic:
- Periods (for aggregate='sum'): (da * period_weights).sum(dim='period') - this gives the total energy across all periods weighted by their duration
- Periods (for aggregate='mean'): (da * period_weights).sum(dim='period') / period_weights.sum() - weighted mean
- Scenarios: Always uses normalized weights (sum to 1) for weighted averaging, since scenarios represent probability-weighted alternatives
* Add colors to sankey
* Add sizes
* Add size filtering
* Include storage sizes
* Remove storage sizes
* Add charge state and status accessor
* Summary of Changes
1. Added new methods to PlotAccessor (plot_accessors.py)
charge_states() (line 658):
- Returns a Dataset with each storage's charge state as a variable
- Supports filtering with include/exclude parameters
- Default plot: line chart
on_states() (line 753):
- Returns a Dataset with each component's |status variable
- Supports filtering with include/exclude parameters
- Default plot: heatmap (good for binary data visualization)
2. Added data building helper functions (plot_accessors.py)
build_flow_rates(results) (line 315):
- Builds a DataArray containing flow rates for all flows
- Used internally by PlotAccessor methods
build_flow_hours(results) (line 333):
- Builds a DataArray containing flow hours for all flows
build_sizes(results) (line 347):
- Builds a DataArray containing sizes for all flows
_filter_dataarray_by_coord(da, **kwargs) (line 284):
- Helper for filtering DataArrays by coordinate values
3. Deprecated old Results methods (results.py)
The following methods now emit DeprecationWarning:
- results.flow_rates() → Use results.plot.flows(plot=False).data
- results.flow_hours() → Use results.plot.flows(unit='flow_hours', plot=False).data
- results.sizes() → Use results.plot.sizes(plot=False).data
4. Updated PlotAccessor methods to use new helpers
- flows() now uses build_flow_rates() / build_flow_hours() directly
- sizes() now uses build_sizes() directly
- sankey() now uses build_flow_hours() directly
This ensures the deprecation warnings only fire when users directly call the old methods, not when using the plot accessor
* 1. New methods added to PlotAccessor
- charge_states(): Returns Dataset with all storage charge states
- on_states(): Returns Dataset with all component status variables (heatmap display)
2. Data building helper functions (plot_accessors.py)
- build_flow_rates(results): Builds DataArray of flow rates
- build_flow_hours(results): Builds DataArray of flow hours
- build_sizes(results): Builds DataArray of sizes
- _filter_dataarray_by_coord(da, **kwargs): Filter helper
- _assign_flow_coords(da, results): Add flow coordinates
3. Caching in PlotAccessor
Added lazy-cached properties for expensive computations:
- _all_flow_rates - cached DataArray of all flow rates
- _all_flow_hours - cached DataArray of all flow hours
- _all_sizes - cached DataArray of all sizes
- _all_charge_states - cached Dataset of all storage charge states
- _all_status_vars - cached Dataset of all status variables
4. Deprecated methods in Results class
Added deprecation warnings to:
- results.flow_rates() → Use results.plot.flows(plot=False).data
- results.flow_hours() → Use results.plot.flows(unit='flow_hours', plot=False).data
- results.sizes() → Use results.plot.sizes(plot=False).data
5. Updated PlotAccessor methods to use cached properties
- flows() uses _all_flow_rates / _all_flow_hours
- sankey() uses _all_flow_hours
- sizes() uses _all_sizes
- charge_states() uses _all_charge_states
- on_states() uses _all_status_vars
* Move deprectated functionality into results.py instead of porting to the new module
* Revert to simply deprectae old methods without forwarding to new code
* Remove planning file
* Update plotting methods for new datasets
* 1. Renamed data properties in PlotAccessor to use all_ prefix:
- all_flow_rates - All flow rates as Dataset
- all_flow_hours - All flow hours as Dataset
- all_sizes - All flow sizes as Dataset
- all_charge_states - All storage charge states as Dataset
- all_on_states - All component on/off status as Dataset
2. Updated internal references - All usages in flows(), sankey(), sizes(), charge_states(), and on_states() methods now use the new names.
3. Updated deprecation messages in results.py to point to the new API:
- results.flow_rates() → results.plot.all_flow_rates
- results.flow_hours() → results.plot.all_flow_hours
- results.sizes() → results.plot.all_sizes
4. Updated docstring examples in PlotAccessor to use the new all_* names.
* Update deprecations messages
* Update deprecations messages
* Thsi seems much better.
* Updaet docstrings and variable name generation in plotting acessor
* Change __ to _ in private dataset caching
* Revert breaking io changes
* New solution storing interface
* Add new focused statistics and plot accessors
* Renamed all properties:
- all_flow_rates → flow_rates
- all_flow_hours → flow_hours
- all_sizes → sizes
- all_charge_states → charge_states
* Cache Statistics
* Invalidate caches
* Add effect related statistics
* Simplify statistics accessor to rely on flow_system directly instead of solution attrs
* Fix heatma fallback for 1D Data
* Add topology accessor
* All deprecation warnings in the codebase now consistently use the format will be removed in v{DEPRECATION_REMOVAL_VERSION}.
* Update tests
* created comprehensive documentation for all FlowSystem accessors
* Update results documentation
* Update results documentation
* Update effect statistics
* Update effect statistics
* Update effect statistics
* Add mkdocs plotly plugin
* Add section about custom constraints
* documentation updates:
docs/user-guide/results/index.md:
- Updated table to replace effects_per_component with temporal_effects, periodic_effects, total_effects, and effect_share_factors
- Fixed flow_hours['Boiler(Q_th)|flow_rate'] → flow_hours['Boiler(Q_th)']
- Fixed sizes['Boiler(Q_th)|size'] → sizes['Boiler(Q_th)']
- Replaced effects_per_component example with new effect properties and groupby examples
- Updated complete example to use total_effects
docs/user-guide/results-plotting.md:
- Fixed colors example from 'Boiler(Q_th)|flow_rate' → 'Boiler(Q_th)'
- Fixed duration_curve examples to use clean labels
docs/user-guide/migration-guide-v6.md:
- Added new "Statistics Accessor" section explaining the clean labels and new effect properties
* implemented the effects() method in StatisticsPlotAccessor at flixopt/statistics_accessor.py:1132-1258.
Summary of what was done:
1. Implemented effects() method in StatisticsPlotAccessor class that was missing but documented
- Takes aspect parameter: 'total', 'temporal', or 'periodic'
- Takes effect parameter to filter to a specific effect (e.g., 'costs', 'CO2')
- Takes by parameter: 'component' or 'time' for grouping
- Supports all standard plotting parameters: select, colors, facet_col, facet_row, show
- Returns PlotResult with both data and figure
2. Verified the implementation works with all parameter combinations:
- Default call: flow_system.statistics.plot.effects()
- Specific effect: flow_system.statistics.plot.effects(effect='costs')
- Temporal aspect: flow_system.statistics.plot.effects(aspect='temporal')
- Temporal by time: flow_system.statistics.plot.effects(aspect='temporal', by='time')
- Periodic aspect: flow_system.statistics.plot.effects(aspect='periodic')
* Remove intermediate plot accessor
* 1. pyproject.toml: Removed duplicate mkdocs-plotly-plugin>=0.1.3 entry (kept the exact pin ==0.1.3)
2. flixopt/plotting.py: Fixed dimension name consistency by using squeezed_data.name instead of data.name in the fallback heatmap logic
3. flixopt/statistics_accessor.py:
- Fixed _dataset_to_long_df() to only use coordinates that are actually present as columns after reset_index()
- Fixed the nested loop inefficiency with include_flows by pre-computing the flows list outside the loop
- (Previously fixed) Fixed asymmetric NaN handling in validation check
* _create_effects_dataset method in statistics_accessor.py was simplified:
1. Detect contributors from solution data variables instead of assuming they're only flows
- Uses regex pattern to find {contributor}->{effect}(temporal|periodic) variables
- Contributors can be flows OR components (e.g., components with effects_per_active_hour)
2. Exclude effect-to-effect shares
- Filters out contributors whose base name matches any effect label
- For example, costs(temporal) is excluded because costs is an effect label
- These intermediate shares are already included in the computation
3. Removed the unused _compute_effect_total method
- The new simplified implementation directly looks up shares from the solution
- Uses effect_share_factors for conversion between effects
4. Key insight from user: The solution already contains properly computed share values including all effect-to-effect conversions. The computation uses conversion
factors because derived effects (like Effect1 which shares 0.5 from costs) don't have direct {flow}->Effect1(temporal) variables - only the source effect shares exist
({flow}->costs(temporal)).
* Update docs
* Improve to_netcdf method
* Update examples
* Fix IIS computaion flag
* Fix examples
* Fix faceting in heatmap and use period as facet col everywhere
* Inline plotting methods to deprecate plotting.py
* Fix test
* Simplify Color Management
* ColorType is now defined in color_processing.py and imported into statistics_accessor.py.
* Fix ColorType typing
* Add color accessor
* Ensure io
* Add carrier class
* implemented Carrier as a proper Interface subclass with container support. Here's what was done:
1. Carrier class (flixopt/carrier.py)
- Now inherits from Interface for serialization capabilities
- Has transform_data() method (no-op since carriers have no time-series data)
- Has label property for container keying
- Maintains equality comparison with both Carrier objects and strings
2. CarrierContainer class (flixopt/carrier.py)
- Inherits from ContainerMixin['Carrier']
- Provides dict-like access with nice repr and error messages
- Uses carrier.name for keying
3. FlowSystem updates (flixopt/flow_system.py)
- _carriers is now a CarrierContainer instead of a plain dict
- carriers property returns the CarrierContainer
- add_carrier() uses the container's add() method
- Serialization updated to include carriers in to_dataset() and restore them in from_dataset()
4. Exports (flixopt/__init__.py)
- Both Carrier and CarrierContainer are now exported
* Inline plotting methods to deprecate plotting.py (#508)
* Inline plotting methods to deprecate plotting.py
* Fix test
* Simplify Color Management
* ColorType is now defined in color_processing.py and imported into statistics_accessor.py.
* Fix ColorType typing
* statistics_accessor.py - Heatmap colors type safety (lines 121-148, 820-853)
- Changed _heatmap_figure() parameter type from colors: ColorType = None to colors: str | list[str] | None = None
- Changed heatmap() method parameter type similarly
- Updated docstrings to clarify that dicts are not supported for heatmaps since px.imshow's color_continuous_scale only accepts colorscale names or lists
2. statistics_accessor.py - Use configured qualitative colorscale (lines 284, 315)
- Updated _create_stacked_bar() to use CONFIG.Plotting.default_qualitative_colorscale as the default colorscale
- Updated _create_line() similarly
- This ensures user-configured CONFIG.Plotting.default_qualitative_colorscale affects all bar/line plots consistently
3. topology_accessor.py - Path type alignment (lines 219-222)
- Added normalization of path=False to None before calling _plot_network()
- This resolves the type mismatch where TopologyAccessor.plot() accepts bool | str | Path but _plot_network() only accepts str | Path | None
* fix usage if index name in aggregation plot
* Add to docs
* Improve carrier colors and defaults
* Update default carriers and colors
* Update config
* Update config
* Move default carriers to config.py
* Change default carrier handling
* Add color handling
* Rmeove meta_data color handling
* Add carrierst to examples
* Improve plotting acessor
* Improve _resolve_variable_names
* Improve _resolve_variable_names
* Simplify coloring and remove color accessor
* Add connected_and_transformed handling
* Improve error message in container
* Methods moved to TransformAccessor (transform_accessor.py):
- sel() - select by label
- isel() - select by integer index
- resample() - resample time dimension
- Helper methods: _dataset_sel, _dataset_isel, _dataset_resample, _resample_by_dimension_groups
2. Solution is dropped: All transform methods return a new FlowSystem with no solution - the user must re-optimize the transformed system.
3. Deprecation warnings: The old flow_system.sel(), flow_system.isel(), and flow_system.resample() methods now emit deprecation warnings and forward to the new
TransformAccessor methods.
4. Backward compatible: Existing code still works, just with deprecation warnings.
* Documentation updated
* Re-add _dataset_sel and other helper methods for proper deprectation. ALso fix new methods to be classmethods
* BUGFIX: Carrier from dataset
* Update docs
---
docs/user-guide/core-concepts.md | 49 ++++
docs/user-guide/migration-guide-v6.md | 34 ++-
docs/user-guide/optimization/index.md | 50 ++++
examples/01_Simple/simple_example.py | 1 -
flixopt/flow_system.py | 299 ++++++++---------------
flixopt/transform_accessor.py | 339 +++++++++++++++++++++++++-
6 files changed, 572 insertions(+), 200 deletions(-)
diff --git a/docs/user-guide/core-concepts.md b/docs/user-guide/core-concepts.md
index 78e38ade7..14e5723d6 100644
--- a/docs/user-guide/core-concepts.md
+++ b/docs/user-guide/core-concepts.md
@@ -180,6 +180,55 @@ flow_system.statistics.plot.balance('HeatBus')
| **Effect** | Metric to track/optimize | Costs, emissions, energy use |
| **FlowSystem** | Complete model | Your entire system |
+## FlowSystem API at a Glance
+
+The `FlowSystem` is the central object in flixOpt. After building your model, all operations are accessed through the FlowSystem and its **accessors**:
+
+```python
+flow_system = fx.FlowSystem(timesteps)
+flow_system.add_elements(...)
+
+# Optimize
+flow_system.optimize(solver)
+
+# Access results
+flow_system.solution # Raw xarray Dataset
+flow_system.statistics.flow_hours # Aggregated statistics
+flow_system.statistics.plot.balance() # Visualization
+
+# Transform (returns new FlowSystem)
+fs_subset = flow_system.transform.sel(time=slice(...))
+
+# Inspect structure
+flow_system.topology.plot()
+```
+
+### Accessor Overview
+
+| Accessor | Purpose | Key Methods |
+|----------|---------|-------------|
+| **`solution`** | Raw optimization results | xarray Dataset with all variables |
+| **`statistics`** | Aggregated data | `flow_rates`, `flow_hours`, `sizes`, `charge_states`, `total_effects` |
+| **`statistics.plot`** | Visualization | `balance()`, `heatmap()`, `sankey()`, `effects()`, `storage()` |
+| **`transform`** | Create modified copies | `sel()`, `isel()`, `resample()`, `cluster()` |
+| **`topology`** | Network structure | `plot()`, `start_app()`, `infos()` |
+
+### Element Access
+
+Access elements directly from the FlowSystem:
+
+```python
+# Access by label
+flow_system.components['Boiler'] # Get a component
+flow_system.buses['Heat'] # Get a bus
+flow_system.flows['Boiler(Q_th)'] # Get a flow
+flow_system.effects['costs'] # Get an effect
+
+# Element-specific solutions
+flow_system.components['Boiler'].solution
+flow_system.flows['Boiler(Q_th)'].solution
+```
+
## Beyond Energy Systems
While our example used a heating system, flixOpt works for any flow-based optimization:
diff --git a/docs/user-guide/migration-guide-v6.md b/docs/user-guide/migration-guide-v6.md
index 8b50312ee..164ff5a28 100644
--- a/docs/user-guide/migration-guide-v6.md
+++ b/docs/user-guide/migration-guide-v6.md
@@ -343,20 +343,52 @@ stats.total_effects['costs'].groupby('component_type').sum()
| **Replace Optimization class** | Use `flow_system.optimize(solver)` instead |
| **Update results access** | Use `flow_system.solution['var_name']` pattern |
| **Update I/O code** | Use `to_netcdf()` / `from_netcdf()` |
+| **Update transform methods** | Use `flow_system.transform.sel/isel/resample()` instead |
| **Test thoroughly** | Verify results match v5.x outputs |
| **Remove deprecated imports** | Remove `fx.Optimization`, `fx.Results` |
---
+## Transform Methods Moved to Accessor
+
+The `sel()`, `isel()`, and `resample()` methods have been moved from `FlowSystem` to the `TransformAccessor`:
+
+=== "Old (deprecated)"
+ ```python
+ # These still work but emit deprecation warnings
+ fs_subset = flow_system.sel(time=slice('2023-01-01', '2023-06-30'))
+ fs_indexed = flow_system.isel(time=slice(0, 24))
+ fs_resampled = flow_system.resample(time='4h', method='mean')
+ ```
+
+=== "New (recommended)"
+ ```python
+ # Use the transform accessor
+ fs_subset = flow_system.transform.sel(time=slice('2023-01-01', '2023-06-30'))
+ fs_indexed = flow_system.transform.isel(time=slice(0, 24))
+ fs_resampled = flow_system.transform.resample(time='4h', method='mean')
+ ```
+
+!!! info "Solution is dropped"
+ All transform methods return a **new FlowSystem without a solution**. You must re-optimize the transformed system:
+ ```python
+ fs_subset = flow_system.transform.sel(time=slice('2023-01-01', '2023-01-31'))
+ fs_subset.optimize(solver) # Re-optimize the subset
+ ```
+
+---
+
## Deprecation Timeline
| Version | Status |
|---------|--------|
| v5.x | `Optimization` class deprecated with warning |
-| v6.0.0 | `Optimization` class removed |
+| v6.0.0 | `Optimization` class removed, `sel/isel/resample` methods deprecated |
!!! warning "Update your code"
The `Optimization` and `Results` classes are deprecated and will be removed in a future version.
+ The `flow_system.sel()`, `flow_system.isel()`, and `flow_system.resample()` methods are deprecated
+ in favor of `flow_system.transform.sel/isel/resample()`.
Update your code to the new API to avoid breaking changes when upgrading.
---
diff --git a/docs/user-guide/optimization/index.md b/docs/user-guide/optimization/index.md
index 07c96454c..b1bd0caf6 100644
--- a/docs/user-guide/optimization/index.md
+++ b/docs/user-guide/optimization/index.md
@@ -93,6 +93,56 @@ print(clustered_fs.solution)
| Standard | Small-Medium | Slow | Optimal |
| Clustered | Very Large | Fast | Approximate |
+## Transform Accessor
+
+The `transform` accessor provides methods to create modified copies of your FlowSystem. All transform methods return a **new FlowSystem without a solution** — you must re-optimize the transformed system.
+
+### Selecting Subsets
+
+Select a subset of your data by label or index:
+
+```python
+# Select by label (like xarray.sel)
+fs_january = flow_system.transform.sel(time=slice('2024-01-01', '2024-01-31'))
+fs_scenario = flow_system.transform.sel(scenario='base')
+
+# Select by integer index (like xarray.isel)
+fs_first_week = flow_system.transform.isel(time=slice(0, 168))
+fs_first_scenario = flow_system.transform.isel(scenario=0)
+
+# Re-optimize the subset
+fs_january.optimize(fx.solvers.HighsSolver())
+```
+
+### Resampling Time Series
+
+Change the temporal resolution of your FlowSystem:
+
+```python
+# Resample to 4-hour intervals
+fs_4h = flow_system.transform.resample(time='4h', method='mean')
+
+# Resample to daily
+fs_daily = flow_system.transform.resample(time='1D', method='mean')
+
+# Re-optimize with new resolution
+fs_4h.optimize(fx.solvers.HighsSolver())
+```
+
+**Available resampling methods:** `'mean'`, `'sum'`, `'max'`, `'min'`, `'first'`, `'last'`
+
+### Clustering
+
+See [Clustered Optimization](#clustered-optimization) above.
+
+### Use Cases
+
+| Method | Use Case |
+|--------|----------|
+| `sel()` / `isel()` | Analyze specific time periods, scenarios, or periods |
+| `resample()` | Reduce problem size, test at lower resolution |
+| `cluster()` | Investment planning with typical periods |
+
## Custom Constraints
flixOpt is built on [linopy](https://github.com/PyPSA/linopy), allowing you to add custom constraints beyond what's available through the standard API.
diff --git a/examples/01_Simple/simple_example.py b/examples/01_Simple/simple_example.py
index e8185e248..b63260ece 100644
--- a/examples/01_Simple/simple_example.py
+++ b/examples/01_Simple/simple_example.py
@@ -116,7 +116,6 @@
flow_system.statistics.plot.balance('Storage')
flow_system.statistics.plot.heatmap('CHP(Q_th)')
flow_system.statistics.plot.heatmap('Storage')
- flow_system.statistics.plot.heatmap('Storage')
# Access data as xarray Datasets
print(flow_system.statistics.flow_rates)
diff --git a/flixopt/flow_system.py b/flixopt/flow_system.py
index ee1a10261..153354cce 100644
--- a/flixopt/flow_system.py
+++ b/flixopt/flow_system.py
@@ -8,7 +8,6 @@
import logging
import pathlib
import warnings
-from collections import defaultdict
from itertools import chain
from typing import TYPE_CHECKING, Any, Literal
@@ -1619,29 +1618,22 @@ def _dataset_sel(
Returns:
xr.Dataset: Selected dataset
"""
- indexers = {}
- if time is not None:
- indexers['time'] = time
- if period is not None:
- indexers['period'] = period
- if scenario is not None:
- indexers['scenario'] = scenario
-
- if not indexers:
- return dataset
-
- result = dataset.sel(**indexers)
-
- # Update time-related attributes if time was selected
- if 'time' in indexers:
- result = cls._update_time_metadata(result, hours_of_last_timestep, hours_of_previous_timesteps)
-
- # Update period-related attributes if period was selected
- # This recalculates period_weights and weights from the new period index
- if 'period' in indexers:
- result = cls._update_period_metadata(result)
+ warnings.warn(
+ f'\n_dataset_sel() is deprecated and will be removed in {DEPRECATION_REMOVAL_VERSION}. '
+ 'Use TransformAccessor._dataset_sel() instead.',
+ DeprecationWarning,
+ stacklevel=2,
+ )
+ from .transform_accessor import TransformAccessor
- return result
+ return TransformAccessor._dataset_sel(
+ dataset,
+ time=time,
+ period=period,
+ scenario=scenario,
+ hours_of_last_timestep=hours_of_last_timestep,
+ hours_of_previous_timesteps=hours_of_previous_timesteps,
+ )
def sel(
self,
@@ -1652,8 +1644,8 @@ def sel(
"""
Select a subset of the flowsystem by label.
- For power users: Use FlowSystem._dataset_sel() to chain operations on datasets
- without conversion overhead. See _dataset_sel() documentation.
+ .. deprecated::
+ Use ``flow_system.transform.sel()`` instead. Will be removed in v6.0.0.
Args:
time: Time selection (e.g., slice('2023-01-01', '2023-12-31'), '2023-06-15')
@@ -1661,17 +1653,15 @@ def sel(
scenario: Scenario selection (e.g., 'scenario1', or list of scenarios)
Returns:
- FlowSystem: New FlowSystem with selected data
+ FlowSystem: New FlowSystem with selected data (no solution).
"""
- if time is None and period is None and scenario is None:
- return self.copy()
-
- if not self.connected_and_transformed:
- self.connect_and_transform()
-
- ds = self.to_dataset()
- ds = self._dataset_sel(ds, time=time, period=period, scenario=scenario)
- return self.__class__.from_dataset(ds)
+ warnings.warn(
+ f'\nsel() is deprecated and will be removed in {DEPRECATION_REMOVAL_VERSION}. '
+ 'Use flow_system.transform.sel() instead.',
+ DeprecationWarning,
+ stacklevel=2,
+ )
+ return self.transform.sel(time=time, period=period, scenario=scenario)
@classmethod
def _dataset_isel(
@@ -1700,29 +1690,22 @@ def _dataset_isel(
Returns:
xr.Dataset: Selected dataset
"""
- indexers = {}
- if time is not None:
- indexers['time'] = time
- if period is not None:
- indexers['period'] = period
- if scenario is not None:
- indexers['scenario'] = scenario
-
- if not indexers:
- return dataset
-
- result = dataset.isel(**indexers)
-
- # Update time-related attributes if time was selected
- if 'time' in indexers:
- result = cls._update_time_metadata(result, hours_of_last_timestep, hours_of_previous_timesteps)
-
- # Update period-related attributes if period was selected
- # This recalculates period_weights and weights from the new period index
- if 'period' in indexers:
- result = cls._update_period_metadata(result)
+ warnings.warn(
+ f'\n_dataset_isel() is deprecated and will be removed in {DEPRECATION_REMOVAL_VERSION}. '
+ 'Use TransformAccessor._dataset_isel() instead.',
+ DeprecationWarning,
+ stacklevel=2,
+ )
+ from .transform_accessor import TransformAccessor
- return result
+ return TransformAccessor._dataset_isel(
+ dataset,
+ time=time,
+ period=period,
+ scenario=scenario,
+ hours_of_last_timestep=hours_of_last_timestep,
+ hours_of_previous_timesteps=hours_of_previous_timesteps,
+ )
def isel(
self,
@@ -1733,109 +1716,24 @@ def isel(
"""
Select a subset of the flowsystem by integer indices.
- For power users: Use FlowSystem._dataset_isel() to chain operations on datasets
- without conversion overhead. See _dataset_sel() documentation.
+ .. deprecated::
+ Use ``flow_system.transform.isel()`` instead. Will be removed in v6.0.0.
Args:
time: Time selection by integer index (e.g., slice(0, 100), 50, or [0, 5, 10])
- period: Period selection by integer index (e.g., slice(0, 100), 50, or [0, 5, 10])
- scenario: Scenario selection by integer index (e.g., slice(0, 3), 50, or [0, 5, 10])
+ period: Period selection by integer index
+ scenario: Scenario selection by integer index
Returns:
- FlowSystem: New FlowSystem with selected data
- """
- if time is None and period is None and scenario is None:
- return self.copy()
-
- if not self.connected_and_transformed:
- self.connect_and_transform()
-
- ds = self.to_dataset()
- ds = self._dataset_isel(ds, time=time, period=period, scenario=scenario)
- return self.__class__.from_dataset(ds)
-
- @classmethod
- def _resample_by_dimension_groups(
- cls,
- time_dataset: xr.Dataset,
- time: str,
- method: str,
- **kwargs: Any,
- ) -> xr.Dataset:
+ FlowSystem: New FlowSystem with selected data (no solution).
"""
- Resample variables grouped by their dimension structure to avoid broadcasting.
-
- This method groups variables by their non-time dimensions before resampling,
- which provides two key benefits:
-
- 1. **Performance**: Resampling many variables with the same dimensions together
- is significantly faster than resampling each variable individually.
-
- 2. **Safety**: Prevents xarray from broadcasting variables with different
- dimensions into a larger dimensional space filled with NaNs, which would
- cause memory bloat and computational inefficiency.
-
- Example:
- Without grouping (problematic):
- var1: (time, location, tech) shape (8000, 10, 2)
- var2: (time, region) shape (8000, 5)
- concat → (variable, time, location, tech, region) ← Unwanted broadcasting!
-
- With grouping (safe and fast):
- Group 1: [var1, var3, ...] with dims (time, location, tech)
- Group 2: [var2, var4, ...] with dims (time, region)
- Each group resampled separately → No broadcasting, optimal performance!
-
- Args:
- time_dataset: Dataset containing only variables with time dimension
- time: Resampling frequency (e.g., '2h', '1D', '1M')
- method: Resampling method name (e.g., 'mean', 'sum', 'first')
- **kwargs: Additional arguments passed to xarray.resample()
-
- Returns:
- Resampled dataset with original dimension structure preserved
- """
- # Group variables by dimensions (excluding time)
- dim_groups = defaultdict(list)
- for var_name, var in time_dataset.data_vars.items():
- dims_key = tuple(sorted(d for d in var.dims if d != 'time'))
- dim_groups[dims_key].append(var_name)
-
- # Handle empty case: no time-dependent variables
- if not dim_groups:
- return getattr(time_dataset.resample(time=time, **kwargs), method)()
-
- # Resample each group separately using DataArray concat (faster)
- resampled_groups = []
- for var_names in dim_groups.values():
- # Skip empty groups
- if not var_names:
- continue
-
- # Concat variables into a single DataArray with 'variable' dimension
- # Use combine_attrs='drop_conflicts' to handle attribute conflicts
- stacked = xr.concat(
- [time_dataset[name] for name in var_names],
- dim=pd.Index(var_names, name='variable'),
- combine_attrs='drop_conflicts',
- )
-
- # Resample the DataArray (faster than resampling Dataset)
- resampled = getattr(stacked.resample(time=time, **kwargs), method)()
-
- # Convert back to Dataset using the 'variable' dimension
- resampled_dataset = resampled.to_dataset(dim='variable')
- resampled_groups.append(resampled_dataset)
-
- # Merge all resampled groups, handling empty list case
- if not resampled_groups:
- return time_dataset # Return empty dataset as-is
-
- if len(resampled_groups) == 1:
- return resampled_groups[0]
-
- # Merge multiple groups with combine_attrs to avoid conflicts
- return xr.merge(resampled_groups, combine_attrs='drop_conflicts')
+ warnings.warn(
+ f'\nisel() is deprecated and will be removed in {DEPRECATION_REMOVAL_VERSION}. '
+ 'Use flow_system.transform.isel() instead.',
+ DeprecationWarning,
+ stacklevel=2,
+ )
+ return self.transform.isel(time=time, period=period, scenario=scenario)
@classmethod
def _dataset_resample(
@@ -1866,36 +1764,47 @@ def _dataset_resample(
Returns:
xr.Dataset: Resampled dataset
"""
- # Validate method
- available_methods = ['mean', 'sum', 'max', 'min', 'first', 'last', 'std', 'var', 'median', 'count']
- if method not in available_methods:
- raise ValueError(f'Unsupported resampling method: {method}. Available: {available_methods}')
-
- # Preserve original dataset attributes (especially the reference structure)
- original_attrs = dict(dataset.attrs)
-
- # Separate time and non-time variables
- time_var_names = [v for v in dataset.data_vars if 'time' in dataset[v].dims]
- non_time_var_names = [v for v in dataset.data_vars if v not in time_var_names]
-
- # Only resample variables that have time dimension
- time_dataset = dataset[time_var_names]
+ warnings.warn(
+ f'\n_dataset_resample() is deprecated and will be removed in {DEPRECATION_REMOVAL_VERSION}. '
+ 'Use TransformAccessor._dataset_resample() instead.',
+ DeprecationWarning,
+ stacklevel=2,
+ )
+ from .transform_accessor import TransformAccessor
- # Resample with dimension grouping to avoid broadcasting
- resampled_time_dataset = cls._resample_by_dimension_groups(time_dataset, freq, method, **kwargs)
+ return TransformAccessor._dataset_resample(
+ dataset,
+ freq=freq,
+ method=method,
+ hours_of_last_timestep=hours_of_last_timestep,
+ hours_of_previous_timesteps=hours_of_previous_timesteps,
+ **kwargs,
+ )
- # Combine resampled time variables with non-time variables
- if non_time_var_names:
- non_time_dataset = dataset[non_time_var_names]
- result = xr.merge([resampled_time_dataset, non_time_dataset])
- else:
- result = resampled_time_dataset
+ @classmethod
+ def _resample_by_dimension_groups(
+ cls,
+ time_dataset: xr.Dataset,
+ time: str,
+ method: str,
+ **kwargs: Any,
+ ) -> xr.Dataset:
+ """
+ Resample variables grouped by their dimension structure to avoid broadcasting.
- # Restore original attributes (xr.merge can drop them)
- result.attrs.update(original_attrs)
+ .. deprecated::
+ Use ``TransformAccessor._resample_by_dimension_groups()`` instead.
+ Will be removed in v6.0.0.
+ """
+ warnings.warn(
+ f'\n_resample_by_dimension_groups() is deprecated and will be removed in {DEPRECATION_REMOVAL_VERSION}. '
+ 'Use TransformAccessor._resample_by_dimension_groups() instead.',
+ DeprecationWarning,
+ stacklevel=2,
+ )
+ from .transform_accessor import TransformAccessor
- # Update time-related attributes based on new time index
- return cls._update_time_metadata(result, hours_of_last_timestep, hours_of_previous_timesteps)
+ return TransformAccessor._resample_by_dimension_groups(time_dataset, time, method, **kwargs)
def resample(
self,
@@ -1906,36 +1815,34 @@ def resample(
**kwargs: Any,
) -> FlowSystem:
"""
- Create a resampled FlowSystem by resampling data along the time dimension (like xr.Dataset.resample()).
- Only resamples data variables that have a time dimension.
+ Create a resampled FlowSystem by resampling data along the time dimension.
- For power users: Use FlowSystem._dataset_resample() to chain operations on datasets
- without conversion overhead. See _dataset_sel() documentation.
+ .. deprecated::
+ Use ``flow_system.transform.resample()`` instead. Will be removed in v6.0.0.
Args:
time: Resampling frequency (e.g., '3h', '2D', '1M')
method: Resampling method. Recommended: 'mean', 'first', 'last', 'max', 'min'
- hours_of_last_timestep: Duration of the last timestep after resampling. If None, computed from the last time interval.
- hours_of_previous_timesteps: Duration of previous timesteps after resampling. If None, computed from the first time interval.
- Can be a scalar or array.
+ hours_of_last_timestep: Duration of the last timestep after resampling.
+ hours_of_previous_timesteps: Duration of previous timesteps after resampling.
**kwargs: Additional arguments passed to xarray.resample()
Returns:
- FlowSystem: New resampled FlowSystem
+ FlowSystem: New resampled FlowSystem (no solution).
"""
- if not self.connected_and_transformed:
- self.connect_and_transform()
-
- ds = self.to_dataset()
- ds = self._dataset_resample(
- ds,
- freq=time,
+ warnings.warn(
+ f'\nresample() is deprecated and will be removed in {DEPRECATION_REMOVAL_VERSION}. '
+ 'Use flow_system.transform.resample() instead.',
+ DeprecationWarning,
+ stacklevel=2,
+ )
+ return self.transform.resample(
+ time=time,
method=method,
hours_of_last_timestep=hours_of_last_timestep,
hours_of_previous_timesteps=hours_of_previous_timesteps,
**kwargs,
)
- return self.__class__.from_dataset(ds)
@property
def connected_and_transformed(self) -> bool:
diff --git a/flixopt/transform_accessor.py b/flixopt/transform_accessor.py
index 028d83bca..cb0d87872 100644
--- a/flixopt/transform_accessor.py
+++ b/flixopt/transform_accessor.py
@@ -2,15 +2,21 @@
Transform accessor for FlowSystem.
This module provides the TransformAccessor class that enables
-transformations on FlowSystem like clustering and MGA.
+transformations on FlowSystem like clustering, selection, and resampling.
"""
from __future__ import annotations
import logging
-from typing import TYPE_CHECKING
+from collections import defaultdict
+from typing import TYPE_CHECKING, Any, Literal
+
+import pandas as pd
+import xarray as xr
if TYPE_CHECKING:
+ import numpy as np
+
from .clustering import ClusteringParameters
from .flow_system import FlowSystem
@@ -193,6 +199,335 @@ def _calculate_clustering_weights(ds) -> dict[str, float]:
return weights
+ def sel(
+ self,
+ time: str | slice | list[str] | pd.Timestamp | pd.DatetimeIndex | None = None,
+ period: int | slice | list[int] | pd.Index | None = None,
+ scenario: str | slice | list[str] | pd.Index | None = None,
+ ) -> FlowSystem:
+ """
+ Select a subset of the FlowSystem by label.
+
+ Creates a new FlowSystem with data selected along the specified dimensions.
+ The returned FlowSystem has no solution (it must be re-optimized).
+
+ Args:
+ time: Time selection (e.g., slice('2023-01-01', '2023-12-31'), '2023-06-15')
+ period: Period selection (e.g., slice(2023, 2024), or list of periods)
+ scenario: Scenario selection (e.g., 'scenario1', or list of scenarios)
+
+ Returns:
+ FlowSystem: New FlowSystem with selected data (no solution).
+
+ Examples:
+ >>> # Select specific time range
+ >>> fs_jan = flow_system.transform.sel(time=slice('2023-01-01', '2023-01-31'))
+ >>> fs_jan.optimize(solver)
+
+ >>> # Select single scenario
+ >>> fs_base = flow_system.transform.sel(scenario='Base Case')
+ """
+ from .flow_system import FlowSystem
+
+ if time is None and period is None and scenario is None:
+ result = self._fs.copy()
+ result.solution = None
+ return result
+
+ if not self._fs.connected_and_transformed:
+ self._fs.connect_and_transform()
+
+ ds = self._fs.to_dataset()
+ ds = self._dataset_sel(ds, time=time, period=period, scenario=scenario)
+ return FlowSystem.from_dataset(ds) # from_dataset doesn't include solution
+
+ def isel(
+ self,
+ time: int | slice | list[int] | None = None,
+ period: int | slice | list[int] | None = None,
+ scenario: int | slice | list[int] | None = None,
+ ) -> FlowSystem:
+ """
+ Select a subset of the FlowSystem by integer indices.
+
+ Creates a new FlowSystem with data selected along the specified dimensions.
+ The returned FlowSystem has no solution (it must be re-optimized).
+
+ Args:
+ time: Time selection by integer index (e.g., slice(0, 100), 50, or [0, 5, 10])
+ period: Period selection by integer index
+ scenario: Scenario selection by integer index
+
+ Returns:
+ FlowSystem: New FlowSystem with selected data (no solution).
+
+ Examples:
+ >>> # Select first 24 timesteps
+ >>> fs_day1 = flow_system.transform.isel(time=slice(0, 24))
+ >>> fs_day1.optimize(solver)
+
+ >>> # Select first scenario
+ >>> fs_first = flow_system.transform.isel(scenario=0)
+ """
+ from .flow_system import FlowSystem
+
+ if time is None and period is None and scenario is None:
+ result = self._fs.copy()
+ result.solution = None
+ return result
+
+ if not self._fs.connected_and_transformed:
+ self._fs.connect_and_transform()
+
+ ds = self._fs.to_dataset()
+ ds = self._dataset_isel(ds, time=time, period=period, scenario=scenario)
+ return FlowSystem.from_dataset(ds) # from_dataset doesn't include solution
+
+ def resample(
+ self,
+ time: str,
+ method: Literal['mean', 'sum', 'max', 'min', 'first', 'last', 'std', 'var', 'median', 'count'] = 'mean',
+ hours_of_last_timestep: int | float | None = None,
+ hours_of_previous_timesteps: int | float | np.ndarray | None = None,
+ **kwargs: Any,
+ ) -> FlowSystem:
+ """
+ Create a resampled FlowSystem by resampling data along the time dimension.
+
+ Creates a new FlowSystem with resampled time series data.
+ The returned FlowSystem has no solution (it must be re-optimized).
+
+ Args:
+ time: Resampling frequency (e.g., '3h', '2D', '1M')
+ method: Resampling method. Recommended: 'mean', 'first', 'last', 'max', 'min'
+ hours_of_last_timestep: Duration of the last timestep after resampling.
+ If None, computed from the last time interval.
+ hours_of_previous_timesteps: Duration of previous timesteps after resampling.
+ If None, computed from the first time interval. Can be a scalar or array.
+ **kwargs: Additional arguments passed to xarray.resample()
+
+ Returns:
+ FlowSystem: New resampled FlowSystem (no solution).
+
+ Examples:
+ >>> # Resample to 4-hour intervals
+ >>> fs_4h = flow_system.transform.resample(time='4h', method='mean')
+ >>> fs_4h.optimize(solver)
+
+ >>> # Resample to daily with max values
+ >>> fs_daily = flow_system.transform.resample(time='1D', method='max')
+ """
+ from .flow_system import FlowSystem
+
+ if not self._fs.connected_and_transformed:
+ self._fs.connect_and_transform()
+
+ ds = self._fs.to_dataset()
+ ds = self._dataset_resample(
+ ds,
+ freq=time,
+ method=method,
+ hours_of_last_timestep=hours_of_last_timestep,
+ hours_of_previous_timesteps=hours_of_previous_timesteps,
+ **kwargs,
+ )
+ return FlowSystem.from_dataset(ds) # from_dataset doesn't include solution
+
+ # --- Class methods for dataset operations (can be called without instance) ---
+
+ @classmethod
+ def _dataset_sel(
+ cls,
+ dataset: xr.Dataset,
+ time: str | slice | list[str] | pd.Timestamp | pd.DatetimeIndex | None = None,
+ period: int | slice | list[int] | pd.Index | None = None,
+ scenario: str | slice | list[str] | pd.Index | None = None,
+ hours_of_last_timestep: int | float | None = None,
+ hours_of_previous_timesteps: int | float | np.ndarray | None = None,
+ ) -> xr.Dataset:
+ """
+ Select subset of dataset by label.
+
+ Args:
+ dataset: xarray Dataset from FlowSystem.to_dataset()
+ time: Time selection (e.g., '2020-01', slice('2020-01-01', '2020-06-30'))
+ period: Period selection (e.g., 2020, slice(2020, 2022))
+ scenario: Scenario selection (e.g., 'Base Case', ['Base Case', 'High Demand'])
+ hours_of_last_timestep: Duration of the last timestep.
+ hours_of_previous_timesteps: Duration of previous timesteps.
+
+ Returns:
+ xr.Dataset: Selected dataset
+ """
+ from .flow_system import FlowSystem
+
+ indexers = {}
+ if time is not None:
+ indexers['time'] = time
+ if period is not None:
+ indexers['period'] = period
+ if scenario is not None:
+ indexers['scenario'] = scenario
+
+ if not indexers:
+ return dataset
+
+ result = dataset.sel(**indexers)
+
+ if 'time' in indexers:
+ result = FlowSystem._update_time_metadata(result, hours_of_last_timestep, hours_of_previous_timesteps)
+
+ if 'period' in indexers:
+ result = FlowSystem._update_period_metadata(result)
+
+ return result
+
+ @classmethod
+ def _dataset_isel(
+ cls,
+ dataset: xr.Dataset,
+ time: int | slice | list[int] | None = None,
+ period: int | slice | list[int] | None = None,
+ scenario: int | slice | list[int] | None = None,
+ hours_of_last_timestep: int | float | None = None,
+ hours_of_previous_timesteps: int | float | np.ndarray | None = None,
+ ) -> xr.Dataset:
+ """
+ Select subset of dataset by integer index.
+
+ Args:
+ dataset: xarray Dataset from FlowSystem.to_dataset()
+ time: Time selection by index
+ period: Period selection by index
+ scenario: Scenario selection by index
+ hours_of_last_timestep: Duration of the last timestep.
+ hours_of_previous_timesteps: Duration of previous timesteps.
+
+ Returns:
+ xr.Dataset: Selected dataset
+ """
+ from .flow_system import FlowSystem
+
+ indexers = {}
+ if time is not None:
+ indexers['time'] = time
+ if period is not None:
+ indexers['period'] = period
+ if scenario is not None:
+ indexers['scenario'] = scenario
+
+ if not indexers:
+ return dataset
+
+ result = dataset.isel(**indexers)
+
+ if 'time' in indexers:
+ result = FlowSystem._update_time_metadata(result, hours_of_last_timestep, hours_of_previous_timesteps)
+
+ if 'period' in indexers:
+ result = FlowSystem._update_period_metadata(result)
+
+ return result
+
+ @classmethod
+ def _dataset_resample(
+ cls,
+ dataset: xr.Dataset,
+ freq: str,
+ method: Literal['mean', 'sum', 'max', 'min', 'first', 'last', 'std', 'var', 'median', 'count'] = 'mean',
+ hours_of_last_timestep: int | float | None = None,
+ hours_of_previous_timesteps: int | float | np.ndarray | None = None,
+ **kwargs: Any,
+ ) -> xr.Dataset:
+ """
+ Resample dataset along time dimension.
+
+ Args:
+ dataset: xarray Dataset from FlowSystem.to_dataset()
+ freq: Resampling frequency (e.g., '2h', '1D', '1M')
+ method: Resampling method (e.g., 'mean', 'sum', 'first')
+ hours_of_last_timestep: Duration of the last timestep after resampling.
+ hours_of_previous_timesteps: Duration of previous timesteps after resampling.
+ **kwargs: Additional arguments passed to xarray.resample()
+
+ Returns:
+ xr.Dataset: Resampled dataset
+ """
+ from .flow_system import FlowSystem
+
+ available_methods = ['mean', 'sum', 'max', 'min', 'first', 'last', 'std', 'var', 'median', 'count']
+ if method not in available_methods:
+ raise ValueError(f'Unsupported resampling method: {method}. Available: {available_methods}')
+
+ original_attrs = dict(dataset.attrs)
+
+ time_var_names = [v for v in dataset.data_vars if 'time' in dataset[v].dims]
+ non_time_var_names = [v for v in dataset.data_vars if v not in time_var_names]
+
+ time_dataset = dataset[time_var_names]
+ resampled_time_dataset = cls._resample_by_dimension_groups(time_dataset, freq, method, **kwargs)
+
+ if non_time_var_names:
+ non_time_dataset = dataset[non_time_var_names]
+ result = xr.merge([resampled_time_dataset, non_time_dataset])
+ else:
+ result = resampled_time_dataset
+
+ result.attrs.update(original_attrs)
+ return FlowSystem._update_time_metadata(result, hours_of_last_timestep, hours_of_previous_timesteps)
+
+ @staticmethod
+ def _resample_by_dimension_groups(
+ time_dataset: xr.Dataset,
+ time: str,
+ method: str,
+ **kwargs: Any,
+ ) -> xr.Dataset:
+ """
+ Resample variables grouped by their dimension structure to avoid broadcasting.
+
+ Groups variables by their non-time dimensions before resampling for performance
+ and to prevent xarray from broadcasting variables with different dimensions.
+
+ Args:
+ time_dataset: Dataset containing only variables with time dimension
+ time: Resampling frequency (e.g., '2h', '1D', '1M')
+ method: Resampling method name (e.g., 'mean', 'sum', 'first')
+ **kwargs: Additional arguments passed to xarray.resample()
+
+ Returns:
+ Resampled dataset with original dimension structure preserved
+ """
+ dim_groups = defaultdict(list)
+ for var_name, var in time_dataset.data_vars.items():
+ dims_key = tuple(sorted(d for d in var.dims if d != 'time'))
+ dim_groups[dims_key].append(var_name)
+
+ if not dim_groups:
+ return getattr(time_dataset.resample(time=time, **kwargs), method)()
+
+ resampled_groups = []
+ for var_names in dim_groups.values():
+ if not var_names:
+ continue
+
+ stacked = xr.concat(
+ [time_dataset[name] for name in var_names],
+ dim=pd.Index(var_names, name='variable'),
+ combine_attrs='drop_conflicts',
+ )
+ resampled = getattr(stacked.resample(time=time, **kwargs), method)()
+ resampled_dataset = resampled.to_dataset(dim='variable')
+ resampled_groups.append(resampled_dataset)
+
+ if not resampled_groups:
+ return time_dataset
+
+ if len(resampled_groups) == 1:
+ return resampled_groups[0]
+
+ return xr.merge(resampled_groups, combine_attrs='drop_conflicts')
+
# Future methods can be added here:
#
# def mga(self, alternatives: int = 5) -> FlowSystem:
From 1601cac96b06f73c5f331b89516350d7cb132904 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Tue, 9 Dec 2025 22:06:30 +0100
Subject: [PATCH 19/49] Add recipies for plotting data (#516)
---
docs/user-guide/recipes/index.md | 21 +--
.../recipes/plotting-custom-data.md | 125 ++++++++++++++++++
mkdocs.yml | 4 +-
3 files changed, 133 insertions(+), 17 deletions(-)
create mode 100644 docs/user-guide/recipes/plotting-custom-data.md
diff --git a/docs/user-guide/recipes/index.md b/docs/user-guide/recipes/index.md
index 0317b2c70..38c7fa001 100644
--- a/docs/user-guide/recipes/index.md
+++ b/docs/user-guide/recipes/index.md
@@ -1,22 +1,10 @@
# Recipes
-**Coming Soon!** 🚧
+Short, focused code snippets showing **how to do specific things** in FlixOpt. Unlike full examples, recipes focus on a single concept.
-This section will contain quick, copy-paste ready code snippets for common FlixOpt patterns.
+## Available Recipes
----
-
-## What Will Be Here?
-
-Short, focused code snippets showing **how to do specific things** in FlixOpt:
-
-- Common modeling patterns
-- Integration with other tools
-- Performance optimizations
-- Domain-specific solutions
-- Data analysis shortcuts
-
-Unlike full examples, recipes will be focused snippets showing a single concept.
+- [Plotting Custom Data](plotting-custom-data.md) - Create faceted plots with your own xarray data using Plotly Express
---
@@ -37,9 +25,10 @@ Unlike full examples, recipes will be focused snippets showing a single concept.
## Want to Contribute?
-**We need your help!** If you have recurring modeling patterns or clever solutions to share, please contribute via [GitHub issues](https://github.com/flixopt/flixopt/issues) or pull requests.
+If you have recurring modeling patterns or clever solutions to share, please contribute via [GitHub issues](https://github.com/flixopt/flixopt/issues) or pull requests.
Guidelines:
+
1. Keep it short (< 100 lines of code)
2. Focus on one specific technique
3. Add brief explanation and when to use it
diff --git a/docs/user-guide/recipes/plotting-custom-data.md b/docs/user-guide/recipes/plotting-custom-data.md
new file mode 100644
index 000000000..3c539e6ce
--- /dev/null
+++ b/docs/user-guide/recipes/plotting-custom-data.md
@@ -0,0 +1,125 @@
+# Plotting Custom Data
+
+The plot accessor (`flow_system.statistics.plot`) is designed for visualizing optimization results using element labels. If you want to create faceted plots with your own custom data (not from a FlowSystem), you can use Plotly Express directly with xarray data.
+
+## Faceted Plots with Custom xarray Data
+
+The key is converting your xarray Dataset to a long-form DataFrame that Plotly Express expects:
+
+```python
+import xarray as xr
+import pandas as pd
+import plotly.express as px
+
+# Your custom xarray Dataset
+my_data = xr.Dataset({
+ 'Solar': (['time', 'scenario'], solar_values),
+ 'Wind': (['time', 'scenario'], wind_values),
+ 'Demand': (['time', 'scenario'], demand_values),
+}, coords={
+ 'time': timestamps,
+ 'scenario': ['Base', 'High RE', 'Low Demand']
+})
+
+# Convert to long-form DataFrame for Plotly Express
+df = (
+ my_data
+ .to_dataframe()
+ .reset_index()
+ .melt(
+ id_vars=['time', 'scenario'], # Keep as columns
+ var_name='variable',
+ value_name='value'
+ )
+)
+
+# Faceted stacked bar chart
+fig = px.bar(
+ df,
+ x='time',
+ y='value',
+ color='variable',
+ facet_col='scenario',
+ barmode='relative',
+ title='Energy Balance by Scenario'
+)
+fig.show()
+
+# Faceted line plot
+fig = px.line(
+ df,
+ x='time',
+ y='value',
+ color='variable',
+ facet_col='scenario'
+)
+fig.show()
+
+# Faceted area chart
+fig = px.area(
+ df,
+ x='time',
+ y='value',
+ color='variable',
+ facet_col='scenario'
+)
+fig.show()
+```
+
+## Common Plotly Express Faceting Options
+
+| Parameter | Description |
+|-----------|-------------|
+| `facet_col` | Dimension for column subplots |
+| `facet_row` | Dimension for row subplots |
+| `animation_frame` | Dimension for animation slider |
+| `facet_col_wrap` | Number of columns before wrapping |
+
+```python
+# Row and column facets
+fig = px.line(df, x='time', y='value', color='variable',
+ facet_col='scenario', facet_row='region')
+
+# Animation over time periods
+fig = px.bar(df, x='variable', y='value', color='variable',
+ animation_frame='period', barmode='group')
+
+# Wrap columns
+fig = px.line(df, x='time', y='value', color='variable',
+ facet_col='scenario', facet_col_wrap=2)
+```
+
+## Heatmaps with Custom Data
+
+For heatmaps, you can pass 2D arrays directly to `px.imshow`:
+
+```python
+import plotly.express as px
+
+# 2D data (e.g., days × hours)
+heatmap_data = my_data['Solar'].sel(scenario='Base').values.reshape(365, 24)
+
+fig = px.imshow(
+ heatmap_data,
+ labels={'x': 'Hour', 'y': 'Day', 'color': 'Power [kW]'},
+ aspect='auto',
+ color_continuous_scale='portland'
+)
+fig.show()
+
+# Faceted heatmaps using subplots
+from plotly.subplots import make_subplots
+import plotly.graph_objects as go
+
+scenarios = ['Base', 'High RE']
+fig = make_subplots(rows=1, cols=len(scenarios), subplot_titles=scenarios)
+
+for i, scenario in enumerate(scenarios, 1):
+ data = my_data['Solar'].sel(scenario=scenario).values.reshape(365, 24)
+ fig.add_trace(go.Heatmap(z=data, colorscale='portland'), row=1, col=i)
+
+fig.update_layout(title='Solar Output by Scenario')
+fig.show()
+```
+
+This approach gives you full control over your visualizations while leveraging Plotly's powerful faceting capabilities.
diff --git a/mkdocs.yml b/mkdocs.yml
index f966e76f7..278081889 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -37,7 +37,9 @@ nav:
- Investment: user-guide/mathematical-notation/features/InvestParameters.md
- Status: user-guide/mathematical-notation/features/StatusParameters.md
- Piecewise: user-guide/mathematical-notation/features/Piecewise.md
- - Recipes: user-guide/recipes/index.md
+ - Recipes:
+ - user-guide/recipes/index.md
+ - Plotting Custom Data: user-guide/recipes/plotting-custom-data.md
- Support:
- FAQ: user-guide/faq.md
- Troubleshooting: user-guide/troubleshooting.md
From 9faf98b44a1ea2fb11212ac1fcfbde6c8b0b1e3b Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Tue, 9 Dec 2025 22:09:16 +0100
Subject: [PATCH 20/49] Invalidate and lock FLow system based on solution
existance (#518)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
* fix: Link status parameters to flow_system
* ⏺ Summary
I've implemented the FlowSystem locking behavior as discussed. Here's what was done:
Core Concept
A FlowSystem is locked (read-only) when solution is not None.
New Features
1. is_locked property (flow_system.py:1127-1131)
- Returns True if the FlowSystem has a solution
2. reset() method (flow_system.py:1145-1168)
- Clears: solution, model, element submodels, variable/constraint names
- Returns self for method chaining
- Allows the FlowSystem to be modified and re-optimized
3. _invalidate_model() helper (flow_system.py:1133-1143)
- Called when adding elements/carriers to a FlowSystem with a model (but no solution)
- Clears model and element state
4. copy() method (flow_system.py:733-767)
- Creates a fresh FlowSystem copy without solution/model
- Supports copy.copy() and copy.deepcopy()
Behavior Changes
| Operation | Before Optimization | After build_model() | After optimize() |
|----------------|-------------------------------|------------------------------------|-------------------------------|
| add_elements() | ✓ Works | ⚠ Works, warns & invalidates model | ✗ RuntimeError |
| add_carriers() | ✓ Works | ⚠ Works, warns & invalidates model | ✗ RuntimeError |
| copy() | Returns copy without solution | Returns copy without solution | Returns copy without solution |
| reset() | No-op | Clears model | Clears solution & model |
Bug Fix
Fixed an issue where StatusParameters created during modeling (for prevent_simultaneous_flows and component-level status) weren't linked to the FlowSystem
(elements.py:957-964, components.py:731-732).
Tests
Added comprehensive tests in tests/test_flow_system_locking.py (28 tests) covering:
- is_locked property behavior
- add_elements() locking and invalidation
- add_carriers() locking and invalidation
- reset() method functionality
- copy() method functionality
- Loaded FlowSystem behavior
* Add invalidation tests
* Add link_to_flow_system method
* Add link_to_flow_system method
* New invalidate() method (flow_system.py:1232-1275)
A public method for manual model invalidation when modifying element attributes after connect_and_transform():
def invalidate(self) -> FlowSystem:
"""Invalidate the model to allow re-transformation after modifying elements."""
- Raises RuntimeError if FlowSystem has a solution (must call reset() first)
- Returns self for method chaining
- Useful when you need to modify after connect_and_transform() but before optimize()
2. Updated docstrings
connect_and_transform() - Added comprehensive docstring explaining:
- What steps it performs
- Warning that attributes become xarray DataArrays after transformation
- Note about idempotency and how to reset with invalidate()
_invalidate_model() - Clarified its role and relationship to public methods
3. New tests (test_flow_system_locking.py:285-409)
Added TestInvalidate class with 8 tests:
- test_invalidate_resets_connected_and_transformed
- test_invalidate_clears_model
- test_invalidate_raises_when_locked
- test_invalidate_returns_self
- test_invalidate_allows_retransformation
- test_modify_element_and_invalidate - full workflow with reset
- test_invalidate_needed_after_transform_before_optimize - pre-optimization modification
- test_reset_already_invalidates - confirms reset already handles invalidation
Key insight from testing
reset() already calls _invalidate_model(), so modifications after reset() automatically take effect on the next optimize(). The new invalidate() method is primarily for the case where:
1. You've called connect_and_transform() manually
2. Haven't optimized yet (no solution)
3. Need to modify element attributes
* Typo
---
flixopt/components.py | 62 ++---
flixopt/effects.py | 38 +--
flixopt/elements.py | 91 ++++---
flixopt/flow_system.py | 205 ++++++++++++++-
flixopt/interface.py | 96 +++----
flixopt/structure.py | 50 +++-
tests/test_flow_system_locking.py | 403 ++++++++++++++++++++++++++++++
7 files changed, 793 insertions(+), 152 deletions(-)
create mode 100644 tests/test_flow_system_locking.py
diff --git a/flixopt/components.py b/flixopt/components.py
index 0cfed39eb..c5913c8e2 100644
--- a/flixopt/components.py
+++ b/flixopt/components.py
@@ -180,11 +180,11 @@ def create_model(self, model: FlowSystemModel) -> LinearConverterModel:
self.submodel = LinearConverterModel(model, self)
return self.submodel
- def _set_flow_system(self, flow_system) -> None:
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
"""Propagate flow_system reference to parent Component and piecewise_conversion."""
- super()._set_flow_system(flow_system)
+ super().link_to_flow_system(flow_system, prefix)
if self.piecewise_conversion is not None:
- self.piecewise_conversion._set_flow_system(flow_system)
+ self.piecewise_conversion.link_to_flow_system(flow_system, self._sub_prefix('PiecewiseConversion'))
def _plausibility_checks(self) -> None:
super()._plausibility_checks()
@@ -216,14 +216,13 @@ def _plausibility_checks(self) -> None:
f'({flow.label_full}).'
)
- def transform_data(self, name_prefix: str = '') -> None:
- prefix = '|'.join(filter(None, [name_prefix, self.label_full]))
- super().transform_data(prefix)
+ def transform_data(self) -> None:
+ super().transform_data()
if self.conversion_factors:
self.conversion_factors = self._transform_conversion_factors()
if self.piecewise_conversion:
self.piecewise_conversion.has_time_dim = True
- self.piecewise_conversion.transform_data(f'{prefix}|PiecewiseConversion')
+ self.piecewise_conversion.transform_data()
def _transform_conversion_factors(self) -> list[dict[str, xr.DataArray]]:
"""Converts all conversion factors to internal datatypes"""
@@ -427,49 +426,50 @@ def create_model(self, model: FlowSystemModel) -> StorageModel:
self.submodel = StorageModel(model, self)
return self.submodel
- def _set_flow_system(self, flow_system) -> None:
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
"""Propagate flow_system reference to parent Component and capacity_in_flow_hours if it's InvestParameters."""
- super()._set_flow_system(flow_system)
+ super().link_to_flow_system(flow_system, prefix)
if isinstance(self.capacity_in_flow_hours, InvestParameters):
- self.capacity_in_flow_hours._set_flow_system(flow_system)
+ self.capacity_in_flow_hours.link_to_flow_system(flow_system, self._sub_prefix('InvestParameters'))
- def transform_data(self, name_prefix: str = '') -> None:
- prefix = '|'.join(filter(None, [name_prefix, self.label_full]))
- super().transform_data(prefix)
+ def transform_data(self) -> None:
+ super().transform_data()
self.relative_minimum_charge_state = self._fit_coords(
- f'{prefix}|relative_minimum_charge_state', self.relative_minimum_charge_state
+ f'{self.prefix}|relative_minimum_charge_state', self.relative_minimum_charge_state
)
self.relative_maximum_charge_state = self._fit_coords(
- f'{prefix}|relative_maximum_charge_state', self.relative_maximum_charge_state
+ f'{self.prefix}|relative_maximum_charge_state', self.relative_maximum_charge_state
+ )
+ self.eta_charge = self._fit_coords(f'{self.prefix}|eta_charge', self.eta_charge)
+ self.eta_discharge = self._fit_coords(f'{self.prefix}|eta_discharge', self.eta_discharge)
+ self.relative_loss_per_hour = self._fit_coords(
+ f'{self.prefix}|relative_loss_per_hour', self.relative_loss_per_hour
)
- self.eta_charge = self._fit_coords(f'{prefix}|eta_charge', self.eta_charge)
- self.eta_discharge = self._fit_coords(f'{prefix}|eta_discharge', self.eta_discharge)
- self.relative_loss_per_hour = self._fit_coords(f'{prefix}|relative_loss_per_hour', self.relative_loss_per_hour)
if not isinstance(self.initial_charge_state, str):
self.initial_charge_state = self._fit_coords(
- f'{prefix}|initial_charge_state', self.initial_charge_state, dims=['period', 'scenario']
+ f'{self.prefix}|initial_charge_state', self.initial_charge_state, dims=['period', 'scenario']
)
self.minimal_final_charge_state = self._fit_coords(
- f'{prefix}|minimal_final_charge_state', self.minimal_final_charge_state, dims=['period', 'scenario']
+ f'{self.prefix}|minimal_final_charge_state', self.minimal_final_charge_state, dims=['period', 'scenario']
)
self.maximal_final_charge_state = self._fit_coords(
- f'{prefix}|maximal_final_charge_state', self.maximal_final_charge_state, dims=['period', 'scenario']
+ f'{self.prefix}|maximal_final_charge_state', self.maximal_final_charge_state, dims=['period', 'scenario']
)
self.relative_minimum_final_charge_state = self._fit_coords(
- f'{prefix}|relative_minimum_final_charge_state',
+ f'{self.prefix}|relative_minimum_final_charge_state',
self.relative_minimum_final_charge_state,
dims=['period', 'scenario'],
)
self.relative_maximum_final_charge_state = self._fit_coords(
- f'{prefix}|relative_maximum_final_charge_state',
+ f'{self.prefix}|relative_maximum_final_charge_state',
self.relative_maximum_final_charge_state,
dims=['period', 'scenario'],
)
if isinstance(self.capacity_in_flow_hours, InvestParameters):
- self.capacity_in_flow_hours.transform_data(f'{prefix}|InvestParameters')
+ self.capacity_in_flow_hours.transform_data()
else:
self.capacity_in_flow_hours = self._fit_coords(
- f'{prefix}|capacity_in_flow_hours', self.capacity_in_flow_hours, dims=['period', 'scenario']
+ f'{self.prefix}|capacity_in_flow_hours', self.capacity_in_flow_hours, dims=['period', 'scenario']
)
def _plausibility_checks(self) -> None:
@@ -714,11 +714,10 @@ def create_model(self, model) -> TransmissionModel:
self.submodel = TransmissionModel(model, self)
return self.submodel
- def transform_data(self, name_prefix: str = '') -> None:
- prefix = '|'.join(filter(None, [name_prefix, self.label_full]))
- super().transform_data(prefix)
- self.relative_losses = self._fit_coords(f'{prefix}|relative_losses', self.relative_losses)
- self.absolute_losses = self._fit_coords(f'{prefix}|absolute_losses', self.absolute_losses)
+ def transform_data(self) -> None:
+ super().transform_data()
+ self.relative_losses = self._fit_coords(f'{self.prefix}|relative_losses', self.relative_losses)
+ self.absolute_losses = self._fit_coords(f'{self.prefix}|absolute_losses', self.absolute_losses)
class TransmissionModel(ComponentModel):
@@ -729,6 +728,9 @@ def __init__(self, model: FlowSystemModel, element: Transmission):
for flow in element.inputs + element.outputs:
if flow.status_parameters is None:
flow.status_parameters = StatusParameters()
+ flow.status_parameters.link_to_flow_system(
+ model.flow_system, f'{flow.label_full}|status_parameters'
+ )
super().__init__(model, element)
diff --git a/flixopt/effects.py b/flixopt/effects.py
index 5dd53258f..a7aae4bf4 100644
--- a/flixopt/effects.py
+++ b/flixopt/effects.py
@@ -237,50 +237,56 @@ def __init__(
self.minimum_over_periods = minimum_over_periods
self.maximum_over_periods = maximum_over_periods
- def transform_data(self, name_prefix: str = '') -> None:
- prefix = '|'.join(filter(None, [name_prefix, self.label_full]))
- self.minimum_per_hour = self._fit_coords(f'{prefix}|minimum_per_hour', self.minimum_per_hour)
- self.maximum_per_hour = self._fit_coords(f'{prefix}|maximum_per_hour', self.maximum_per_hour)
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
+ """Link this effect to a FlowSystem.
+
+ Elements use their label_full as prefix by default, ignoring the passed prefix.
+ """
+ super().link_to_flow_system(flow_system, self.label_full)
+
+ def transform_data(self) -> None:
+ self.minimum_per_hour = self._fit_coords(f'{self.prefix}|minimum_per_hour', self.minimum_per_hour)
+ self.maximum_per_hour = self._fit_coords(f'{self.prefix}|maximum_per_hour', self.maximum_per_hour)
self.share_from_temporal = self._fit_effect_coords(
prefix=None,
effect_values=self.share_from_temporal,
- suffix=f'(temporal)->{prefix}(temporal)',
+ suffix=f'(temporal)->{self.prefix}(temporal)',
dims=['time', 'period', 'scenario'],
)
self.share_from_periodic = self._fit_effect_coords(
prefix=None,
effect_values=self.share_from_periodic,
- suffix=f'(periodic)->{prefix}(periodic)',
+ suffix=f'(periodic)->{self.prefix}(periodic)',
dims=['period', 'scenario'],
)
self.minimum_temporal = self._fit_coords(
- f'{prefix}|minimum_temporal', self.minimum_temporal, dims=['period', 'scenario']
+ f'{self.prefix}|minimum_temporal', self.minimum_temporal, dims=['period', 'scenario']
)
self.maximum_temporal = self._fit_coords(
- f'{prefix}|maximum_temporal', self.maximum_temporal, dims=['period', 'scenario']
+ f'{self.prefix}|maximum_temporal', self.maximum_temporal, dims=['period', 'scenario']
)
self.minimum_periodic = self._fit_coords(
- f'{prefix}|minimum_periodic', self.minimum_periodic, dims=['period', 'scenario']
+ f'{self.prefix}|minimum_periodic', self.minimum_periodic, dims=['period', 'scenario']
)
self.maximum_periodic = self._fit_coords(
- f'{prefix}|maximum_periodic', self.maximum_periodic, dims=['period', 'scenario']
+ f'{self.prefix}|maximum_periodic', self.maximum_periodic, dims=['period', 'scenario']
)
self.minimum_total = self._fit_coords(
- f'{prefix}|minimum_total', self.minimum_total, dims=['period', 'scenario']
+ f'{self.prefix}|minimum_total', self.minimum_total, dims=['period', 'scenario']
)
self.maximum_total = self._fit_coords(
- f'{prefix}|maximum_total', self.maximum_total, dims=['period', 'scenario']
+ f'{self.prefix}|maximum_total', self.maximum_total, dims=['period', 'scenario']
)
self.minimum_over_periods = self._fit_coords(
- f'{prefix}|minimum_over_periods', self.minimum_over_periods, dims=['scenario']
+ f'{self.prefix}|minimum_over_periods', self.minimum_over_periods, dims=['scenario']
)
self.maximum_over_periods = self._fit_coords(
- f'{prefix}|maximum_over_periods', self.maximum_over_periods, dims=['scenario']
+ f'{self.prefix}|maximum_over_periods', self.maximum_over_periods, dims=['scenario']
)
self.period_weights = self._fit_coords(
- f'{prefix}|period_weights', self.period_weights, dims=['period', 'scenario']
+ f'{self.prefix}|period_weights', self.period_weights, dims=['period', 'scenario']
)
def create_model(self, model: FlowSystemModel) -> EffectModel:
@@ -670,7 +676,7 @@ def _do_modeling(self):
penalty_effect = self.effects._create_penalty_effect()
# Link to FlowSystem (should already be linked, but ensure it)
if penalty_effect._flow_system is None:
- penalty_effect._set_flow_system(self._model.flow_system)
+ penalty_effect.link_to_flow_system(self._model.flow_system)
# Create EffectModel for each effect
for effect in self.effects.values():
diff --git a/flixopt/elements.py b/flixopt/elements.py
index d2ebf7ac0..d97ff3ffb 100644
--- a/flixopt/elements.py
+++ b/flixopt/elements.py
@@ -20,7 +20,6 @@
Element,
ElementModel,
FlowSystemModel,
- Interface,
register_class_for_io,
)
@@ -111,21 +110,23 @@ def create_model(self, model: FlowSystemModel) -> ComponentModel:
self.submodel = ComponentModel(model, self)
return self.submodel
- def _set_flow_system(self, flow_system) -> None:
- """Propagate flow_system reference to nested Interface objects and flows."""
- super()._set_flow_system(flow_system)
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
+ """Propagate flow_system reference to nested Interface objects and flows.
+
+ Elements use their label_full as prefix by default, ignoring the passed prefix.
+ """
+ super().link_to_flow_system(flow_system, self.label_full)
if self.status_parameters is not None:
- self.status_parameters._set_flow_system(flow_system)
+ self.status_parameters.link_to_flow_system(flow_system, self._sub_prefix('status_parameters'))
for flow in self.inputs + self.outputs:
- flow._set_flow_system(flow_system)
+ flow.link_to_flow_system(flow_system)
- def transform_data(self, name_prefix: str = '') -> None:
- prefix = '|'.join(filter(None, [name_prefix, self.label_full]))
+ def transform_data(self) -> None:
if self.status_parameters is not None:
- self.status_parameters.transform_data(prefix)
+ self.status_parameters.transform_data()
for flow in self.inputs + self.outputs:
- flow.transform_data() # Flow doesnt need the name_prefix
+ flow.transform_data()
def _check_unique_flow_labels(self):
all_flow_labels = [flow.label for flow in self.inputs + self.outputs]
@@ -269,16 +270,18 @@ def create_model(self, model: FlowSystemModel) -> BusModel:
self.submodel = BusModel(model, self)
return self.submodel
- def _set_flow_system(self, flow_system) -> None:
- """Propagate flow_system reference to nested flows."""
- super()._set_flow_system(flow_system)
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
+ """Propagate flow_system reference to nested flows.
+
+ Elements use their label_full as prefix by default, ignoring the passed prefix.
+ """
+ super().link_to_flow_system(flow_system, self.label_full)
for flow in self.inputs + self.outputs:
- flow._set_flow_system(flow_system)
+ flow.link_to_flow_system(flow_system)
- def transform_data(self, name_prefix: str = '') -> None:
- prefix = '|'.join(filter(None, [name_prefix, self.label_full]))
+ def transform_data(self) -> None:
self.imbalance_penalty_per_flow_hour = self._fit_coords(
- f'{prefix}|imbalance_penalty_per_flow_hour', self.imbalance_penalty_per_flow_hour
+ f'{self.prefix}|imbalance_penalty_per_flow_hour', self.imbalance_penalty_per_flow_hour
)
def _plausibility_checks(self) -> None:
@@ -505,45 +508,49 @@ def create_model(self, model: FlowSystemModel) -> FlowModel:
self.submodel = FlowModel(model, self)
return self.submodel
- def _set_flow_system(self, flow_system) -> None:
- """Propagate flow_system reference to nested Interface objects."""
- super()._set_flow_system(flow_system)
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
+ """Propagate flow_system reference to nested Interface objects.
+
+ Elements use their label_full as prefix by default, ignoring the passed prefix.
+ """
+ super().link_to_flow_system(flow_system, self.label_full)
if self.status_parameters is not None:
- self.status_parameters._set_flow_system(flow_system)
- if isinstance(self.size, Interface):
- self.size._set_flow_system(flow_system)
-
- def transform_data(self, name_prefix: str = '') -> None:
- prefix = '|'.join(filter(None, [name_prefix, self.label_full]))
- self.relative_minimum = self._fit_coords(f'{prefix}|relative_minimum', self.relative_minimum)
- self.relative_maximum = self._fit_coords(f'{prefix}|relative_maximum', self.relative_maximum)
- self.fixed_relative_profile = self._fit_coords(f'{prefix}|fixed_relative_profile', self.fixed_relative_profile)
- self.effects_per_flow_hour = self._fit_effect_coords(prefix, self.effects_per_flow_hour, 'per_flow_hour')
+ self.status_parameters.link_to_flow_system(flow_system, self._sub_prefix('status_parameters'))
+ if isinstance(self.size, InvestParameters):
+ self.size.link_to_flow_system(flow_system, self._sub_prefix('InvestParameters'))
+
+ def transform_data(self) -> None:
+ self.relative_minimum = self._fit_coords(f'{self.prefix}|relative_minimum', self.relative_minimum)
+ self.relative_maximum = self._fit_coords(f'{self.prefix}|relative_maximum', self.relative_maximum)
+ self.fixed_relative_profile = self._fit_coords(
+ f'{self.prefix}|fixed_relative_profile', self.fixed_relative_profile
+ )
+ self.effects_per_flow_hour = self._fit_effect_coords(self.prefix, self.effects_per_flow_hour, 'per_flow_hour')
self.flow_hours_max = self._fit_coords(
- f'{prefix}|flow_hours_max', self.flow_hours_max, dims=['period', 'scenario']
+ f'{self.prefix}|flow_hours_max', self.flow_hours_max, dims=['period', 'scenario']
)
self.flow_hours_min = self._fit_coords(
- f'{prefix}|flow_hours_min', self.flow_hours_min, dims=['period', 'scenario']
+ f'{self.prefix}|flow_hours_min', self.flow_hours_min, dims=['period', 'scenario']
)
self.flow_hours_max_over_periods = self._fit_coords(
- f'{prefix}|flow_hours_max_over_periods', self.flow_hours_max_over_periods, dims=['scenario']
+ f'{self.prefix}|flow_hours_max_over_periods', self.flow_hours_max_over_periods, dims=['scenario']
)
self.flow_hours_min_over_periods = self._fit_coords(
- f'{prefix}|flow_hours_min_over_periods', self.flow_hours_min_over_periods, dims=['scenario']
+ f'{self.prefix}|flow_hours_min_over_periods', self.flow_hours_min_over_periods, dims=['scenario']
)
self.load_factor_max = self._fit_coords(
- f'{prefix}|load_factor_max', self.load_factor_max, dims=['period', 'scenario']
+ f'{self.prefix}|load_factor_max', self.load_factor_max, dims=['period', 'scenario']
)
self.load_factor_min = self._fit_coords(
- f'{prefix}|load_factor_min', self.load_factor_min, dims=['period', 'scenario']
+ f'{self.prefix}|load_factor_min', self.load_factor_min, dims=['period', 'scenario']
)
if self.status_parameters is not None:
- self.status_parameters.transform_data(prefix)
+ self.status_parameters.transform_data()
if isinstance(self.size, InvestParameters):
- self.size.transform_data(prefix)
+ self.size.transform_data()
else:
- self.size = self._fit_coords(f'{prefix}|size', self.size, dims=['period', 'scenario'])
+ self.size = self._fit_coords(f'{self.prefix}|size', self.size, dims=['period', 'scenario'])
def _plausibility_checks(self) -> None:
# TODO: Incorporate into Variable? (Lower_bound can not be greater than upper bound
@@ -955,11 +962,17 @@ def _do_modeling(self):
for flow in all_flows:
if flow.status_parameters is None:
flow.status_parameters = StatusParameters()
+ flow.status_parameters.link_to_flow_system(
+ self._model.flow_system, f'{flow.label_full}|status_parameters'
+ )
if self.element.prevent_simultaneous_flows:
for flow in self.element.prevent_simultaneous_flows:
if flow.status_parameters is None:
flow.status_parameters = StatusParameters()
+ flow.status_parameters.link_to_flow_system(
+ self._model.flow_system, f'{flow.label_full}|status_parameters'
+ )
# Create FlowModels (which creates their variables and constraints)
for flow in all_flows:
diff --git a/flixopt/flow_system.py b/flixopt/flow_system.py
index 153354cce..bae700b85 100644
--- a/flixopt/flow_system.py
+++ b/flixopt/flow_system.py
@@ -730,6 +730,50 @@ def from_netcdf(cls, path: str | pathlib.Path) -> FlowSystem:
flow_system.name = path.stem
return flow_system
+ def copy(self) -> FlowSystem:
+ """Create a copy of the FlowSystem without optimization state.
+
+ Creates a new FlowSystem with copies of all elements, but without:
+ - The solution dataset
+ - The optimization model
+ - Element submodels and variable/constraint names
+
+ This is useful for creating variations of a FlowSystem for different
+ optimization scenarios without affecting the original.
+
+ Returns:
+ A new FlowSystem instance that can be modified and optimized independently.
+
+ Examples:
+ >>> original = FlowSystem(timesteps)
+ >>> original.add_elements(boiler, bus)
+ >>> original.optimize(solver) # Original now has solution
+ >>>
+ >>> # Create a copy to try different parameters
+ >>> variant = original.copy() # No solution, can be modified
+ >>> variant.add_elements(new_component)
+ >>> variant.optimize(solver)
+ """
+ # Temporarily clear solution to use standard serialization without solution data
+ original_solution = self._solution
+ self._solution = None
+ try:
+ ds = self.to_dataset()
+ finally:
+ self._solution = original_solution
+
+ # Create new FlowSystem from dataset (without solution)
+ new_fs = FlowSystem.from_dataset(ds.copy(deep=True))
+ return new_fs
+
+ def __copy__(self):
+ """Support for copy.copy()."""
+ return self.copy()
+
+ def __deepcopy__(self, memo):
+ """Support for copy.deepcopy()."""
+ return self.copy()
+
def get_structure(self, clean: bool = False, stats: bool = False) -> dict:
"""
Get FlowSystem structure.
@@ -827,7 +871,31 @@ def fit_effects_to_model_coords(
}
def connect_and_transform(self):
- """Transform data for all elements using the new simplified approach."""
+ """Connect the network and transform all element data to model coordinates.
+
+ This method performs the following steps:
+
+ 1. Connects flows to buses (establishing the network topology)
+ 2. Registers any missing carriers from CONFIG defaults
+ 3. Assigns colors to elements without explicit colors
+ 4. Transforms all element data to xarray DataArrays aligned with
+ FlowSystem coordinates (time, period, scenario)
+ 5. Validates system integrity
+
+ This is called automatically by :meth:`build_model` and :meth:`optimize`.
+
+ Warning:
+ After this method runs, element attributes (e.g., ``flow.size``,
+ ``flow.relative_minimum``) contain transformed xarray DataArrays,
+ not the original input values. If you modify element attributes after
+ transformation, call :meth:`invalidate` to ensure the changes take
+ effect on the next optimization.
+
+ Note:
+ This method is idempotent within a single model lifecycle - calling
+ it multiple times has no effect once ``connected_and_transformed``
+ is True. Use :meth:`invalidate` to reset this flag.
+ """
if self.connected_and_transformed:
logger.debug('FlowSystem already connected and transformed')
return
@@ -884,13 +952,23 @@ def add_elements(self, *elements: Element) -> None:
Args:
*elements: childs of Element like Boiler, HeatPump, Bus,...
modeling Elements
+
+ Raises:
+ RuntimeError: If the FlowSystem is locked (has a solution).
+ Call `reset()` to unlock it first.
"""
- if self.connected_and_transformed:
+ if self.is_locked:
+ raise RuntimeError(
+ 'Cannot add elements to a FlowSystem that has a solution. '
+ 'Call `reset()` first to clear the solution and allow modifications.'
+ )
+
+ if self.model is not None:
warnings.warn(
- 'You are adding elements to an already connected FlowSystem. This is not recommended (But it works).',
+ 'Adding elements to a FlowSystem with an existing model. The model will be invalidated.',
stacklevel=2,
)
- self._connected_and_transformed = False
+ self._invalidate_model()
for new_element in list(elements):
# Validate element type first
@@ -924,6 +1002,10 @@ def add_carriers(self, *carriers: Carrier) -> None:
Args:
carrier: A Carrier object defining the carrier properties.
+ Raises:
+ RuntimeError: If the FlowSystem is locked (has a solution).
+ Call `reset()` to unlock it first.
+
Examples:
```python
import flixopt as fx
@@ -941,12 +1023,18 @@ def add_carriers(self, *carriers: Carrier) -> None:
# The carrier color will be used in plots automatically
```
"""
- if self.connected_and_transformed:
+ if self.is_locked:
+ raise RuntimeError(
+ 'Cannot add carriers to a FlowSystem that has a solution. '
+ 'Call `reset()` first to clear the solution and allow modifications.'
+ )
+
+ if self.model is not None:
warnings.warn(
- 'You are adding a carrier to an already connected FlowSystem. This is not recommended (But it works).',
+ 'Adding carriers to a FlowSystem with an existing model. The model will be invalidated.',
stacklevel=2,
)
- self._connected_and_transformed = False
+ self._invalidate_model()
for carrier in list(carriers):
if not isinstance(carrier, Carrier):
@@ -1120,6 +1208,103 @@ def solution(self, value: xr.Dataset | None) -> None:
self._solution = value
self._statistics = None # Invalidate cached statistics
+ @property
+ def is_locked(self) -> bool:
+ """Check if the FlowSystem is locked (has a solution).
+
+ A locked FlowSystem cannot be modified. Use `reset()` to unlock it.
+ """
+ return self._solution is not None
+
+ def _invalidate_model(self) -> None:
+ """Invalidate the model and element submodels when structure changes.
+
+ This clears the model, resets the ``connected_and_transformed`` flag,
+ and clears all element submodels and variable/constraint names.
+
+ Called internally by :meth:`add_elements`, :meth:`add_carriers`,
+ :meth:`reset`, and :meth:`invalidate`.
+
+ See Also:
+ :meth:`invalidate`: Public method for manual invalidation.
+ :meth:`reset`: Clears solution and invalidates (for locked FlowSystems).
+ """
+ self.model = None
+ self._connected_and_transformed = False
+ for element in self.values():
+ element.submodel = None
+ element._variable_names = []
+ element._constraint_names = []
+
+ def reset(self) -> FlowSystem:
+ """Clear optimization state to allow modifications.
+
+ This method unlocks the FlowSystem by clearing:
+ - The solution dataset
+ - The optimization model
+ - All element submodels and variable/constraint names
+ - The connected_and_transformed flag
+
+ After calling reset(), the FlowSystem can be modified again
+ (e.g., adding elements or carriers).
+
+ Returns:
+ Self, for method chaining.
+
+ Examples:
+ >>> flow_system.optimize(solver) # FlowSystem is now locked
+ >>> flow_system.add_elements(new_bus) # Raises RuntimeError
+ >>> flow_system.reset() # Unlock the FlowSystem
+ >>> flow_system.add_elements(new_bus) # Now works
+ """
+ self.solution = None # Also clears _statistics via setter
+ self._invalidate_model()
+ return self
+
+ def invalidate(self) -> FlowSystem:
+ """Invalidate the model to allow re-transformation after modifying elements.
+
+ Call this after modifying existing element attributes (e.g., ``flow.size``,
+ ``flow.relative_minimum``) to ensure changes take effect on the next
+ optimization. The next call to :meth:`optimize` or :meth:`build_model`
+ will re-run :meth:`connect_and_transform`.
+
+ Note:
+ Adding new elements via :meth:`add_elements` automatically invalidates
+ the model. This method is only needed when modifying attributes of
+ elements that are already part of the FlowSystem.
+
+ Returns:
+ Self, for method chaining.
+
+ Raises:
+ RuntimeError: If the FlowSystem has a solution. Call :meth:`reset`
+ first to clear the solution.
+
+ Examples:
+ Modify a flow's size and re-optimize:
+
+ >>> flow_system.optimize(solver)
+ >>> flow_system.reset() # Clear solution first
+ >>> flow_system.components['Boiler'].inputs[0].size = 200
+ >>> flow_system.invalidate()
+ >>> flow_system.optimize(solver) # Re-runs connect_and_transform
+
+ Modify before first optimization:
+
+ >>> flow_system.connect_and_transform()
+ >>> # Oops, need to change something
+ >>> flow_system.components['Boiler'].inputs[0].size = 200
+ >>> flow_system.invalidate()
+ >>> flow_system.optimize(solver) # Changes take effect
+ """
+ if self.is_locked:
+ raise RuntimeError(
+ 'Cannot invalidate a FlowSystem with a solution. Call `reset()` first to clear the solution.'
+ )
+ self._invalidate_model()
+ return self
+
@property
def optimize(self) -> OptimizeAccessor:
"""
@@ -1345,12 +1530,12 @@ def _validate_system_integrity(self) -> None:
def _add_effects(self, *args: Effect) -> None:
for effect in args:
- effect._set_flow_system(self) # Link element to FlowSystem
+ effect.link_to_flow_system(self) # Link element to FlowSystem
self.effects.add_effects(*args)
def _add_components(self, *components: Component) -> None:
for new_component in list(components):
- new_component._set_flow_system(self) # Link element to FlowSystem
+ new_component.link_to_flow_system(self) # Link element to FlowSystem
self.components.add(new_component) # Add to existing components
# Invalidate cache once after all additions
if components:
@@ -1358,7 +1543,7 @@ def _add_components(self, *components: Component) -> None:
def _add_buses(self, *buses: Bus):
for new_bus in list(buses):
- new_bus._set_flow_system(self) # Link element to FlowSystem
+ new_bus.link_to_flow_system(self) # Link element to FlowSystem
self.buses.add(new_bus) # Add to existing buses
# Invalidate cache once after all additions
if buses:
diff --git a/flixopt/interface.py b/flixopt/interface.py
index 7995d5e78..7787eec18 100644
--- a/flixopt/interface.py
+++ b/flixopt/interface.py
@@ -74,10 +74,10 @@ def __init__(self, start: Numeric_TPS, end: Numeric_TPS):
self.end = end
self.has_time_dim = False
- def transform_data(self, name_prefix: str = '') -> None:
+ def transform_data(self) -> None:
dims = None if self.has_time_dim else ['period', 'scenario']
- self.start = self._fit_coords(f'{name_prefix}|start', self.start, dims=dims)
- self.end = self._fit_coords(f'{name_prefix}|end', self.end, dims=dims)
+ self.start = self._fit_coords(f'{self.prefix}|start', self.start, dims=dims)
+ self.end = self._fit_coords(f'{self.prefix}|end', self.end, dims=dims)
@register_class_for_io
@@ -226,15 +226,15 @@ def __getitem__(self, index) -> Piece:
def __iter__(self) -> Iterator[Piece]:
return iter(self.pieces) # Enables iteration like for piece in piecewise: ...
- def _set_flow_system(self, flow_system) -> None:
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
"""Propagate flow_system reference to nested Piece objects."""
- super()._set_flow_system(flow_system)
- for piece in self.pieces:
- piece._set_flow_system(flow_system)
-
- def transform_data(self, name_prefix: str = '') -> None:
+ super().link_to_flow_system(flow_system, prefix)
for i, piece in enumerate(self.pieces):
- piece.transform_data(f'{name_prefix}|Piece{i}')
+ piece.link_to_flow_system(flow_system, self._sub_prefix(f'Piece{i}'))
+
+ def transform_data(self) -> None:
+ for piece in self.pieces:
+ piece.transform_data()
@register_class_for_io
@@ -458,15 +458,15 @@ def items(self):
"""
return self.piecewises.items()
- def _set_flow_system(self, flow_system) -> None:
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
"""Propagate flow_system reference to nested Piecewise objects."""
- super()._set_flow_system(flow_system)
- for piecewise in self.piecewises.values():
- piecewise._set_flow_system(flow_system)
-
- def transform_data(self, name_prefix: str = '') -> None:
+ super().link_to_flow_system(flow_system, prefix)
for name, piecewise in self.piecewises.items():
- piecewise.transform_data(f'{name_prefix}|{name}')
+ piecewise.link_to_flow_system(flow_system, self._sub_prefix(name))
+
+ def transform_data(self) -> None:
+ for piecewise in self.piecewises.values():
+ piecewise.transform_data()
@register_class_for_io
@@ -676,17 +676,17 @@ def has_time_dim(self, value):
for piecewise in self.piecewise_shares.values():
piecewise.has_time_dim = value
- def _set_flow_system(self, flow_system) -> None:
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
"""Propagate flow_system reference to nested Piecewise objects."""
- super()._set_flow_system(flow_system)
- self.piecewise_origin._set_flow_system(flow_system)
- for piecewise in self.piecewise_shares.values():
- piecewise._set_flow_system(flow_system)
-
- def transform_data(self, name_prefix: str = '') -> None:
- self.piecewise_origin.transform_data(f'{name_prefix}|PiecewiseEffects|origin')
+ super().link_to_flow_system(flow_system, prefix)
+ self.piecewise_origin.link_to_flow_system(flow_system, self._sub_prefix('origin'))
for effect, piecewise in self.piecewise_shares.items():
- piecewise.transform_data(f'{name_prefix}|PiecewiseEffects|{effect}')
+ piecewise.link_to_flow_system(flow_system, self._sub_prefix(effect))
+
+ def transform_data(self) -> None:
+ self.piecewise_origin.transform_data()
+ for piecewise in self.piecewise_shares.values():
+ piecewise.transform_data()
@register_class_for_io
@@ -904,27 +904,27 @@ def __init__(
self.maximum_size = maximum_size if maximum_size is not None else CONFIG.Modeling.big # default maximum
self.linked_periods = linked_periods
- def _set_flow_system(self, flow_system) -> None:
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
"""Propagate flow_system reference to nested PiecewiseEffects object if present."""
- super()._set_flow_system(flow_system)
+ super().link_to_flow_system(flow_system, prefix)
if self.piecewise_effects_of_investment is not None:
- self.piecewise_effects_of_investment._set_flow_system(flow_system)
+ self.piecewise_effects_of_investment.link_to_flow_system(flow_system, self._sub_prefix('PiecewiseEffects'))
- def transform_data(self, name_prefix: str = '') -> None:
+ def transform_data(self) -> None:
self.effects_of_investment = self._fit_effect_coords(
- prefix=name_prefix,
+ prefix=self.prefix,
effect_values=self.effects_of_investment,
suffix='effects_of_investment',
dims=['period', 'scenario'],
)
self.effects_of_retirement = self._fit_effect_coords(
- prefix=name_prefix,
+ prefix=self.prefix,
effect_values=self.effects_of_retirement,
suffix='effects_of_retirement',
dims=['period', 'scenario'],
)
self.effects_of_investment_per_size = self._fit_effect_coords(
- prefix=name_prefix,
+ prefix=self.prefix,
effect_values=self.effects_of_investment_per_size,
suffix='effects_of_investment_per_size',
dims=['period', 'scenario'],
@@ -932,13 +932,13 @@ def transform_data(self, name_prefix: str = '') -> None:
if self.piecewise_effects_of_investment is not None:
self.piecewise_effects_of_investment.has_time_dim = False
- self.piecewise_effects_of_investment.transform_data(f'{name_prefix}|PiecewiseEffects')
+ self.piecewise_effects_of_investment.transform_data()
self.minimum_size = self._fit_coords(
- f'{name_prefix}|minimum_size', self.minimum_size, dims=['period', 'scenario']
+ f'{self.prefix}|minimum_size', self.minimum_size, dims=['period', 'scenario']
)
self.maximum_size = self._fit_coords(
- f'{name_prefix}|maximum_size', self.maximum_size, dims=['period', 'scenario']
+ f'{self.prefix}|maximum_size', self.maximum_size, dims=['period', 'scenario']
)
# Convert tuple (first_period, last_period) to DataArray if needed
if isinstance(self.linked_periods, (tuple, list)):
@@ -965,9 +965,9 @@ def transform_data(self, name_prefix: str = '') -> None:
logger.debug(f'Computed {self.linked_periods=}')
self.linked_periods = self._fit_coords(
- f'{name_prefix}|linked_periods', self.linked_periods, dims=['period', 'scenario']
+ f'{self.prefix}|linked_periods', self.linked_periods, dims=['period', 'scenario']
)
- self.fixed_size = self._fit_coords(f'{name_prefix}|fixed_size', self.fixed_size, dims=['period', 'scenario'])
+ self.fixed_size = self._fit_coords(f'{self.prefix}|fixed_size', self.fixed_size, dims=['period', 'scenario'])
@property
def minimum_or_fixed_size(self) -> Numeric_PS:
@@ -1215,29 +1215,29 @@ def __init__(
self.startup_limit = startup_limit
self.force_startup_tracking: bool = force_startup_tracking
- def transform_data(self, name_prefix: str = '') -> None:
+ def transform_data(self) -> None:
self.effects_per_startup = self._fit_effect_coords(
- prefix=name_prefix,
+ prefix=self.prefix,
effect_values=self.effects_per_startup,
suffix='per_startup',
)
self.effects_per_active_hour = self._fit_effect_coords(
- prefix=name_prefix,
+ prefix=self.prefix,
effect_values=self.effects_per_active_hour,
suffix='per_active_hour',
)
- self.min_uptime = self._fit_coords(f'{name_prefix}|min_uptime', self.min_uptime)
- self.max_uptime = self._fit_coords(f'{name_prefix}|max_uptime', self.max_uptime)
- self.min_downtime = self._fit_coords(f'{name_prefix}|min_downtime', self.min_downtime)
- self.max_downtime = self._fit_coords(f'{name_prefix}|max_downtime', self.max_downtime)
+ self.min_uptime = self._fit_coords(f'{self.prefix}|min_uptime', self.min_uptime)
+ self.max_uptime = self._fit_coords(f'{self.prefix}|max_uptime', self.max_uptime)
+ self.min_downtime = self._fit_coords(f'{self.prefix}|min_downtime', self.min_downtime)
+ self.max_downtime = self._fit_coords(f'{self.prefix}|max_downtime', self.max_downtime)
self.active_hours_max = self._fit_coords(
- f'{name_prefix}|active_hours_max', self.active_hours_max, dims=['period', 'scenario']
+ f'{self.prefix}|active_hours_max', self.active_hours_max, dims=['period', 'scenario']
)
self.active_hours_min = self._fit_coords(
- f'{name_prefix}|active_hours_min', self.active_hours_min, dims=['period', 'scenario']
+ f'{self.prefix}|active_hours_min', self.active_hours_min, dims=['period', 'scenario']
)
self.startup_limit = self._fit_coords(
- f'{name_prefix}|startup_limit', self.startup_limit, dims=['period', 'scenario']
+ f'{self.prefix}|startup_limit', self.startup_limit, dims=['period', 'scenario']
)
@property
diff --git a/flixopt/structure.py b/flixopt/structure.py
index d00066683..da4eee0f6 100644
--- a/flixopt/structure.py
+++ b/flixopt/structure.py
@@ -316,14 +316,13 @@ class Interface:
- Recursive handling of complex nested structures
Subclasses must implement:
- transform_data(name_prefix=''): Transform data to match FlowSystem dimensions
+ transform_data(): Transform data to match FlowSystem dimensions
"""
- def transform_data(self, name_prefix: str = '') -> None:
+ def transform_data(self) -> None:
"""Transform the data of the interface to match the FlowSystem's dimensions.
- Args:
- name_prefix: The prefix to use for the names of the variables. Defaults to '', which results in no prefix.
+ Uses `self._prefix` (set during `link_to_flow_system()`) to name transformed data.
Raises:
NotImplementedError: Must be implemented by subclasses
@@ -335,20 +334,53 @@ def transform_data(self, name_prefix: str = '') -> None:
"""
raise NotImplementedError('Every Interface subclass needs a transform_data() method')
- def _set_flow_system(self, flow_system: FlowSystem) -> None:
- """Store flow_system reference and propagate to nested Interface objects.
+ @property
+ def prefix(self) -> str:
+ """The prefix used for naming transformed data (e.g., 'Boiler(Q_th)|status_parameters')."""
+ return getattr(self, '_prefix', '')
+
+ def _sub_prefix(self, name: str) -> str:
+ """Build a prefix for a nested interface by appending name to current prefix."""
+ return f'{self._prefix}|{name}' if self._prefix else name
+
+ def link_to_flow_system(self, flow_system: FlowSystem, prefix: str = '') -> None:
+ """Link this interface and all nested interfaces to a FlowSystem.
This method is called automatically during element registration to enable
elements to access FlowSystem properties without passing the reference
- through every method call.
+ through every method call. It also sets the prefix used for naming
+ transformed data.
Subclasses with nested Interface objects should override this method
- to explicitly propagate the reference to their nested interfaces.
+ to propagate the link to their nested interfaces by calling
+ `super().link_to_flow_system(flow_system, prefix)` first, then linking
+ nested objects with appropriate prefixes.
Args:
- flow_system: The FlowSystem that this interface belongs to
+ flow_system: The FlowSystem to link to
+ prefix: The prefix for naming transformed data (e.g., 'Boiler(Q_th)')
+
+ Examples:
+ Override in a subclass with nested interfaces:
+
+ ```python
+ def link_to_flow_system(self, flow_system, prefix: str = '') -> None:
+ super().link_to_flow_system(flow_system, prefix)
+ if self.nested_interface is not None:
+ self.nested_interface.link_to_flow_system(flow_system, f'{prefix}|nested' if prefix else 'nested')
+ ```
+
+ Creating an Interface dynamically during modeling:
+
+ ```python
+ # In a Model class
+ if flow.status_parameters is None:
+ flow.status_parameters = StatusParameters()
+ flow.status_parameters.link_to_flow_system(self._model.flow_system, f'{flow.label_full}')
+ ```
"""
self._flow_system = flow_system
+ self._prefix = prefix
@property
def flow_system(self) -> FlowSystem:
diff --git a/tests/test_flow_system_locking.py b/tests/test_flow_system_locking.py
new file mode 100644
index 000000000..68d3ec010
--- /dev/null
+++ b/tests/test_flow_system_locking.py
@@ -0,0 +1,403 @@
+"""
+Tests for FlowSystem locking behavior (read-only after optimization).
+
+A FlowSystem becomes locked (read-only) when it has a solution.
+This prevents accidental modifications to a system that has already been optimized.
+"""
+
+import copy
+import warnings
+
+import pytest
+
+import flixopt as fx
+
+# Note: We use simple_flow_system fixture from conftest.py
+
+
+class TestIsLocked:
+ """Test the is_locked property."""
+
+ def test_not_locked_initially(self, simple_flow_system):
+ """A new FlowSystem should not be locked."""
+ assert simple_flow_system.is_locked is False
+
+ def test_not_locked_after_build_model(self, simple_flow_system):
+ """FlowSystem should not be locked after build_model (no solution yet)."""
+ simple_flow_system.build_model()
+ assert simple_flow_system.is_locked is False
+
+ def test_locked_after_optimization(self, simple_flow_system, highs_solver):
+ """FlowSystem should be locked after optimization."""
+ simple_flow_system.optimize(highs_solver)
+ assert simple_flow_system.is_locked is True
+
+ def test_not_locked_after_reset(self, simple_flow_system, highs_solver):
+ """FlowSystem should not be locked after reset."""
+ simple_flow_system.optimize(highs_solver)
+ assert simple_flow_system.is_locked is True
+
+ simple_flow_system.reset()
+ assert simple_flow_system.is_locked is False
+
+
+class TestAddElementsLocking:
+ """Test that add_elements respects locking."""
+
+ def test_add_elements_before_optimization(self, simple_flow_system):
+ """Should be able to add elements before optimization."""
+ new_bus = fx.Bus('NewBus')
+ simple_flow_system.add_elements(new_bus)
+ assert 'NewBus' in simple_flow_system.buses
+
+ def test_add_elements_raises_when_locked(self, simple_flow_system, highs_solver):
+ """Should raise RuntimeError when adding elements to a locked FlowSystem."""
+ simple_flow_system.optimize(highs_solver)
+
+ new_bus = fx.Bus('NewBus')
+ with pytest.raises(RuntimeError, match='Cannot add elements.*reset\\(\\)'):
+ simple_flow_system.add_elements(new_bus)
+
+ def test_add_elements_after_reset(self, simple_flow_system, highs_solver):
+ """Should be able to add elements after reset."""
+ simple_flow_system.optimize(highs_solver)
+ simple_flow_system.reset()
+
+ new_bus = fx.Bus('NewBus')
+ simple_flow_system.add_elements(new_bus)
+ assert 'NewBus' in simple_flow_system.buses
+
+ def test_add_elements_invalidates_model(self, simple_flow_system):
+ """Adding elements to a FlowSystem with a model should invalidate the model."""
+ simple_flow_system.build_model()
+ assert simple_flow_system.model is not None
+
+ new_bus = fx.Bus('NewBus')
+ with warnings.catch_warnings(record=True) as w:
+ warnings.simplefilter('always')
+ simple_flow_system.add_elements(new_bus)
+ assert len(w) == 1
+ assert 'model will be invalidated' in str(w[0].message)
+
+ assert simple_flow_system.model is None
+
+
+class TestAddCarriersLocking:
+ """Test that add_carriers respects locking."""
+
+ def test_add_carriers_before_optimization(self, simple_flow_system):
+ """Should be able to add carriers before optimization."""
+ carrier = fx.Carrier('biogas', '#00FF00', 'kW')
+ simple_flow_system.add_carriers(carrier)
+ assert 'biogas' in simple_flow_system.carriers
+
+ def test_add_carriers_raises_when_locked(self, simple_flow_system, highs_solver):
+ """Should raise RuntimeError when adding carriers to a locked FlowSystem."""
+ simple_flow_system.optimize(highs_solver)
+
+ carrier = fx.Carrier('biogas', '#00FF00', 'kW')
+ with pytest.raises(RuntimeError, match='Cannot add carriers.*reset\\(\\)'):
+ simple_flow_system.add_carriers(carrier)
+
+ def test_add_carriers_after_reset(self, simple_flow_system, highs_solver):
+ """Should be able to add carriers after reset."""
+ simple_flow_system.optimize(highs_solver)
+ simple_flow_system.reset()
+
+ carrier = fx.Carrier('biogas', '#00FF00', 'kW')
+ simple_flow_system.add_carriers(carrier)
+ assert 'biogas' in simple_flow_system.carriers
+
+ def test_add_carriers_invalidates_model(self, simple_flow_system):
+ """Adding carriers to a FlowSystem with a model should invalidate the model."""
+ simple_flow_system.build_model()
+ assert simple_flow_system.model is not None
+
+ carrier = fx.Carrier('biogas', '#00FF00', 'kW')
+ with warnings.catch_warnings(record=True) as w:
+ warnings.simplefilter('always')
+ simple_flow_system.add_carriers(carrier)
+ assert len(w) == 1
+ assert 'model will be invalidated' in str(w[0].message)
+
+ assert simple_flow_system.model is None
+
+
+class TestReset:
+ """Test the reset method."""
+
+ def test_reset_clears_solution(self, simple_flow_system, highs_solver):
+ """Reset should clear the solution."""
+ simple_flow_system.optimize(highs_solver)
+ assert simple_flow_system.solution is not None
+
+ simple_flow_system.reset()
+ assert simple_flow_system.solution is None
+
+ def test_reset_clears_model(self, simple_flow_system, highs_solver):
+ """Reset should clear the model."""
+ simple_flow_system.optimize(highs_solver)
+ assert simple_flow_system.model is not None
+
+ simple_flow_system.reset()
+ assert simple_flow_system.model is None
+
+ def test_reset_clears_element_submodels(self, simple_flow_system, highs_solver):
+ """Reset should clear element submodels."""
+ simple_flow_system.optimize(highs_solver)
+
+ # Check that elements have submodels after optimization
+ boiler = simple_flow_system.components['Boiler']
+ assert boiler.submodel is not None
+ assert len(boiler._variable_names) > 0
+
+ simple_flow_system.reset()
+
+ # Check that submodels are cleared
+ assert boiler.submodel is None
+ assert len(boiler._variable_names) == 0
+
+ def test_reset_returns_self(self, simple_flow_system, highs_solver):
+ """Reset should return self for method chaining."""
+ simple_flow_system.optimize(highs_solver)
+ result = simple_flow_system.reset()
+ assert result is simple_flow_system
+
+ def test_reset_allows_reoptimization(self, simple_flow_system, highs_solver):
+ """After reset, FlowSystem can be optimized again."""
+ simple_flow_system.optimize(highs_solver)
+ original_cost = simple_flow_system.solution['costs'].item()
+
+ simple_flow_system.reset()
+ simple_flow_system.optimize(highs_solver)
+
+ assert simple_flow_system.solution is not None
+ # Cost should be the same since system structure didn't change
+ assert simple_flow_system.solution['costs'].item() == pytest.approx(original_cost)
+
+
+class TestCopy:
+ """Test the copy method."""
+
+ def test_copy_creates_new_instance(self, simple_flow_system):
+ """Copy should create a new FlowSystem instance."""
+ copy_fs = simple_flow_system.copy()
+ assert copy_fs is not simple_flow_system
+
+ def test_copy_preserves_elements(self, simple_flow_system):
+ """Copy should preserve all elements."""
+ copy_fs = simple_flow_system.copy()
+
+ assert set(copy_fs.components.keys()) == set(simple_flow_system.components.keys())
+ assert set(copy_fs.buses.keys()) == set(simple_flow_system.buses.keys())
+
+ def test_copy_does_not_copy_solution(self, simple_flow_system, highs_solver):
+ """Copy should not include the solution."""
+ simple_flow_system.optimize(highs_solver)
+ assert simple_flow_system.solution is not None
+
+ copy_fs = simple_flow_system.copy()
+ assert copy_fs.solution is None
+
+ def test_copy_does_not_copy_model(self, simple_flow_system, highs_solver):
+ """Copy should not include the model."""
+ simple_flow_system.optimize(highs_solver)
+ assert simple_flow_system.model is not None
+
+ copy_fs = simple_flow_system.copy()
+ assert copy_fs.model is None
+
+ def test_copy_is_not_locked(self, simple_flow_system, highs_solver):
+ """Copy should not be locked even if original is."""
+ simple_flow_system.optimize(highs_solver)
+ assert simple_flow_system.is_locked is True
+
+ copy_fs = simple_flow_system.copy()
+ assert copy_fs.is_locked is False
+
+ def test_copy_can_be_modified(self, simple_flow_system, highs_solver):
+ """Copy should be modifiable even if original is locked."""
+ simple_flow_system.optimize(highs_solver)
+
+ copy_fs = simple_flow_system.copy()
+ new_bus = fx.Bus('NewBus')
+ copy_fs.add_elements(new_bus) # Should not raise
+ assert 'NewBus' in copy_fs.buses
+
+ def test_copy_can_be_optimized_independently(self, simple_flow_system, highs_solver):
+ """Copy can be optimized independently of original."""
+ simple_flow_system.optimize(highs_solver)
+ original_cost = simple_flow_system.solution['costs'].item()
+
+ copy_fs = simple_flow_system.copy()
+ copy_fs.optimize(highs_solver)
+
+ # Both should have solutions
+ assert simple_flow_system.solution is not None
+ assert copy_fs.solution is not None
+
+ # Costs should be equal (same system)
+ assert copy_fs.solution['costs'].item() == pytest.approx(original_cost)
+
+ def test_python_copy_uses_copy_method(self, simple_flow_system, highs_solver):
+ """copy.copy() should use the custom copy method."""
+ simple_flow_system.optimize(highs_solver)
+
+ copy_fs = copy.copy(simple_flow_system)
+ assert copy_fs.solution is None
+ assert copy_fs.is_locked is False
+
+ def test_python_deepcopy_uses_copy_method(self, simple_flow_system, highs_solver):
+ """copy.deepcopy() should use the custom copy method."""
+ simple_flow_system.optimize(highs_solver)
+
+ copy_fs = copy.deepcopy(simple_flow_system)
+ assert copy_fs.solution is None
+ assert copy_fs.is_locked is False
+
+
+class TestLoadedFlowSystem:
+ """Test that loaded FlowSystems respect locking."""
+
+ def test_loaded_fs_with_solution_is_locked(self, simple_flow_system, highs_solver, tmp_path):
+ """A FlowSystem loaded from file with solution should be locked."""
+ simple_flow_system.optimize(highs_solver)
+ filepath = tmp_path / 'test_fs.nc'
+ simple_flow_system.to_netcdf(filepath)
+
+ loaded_fs = fx.FlowSystem.from_netcdf(filepath)
+ assert loaded_fs.is_locked is True
+
+ def test_loaded_fs_can_be_reset(self, simple_flow_system, highs_solver, tmp_path):
+ """A loaded FlowSystem can be reset to allow modifications."""
+ simple_flow_system.optimize(highs_solver)
+ filepath = tmp_path / 'test_fs.nc'
+ simple_flow_system.to_netcdf(filepath)
+
+ loaded_fs = fx.FlowSystem.from_netcdf(filepath)
+ loaded_fs.reset()
+
+ assert loaded_fs.is_locked is False
+ new_bus = fx.Bus('NewBus')
+ loaded_fs.add_elements(new_bus) # Should not raise
+
+
+class TestInvalidate:
+ """Test the invalidate method for manual model invalidation."""
+
+ def test_invalidate_resets_connected_and_transformed(self, simple_flow_system):
+ """Invalidate should reset the connected_and_transformed flag."""
+ simple_flow_system.connect_and_transform()
+ assert simple_flow_system.connected_and_transformed is True
+
+ simple_flow_system.invalidate()
+ assert simple_flow_system.connected_and_transformed is False
+
+ def test_invalidate_clears_model(self, simple_flow_system):
+ """Invalidate should clear the model."""
+ simple_flow_system.build_model()
+ assert simple_flow_system.model is not None
+
+ simple_flow_system.invalidate()
+ assert simple_flow_system.model is None
+
+ def test_invalidate_raises_when_locked(self, simple_flow_system, highs_solver):
+ """Invalidate should raise RuntimeError when FlowSystem has a solution."""
+ simple_flow_system.optimize(highs_solver)
+
+ with pytest.raises(RuntimeError, match='Cannot invalidate.*reset\\(\\)'):
+ simple_flow_system.invalidate()
+
+ def test_invalidate_returns_self(self, simple_flow_system):
+ """Invalidate should return self for method chaining."""
+ simple_flow_system.connect_and_transform()
+ result = simple_flow_system.invalidate()
+ assert result is simple_flow_system
+
+ def test_invalidate_allows_retransformation(self, simple_flow_system, highs_solver):
+ """After invalidate, connect_and_transform should run again."""
+ simple_flow_system.connect_and_transform()
+ assert simple_flow_system.connected_and_transformed is True
+
+ simple_flow_system.invalidate()
+ assert simple_flow_system.connected_and_transformed is False
+
+ # Should be able to connect_and_transform again
+ simple_flow_system.connect_and_transform()
+ assert simple_flow_system.connected_and_transformed is True
+
+ def test_modify_element_and_invalidate(self, simple_flow_system, highs_solver):
+ """Test the workflow: optimize -> reset -> modify -> invalidate -> re-optimize."""
+ # First optimization
+ simple_flow_system.optimize(highs_solver)
+ original_cost = simple_flow_system.solution['costs'].item()
+
+ # Reset to unlock
+ simple_flow_system.reset()
+
+ # Modify an element attribute (increase gas price, which should increase costs)
+ gas_tariff = simple_flow_system.components['Gastarif']
+ original_effects = gas_tariff.outputs[0].effects_per_flow_hour
+ # Double the cost effect
+ gas_tariff.outputs[0].effects_per_flow_hour = {effect: value * 2 for effect, value in original_effects.items()}
+
+ # Invalidate to trigger re-transformation
+ simple_flow_system.invalidate()
+
+ # Re-optimize
+ simple_flow_system.optimize(highs_solver)
+ new_cost = simple_flow_system.solution['costs'].item()
+
+ # Cost should have increased due to higher gas price
+ assert new_cost > original_cost
+
+ def test_invalidate_needed_after_transform_before_optimize(self, simple_flow_system, highs_solver):
+ """Invalidate is needed to apply changes made after connect_and_transform but before optimize."""
+ # Connect and transform (but don't optimize yet)
+ simple_flow_system.connect_and_transform()
+
+ # Modify an attribute - double the gas costs
+ gas_tariff = simple_flow_system.components['Gastarif']
+ original_effects = gas_tariff.outputs[0].effects_per_flow_hour
+ gas_tariff.outputs[0].effects_per_flow_hour = {effect: value * 2 for effect, value in original_effects.items()}
+
+ # Call invalidate to ensure re-transformation
+ simple_flow_system.invalidate()
+ assert simple_flow_system.connected_and_transformed is False
+
+ # Now optimize - the doubled values should take effect
+ simple_flow_system.optimize(highs_solver)
+ cost_with_doubled = simple_flow_system.solution['costs'].item()
+
+ # Reset and use original values
+ simple_flow_system.reset()
+ gas_tariff.outputs[0].effects_per_flow_hour = {
+ effect: value / 2 for effect, value in gas_tariff.outputs[0].effects_per_flow_hour.items()
+ }
+ simple_flow_system.optimize(highs_solver)
+ cost_with_original = simple_flow_system.solution['costs'].item()
+
+ # The doubled costs should result in higher total cost
+ assert cost_with_doubled > cost_with_original
+
+ def test_reset_already_invalidates(self, simple_flow_system, highs_solver):
+ """Reset already invalidates, so modifications after reset take effect."""
+ # First optimization
+ simple_flow_system.optimize(highs_solver)
+ original_cost = simple_flow_system.solution['costs'].item()
+
+ # Reset - this already calls _invalidate_model()
+ simple_flow_system.reset()
+ assert simple_flow_system.connected_and_transformed is False
+
+ # Modify an element attribute
+ gas_tariff = simple_flow_system.components['Gastarif']
+ original_effects = gas_tariff.outputs[0].effects_per_flow_hour
+ gas_tariff.outputs[0].effects_per_flow_hour = {effect: value * 2 for effect, value in original_effects.items()}
+
+ # Re-optimize - changes take effect because reset already invalidated
+ simple_flow_system.optimize(highs_solver)
+ new_cost = simple_flow_system.solution['costs'].item()
+
+ # Cost should have increased
+ assert new_cost > original_cost
From 62aac6916479308603a4aee83bd6afed83f6daff Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Tue, 9 Dec 2025 22:09:57 +0100
Subject: [PATCH 21/49] Add better and more versitile sankey diagrams (#514)
* Update sankey figure building
* fix: sankey
* fix: effects sankey
* Add sankey diagramm tests
* Add sankey diagramm tests
* Minor nitpicks
* All three failing tests are now fixed. Here's a summary of the changes made:
Summary of Fixes
1. test_statistics_sizes_includes_all_flows - Fixed
Problem: The statistics.sizes property was returning storage capacity sizes (like Speicher) which are not flow labels. The test expected only flow sizes.
Fix in flixopt/statistics_accessor.py (lines 419-427):
- Modified sizes property to filter only flow sizes by checking if the variable name (minus |size suffix) matches a flow label in self._fs.flows.keys()
2. test_sankey_sizes_mode - Fixed
Problem: The sankey diagram with mode='sizes' returned empty links because the test fixture (simple_flow_system) didn't have any flows with InvestParameters.
Fix in tests/conftest.py (lines 268-272):
- Modified Storage.simple() to use fx.InvestParameters(fixed_size=1e4, mandatory=True) on the charging flow, ensuring there's at least one flow with investment
parameters for testing.
3. test_sankey_sizes_max_size_filter - Fixed
Problem: The sankey method didn't have a max_size parameter, so passing it caused the parameter to be forwarded to plotly_kwargs and then to update_layout(), which
failed with "Invalid property specified for object of type plotly.graph_objs.Layout: 'max_size'".
Fix in flixopt/statistics_accessor.py (lines 1351, 1367, 1392-1395):
- Added max_size: float | None = None parameter to the sankey method signature
- Added filtering logic to apply max_size filter when in mode='sizes'
* Add new sankey network topology plot
---
flixopt/config.py | 2 +-
flixopt/flow_system.py | 8 +-
flixopt/statistics_accessor.py | 298 +++++++++++++++++++++++-----
flixopt/topology_accessor.py | 161 ++++++++++++++-
tests/conftest.py | 6 +-
tests/test_solution_and_plotting.py | 170 ++++++++++++++++
tests/test_topology_accessor.py | 78 +++++++-
7 files changed, 651 insertions(+), 72 deletions(-)
diff --git a/flixopt/config.py b/flixopt/config.py
index 4d4571dcd..aaa3b34d2 100644
--- a/flixopt/config.py
+++ b/flixopt/config.py
@@ -20,7 +20,7 @@
COLORLOG_AVAILABLE = False
escape_codes = None
-__all__ = ['CONFIG', 'MultilineFormatter', 'SUCCESS_LEVEL']
+__all__ = ['CONFIG', 'MultilineFormatter', 'SUCCESS_LEVEL', 'DEPRECATION_REMOVAL_VERSION']
if COLORLOG_AVAILABLE:
__all__.append('ColoredMultilineFormatter')
diff --git a/flixopt/flow_system.py b/flixopt/flow_system.py
index bae700b85..ce7bd0658 100644
--- a/flixopt/flow_system.py
+++ b/flixopt/flow_system.py
@@ -1426,13 +1426,7 @@ def plot_network(
Visualizes the network structure of a FlowSystem using PyVis.
"""
- warnings.warn(
- f'plot_network() is deprecated and will be removed in v{DEPRECATION_REMOVAL_VERSION}. '
- 'Use flow_system.topology.plot() instead.',
- DeprecationWarning,
- stacklevel=2,
- )
- return self.topology.plot(path=path, controls=controls, show=show)
+ return self.topology.plot_legacy(path=path, controls=controls, show=show)
def start_network_app(self) -> None:
"""
diff --git a/flixopt/statistics_accessor.py b/flixopt/statistics_accessor.py
index 2927c42a6..2be1b5823 100644
--- a/flixopt/statistics_accessor.py
+++ b/flixopt/statistics_accessor.py
@@ -417,7 +417,11 @@ def sizes(self) -> xr.Dataset:
"""All flow sizes as a Dataset with flow labels as variable names."""
self._require_solution()
if self._sizes is None:
- size_vars = [v for v in self._fs.solution.data_vars if v.endswith('|size')]
+ # Get flow labels to filter only flow sizes (not storage capacity sizes)
+ flow_labels = set(self._fs.flows.keys())
+ size_vars = [
+ v for v in self._fs.solution.data_vars if v.endswith('|size') and v.replace('|size', '') in flow_labels
+ ]
self._sizes = xr.Dataset({v.replace('|size', ''): self._fs.solution[v] for v in size_vars})
return self._sizes
@@ -1094,69 +1098,186 @@ def flows(
return PlotResult(data=ds, figure=fig)
- def sankey(
+ def _prepare_sankey_data(
self,
- *,
- timestep: int | str | None = None,
- aggregate: Literal['sum', 'mean'] = 'sum',
- select: SelectType | None = None,
- colors: ColorType | None = None,
- show: bool | None = None,
- **plotly_kwargs: Any,
- ) -> PlotResult:
- """Plot Sankey diagram of energy/material flow hours.
+ mode: Literal['flow_hours', 'sizes', 'peak_flow'],
+ timestep: int | str | None,
+ aggregate: Literal['sum', 'mean'],
+ select: SelectType | None,
+ ) -> tuple[xr.Dataset, str]:
+ """Prepare data for Sankey diagram based on mode.
Args:
- timestep: Specific timestep to show, or None for aggregation.
- aggregate: How to aggregate if timestep is None.
+ mode: What to display - flow_hours, sizes, or peak_flow.
+ timestep: Specific timestep (only for flow_hours mode).
+ aggregate: Aggregation method (only for flow_hours mode).
select: xarray-style selection.
- colors: Color specification for nodes (colorscale name, color list, or label-to-color dict).
- show: Whether to display.
Returns:
- PlotResult with Sankey flow data.
+ Tuple of (prepared Dataset, title string).
"""
- self._stats._require_solution()
-
- ds = self._stats.flow_hours.copy()
-
- # Apply weights
- if 'period' in ds.dims and self._fs.period_weights is not None:
- ds = ds * self._fs.period_weights
- if 'scenario' in ds.dims and self._fs.scenario_weights is not None:
- weights = self._fs.scenario_weights / self._fs.scenario_weights.sum()
- ds = ds * weights
+ if mode == 'sizes':
+ ds = self._stats.sizes.copy()
+ title = 'Investment Sizes (Capacities)'
+ elif mode == 'peak_flow':
+ ds = self._stats.flow_rates.copy()
+ ds = _apply_selection(ds, select)
+ if 'time' in ds.dims:
+ ds = ds.max(dim='time')
+ for dim in ['period', 'scenario']:
+ if dim in ds.dims:
+ ds = ds.max(dim=dim)
+ return ds, 'Peak Flow Rates'
+ else: # flow_hours
+ ds = self._stats.flow_hours.copy()
+ title = 'Energy Flow'
+
+ # Apply weights for flow_hours
+ if mode == 'flow_hours':
+ if 'period' in ds.dims and self._fs.period_weights is not None:
+ ds = ds * self._fs.period_weights
+ if 'scenario' in ds.dims and self._fs.scenario_weights is not None:
+ weights = self._fs.scenario_weights / self._fs.scenario_weights.sum()
+ ds = ds * weights
ds = _apply_selection(ds, select)
- if timestep is not None:
- if isinstance(timestep, int):
- ds = ds.isel(time=timestep)
- else:
- ds = ds.sel(time=timestep)
- elif 'time' in ds.dims:
- ds = getattr(ds, aggregate)(dim='time')
+ # Time aggregation (only for flow_hours)
+ if mode == 'flow_hours':
+ if timestep is not None:
+ if isinstance(timestep, int):
+ ds = ds.isel(time=timestep)
+ else:
+ ds = ds.sel(time=timestep)
+ elif 'time' in ds.dims:
+ ds = getattr(ds, aggregate)(dim='time')
+ # Collapse remaining dimensions
for dim in ['period', 'scenario']:
if dim in ds.dims:
- ds = ds.sum(dim=dim)
+ ds = ds.sum(dim=dim) if mode == 'flow_hours' else ds.max(dim=dim)
+
+ return ds, title
+
+ def _build_effects_sankey(
+ self,
+ select: SelectType | None,
+ colors: ColorType | None,
+ **plotly_kwargs: Any,
+ ) -> tuple[go.Figure, xr.Dataset]:
+ """Build Sankey diagram showing contributions from components to effects.
+
+ Creates a Sankey with:
+ - Left side: Components (grouped by type)
+ - Right side: Effects (costs, CO2, etc.)
+ - Links: Contributions from each component to each effect
+
+ Args:
+ select: xarray-style selection.
+ colors: Color specification for nodes.
+ **plotly_kwargs: Additional Plotly layout arguments.
+
+ Returns:
+ Tuple of (Plotly Figure, Dataset with link data).
+ """
+ total_effects = self._stats.total_effects
+
+ # Collect all links: component -> effect
+ nodes: set[str] = set()
+ links: dict[str, list] = {'source': [], 'target': [], 'value': [], 'label': []}
+
+ for effect_name in total_effects.data_vars:
+ effect_data = total_effects[effect_name]
+ effect_data = _apply_selection(effect_data, select)
+
+ # Sum over any remaining dimensions
+ for dim in ['period', 'scenario']:
+ if dim in effect_data.dims:
+ effect_data = effect_data.sum(dim=dim)
+
+ contributors = effect_data.coords['contributor'].values
+ components = effect_data.coords['component'].values
+
+ for contributor, component in zip(contributors, components, strict=False):
+ value = float(effect_data.sel(contributor=contributor).values)
+ if not np.isfinite(value) or abs(value) < 1e-6:
+ continue
+
+ # Use component as source node, effect as target
+ source = str(component)
+ target = f'[{effect_name}]' # Bracket notation to distinguish effects
+
+ nodes.add(source)
+ nodes.add(target)
+ links['source'].append(source)
+ links['target'].append(target)
+ links['value'].append(abs(value))
+ links['label'].append(f'{contributor} → {effect_name}: {value:.2f}')
+
+ # Create figure
+ node_list = list(nodes)
+ node_indices = {n: i for i, n in enumerate(node_list)}
+
+ color_map = process_colors(colors, node_list)
+ node_colors = [color_map[node] for node in node_list]
+
+ fig = go.Figure(
+ data=[
+ go.Sankey(
+ node=dict(
+ pad=15, thickness=20, line=dict(color='black', width=0.5), label=node_list, color=node_colors
+ ),
+ link=dict(
+ source=[node_indices[s] for s in links['source']],
+ target=[node_indices[t] for t in links['target']],
+ value=links['value'],
+ label=links['label'],
+ ),
+ )
+ ]
+ )
+ fig.update_layout(title='Effect Contributions by Component', **plotly_kwargs)
+
+ sankey_ds = xr.Dataset(
+ {'value': ('link', links['value'])},
+ coords={
+ 'link': range(len(links['value'])),
+ 'source': ('link', links['source']),
+ 'target': ('link', links['target']),
+ 'label': ('link', links['label']),
+ },
+ )
+
+ return fig, sankey_ds
+
+ def _build_sankey_links(
+ self,
+ ds: xr.Dataset,
+ min_value: float = 1e-6,
+ ) -> tuple[set[str], dict[str, list]]:
+ """Build Sankey nodes and links from flow data.
- # Build Sankey
- nodes = set()
- links = {'source': [], 'target': [], 'value': [], 'label': []}
+ Args:
+ ds: Dataset with flow values (one variable per flow).
+ min_value: Minimum value threshold to include a link.
+
+ Returns:
+ Tuple of (nodes set, links dict with source/target/value/label).
+ """
+ nodes: set[str] = set()
+ links: dict[str, list] = {'source': [], 'target': [], 'value': [], 'label': []}
for flow in self._fs.flows.values():
label = flow.label_full
if label not in ds:
continue
value = float(ds[label].values)
- if abs(value) < 1e-6:
+ if abs(value) < min_value:
continue
- # Determine source/target based on flow direction
- # is_input_in_component: True means bus -> component, False means component -> bus
+ # flow.bus and flow.component are already strings (bus label, component label_full)
bus_label = flow.bus
- comp_label = flow.component.label_full
+ comp_label = flow.component
if flow.is_input_in_component:
source = bus_label
@@ -1172,6 +1293,28 @@ def sankey(
links['value'].append(abs(value))
links['label'].append(label)
+ return nodes, links
+
+ def _create_sankey_figure(
+ self,
+ nodes: set[str],
+ links: dict[str, list],
+ colors: ColorType | None,
+ title: str,
+ **plotly_kwargs: Any,
+ ) -> go.Figure:
+ """Create Plotly Sankey figure.
+
+ Args:
+ nodes: Set of node labels.
+ links: Dict with source, target, value, label lists.
+ colors: Color specification for nodes.
+ title: Figure title.
+ **plotly_kwargs: Additional Plotly layout arguments.
+
+ Returns:
+ Plotly Figure with Sankey diagram.
+ """
node_list = list(nodes)
node_indices = {n: i for i, n in enumerate(node_list)}
@@ -1193,12 +1336,75 @@ def sankey(
)
]
)
- fig.update_layout(title='Energy Flow Sankey', **plotly_kwargs)
+ fig.update_layout(title=title, **plotly_kwargs)
+ return fig
- sankey_ds = xr.Dataset(
- {'value': ('link', links['value'])},
- coords={'link': links['label'], 'source': ('link', links['source']), 'target': ('link', links['target'])},
- )
+ def sankey(
+ self,
+ *,
+ mode: Literal['flow_hours', 'sizes', 'peak_flow', 'effects'] = 'flow_hours',
+ timestep: int | str | None = None,
+ aggregate: Literal['sum', 'mean'] = 'sum',
+ select: SelectType | None = None,
+ max_size: float | None = None,
+ colors: ColorType | None = None,
+ show: bool | None = None,
+ **plotly_kwargs: Any,
+ ) -> PlotResult:
+ """Plot Sankey diagram of the flow system.
+
+ Args:
+ mode: What to display:
+ - 'flow_hours': Energy/material amounts (default)
+ - 'sizes': Investment capacities
+ - 'peak_flow': Maximum flow rates
+ - 'effects': Component contributions to all effects (costs, CO2, etc.)
+ timestep: Specific timestep to show, or None for aggregation (flow_hours only).
+ aggregate: How to aggregate if timestep is None ('sum' or 'mean', flow_hours only).
+ select: xarray-style selection.
+ max_size: Filter flows with sizes exceeding this value (sizes mode only).
+ colors: Color specification for nodes (colorscale name, color list, or label-to-color dict).
+ show: Whether to display.
+ **plotly_kwargs: Additional arguments passed to Plotly layout.
+
+ Returns:
+ PlotResult with Sankey flow data and figure.
+
+ Examples:
+ >>> # Show energy flows (default)
+ >>> flow_system.statistics.plot.sankey()
+ >>> # Show investment sizes/capacities
+ >>> flow_system.statistics.plot.sankey(mode='sizes')
+ >>> # Show peak flow rates
+ >>> flow_system.statistics.plot.sankey(mode='peak_flow')
+ >>> # Show effect contributions (components -> effects like costs, CO2)
+ >>> flow_system.statistics.plot.sankey(mode='effects')
+ """
+ self._stats._require_solution()
+
+ if mode == 'effects':
+ fig, sankey_ds = self._build_effects_sankey(select, colors, **plotly_kwargs)
+ else:
+ ds, title = self._prepare_sankey_data(mode, timestep, aggregate, select)
+
+ # Apply max_size filter for sizes mode
+ if max_size is not None and mode == 'sizes' and ds.data_vars:
+ valid_labels = [lbl for lbl in ds.data_vars if float(ds[lbl].max()) < max_size]
+ ds = ds[valid_labels]
+
+ nodes, links = self._build_sankey_links(ds)
+ fig = self._create_sankey_figure(nodes, links, colors, title, **plotly_kwargs)
+
+ n_links = len(links['value'])
+ sankey_ds = xr.Dataset(
+ {'value': ('link', links['value'])},
+ coords={
+ 'link': range(n_links),
+ 'source': ('link', links['source']),
+ 'target': ('link', links['target']),
+ 'label': ('link', links['label']),
+ },
+ )
if show is None:
show = CONFIG.Plotting.default_show
diff --git a/flixopt/topology_accessor.py b/flixopt/topology_accessor.py
index de4f83685..6e0980ae3 100644
--- a/flixopt/topology_accessor.py
+++ b/flixopt/topology_accessor.py
@@ -11,7 +11,12 @@
import pathlib
import warnings
from itertools import chain
-from typing import TYPE_CHECKING, Literal
+from typing import TYPE_CHECKING, Any, Literal
+
+import plotly.graph_objects as go
+
+from .color_processing import ColorType, process_colors
+from .config import CONFIG, DEPRECATION_REMOVAL_VERSION
if TYPE_CHECKING:
import pyvis
@@ -176,6 +181,142 @@ def infos(self) -> tuple[dict[str, dict[str, str]], dict[str, dict[str, str]]]:
return nodes, edges
def plot(
+ self,
+ colors: ColorType | None = None,
+ show: bool | None = None,
+ **plotly_kwargs: Any,
+ ) -> go.Figure:
+ """
+ Visualize the network structure as a Sankey diagram using Plotly.
+
+ Creates a Sankey diagram showing the topology of the flow system,
+ with buses and components as nodes, and flows as links between them.
+ All links have equal width since no solution data is used.
+
+ Args:
+ colors: Color specification for nodes (buses).
+ - `None`: Uses default color palette based on buses.
+ - `str`: Plotly colorscale name (e.g., 'Viridis', 'Blues').
+ - `list`: List of colors to cycle through.
+ - `dict`: Maps bus labels to specific colors.
+ Links inherit colors from their connected bus.
+ show: Whether to display the figure in the browser.
+ - `None`: Uses default from CONFIG.Plotting.default_show.
+ **plotly_kwargs: Additional arguments passed to Plotly layout.
+
+ Returns:
+ Plotly Figure with the Sankey diagram.
+
+ Examples:
+ >>> flow_system.topology.plot()
+ >>> flow_system.topology.plot(show=True)
+ >>> flow_system.topology.plot(colors='Viridis')
+ >>> flow_system.topology.plot(colors={'ElectricityBus': 'gold', 'HeatBus': 'red'})
+
+ Notes:
+ This visualization shows the network structure without optimization results.
+ For visualizations that include flow values, use `flow_system.statistics.plot.sankey()`
+ after running an optimization.
+
+ Hover over nodes and links to see detailed element information.
+
+ See Also:
+ - `plot_legacy()`: Previous PyVis-based network visualization.
+ - `statistics.plot.sankey()`: Sankey with actual flow values from optimization.
+ """
+ if not self._fs.connected_and_transformed:
+ self._fs.connect_and_transform()
+
+ # Build nodes and links from topology
+ nodes: set[str] = set()
+ links: dict[str, list] = {
+ 'source': [],
+ 'target': [],
+ 'value': [],
+ 'label': [],
+ 'customdata': [], # For hover text
+ }
+
+ # Collect node hover info (format repr for HTML display)
+ node_hover: dict[str, str] = {}
+ for comp in self._fs.components.values():
+ node_hover[comp.label] = repr(comp).replace('\n', '
')
+ for bus in self._fs.buses.values():
+ node_hover[bus.label] = repr(bus).replace('\n', '
')
+
+ for flow in self._fs.flows.values():
+ bus_label = flow.bus
+ comp_label = flow.component
+
+ if flow.is_input_in_component:
+ source = bus_label
+ target = comp_label
+ else:
+ source = comp_label
+ target = bus_label
+
+ nodes.add(source)
+ nodes.add(target)
+ links['source'].append(source)
+ links['target'].append(target)
+ links['value'].append(1) # Equal width for all links (no solution data)
+ links['label'].append(flow.label_full)
+ links['customdata'].append(repr(flow).replace('\n', '
')) # Flow repr for hover
+
+ # Create figure
+ node_list = list(nodes)
+ node_indices = {n: i for i, n in enumerate(node_list)}
+
+ # Get colors for buses only, then apply to all nodes
+ bus_labels = [bus.label for bus in self._fs.buses.values()]
+ bus_color_map = process_colors(colors, bus_labels)
+
+ # Assign colors to nodes: buses get their color, components get a neutral gray
+ node_colors = []
+ for node in node_list:
+ if node in bus_color_map:
+ node_colors.append(bus_color_map[node])
+ else:
+ # Component - use a neutral gray
+ node_colors.append('#808080')
+
+ # Build hover text for nodes
+ node_customdata = [node_hover.get(node, node) for node in node_list]
+
+ fig = go.Figure(
+ data=[
+ go.Sankey(
+ node=dict(
+ pad=15,
+ thickness=20,
+ line=dict(color='black', width=0.5),
+ label=node_list,
+ color=node_colors,
+ customdata=node_customdata,
+ hovertemplate='%{customdata}
',
+ ),
+ link=dict(
+ source=[node_indices[s] for s in links['source']],
+ target=[node_indices[t] for t in links['target']],
+ value=links['value'],
+ label=links['label'],
+ customdata=links['customdata'],
+ hovertemplate='%{customdata}
',
+ ),
+ )
+ ]
+ )
+ title = plotly_kwargs.pop('title', 'Flow System Topology')
+ fig.update_layout(title=title, **plotly_kwargs)
+
+ if show is None:
+ show = CONFIG.Plotting.default_show
+ if show:
+ fig.show()
+
+ return fig
+
+ def plot_legacy(
self,
path: bool | str | pathlib.Path = 'flow_system.html',
controls: bool
@@ -187,6 +328,10 @@ def plot(
"""
Visualize the network structure using PyVis, saving it as an interactive HTML file.
+ .. deprecated::
+ Use `plot()` instead for the new Plotly-based Sankey visualization.
+ This method is kept for backwards compatibility.
+
Args:
path: Path to save the HTML visualization.
- `False`: Visualization is created but not saved.
@@ -203,9 +348,9 @@ def plot(
or `None` if `pyvis` is not installed.
Examples:
- >>> flow_system.topology.plot()
- >>> flow_system.topology.plot(show=False)
- >>> flow_system.topology.plot(path='output/network.html', controls=['nodes', 'layout'])
+ >>> flow_system.topology.plot_legacy()
+ >>> flow_system.topology.plot_legacy(show=False)
+ >>> flow_system.topology.plot_legacy(path='output/network.html', controls=['nodes', 'layout'])
Notes:
This function requires `pyvis`. If not installed, the function prints
@@ -213,8 +358,12 @@ def plot(
Nodes are styled based on type (circles for buses, boxes for components)
and annotated with node information.
"""
- from .config import CONFIG
-
+ warnings.warn(
+ f'This method is deprecated and will be removed in v{DEPRECATION_REMOVAL_VERSION}. '
+ 'Use flow_system.topology.plot() instead.',
+ DeprecationWarning,
+ stacklevel=2,
+ )
node_infos, edge_infos = self.infos()
# Normalize path=False to None for _plot_network compatibility
normalized_path = None if path is False else path
diff --git a/tests/conftest.py b/tests/conftest.py
index 9d76097ee..15c7509d3 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -265,7 +265,11 @@ def simple(timesteps_length=9):
return fx.Storage(
'Speicher',
- charging=fx.Flow('Q_th_load', bus='Fernwärme', size=1e4),
+ charging=fx.Flow(
+ 'Q_th_load',
+ bus='Fernwärme',
+ size=fx.InvestParameters(fixed_size=1e4, mandatory=True), # Investment for testing sizes
+ ),
discharging=fx.Flow('Q_th_unload', bus='Fernwärme', size=1e4),
capacity_in_flow_hours=fx.InvestParameters(effects_of_investment=20, fixed_size=30, mandatory=True),
initial_charge_state=0,
diff --git a/tests/test_solution_and_plotting.py b/tests/test_solution_and_plotting.py
index e5c96da33..2d87b595e 100644
--- a/tests/test_solution_and_plotting.py
+++ b/tests/test_solution_and_plotting.py
@@ -162,6 +162,61 @@ def test_element_solution_raises_for_unlinked_element(self):
_ = boiler.solution
+# ============================================================================
+# STATISTICS ACCESSOR TESTS
+# ============================================================================
+
+
+class TestStatisticsAccessor:
+ """Tests for flow_system.statistics accessor."""
+
+ def test_statistics_sizes_includes_all_flows(self, simple_flow_system, highs_solver):
+ """Test that statistics.sizes includes all flow sizes (from InvestParameters)."""
+ simple_flow_system.optimize(highs_solver)
+
+ sizes = simple_flow_system.statistics.sizes
+
+ assert isinstance(sizes, xr.Dataset)
+ # Should have sizes for flows with InvestParameters
+ assert len(sizes.data_vars) > 0
+
+ # Check that all size labels are valid flow labels
+ flow_labels = [f.label_full for f in simple_flow_system.flows.values()]
+ for label in sizes.data_vars:
+ assert label in flow_labels, f'Size label {label} should be a valid flow'
+
+ def test_statistics_sizes_returns_correct_values(self, simple_flow_system, highs_solver):
+ """Test that statistics.sizes returns correct size values."""
+ simple_flow_system.optimize(highs_solver)
+
+ sizes = simple_flow_system.statistics.sizes
+
+ # Check that all values are positive (sizes should be > 0)
+ for label in sizes.data_vars:
+ value = float(sizes[label].values) if sizes[label].dims == () else float(sizes[label].max().values)
+ assert value > 0, f'Size for {label} should be positive'
+
+ def test_statistics_flow_rates(self, simple_flow_system, highs_solver):
+ """Test that statistics.flow_rates returns flow rate data."""
+ simple_flow_system.optimize(highs_solver)
+
+ flow_rates = simple_flow_system.statistics.flow_rates
+
+ assert isinstance(flow_rates, xr.Dataset)
+ assert len(flow_rates.data_vars) > 0
+ # Flow rates should have time dimension
+ assert 'time' in flow_rates.dims
+
+ def test_statistics_flow_hours(self, simple_flow_system, highs_solver):
+ """Test that statistics.flow_hours returns energy data."""
+ simple_flow_system.optimize(highs_solver)
+
+ flow_hours = simple_flow_system.statistics.flow_hours
+
+ assert isinstance(flow_hours, xr.Dataset)
+ assert len(flow_hours.data_vars) > 0
+
+
# ============================================================================
# PLOTTING WITH OPTIMIZED DATA TESTS
# ============================================================================
@@ -601,3 +656,118 @@ def test_export_matplotlib_to_png(self, simple_flow_system, highs_solver, tmp_pa
plotting.export_figure((fig, ax), default_path=png_path, save=True, show=False)
assert png_path.exists()
plt.close(fig)
+
+
+# ============================================================================
+# SANKEY DIAGRAM TESTS
+# ============================================================================
+
+
+class TestSankeyDiagram:
+ """Tests for Sankey diagram functionality."""
+
+ def test_sankey_flow_hours_mode(self, simple_flow_system, highs_solver):
+ """Test Sankey diagram with flow_hours mode (default)."""
+ simple_flow_system.optimize(highs_solver)
+
+ result = simple_flow_system.statistics.plot.sankey(show=False)
+
+ assert result.figure is not None
+ assert result.data is not None
+ assert 'value' in result.data
+ assert 'source' in result.data.coords
+ assert 'target' in result.data.coords
+ assert len(result.data.link) > 0
+
+ def test_sankey_peak_flow_mode(self, simple_flow_system, highs_solver):
+ """Test Sankey diagram with peak_flow mode."""
+ simple_flow_system.optimize(highs_solver)
+
+ result = simple_flow_system.statistics.plot.sankey(mode='peak_flow', show=False)
+
+ assert result.figure is not None
+ assert result.data is not None
+ assert len(result.data.link) > 0
+
+ def test_sankey_sizes_mode(self, simple_flow_system, highs_solver):
+ """Test Sankey diagram with sizes mode shows investment sizes."""
+ simple_flow_system.optimize(highs_solver)
+
+ result = simple_flow_system.statistics.plot.sankey(mode='sizes', show=False)
+
+ assert result.figure is not None
+ assert result.data is not None
+ # Should have some flows with investment sizes
+ assert len(result.data.link) > 0
+
+ def test_sankey_sizes_max_size_filter(self, simple_flow_system, highs_solver):
+ """Test that max_size parameter filters large sizes."""
+ simple_flow_system.optimize(highs_solver)
+
+ # Get all sizes (no filter)
+ result_all = simple_flow_system.statistics.plot.sankey(mode='sizes', max_size=None, show=False)
+
+ # Get filtered sizes
+ result_filtered = simple_flow_system.statistics.plot.sankey(mode='sizes', max_size=100, show=False)
+
+ # Filtered should have fewer or equal links
+ assert len(result_filtered.data.link) <= len(result_all.data.link)
+
+ def test_sankey_effects_mode(self, simple_flow_system, highs_solver):
+ """Test Sankey diagram with effects mode."""
+ simple_flow_system.optimize(highs_solver)
+
+ result = simple_flow_system.statistics.plot.sankey(mode='effects', show=False)
+
+ assert result.figure is not None
+ assert result.data is not None
+ # Should have component -> effect links
+ assert len(result.data.link) > 0
+ # Effects should appear in targets with bracket notation
+ targets = list(result.data.target.values)
+ assert any('[' in str(t) for t in targets), 'Effects should appear as [effect_name] in targets'
+
+ def test_sankey_effects_includes_costs_and_co2(self, simple_flow_system, highs_solver):
+ """Test that effects mode includes both costs and CO2."""
+ simple_flow_system.optimize(highs_solver)
+
+ result = simple_flow_system.statistics.plot.sankey(mode='effects', show=False)
+
+ targets = [str(t) for t in result.data.target.values]
+ # Should have at least costs effect
+ assert '[costs]' in targets, 'Should include costs effect'
+
+ def test_sankey_with_timestep_selection(self, simple_flow_system, highs_solver):
+ """Test Sankey with specific timestep."""
+ simple_flow_system.optimize(highs_solver)
+
+ result = simple_flow_system.statistics.plot.sankey(timestep=0, show=False)
+
+ assert result.figure is not None
+ assert len(result.data.link) > 0
+
+ def test_sankey_with_mean_aggregate(self, simple_flow_system, highs_solver):
+ """Test Sankey with mean aggregation."""
+ simple_flow_system.optimize(highs_solver)
+
+ result_sum = simple_flow_system.statistics.plot.sankey(aggregate='sum', show=False)
+ result_mean = simple_flow_system.statistics.plot.sankey(aggregate='mean', show=False)
+
+ # Both should produce valid results
+ assert result_sum.figure is not None
+ assert result_mean.figure is not None
+ # Mean values should be smaller than sum values
+ sum_total = sum(result_sum.data.value.values)
+ mean_total = sum(result_mean.data.value.values)
+ assert mean_total < sum_total, 'Mean should produce smaller values than sum'
+
+ def test_sankey_returns_plot_result(self, simple_flow_system, highs_solver):
+ """Test that sankey returns PlotResult with figure and data."""
+ simple_flow_system.optimize(highs_solver)
+
+ result = simple_flow_system.statistics.plot.sankey(show=False)
+
+ # Check PlotResult structure
+ assert hasattr(result, 'figure')
+ assert hasattr(result, 'data')
+ assert isinstance(result.data, xr.Dataset)
diff --git a/tests/test_topology_accessor.py b/tests/test_topology_accessor.py
index b1e3fdf31..dc9657726 100644
--- a/tests/test_topology_accessor.py
+++ b/tests/test_topology_accessor.py
@@ -3,6 +3,7 @@
import tempfile
from pathlib import Path
+import plotly.graph_objects as go
import pytest
import flixopt as fx
@@ -64,37 +65,92 @@ def test_infos_contains_all_elements(self, flow_system):
class TestTopologyPlot:
- """Tests for topology.plot() method."""
+ """Tests for topology.plot() method (Sankey-based)."""
+
+ def test_plot_returns_plotly_figure(self, flow_system):
+ """Test that plot() returns a Plotly Figure."""
+ result = flow_system.topology.plot(show=False)
+ assert isinstance(result, go.Figure)
+
+ def test_plot_contains_sankey_trace(self, flow_system):
+ """Test that the figure contains a Sankey trace."""
+ fig = flow_system.topology.plot(show=False)
+ assert len(fig.data) == 1
+ assert isinstance(fig.data[0], go.Sankey)
+
+ def test_plot_has_correct_title(self, flow_system):
+ """Test that the figure has the correct title."""
+ fig = flow_system.topology.plot(show=False)
+ assert fig.layout.title.text == 'Flow System Topology'
+
+ def test_plot_with_custom_title(self, flow_system):
+ """Test that custom title can be passed via plotly_kwargs."""
+ fig = flow_system.topology.plot(show=False, title='Custom Title')
+ assert fig.layout.title.text == 'Custom Title'
+
+ def test_plot_contains_all_nodes(self, flow_system):
+ """Test that the Sankey contains all buses and components as nodes."""
+ fig = flow_system.topology.plot(show=False)
+ sankey = fig.data[0]
+ node_labels = set(sankey.node.label)
+
+ # All buses should be in nodes
+ for bus in flow_system.buses.values():
+ assert bus.label in node_labels
+
+ # All components should be in nodes
+ for comp in flow_system.components.values():
+ assert comp.label in node_labels
+
+ def test_plot_contains_all_flows_as_links(self, flow_system):
+ """Test that all flows are represented as links."""
+ fig = flow_system.topology.plot(show=False)
+ sankey = fig.data[0]
+ link_labels = set(sankey.link.label)
+
+ # All flows should be represented as links
+ for flow in flow_system.flows.values():
+ assert flow.label_full in link_labels
+
+ def test_plot_with_colors(self, flow_system):
+ """Test that colors parameter is accepted."""
+ # Should not raise
+ flow_system.topology.plot(colors='Viridis', show=False)
+ flow_system.topology.plot(colors=['red', 'blue', 'green'], show=False)
+
+
+class TestTopologyPlotLegacy:
+ """Tests for topology.plot_legacy() method (PyVis-based)."""
- def test_plot_returns_network_or_none(self, flow_system):
- """Test that plot() returns a pyvis Network or None."""
+ def test_plot_legacy_returns_network_or_none(self, flow_system):
+ """Test that plot_legacy() returns a pyvis Network or None."""
try:
import pyvis
- result = flow_system.topology.plot(path=False, show=False)
+ result = flow_system.topology.plot_legacy(path=False, show=False)
assert result is None or isinstance(result, pyvis.network.Network)
except ImportError:
# pyvis not installed, should return None
- result = flow_system.topology.plot(path=False, show=False)
+ result = flow_system.topology.plot_legacy(path=False, show=False)
assert result is None
- def test_plot_creates_html_file(self, flow_system):
- """Test that plot() creates an HTML file when path is specified."""
+ def test_plot_legacy_creates_html_file(self, flow_system):
+ """Test that plot_legacy() creates an HTML file when path is specified."""
pytest.importorskip('pyvis')
with tempfile.TemporaryDirectory() as tmpdir:
html_path = Path(tmpdir) / 'network.html'
- flow_system.topology.plot(path=str(html_path), show=False)
+ flow_system.topology.plot_legacy(path=str(html_path), show=False)
assert html_path.exists()
content = html_path.read_text()
assert '' in content.lower() or '
Date: Tue, 9 Dec 2025 22:28:20 +0100
Subject: [PATCH 22/49] Update tests for new plot method
---
tests/test_solution_and_plotting.py | 32 ++++++++++++++++-------------
1 file changed, 18 insertions(+), 14 deletions(-)
diff --git a/tests/test_solution_and_plotting.py b/tests/test_solution_and_plotting.py
index 2d87b595e..b669431b9 100644
--- a/tests/test_solution_and_plotting.py
+++ b/tests/test_solution_and_plotting.py
@@ -426,24 +426,28 @@ def test_heatmap_with_matplotlib(self, long_time_data):
class TestNetworkVisualization:
"""Tests for network visualization functionality."""
- def test_plot_network_returns_network(self, simple_flow_system):
- """Test that plot_network returns a Network object."""
- pytest.importorskip('pyvis')
- network = simple_flow_system.plot_network(path=False, show=False)
- assert network is not None
-
- def test_plot_network_creates_html(self, simple_flow_system, tmp_path):
- """Test that plot_network creates HTML file."""
+ def test_topology_plot_returns_figure(self, simple_flow_system):
+ """Test that topology.plot() returns a Plotly Figure."""
+ import plotly.graph_objects as go
+
+ fig = simple_flow_system.topology.plot(show=False)
+ assert fig is not None
+ assert isinstance(fig, go.Figure)
+
+ def test_topology_plot_creates_html(self, simple_flow_system, tmp_path):
+ """Test that topology.plot() figure can be saved to HTML file."""
html_path = tmp_path / 'network.html'
- simple_flow_system.plot_network(path=str(html_path), show=False)
+ fig = simple_flow_system.topology.plot(show=False)
+ fig.write_html(str(html_path))
assert html_path.exists()
- def test_network_contains_all_buses(self, simple_flow_system):
- """Test that network contains all buses."""
- network = simple_flow_system.plot_network(path=False, show=False)
+ def test_topology_plot_contains_all_buses(self, simple_flow_system):
+ """Test that topology plot contains all buses in the Sankey diagram."""
+ fig = simple_flow_system.topology.plot(show=False)
- # Get node labels
- node_labels = [node['label'] for node in network.nodes]
+ # Get node labels from the Sankey diagram
+ sankey_data = fig.data[0]
+ node_labels = list(sankey_data.node.label)
# Check that buses are in network
for bus_label in simple_flow_system.buses.keys():
From 5d32ae902928b93deaabf71abe37851a15726993 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Wed, 10 Dec 2025 09:26:12 +0100
Subject: [PATCH 23/49] Extract docs build and deploy into separate workflow
(#520)
* Extract docs build into separate workflow
* Fix workflow
* docs deploy job uses the uploaded artifact
---
.github/workflows/docs.yaml | 108 +++++++++++++++++++++++++++++++++
.github/workflows/release.yaml | 38 ++----------
2 files changed, 112 insertions(+), 34 deletions(-)
create mode 100644 .github/workflows/docs.yaml
diff --git a/.github/workflows/docs.yaml b/.github/workflows/docs.yaml
new file mode 100644
index 000000000..d5fdc5b00
--- /dev/null
+++ b/.github/workflows/docs.yaml
@@ -0,0 +1,108 @@
+name: Docs
+
+on:
+ push:
+ branches: [main]
+ paths:
+ - 'docs/**'
+ - 'mkdocs.yml'
+ - 'flixopt/**'
+ pull_request:
+ paths:
+ - 'docs/**'
+ - 'mkdocs.yml'
+ workflow_dispatch:
+ workflow_call:
+ inputs:
+ deploy:
+ type: boolean
+ default: false
+ version:
+ type: string
+ required: false
+
+concurrency:
+ group: ${{ github.workflow }}-${{ github.ref }}
+ cancel-in-progress: true
+
+env:
+ PYTHON_VERSION: "3.11"
+ MPLBACKEND: Agg
+ PLOTLY_RENDERER: json
+
+jobs:
+ build:
+ name: Build documentation
+ runs-on: ubuntu-24.04
+ timeout-minutes: 30
+ steps:
+ - uses: actions/checkout@v5
+ with:
+ fetch-depth: 0
+
+ - uses: astral-sh/setup-uv@v6
+ with:
+ version: "0.9.10"
+ enable-cache: true
+
+ - uses: actions/setup-python@v6
+ with:
+ python-version: ${{ env.PYTHON_VERSION }}
+
+ - name: Extract changelog
+ run: |
+ uv pip install --system packaging
+ python scripts/extract_changelog.py
+
+ - name: Install dependencies
+ run: uv pip install --system ".[docs]"
+
+ - name: Build docs
+ run: mkdocs build --strict
+
+ - uses: actions/upload-artifact@v4
+ with:
+ name: docs
+ path: site/
+ retention-days: 7
+
+ deploy:
+ name: Deploy documentation
+ needs: build
+ if: ${{ inputs.deploy == true }}
+ runs-on: ubuntu-24.04
+ permissions:
+ contents: write
+ steps:
+ - uses: actions/checkout@v5
+ with:
+ fetch-depth: 0
+
+ - uses: astral-sh/setup-uv@v6
+ with:
+ version: "0.9.10"
+ enable-cache: true
+
+ - uses: actions/setup-python@v6
+ with:
+ python-version: ${{ env.PYTHON_VERSION }}
+
+ - name: Install mike
+ run: uv pip install --system mike
+
+ - uses: actions/download-artifact@v4
+ with:
+ name: docs
+ path: site/
+
+ - name: Configure Git
+ run: |
+ git config user.name "github-actions[bot]"
+ git config user.email "41898282+github-actions[bot]@users.noreply.github.com"
+
+ - name: Deploy docs
+ run: |
+ VERSION=${{ inputs.version }}
+ VERSION=${VERSION#v}
+ mike deploy --push --update-aliases --no-build $VERSION latest
+ mike set-default --push latest
diff --git a/.github/workflows/release.yaml b/.github/workflows/release.yaml
index 4f1edd3e8..2bf49bfc1 100644
--- a/.github/workflows/release.yaml
+++ b/.github/workflows/release.yaml
@@ -188,37 +188,7 @@ jobs:
name: Deploy documentation
needs: [create-release]
if: "!contains(github.ref, 'alpha') && !contains(github.ref, 'beta') && !contains(github.ref, 'rc')"
- runs-on: ubuntu-24.04
- permissions:
- contents: write
- steps:
- - uses: actions/checkout@v5
- with:
- fetch-depth: 0
-
- - uses: astral-sh/setup-uv@v6
- with:
- version: "0.9.10"
-
- - uses: actions/setup-python@v6
- with:
- python-version: ${{ env.PYTHON_VERSION }}
-
- - name: Extract changelog
- run: |
- uv pip install --system packaging
- python scripts/extract_changelog.py
-
- - name: Install docs dependencies
- run: uv pip install --system ".[docs]"
-
- - name: Configure Git
- run: |
- git config user.name github-actions[bot]
- git config user.email 41898282+github-actions[bot]@users.noreply.github.com
-
- - name: Deploy docs
- run: |
- VERSION=${GITHUB_REF#refs/tags/v}
- mike deploy --push --update-aliases $VERSION latest
- mike set-default --push latest
+ uses: ./.github/workflows/docs.yaml
+ with:
+ deploy: true
+ version: ${{ github.ref_name }}
From b0202b90dad0b17daf1c9a69c205ec30258825f9 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Wed, 10 Dec 2025 09:50:54 +0100
Subject: [PATCH 24/49] fix: docs build CI
---
.github/workflows/docs.yaml | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/.github/workflows/docs.yaml b/.github/workflows/docs.yaml
index d5fdc5b00..4424d5122 100644
--- a/.github/workflows/docs.yaml
+++ b/.github/workflows/docs.yaml
@@ -51,8 +51,8 @@ jobs:
- name: Extract changelog
run: |
- uv pip install --system packaging
- python scripts/extract_changelog.py
+ cp CHANGELOG.md docs/changelog.md
+ python scripts/format_changelog.py
- name: Install dependencies
run: uv pip install --system ".[docs]"
From 92fede12aca12b676e300438c7e4d953ef512562 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Wed, 10 Dec 2025 15:22:45 +0100
Subject: [PATCH 25/49] Minor nitpicks
---
docs/home/citing.md | 2 +-
docs/home/license.md | 2 +-
docs/user-guide/building-models/index.md | 2 +-
.../two_stage_optimization.py | 3 ++-
flixopt/features.py | 4 ++--
flixopt/flow_system.py | 1 +
flixopt/statistics_accessor.py | 2 +-
flixopt/topology_accessor.py | 10 ----------
flixopt/transform_accessor.py | 6 ++++--
scripts/format_changelog.py | 11 ++++++++---
tests/deprecated/conftest.py | 8 ++++----
11 files changed, 25 insertions(+), 26 deletions(-)
diff --git a/docs/home/citing.md b/docs/home/citing.md
index 6fd1a6020..a4f900d18 100644
--- a/docs/home/citing.md
+++ b/docs/home/citing.md
@@ -12,7 +12,7 @@ If you've published research using flixOpt, please let us know! We'd love to fea
### List of Publications
-*Coming soon: A list of academic publications that have used flixOpt*
+Coming soon: A list of academic publications that have used flixOpt.
## Contributing Back
diff --git a/docs/home/license.md b/docs/home/license.md
index d00755a0b..e0b0266a4 100644
--- a/docs/home/license.md
+++ b/docs/home/license.md
@@ -4,7 +4,7 @@ flixOpt is released under the MIT License.
## MIT License
-```
+```text
MIT License
Copyright (c) 2022 Chair of Building Energy Systems and Heat Supply - TU Dresden
diff --git a/docs/user-guide/building-models/index.md b/docs/user-guide/building-models/index.md
index 27808ea56..1133d5cde 100644
--- a/docs/user-guide/building-models/index.md
+++ b/docs/user-guide/building-models/index.md
@@ -9,7 +9,7 @@ Learn how to construct FlowSystem models step by step:
- Creating buses and flows
- Adding components (Sources, Sinks, Converters, Storage)
- Configuring effects and objectives
-- Using advanced features (Investment, On/Off, Piecewise)
+- Using advanced features (Investment, Status, Piecewise)
## Getting Started
diff --git a/examples/05_Two-stage-optimization/two_stage_optimization.py b/examples/05_Two-stage-optimization/two_stage_optimization.py
index bf7f13a39..3f3278477 100644
--- a/examples/05_Two-stage-optimization/two_stage_optimization.py
+++ b/examples/05_Two-stage-optimization/two_stage_optimization.py
@@ -11,6 +11,7 @@
import pathlib
import timeit
+import numpy as np
import pandas as pd
import xarray as xr
@@ -141,7 +142,7 @@
# Verify sizes were correctly fixed
dispatch_sizes = calculation_dispatch.flow_system.statistics.sizes
sizing_sizes = calculation_sizing.flow_system.statistics.sizes
- if (dispatch_sizes.round(5).to_dataarray() == sizing_sizes.round(5).to_dataarray()).all().item():
+ if np.allclose(dispatch_sizes.to_dataarray(), sizing_sizes.to_dataarray(), rtol=1e-5):
logger.info('Sizes were correctly equalized')
else:
raise RuntimeError('Sizes were not correctly equalized')
diff --git a/flixopt/features.py b/flixopt/features.py
index cd9e07151..4dfe48964 100644
--- a/flixopt/features.py
+++ b/flixopt/features.py
@@ -156,7 +156,7 @@ class StatusModel(Submodel):
state transitions, duration tracking, and operational effects.
Mathematical Formulation:
- See
+ See
"""
def __init__(
@@ -345,7 +345,7 @@ def _get_previous_downtime(self):
if self._previous_status is None:
return hours_per_step
else:
- return ModelingUtilities.compute_consecutive_hours_in_state(self._previous_status * -1 + 1, hours_per_step)
+ return ModelingUtilities.compute_consecutive_hours_in_state(1 - self._previous_status, hours_per_step)
class PieceModel(Submodel):
diff --git a/flixopt/flow_system.py b/flixopt/flow_system.py
index ce7bd0658..e7e1ce0cc 100644
--- a/flixopt/flow_system.py
+++ b/flixopt/flow_system.py
@@ -640,6 +640,7 @@ def from_dataset(cls, ds: xr.Dataset) -> FlowSystem:
else None,
scenario_independent_sizes=reference_structure.get('scenario_independent_sizes', True),
scenario_independent_flow_rates=reference_structure.get('scenario_independent_flow_rates', False),
+ name=reference_structure.get('name'),
)
# Restore components
diff --git a/flixopt/statistics_accessor.py b/flixopt/statistics_accessor.py
index 2be1b5823..0cdd2f5ba 100644
--- a/flixopt/statistics_accessor.py
+++ b/flixopt/statistics_accessor.py
@@ -985,7 +985,7 @@ def heatmap(
heatmap_dims = ['time'] if 'time' in da.dims else list(da.dims)[:1]
# Keep only dims we need
- keep_dims = set(heatmap_dims) | {actual_facet, actual_animation} - {None}
+ keep_dims = set(heatmap_dims) | {d for d in [actual_facet, actual_animation] if d is not None}
for dim in [d for d in da.dims if d not in keep_dims]:
da = da.isel({dim: 0}, drop=True) if da.sizes[dim] > 1 else da.squeeze(dim, drop=True)
diff --git a/flixopt/topology_accessor.py b/flixopt/topology_accessor.py
index 6e0980ae3..2bbb5e782 100644
--- a/flixopt/topology_accessor.py
+++ b/flixopt/topology_accessor.py
@@ -427,16 +427,6 @@ def stop_app(self) -> None:
Examples:
>>> flow_system.topology.stop_app()
"""
- from .network_app import DASH_CYTOSCAPE_AVAILABLE, VISUALIZATION_ERROR
-
- if not DASH_CYTOSCAPE_AVAILABLE:
- raise ImportError(
- f'Network visualization requires optional dependencies. '
- f'Install with: `pip install flixopt[network_viz]`, `pip install flixopt[full]` '
- f'or: `pip install dash dash-cytoscape dash-daq networkx werkzeug`. '
- f'Original error: {VISUALIZATION_ERROR}'
- )
-
if self._fs._network_app is None:
logger.warning("No network app is currently running. Can't stop it")
return
diff --git a/flixopt/transform_accessor.py b/flixopt/transform_accessor.py
index cb0d87872..bf2a7ed5e 100644
--- a/flixopt/transform_accessor.py
+++ b/flixopt/transform_accessor.py
@@ -503,7 +503,8 @@ def _resample_by_dimension_groups(
dims_key = tuple(sorted(d for d in var.dims if d != 'time'))
dim_groups[dims_key].append(var_name)
- if not dim_groups:
+ # Note: defaultdict is always truthy, so we check length explicitly
+ if len(dim_groups) == 0:
return getattr(time_dataset.resample(time=time, **kwargs), method)()
resampled_groups = []
@@ -521,7 +522,8 @@ def _resample_by_dimension_groups(
resampled_groups.append(resampled_dataset)
if not resampled_groups:
- return time_dataset
+ # No data variables to resample, but still resample coordinates
+ return getattr(time_dataset.resample(time=time, **kwargs), method)()
if len(resampled_groups) == 1:
return resampled_groups[0]
diff --git a/scripts/format_changelog.py b/scripts/format_changelog.py
index 48feddc09..891b10c77 100644
--- a/scripts/format_changelog.py
+++ b/scripts/format_changelog.py
@@ -46,16 +46,21 @@ def format_version_header(match) -> str:
# Format the date
formatted_date = format_date(date_str)
+ # Normalise to a Git tag-style version (e.g. "v4.0.0") for URL, display text and id
+ version_tag = version if version.startswith('v') else f'v{version}'
+
# Create the new header
- github_url = f'https://github.com/flixOpt/flixopt/releases/tag/v{version}'
- new_header = f'## [**{version}**]({github_url})
{formatted_date} {{ id="{version}" }}'
+ github_url = f'https://github.com/flixOpt/flixopt/releases/tag/{version_tag}'
+ new_header = f'## [**{version_tag}**]({github_url})
{formatted_date} {{ id="{version_tag}" }}'
return new_header
def main():
"""Process the changelog file."""
- changelog_path = Path('docs/changelog.md')
+ script_dir = Path(__file__).resolve().parent
+ repo_root = script_dir.parent # assumes this file lives in
/scripts/
+ changelog_path = repo_root / 'docs' / 'changelog.md'
if not changelog_path.exists():
print(f'❌ {changelog_path} not found')
diff --git a/tests/deprecated/conftest.py b/tests/deprecated/conftest.py
index e24dcaa72..8b22ba128 100644
--- a/tests/deprecated/conftest.py
+++ b/tests/deprecated/conftest.py
@@ -341,13 +341,13 @@ def electrical_complex(timesteps_length=9):
@staticmethod
def random_thermal(length=10, seed=42):
- np.random.seed(seed)
- return np.array([np.random.random() for _ in range(length)]) * 180
+ rng = np.random.default_rng(seed)
+ return rng.random(length) * 180
@staticmethod
def random_electrical(length=10, seed=42):
- np.random.seed(seed)
- return (np.array([np.random.random() for _ in range(length)]) + 0.5) / 1.5 * 50
+ rng = np.random.default_rng(seed)
+ return (rng.random(length) + 0.5) / 1.5 * 50
class Sinks:
From 75c0aed893a1abb33a053b9bad38aab9b1915859 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Wed, 10 Dec 2025 16:25:22 +0100
Subject: [PATCH 26/49] revert: solution always having an extra timestep (#523)
* Reverted the time index handling to keep the original solution with charge_state including the extra timestep. All other variables now have NaN on the final timestep
instead of being truncated.
Changes Made:
1. flixopt/structure.py:191-206 - Removed the code that:
- Extracted final charge states into separate |final variables
- Reindexed the solution to regular timesteps
2. tests/test_solution_and_plotting.py:78-80 - Removed the assertion expecting the Speicher|charge_state|final variable
3. tests/test_integration.py:168-178 - Updated the charge_state expectation to include the extra timestep value (10.0 at the end)
4. tests/conftest.py:695-718 and tests/deprecated/conftest.py:694-717 - Updated the assert_almost_equal_numeric function to handle the extra timestep by trimming
arrays when the extra values are NaN (for non-charge_state variables)
Result:
- charge_state variables now include len(timesteps) + 1 values, with the final value being the actual final charge state
- All other time-indexed variables have len(timesteps) + 1 values with NaN at the final timestep (due to xarray coordinate merging)
- All 1329 tests pass
* Verify that time index always has extra timestep in solution!
* fixup test
* Update new tests for nan as last timestep
* Update some comments and add warnings in tests for nan handling
* Update docstring
* bugfix: revert
---
flixopt/flow_system.py | 17 +++++++++-
flixopt/structure.py | 20 +++--------
tests/conftest.py | 20 ++++++++++-
tests/deprecated/conftest.py | 20 ++++++++++-
tests/deprecated/test_functional.py | 17 +++++-----
tests/test_functional.py | 52 ++++++++++++++---------------
tests/test_integration.py | 9 ++---
tests/test_solution_and_plotting.py | 3 +-
8 files changed, 96 insertions(+), 62 deletions(-)
diff --git a/flixopt/flow_system.py b/flixopt/flow_system.py
index e7e1ce0cc..0de7b6536 100644
--- a/flixopt/flow_system.py
+++ b/flixopt/flow_system.py
@@ -1200,7 +1200,22 @@ def solve(self, solver: _Solver) -> FlowSystem:
@property
def solution(self) -> xr.Dataset | None:
- """Get the solution dataset."""
+ """
+ Access the optimization solution as an xarray Dataset.
+
+ The solution is indexed by ``timesteps_extra`` (the original timesteps plus
+ one additional timestep at the end). Variables that do not have data for the
+ extra timestep (most variables except storage charge states) will contain
+ NaN values at the final timestep.
+
+ Returns:
+ xr.Dataset: The solution dataset with all optimization variable results,
+ or None if the model hasn't been solved yet.
+
+ Example:
+ >>> flow_system.optimize(solver)
+ >>> flow_system.solution.isel(time=slice(None, -1)) # Exclude trailing NaN (and final charge states)
+ """
return self._solution
@solution.setter
diff --git a/flixopt/structure.py b/flixopt/structure.py
index da4eee0f6..63d028660 100644
--- a/flixopt/structure.py
+++ b/flixopt/structure.py
@@ -166,6 +166,7 @@ def _add_scenario_equality_constraints(self):
@property
def solution(self):
+ """Build solution dataset, reindexing to timesteps_extra for consistency."""
solution = super().solution
solution['objective'] = self.objective.value
solution.attrs = {
@@ -188,21 +189,10 @@ def solution(self):
for flow in sorted(self.flow_system.flows.values(), key=lambda flow: flow.label_full.upper())
},
}
- # Handle extra timestep from storage charge_state variables.
- # Storage charge_state uses extra_timestep=True which causes linopy/xarray to
- # merge all time coordinates to include the extra timestep with NaN for other vars.
- # We extract the final charge state as separate variables and reindex to regular timesteps.
- if 'time' in solution.coords and len(solution.coords['time']) > len(self.flow_system.timesteps):
- # Collect final states first to avoid modifying during iteration
- final_states = {}
- for var_name in solution.data_vars:
- if var_name.endswith('|charge_state') and 'time' in solution[var_name].dims:
- # Extract final charge state as separate variable
- final_states[f'{var_name}|final'] = solution[var_name].isel(time=-1)
- # Add all final states at once
- solution = solution.assign(final_states)
- # Reindex all variables to regular timesteps
- solution = solution.reindex(time=self.flow_system.timesteps)
+ # Ensure solution is always indexed by timesteps_extra for consistency.
+ # Variables without extra timestep data will have NaN at the final timestep.
+ if 'time' in solution.coords and not solution.indexes['time'].equals(self.flow_system.timesteps_extra):
+ solution = solution.reindex(time=self.flow_system.timesteps_extra)
return solution
@property
diff --git a/tests/conftest.py b/tests/conftest.py
index 15c7509d3..49734911a 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -5,6 +5,7 @@
"""
import os
+import warnings
from collections.abc import Iterable
import linopy.testing
@@ -696,7 +697,10 @@ def assert_almost_equal_numeric(
actual, desired, err_msg, relative_error_range_in_percent=0.011, absolute_tolerance=1e-7
):
"""
- Custom assertion function for comparing numeric values with relative and absolute tolerances
+ Custom assertion function for comparing numeric values with relative and absolute tolerances.
+
+ Handles the extra timestep in solutions by trimming actual arrays to match desired length
+ when the extra values are NaN (from storage charge_state variables using extra_timestep).
"""
relative_tol = relative_error_range_in_percent / 100
@@ -704,6 +708,20 @@ def assert_almost_equal_numeric(
delta = abs(relative_tol * desired) if desired != 0 else absolute_tolerance
assert np.isclose(actual, desired, atol=delta), err_msg
else:
+ actual = np.asarray(actual)
+ desired = np.asarray(desired)
+ # Handle extra timestep: trim actual to desired length if extra values are NaN
+ if actual.shape != desired.shape and actual.ndim == 1 and desired.ndim == 1:
+ if len(actual) > len(desired):
+ extra = actual[len(desired) :]
+ if np.all(np.isnan(extra)):
+ # Warn if trimming more than the expected single extra timestep
+ if len(extra) > 1:
+ warnings.warn(
+ f'Trimming {len(extra)} NaN values from actual array (expected 1)',
+ stacklevel=2,
+ )
+ actual = actual[: len(desired)]
np.testing.assert_allclose(actual, desired, rtol=relative_tol, atol=absolute_tolerance, err_msg=err_msg)
diff --git a/tests/deprecated/conftest.py b/tests/deprecated/conftest.py
index 8b22ba128..b6ec5ac4b 100644
--- a/tests/deprecated/conftest.py
+++ b/tests/deprecated/conftest.py
@@ -8,6 +8,7 @@
"""
import os
+import warnings
from collections.abc import Iterable
import linopy.testing
@@ -695,7 +696,10 @@ def assert_almost_equal_numeric(
actual, desired, err_msg, relative_error_range_in_percent=0.011, absolute_tolerance=1e-7
):
"""
- Custom assertion function for comparing numeric values with relative and absolute tolerances
+ Custom assertion function for comparing numeric values with relative and absolute tolerances.
+
+ Handles the extra timestep in solutions by trimming actual arrays to match desired length
+ when the extra values are NaN (from storage charge_state variables using extra_timestep).
"""
relative_tol = relative_error_range_in_percent / 100
@@ -703,6 +707,20 @@ def assert_almost_equal_numeric(
delta = abs(relative_tol * desired) if desired != 0 else absolute_tolerance
assert np.isclose(actual, desired, atol=delta), err_msg
else:
+ actual = np.asarray(actual)
+ desired = np.asarray(desired)
+ # Handle extra timestep: trim actual to desired length if extra values are NaN
+ if actual.shape != desired.shape and actual.ndim == 1 and desired.ndim == 1:
+ if len(actual) > len(desired):
+ extra = actual[len(desired) :]
+ if np.all(np.isnan(extra)):
+ # Warn if trimming more than the expected single extra timestep
+ if len(extra) > 1:
+ warnings.warn(
+ f'Trimming {len(extra)} NaN values from actual array (expected 1)',
+ stacklevel=2,
+ )
+ actual = actual[: len(desired)]
np.testing.assert_allclose(actual, desired, rtol=relative_tol, atol=absolute_tolerance, err_msg=err_msg)
diff --git a/tests/deprecated/test_functional.py b/tests/deprecated/test_functional.py
index 34d16819c..c72754003 100644
--- a/tests/deprecated/test_functional.py
+++ b/tests/deprecated/test_functional.py
@@ -23,6 +23,7 @@
from numpy.testing import assert_allclose
import flixopt as fx
+from tests.deprecated.conftest import assert_almost_equal_numeric
np.random.seed(45)
@@ -114,25 +115,23 @@ def test_minimal_model(solver_fixture, time_steps_fixture):
assert_allclose(flow_system.solution['costs'].values, 80, rtol=1e-5, atol=1e-10)
- assert_allclose(
+ # Use assert_almost_equal_numeric to handle extra timestep with NaN
+ assert_almost_equal_numeric(
flow_system.solution['Boiler(Q_th)|flow_rate'].values,
[-0.0, 10.0, 20.0, -0.0, 10.0],
- rtol=1e-5,
- atol=1e-10,
+ 'Boiler flow_rate doesnt match expected value',
)
- assert_allclose(
+ assert_almost_equal_numeric(
flow_system.solution['costs(temporal)|per_timestep'].values,
[-0.0, 20.0, 40.0, -0.0, 20.0],
- rtol=1e-5,
- atol=1e-10,
+ 'costs per_timestep doesnt match expected value',
)
- assert_allclose(
+ assert_almost_equal_numeric(
flow_system.solution['Gastarif(Gas)->costs(temporal)'].values,
[-0.0, 20.0, 40.0, -0.0, 20.0],
- rtol=1e-5,
- atol=1e-10,
+ 'Gastarif costs doesnt match expected value',
)
diff --git a/tests/test_functional.py b/tests/test_functional.py
index 24322a6e0..8cf67cff9 100644
--- a/tests/test_functional.py
+++ b/tests/test_functional.py
@@ -115,21 +115,21 @@ def test_minimal_model(solver_fixture, time_steps_fixture):
assert_allclose(flow_system.solution['costs'].values, 80, rtol=1e-5, atol=1e-10)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler(Q_th)|flow_rate'].values[:-1],
[-0.0, 10.0, 20.0, -0.0, 10.0],
rtol=1e-5,
atol=1e-10,
)
assert_allclose(
- flow_system.solution['costs(temporal)|per_timestep'].values,
+ flow_system.solution['costs(temporal)|per_timestep'].values[:-1],
[-0.0, 20.0, 40.0, -0.0, 20.0],
rtol=1e-5,
atol=1e-10,
)
assert_allclose(
- flow_system.solution['Gastarif(Gas)->costs(temporal)'].values,
+ flow_system.solution['Gastarif(Gas)->costs(temporal)'].values[:-1],
[-0.0, 20.0, 40.0, -0.0, 20.0],
rtol=1e-5,
atol=1e-10,
@@ -343,14 +343,14 @@ def test_on(solver_fixture, time_steps_fixture):
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|status'].values,
+ flow_system.solution['Boiler(Q_th)|status'].values[:-1],
[0, 1, 1, 0, 1],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler__Q_th__on" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler(Q_th)|flow_rate'].values[:-1],
[0, 10, 20, 0, 10],
rtol=1e-5,
atol=1e-10,
@@ -385,21 +385,21 @@ def test_off(solver_fixture, time_steps_fixture):
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|status'].values,
+ flow_system.solution['Boiler(Q_th)|status'].values[:-1],
[0, 1, 1, 0, 1],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler__Q_th__on" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|inactive'].values,
- 1 - flow_system.solution['Boiler(Q_th)|status'].values,
+ flow_system.solution['Boiler(Q_th)|inactive'].values[:-1],
+ 1 - flow_system.solution['Boiler(Q_th)|status'].values[:-1],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler__Q_th__off" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler(Q_th)|flow_rate'].values[:-1],
[0, 10, 20, 0, 10],
rtol=1e-5,
atol=1e-10,
@@ -434,28 +434,28 @@ def test_startup_shutdown(solver_fixture, time_steps_fixture):
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|status'].values,
+ flow_system.solution['Boiler(Q_th)|status'].values[:-1],
[0, 1, 1, 0, 1],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler__Q_th__on" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|startup'].values,
+ flow_system.solution['Boiler(Q_th)|startup'].values[:-1],
[0, 1, 0, 0, 1],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler__Q_th__switch_on" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|shutdown'].values,
+ flow_system.solution['Boiler(Q_th)|shutdown'].values[:-1],
[0, 0, 0, 1, 0],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler__Q_th__switch_on" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler(Q_th)|flow_rate'].values[:-1],
[0, 10, 20, 0, 10],
rtol=1e-5,
atol=1e-10,
@@ -496,14 +496,14 @@ def test_on_total_max(solver_fixture, time_steps_fixture):
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|status'].values,
+ flow_system.solution['Boiler(Q_th)|status'].values[:-1],
[0, 0, 1, 0, 0],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler__Q_th__on" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler(Q_th)|flow_rate'].values[:-1],
[0, 0, 20, 0, 0],
rtol=1e-5,
atol=1e-10,
@@ -552,14 +552,14 @@ def test_on_total_bounds(solver_fixture, time_steps_fixture):
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|status'].values,
+ flow_system.solution['Boiler(Q_th)|status'].values[:-1],
[0, 0, 1, 0, 1],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler__Q_th__on" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler(Q_th)|flow_rate'].values[:-1],
[0, 0, 20, 0, 12 - 1e-5],
rtol=1e-5,
atol=1e-10,
@@ -567,14 +567,14 @@ def test_on_total_bounds(solver_fixture, time_steps_fixture):
)
assert_allclose(
- sum(flow_system.solution['Boiler_backup(Q_th)|status'].values),
+ sum(flow_system.solution['Boiler_backup(Q_th)|status'].values[:-1]),
3,
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler_backup__Q_th__on" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler_backup(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler_backup(Q_th)|flow_rate'].values[:-1],
[0, 10, 1.0e-05, 0, 1.0e-05],
rtol=1e-5,
atol=1e-10,
@@ -617,14 +617,14 @@ def test_consecutive_uptime_downtime(solver_fixture, time_steps_fixture):
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|status'].values,
+ flow_system.solution['Boiler(Q_th)|status'].values[:-1],
[1, 1, 0, 1, 1],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler__Q_th__on" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler(Q_th)|flow_rate'].values[:-1],
[5, 10, 0, 18, 12],
rtol=1e-5,
atol=1e-10,
@@ -632,7 +632,7 @@ def test_consecutive_uptime_downtime(solver_fixture, time_steps_fixture):
)
assert_allclose(
- flow_system.solution['Boiler_backup(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler_backup(Q_th)|flow_rate'].values[:-1],
[0, 0, 20, 0, 0],
rtol=1e-5,
atol=1e-10,
@@ -677,21 +677,21 @@ def test_consecutive_off(solver_fixture, time_steps_fixture):
)
assert_allclose(
- flow_system.solution['Boiler_backup(Q_th)|status'].values,
+ flow_system.solution['Boiler_backup(Q_th)|status'].values[:-1],
[0, 0, 1, 0, 0],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler_backup__Q_th__on" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler_backup(Q_th)|inactive'].values,
+ flow_system.solution['Boiler_backup(Q_th)|inactive'].values[:-1],
[1, 1, 0, 1, 1],
rtol=1e-5,
atol=1e-10,
err_msg='"Boiler_backup__Q_th__off" does not have the right value',
)
assert_allclose(
- flow_system.solution['Boiler_backup(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler_backup(Q_th)|flow_rate'].values[:-1],
[0, 0, 1e-5, 0, 0],
rtol=1e-5,
atol=1e-10,
@@ -699,7 +699,7 @@ def test_consecutive_off(solver_fixture, time_steps_fixture):
)
assert_allclose(
- flow_system.solution['Boiler(Q_th)|flow_rate'].values,
+ flow_system.solution['Boiler(Q_th)|flow_rate'].values[:-1],
[5, 0, 20 - 1e-5, 18, 12],
rtol=1e-5,
atol=1e-10,
diff --git a/tests/test_integration.py b/tests/test_integration.py
index 92a20841a..d33bb54e8 100644
--- a/tests/test_integration.py
+++ b/tests/test_integration.py
@@ -165,17 +165,12 @@ def test_basic_flow_system(self, flow_system_base, highs_solver):
[-45.0, -69.71111111, 15.0, -10.0, 36.06697198, -55.0, 20.0, 20.0, 20.0],
'Speicher nettoFlow doesnt match expected value',
)
- # charge_state now has len(timesteps) values, with final state in separate variable
+ # charge_state includes extra timestep for final charge state (len = timesteps + 1)
assert_almost_equal_numeric(
flow_system_base.solution['Speicher|charge_state'].values,
- [0.0, 40.5, 100.0, 77.0, 79.84, 37.38582802, 83.89496178, 57.18336484, 32.60869565],
+ [0.0, 40.5, 100.0, 77.0, 79.84, 37.38582802, 83.89496178, 57.18336484, 32.60869565, 10.0],
'Speicher charge_state doesnt match expected value',
)
- assert_almost_equal_numeric(
- flow_system_base.solution['Speicher|charge_state|final'].values,
- 10.0,
- 'Speicher final charge_state doesnt match expected value',
- )
assert_almost_equal_numeric(
flow_system_base.solution['Speicher|PiecewiseEffects|costs'].values,
diff --git a/tests/test_solution_and_plotting.py b/tests/test_solution_and_plotting.py
index b669431b9..88d92e91f 100644
--- a/tests/test_solution_and_plotting.py
+++ b/tests/test_solution_and_plotting.py
@@ -75,9 +75,8 @@ def test_solution_contains_storage_variables(self, simple_flow_system, highs_sol
simple_flow_system.optimize(highs_solver)
solution = simple_flow_system.solution
- # Check storage charge state
+ # Check storage charge state (includes extra timestep for final state)
assert 'Speicher|charge_state' in solution
- assert 'Speicher|charge_state|final' in solution
def test_solution_item_returns_scalar(self, simple_flow_system, highs_solver):
"""Verify .item() returns Python scalar for 0-d arrays."""
From f3dc1e14897b43af86ddd2634f401ab807238437 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Wed, 10 Dec 2025 16:59:31 +0100
Subject: [PATCH 27/49] Add new user facing notebooks with better user stories
(#515)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
* Add planning doc
* Finalize planning
* Add plotting acessor
* Add plotting acessor
* Add tests
* Improve
* Improve
* Update docs
* Updated the plotting API so that .data always returns xarray DataArray or Dataset instead of pandas DataFrame.
* All .data now returns xr.Dataset consistently.
* Fixed Inconsistencies and Unused Parameters
* New Plot Accessors
results.plot.variable(pattern)
Plots the same variable type across multiple elements for easy comparison.
# All binary operation states across all components
results.plot.variable('on')
# All flow_rates, filtered to Boiler-related elements
results.plot.variable('flow_rate', include='Boiler')
# All storage charge states
results.plot.variable('charge_state')
# With aggregation
results.plot.variable('flow_rate', aggregate='sum')
Key features:
- Searches all elements for variables matching the pattern
- Filter with include/exclude on element names
- Supports aggregation, faceting, and animation
- Returns Dataset with element names as variables
results.plot.duration_curve(variables)
Plots load duration curves (sorted time series) showing utilization patterns.
# Single variable
results.plot.duration_curve('Boiler(Q_th)|flow_rate')
# Multiple variables
results.plot.duration_curve(['CHP|on', 'Boiler|on'])
# Normalized x-axis (0-100%)
results.plot.duration_curve('demand', normalize=True)
Key features:
- Sorts values from highest to lowest
- Shows how often each power level is reached
- normalize=True shows percentage of time on x-axis
- Returns Dataset with duration_hours or duration_pct dimension
* Fix duration curve
* Fix duration curve
* Fix duration curve
* Fix duration curve
* xr.apply_ufunc to sort along the time axis while preserving all other dimensions automatically
* ⏺ The example runs successfully. Now let me summarize the fixes:
Summary of Fixes
I addressed the actionable code review comments from CodeRabbitAI:
1. Documentation Issue - reshape parameter name ✓ (No fix needed)
The CodeRabbitAI comment was incorrect. The public API parameter in PlotAccessor.heatmap() is correctly named reshape (line 335). The reshape_time parameter exists in the lower-level heatmap_with_plotly function, but the documentation correctly shows the public API parameter.
2. Fixed simple_example.py (lines 129-130)
Problem: The example called balance() and duration_curve() without required arguments, which would cause TypeError at runtime.
Fix: Added the required arguments:
- optimization.results.plot.balance('Fernwärme') - specifying the bus to plot
- optimization.results.plot.duration_curve('Boiler(Q_th)|flow_rate') - specifying the variable to plot
3. Fixed variable collision in plot_accessors.py (lines 985-988)
Problem: When building the Dataset in the variable() method, using element names as keys could cause collisions if multiple variables from the same element matched the pattern (e.g., 'Boiler|flow_rate' and 'Boiler|flow_rate_max' would both map to 'Boiler', with the latter silently overwriting the former).
Fix: Changed to use the full variable names as keys instead of just element names:
ds = xr.Dataset({var_name: self._results.solution[var_name] for var_name in filtered_vars})
All tests pass (40 passed, 1 skipped) and the example runs successfully.
* make variable names public in results
* Fix sankey
* Fix effects()
* Fix effects
* Remove bargaps
* made faceting consistent across all plot methods:
| Method | facet_col | facet_row |
|------------------|-------------------------------------------|-----------------------------|
| balance() | 'scenario' | 'period' |
| heatmap() | 'scenario' | 'period' |
| storage() | 'scenario' | 'period' |
| flows() | 'scenario' | 'period' |
| effects() | 'scenario' | 'period' |
| variable() | 'scenario' | 'period' |
| duration_curve() | 'scenario' | 'period' (already had this) |
| compare() | N/A (uses its own mode='overlay'/'facet') | |
| sankey() | N/A (aggregates to single diagram) | |
Removed animate_by parameter from all methods
* Update storage method
* Remove mode parameter for simpli
| Method | Default mode |
|------------------|---------------------------------------------------|
| balance() | stacked_bar |
| storage() | stacked_bar (flows) + line (charge state overlay) |
| flows() | line |
| variable() | line |
| duration_curve() | line |
| effects() | bar |
* Make plotting_accessors.py more self contained
* Use faster to_long()
* Add 0-dim case
* sankey diagram now properly handles scenarios and periods:
Changes made:
1. Period aggregation with weights: Uses period_weights from flow_system to properly weight periods by their duration
2. Scenario aggregation with weights: Uses normalized scenario_weights to compute a weighted average across scenarios
3. Selection support: Users can filter specific scenarios/periods via select parameter before aggregation
Weighting logic:
- Periods (for aggregate='sum'): (da * period_weights).sum(dim='period') - this gives the total energy across all periods weighted by their duration
- Periods (for aggregate='mean'): (da * period_weights).sum(dim='period') / period_weights.sum() - weighted mean
- Scenarios: Always uses normalized weights (sum to 1) for weighted averaging, since scenarios represent probability-weighted alternatives
* Add colors to sankey
* Add sizes
* Add size filtering
* Include storage sizes
* Remove storage sizes
* Add charge state and status accessor
* Summary of Changes
1. Added new methods to PlotAccessor (plot_accessors.py)
charge_states() (line 658):
- Returns a Dataset with each storage's charge state as a variable
- Supports filtering with include/exclude parameters
- Default plot: line chart
on_states() (line 753):
- Returns a Dataset with each component's |status variable
- Supports filtering with include/exclude parameters
- Default plot: heatmap (good for binary data visualization)
2. Added data building helper functions (plot_accessors.py)
build_flow_rates(results) (line 315):
- Builds a DataArray containing flow rates for all flows
- Used internally by PlotAccessor methods
build_flow_hours(results) (line 333):
- Builds a DataArray containing flow hours for all flows
build_sizes(results) (line 347):
- Builds a DataArray containing sizes for all flows
_filter_dataarray_by_coord(da, **kwargs) (line 284):
- Helper for filtering DataArrays by coordinate values
3. Deprecated old Results methods (results.py)
The following methods now emit DeprecationWarning:
- results.flow_rates() → Use results.plot.flows(plot=False).data
- results.flow_hours() → Use results.plot.flows(unit='flow_hours', plot=False).data
- results.sizes() → Use results.plot.sizes(plot=False).data
4. Updated PlotAccessor methods to use new helpers
- flows() now uses build_flow_rates() / build_flow_hours() directly
- sizes() now uses build_sizes() directly
- sankey() now uses build_flow_hours() directly
This ensures the deprecation warnings only fire when users directly call the old methods, not when using the plot accessor
* 1. New methods added to PlotAccessor
- charge_states(): Returns Dataset with all storage charge states
- on_states(): Returns Dataset with all component status variables (heatmap display)
2. Data building helper functions (plot_accessors.py)
- build_flow_rates(results): Builds DataArray of flow rates
- build_flow_hours(results): Builds DataArray of flow hours
- build_sizes(results): Builds DataArray of sizes
- _filter_dataarray_by_coord(da, **kwargs): Filter helper
- _assign_flow_coords(da, results): Add flow coordinates
3. Caching in PlotAccessor
Added lazy-cached properties for expensive computations:
- _all_flow_rates - cached DataArray of all flow rates
- _all_flow_hours - cached DataArray of all flow hours
- _all_sizes - cached DataArray of all sizes
- _all_charge_states - cached Dataset of all storage charge states
- _all_status_vars - cached Dataset of all status variables
4. Deprecated methods in Results class
Added deprecation warnings to:
- results.flow_rates() → Use results.plot.flows(plot=False).data
- results.flow_hours() → Use results.plot.flows(unit='flow_hours', plot=False).data
- results.sizes() → Use results.plot.sizes(plot=False).data
5. Updated PlotAccessor methods to use cached properties
- flows() uses _all_flow_rates / _all_flow_hours
- sankey() uses _all_flow_hours
- sizes() uses _all_sizes
- charge_states() uses _all_charge_states
- on_states() uses _all_status_vars
* Move deprectated functionality into results.py instead of porting to the new module
* Revert to simply deprectae old methods without forwarding to new code
* Remove planning file
* Update plotting methods for new datasets
* 1. Renamed data properties in PlotAccessor to use all_ prefix:
- all_flow_rates - All flow rates as Dataset
- all_flow_hours - All flow hours as Dataset
- all_sizes - All flow sizes as Dataset
- all_charge_states - All storage charge states as Dataset
- all_on_states - All component on/off status as Dataset
2. Updated internal references - All usages in flows(), sankey(), sizes(), charge_states(), and on_states() methods now use the new names.
3. Updated deprecation messages in results.py to point to the new API:
- results.flow_rates() → results.plot.all_flow_rates
- results.flow_hours() → results.plot.all_flow_hours
- results.sizes() → results.plot.all_sizes
4. Updated docstring examples in PlotAccessor to use the new all_* names.
* Update deprecations messages
* Update deprecations messages
* Thsi seems much better.
* Updaet docstrings and variable name generation in plotting acessor
* Change __ to _ in private dataset caching
* Revert breaking io changes
* New solution storing interface
* Add new focused statistics and plot accessors
* Renamed all properties:
- all_flow_rates → flow_rates
- all_flow_hours → flow_hours
- all_sizes → sizes
- all_charge_states → charge_states
* Cache Statistics
* Invalidate caches
* Add effect related statistics
* Simplify statistics accessor to rely on flow_system directly instead of solution attrs
* Fix heatma fallback for 1D Data
* Add topology accessor
* All deprecation warnings in the codebase now consistently use the format will be removed in v{DEPRECATION_REMOVAL_VERSION}.
* Update tests
* created comprehensive documentation for all FlowSystem accessors
* Update results documentation
* Update results documentation
* Update effect statistics
* Update effect statistics
* Update effect statistics
* Add mkdocs plotly plugin
* Add section about custom constraints
* documentation updates:
docs/user-guide/results/index.md:
- Updated table to replace effects_per_component with temporal_effects, periodic_effects, total_effects, and effect_share_factors
- Fixed flow_hours['Boiler(Q_th)|flow_rate'] → flow_hours['Boiler(Q_th)']
- Fixed sizes['Boiler(Q_th)|size'] → sizes['Boiler(Q_th)']
- Replaced effects_per_component example with new effect properties and groupby examples
- Updated complete example to use total_effects
docs/user-guide/results-plotting.md:
- Fixed colors example from 'Boiler(Q_th)|flow_rate' → 'Boiler(Q_th)'
- Fixed duration_curve examples to use clean labels
docs/user-guide/migration-guide-v6.md:
- Added new "Statistics Accessor" section explaining the clean labels and new effect properties
* implemented the effects() method in StatisticsPlotAccessor at flixopt/statistics_accessor.py:1132-1258.
Summary of what was done:
1. Implemented effects() method in StatisticsPlotAccessor class that was missing but documented
- Takes aspect parameter: 'total', 'temporal', or 'periodic'
- Takes effect parameter to filter to a specific effect (e.g., 'costs', 'CO2')
- Takes by parameter: 'component' or 'time' for grouping
- Supports all standard plotting parameters: select, colors, facet_col, facet_row, show
- Returns PlotResult with both data and figure
2. Verified the implementation works with all parameter combinations:
- Default call: flow_system.statistics.plot.effects()
- Specific effect: flow_system.statistics.plot.effects(effect='costs')
- Temporal aspect: flow_system.statistics.plot.effects(aspect='temporal')
- Temporal by time: flow_system.statistics.plot.effects(aspect='temporal', by='time')
- Periodic aspect: flow_system.statistics.plot.effects(aspect='periodic')
* Remove intermediate plot accessor
* 1. pyproject.toml: Removed duplicate mkdocs-plotly-plugin>=0.1.3 entry (kept the exact pin ==0.1.3)
2. flixopt/plotting.py: Fixed dimension name consistency by using squeezed_data.name instead of data.name in the fallback heatmap logic
3. flixopt/statistics_accessor.py:
- Fixed _dataset_to_long_df() to only use coordinates that are actually present as columns after reset_index()
- Fixed the nested loop inefficiency with include_flows by pre-computing the flows list outside the loop
- (Previously fixed) Fixed asymmetric NaN handling in validation check
* _create_effects_dataset method in statistics_accessor.py was simplified:
1. Detect contributors from solution data variables instead of assuming they're only flows
- Uses regex pattern to find {contributor}->{effect}(temporal|periodic) variables
- Contributors can be flows OR components (e.g., components with effects_per_active_hour)
2. Exclude effect-to-effect shares
- Filters out contributors whose base name matches any effect label
- For example, costs(temporal) is excluded because costs is an effect label
- These intermediate shares are already included in the computation
3. Removed the unused _compute_effect_total method
- The new simplified implementation directly looks up shares from the solution
- Uses effect_share_factors for conversion between effects
4. Key insight from user: The solution already contains properly computed share values including all effect-to-effect conversions. The computation uses conversion
factors because derived effects (like Effect1 which shares 0.5 from costs) don't have direct {flow}->Effect1(temporal) variables - only the source effect shares exist
({flow}->costs(temporal)).
* Update docs
* Improve to_netcdf method
* Update examples
* Fix IIS computaion flag
* Fix examples
* Fix faceting in heatmap and use period as facet col everywhere
* Inline plotting methods to deprecate plotting.py
* Fix test
* Simplify Color Management
* ColorType is now defined in color_processing.py and imported into statistics_accessor.py.
* Fix ColorType typing
* Add color accessor
* Ensure io
* Add carrier class
* implemented Carrier as a proper Interface subclass with container support. Here's what was done:
1. Carrier class (flixopt/carrier.py)
- Now inherits from Interface for serialization capabilities
- Has transform_data() method (no-op since carriers have no time-series data)
- Has label property for container keying
- Maintains equality comparison with both Carrier objects and strings
2. CarrierContainer class (flixopt/carrier.py)
- Inherits from ContainerMixin['Carrier']
- Provides dict-like access with nice repr and error messages
- Uses carrier.name for keying
3. FlowSystem updates (flixopt/flow_system.py)
- _carriers is now a CarrierContainer instead of a plain dict
- carriers property returns the CarrierContainer
- add_carrier() uses the container's add() method
- Serialization updated to include carriers in to_dataset() and restore them in from_dataset()
4. Exports (flixopt/__init__.py)
- Both Carrier and CarrierContainer are now exported
* Inline plotting methods to deprecate plotting.py (#508)
* Inline plotting methods to deprecate plotting.py
* Fix test
* Simplify Color Management
* ColorType is now defined in color_processing.py and imported into statistics_accessor.py.
* Fix ColorType typing
* statistics_accessor.py - Heatmap colors type safety (lines 121-148, 820-853)
- Changed _heatmap_figure() parameter type from colors: ColorType = None to colors: str | list[str] | None = None
- Changed heatmap() method parameter type similarly
- Updated docstrings to clarify that dicts are not supported for heatmaps since px.imshow's color_continuous_scale only accepts colorscale names or lists
2. statistics_accessor.py - Use configured qualitative colorscale (lines 284, 315)
- Updated _create_stacked_bar() to use CONFIG.Plotting.default_qualitative_colorscale as the default colorscale
- Updated _create_line() similarly
- This ensures user-configured CONFIG.Plotting.default_qualitative_colorscale affects all bar/line plots consistently
3. topology_accessor.py - Path type alignment (lines 219-222)
- Added normalization of path=False to None before calling _plot_network()
- This resolves the type mismatch where TopologyAccessor.plot() accepts bool | str | Path but _plot_network() only accepts str | Path | None
* fix usage if index name in aggregation plot
* Add to docs
* Improve carrier colors and defaults
* Update default carriers and colors
* Update config
* Update config
* Move default carriers to config.py
* Change default carrier handling
* Add color handling
* Rmeove meta_data color handling
* Add carrierst to examples
* Improve plotting acessor
* Improve _resolve_variable_names
* Improve _resolve_variable_names
* Simplify coloring and remove color accessor
* Add connected_and_transformed handling
* Improve error message in container
* Methods moved to TransformAccessor (transform_accessor.py):
- sel() - select by label
- isel() - select by integer index
- resample() - resample time dimension
- Helper methods: _dataset_sel, _dataset_isel, _dataset_resample, _resample_by_dimension_groups
2. Solution is dropped: All transform methods return a new FlowSystem with no solution - the user must re-optimize the transformed system.
3. Deprecation warnings: The old flow_system.sel(), flow_system.isel(), and flow_system.resample() methods now emit deprecation warnings and forward to the new
TransformAccessor methods.
4. Backward compatible: Existing code still works, just with deprecation warnings.
* Documentation updated
* Re-add _dataset_sel and other helper methods for proper deprectation. ALso fix new methods to be classmethods
* BUGFIX: Carrier from dataset
* Update docs
* Add notebook examples instead of raw py files for docs
* Execute on docs buildt
* Add notebooks and new config util andmore notebook related stuff
* Fix notebooks
* Fix notebooks and config.py
* docstring typo
* Update notebooks
* Add fix_sizes method and use in two stage optimization notebook
* Change notebook config
* Dont get size as float in fix sizes!
* Update notebook
* fix: fix_sizes() to handle var names properly
* Add imbalance penalty to prevent infeasibility in Fernwärme Bus
* Remove putputs from all notbeooks for git
* Update the two stage notebook
* Update notebooks with user stories
* Add new index to docs
* Update notebooks to use plotly instead of matplotlib
* fix: Use plotly express
* fix: Use plotly express
* fix: Use plotly express
* Adjust plots
* Bugfix: Add _update_scenario_metadata method
* fix: _update_scenario_metadata method
* Get all notebooks running
* Improve notebooks for more interesting results
* Fix conversion factor
* Fix conversion factor
* Update notebooks and bugfix sankey
* Add charge state and storages plots
* improve charge state plot
* Add Piecewise plots and improve Notebooks (#519)
* Build notebooks in parralel in CI
* Revert "Build notebooks in parralel in CI"
This reverts commit 0f1153cd358fadfcf1fc705008a1a27cf1c0107d.
* Fix dependencies in docs workflow
* Use extra css
* Use extra css
* Use extra css
* Use extra css
* Fix notebook
* Add new statistics for sizes, flow_sizes and storage_sizes
* Fixed broken links in docs
* Fix mkdocs buildt noebooks on build
* Remove old example notebooks and rename folder to notebooks
* Add .storages property to FlowSystem
* fix broken links in docs
* Imrpove data extraction
* Imrpove data extraction
* Remove examples and test_examples.py
---
.github/workflows/docs.yaml | 2 +-
.pre-commit-config.yaml | 6 +
docs/examples/00-Minimal Example.md | 5 -
docs/examples/01-Basic Example.md | 5 -
docs/examples/02-Complex Example.md | 10 -
docs/examples/03-Optimization Modes.md | 5 -
docs/examples/04-Scenarios.md | 5 -
docs/examples/05-Two-stage-optimization.md | 5 -
docs/examples/index.md | 14 -
docs/home/installation.md | 2 +-
docs/home/quick-start.md | 2 +-
docs/index.md | 4 +-
docs/notebooks/01-quickstart.ipynb | 293 +
docs/notebooks/02-heat-system.ipynb | 413 +
.../03-investment-optimization.ipynb | 478 +
.../04-operational-constraints.ipynb | 458 +
docs/notebooks/05-multi-carrier-system.ipynb | 560 +
docs/notebooks/06-piecewise-efficiency.ipynb | 646 +
docs/notebooks/07-scenarios-and-periods.ipynb | 564 +
.../08-large-scale-optimization.ipynb | 538 +
docs/notebooks/index.md | 44 +
docs/overrides/main.html | 11 +
docs/stylesheets/extra.css | 162 +
docs/user-guide/building-models/index.md | 2 +-
docs/user-guide/core-concepts.md | 2 +-
docs/user-guide/index.md | 4 +-
docs/user-guide/optimization/index.md | 2 +-
docs/user-guide/results-plotting.md | 2 +-
docs/user-guide/results/index.md | 2 +-
docs/user-guide/support.md | 2 +-
examples/00_Minmal/minimal_example.py | 36 -
examples/01_Simple/simple_example.py | 126 -
examples/02_Complex/complex_example.py | 207 -
.../02_Complex/complex_example_results.py | 38 -
.../example_optimization_modes.py | 245 -
examples/04_Scenarios/scenario_example.py | 214 -
.../two_stage_optimization.py | 186 -
examples/resources/Zeitreihen2020.csv | 35137 ----------------
flixopt/config.py | 38 +
flixopt/flow_system.py | 37 +-
flixopt/interface.py | 164 +
flixopt/statistics_accessor.py | 224 +-
flixopt/transform_accessor.py | 125 +
mkdocs.yml | 30 +-
pyproject.toml | 2 +
tests/deprecated/test_examples.py | 94 -
tests/test_examples.py | 94 -
tests/test_solution_and_plotting.py | 8 +-
48 files changed, 4794 insertions(+), 36459 deletions(-)
delete mode 100644 docs/examples/00-Minimal Example.md
delete mode 100644 docs/examples/01-Basic Example.md
delete mode 100644 docs/examples/02-Complex Example.md
delete mode 100644 docs/examples/03-Optimization Modes.md
delete mode 100644 docs/examples/04-Scenarios.md
delete mode 100644 docs/examples/05-Two-stage-optimization.md
delete mode 100644 docs/examples/index.md
create mode 100644 docs/notebooks/01-quickstart.ipynb
create mode 100644 docs/notebooks/02-heat-system.ipynb
create mode 100644 docs/notebooks/03-investment-optimization.ipynb
create mode 100644 docs/notebooks/04-operational-constraints.ipynb
create mode 100644 docs/notebooks/05-multi-carrier-system.ipynb
create mode 100644 docs/notebooks/06-piecewise-efficiency.ipynb
create mode 100644 docs/notebooks/07-scenarios-and-periods.ipynb
create mode 100644 docs/notebooks/08-large-scale-optimization.ipynb
create mode 100644 docs/notebooks/index.md
create mode 100644 docs/overrides/main.html
delete mode 100644 examples/00_Minmal/minimal_example.py
delete mode 100644 examples/01_Simple/simple_example.py
delete mode 100644 examples/02_Complex/complex_example.py
delete mode 100644 examples/02_Complex/complex_example_results.py
delete mode 100644 examples/03_Optimization_modes/example_optimization_modes.py
delete mode 100644 examples/04_Scenarios/scenario_example.py
delete mode 100644 examples/05_Two-stage-optimization/two_stage_optimization.py
delete mode 100644 examples/resources/Zeitreihen2020.csv
delete mode 100644 tests/deprecated/test_examples.py
delete mode 100644 tests/test_examples.py
diff --git a/.github/workflows/docs.yaml b/.github/workflows/docs.yaml
index 4424d5122..762062604 100644
--- a/.github/workflows/docs.yaml
+++ b/.github/workflows/docs.yaml
@@ -55,7 +55,7 @@ jobs:
python scripts/format_changelog.py
- name: Install dependencies
- run: uv pip install --system ".[docs]"
+ run: uv pip install --system ".[docs,full]"
- name: Build docs
run: mkdocs build --strict
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index e39033067..76c32d069 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -14,3 +14,9 @@ repos:
- id: ruff-check
args: [ --fix ]
- id: ruff-format
+
+ - repo: https://github.com/kynan/nbstripout
+ rev: 0.8.1
+ hooks:
+ - id: nbstripout
+ files: ^docs/examples.*\.ipynb$
diff --git a/docs/examples/00-Minimal Example.md b/docs/examples/00-Minimal Example.md
deleted file mode 100644
index a568cd9c9..000000000
--- a/docs/examples/00-Minimal Example.md
+++ /dev/null
@@ -1,5 +0,0 @@
-# Minimal Example
-
-```python
-{! ../examples/00_Minmal/minimal_example.py !}
-```
diff --git a/docs/examples/01-Basic Example.md b/docs/examples/01-Basic Example.md
deleted file mode 100644
index 6c6bfbee3..000000000
--- a/docs/examples/01-Basic Example.md
+++ /dev/null
@@ -1,5 +0,0 @@
-# Simple example
-
-```python
-{! ../examples/01_Simple/simple_example.py !}
-```
diff --git a/docs/examples/02-Complex Example.md b/docs/examples/02-Complex Example.md
deleted file mode 100644
index 48868cdb0..000000000
--- a/docs/examples/02-Complex Example.md
+++ /dev/null
@@ -1,10 +0,0 @@
-# Complex example
-This saves the results of a calculation to file and reloads them to analyze the results
-## Build the Model
-```python
-{! ../examples/02_Complex/complex_example.py !}
-```
-## Load the Results from file
-```python
-{! ../examples/02_Complex/complex_example_results.py !}
-```
diff --git a/docs/examples/03-Optimization Modes.md b/docs/examples/03-Optimization Modes.md
deleted file mode 100644
index 880366906..000000000
--- a/docs/examples/03-Optimization Modes.md
+++ /dev/null
@@ -1,5 +0,0 @@
-# Optimization Modes Comparison
-**Note:** This example relies on time series data. You can find it in the `examples` folder of the FlixOpt repository.
-```python
-{! ../examples/03_Optimization_modes/example_optimization_modes.py !}
-```
diff --git a/docs/examples/04-Scenarios.md b/docs/examples/04-Scenarios.md
deleted file mode 100644
index b528bb6f3..000000000
--- a/docs/examples/04-Scenarios.md
+++ /dev/null
@@ -1,5 +0,0 @@
-# Scenario example
-
-```python
-{! ../examples/04_Scenarios/scenario_example.py !}
-```
diff --git a/docs/examples/05-Two-stage-optimization.md b/docs/examples/05-Two-stage-optimization.md
deleted file mode 100644
index 5cb94e325..000000000
--- a/docs/examples/05-Two-stage-optimization.md
+++ /dev/null
@@ -1,5 +0,0 @@
-# Two-stage optimization
-
-```python
-{! ../examples/05_Two-stage-optimization/two_stage_optimization.py !}
-```
diff --git a/docs/examples/index.md b/docs/examples/index.md
deleted file mode 100644
index b5534b8e3..000000000
--- a/docs/examples/index.md
+++ /dev/null
@@ -1,14 +0,0 @@
-# Examples
-
-Here you can find a collection of examples that demonstrate how to use FlixOpt.
-
-We work on improving this gallery. If you have something to share, please contact us!
-
-## Available Examples
-
-1. [Minimal Example](00-Minimal Example.md) - The simplest possible FlixOpt model
-2. [Simple Example](01-Basic Example.md) - A basic example with more features
-3. [Complex Example](02-Complex Example.md) - A comprehensive example with result saving and loading
-4. [Optimization Modes](03-Optimization Modes.md) - Comparison of different optimization modes
-5. [Scenarios](04-Scenarios.md) - Working with scenarios in FlixOpt
-6. [Two-stage Optimization](05-Two-stage-optimization.md) - Two-stage optimization approach
diff --git a/docs/home/installation.md b/docs/home/installation.md
index afb24172b..d61022074 100644
--- a/docs/home/installation.md
+++ b/docs/home/installation.md
@@ -87,5 +87,5 @@ For more details on logging configuration, see the [`CONFIG.Logging`][flixopt.co
## Next Steps
- Follow the [Quick Start](quick-start.md) guide
-- Explore the [Minimal Example](../examples/00-Minimal Example.md)
+- Explore the [Minimal Example](../notebooks/01-quickstart.ipynb)
- Read about [Core Concepts](../user-guide/core-concepts.md)
diff --git a/docs/home/quick-start.md b/docs/home/quick-start.md
index d95e53c90..7bbc88172 100644
--- a/docs/home/quick-start.md
+++ b/docs/home/quick-start.md
@@ -130,7 +130,7 @@ loaded_fs = fx.FlowSystem.from_netcdf('results/solar_battery.nc')
Now that you've created your first model, you can:
- **Learn the concepts** - Read the [Core Concepts](../user-guide/core-concepts.md) guide
-- **Explore examples** - Check out more [Examples](../examples/index.md)
+- **Explore examples** - Check out more [Examples](../notebooks/index.md)
- **Deep dive** - Study the [Mathematical Formulation](../user-guide/mathematical-notation/index.md)
- **Build complex models** - Use [Recipes](../user-guide/recipes/index.md) for common patterns
diff --git a/docs/index.md b/docs/index.md
index 70fd15bf4..f8509e24c 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -14,7 +14,7 @@ title: Home
🚀 Get Started
- 💡 View Examples
+ 💡 View Examples
⭐ GitHub
@@ -30,7 +30,7 @@ title: Home
New to FlixOpt? Start here with installation and your first model
-- :bulb: **[Examples Gallery](examples/)**
+- :bulb: **[Examples Gallery](notebooks/)**
---
diff --git a/docs/notebooks/01-quickstart.ipynb b/docs/notebooks/01-quickstart.ipynb
new file mode 100644
index 000000000..c7178c750
--- /dev/null
+++ b/docs/notebooks/01-quickstart.ipynb
@@ -0,0 +1,293 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "0",
+ "metadata": {},
+ "source": [
+ "# Quickstart: Heating a Small Workshop\n",
+ "\n",
+ "## User Story\n",
+ "\n",
+ "> *You manage a small workshop that needs heating. You have a gas boiler and want to find the optimal operation schedule to minimize heating costs over the next few hours.*\n",
+ "\n",
+ "This notebook introduces the **core concepts** of flixopt:\n",
+ "\n",
+ "- **FlowSystem**: The container for your energy system model\n",
+ "- **Bus**: Balance nodes where energy flows meet\n",
+ "- **Effect**: Quantities to track and optimize (costs, emissions)\n",
+ "- **Components**: Equipment like boilers, sources, and sinks\n",
+ "- **Flow**: Connections between components and buses"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1",
+ "metadata": {},
+ "source": [
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import pandas as pd\n",
+ "import plotly.express as px\n",
+ "import xarray as xr\n",
+ "\n",
+ "import flixopt as fx\n",
+ "\n",
+ "fx.CONFIG.notebook()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3",
+ "metadata": {},
+ "source": [
+ "## Define the Time Horizon\n",
+ "\n",
+ "Every optimization needs a time horizon. Here we model a simple 4-hour period:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "4",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "timesteps = pd.date_range('2024-01-15 08:00', periods=4, freq='h')\n",
+ "print(f'Optimizing from {timesteps[0]} to {timesteps[-1]}')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5",
+ "metadata": {},
+ "source": [
+ "## Define the Heat Demand\n",
+ "\n",
+ "The workshop has varying heat demand throughout the morning:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "6",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Heat demand in kW for each hour - using xarray\n",
+ "heat_demand = xr.DataArray(\n",
+ " [30, 50, 45, 25],\n",
+ " dims=['time'],\n",
+ " coords={'time': timesteps},\n",
+ " name='Heat Demand [kW]',\n",
+ ")\n",
+ "\n",
+ "# Visualize the demand with plotly\n",
+ "fig = px.bar(x=heat_demand.time.values, y=heat_demand.values, labels={'x': 'Time', 'y': 'Heat Demand [kW]'})\n",
+ "fig"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7",
+ "metadata": {},
+ "source": [
+ "## Build the Energy System Model\n",
+ "\n",
+ "Now we create the FlowSystem and add all components:\n",
+ "\n",
+ "```\n",
+ " Gas Supply ──► [Gas Bus] ──► Boiler ──► [Heat Bus] ──► Workshop\n",
+ " € η=90% Demand\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Create the FlowSystem container\n",
+ "flow_system = fx.FlowSystem(timesteps)\n",
+ "\n",
+ "flow_system.add_elements(\n",
+ " # === Buses: Balance nodes for energy carriers ===\n",
+ " fx.Bus('Gas'), # Natural gas network connection\n",
+ " fx.Bus('Heat'), # Heat distribution within workshop\n",
+ " # === Effect: What we want to minimize ===\n",
+ " fx.Effect('costs', '€', 'Total Costs', is_standard=True, is_objective=True),\n",
+ " # === Gas Supply: Unlimited gas at 0.08 €/kWh ===\n",
+ " fx.Source(\n",
+ " 'GasGrid',\n",
+ " outputs=[fx.Flow('Gas', bus='Gas', size=1000, effects_per_flow_hour=0.08)],\n",
+ " ),\n",
+ " # === Boiler: Converts gas to heat at 90% efficiency ===\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'Boiler',\n",
+ " thermal_efficiency=0.9,\n",
+ " thermal_flow=fx.Flow('Heat', bus='Heat', size=100), # 100 kW capacity\n",
+ " fuel_flow=fx.Flow('Gas', bus='Gas'),\n",
+ " ),\n",
+ " # === Workshop: Heat demand that must be met ===\n",
+ " fx.Sink(\n",
+ " 'Workshop',\n",
+ " inputs=[fx.Flow('Heat', bus='Heat', size=1, fixed_relative_profile=heat_demand.values)],\n",
+ " ),\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9",
+ "metadata": {},
+ "source": [
+ "## Run the Optimization\n",
+ "\n",
+ "Now we solve the model using the HiGHS solver (open-source, included with flixopt):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "10",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.optimize(fx.solvers.HighsSolver());"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "11",
+ "metadata": {},
+ "source": [
+ "## Analyze Results\n",
+ "\n",
+ "### Heat Balance\n",
+ "\n",
+ "The `statistics.plot.balance()` method shows how each bus is balanced:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "12",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('Heat')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "13",
+ "metadata": {},
+ "source": [
+ "### Total Costs\n",
+ "\n",
+ "Access the optimized objective value:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "14",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "total_costs = flow_system.solution['costs'].item()\n",
+ "total_heat = float(heat_demand.sum())\n",
+ "gas_consumed = total_heat / 0.9 # Account for boiler efficiency\n",
+ "\n",
+ "print(f'Total heat demand: {total_heat:.1f} kWh')\n",
+ "print(f'Gas consumed: {gas_consumed:.1f} kWh')\n",
+ "print(f'Total costs: {total_costs:.2f} €')\n",
+ "print(f'Average cost: {total_costs / total_heat:.3f} €/kWh_heat')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "15",
+ "metadata": {},
+ "source": [
+ "### Flow Rates Over Time\n",
+ "\n",
+ "Visualize all flow rates using the built-in plotting accessor:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "16",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Plot all flow rates\n",
+ "flow_system.statistics.plot.flows()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "17",
+ "metadata": {},
+ "source": [
+ "### Energy Flow Sankey\n",
+ "\n",
+ "A Sankey diagram visualizes the total energy flows through the system:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "18",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.sankey()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "19",
+ "metadata": {},
+ "source": [
+ "## Summary\n",
+ "\n",
+ "In this quickstart, you learned the **basic workflow**:\n",
+ "\n",
+ "1. **Create** a `FlowSystem` with timesteps\n",
+ "2. **Add** buses, effects, and components\n",
+ "3. **Optimize** with `flow_system.optimize(solver)`\n",
+ "4. **Analyze** results via `flow_system.statistics`\n",
+ "\n",
+ "### Next Steps\n",
+ "\n",
+ "- **[02-heat-system](02-heat-system.ipynb)**: Add thermal storage to shift loads\n",
+ "- **[03-investment-optimization](03-investment-optimization.ipynb)**: Optimize equipment sizing"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python",
+ "version": "3.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/notebooks/02-heat-system.ipynb b/docs/notebooks/02-heat-system.ipynb
new file mode 100644
index 000000000..933366e25
--- /dev/null
+++ b/docs/notebooks/02-heat-system.ipynb
@@ -0,0 +1,413 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "0",
+ "metadata": {},
+ "source": [
+ "# District Heating System with Thermal Storage\n",
+ "\n",
+ "## User Story\n",
+ "\n",
+ "> *You operate a small district heating network serving an office building. The system has a gas boiler and a thermal storage tank. Electricity prices vary throughout the day, and you want to optimize when to charge/discharge the storage to minimize costs.*\n",
+ "\n",
+ "This notebook introduces:\n",
+ "\n",
+ "- **Storage**: Thermal buffer tanks with charging/discharging\n",
+ "- **Time series data**: Using real demand profiles\n",
+ "- **Multiple components**: Combining boiler, storage, and loads\n",
+ "- **Result visualization**: Heatmaps, balance plots, and charge states"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1",
+ "metadata": {},
+ "source": [
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import plotly.express as px\n",
+ "import xarray as xr\n",
+ "\n",
+ "import flixopt as fx\n",
+ "\n",
+ "fx.CONFIG.notebook()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3",
+ "metadata": {},
+ "source": [
+ "## Define Time Horizon and Demand\n",
+ "\n",
+ "We model one week with hourly resolution. The office has typical weekday patterns:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "4",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# One week, hourly resolution\n",
+ "timesteps = pd.date_range('2024-01-15', periods=168, freq='h')\n",
+ "\n",
+ "# Create realistic office heat demand pattern\n",
+ "hours = np.arange(168)\n",
+ "hour_of_day = hours % 24\n",
+ "day_of_week = (hours // 24) % 7\n",
+ "\n",
+ "# Base demand pattern (kW)\n",
+ "base_demand = np.where(\n",
+ " (hour_of_day >= 7) & (hour_of_day <= 18), # Office hours\n",
+ " 80, # Daytime\n",
+ " 30, # Night setback\n",
+ ")\n",
+ "\n",
+ "# Reduce on weekends (days 5, 6)\n",
+ "weekend_factor = np.where(day_of_week >= 5, 0.5, 1.0)\n",
+ "heat_demand = base_demand * weekend_factor\n",
+ "\n",
+ "# Add some random variation\n",
+ "np.random.seed(42)\n",
+ "heat_demand = heat_demand + np.random.normal(0, 5, len(heat_demand))\n",
+ "heat_demand = np.clip(heat_demand, 20, 100)\n",
+ "\n",
+ "print(f'Time range: {timesteps[0]} to {timesteps[-1]}')\n",
+ "print(f'Peak demand: {heat_demand.max():.1f} kW')\n",
+ "print(f'Total demand: {heat_demand.sum():.0f} kWh')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Visualize the demand pattern with plotly\n",
+ "demand_series = xr.DataArray(heat_demand, dims=['time'], coords={'time': timesteps}, name='Heat Demand [kW]')\n",
+ "fig = px.line(\n",
+ " x=demand_series.time.values,\n",
+ " y=demand_series.values,\n",
+ " title='Office Heat Demand Profile',\n",
+ " labels={'x': 'Time', 'y': 'kW'},\n",
+ ")\n",
+ "fig"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6",
+ "metadata": {},
+ "source": [
+ "## Define Gas Prices\n",
+ "\n",
+ "Gas prices vary with time-of-use tariffs:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Time-of-use gas prices (€/kWh)\n",
+ "gas_price = np.where(\n",
+ " (hour_of_day >= 6) & (hour_of_day <= 22),\n",
+ " 0.08, # Peak: 6am-10pm\n",
+ " 0.05, # Off-peak: 10pm-6am\n",
+ ")\n",
+ "\n",
+ "fig = px.line(x=timesteps, y=gas_price, title='Gas Price [€/kWh]', labels={'x': 'Time', 'y': '€/kWh'})\n",
+ "fig"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8",
+ "metadata": {},
+ "source": [
+ "## Build the Energy System\n",
+ "\n",
+ "The system includes:\n",
+ "- Gas boiler (150 kW thermal capacity)\n",
+ "- Thermal storage tank (500 kWh capacity)\n",
+ "- Office building heat demand\n",
+ "\n",
+ "```\n",
+ "Gas Grid ──► [Gas] ──► Boiler ──► [Heat] ◄──► Storage\n",
+ " │\n",
+ " ▼\n",
+ " Office\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system = fx.FlowSystem(timesteps)\n",
+ "\n",
+ "flow_system.add_elements(\n",
+ " # === Buses ===\n",
+ " fx.Bus('Gas'),\n",
+ " fx.Bus('Heat'),\n",
+ " # === Effect ===\n",
+ " fx.Effect('costs', '€', 'Operating Costs', is_standard=True, is_objective=True),\n",
+ " # === Gas Supply with time-varying price ===\n",
+ " fx.Source(\n",
+ " 'GasGrid',\n",
+ " outputs=[fx.Flow('Gas', bus='Gas', size=500, effects_per_flow_hour=gas_price)],\n",
+ " ),\n",
+ " # === Gas Boiler: 150 kW, 92% efficiency ===\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'Boiler',\n",
+ " thermal_efficiency=0.92,\n",
+ " thermal_flow=fx.Flow('Heat', bus='Heat', size=150),\n",
+ " fuel_flow=fx.Flow('Gas', bus='Gas'),\n",
+ " ),\n",
+ " # === Thermal Storage: 500 kWh tank ===\n",
+ " fx.Storage(\n",
+ " 'ThermalStorage',\n",
+ " capacity_in_flow_hours=500, # 500 kWh capacity\n",
+ " initial_charge_state=250, # Start half-full\n",
+ " minimal_final_charge_state=200, # End with at least 200 kWh\n",
+ " eta_charge=0.98, # 98% charging efficiency\n",
+ " eta_discharge=0.98, # 98% discharging efficiency\n",
+ " relative_loss_per_hour=0.005, # 0.5% heat loss per hour\n",
+ " charging=fx.Flow('Charge', bus='Heat', size=100), # Max 100 kW charging\n",
+ " discharging=fx.Flow('Discharge', bus='Heat', size=100), # Max 100 kW discharging\n",
+ " ),\n",
+ " # === Office Heat Demand ===\n",
+ " fx.Sink(\n",
+ " 'Office',\n",
+ " inputs=[fx.Flow('Heat', bus='Heat', size=1, fixed_relative_profile=heat_demand)],\n",
+ " ),\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "10",
+ "metadata": {},
+ "source": [
+ "## Run Optimization"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "11",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0.01));"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "12",
+ "metadata": {},
+ "source": [
+ "## Analyze Results\n",
+ "\n",
+ "### Heat Balance\n",
+ "\n",
+ "See how the boiler and storage work together to meet demand:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "13",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('Heat')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "14",
+ "metadata": {},
+ "source": [
+ "### Storage Charge State\n",
+ "\n",
+ "Track how the storage level varies over time:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "15",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('ThermalStorage')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "16",
+ "metadata": {},
+ "source": [
+ "### Heatmap Visualization\n",
+ "\n",
+ "Heatmaps show patterns across hours and days:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "17",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.heatmap('Boiler(Heat)')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "18",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.heatmap('ThermalStorage')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "19",
+ "metadata": {},
+ "source": [
+ "### Cost Analysis"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "20",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "total_costs = flow_system.solution['costs'].item()\n",
+ "total_heat = heat_demand.sum()\n",
+ "\n",
+ "print(f'Total operating costs: {total_costs:.2f} €')\n",
+ "print(f'Total heat delivered: {total_heat:.0f} kWh')\n",
+ "print(f'Average cost: {total_costs / total_heat * 100:.2f} ct/kWh')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "21",
+ "metadata": {},
+ "source": [
+ "### Flow Rates and Charge States\n",
+ "\n",
+ "Visualize all flow rates and storage charge states:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "22",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Plot all flow rates\n",
+ "flow_system.statistics.plot.flows()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "23",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Plot storage charge states\n",
+ "flow_system.statistics.plot.storage('ThermalStorage')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "24",
+ "metadata": {},
+ "source": [
+ "### Energy Flow Sankey\n",
+ "\n",
+ "A Sankey diagram visualizes the total energy flows through the system:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "25",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.sankey()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "26",
+ "metadata": {},
+ "source": [
+ "## Key Insights\n",
+ "\n",
+ "The optimization reveals how storage enables **load shifting**:\n",
+ "\n",
+ "1. **Charge during off-peak**: When gas is cheap (night), the boiler runs at higher output to charge the storage\n",
+ "2. **Discharge during peak**: During expensive periods, storage supplements the boiler\n",
+ "3. **Weekend patterns**: Lower demand allows more storage cycling\n",
+ "\n",
+ "## Summary\n",
+ "\n",
+ "You learned how to:\n",
+ "\n",
+ "- Add **Storage** components with efficiency and losses\n",
+ "- Use **time-varying prices** in effects\n",
+ "- Visualize results with **heatmaps** and **balance plots**\n",
+ "- Access raw data via **statistics.flow_rates** and **statistics.charge_states**\n",
+ "\n",
+ "### Next Steps\n",
+ "\n",
+ "- **[03-investment-optimization](03-investment-optimization.ipynb)**: Optimize storage size\n",
+ "- **[04-operational-constraints](04-operational-constraints.ipynb)**: Add startup costs and minimum run times"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python",
+ "version": "3.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/notebooks/03-investment-optimization.ipynb b/docs/notebooks/03-investment-optimization.ipynb
new file mode 100644
index 000000000..c20d77f0a
--- /dev/null
+++ b/docs/notebooks/03-investment-optimization.ipynb
@@ -0,0 +1,478 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "0",
+ "metadata": {},
+ "source": [
+ "# Investment Optimization: Sizing a Solar Heating System\n",
+ "\n",
+ "## User Story\n",
+ "\n",
+ "> *You're designing a solar thermal system for a swimming pool. You need to decide: How large should the solar collectors be? How big should the buffer tank be? The goal is to minimize total costs (investment + operation) over the planning horizon.*\n",
+ "\n",
+ "This notebook introduces:\n",
+ "\n",
+ "- **InvestParameters**: Define investment decisions with size bounds and costs\n",
+ "- **Investment costs**: Fixed costs and size-dependent costs\n",
+ "- **Optimal sizing**: Let the optimizer find the best equipment sizes\n",
+ "- **Trade-off analysis**: Balance investment vs. operating costs"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1",
+ "metadata": {},
+ "source": [
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import plotly.express as px\n",
+ "import xarray as xr\n",
+ "\n",
+ "import flixopt as fx\n",
+ "\n",
+ "fx.CONFIG.notebook()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3",
+ "metadata": {},
+ "source": [
+ "## System Description\n",
+ "\n",
+ "The swimming pool heating system:\n",
+ "\n",
+ "- **Solar collectors**: Convert solar radiation to heat (size to be optimized)\n",
+ "- **Gas boiler**: Backup heating when solar is insufficient (existing, 200 kW)\n",
+ "- **Buffer tank**: Store excess solar heat (size to be optimized)\n",
+ "- **Pool**: Constant heat demand of 150 kW during operating hours\n",
+ "\n",
+ "```\n",
+ " ☀️ Solar ──► [Heat] ◄── Boiler ◄── [Gas]\n",
+ " │\n",
+ " ▼\n",
+ " Buffer Tank\n",
+ " │\n",
+ " ▼\n",
+ " Pool 🏊\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4",
+ "metadata": {},
+ "source": [
+ "## Define Time Horizon and Profiles\n",
+ "\n",
+ "We model one representative summer week:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# One week in summer, hourly\n",
+ "timesteps = pd.date_range('2024-07-15', periods=168, freq='h')\n",
+ "hours = np.arange(168)\n",
+ "hour_of_day = hours % 24\n",
+ "\n",
+ "# Solar radiation profile (kW/m² equivalent, simplified)\n",
+ "# Peak around noon, zero at night\n",
+ "solar_profile = np.maximum(0, np.sin((hour_of_day - 6) * np.pi / 12)) * 0.8\n",
+ "solar_profile = np.where((hour_of_day >= 6) & (hour_of_day <= 20), solar_profile, 0)\n",
+ "\n",
+ "# Add some cloud variation\n",
+ "np.random.seed(42)\n",
+ "cloud_factor = np.random.uniform(0.6, 1.0, len(timesteps))\n",
+ "solar_profile = solar_profile * cloud_factor\n",
+ "\n",
+ "# Pool operates 8am-10pm, constant demand when open\n",
+ "pool_demand = np.where((hour_of_day >= 8) & (hour_of_day <= 22), 150, 50) # kW\n",
+ "\n",
+ "print(f'Peak solar: {solar_profile.max():.2f} kW/kW_installed')\n",
+ "print(f'Pool demand: {pool_demand.max():.0f} kW (open), {pool_demand.min():.0f} kW (closed)')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "6",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Visualize profiles with plotly - using xarray and faceting\n",
+ "profiles = xr.Dataset(\n",
+ " {\n",
+ " 'Solar Profile [kW/kW]': xr.DataArray(solar_profile, dims=['time'], coords={'time': timesteps}),\n",
+ " 'Pool Demand [kW]': xr.DataArray(pool_demand, dims=['time'], coords={'time': timesteps}),\n",
+ " }\n",
+ ")\n",
+ "\n",
+ "# Convert to long format for faceting\n",
+ "df = profiles.to_dataframe().reset_index().melt(id_vars='time', var_name='variable', value_name='value')\n",
+ "fig = px.line(df, x='time', y='value', facet_col='variable', height=300)\n",
+ "fig.update_yaxes(matches=None, showticklabels=True)\n",
+ "fig.for_each_annotation(lambda a: a.update(text=a.text.split('=')[-1]))\n",
+ "fig"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7",
+ "metadata": {},
+ "source": [
+ "## Define Costs\n",
+ "\n",
+ "Investment costs are **annualized** (€/year) to compare with operating costs:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Cost parameters\n",
+ "GAS_PRICE = 0.12 # €/kWh - high gas price makes solar attractive\n",
+ "\n",
+ "# Solar collectors: 400 €/kW installed, 20-year lifetime → ~25 €/kW/year annualized\n",
+ "# (simplified, real calculation would include interest rate)\n",
+ "SOLAR_COST_PER_KW = 20 # €/kW/year\n",
+ "\n",
+ "# Buffer tank: 50 €/kWh capacity, 30-year lifetime → ~2 €/kWh/year\n",
+ "TANK_COST_PER_KWH = 1.5 # €/kWh/year\n",
+ "\n",
+ "# Scale factor: We model 1 week, but costs are annual\n",
+ "# So we scale investment costs to weekly equivalent\n",
+ "WEEKS_PER_YEAR = 52\n",
+ "SOLAR_COST_WEEKLY = SOLAR_COST_PER_KW / WEEKS_PER_YEAR\n",
+ "TANK_COST_WEEKLY = TANK_COST_PER_KWH / WEEKS_PER_YEAR\n",
+ "\n",
+ "print(f'Solar cost: {SOLAR_COST_WEEKLY:.3f} €/kW/week')\n",
+ "print(f'Tank cost: {TANK_COST_WEEKLY:.4f} €/kWh/week')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9",
+ "metadata": {},
+ "source": [
+ "## Build the System with Investment Options\n",
+ "\n",
+ "Use `InvestParameters` to define which sizes should be optimized:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "10",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system = fx.FlowSystem(timesteps)\n",
+ "\n",
+ "flow_system.add_elements(\n",
+ " # === Buses ===\n",
+ " fx.Bus('Heat'),\n",
+ " fx.Bus('Gas'),\n",
+ " # === Effects ===\n",
+ " fx.Effect('costs', '€', 'Total Costs', is_standard=True, is_objective=True),\n",
+ " # === Gas Supply ===\n",
+ " fx.Source(\n",
+ " 'GasGrid',\n",
+ " outputs=[fx.Flow('Gas', bus='Gas', size=500, effects_per_flow_hour=GAS_PRICE)],\n",
+ " ),\n",
+ " # === Gas Boiler (existing, fixed size) ===\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'GasBoiler',\n",
+ " thermal_efficiency=0.92,\n",
+ " thermal_flow=fx.Flow('Heat', bus='Heat', size=200), # 200 kW existing\n",
+ " fuel_flow=fx.Flow('Gas', bus='Gas'),\n",
+ " ),\n",
+ " # === Solar Collectors (size to be optimized) ===\n",
+ " fx.Source(\n",
+ " 'SolarCollectors',\n",
+ " outputs=[\n",
+ " fx.Flow(\n",
+ " 'Heat',\n",
+ " bus='Heat',\n",
+ " # Investment optimization: find optimal size between 0-500 kW\n",
+ " size=fx.InvestParameters(\n",
+ " minimum_size=0,\n",
+ " maximum_size=500,\n",
+ " effects_of_investment_per_size={'costs': SOLAR_COST_WEEKLY},\n",
+ " ),\n",
+ " # Solar output depends on radiation profile\n",
+ " fixed_relative_profile=solar_profile,\n",
+ " )\n",
+ " ],\n",
+ " ),\n",
+ " # === Buffer Tank (size to be optimized) ===\n",
+ " fx.Storage(\n",
+ " 'BufferTank',\n",
+ " # Investment optimization: find optimal capacity between 0-2000 kWh\n",
+ " capacity_in_flow_hours=fx.InvestParameters(\n",
+ " minimum_size=0,\n",
+ " maximum_size=2000,\n",
+ " effects_of_investment_per_size={'costs': TANK_COST_WEEKLY},\n",
+ " ),\n",
+ " initial_charge_state=0,\n",
+ " eta_charge=0.95,\n",
+ " eta_discharge=0.95,\n",
+ " relative_loss_per_hour=0.01, # 1% loss per hour\n",
+ " charging=fx.Flow('Charge', bus='Heat', size=200),\n",
+ " discharging=fx.Flow('Discharge', bus='Heat', size=200),\n",
+ " ),\n",
+ " # === Pool Heat Demand ===\n",
+ " fx.Sink(\n",
+ " 'Pool',\n",
+ " inputs=[fx.Flow('Heat', bus='Heat', size=1, fixed_relative_profile=pool_demand)],\n",
+ " ),\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "11",
+ "metadata": {},
+ "source": [
+ "## Run Optimization"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "12",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0.01));"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "13",
+ "metadata": {},
+ "source": [
+ "## Analyze Investment Decisions\n",
+ "\n",
+ "### Optimal Sizes"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "14",
+ "metadata": {},
+ "outputs": [],
+ "source": "solar_size = flow_system.statistics.sizes['SolarCollectors(Heat)'].item()\ntank_size = flow_system.statistics.sizes['BufferTank'].item()\n\nprint('=== Optimal Investment Decisions ===')\nprint(f'Solar collectors: {solar_size:.1f} kW')\nprint(f'Buffer tank: {tank_size:.1f} kWh')\nprint(f'Tank-to-solar ratio: {tank_size / solar_size:.1f} kWh/kW' if solar_size > 0 else 'N/A')"
+ },
+ {
+ "cell_type": "markdown",
+ "id": "15",
+ "metadata": {},
+ "source": [
+ "### Visualize Sizes"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "16",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.sizes()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "17",
+ "metadata": {},
+ "source": [
+ "### Cost Breakdown"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "18",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "total_costs = flow_system.solution['costs'].item()\n",
+ "\n",
+ "# Calculate cost components\n",
+ "solar_invest = solar_size * SOLAR_COST_WEEKLY\n",
+ "tank_invest = tank_size * TANK_COST_WEEKLY\n",
+ "gas_costs = total_costs - solar_invest - tank_invest\n",
+ "\n",
+ "print('=== Weekly Cost Breakdown ===')\n",
+ "print(f'Solar investment: {solar_invest:.2f} € ({solar_invest / total_costs * 100:.1f}%)')\n",
+ "print(f'Tank investment: {tank_invest:.2f} € ({tank_invest / total_costs * 100:.1f}%)')\n",
+ "print(f'Gas operating: {gas_costs:.2f} € ({gas_costs / total_costs * 100:.1f}%)')\n",
+ "print('─────────────────────────────')\n",
+ "print(f'Total: {total_costs:.2f} €')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "19",
+ "metadata": {},
+ "source": [
+ "### System Operation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "20",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('Heat')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "21",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.heatmap('SolarCollectors(Heat)')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "22",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('BufferTank')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "23",
+ "metadata": {},
+ "source": [
+ "## Compare: What if No Solar?\n",
+ "\n",
+ "Let's see how much the solar system saves:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "24",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Gas-only scenario\n",
+ "total_demand = pool_demand.sum()\n",
+ "gas_only_cost = total_demand / 0.92 * GAS_PRICE # All heat from gas boiler\n",
+ "\n",
+ "savings = gas_only_cost - total_costs\n",
+ "savings_pct = savings / gas_only_cost * 100\n",
+ "\n",
+ "print('=== Comparison with Gas-Only ===')\n",
+ "print(f'Gas-only cost: {gas_only_cost:.2f} €/week')\n",
+ "print(f'With solar: {total_costs:.2f} €/week')\n",
+ "print(f'Savings: {savings:.2f} €/week ({savings_pct:.1f}%)')\n",
+ "print(f'Annual savings: {savings * 52:.0f} €/year')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "25",
+ "metadata": {},
+ "source": [
+ "### Energy Flow Sankey\n",
+ "\n",
+ "A Sankey diagram visualizes the total energy flows through the system:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "26",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.sankey()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "27",
+ "metadata": {},
+ "source": [
+ "## Key Concepts\n",
+ "\n",
+ "### InvestParameters Options\n",
+ "\n",
+ "```python\n",
+ "fx.InvestParameters(\n",
+ " minimum_size=0, # Lower bound (can be 0 for optional)\n",
+ " maximum_size=500, # Upper bound\n",
+ " fixed_size=100, # Or: fixed size (binary decision)\n",
+ " mandatory=True, # Force investment to happen\n",
+ " effects_of_investment={'costs': 1000}, # Fixed cost if invested\n",
+ " effects_of_investment_per_size={'costs': 25}, # Cost per unit size\n",
+ ")\n",
+ "```\n",
+ "\n",
+ "### Where to Use InvestParameters\n",
+ "\n",
+ "- **Flow.size**: Optimize converter/source/sink capacity\n",
+ "- **Storage.capacity_in_flow_hours**: Optimize storage capacity\n",
+ "\n",
+ "## Summary\n",
+ "\n",
+ "You learned how to:\n",
+ "\n",
+ "- Define **investment decisions** with `InvestParameters`\n",
+ "- Set **size bounds** (minimum/maximum)\n",
+ "- Add **investment costs** (per-size and fixed)\n",
+ "- Access **optimal sizes** via `statistics.sizes`\n",
+ "- Visualize sizes with `statistics.plot.sizes()`\n",
+ "\n",
+ "### Next Steps\n",
+ "\n",
+ "- **[04-operational-constraints](04-operational-constraints.ipynb)**: Add startup costs and minimum run times\n",
+ "- **[05-multi-carrier-system](05-multi-carrier-system.ipynb)**: Model combined heat and power"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python",
+ "version": "3.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/notebooks/04-operational-constraints.ipynb b/docs/notebooks/04-operational-constraints.ipynb
new file mode 100644
index 000000000..f2505ed41
--- /dev/null
+++ b/docs/notebooks/04-operational-constraints.ipynb
@@ -0,0 +1,458 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "0",
+ "metadata": {},
+ "source": [
+ "# Operational Constraints: Industrial Boiler with Startup Costs\n",
+ "\n",
+ "## User Story\n",
+ "\n",
+ "> *You operate an industrial steam boiler for a factory. The boiler has significant startup costs (fuel for warmup, operator time) and can't be cycled on/off frequently due to thermal stress. You need to find an operating schedule that minimizes costs while respecting these operational constraints.*\n",
+ "\n",
+ "This notebook introduces:\n",
+ "\n",
+ "- **StatusParameters**: Model on/off decisions with constraints\n",
+ "- **Startup costs**: Penalties for turning equipment on\n",
+ "- **Minimum uptime/downtime**: Prevent rapid cycling\n",
+ "- **Minimum load**: Equipment can't run below a certain output"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1",
+ "metadata": {},
+ "source": [
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import plotly.express as px\n",
+ "import xarray as xr\n",
+ "\n",
+ "import flixopt as fx\n",
+ "\n",
+ "fx.CONFIG.notebook()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3",
+ "metadata": {},
+ "source": [
+ "## System Description\n",
+ "\n",
+ "The factory has:\n",
+ "\n",
+ "- **Industrial boiler**: 500 kW capacity, startup cost of 50€, minimum 4h uptime\n",
+ "- **Small backup boiler**: 100 kW, no startup constraints (always available)\n",
+ "- **Steam demand**: Varies with production schedule (high during shifts, low overnight)\n",
+ "\n",
+ "The main boiler is more efficient but has operational constraints. The backup is less efficient but flexible."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4",
+ "metadata": {},
+ "source": [
+ "## Define Time Horizon and Demand"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# 3 days, hourly resolution\n",
+ "timesteps = pd.date_range('2024-03-11', periods=72, freq='h')\n",
+ "hours = np.arange(72)\n",
+ "hour_of_day = hours % 24\n",
+ "\n",
+ "# Factory operates in shifts:\n",
+ "# - Day shift (6am-2pm): 400 kW\n",
+ "# - Evening shift (2pm-10pm): 350 kW\n",
+ "# - Night (10pm-6am): 80 kW (maintenance heating only)\n",
+ "\n",
+ "steam_demand = np.select(\n",
+ " [\n",
+ " (hour_of_day >= 6) & (hour_of_day < 14), # Day shift\n",
+ " (hour_of_day >= 14) & (hour_of_day < 22), # Evening shift\n",
+ " ],\n",
+ " [400, 350],\n",
+ " default=80, # Night\n",
+ ")\n",
+ "\n",
+ "# Add some variation\n",
+ "np.random.seed(123)\n",
+ "steam_demand = steam_demand + np.random.normal(0, 20, len(steam_demand))\n",
+ "steam_demand = np.clip(steam_demand, 50, 450).astype(float)\n",
+ "\n",
+ "print(f'Peak demand: {steam_demand.max():.0f} kW')\n",
+ "print(f'Min demand: {steam_demand.min():.0f} kW')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "6",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "px.line(x=timesteps, y=steam_demand, title='Factory Steam Demand', labels={'x': 'Time', 'y': 'kW'})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7",
+ "metadata": {},
+ "source": [
+ "## Build System with Operational Constraints"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system = fx.FlowSystem(timesteps)\n",
+ "\n",
+ "flow_system.add_elements(\n",
+ " # === Buses ===\n",
+ " fx.Bus('Gas'),\n",
+ " fx.Bus('Steam'),\n",
+ " # === Effect ===\n",
+ " fx.Effect('costs', '€', 'Operating Costs', is_standard=True, is_objective=True),\n",
+ " # === Gas Supply ===\n",
+ " fx.Source(\n",
+ " 'GasGrid',\n",
+ " outputs=[fx.Flow('Gas', bus='Gas', size=1000, effects_per_flow_hour=0.06)],\n",
+ " ),\n",
+ " # === Main Industrial Boiler (with operational constraints) ===\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'MainBoiler',\n",
+ " thermal_efficiency=0.94, # High efficiency\n",
+ " # StatusParameters define on/off behavior\n",
+ " status_parameters=fx.StatusParameters(\n",
+ " effects_per_startup={'costs': 50}, # 50€ startup cost\n",
+ " min_uptime=4, # Must run at least 4 hours once started\n",
+ " min_downtime=2, # Must stay off at least 2 hours\n",
+ " ),\n",
+ " thermal_flow=fx.Flow(\n",
+ " 'Steam',\n",
+ " bus='Steam',\n",
+ " size=500,\n",
+ " relative_minimum=0.3, # Minimum load: 30% = 150 kW\n",
+ " ),\n",
+ " fuel_flow=fx.Flow('Gas', bus='Gas'),\n",
+ " ),\n",
+ " # === Backup Boiler (flexible, but less efficient) ===\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'BackupBoiler',\n",
+ " thermal_efficiency=0.85, # Lower efficiency\n",
+ " # No status parameters = can turn on/off freely\n",
+ " thermal_flow=fx.Flow('Steam', bus='Steam', size=150),\n",
+ " fuel_flow=fx.Flow('Gas', bus='Gas'),\n",
+ " ),\n",
+ " # === Factory Steam Demand ===\n",
+ " fx.Sink(\n",
+ " 'Factory',\n",
+ " inputs=[fx.Flow('Steam', bus='Steam', size=1, fixed_relative_profile=steam_demand)],\n",
+ " ),\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9",
+ "metadata": {},
+ "source": [
+ "## Run Optimization"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "10",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0.01));"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "11",
+ "metadata": {},
+ "source": [
+ "## Analyze Results\n",
+ "\n",
+ "### Steam Balance\n",
+ "\n",
+ "See how the two boilers share the load:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "12",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('Steam')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "13",
+ "metadata": {},
+ "source": [
+ "### Main Boiler Operation\n",
+ "\n",
+ "Notice how the main boiler:\n",
+ "- Runs continuously during production (respecting min uptime)\n",
+ "- Stays above minimum load (30%)\n",
+ "- Shuts down during low-demand periods"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "14",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.heatmap('MainBoiler(Steam)')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "15",
+ "metadata": {},
+ "source": [
+ "### On/Off Status\n",
+ "\n",
+ "Track the boiler's operational status:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "16",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Merge solution DataArrays directly - xarray aligns coordinates automatically\n",
+ "status_ds = xr.Dataset(\n",
+ " {\n",
+ " 'Status': flow_system.solution['MainBoiler|status'],\n",
+ " 'Steam Production [kW]': flow_system.solution['MainBoiler(Steam)|flow_rate'],\n",
+ " }\n",
+ ")\n",
+ "\n",
+ "df = status_ds.to_dataframe().reset_index().melt(id_vars='time', var_name='variable', value_name='value')\n",
+ "fig = px.line(df, x='time', y='value', facet_col='variable', height=300, title='Main Boiler Operation')\n",
+ "fig.update_yaxes(matches=None, showticklabels=True)\n",
+ "fig.for_each_annotation(lambda a: a.update(text=a.text.split('=')[-1]))\n",
+ "fig"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "17",
+ "metadata": {},
+ "source": [
+ "### Startup Count and Costs"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "18",
+ "metadata": {},
+ "outputs": [],
+ "source": "total_startups = int(flow_system.solution['MainBoiler|startup'].sum().item())\ntotal_costs = flow_system.solution['costs'].item()\nstartup_costs = total_startups * 50\ngas_costs = total_costs - startup_costs\n\nprint('=== Cost Breakdown ===')\nprint(f'Number of startups: {total_startups}')\nprint(f'Startup costs: {startup_costs:.0f} €')\nprint(f'Gas costs: {gas_costs:.2f} €')\nprint(f'Total costs: {total_costs:.2f} €')"
+ },
+ {
+ "cell_type": "markdown",
+ "id": "19",
+ "metadata": {},
+ "source": [
+ "### Duration Curves\n",
+ "\n",
+ "See how often each boiler operates at different load levels:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "20",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.duration_curve('MainBoiler(Steam)')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "21",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.duration_curve('BackupBoiler(Steam)')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "22",
+ "metadata": {},
+ "source": [
+ "## Compare: Without Operational Constraints\n",
+ "\n",
+ "What if the main boiler had no startup costs or minimum uptime?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "23",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Build unconstrained system\n",
+ "fs_unconstrained = fx.FlowSystem(timesteps)\n",
+ "\n",
+ "fs_unconstrained.add_elements(\n",
+ " fx.Bus('Gas'),\n",
+ " fx.Bus('Steam'),\n",
+ " fx.Effect('costs', '€', 'Operating Costs', is_standard=True, is_objective=True),\n",
+ " fx.Source('GasGrid', outputs=[fx.Flow('Gas', bus='Gas', size=1000, effects_per_flow_hour=0.06)]),\n",
+ " # Main boiler WITHOUT status parameters\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'MainBoiler',\n",
+ " thermal_efficiency=0.94,\n",
+ " thermal_flow=fx.Flow('Steam', bus='Steam', size=500),\n",
+ " fuel_flow=fx.Flow('Gas', bus='Gas'),\n",
+ " ),\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'BackupBoiler',\n",
+ " thermal_efficiency=0.85,\n",
+ " thermal_flow=fx.Flow('Steam', bus='Steam', size=150),\n",
+ " fuel_flow=fx.Flow('Gas', bus='Gas'),\n",
+ " ),\n",
+ " fx.Sink('Factory', inputs=[fx.Flow('Steam', bus='Steam', size=1, fixed_relative_profile=steam_demand)]),\n",
+ ")\n",
+ "\n",
+ "fs_unconstrained.optimize(fx.solvers.HighsSolver())\n",
+ "unconstrained_costs = fs_unconstrained.solution['costs'].item()\n",
+ "\n",
+ "print('=== Comparison ===')\n",
+ "print(f'With constraints: {total_costs:.2f} €')\n",
+ "print(f'Without constraints: {unconstrained_costs:.2f} €')\n",
+ "print(\n",
+ " f'Constraint cost: {total_costs - unconstrained_costs:.2f} € ({(total_costs - unconstrained_costs) / unconstrained_costs * 100:.1f}%)'\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "24",
+ "metadata": {},
+ "source": [
+ "### Energy Flow Sankey\n",
+ "\n",
+ "A Sankey diagram visualizes the total energy flows through the system:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "25",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.sankey()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "26",
+ "metadata": {},
+ "source": [
+ "## Key Concepts\n",
+ "\n",
+ "### StatusParameters Options\n",
+ "\n",
+ "```python\n",
+ "fx.StatusParameters(\n",
+ " # Startup/shutdown costs\n",
+ " effects_per_startup={'costs': 50}, # Cost per startup event\n",
+ " effects_per_shutdown={'costs': 10}, # Cost per shutdown event\n",
+ " \n",
+ " # Time constraints\n",
+ " min_uptime=4, # Minimum hours running once started\n",
+ " min_downtime=2, # Minimum hours off once stopped\n",
+ " \n",
+ " # Startup limits\n",
+ " max_startups=10, # Maximum startups per period\n",
+ ")\n",
+ "```\n",
+ "\n",
+ "### Minimum Load\n",
+ "\n",
+ "Set via `Flow.relative_minimum`:\n",
+ "```python\n",
+ "fx.Flow('Steam', bus='Steam', size=500, relative_minimum=0.3) # Min 30% load\n",
+ "```\n",
+ "\n",
+ "### When Status is Active\n",
+ "\n",
+ "- When `StatusParameters` is set, a binary on/off variable is created\n",
+ "- Flow is zero when status=0, within bounds when status=1\n",
+ "- Without `StatusParameters`, flow can vary continuously from 0 to max\n",
+ "\n",
+ "## Summary\n",
+ "\n",
+ "You learned how to:\n",
+ "\n",
+ "- Add **startup costs** with `effects_per_startup`\n",
+ "- Set **minimum run times** with `min_uptime` and `min_downtime`\n",
+ "- Define **minimum load** with `relative_minimum`\n",
+ "- Access **status variables** from the solution\n",
+ "- Use **duration curves** to analyze operation patterns\n",
+ "\n",
+ "### Next Steps\n",
+ "\n",
+ "- **[05-multi-carrier-system](05-multi-carrier-system.ipynb)**: Model CHP with electricity and heat\n",
+ "- **[06-piecewise-efficiency](06-piecewise-efficiency.ipynb)**: Variable efficiency at different loads"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python",
+ "version": "3.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/notebooks/05-multi-carrier-system.ipynb b/docs/notebooks/05-multi-carrier-system.ipynb
new file mode 100644
index 000000000..50c59dd3e
--- /dev/null
+++ b/docs/notebooks/05-multi-carrier-system.ipynb
@@ -0,0 +1,560 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "0",
+ "metadata": {},
+ "source": [
+ "# Multi-Carrier System: Hospital with CHP\n",
+ "\n",
+ "## User Story\n",
+ "\n",
+ "> *You're the energy manager of a hospital. The facility needs both electricity and heat around the clock. You have a Combined Heat and Power (CHP) unit that produces both simultaneously, plus a gas boiler for backup heat and a grid connection for electricity. Your goal is to minimize energy costs while ensuring reliable supply.*\n",
+ "\n",
+ "This notebook introduces:\n",
+ "\n",
+ "- **Multiple energy carriers**: Electricity, heat, and gas in one system\n",
+ "- **CHP (Cogeneration)**: Equipment producing multiple outputs\n",
+ "- **Electricity market**: Buying and selling to the grid\n",
+ "- **Carrier colors**: Visual distinction between energy types"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1",
+ "metadata": {},
+ "source": [
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import plotly.express as px\n",
+ "import xarray as xr\n",
+ "\n",
+ "import flixopt as fx\n",
+ "\n",
+ "fx.CONFIG.notebook()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3",
+ "metadata": {},
+ "source": [
+ "## System Description\n",
+ "\n",
+ "The hospital energy system:\n",
+ "\n",
+ "```\n",
+ " Grid Buy ──►\n",
+ " [Electricity] ──► Hospital Elec. Load\n",
+ " Grid Sell ◄── ▲\n",
+ " │\n",
+ " Gas Grid ──► [Gas] ──► CHP ──────┘\n",
+ " │ │\n",
+ " │ ▼\n",
+ " │ [Heat] ──► Hospital Heat Load\n",
+ " │ ▲\n",
+ " └──► Boiler\n",
+ "```\n",
+ "\n",
+ "**Equipment:**\n",
+ "- **CHP**: 200 kW electrical, ~250 kW thermal (η_el=40%, η_th=50%)\n",
+ "- **Gas Boiler**: 400 kW thermal backup\n",
+ "- **Grid**: Buy electricity at variable prices, sell at lower prices"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4",
+ "metadata": {},
+ "source": [
+ "## Define Time Horizon and Demand Profiles"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# One week, hourly\n",
+ "timesteps = pd.date_range('2024-02-05', periods=168, freq='h')\n",
+ "hours = np.arange(168)\n",
+ "hour_of_day = hours % 24\n",
+ "\n",
+ "# Hospital electricity demand (kW)\n",
+ "# Base load + daily pattern (higher during day for equipment, lighting)\n",
+ "elec_base = 150 # 24/7 critical systems\n",
+ "elec_daily = 100 * np.sin((hour_of_day - 6) * np.pi / 12) # Peak at noon\n",
+ "elec_daily = np.maximum(0, elec_daily)\n",
+ "electricity_demand = elec_base + elec_daily\n",
+ "\n",
+ "# Hospital heat demand (kW)\n",
+ "# Higher in morning, drops during day, increases for hot water in evening\n",
+ "heat_pattern = np.select(\n",
+ " [\n",
+ " (hour_of_day >= 5) & (hour_of_day < 9), # Morning warmup\n",
+ " (hour_of_day >= 9) & (hour_of_day < 17), # Daytime\n",
+ " (hour_of_day >= 17) & (hour_of_day < 22), # Evening\n",
+ " ],\n",
+ " [350, 250, 300],\n",
+ " default=200, # Night\n",
+ ")\n",
+ "heat_demand = heat_pattern.astype(float)\n",
+ "\n",
+ "# Add random variation\n",
+ "np.random.seed(456)\n",
+ "electricity_demand += np.random.normal(0, 15, len(timesteps))\n",
+ "heat_demand += np.random.normal(0, 20, len(timesteps))\n",
+ "electricity_demand = np.clip(electricity_demand, 100, 300)\n",
+ "heat_demand = np.clip(heat_demand, 150, 400)\n",
+ "\n",
+ "print(f'Electricity: {electricity_demand.min():.0f} - {electricity_demand.max():.0f} kW')\n",
+ "print(f'Heat: {heat_demand.min():.0f} - {heat_demand.max():.0f} kW')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "6",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Electricity prices (€/kWh)\n",
+ "# Time-of-use: expensive during day, cheaper at night\n",
+ "elec_buy_price = np.where(\n",
+ " (hour_of_day >= 7) & (hour_of_day <= 21),\n",
+ " 0.35, # Peak - high electricity prices make CHP attractive\n",
+ " 0.20, # Off-peak\n",
+ ")\n",
+ "\n",
+ "# Feed-in tariff (sell price) - allows selling excess CHP electricity\n",
+ "elec_sell_price = 0.12 # Fixed feed-in rate\n",
+ "\n",
+ "# Gas price - relatively low, favoring gas-based generation\n",
+ "gas_price = 0.05 # €/kWh"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Visualize demands and prices with plotly - using xarray and faceting\n",
+ "profiles = xr.Dataset(\n",
+ " {\n",
+ " 'Electricity Demand [kW]': xr.DataArray(electricity_demand, dims=['time'], coords={'time': timesteps}),\n",
+ " 'Heat Demand [kW]': xr.DataArray(heat_demand, dims=['time'], coords={'time': timesteps}),\n",
+ " 'Elec. Buy Price [€/kWh]': xr.DataArray(elec_buy_price, dims=['time'], coords={'time': timesteps}),\n",
+ " }\n",
+ ")\n",
+ "\n",
+ "df = profiles.to_dataframe().reset_index().melt(id_vars='time', var_name='variable', value_name='value')\n",
+ "fig = px.line(df, x='time', y='value', facet_col='variable', height=300)\n",
+ "fig.update_yaxes(matches=None, showticklabels=True)\n",
+ "fig.for_each_annotation(lambda a: a.update(text=a.text.split('=')[-1]))\n",
+ "fig"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8",
+ "metadata": {},
+ "source": [
+ "## Build the Multi-Carrier System"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system = fx.FlowSystem(timesteps)\n",
+ "\n",
+ "flow_system.add_elements(\n",
+ " # === Buses with carriers for visual distinction ===\n",
+ " fx.Bus('Electricity', carrier='electricity'),\n",
+ " fx.Bus('Heat', carrier='heat'),\n",
+ " fx.Bus('Gas', carrier='gas'),\n",
+ " # === Effects ===\n",
+ " fx.Effect('costs', '€', 'Total Costs', is_standard=True, is_objective=True),\n",
+ " fx.Effect('CO2', 'kg', 'CO2 Emissions'), # Track emissions too\n",
+ " # === Gas Supply ===\n",
+ " fx.Source(\n",
+ " 'GasGrid',\n",
+ " outputs=[\n",
+ " fx.Flow(\n",
+ " 'Gas',\n",
+ " bus='Gas',\n",
+ " size=1000,\n",
+ " effects_per_flow_hour={'costs': gas_price, 'CO2': 0.2}, # Gas: 0.2 kg CO2/kWh\n",
+ " )\n",
+ " ],\n",
+ " ),\n",
+ " # === Electricity Grid (buy) ===\n",
+ " fx.Source(\n",
+ " 'GridBuy',\n",
+ " outputs=[\n",
+ " fx.Flow(\n",
+ " 'Electricity',\n",
+ " bus='Electricity',\n",
+ " size=500,\n",
+ " effects_per_flow_hour={'costs': elec_buy_price, 'CO2': 0.4}, # Grid: 0.4 kg CO2/kWh\n",
+ " )\n",
+ " ],\n",
+ " ),\n",
+ " # === Electricity Grid (sell) - negative cost = revenue ===\n",
+ " fx.Sink(\n",
+ " 'GridSell',\n",
+ " inputs=[\n",
+ " fx.Flow(\n",
+ " 'Electricity',\n",
+ " bus='Electricity',\n",
+ " size=200,\n",
+ " effects_per_flow_hour={'costs': -elec_sell_price}, # Negative = income\n",
+ " )\n",
+ " ],\n",
+ " ),\n",
+ " # === CHP Unit (Combined Heat and Power) ===\n",
+ " fx.linear_converters.CHP(\n",
+ " 'CHP',\n",
+ " electrical_efficiency=0.40, # 40% to electricity\n",
+ " thermal_efficiency=0.50, # 50% to heat (total: 90%)\n",
+ " status_parameters=fx.StatusParameters(\n",
+ " effects_per_startup={'costs': 30},\n",
+ " min_uptime=3,\n",
+ " ),\n",
+ " electrical_flow=fx.Flow('P_el', bus='Electricity', size=200),\n",
+ " thermal_flow=fx.Flow('Q_th', bus='Heat', size=250),\n",
+ " fuel_flow=fx.Flow(\n",
+ " 'Q_fuel',\n",
+ " bus='Gas',\n",
+ " size=500,\n",
+ " relative_minimum=0.4, # Min 40% load\n",
+ " ),\n",
+ " ),\n",
+ " # === Gas Boiler (heat only) ===\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'Boiler',\n",
+ " thermal_efficiency=0.92,\n",
+ " thermal_flow=fx.Flow('Q_th', bus='Heat', size=400),\n",
+ " fuel_flow=fx.Flow('Q_fuel', bus='Gas'),\n",
+ " ),\n",
+ " # === Hospital Loads ===\n",
+ " fx.Sink(\n",
+ " 'HospitalElec',\n",
+ " inputs=[fx.Flow('Load', bus='Electricity', size=1, fixed_relative_profile=electricity_demand)],\n",
+ " ),\n",
+ " fx.Sink(\n",
+ " 'HospitalHeat',\n",
+ " inputs=[fx.Flow('Load', bus='Heat', size=1, fixed_relative_profile=heat_demand)],\n",
+ " ),\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "10",
+ "metadata": {},
+ "source": [
+ "## Run Optimization"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "11",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0.01));"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "12",
+ "metadata": {},
+ "source": [
+ "## Analyze Results\n",
+ "\n",
+ "### Electricity Balance"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "13",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('Electricity')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "14",
+ "metadata": {},
+ "source": [
+ "### Heat Balance"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "15",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('Heat')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "16",
+ "metadata": {},
+ "source": [
+ "### Gas Balance"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "17",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('Gas')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "18",
+ "metadata": {},
+ "source": [
+ "### CHP Operation Pattern"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "19",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.heatmap('CHP(P_el)')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "20",
+ "metadata": {},
+ "source": [
+ "### Cost and Emissions Summary"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "21",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "total_costs = flow_system.solution['costs'].item()\n",
+ "total_co2 = flow_system.solution['CO2'].item()\n",
+ "\n",
+ "# Energy flows\n",
+ "flow_rates = flow_system.statistics.flow_rates\n",
+ "grid_buy = flow_rates['GridBuy(Electricity)'].sum().item()\n",
+ "grid_sell = flow_rates['GridSell(Electricity)'].sum().item()\n",
+ "chp_elec = flow_rates['CHP(P_el)'].sum().item()\n",
+ "chp_heat = flow_rates['CHP(Q_th)'].sum().item()\n",
+ "boiler_heat = flow_rates['Boiler(Q_th)'].sum().item()\n",
+ "\n",
+ "total_elec = electricity_demand.sum()\n",
+ "total_heat = heat_demand.sum()\n",
+ "\n",
+ "print('=== Energy Summary ===')\n",
+ "print(f'Total electricity demand: {total_elec:.0f} kWh')\n",
+ "print(f' - From CHP: {chp_elec:.0f} kWh ({chp_elec / total_elec * 100:.1f}%)')\n",
+ "print(f' - From Grid: {grid_buy:.0f} kWh ({grid_buy / total_elec * 100:.1f}%)')\n",
+ "print(f' - Sold to Grid: {grid_sell:.0f} kWh')\n",
+ "print()\n",
+ "print(f'Total heat demand: {total_heat:.0f} kWh')\n",
+ "print(f' - From CHP: {chp_heat:.0f} kWh ({chp_heat / total_heat * 100:.1f}%)')\n",
+ "print(f' - From Boiler: {boiler_heat:.0f} kWh ({boiler_heat / total_heat * 100:.1f}%)')\n",
+ "print()\n",
+ "print('=== Costs & Emissions ===')\n",
+ "print(f'Total costs: {total_costs:.2f} €')\n",
+ "print(f'Total CO2: {total_co2:.0f} kg')\n",
+ "print(f'Specific costs: {total_costs / (total_elec + total_heat) * 100:.2f} ct/kWh')\n",
+ "print(f'Specific CO2: {total_co2 / (total_elec + total_heat) * 1000:.1f} g/kWh')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "22",
+ "metadata": {},
+ "source": [
+ "### Compare: What if No CHP?\n",
+ "\n",
+ "How much does the CHP save compared to buying all electricity?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "23",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Build system without CHP\n",
+ "fs_no_chp = fx.FlowSystem(timesteps)\n",
+ "\n",
+ "fs_no_chp.add_elements(\n",
+ " fx.Bus('Electricity', carrier='electricity'),\n",
+ " fx.Bus('Heat', carrier='heat'),\n",
+ " fx.Bus('Gas', carrier='gas'),\n",
+ " fx.Effect('costs', '€', 'Total Costs', is_standard=True, is_objective=True),\n",
+ " fx.Effect('CO2', 'kg', 'CO2 Emissions'),\n",
+ " fx.Source(\n",
+ " 'GasGrid',\n",
+ " outputs=[fx.Flow('Gas', bus='Gas', size=1000, effects_per_flow_hour={'costs': gas_price, 'CO2': 0.2})],\n",
+ " ),\n",
+ " fx.Source(\n",
+ " 'GridBuy',\n",
+ " outputs=[\n",
+ " fx.Flow(\n",
+ " 'Electricity', bus='Electricity', size=500, effects_per_flow_hour={'costs': elec_buy_price, 'CO2': 0.4}\n",
+ " )\n",
+ " ],\n",
+ " ),\n",
+ " # Only boiler for heat\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'Boiler',\n",
+ " thermal_efficiency=0.92,\n",
+ " thermal_flow=fx.Flow('Q_th', bus='Heat', size=500),\n",
+ " fuel_flow=fx.Flow('Q_fuel', bus='Gas'),\n",
+ " ),\n",
+ " fx.Sink(\n",
+ " 'HospitalElec', inputs=[fx.Flow('Load', bus='Electricity', size=1, fixed_relative_profile=electricity_demand)]\n",
+ " ),\n",
+ " fx.Sink('HospitalHeat', inputs=[fx.Flow('Load', bus='Heat', size=1, fixed_relative_profile=heat_demand)]),\n",
+ ")\n",
+ "\n",
+ "fs_no_chp.optimize(fx.solvers.HighsSolver())\n",
+ "\n",
+ "no_chp_costs = fs_no_chp.solution['costs'].item()\n",
+ "no_chp_co2 = fs_no_chp.solution['CO2'].item()\n",
+ "\n",
+ "print('=== CHP Benefit Analysis ===')\n",
+ "print(f'Without CHP: {no_chp_costs:.2f} € / {no_chp_co2:.0f} kg CO2')\n",
+ "print(f'With CHP: {total_costs:.2f} € / {total_co2:.0f} kg CO2')\n",
+ "print(f'Cost savings: {no_chp_costs - total_costs:.2f} € ({(no_chp_costs - total_costs) / no_chp_costs * 100:.1f}%)')\n",
+ "print(f'CO2 reduction: {no_chp_co2 - total_co2:.0f} kg ({(no_chp_co2 - total_co2) / no_chp_co2 * 100:.1f}%)')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "24",
+ "metadata": {},
+ "source": [
+ "### Energy Flow Sankey\n",
+ "\n",
+ "A Sankey diagram visualizes the total energy flows through the multi-carrier system:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "25",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.sankey()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "26",
+ "metadata": {},
+ "source": [
+ "## Key Concepts\n",
+ "\n",
+ "### Multi-Carrier Systems\n",
+ "\n",
+ "- Multiple buses for different energy carriers (electricity, heat, gas)\n",
+ "- Components can connect to multiple buses (CHP produces both electricity and heat)\n",
+ "- Carriers enable automatic coloring in visualizations\n",
+ "\n",
+ "### CHP Modeling\n",
+ "\n",
+ "```python\n",
+ "fx.linear_converters.CHP(\n",
+ " 'CHP',\n",
+ " electrical_efficiency=0.40, # Fuel → Electricity\n",
+ " thermal_efficiency=0.50, # Fuel → Heat\n",
+ " # Total efficiency = 0.40 + 0.50 = 0.90 (90%)\n",
+ " electrical_flow=fx.Flow('P_el', bus='Electricity', size=200),\n",
+ " thermal_flow=fx.Flow('Q_th', bus='Heat', size=250),\n",
+ " fuel_flow=fx.Flow('Q_fuel', bus='Gas', size=500),\n",
+ ")\n",
+ "```\n",
+ "\n",
+ "### Electricity Markets\n",
+ "\n",
+ "- **Buy**: Source with positive cost\n",
+ "- **Sell**: Sink with negative cost (= revenue)\n",
+ "- Different prices for buy vs. sell (spread)\n",
+ "\n",
+ "### Tracking Multiple Effects\n",
+ "\n",
+ "```python\n",
+ "fx.Effect('costs', '€', 'Total Costs', is_objective=True) # Minimize this\n",
+ "fx.Effect('CO2', 'kg', 'CO2 Emissions') # Just track, don't optimize\n",
+ "```\n",
+ "\n",
+ "## Summary\n",
+ "\n",
+ "You learned how to:\n",
+ "\n",
+ "- Model **multiple energy carriers** (electricity, heat, gas)\n",
+ "- Use **CHP** for combined heat and power production\n",
+ "- Model **electricity markets** with buy/sell prices\n",
+ "- Track **multiple effects** (costs and emissions)\n",
+ "- Analyze **multi-carrier balances**\n",
+ "\n",
+ "### Next Steps\n",
+ "\n",
+ "- **[06-piecewise-efficiency](06-piecewise-efficiency.ipynb)**: Model variable efficiency curves\n",
+ "- **[07-scenarios-and-periods](07-scenarios-and-periods.ipynb)**: Plan under uncertainty"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python",
+ "version": "3.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/notebooks/06-piecewise-efficiency.ipynb b/docs/notebooks/06-piecewise-efficiency.ipynb
new file mode 100644
index 000000000..ce87a93c6
--- /dev/null
+++ b/docs/notebooks/06-piecewise-efficiency.ipynb
@@ -0,0 +1,646 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "0",
+ "metadata": {},
+ "source": [
+ "# Piecewise Efficiency: Heat Pump with Variable COP\n",
+ "\n",
+ "## User Story\n",
+ "\n",
+ "> *You're installing a heat pump for a commercial building. The heat pump's efficiency (COP - Coefficient of Performance) varies with the outdoor temperature: it's more efficient in mild weather than in cold weather. You want to model this realistically to accurately predict operating costs.*\n",
+ "\n",
+ "This notebook introduces:\n",
+ "\n",
+ "- **Piecewise linear functions**: Approximate non-linear behavior\n",
+ "- **Variable efficiency**: COP changes with operating conditions\n",
+ "- **LinearConverter with segments**: Multiple operating points\n",
+ "- **Piecewise effects**: Non-linear cost curves"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1",
+ "metadata": {},
+ "source": [
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import plotly.express as px\n",
+ "import xarray as xr\n",
+ "\n",
+ "import flixopt as fx\n",
+ "\n",
+ "fx.CONFIG.notebook()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3",
+ "metadata": {},
+ "source": [
+ "## The Problem: Variable Heat Pump Efficiency\n",
+ "\n",
+ "A heat pump's COP (Coefficient of Performance) depends on the temperature difference between source and sink:\n",
+ "\n",
+ "- **Mild weather** (10°C outside): COP ≈ 4.5 (1 kWh electricity → 4.5 kWh heat)\n",
+ "- **Cold weather** (-5°C outside): COP ≈ 2.5 (1 kWh electricity → 2.5 kWh heat)\n",
+ "\n",
+ "This non-linear relationship can be approximated using piecewise linear segments."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4",
+ "metadata": {},
+ "source": [
+ "## Define Time Series Data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# One winter week\n",
+ "timesteps = pd.date_range('2024-01-22', periods=168, freq='h')\n",
+ "hours = np.arange(168)\n",
+ "hour_of_day = hours % 24\n",
+ "\n",
+ "# Outdoor temperature: daily cycle with cold nights\n",
+ "temp_base = 2 # Average temp\n",
+ "temp_amplitude = 5 # Daily variation\n",
+ "outdoor_temp = temp_base + temp_amplitude * np.sin((hour_of_day - 6) * np.pi / 12)\n",
+ "\n",
+ "# Add day-to-day variation\n",
+ "np.random.seed(789)\n",
+ "daily_offset = np.repeat(np.random.uniform(-3, 3, 7), 24)\n",
+ "outdoor_temp = outdoor_temp + daily_offset"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "6",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Heat demand: inversely related to outdoor temp (higher demand when colder)\n",
+ "heat_demand = 200 - 8 * outdoor_temp\n",
+ "heat_demand = np.clip(heat_demand, 100, 300)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Visualize with plotly - using xarray and faceting\n",
+ "profiles = xr.Dataset(\n",
+ " {\n",
+ " 'Outdoor Temp [°C]': xr.DataArray(outdoor_temp, dims=['time'], coords={'time': timesteps}),\n",
+ " 'Heat Demand [kW]': xr.DataArray(heat_demand, dims=['time'], coords={'time': timesteps}),\n",
+ " }\n",
+ ")\n",
+ "\n",
+ "df = profiles.to_dataframe().reset_index().melt(id_vars='time', var_name='variable', value_name='value')\n",
+ "fig = px.line(df, x='time', y='value', facet_col='variable', height=300)\n",
+ "fig.update_yaxes(matches=None, showticklabels=True)\n",
+ "fig.for_each_annotation(lambda a: a.update(text=a.text.split('=')[-1]))\n",
+ "fig"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8",
+ "metadata": {},
+ "source": [
+ "## Calculate Time-Varying COP\n",
+ "\n",
+ "The COP depends on outdoor temperature. We use a simplified Carnot-based formula:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# COP calculation (simplified): Real COP ≈ 0.45 * Carnot COP\n",
+ "T_supply = 45 + 273.15 # Supply temperature 45°C in Kelvin\n",
+ "T_source = outdoor_temp + 273.15 # Outdoor temp in Kelvin\n",
+ "\n",
+ "carnot_cop = T_supply / (T_supply - T_source)\n",
+ "real_cop = 0.45 * carnot_cop\n",
+ "real_cop = np.clip(real_cop, 2.0, 5.0) # Physical limits"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "10",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Plot COP vs temperature using plotly\n",
+ "px.scatter(\n",
+ " x=outdoor_temp,\n",
+ " y=real_cop,\n",
+ " title='Heat Pump COP vs Outdoor Temperature',\n",
+ " labels={'x': 'Outdoor Temperature [°C]', 'y': 'COP'},\n",
+ " opacity=0.5,\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "11",
+ "metadata": {},
+ "source": [
+ "## Approach 1: Simple Model with Time-Varying Efficiency\n",
+ "\n",
+ "The simplest approach: use time-varying conversion factors directly."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "12",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system = fx.FlowSystem(timesteps)\n",
+ "\n",
+ "flow_system.add_elements(\n",
+ " fx.Bus('Electricity', carrier='electricity'),\n",
+ " fx.Bus('Heat', carrier='heat'),\n",
+ " fx.Effect('costs', '€', 'Operating Costs', is_standard=True, is_objective=True),\n",
+ " fx.Source('Grid', outputs=[fx.Flow('Elec', bus='Electricity', size=500, effects_per_flow_hour=0.30)]),\n",
+ " fx.LinearConverter(\n",
+ " 'HeatPump',\n",
+ " inputs=[fx.Flow('Elec', bus='Electricity', size=150)],\n",
+ " outputs=[fx.Flow('Heat', bus='Heat', size=500)],\n",
+ " conversion_factors=[{'Elec': real_cop, 'Heat': 1}], # Time-varying COP\n",
+ " ),\n",
+ " fx.Sink('Building', inputs=[fx.Flow('Heat', bus='Heat', size=1, fixed_relative_profile=heat_demand)]),\n",
+ ")\n",
+ "\n",
+ "flow_system.optimize(fx.solvers.HighsSolver())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "13",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('Heat')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "14",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('Electricity')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "15",
+ "metadata": {},
+ "source": [
+ "## Approach 2: Simple vs Piecewise Efficiency - Model Refinement\n",
+ "\n",
+ "Real equipment often has non-linear efficiency curves. Let's compare:\n",
+ "1. **Simple model**: Constant average efficiency\n",
+ "2. **Refined model**: Piecewise linear efficiency that varies with load\n",
+ "\n",
+ "This demonstrates how to progressively refine a model for more accurate results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "16",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Gas engine efficiency varies with load:\n",
+ "# - Part load: lower efficiency\n",
+ "# - Mid load: optimal efficiency (~42%)\n",
+ "# - Full load: slightly lower efficiency\n",
+ "\n",
+ "SIMPLE_EFFICIENCY = 0.38 # Average efficiency for simple model\n",
+ "\n",
+ "# Piecewise model: efficiency varies by operating segment\n",
+ "piecewise_efficiency = fx.PiecewiseConversion(\n",
+ " {\n",
+ " 'Fuel': fx.Piecewise(\n",
+ " [\n",
+ " fx.Piece(start=78, end=132), # Part load\n",
+ " fx.Piece(start=132, end=179), # Mid load (optimal)\n",
+ " fx.Piece(start=179, end=250), # High load\n",
+ " ]\n",
+ " ),\n",
+ " 'Elec': fx.Piecewise(\n",
+ " [\n",
+ " fx.Piece(start=25, end=50),\n",
+ " fx.Piece(start=50, end=75),\n",
+ " fx.Piece(start=75, end=100),\n",
+ " ]\n",
+ " ),\n",
+ " }\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "17",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# 2-day demand profile\n",
+ "timesteps_simple = pd.date_range('2024-01-22', periods=48, freq='h')\n",
+ "elec_demand_simple = np.concatenate([np.linspace(30, 90, 24), np.linspace(90, 30, 24)])\n",
+ "\n",
+ "# MODEL 1: Simple constant efficiency\n",
+ "fs_simple = fx.FlowSystem(timesteps_simple)\n",
+ "fs_simple.add_elements(\n",
+ " fx.Bus('Gas', carrier='gas'),\n",
+ " fx.Bus('Electricity', carrier='electricity'),\n",
+ " fx.Effect('costs', '€', 'Costs', is_standard=True, is_objective=True),\n",
+ " fx.Source('GasGrid', outputs=[fx.Flow('Gas', bus='Gas', size=500, effects_per_flow_hour=0.05)]),\n",
+ " fx.LinearConverter(\n",
+ " 'GasEngine',\n",
+ " inputs=[fx.Flow('Fuel', bus='Gas', size=300)],\n",
+ " outputs=[fx.Flow('Elec', bus='Electricity', size=100)],\n",
+ " conversion_factors=[{'Fuel': 1, 'Elec': SIMPLE_EFFICIENCY}],\n",
+ " ),\n",
+ " fx.Sink('Load', inputs=[fx.Flow('Elec', bus='Electricity', size=1, fixed_relative_profile=elec_demand_simple)]),\n",
+ ")\n",
+ "fs_simple.optimize(fx.solvers.HighsSolver())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "18",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# MODEL 2: Piecewise efficiency (load-dependent)\n",
+ "fs_piecewise = fx.FlowSystem(timesteps_simple)\n",
+ "fs_piecewise.add_elements(\n",
+ " fx.Bus('Gas', carrier='gas'),\n",
+ " fx.Bus('Electricity', carrier='electricity'),\n",
+ " fx.Effect('costs', '€', 'Costs', is_standard=True, is_objective=True),\n",
+ " fx.Source('GasGrid', outputs=[fx.Flow('Gas', bus='Gas', size=500, effects_per_flow_hour=0.05)]),\n",
+ " fx.LinearConverter(\n",
+ " 'GasEngine',\n",
+ " inputs=[fx.Flow('Fuel', bus='Gas')],\n",
+ " outputs=[fx.Flow('Elec', bus='Electricity')],\n",
+ " piecewise_conversion=piecewise_efficiency,\n",
+ " ),\n",
+ " fx.Sink('Load', inputs=[fx.Flow('Elec', bus='Electricity', size=1, fixed_relative_profile=elec_demand_simple)]),\n",
+ ")\n",
+ "fs_piecewise.optimize(fx.solvers.HighsSolver())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "19",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Visualize the piecewise conversion curve\n",
+ "fs_piecewise.components['GasEngine'].piecewise_conversion.plot(\n",
+ " x_flow='Fuel', title='Gas Engine: Fuel Input vs Electricity Output'\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "20",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Compare: Simple vs Piecewise efficiency\n",
+ "print(f'Simple model: {fs_simple.solution[\"costs\"].item():.2f} €')\n",
+ "print(f'Piecewise model: {fs_piecewise.solution[\"costs\"].item():.2f} €')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "21",
+ "metadata": {},
+ "source": [
+ "## Approach 3: Simple vs Piecewise Investment Costs\n",
+ "\n",
+ "Investment costs often have economies of scale - larger systems cost less per unit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "22",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fs_piecewise.statistics.plot.balance('Gas')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "23",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Investment costs (daily amortized)\n",
+ "SIMPLE_INVEST_COST = 0.20 # €/kWh constant\n",
+ "\n",
+ "# Piecewise: economies of scale (0.20 → 0.15 → 0.10 €/kWh)\n",
+ "piecewise_invest_costs = fx.PiecewiseEffects(\n",
+ " piecewise_origin=fx.Piecewise(\n",
+ " [\n",
+ " fx.Piece(start=0, end=100),\n",
+ " fx.Piece(start=100, end=300),\n",
+ " fx.Piece(start=300, end=600),\n",
+ " ]\n",
+ " ),\n",
+ " piecewise_shares={\n",
+ " 'costs': fx.Piecewise(\n",
+ " [\n",
+ " fx.Piece(start=0, end=20), # 0.20 €/kWh\n",
+ " fx.Piece(start=20, end=50), # 0.15 €/kWh\n",
+ " fx.Piece(start=50, end=80), # 0.10 €/kWh\n",
+ " ]\n",
+ " )\n",
+ " },\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "24",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Base system: Price arbitrage scenario (3 days)\n",
+ "timesteps_invest = pd.date_range('2024-01-22', periods=72, freq='h')\n",
+ "\n",
+ "heat_demand_invest = np.tile(\n",
+ " np.concatenate(\n",
+ " [\n",
+ " np.full(8, 100),\n",
+ " np.full(4, 120),\n",
+ " np.full(4, 110),\n",
+ " np.full(4, 130),\n",
+ " np.full(4, 105),\n",
+ " ]\n",
+ " ),\n",
+ " 3,\n",
+ ")\n",
+ "\n",
+ "energy_price_invest = np.tile(\n",
+ " np.concatenate(\n",
+ " [\n",
+ " np.full(8, 0.08),\n",
+ " np.full(4, 0.20),\n",
+ " np.full(4, 0.12),\n",
+ " np.full(4, 0.25),\n",
+ " np.full(4, 0.10),\n",
+ " ]\n",
+ " ),\n",
+ " 3,\n",
+ ")\n",
+ "\n",
+ "fs_base = fx.FlowSystem(timesteps_invest)\n",
+ "fs_base.add_elements(\n",
+ " fx.Bus('Heat', carrier='heat'),\n",
+ " fx.Effect('costs', '€', 'Costs', is_standard=True, is_objective=True),\n",
+ " fx.Source('HeatSource', outputs=[fx.Flow('Heat', bus='Heat', size=300, effects_per_flow_hour=energy_price_invest)]),\n",
+ " fx.Sink('HeatSink', inputs=[fx.Flow('Heat', bus='Heat', size=1, fixed_relative_profile=heat_demand_invest)]),\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "25",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# MODEL 1: Simple linear investment costs\n",
+ "fs_simple_invest = fs_base.copy()\n",
+ "fs_simple_invest.add_elements(\n",
+ " fx.Storage(\n",
+ " 'ThermalStorage',\n",
+ " charging=fx.Flow('charge', bus='Heat', size=200),\n",
+ " discharging=fx.Flow('discharge', bus='Heat', size=200),\n",
+ " capacity_in_flow_hours=fx.InvestParameters(\n",
+ " effects_of_investment_per_size=SIMPLE_INVEST_COST,\n",
+ " minimum_size=0,\n",
+ " maximum_size=600,\n",
+ " ),\n",
+ " initial_charge_state=0,\n",
+ " eta_charge=0.95,\n",
+ " eta_discharge=0.95,\n",
+ " relative_loss_per_hour=0.005,\n",
+ " ),\n",
+ ")\n",
+ "fs_simple_invest.optimize(fx.solvers.HighsSolver())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "26",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# MODEL 2: Piecewise investment costs (economies of scale)\n",
+ "fs_piecewise_invest = fs_base.copy()\n",
+ "fs_piecewise_invest.add_elements(\n",
+ " fx.Storage(\n",
+ " 'ThermalStorage',\n",
+ " charging=fx.Flow('charge', bus='Heat', size=200),\n",
+ " discharging=fx.Flow('discharge', bus='Heat', size=200),\n",
+ " capacity_in_flow_hours=fx.InvestParameters(\n",
+ " piecewise_effects_of_investment=piecewise_invest_costs,\n",
+ " minimum_size=0,\n",
+ " maximum_size=600,\n",
+ " ),\n",
+ " initial_charge_state=0,\n",
+ " eta_charge=0.95,\n",
+ " eta_discharge=0.95,\n",
+ " relative_loss_per_hour=0.005,\n",
+ " ),\n",
+ ")\n",
+ "fs_piecewise_invest.optimize(fx.solvers.HighsSolver())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "27",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Visualize the piecewise investment cost curve\n",
+ "# Access through the storage component after it's part of the FlowSystem\n",
+ "fs_piecewise_invest.components['ThermalStorage'].capacity_in_flow_hours.piecewise_effects_of_investment.plot(\n",
+ " title='Storage Investment Costs (Economies of Scale)'\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "28",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Compare: Simple vs Piecewise investment\n",
+ "print(\n",
+ " f'Simple model: {fs_simple_invest.solution[\"ThermalStorage|size\"].item():.0f} kWh, {fs_simple_invest.solution[\"costs\"].item():.2f} €'\n",
+ ")\n",
+ "print(\n",
+ " f'Piecewise model: {fs_piecewise_invest.solution[\"ThermalStorage|size\"].item():.0f} kWh, {fs_piecewise_invest.solution[\"costs\"].item():.2f} €'\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "29",
+ "metadata": {},
+ "source": [
+ "### Visualize Storage Operation and Energy Flows"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "30",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Storage operation visualization\n",
+ "fs_piecewise_invest.statistics.plot.heatmap('ThermalStorage')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "31",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fs_piecewise_invest.statistics.plot.sankey()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "32",
+ "metadata": {},
+ "source": [
+ "## Key Concepts\n",
+ "\n",
+ "### Time-Varying Conversion Factors\n",
+ "\n",
+ "For temperature-dependent efficiency, use arrays with flow labels as keys:\n",
+ "```python\n",
+ "fx.LinearConverter(\n",
+ " 'HeatPump',\n",
+ " inputs=[fx.Flow('Elec', bus='Electricity', size=150)],\n",
+ " outputs=[fx.Flow('Heat', bus='Heat', size=500)],\n",
+ " # Equation: Elec * COP = Heat * 1\n",
+ " conversion_factors=[{'Elec': cop_array, 'Heat': 1}],\n",
+ ")\n",
+ "```\n",
+ "\n",
+ "### Piecewise Linear Functions\n",
+ "\n",
+ "For non-linear relationships (part-load efficiency), use `PiecewiseConversion`:\n",
+ "```python\n",
+ "fx.PiecewiseConversion({\n",
+ " 'Fuel': fx.Piecewise([\n",
+ " fx.Piece(start=78, end=132), # Segment 1\n",
+ " fx.Piece(start=132, end=179), # Segment 2\n",
+ " ]),\n",
+ " 'Elec': fx.Piecewise([\n",
+ " fx.Piece(start=25, end=50), # Segment 1\n",
+ " fx.Piece(start=50, end=75), # Segment 2\n",
+ " ]),\n",
+ "})\n",
+ "```\n",
+ "\n",
+ "### When to Use Each Approach\n",
+ "\n",
+ "| Approach | Use Case | Complexity |\n",
+ "|----------|----------|------------|\n",
+ "| Time-varying factors | Efficiency depends on external conditions (temp, price) | Low |\n",
+ "| PiecewiseConversion | Efficiency depends on load level | Medium |\n",
+ "| PiecewiseEffects | Non-linear costs (economies of scale) | Medium |\n",
+ "\n",
+ "## Summary\n",
+ "\n",
+ "You learned how to:\n",
+ "\n",
+ "- Model **time-varying efficiency** using conversion factor arrays\n",
+ "- Use **PiecewiseConversion** for load-dependent efficiency curves\n",
+ "- Apply **PiecewiseEffects** for non-linear cost functions\n",
+ "- Choose the right approach for your modeling needs\n",
+ "\n",
+ "### Next Steps\n",
+ "\n",
+ "- **[07-scenarios-and-periods](07-scenarios-and-periods.ipynb)**: Multi-scenario planning\n",
+ "- **[08-large-scale-optimization](08-large-scale-optimization.ipynb)**: Computational efficiency techniques"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.11.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/notebooks/07-scenarios-and-periods.ipynb b/docs/notebooks/07-scenarios-and-periods.ipynb
new file mode 100644
index 000000000..3daee6bb4
--- /dev/null
+++ b/docs/notebooks/07-scenarios-and-periods.ipynb
@@ -0,0 +1,564 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "0",
+ "metadata": {},
+ "source": [
+ "# Scenarios and Periods: Investment Planning Under Uncertainty\n",
+ "\n",
+ "## User Story\n",
+ "\n",
+ "> *You're planning a district heating system for a new residential development. The project spans 3 years, and you face uncertainty: Will the winter be mild or harsh? Will gas prices stay stable or spike? You need to make investment decisions today that work well across multiple possible futures.*\n",
+ "\n",
+ "This notebook introduces:\n",
+ "\n",
+ "- **Periods**: Multiple planning years with different conditions\n",
+ "- **Scenarios**: Uncertain futures (mild vs. harsh winter)\n",
+ "- **Scenario weights**: Probability-weighted optimization\n",
+ "- **Multi-dimensional data**: Parameters that vary by time, period, and scenario"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1",
+ "metadata": {},
+ "source": [
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import plotly.express as px\n",
+ "\n",
+ "import flixopt as fx\n",
+ "\n",
+ "fx.CONFIG.notebook()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3",
+ "metadata": {},
+ "source": [
+ "## The Planning Problem\n",
+ "\n",
+ "We're designing a heating system with:\n",
+ "\n",
+ "- **3 periods** (years): 2024, 2025, 2026 - gas prices expected to rise\n",
+ "- **2 scenarios**: \"Mild Winter\" (60% probability) and \"Harsh Winter\" (40% probability)\n",
+ "- **Investment decision**: Size of CHP unit (made once, works across all futures)\n",
+ "\n",
+ "The optimizer finds the investment that minimizes **expected cost** across all scenarios."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4",
+ "metadata": {},
+ "source": [
+ "## Define Dimensions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Time horizon: one representative winter week\n",
+ "timesteps = pd.date_range('2024-01-15', periods=168, freq='h') # 7 days\n",
+ "\n",
+ "# Planning periods (years)\n",
+ "periods = pd.Index([2024, 2025, 2026], name='period')\n",
+ "\n",
+ "# Scenarios with probabilities\n",
+ "scenarios = pd.Index(['Mild Winter', 'Harsh Winter'], name='scenario')\n",
+ "scenario_weights = np.array([0.6, 0.4]) # 60% mild, 40% harsh\n",
+ "\n",
+ "print(f'Time dimension: {len(timesteps)} hours')\n",
+ "print(f'Periods: {list(periods)}')\n",
+ "print(f'Scenarios: {list(scenarios)}')\n",
+ "print(f'Scenario weights: {dict(zip(scenarios, scenario_weights, strict=False))}')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6",
+ "metadata": {},
+ "source": [
+ "## Create Scenario-Dependent Demand Profiles\n",
+ "\n",
+ "Heat demand differs significantly between mild and harsh winters:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "hours = np.arange(168)\n",
+ "hour_of_day = hours % 24\n",
+ "\n",
+ "# Base daily pattern (kW): higher in morning/evening\n",
+ "daily_pattern = np.select(\n",
+ " [\n",
+ " (hour_of_day >= 6) & (hour_of_day < 9), # Morning peak\n",
+ " (hour_of_day >= 9) & (hour_of_day < 17), # Daytime\n",
+ " (hour_of_day >= 17) & (hour_of_day < 22), # Evening peak\n",
+ " ],\n",
+ " [180, 120, 160],\n",
+ " default=100, # Night\n",
+ ").astype(float)\n",
+ "\n",
+ "# Add random variation\n",
+ "np.random.seed(42)\n",
+ "noise = np.random.normal(0, 10, len(timesteps))\n",
+ "\n",
+ "# Mild winter: lower demand\n",
+ "mild_demand = daily_pattern * 0.8 + noise\n",
+ "mild_demand = np.clip(mild_demand, 60, 200)\n",
+ "\n",
+ "# Harsh winter: higher demand\n",
+ "harsh_demand = daily_pattern * 1.3 + noise * 1.5\n",
+ "harsh_demand = np.clip(harsh_demand, 100, 280)\n",
+ "\n",
+ "# Create DataFrame with scenario columns (flixopt uses column names to match scenarios)\n",
+ "heat_demand = pd.DataFrame(\n",
+ " {\n",
+ " 'Mild Winter': mild_demand,\n",
+ " 'Harsh Winter': harsh_demand,\n",
+ " },\n",
+ " index=timesteps,\n",
+ ")\n",
+ "\n",
+ "print(f'Mild winter demand: {mild_demand.min():.0f} - {mild_demand.max():.0f} kW')\n",
+ "print(f'Harsh winter demand: {harsh_demand.min():.0f} - {harsh_demand.max():.0f} kW')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Visualize demand scenarios with plotly\n",
+ "fig = px.line(\n",
+ " heat_demand.iloc[:48],\n",
+ " title='Heat Demand by Scenario (First 2 Days)',\n",
+ " labels={'index': 'Time', 'value': 'kW', 'variable': 'Scenario'},\n",
+ ")\n",
+ "fig.update_traces(mode='lines')\n",
+ "fig"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9",
+ "metadata": {},
+ "source": [
+ "## Create Period-Dependent Prices\n",
+ "\n",
+ "Energy prices change across planning years:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "10",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Gas prices by period (€/kWh) - expected to rise\n",
+ "gas_prices = np.array([0.06, 0.08, 0.10]) # 2024, 2025, 2026\n",
+ "\n",
+ "# Electricity sell prices by period (€/kWh) - CHP revenue\n",
+ "elec_prices = np.array([0.28, 0.34, 0.43]) # Rising with gas\n",
+ "\n",
+ "print('Gas prices by period:')\n",
+ "for period, price in zip(periods, gas_prices, strict=False):\n",
+ " print(f' {period}: {price:.2f} €/kWh')\n",
+ "\n",
+ "print('\\nElectricity sell prices by period:')\n",
+ "for period, price in zip(periods, elec_prices, strict=False):\n",
+ " print(f' {period}: {price:.2f} €/kWh')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "11",
+ "metadata": {},
+ "source": [
+ "## Build the Flow System\n",
+ "\n",
+ "Initialize with all dimensions:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "12",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system = fx.FlowSystem(\n",
+ " timesteps=timesteps,\n",
+ " periods=periods,\n",
+ " scenarios=scenarios,\n",
+ " scenario_weights=scenario_weights,\n",
+ ")\n",
+ "\n",
+ "print(flow_system)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "13",
+ "metadata": {},
+ "source": [
+ "## Add Components"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "14",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.add_elements(\n",
+ " # === Buses ===\n",
+ " fx.Bus('Electricity', carrier='electricity'),\n",
+ " fx.Bus('Heat', carrier='heat'),\n",
+ " fx.Bus('Gas', carrier='gas'),\n",
+ " # === Effects ===\n",
+ " fx.Effect('costs', '€', 'Total Costs', is_standard=True, is_objective=True),\n",
+ " # === Gas Supply (price varies by period) ===\n",
+ " fx.Source(\n",
+ " 'GasGrid',\n",
+ " outputs=[\n",
+ " fx.Flow(\n",
+ " 'Gas',\n",
+ " bus='Gas',\n",
+ " size=1000,\n",
+ " effects_per_flow_hour=gas_prices, # Array = varies by period\n",
+ " )\n",
+ " ],\n",
+ " ),\n",
+ " # === CHP Unit (investment decision) ===\n",
+ " fx.linear_converters.CHP(\n",
+ " 'CHP',\n",
+ " electrical_efficiency=0.35,\n",
+ " thermal_efficiency=0.50,\n",
+ " electrical_flow=fx.Flow(\n",
+ " 'P_el',\n",
+ " bus='Electricity',\n",
+ " # Investment optimization: find optimal CHP size\n",
+ " size=fx.InvestParameters(\n",
+ " minimum_size=0,\n",
+ " maximum_size=100,\n",
+ " effects_of_investment_per_size={'costs': 50}, # 50 €/kW annualized\n",
+ " ),\n",
+ " relative_minimum=0.3,\n",
+ " ),\n",
+ " thermal_flow=fx.Flow('Q_th', bus='Heat'),\n",
+ " fuel_flow=fx.Flow('Q_fuel', bus='Gas'),\n",
+ " ),\n",
+ " # === Gas Boiler (existing backup) ===\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'Boiler',\n",
+ " thermal_efficiency=0.90,\n",
+ " thermal_flow=fx.Flow('Q_th', bus='Heat', size=500),\n",
+ " fuel_flow=fx.Flow('Q_fuel', bus='Gas'),\n",
+ " ),\n",
+ " # === Electricity Sales (revenue varies by period) ===\n",
+ " fx.Sink(\n",
+ " 'ElecSales',\n",
+ " inputs=[\n",
+ " fx.Flow(\n",
+ " 'P_el',\n",
+ " bus='Electricity',\n",
+ " size=100,\n",
+ " effects_per_flow_hour=-elec_prices, # Negative = revenue\n",
+ " )\n",
+ " ],\n",
+ " ),\n",
+ " # === Heat Demand (varies by scenario) ===\n",
+ " fx.Sink(\n",
+ " 'HeatDemand',\n",
+ " inputs=[\n",
+ " fx.Flow(\n",
+ " 'Q_th',\n",
+ " bus='Heat',\n",
+ " size=1,\n",
+ " fixed_relative_profile=heat_demand, # DataFrame with scenario columns\n",
+ " )\n",
+ " ],\n",
+ " ),\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "15",
+ "metadata": {},
+ "source": [
+ "## Run Optimization"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "16",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0.01));"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "17",
+ "metadata": {},
+ "source": [
+ "## Analyze Results\n",
+ "\n",
+ "### Optimal Investment Decision"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "18",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "chp_size = flow_system.statistics.sizes['CHP(P_el)']\n",
+ "total_cost = flow_system.solution['costs']\n",
+ "\n",
+ "print('=== Investment Decision ===')\n",
+ "print(f'Optimal CHP size: {chp_size.round(1).to_pandas()} kW electrical')\n",
+ "print(f'Thermal capacity: {(chp_size * 0.50 / 0.35).round(1).to_pandas()} kW')\n",
+ "print(f'\\nExpected total cost: {total_cost.round(2).to_pandas()} €')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "19",
+ "metadata": {},
+ "source": [
+ "### Heat Balance by Scenario\n",
+ "\n",
+ "See how the system operates differently in each scenario:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "20",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.balance('Heat')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "21",
+ "metadata": {},
+ "source": [
+ "### CHP Operation Patterns"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "22",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.heatmap('CHP(Q_th)')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "23",
+ "metadata": {},
+ "source": [
+ "### Multi-Dimensional Data Access\n",
+ "\n",
+ "Results include all dimensions (time, period, scenario):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "24",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# View dimensions\n",
+ "flow_rates = flow_system.statistics.flow_rates\n",
+ "print('Flow rates dimensions:', dict(flow_rates.sizes))\n",
+ "\n",
+ "# Plot flow rates\n",
+ "flow_system.statistics.plot.flows()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "25",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# CHP operation in harsh winter vs mild winter\n",
+ "chp_heat = flow_rates['CHP(Q_th)']\n",
+ "\n",
+ "print('CHP Heat Output Statistics:')\n",
+ "for scenario in scenarios:\n",
+ " scenario_data = chp_heat.sel(scenario=scenario)\n",
+ " print(f'\\n{scenario}:')\n",
+ " for period in periods:\n",
+ " period_data = scenario_data.sel(period=period)\n",
+ " print(f' {period}: avg={period_data.mean().item():.1f} kW, max={period_data.max().item():.1f} kW')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "26",
+ "metadata": {},
+ "source": [
+ "## Sensitivity: What if Only Mild Winter?\n",
+ "\n",
+ "Compare optimal CHP size if we only planned for mild winters:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "27",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Select only the mild winter scenario\n",
+ "fs_mild = flow_system.transform.sel(scenario='Mild Winter')\n",
+ "fs_mild.optimize(fx.solvers.HighsSolver(mip_gap=0.01))\n",
+ "\n",
+ "chp_size_mild = fs_mild.statistics.sizes['CHP(P_el)']\n",
+ "\n",
+ "print('=== Comparison ===')\n",
+ "print(f'CHP size (both scenarios): {chp_size.max(\"scenario\").round(2).values} kW')\n",
+ "print(f'CHP size (mild only): {chp_size_mild.round(2).values} kW')\n",
+ "print(f'\\nPlanning for uncertainty adds {(chp_size - chp_size_mild).round(2).values} kW capacity')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "28",
+ "metadata": {},
+ "source": [
+ "### Energy Flow Sankey\n",
+ "\n",
+ "A Sankey diagram visualizes the total energy flows through the system:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "29",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "flow_system.statistics.plot.sankey()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "30",
+ "metadata": {},
+ "source": [
+ "## Key Concepts\n",
+ "\n",
+ "### Multi-Dimensional FlowSystem\n",
+ "\n",
+ "```python\n",
+ "flow_system = fx.FlowSystem(\n",
+ " timesteps=timesteps, # Time dimension\n",
+ " periods=periods, # Planning periods (years)\n",
+ " scenarios=scenarios, # Uncertain futures\n",
+ " scenario_weights=weights, # Probabilities\n",
+ ")\n",
+ "```\n",
+ "\n",
+ "### Dimension-Varying Parameters\n",
+ "\n",
+ "| Data Shape | Meaning |\n",
+ "|------------|----------|\n",
+ "| Scalar | Same for all time/period/scenario |\n",
+ "| Array (n_periods,) | Varies by period |\n",
+ "| Array (n_scenarios,) | Varies by scenario |\n",
+ "| DataFrame with columns | Columns match scenario names |\n",
+ "| Full array (time, period, scenario) | Full specification |\n",
+ "\n",
+ "### Scenario Optimization\n",
+ "\n",
+ "The optimizer minimizes **expected cost**:\n",
+ "$$\\min \\sum_s w_s \\cdot \\text{Cost}_s$$\n",
+ "\n",
+ "where $w_s$ is the scenario weight (probability).\n",
+ "\n",
+ "### Selection Methods\n",
+ "\n",
+ "```python\n",
+ "# Select specific scenario\n",
+ "fs_mild = flow_system.transform.sel(scenario='Mild Winter')\n",
+ "\n",
+ "# Select specific period\n",
+ "fs_2025 = flow_system.transform.sel(period=2025)\n",
+ "\n",
+ "# Select time range\n",
+ "fs_day1 = flow_system.transform.sel(time=slice('2024-01-15', '2024-01-16'))\n",
+ "```\n",
+ "\n",
+ "## Summary\n",
+ "\n",
+ "You learned how to:\n",
+ "\n",
+ "- Define **multiple periods** for multi-year planning\n",
+ "- Create **scenarios** for uncertain futures\n",
+ "- Use **scenario weights** for probability-weighted optimization\n",
+ "- Pass **dimension-varying parameters** (arrays and DataFrames)\n",
+ "- **Select** specific scenarios or periods for analysis\n",
+ "\n",
+ "### Next Steps\n",
+ "\n",
+ "- **[08-large-scale-optimization](08-large-scale-optimization.ipynb)**: Speed up large problems with resampling and clustering"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python",
+ "version": "3.11.0"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/notebooks/08-large-scale-optimization.ipynb b/docs/notebooks/08-large-scale-optimization.ipynb
new file mode 100644
index 000000000..c2f7af123
--- /dev/null
+++ b/docs/notebooks/08-large-scale-optimization.ipynb
@@ -0,0 +1,538 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "0",
+ "metadata": {},
+ "source": [
+ "# Large-Scale Optimization: Computational Efficiency Techniques\n",
+ "\n",
+ "## User Story\n",
+ "\n",
+ "> *You're planning a district energy system with a full year of hourly data (8,760 timesteps). The optimization takes hours to complete. You need to find ways to get good solutions faster for iterative design exploration.*\n",
+ "\n",
+ "This notebook introduces:\n",
+ "\n",
+ "- **Resampling**: Reduce time resolution (e.g., hourly → 4-hourly)\n",
+ "- **Clustering**: Identify typical periods (e.g., 8 representative days)\n",
+ "- **Two-stage optimization**: Size with reduced data, dispatch at full resolution\n",
+ "- **Speed vs. accuracy trade-offs**: When to use each technique"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1",
+ "metadata": {},
+ "source": [
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import timeit\n",
+ "\n",
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import plotly.express as px\n",
+ "import xarray as xr\n",
+ "\n",
+ "import flixopt as fx\n",
+ "\n",
+ "fx.CONFIG.notebook()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3",
+ "metadata": {},
+ "source": [
+ "## Create a Realistic Annual Dataset\n",
+ "\n",
+ "We simulate one month of hourly data (720 timesteps) to demonstrate the techniques:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "4",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# One month at hourly resolution\n",
+ "timesteps = pd.date_range('2024-01-01', periods=720, freq='h') # 30 days\n",
+ "hours = np.arange(len(timesteps))\n",
+ "hour_of_day = hours % 24\n",
+ "day_of_month = hours // 24\n",
+ "\n",
+ "print(f'Timesteps: {len(timesteps)} hours ({len(timesteps) / 24:.0f} days)')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "np.random.seed(42)\n",
+ "\n",
+ "# Heat demand: daily pattern with weekly variation\n",
+ "daily_pattern = np.select(\n",
+ " [\n",
+ " (hour_of_day >= 6) & (hour_of_day < 9),\n",
+ " (hour_of_day >= 9) & (hour_of_day < 17),\n",
+ " (hour_of_day >= 17) & (hour_of_day < 22),\n",
+ " ],\n",
+ " [200, 150, 180],\n",
+ " default=100,\n",
+ ").astype(float)\n",
+ "\n",
+ "# Add temperature effect (colder mid-month)\n",
+ "temp_effect = 1 + 0.3 * np.sin(day_of_month * np.pi / 30)\n",
+ "heat_demand = daily_pattern * temp_effect + np.random.normal(0, 10, len(timesteps))\n",
+ "heat_demand = np.clip(heat_demand, 80, 300)\n",
+ "\n",
+ "# Electricity price: time-of-use with volatility - high prices make CHP attractive\n",
+ "base_price = np.where((hour_of_day >= 7) & (hour_of_day <= 21), 0.32, 0.18)\n",
+ "elec_price = base_price * (1 + np.random.uniform(-0.15, 0.15, len(timesteps)))\n",
+ "\n",
+ "# Gas price: relatively stable and low\n",
+ "gas_price = 0.05 + np.random.uniform(-0.005, 0.005, len(timesteps))\n",
+ "\n",
+ "print(f'Heat demand: {heat_demand.min():.0f} - {heat_demand.max():.0f} kW')\n",
+ "print(f'Elec price: {elec_price.min():.3f} - {elec_price.max():.3f} €/kWh')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "6",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Visualize first week with plotly - using xarray and faceting\n",
+ "profiles = xr.Dataset(\n",
+ " {\n",
+ " 'Heat Demand [kW]': xr.DataArray(heat_demand[:168], dims=['time'], coords={'time': timesteps[:168]}),\n",
+ " 'Electricity Price [€/kWh]': xr.DataArray(elec_price[:168], dims=['time'], coords={'time': timesteps[:168]}),\n",
+ " }\n",
+ ")\n",
+ "\n",
+ "df = profiles.to_dataframe().reset_index().melt(id_vars='time', var_name='variable', value_name='value')\n",
+ "fig = px.line(df, x='time', y='value', facet_col='variable', height=300)\n",
+ "fig.update_yaxes(matches=None, showticklabels=True)\n",
+ "fig.for_each_annotation(lambda a: a.update(text=a.text.split('=')[-1]))\n",
+ "fig"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7",
+ "metadata": {},
+ "source": [
+ "## Build the Base FlowSystem\n",
+ "\n",
+ "A typical district heating system with investment decisions:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def build_system(timesteps, heat_demand, elec_price, gas_price):\n",
+ " \"\"\"Build a FlowSystem with investment optimization.\"\"\"\n",
+ " fs = fx.FlowSystem(timesteps)\n",
+ "\n",
+ " fs.add_elements(\n",
+ " # Buses\n",
+ " fx.Bus('Electricity', carrier='electricity'),\n",
+ " fx.Bus(\n",
+ " 'Heat', carrier='heat', imbalance_penalty_per_flow_hour=1e5\n",
+ " ), # Allow for imbalance to prevent infeasibilities with fixed sizes\n",
+ " fx.Bus('Gas', carrier='gas'),\n",
+ " # Effects\n",
+ " fx.Effect('costs', '€', 'Total Costs', is_standard=True, is_objective=True),\n",
+ " # Gas Supply\n",
+ " fx.Source(\n",
+ " 'GasGrid',\n",
+ " outputs=[fx.Flow('Gas', bus='Gas', size=1000, effects_per_flow_hour=gas_price)],\n",
+ " ),\n",
+ " # CHP with investment optimization\n",
+ " fx.linear_converters.CHP(\n",
+ " 'CHP',\n",
+ " electrical_efficiency=0.38,\n",
+ " thermal_efficiency=0.47,\n",
+ " electrical_flow=fx.Flow(\n",
+ " 'P_el',\n",
+ " bus='Electricity',\n",
+ " size=fx.InvestParameters(\n",
+ " minimum_size=0,\n",
+ " maximum_size=150,\n",
+ " effects_of_investment_per_size={'costs': 25},\n",
+ " ),\n",
+ " relative_minimum=0.4,\n",
+ " ),\n",
+ " thermal_flow=fx.Flow('Q_th', bus='Heat'),\n",
+ " fuel_flow=fx.Flow('Q_fuel', bus='Gas'),\n",
+ " ),\n",
+ " # Gas Boiler with investment optimization\n",
+ " fx.linear_converters.Boiler(\n",
+ " 'Boiler',\n",
+ " thermal_efficiency=0.92,\n",
+ " thermal_flow=fx.Flow(\n",
+ " 'Q_th',\n",
+ " bus='Heat',\n",
+ " size=fx.InvestParameters(\n",
+ " minimum_size=0,\n",
+ " maximum_size=400,\n",
+ " effects_of_investment_per_size={'costs': 8},\n",
+ " ),\n",
+ " ),\n",
+ " fuel_flow=fx.Flow('Q_fuel', bus='Gas'),\n",
+ " ),\n",
+ " # Thermal Storage with investment optimization\n",
+ " fx.Storage(\n",
+ " 'Storage',\n",
+ " capacity_in_flow_hours=fx.InvestParameters(\n",
+ " minimum_size=0,\n",
+ " maximum_size=1000,\n",
+ " effects_of_investment_per_size={'costs': 0.5}, # Cheap storage\n",
+ " ),\n",
+ " initial_charge_state=0,\n",
+ " eta_charge=0.98,\n",
+ " eta_discharge=0.98,\n",
+ " relative_loss_per_hour=0.005, # Low losses\n",
+ " charging=fx.Flow('Charge', bus='Heat', size=150),\n",
+ " discharging=fx.Flow('Discharge', bus='Heat', size=150),\n",
+ " ),\n",
+ " # Electricity Sales\n",
+ " fx.Sink(\n",
+ " 'ElecSales',\n",
+ " inputs=[fx.Flow('P_el', bus='Electricity', size=200, effects_per_flow_hour=-elec_price)],\n",
+ " ),\n",
+ " # Heat Demand\n",
+ " fx.Sink(\n",
+ " 'HeatDemand',\n",
+ " inputs=[fx.Flow('Q_th', bus='Heat', size=1, fixed_relative_profile=heat_demand)],\n",
+ " ),\n",
+ " )\n",
+ "\n",
+ " return fs\n",
+ "\n",
+ "\n",
+ "# Build the base system\n",
+ "flow_system = build_system(timesteps, heat_demand, elec_price, gas_price)\n",
+ "print(f'Base system: {len(timesteps)} timesteps')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9",
+ "metadata": {},
+ "source": [
+ "## Technique 1: Resampling\n",
+ "\n",
+ "Reduce time resolution to speed up optimization:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "10",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "solver = fx.solvers.HighsSolver(mip_gap=0.01)\n",
+ "\n",
+ "# Resample from 1h to 4h resolution\n",
+ "fs_resampled = flow_system.transform.resample('4h')\n",
+ "\n",
+ "print(f'Original: {len(flow_system.timesteps)} timesteps')\n",
+ "print(f'Resampled: {len(fs_resampled.timesteps)} timesteps')\n",
+ "print(f'Reduction: {(1 - len(fs_resampled.timesteps) / len(flow_system.timesteps)) * 100:.0f}%')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "11",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Optimize resampled system\n",
+ "start = timeit.default_timer()\n",
+ "fs_resampled.optimize(solver)\n",
+ "time_resampled = timeit.default_timer() - start\n",
+ "\n",
+ "print(f'\\nResampled optimization: {time_resampled:.2f} seconds')\n",
+ "print(f'Cost: {fs_resampled.solution[\"costs\"].item():.2f} €')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "12",
+ "metadata": {},
+ "source": [
+ "## Technique 2: Two-Stage Optimization\n",
+ "\n",
+ "1. **Stage 1**: Size components with resampled data (fast)\n",
+ "2. **Stage 2**: Fix sizes and optimize dispatch at full resolution"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "13",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Stage 1: Sizing with resampled data\n",
+ "start = timeit.default_timer()\n",
+ "fs_sizing = flow_system.transform.resample('4h')\n",
+ "fs_sizing.optimize(solver)\n",
+ "time_stage1 = timeit.default_timer() - start\n",
+ "\n",
+ "print('=== Stage 1: Sizing ===')\n",
+ "print(f'Time: {time_stage1:.2f} seconds')\n",
+ "print('\\nOptimized sizes:')\n",
+ "for name, size in fs_sizing.statistics.sizes.items():\n",
+ " print(f' {name}: {float(size.item()):.1f}')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "14",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Stage 2: Dispatch at full resolution with fixed sizes\n",
+ "start = timeit.default_timer()\n",
+ "fs_dispatch = flow_system.transform.fix_sizes(fs_sizing.statistics.sizes)\n",
+ "fs_dispatch.optimize(solver)\n",
+ "time_stage2 = timeit.default_timer() - start\n",
+ "\n",
+ "print('=== Stage 2: Dispatch ===')\n",
+ "print(f'Time: {time_stage2:.2f} seconds')\n",
+ "print(f'Cost: {fs_dispatch.solution[\"costs\"].item():.2f} €')\n",
+ "print(f'\\nTotal two-stage time: {time_stage1 + time_stage2:.2f} seconds')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "15",
+ "metadata": {},
+ "source": [
+ "## Technique 3: Full Optimization (Baseline)\n",
+ "\n",
+ "For comparison, solve the full problem:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "16",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "start = timeit.default_timer()\n",
+ "fs_full = flow_system.copy()\n",
+ "fs_full.optimize(solver)\n",
+ "time_full = timeit.default_timer() - start\n",
+ "\n",
+ "print('=== Full Optimization ===')\n",
+ "print(f'Time: {time_full:.2f} seconds')\n",
+ "print(f'Cost: {fs_full.solution[\"costs\"].item():.2f} €')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "17",
+ "metadata": {},
+ "source": [
+ "## Compare Results"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "18",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Collect results\n",
+ "results = {\n",
+ " 'Full (baseline)': {\n",
+ " 'Time [s]': time_full,\n",
+ " 'Cost [€]': fs_full.solution['costs'].item(),\n",
+ " 'CHP Size [kW]': fs_full.statistics.sizes['CHP(P_el)'].item(),\n",
+ " 'Boiler Size [kW]': fs_full.statistics.sizes['Boiler(Q_th)'].item(),\n",
+ " 'Storage Size [kWh]': fs_full.statistics.sizes['Storage'].item(),\n",
+ " },\n",
+ " 'Resampled (4h)': {\n",
+ " 'Time [s]': time_resampled,\n",
+ " 'Cost [€]': fs_resampled.solution['costs'].item(),\n",
+ " 'CHP Size [kW]': fs_resampled.statistics.sizes['CHP(P_el)'].item(),\n",
+ " 'Boiler Size [kW]': fs_resampled.statistics.sizes['Boiler(Q_th)'].item(),\n",
+ " 'Storage Size [kWh]': fs_resampled.statistics.sizes['Storage'].item(),\n",
+ " },\n",
+ " 'Two-Stage': {\n",
+ " 'Time [s]': time_stage1 + time_stage2,\n",
+ " 'Cost [€]': fs_dispatch.solution['costs'].item(),\n",
+ " 'CHP Size [kW]': fs_dispatch.statistics.sizes['CHP(P_el)'].item(),\n",
+ " 'Boiler Size [kW]': fs_dispatch.statistics.sizes['Boiler(Q_th)'].item(),\n",
+ " 'Storage Size [kWh]': fs_dispatch.statistics.sizes['Storage'].item(),\n",
+ " },\n",
+ "}\n",
+ "\n",
+ "comparison = pd.DataFrame(results).T\n",
+ "\n",
+ "# Add relative metrics\n",
+ "baseline_cost = comparison.loc['Full (baseline)', 'Cost [€]']\n",
+ "baseline_time = comparison.loc['Full (baseline)', 'Time [s]']\n",
+ "comparison['Cost Gap [%]'] = ((comparison['Cost [€]'] - baseline_cost) / baseline_cost * 100).round(2)\n",
+ "comparison['Speedup'] = (baseline_time / comparison['Time [s]']).round(1)\n",
+ "\n",
+ "comparison.round(2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "19",
+ "metadata": {},
+ "source": [
+ "## Visual Comparison: Heat Balance"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "20",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Full optimization heat balance\n",
+ "fs_full.statistics.plot.balance('Heat')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "21",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Two-stage optimization heat balance\n",
+ "fs_dispatch.statistics.plot.balance('Heat')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "22",
+ "metadata": {},
+ "source": [
+ "### Energy Flow Sankey (Full Optimization)\n",
+ "\n",
+ "A Sankey diagram visualizes the total energy flows:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "23",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fs_full.statistics.plot.sankey()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "24",
+ "metadata": {},
+ "source": [
+ "## When to Use Each Technique\n",
+ "\n",
+ "| Technique | Best For | Trade-off |\n",
+ "|-----------|----------|------------|\n",
+ "| **Full optimization** | Final results, small problems | Slowest, most accurate |\n",
+ "| **Resampling** | Quick screening, trend analysis | Fast, loses temporal detail |\n",
+ "| **Two-stage** | Investment decisions, large problems | Good balance of speed and accuracy |\n",
+ "| **Clustering** | Preserves extreme periods | Requires `tsam` package |\n",
+ "\n",
+ "### Resampling Options\n",
+ "\n",
+ "```python\n",
+ "# Different resolutions\n",
+ "fs_2h = flow_system.transform.resample('2h') # 2-hourly\n",
+ "fs_4h = flow_system.transform.resample('4h') # 4-hourly\n",
+ "fs_daily = flow_system.transform.resample('1D') # Daily\n",
+ "\n",
+ "# Different aggregation methods\n",
+ "fs_mean = flow_system.transform.resample('4h', method='mean') # Default\n",
+ "fs_max = flow_system.transform.resample('4h', method='max') # Preserve peaks\n",
+ "```\n",
+ "\n",
+ "### Two-Stage Workflow\n",
+ "\n",
+ "```python\n",
+ "# Stage 1: Sizing\n",
+ "fs_sizing = flow_system.transform.resample('4h')\n",
+ "fs_sizing.optimize(solver)\n",
+ "\n",
+ "# Stage 2: Dispatch\n",
+ "fs_dispatch = flow_system.transform.fix_sizes(fs_sizing.statistics.sizes)\n",
+ "fs_dispatch.optimize(solver)\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "25",
+ "metadata": {},
+ "source": [
+ "## Summary\n",
+ "\n",
+ "You learned how to:\n",
+ "\n",
+ "- Use **`transform.resample()`** to reduce time resolution\n",
+ "- Apply **two-stage optimization** for large investment problems\n",
+ "- Use **`transform.fix_sizes()`** to lock in investment decisions\n",
+ "- Compare **speed vs. accuracy** trade-offs\n",
+ "\n",
+ "### Key Takeaways\n",
+ "\n",
+ "1. **Start fast**: Use resampling for initial exploration\n",
+ "2. **Iterate**: Refine with two-stage optimization\n",
+ "3. **Validate**: Run full optimization for final results\n",
+ "4. **Monitor**: Check cost gaps to ensure acceptable accuracy\n",
+ "\n",
+ "### Further Reading\n",
+ "\n",
+ "- For clustering with typical periods, see `transform.cluster()` (requires `tsam` package)\n",
+ "- For time selection, see `transform.sel()` and `transform.isel()`"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "name": "python",
+ "version": "3.11.0"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/notebooks/index.md b/docs/notebooks/index.md
new file mode 100644
index 000000000..b8003f6bb
--- /dev/null
+++ b/docs/notebooks/index.md
@@ -0,0 +1,44 @@
+# Examples
+
+Learn flixopt through practical examples organized by topic. Each notebook includes a real-world user story and progressively builds your understanding.
+
+## Getting Started
+
+| Notebook | Description |
+|----------|-------------|
+| [01-Quickstart](01-quickstart.ipynb) | Minimal working example - heat a workshop with a gas boiler |
+| [02-Heat System](02-heat-system.ipynb) | District heating with thermal storage and time-varying prices |
+
+## Investment & Planning
+
+| Notebook | Description |
+|----------|-------------|
+| [03-Investment Optimization](03-investment-optimization.ipynb) | Size a solar heating system - let the optimizer decide equipment sizes |
+| [04-Operational Constraints](04-operational-constraints.ipynb) | Industrial boiler with startup costs, minimum uptime, and load constraints |
+
+## Advanced Modeling
+
+| Notebook | Description |
+|----------|-------------|
+| [05-Multi-Carrier Systems](05-multi-carrier-system.ipynb) | Hospital with CHP producing both electricity and heat |
+| [06-Piecewise Efficiency](06-piecewise-efficiency.ipynb) | Heat pump with temperature-dependent COP and part-load curves |
+
+## Scenarios & Scaling
+
+| Notebook | Description |
+|----------|-------------|
+| [07-Scenarios and Periods](07-scenarios-and-periods.ipynb) | Multi-year planning with uncertain demand scenarios |
+| [08-Large-Scale Optimization](08-large-scale-optimization.ipynb) | Speed up large problems with resampling and two-stage optimization |
+
+## Key Concepts by Notebook
+
+| Concept | Introduced In |
+|---------|---------------|
+| `FlowSystem`, `Bus`, `Flow` | 01-Quickstart |
+| `Storage`, time-varying prices | 02-Heat System |
+| `InvestParameters`, optimal sizing | 03-Investment |
+| `StatusParameters`, startup costs | 04-Operational |
+| Multi-carrier, CHP | 05-Multi-Carrier |
+| `Piecewise`, variable efficiency | 06-Piecewise |
+| Periods, scenarios, weights | 07-Scenarios |
+| `transform.resample()`, `fix_sizes()` | 08-Large-Scale |
diff --git a/docs/overrides/main.html b/docs/overrides/main.html
new file mode 100644
index 000000000..b245acdaa
--- /dev/null
+++ b/docs/overrides/main.html
@@ -0,0 +1,11 @@
+{% extends "base.html" %}
+
+{% block content %}
+{% if page.nb_url %}
+
+ {% include ".icons/material/download.svg" %}
+
+{% endif %}
+
+{{ super() }}
+{% endblock content %}
diff --git a/docs/stylesheets/extra.css b/docs/stylesheets/extra.css
index 0b600fb08..0c84d73e5 100644
--- a/docs/stylesheets/extra.css
+++ b/docs/stylesheets/extra.css
@@ -783,6 +783,168 @@ button:focus-visible {
border-color: rgba(255, 255, 255, 0.2);
}
+/* ============================================================================
+ Jupyter Notebook Styling (syncs with dark/light theme)
+ ========================================================================= */
+
+/* Override Jupyter notebook syntax highlighting to match Material theme */
+/* Use Material's CSS variables for consistent colors */
+.highlight-ipynb { background: var(--md-code-bg-color) !important; color: var(--md-code-fg-color) !important; }
+
+/* Comments */
+.highlight-ipynb .c, .highlight-ipynb .c1, .highlight-ipynb .ch,
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+
+/* Keywords */
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+
+/* Numbers */
+.highlight-ipynb .m, .highlight-ipynb .mb, .highlight-ipynb .mf,
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+
+/* Functions */
+.highlight-ipynb .nf, .highlight-ipynb .fm { color: var(--md-code-hl-function-color, #a846b9) !important; }
+
+/* Constants/Builtins */
+.highlight-ipynb .nb, .highlight-ipynb .bp,
+.highlight-ipynb .kc { color: var(--md-code-hl-constant-color, #6e59d9) !important; }
+
+/* Special */
+.highlight-ipynb .nc, .highlight-ipynb .ne, .highlight-ipynb .nd,
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+
+/* Names/variables */
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+/* Punctuation */
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+
+/* Errors */
+.highlight-ipynb .err { color: var(--md-code-hl-special-color, #db1457) !important; }
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+/* Notebook container */
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+ margin: 1rem 0;
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+/* Code cell styling - clean and modern */
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+ margin: 0.5rem 0;
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+
/* ============================================================================
Footer Alignment Fix
========================================================================= */
diff --git a/docs/user-guide/building-models/index.md b/docs/user-guide/building-models/index.md
index 1133d5cde..d961040bf 100644
--- a/docs/user-guide/building-models/index.md
+++ b/docs/user-guide/building-models/index.md
@@ -16,5 +16,5 @@ Learn how to construct FlowSystem models step by step:
For now, see:
- **[Core Concepts](../core-concepts.md)** - Understand the fundamental building blocks
-- **[Examples](../../examples/index.md)** - Working code you can learn from
+- **[Examples](../../notebooks/index.md)** - Working code you can learn from
- **[Mathematical Notation](../mathematical-notation/index.md)** - Detailed specifications of each element
diff --git a/docs/user-guide/core-concepts.md b/docs/user-guide/core-concepts.md
index 14e5723d6..47e4a882c 100644
--- a/docs/user-guide/core-concepts.md
+++ b/docs/user-guide/core-concepts.md
@@ -243,7 +243,7 @@ While our example used a heating system, flixOpt works for any flow-based optimi
## Next Steps
- **[Building Models](building-models/index.md)** — Step-by-step guide to constructing models
-- **[Examples](../examples/index.md)** — Working code for common scenarios
+- **[Examples](../notebooks/index.md)** — Working code for common scenarios
- **[Mathematical Notation](mathematical-notation/index.md)** — Detailed constraint formulations
## Advanced: Extending with linopy
diff --git a/docs/user-guide/index.md b/docs/user-guide/index.md
index bfb288ea4..d079f645f 100644
--- a/docs/user-guide/index.md
+++ b/docs/user-guide/index.md
@@ -59,14 +59,14 @@ This guide follows a sequential learning path:
### Getting Started
- [Quick Start](../home/quick-start.md) - Build your first model in 5 minutes
-- [Minimal Example](../examples/00-Minimal Example.md) - Simplest possible model
+- [Minimal Example](../notebooks/01-quickstart.ipynb) - Simplest possible model
- [Core Concepts](core-concepts.md) - Understand the fundamentals
### Reference
- [Mathematical Notation](mathematical-notation/index.md) - Detailed specifications
- [API Reference](../api-reference/index.md) - Complete class documentation
-- [Examples](../examples/index.md) - Working code to learn from
+- [Examples](../notebooks/index.md) - Working code to learn from
### Help
diff --git a/docs/user-guide/optimization/index.md b/docs/user-guide/optimization/index.md
index b1bd0caf6..1d36eb9ba 100644
--- a/docs/user-guide/optimization/index.md
+++ b/docs/user-guide/optimization/index.md
@@ -347,6 +347,6 @@ If solutions don't match expectations:
## Next Steps
-- See [Examples](../../examples/03-Optimization Modes.md) for working code
+- See [Examples](../../notebooks/index.md) for working code
- Learn about [Mathematical Notation](../mathematical-notation/index.md)
- Explore [Recipes](../recipes/index.md) for common patterns
diff --git a/docs/user-guide/results-plotting.md b/docs/user-guide/results-plotting.md
index bfb6c8777..c64111772 100644
--- a/docs/user-guide/results-plotting.md
+++ b/docs/user-guide/results-plotting.md
@@ -18,7 +18,7 @@ flow_system.statistics.plot.heatmap('Boiler(Q_th)|flow_rate')
## PlotResult: Data + Figure
-Every plot method returns a [`PlotResult`][flixopt.plot_accessors.PlotResult] object containing both:
+Every plot method returns a [`PlotResult`][flixopt.statistics_accessor.PlotResult] object containing both:
- **`data`**: An xarray Dataset with the prepared data
- **`figure`**: A Plotly Figure object
diff --git a/docs/user-guide/results/index.md b/docs/user-guide/results/index.md
index 5f103dd39..a9b40f7f9 100644
--- a/docs/user-guide/results/index.md
+++ b/docs/user-guide/results/index.md
@@ -280,4 +280,4 @@ flow_system.to_netcdf('results/optimized_system.nc')
## Next Steps
- [Plotting Results](../results-plotting.md) - Detailed plotting documentation
-- [Examples](../../examples/index.md) - Working code examples
+- [Examples](../../notebooks/index.md) - Working code examples
diff --git a/docs/user-guide/support.md b/docs/user-guide/support.md
index 5f26cdd24..517a353a1 100644
--- a/docs/user-guide/support.md
+++ b/docs/user-guide/support.md
@@ -15,7 +15,7 @@ When opening an issue, include:
- [FAQ](faq.md) — Common questions
- [Troubleshooting](troubleshooting.md) — Common issues
-- [Examples](../examples/index.md) — Working code
+- [Examples](../notebooks/index.md) — Working code
- [API Reference](../api-reference/index.md) — Technical docs
## Contributing
diff --git a/examples/00_Minmal/minimal_example.py b/examples/00_Minmal/minimal_example.py
deleted file mode 100644
index 207faa9a9..000000000
--- a/examples/00_Minmal/minimal_example.py
+++ /dev/null
@@ -1,36 +0,0 @@
-"""
-This script shows how to use the flixopt framework to model a super minimalistic energy system in the most concise way possible.
-THis can also be used to create proposals for new features, bug reports etc
-"""
-
-import numpy as np
-import pandas as pd
-
-import flixopt as fx
-
-if __name__ == '__main__':
- fx.CONFIG.silent()
- flow_system = fx.FlowSystem(pd.date_range('2020-01-01', periods=3, freq='h'))
-
- flow_system.add_elements(
- fx.Bus('Heat'),
- fx.Bus('Gas'),
- fx.Effect('Costs', '€', 'Cost', is_standard=True, is_objective=True),
- fx.linear_converters.Boiler(
- 'Boiler',
- thermal_efficiency=0.5,
- thermal_flow=fx.Flow(label='Heat', bus='Heat', size=50),
- fuel_flow=fx.Flow(label='Gas', bus='Gas'),
- ),
- fx.Sink(
- 'Sink',
- inputs=[fx.Flow(label='Demand', bus='Heat', size=1, fixed_relative_profile=np.array([30, 0, 20]))],
- ),
- fx.Source(
- 'Source',
- outputs=[fx.Flow(label='Gas', bus='Gas', size=1000, effects_per_flow_hour=0.04)],
- ),
- )
-
- flow_system.optimize(fx.solvers.HighsSolver(0.01, 60))
- flow_system.statistics.plot.balance('Heat')
diff --git a/examples/01_Simple/simple_example.py b/examples/01_Simple/simple_example.py
deleted file mode 100644
index b63260ece..000000000
--- a/examples/01_Simple/simple_example.py
+++ /dev/null
@@ -1,126 +0,0 @@
-"""
-This script shows how to use the flixopt framework to model a simple energy system.
-"""
-
-import numpy as np
-import pandas as pd
-
-import flixopt as fx
-
-if __name__ == '__main__':
- fx.CONFIG.exploring()
-
- # --- Create Time Series Data ---
- # Heat demand profile (e.g., kW) over time and corresponding power prices
- heat_demand_per_h = np.array([30, 0, 90, 110, 110, 20, 20, 20, 20])
- power_prices = 1 / 1000 * np.array([80, 80, 80, 80, 80, 80, 80, 80, 80])
-
- # Create datetime array starting from '2020-01-01' for the given time period
- timesteps = pd.date_range('2020-01-01', periods=len(heat_demand_per_h), freq='h')
- flow_system = fx.FlowSystem(timesteps=timesteps)
-
- # --- Define Energy Buses ---
- # These represent nodes, where the used medias are balanced (electricity, heat, and gas)
- # Carriers provide automatic color assignment in plots (yellow for electricity, red for heat, etc.)
- flow_system.add_elements(
- fx.Bus(label='Strom', carrier='electricity'),
- fx.Bus(label='Fernwärme', carrier='heat'),
- fx.Bus(label='Gas', carrier='gas'),
- )
-
- # --- Define Effects (Objective and CO2 Emissions) ---
- # Cost effect: used as the optimization objective --> minimizing costs
- costs = fx.Effect(
- label='costs',
- unit='€',
- description='Kosten',
- is_standard=True, # standard effect: no explicit value needed for costs
- is_objective=True, # Minimizing costs as the optimization objective
- share_from_temporal={'CO2': 0.2},
- )
-
- # CO2 emissions effect with an associated cost impact
- CO2 = fx.Effect(
- label='CO2',
- unit='kg',
- description='CO2_e-Emissionen',
- maximum_per_hour=1000, # Max CO2 emissions per hour
- )
-
- # --- Define Flow System Components ---
- # Boiler: Converts fuel (gas) into thermal energy (heat)
- boiler = fx.linear_converters.Boiler(
- label='Boiler',
- thermal_efficiency=0.5,
- thermal_flow=fx.Flow(label='Q_th', bus='Fernwärme', size=50, relative_minimum=0.1, relative_maximum=1),
- fuel_flow=fx.Flow(label='Q_fu', bus='Gas'),
- )
-
- # Combined Heat and Power (CHP): Generates both electricity and heat from fuel
- chp = fx.linear_converters.CHP(
- label='CHP',
- thermal_efficiency=0.5,
- electrical_efficiency=0.4,
- electrical_flow=fx.Flow('P_el', bus='Strom', size=60, relative_minimum=5 / 60),
- thermal_flow=fx.Flow('Q_th', bus='Fernwärme'),
- fuel_flow=fx.Flow('Q_fu', bus='Gas'),
- )
-
- # Storage: Energy storage system with charging and discharging capabilities
- storage = fx.Storage(
- label='Storage',
- charging=fx.Flow('Q_th_load', bus='Fernwärme', size=1000),
- discharging=fx.Flow('Q_th_unload', bus='Fernwärme', size=1000),
- capacity_in_flow_hours=fx.InvestParameters(effects_of_investment=20, fixed_size=30, mandatory=True),
- initial_charge_state=0, # Initial storage state: empty
- relative_maximum_charge_state=1 / 100 * np.array([80, 70, 80, 80, 80, 80, 80, 80, 80]),
- relative_maximum_final_charge_state=0.8,
- eta_charge=0.9,
- eta_discharge=1, # Efficiency factors for charging/discharging
- relative_loss_per_hour=0.08, # 8% loss per hour. Absolute loss depends on current charge state
- prevent_simultaneous_charge_and_discharge=True, # Prevent charging and discharging at the same time
- )
-
- # Heat Demand Sink: Represents a fixed heat demand profile
- heat_sink = fx.Sink(
- label='Heat Demand',
- inputs=[fx.Flow(label='Q_th_Last', bus='Fernwärme', size=1, fixed_relative_profile=heat_demand_per_h)],
- )
-
- # Gas Source: Gas tariff source with associated costs and CO2 emissions
- gas_source = fx.Source(
- label='Gastarif',
- outputs=[
- fx.Flow(label='Q_Gas', bus='Gas', size=1000, effects_per_flow_hour={costs.label: 0.04, CO2.label: 0.3})
- ],
- )
-
- # Power Sink: Represents the export of electricity to the grid
- power_sink = fx.Sink(
- label='Einspeisung', inputs=[fx.Flow(label='P_el', bus='Strom', effects_per_flow_hour=-1 * power_prices)]
- )
-
- # --- Build the Flow System ---
- # Add all defined components and effects to the flow system
- flow_system.add_elements(costs, CO2, boiler, storage, chp, heat_sink, gas_source, power_sink)
-
- # Visualize the flow system for validation purposes
- flow_system.topology.plot()
-
- # --- Define and Solve Optimization ---
- flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0, time_limit_seconds=30))
-
- # --- Analyze Results ---
- # Plotting through statistics accessor - returns PlotResult with .data and .figure
- flow_system.statistics.plot.balance('Fernwärme')
- flow_system.statistics.plot.balance('Storage')
- flow_system.statistics.plot.heatmap('CHP(Q_th)')
- flow_system.statistics.plot.heatmap('Storage')
-
- # Access data as xarray Datasets
- print(flow_system.statistics.flow_rates)
- print(flow_system.statistics.charge_states)
-
- # Duration curve and effects analysis
- flow_system.statistics.plot.duration_curve('Boiler(Q_th)')
- print(flow_system.statistics.temporal_effects)
diff --git a/examples/02_Complex/complex_example.py b/examples/02_Complex/complex_example.py
deleted file mode 100644
index 3f38ff954..000000000
--- a/examples/02_Complex/complex_example.py
+++ /dev/null
@@ -1,207 +0,0 @@
-"""
-This script shows how to use the flixopt framework to model a more complex energy system.
-"""
-
-import numpy as np
-import pandas as pd
-
-import flixopt as fx
-
-if __name__ == '__main__':
- fx.CONFIG.exploring()
-
- # --- Experiment Options ---
- # Configure options for testing various parameters and behaviors
- check_penalty = False
- imbalance_penalty = 1e5
- use_chp_with_piecewise_conversion = True
-
- # --- Define Demand and Price Profiles ---
- # Input data for electricity and heat demands, as well as electricity price
- electricity_demand = np.array([70, 80, 90, 90, 90, 90, 90, 90, 90])
- heat_demand = (
- np.array([30, 0, 90, 110, 2000, 20, 20, 20, 20])
- if check_penalty
- else np.array([30, 0, 90, 110, 110, 20, 20, 20, 20])
- )
- electricity_price = np.array([40, 40, 40, 40, 40, 40, 40, 40, 40])
-
- # --- Define the Flow System, that will hold all elements, and the time steps you want to model ---
- timesteps = pd.date_range('2020-01-01', periods=len(heat_demand), freq='h')
- flow_system = fx.FlowSystem(timesteps) # Create FlowSystem
-
- # --- Define Energy Buses ---
- # Represent node balances (inputs=outputs) for the different energy carriers (electricity, heat, gas) in the system
- # Carriers provide automatic color assignment in plots (yellow for electricity, red for heat, blue for gas)
- flow_system.add_elements(
- fx.Bus('Strom', carrier='electricity', imbalance_penalty_per_flow_hour=imbalance_penalty),
- fx.Bus('Fernwärme', carrier='heat', imbalance_penalty_per_flow_hour=imbalance_penalty),
- fx.Bus('Gas', carrier='gas', imbalance_penalty_per_flow_hour=imbalance_penalty),
- )
-
- # --- Define Effects ---
- # Specify effects related to costs, CO2 emissions, and primary energy consumption
- Costs = fx.Effect('costs', '€', 'Kosten', is_standard=True, is_objective=True, share_from_temporal={'CO2': 0.2})
- CO2 = fx.Effect('CO2', 'kg', 'CO2_e-Emissionen')
- PE = fx.Effect('PE', 'kWh_PE', 'Primärenergie', maximum_total=3.5e3)
-
- # --- Define Components ---
- # 1. Define Boiler Component
- # A gas boiler that converts fuel into thermal output, with investment and on-inactive parameters
- Gaskessel = fx.linear_converters.Boiler(
- 'Kessel',
- thermal_efficiency=0.5, # Efficiency ratio
- status_parameters=fx.StatusParameters(
- effects_per_active_hour={Costs.label: 0, CO2.label: 1000}
- ), # CO2 emissions per hour
- thermal_flow=fx.Flow(
- label='Q_th', # Thermal output
- bus='Fernwärme', # Linked bus
- size=fx.InvestParameters(
- effects_of_investment=1000, # Fixed investment costs
- fixed_size=50, # Fixed size
- mandatory=True, # Forced investment
- effects_of_investment_per_size={Costs.label: 10, PE.label: 2}, # Specific costs
- ),
- load_factor_max=1.0, # Maximum load factor (50 kW)
- load_factor_min=0.1, # Minimum load factor (5 kW)
- relative_minimum=5 / 50, # Minimum part load
- relative_maximum=1, # Maximum part load
- previous_flow_rate=50, # Previous flow rate
- flow_hours_max=1e6, # Total energy flow limit
- status_parameters=fx.StatusParameters(
- active_hours_min=0, # Minimum operating hours
- active_hours_max=1000, # Maximum operating hours
- max_uptime=10, # Max consecutive operating hours
- min_uptime=np.array([1, 1, 1, 1, 1, 2, 2, 2, 2]), # min consecutive operation hours
- max_downtime=10, # Max consecutive inactive hours
- effects_per_startup={Costs.label: 0.01}, # Cost per startup
- startup_limit=1000, # Max number of starts
- ),
- ),
- fuel_flow=fx.Flow(label='Q_fu', bus='Gas', size=200),
- )
-
- # 2. Define CHP Unit
- # Combined Heat and Power unit that generates both electricity and heat from fuel
- bhkw = fx.linear_converters.CHP(
- 'BHKW2',
- thermal_efficiency=0.5,
- electrical_efficiency=0.4,
- status_parameters=fx.StatusParameters(effects_per_startup={Costs.label: 0.01}),
- electrical_flow=fx.Flow('P_el', bus='Strom', size=60, relative_minimum=5 / 60),
- thermal_flow=fx.Flow('Q_th', bus='Fernwärme', size=1e3),
- fuel_flow=fx.Flow('Q_fu', bus='Gas', size=1e3, previous_flow_rate=20), # The CHP was ON previously
- )
-
- # 3. Define CHP with Piecewise Conversion
- # This CHP unit uses piecewise conversion for more dynamic behavior over time
- P_el = fx.Flow('P_el', bus='Strom', size=60, previous_flow_rate=20)
- Q_th = fx.Flow('Q_th', bus='Fernwärme')
- Q_fu = fx.Flow('Q_fu', bus='Gas')
- piecewise_conversion = fx.PiecewiseConversion(
- {
- P_el.label: fx.Piecewise([fx.Piece(5, 30), fx.Piece(40, 60)]),
- Q_th.label: fx.Piecewise([fx.Piece(6, 35), fx.Piece(45, 100)]),
- Q_fu.label: fx.Piecewise([fx.Piece(12, 70), fx.Piece(90, 200)]),
- }
- )
-
- bhkw_2 = fx.LinearConverter(
- 'BHKW2',
- inputs=[Q_fu],
- outputs=[P_el, Q_th],
- piecewise_conversion=piecewise_conversion,
- status_parameters=fx.StatusParameters(effects_per_startup={Costs.label: 0.01}),
- )
-
- # 4. Define Storage Component
- # Storage with variable size and piecewise investment effects
- segmented_investment_effects = fx.PiecewiseEffects(
- piecewise_origin=fx.Piecewise([fx.Piece(5, 25), fx.Piece(25, 100)]),
- piecewise_shares={
- Costs.label: fx.Piecewise([fx.Piece(50, 250), fx.Piece(250, 800)]),
- PE.label: fx.Piecewise([fx.Piece(5, 25), fx.Piece(25, 100)]),
- },
- )
-
- speicher = fx.Storage(
- 'Speicher',
- charging=fx.Flow('Q_th_load', bus='Fernwärme', size=1e4),
- discharging=fx.Flow('Q_th_unload', bus='Fernwärme', size=1e4),
- capacity_in_flow_hours=fx.InvestParameters(
- piecewise_effects_of_investment=segmented_investment_effects, # Investment effects
- mandatory=True, # Forced investment
- minimum_size=0,
- maximum_size=1000, # Optimizing between 0 and 1000 kWh
- ),
- initial_charge_state=0, # Initial charge state
- maximal_final_charge_state=10, # Maximum final charge state
- eta_charge=0.9,
- eta_discharge=1, # Charge/discharge efficiency
- relative_loss_per_hour=0.08, # Energy loss per hour, relative to current charge state
- prevent_simultaneous_charge_and_discharge=True, # Prevent simultaneous charge/discharge
- )
-
- # 5. Define Sinks and Sources
- # 5.a) Heat demand profile
- Waermelast = fx.Sink(
- 'Wärmelast',
- inputs=[
- fx.Flow(
- 'Q_th_Last', # Heat sink
- bus='Fernwärme', # Linked bus
- size=1,
- fixed_relative_profile=heat_demand, # Fixed demand profile
- )
- ],
- )
-
- # 5.b) Gas tariff
- Gasbezug = fx.Source(
- 'Gastarif',
- outputs=[
- fx.Flow(
- 'Q_Gas',
- bus='Gas', # Gas source
- size=1000, # Nominal size
- effects_per_flow_hour={Costs.label: 0.04, CO2.label: 0.3},
- )
- ],
- )
-
- # 5.c) Feed-in of electricity
- Stromverkauf = fx.Sink(
- 'Einspeisung',
- inputs=[
- fx.Flow(
- 'P_el',
- bus='Strom', # Feed-in tariff for electricity
- effects_per_flow_hour=-1 * electricity_price, # Negative price for feed-in
- )
- ],
- )
-
- # --- Build FlowSystem ---
- # Select components to be included in the flow system
- flow_system.add_elements(Costs, CO2, PE, Gaskessel, Waermelast, Gasbezug, Stromverkauf, speicher)
- flow_system.add_elements(bhkw_2) if use_chp_with_piecewise_conversion else flow_system.add_elements(bhkw)
-
- print(flow_system) # Get a string representation of the FlowSystem
- try:
- flow_system.topology.start_app() # Start the network app
- except ImportError as e:
- print(f'Network app requires extra dependencies: {e}')
-
- # --- Solve FlowSystem ---
- flow_system.optimize(fx.solvers.HighsSolver(0.01, 60))
-
- # --- Results ---
- # Save the flow system with solution to file for later analysis
- flow_system.to_netcdf('results/complex_example.nc')
-
- # Plot results using the statistics accessor
- flow_system.statistics.plot.heatmap('BHKW2(Q_th)') # Flow label - auto-resolves to flow_rate
- flow_system.statistics.plot.balance('BHKW2')
- flow_system.statistics.plot.heatmap('Speicher') # Storage label - auto-resolves to charge_state
- flow_system.statistics.plot.balance('Fernwärme')
diff --git a/examples/02_Complex/complex_example_results.py b/examples/02_Complex/complex_example_results.py
deleted file mode 100644
index 6978caff1..000000000
--- a/examples/02_Complex/complex_example_results.py
+++ /dev/null
@@ -1,38 +0,0 @@
-"""
-This script shows how to load results of a prior optimization and how to analyze them.
-"""
-
-import flixopt as fx
-
-if __name__ == '__main__':
- fx.CONFIG.exploring()
-
- # --- Load FlowSystem with Solution ---
- try:
- flow_system = fx.FlowSystem.from_netcdf('results/complex_example.nc')
- except FileNotFoundError as e:
- raise FileNotFoundError(
- f"Results file not found ('results/complex_example.nc'). "
- f"Please ensure that the file is generated by running 'complex_example.py'. "
- f'Original error: {e}'
- ) from e
-
- # --- Basic overview ---
- flow_system.topology.plot()
- flow_system.statistics.plot.balance('Fernwärme')
-
- # --- Detailed Plots ---
- # In-depth plot for individual flow rates
- flow_system.statistics.plot.heatmap('Wärmelast(Q_th_Last)|flow_rate')
-
- # Plot balances for all buses
- for bus in flow_system.buses.values():
- flow_system.statistics.plot.balance(bus.label).to_html(f'results/{bus.label}--balance.html')
-
- # --- Plotting internal variables manually ---
- flow_system.statistics.plot.heatmap('BHKW2(Q_th)|status')
- flow_system.statistics.plot.heatmap('Kessel(Q_th)|status')
-
- # Access data as DataFrames:
- print(flow_system.statistics.flow_rates.to_dataframe())
- print(flow_system.solution.to_dataframe())
diff --git a/examples/03_Optimization_modes/example_optimization_modes.py b/examples/03_Optimization_modes/example_optimization_modes.py
deleted file mode 100644
index 1f9968357..000000000
--- a/examples/03_Optimization_modes/example_optimization_modes.py
+++ /dev/null
@@ -1,245 +0,0 @@
-"""
-This script demonstrates how to use the different calculation types in the flixopt framework
-to model the same energy system. The results will be compared to each other.
-"""
-
-import pathlib
-
-import pandas as pd
-import xarray as xr
-
-import flixopt as fx
-
-
-# Get solutions for plotting for different optimizations
-def get_solutions(optimizations: list, variable: str) -> xr.Dataset:
- dataarrays = []
- for optimization in optimizations:
- if optimization.name == 'Segmented':
- # SegmentedOptimization requires special handling to remove overlaps
- dataarrays.append(optimization.results.solution_without_overlap(variable).rename(optimization.name))
- else:
- # For Full and Clustered, access solution from the flow_system
- dataarrays.append(optimization.flow_system.solution[variable].rename(optimization.name))
- return xr.merge(dataarrays, join='outer')
-
-
-if __name__ == '__main__':
- fx.CONFIG.exploring()
-
- # Calculation Types
- full, segmented, aggregated = True, True, True
-
- # Segmented Properties
- segment_length, overlap_length = 96, 1
-
- # Aggregated Properties
- clustering_parameters = fx.ClusteringParameters(
- hours_per_period=6,
- nr_of_periods=4,
- fix_storage_flows=False,
- aggregate_data_and_fix_non_binary_vars=True,
- percentage_of_period_freedom=0,
- penalty_of_period_freedom=0,
- )
- keep_extreme_periods = True
- imbalance_penalty = 1e5 # or set to None if not needed
-
- # Data Import
- data_import = pd.read_csv(
- pathlib.Path(__file__).parent.parent / 'resources' / 'Zeitreihen2020.csv', index_col=0
- ).sort_index()
- filtered_data = data_import['2020-01-01':'2020-01-07 23:45:00']
- # filtered_data = data_import[0:500] # Alternatively filter by index
-
- filtered_data.index = pd.to_datetime(filtered_data.index)
- timesteps = filtered_data.index
-
- # Access specific columns and convert to 1D-numpy array
- electricity_demand = filtered_data['P_Netz/MW'].to_numpy()
- heat_demand = filtered_data['Q_Netz/MW'].to_numpy()
- electricity_price = filtered_data['Strompr.€/MWh'].to_numpy()
- gas_price = filtered_data['Gaspr.€/MWh'].to_numpy()
-
- # TimeSeriesData objects
- TS_heat_demand = fx.TimeSeriesData(heat_demand)
- TS_electricity_demand = fx.TimeSeriesData(electricity_demand, clustering_weight=0.7)
- TS_electricity_price_sell = fx.TimeSeriesData(-(electricity_price - 0.5), clustering_group='p_el')
- TS_electricity_price_buy = fx.TimeSeriesData(electricity_price + 0.5, clustering_group='p_el')
-
- flow_system = fx.FlowSystem(timesteps)
- flow_system.add_elements(
- fx.Bus('Strom', carrier='electricity', imbalance_penalty_per_flow_hour=imbalance_penalty),
- fx.Bus('Fernwärme', carrier='heat', imbalance_penalty_per_flow_hour=imbalance_penalty),
- fx.Bus('Gas', carrier='gas', imbalance_penalty_per_flow_hour=imbalance_penalty),
- fx.Bus('Kohle', carrier='fuel', imbalance_penalty_per_flow_hour=imbalance_penalty),
- )
-
- # Effects
- costs = fx.Effect('costs', '€', 'Kosten', is_standard=True, is_objective=True)
- CO2 = fx.Effect('CO2', 'kg', 'CO2_e-Emissionen')
- PE = fx.Effect('PE', 'kWh_PE', 'Primärenergie')
-
- # Component Definitions
-
- # 1. Boiler
- a_gaskessel = fx.linear_converters.Boiler(
- 'Kessel',
- thermal_efficiency=0.85,
- thermal_flow=fx.Flow(label='Q_th', bus='Fernwärme'),
- fuel_flow=fx.Flow(
- label='Q_fu',
- bus='Gas',
- size=95,
- relative_minimum=12 / 95,
- previous_flow_rate=20,
- status_parameters=fx.StatusParameters(effects_per_startup=1000),
- ),
- )
-
- # 2. CHP
- a_kwk = fx.linear_converters.CHP(
- 'BHKW2',
- thermal_efficiency=0.58,
- electrical_efficiency=0.22,
- status_parameters=fx.StatusParameters(effects_per_startup=24000),
- electrical_flow=fx.Flow('P_el', bus='Strom', size=200),
- thermal_flow=fx.Flow('Q_th', bus='Fernwärme', size=200),
- fuel_flow=fx.Flow('Q_fu', bus='Kohle', size=288, relative_minimum=87 / 288, previous_flow_rate=100),
- )
-
- # 3. Storage
- a_speicher = fx.Storage(
- 'Speicher',
- capacity_in_flow_hours=684,
- initial_charge_state=137,
- minimal_final_charge_state=137,
- maximal_final_charge_state=158,
- eta_charge=1,
- eta_discharge=1,
- relative_loss_per_hour=0.001,
- prevent_simultaneous_charge_and_discharge=True,
- charging=fx.Flow('Q_th_load', size=137, bus='Fernwärme'),
- discharging=fx.Flow('Q_th_unload', size=158, bus='Fernwärme'),
- )
-
- # 4. Sinks and Sources
- # Heat Load Profile
- a_waermelast = fx.Sink(
- 'Wärmelast', inputs=[fx.Flow('Q_th_Last', bus='Fernwärme', size=1, fixed_relative_profile=TS_heat_demand)]
- )
-
- # Electricity Feed-in
- a_strom_last = fx.Sink(
- 'Stromlast', inputs=[fx.Flow('P_el_Last', bus='Strom', size=1, fixed_relative_profile=TS_electricity_demand)]
- )
-
- # Gas Tariff
- a_gas_tarif = fx.Source(
- 'Gastarif',
- outputs=[
- fx.Flow('Q_Gas', bus='Gas', size=1000, effects_per_flow_hour={costs.label: gas_price, CO2.label: 0.3})
- ],
- )
-
- # Coal Tariff
- a_kohle_tarif = fx.Source(
- 'Kohletarif',
- outputs=[fx.Flow('Q_Kohle', bus='Kohle', size=1000, effects_per_flow_hour={costs.label: 4.6, CO2.label: 0.3})],
- )
-
- # Electricity Tariff and Feed-in
- a_strom_einspeisung = fx.Sink(
- 'Einspeisung', inputs=[fx.Flow('P_el', bus='Strom', size=1000, effects_per_flow_hour=TS_electricity_price_sell)]
- )
-
- a_strom_tarif = fx.Source(
- 'Stromtarif',
- outputs=[
- fx.Flow(
- 'P_el',
- bus='Strom',
- size=1000,
- effects_per_flow_hour={costs.label: TS_electricity_price_buy, CO2.label: 0.3},
- )
- ],
- )
-
- # Flow System Setup
- flow_system.add_elements(costs, CO2, PE)
- flow_system.add_elements(
- a_gaskessel,
- a_waermelast,
- a_strom_last,
- a_gas_tarif,
- a_kohle_tarif,
- a_strom_einspeisung,
- a_strom_tarif,
- a_kwk,
- a_speicher,
- )
- flow_system.topology.plot()
-
- # Optimizations
- optimizations: list[fx.Optimization | fx.ClusteredOptimization | fx.SegmentedOptimization] = []
-
- if full:
- optimization = fx.Optimization('Full', flow_system.copy())
- optimization.do_modeling()
- optimization.solve(fx.solvers.HighsSolver(0.01 / 100, 60))
- optimizations.append(optimization)
-
- if segmented:
- optimization = fx.SegmentedOptimization('Segmented', flow_system.copy(), segment_length, overlap_length)
- optimization.do_modeling_and_solve(fx.solvers.HighsSolver(0.01 / 100, 60))
- optimizations.append(optimization)
-
- if aggregated:
- if keep_extreme_periods:
- clustering_parameters.time_series_for_high_peaks = [TS_heat_demand]
- clustering_parameters.time_series_for_low_peaks = [TS_electricity_demand, TS_heat_demand]
- optimization = fx.ClusteredOptimization('Aggregated', flow_system.copy(), clustering_parameters)
- optimization.do_modeling()
- optimization.solve(fx.solvers.HighsSolver(0.01 / 100, 60))
- optimizations.append(optimization)
-
- # --- Plotting for comparison ---
- fx.plotting.with_plotly(
- get_solutions(optimizations, 'Speicher|charge_state'),
- mode='line',
- title='Charge State Comparison',
- ylabel='Charge state',
- xlabel='Time in h',
- ).write_html('results/Charge State.html')
-
- fx.plotting.with_plotly(
- get_solutions(optimizations, 'BHKW2(Q_th)|flow_rate'),
- mode='line',
- title='BHKW2(Q_th) Flow Rate Comparison',
- ylabel='Flow rate',
- xlabel='Time in h',
- ).write_html('results/BHKW2 Thermal Power.html')
-
- fx.plotting.with_plotly(
- get_solutions(optimizations, 'costs(temporal)|per_timestep'),
- mode='line',
- title='Operation Cost Comparison',
- ylabel='Costs [€]',
- xlabel='Time in h',
- ).write_html('results/Operation Costs.html')
-
- fx.plotting.with_plotly(
- get_solutions(optimizations, 'costs(temporal)|per_timestep').sum('time'),
- mode='stacked_bar',
- title='Total Cost Comparison',
- ylabel='Costs [€]',
- ).update_layout(barmode='group').write_html('results/Total Costs.html')
-
- fx.plotting.with_plotly(
- pd.DataFrame(
- [calc.durations for calc in optimizations], index=[calc.name for calc in optimizations]
- ).to_xarray(),
- mode='stacked_bar',
- ).update_layout(title='Duration Comparison', xaxis_title='Optimization type', yaxis_title='Time (s)').write_html(
- 'results/Speed Comparison.html'
- )
diff --git a/examples/04_Scenarios/scenario_example.py b/examples/04_Scenarios/scenario_example.py
deleted file mode 100644
index 820336e93..000000000
--- a/examples/04_Scenarios/scenario_example.py
+++ /dev/null
@@ -1,214 +0,0 @@
-"""
-This script shows how to use the flixopt framework to model a simple energy system.
-"""
-
-import numpy as np
-import pandas as pd
-
-import flixopt as fx
-
-if __name__ == '__main__':
- fx.CONFIG.exploring()
-
- # Create datetime array starting from '2020-01-01' for one week
- timesteps = pd.date_range('2020-01-01', periods=24 * 7, freq='h')
- scenarios = pd.Index(['Base Case', 'High Demand'])
- periods = pd.Index([2020, 2021, 2022])
-
- # --- Create Time Series Data ---
- # Realistic daily patterns: morning/evening peaks, night/midday lows
- np.random.seed(42)
- n_hours = len(timesteps)
-
- # Heat demand: 24-hour patterns (kW) for Base Case and High Demand scenarios
- base_daily_pattern = np.array(
- [22, 20, 18, 18, 20, 25, 40, 70, 95, 110, 85, 65, 60, 58, 62, 68, 75, 88, 105, 125, 130, 122, 95, 35]
- )
- high_daily_pattern = np.array(
- [28, 25, 22, 22, 24, 30, 52, 88, 118, 135, 105, 80, 75, 72, 75, 82, 92, 108, 128, 148, 155, 145, 115, 48]
- )
-
- # Tile and add variation
- base_demand = np.tile(base_daily_pattern, n_hours // 24 + 1)[:n_hours] * (
- 1 + np.random.uniform(-0.05, 0.05, n_hours)
- )
- high_demand = np.tile(high_daily_pattern, n_hours // 24 + 1)[:n_hours] * (
- 1 + np.random.uniform(-0.07, 0.07, n_hours)
- )
-
- heat_demand_per_h = pd.DataFrame({'Base Case': base_demand, 'High Demand': high_demand}, index=timesteps)
-
- # Power prices: hourly factors (night low, peak high) and period escalation (2020-2022)
- hourly_price_factors = np.array(
- [
- 0.70,
- 0.65,
- 0.62,
- 0.60,
- 0.62,
- 0.70,
- 0.95,
- 1.15,
- 1.30,
- 1.25,
- 1.10,
- 1.00,
- 0.95,
- 0.90,
- 0.88,
- 0.92,
- 1.00,
- 1.10,
- 1.25,
- 1.40,
- 1.35,
- 1.20,
- 0.95,
- 0.80,
- ]
- )
- period_base_prices = np.array([0.075, 0.095, 0.135]) # €/kWh for 2020, 2021, 2022
-
- price_series = np.zeros((n_hours, 3))
- for period_idx, base_price in enumerate(period_base_prices):
- price_series[:, period_idx] = (
- np.tile(hourly_price_factors, n_hours // 24 + 1)[:n_hours]
- * base_price
- * (1 + np.random.uniform(-0.03, 0.03, n_hours))
- )
-
- power_prices = price_series.mean(axis=0)
-
- # Scenario weights: probability of each scenario occurring
- # Base Case: 60% probability, High Demand: 40% probability
- scenario_weights = np.array([0.6, 0.4])
-
- flow_system = fx.FlowSystem(
- timesteps=timesteps, periods=periods, scenarios=scenarios, scenario_weights=scenario_weights
- )
-
- # --- Define Energy Buses ---
- # These represent nodes, where the used medias are balanced (electricity, heat, and gas)
- # Carriers provide automatic color assignment in plots (yellow for electricity, red for heat, blue for gas)
- flow_system.add_elements(
- fx.Bus(label='Strom', carrier='electricity'),
- fx.Bus(label='Fernwärme', carrier='heat'),
- fx.Bus(label='Gas', carrier='gas'),
- )
-
- # --- Define Effects (Objective and CO2 Emissions) ---
- # Cost effect: used as the optimization objective --> minimizing costs
- costs = fx.Effect(
- label='costs',
- unit='€',
- description='Kosten',
- is_standard=True, # standard effect: no explicit value needed for costs
- is_objective=True, # Minimizing costs as the optimization objective
- share_from_temporal={'CO2': 0.2}, # Carbon price: 0.2 €/kg CO2 (e.g., carbon tax)
- )
-
- # CO2 emissions effect with constraint
- # Maximum of 1000 kg CO2/hour represents a regulatory or voluntary emissions limit
- CO2 = fx.Effect(
- label='CO2',
- unit='kg',
- description='CO2_e-Emissionen',
- maximum_per_hour=1000, # Regulatory emissions limit: 1000 kg CO2/hour
- )
-
- # --- Define Flow System Components ---
- # Boiler: Converts fuel (gas) into thermal energy (heat)
- # Modern condensing gas boiler with realistic efficiency
- boiler = fx.linear_converters.Boiler(
- label='Boiler',
- thermal_efficiency=0.92, # Realistic efficiency for modern condensing gas boiler (92%)
- thermal_flow=fx.Flow(
- label='Q_th',
- bus='Fernwärme',
- size=100,
- relative_minimum=0.1,
- relative_maximum=1,
- status_parameters=fx.StatusParameters(),
- ),
- fuel_flow=fx.Flow(label='Q_fu', bus='Gas'),
- )
-
- # Combined Heat and Power (CHP): Generates both electricity and heat from fuel
- # Modern CHP unit with realistic efficiencies (total efficiency ~88%)
- chp = fx.linear_converters.CHP(
- label='CHP',
- thermal_efficiency=0.48, # Realistic thermal efficiency (48%)
- electrical_efficiency=0.40, # Realistic electrical efficiency (40%)
- electrical_flow=fx.Flow(
- 'P_el', bus='Strom', size=80, relative_minimum=5 / 80, status_parameters=fx.StatusParameters()
- ),
- thermal_flow=fx.Flow('Q_th', bus='Fernwärme'),
- fuel_flow=fx.Flow('Q_fu', bus='Gas'),
- )
-
- # Storage: Thermal energy storage system with charging and discharging capabilities
- # Realistic thermal storage parameters (e.g., insulated hot water tank)
- storage = fx.Storage(
- label='Storage',
- charging=fx.Flow('Q_th_load', bus='Fernwärme', size=1000),
- discharging=fx.Flow('Q_th_unload', bus='Fernwärme', size=1000),
- capacity_in_flow_hours=fx.InvestParameters(effects_of_investment=20, fixed_size=30, mandatory=True),
- initial_charge_state=0, # Initial storage state: empty
- relative_maximum_final_charge_state=np.array([0.8, 0.5, 0.1]),
- eta_charge=0.95, # Realistic charging efficiency (~95%)
- eta_discharge=0.98, # Realistic discharging efficiency (~98%)
- relative_loss_per_hour=np.array([0.008, 0.015]), # Realistic thermal losses: 0.8-1.5% per hour
- prevent_simultaneous_charge_and_discharge=True, # Prevent charging and discharging at the same time
- )
-
- # Heat Demand Sink: Represents a fixed heat demand profile
- heat_sink = fx.Sink(
- label='Heat Demand',
- inputs=[fx.Flow(label='Q_th_Last', bus='Fernwärme', size=1, fixed_relative_profile=heat_demand_per_h)],
- )
-
- # Gas Source: Gas tariff source with associated costs and CO2 emissions
- # Realistic gas prices varying by period (reflecting 2020-2022 energy crisis)
- # 2020: 0.04 €/kWh, 2021: 0.06 €/kWh, 2022: 0.11 €/kWh
- gas_prices_per_period = np.array([0.04, 0.06, 0.11])
-
- # CO2 emissions factor for natural gas: ~0.202 kg CO2/kWh (realistic value)
- gas_co2_emissions = 0.202
-
- gas_source = fx.Source(
- label='Gastarif',
- outputs=[
- fx.Flow(
- label='Q_Gas',
- bus='Gas',
- size=1000,
- effects_per_flow_hour={costs.label: gas_prices_per_period, CO2.label: gas_co2_emissions},
- )
- ],
- )
-
- # Power Sink: Represents the export of electricity to the grid
- power_sink = fx.Sink(
- label='Einspeisung', inputs=[fx.Flow(label='P_el', bus='Strom', effects_per_flow_hour=-1 * power_prices)]
- )
-
- # --- Build the Flow System ---
- # Add all defined components and effects to the flow system
- flow_system.add_elements(costs, CO2, boiler, storage, chp, heat_sink, gas_source, power_sink)
-
- # Visualize the flow system for validation purposes
- flow_system.topology.plot()
-
- # --- Define and Solve Optimization ---
- flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0, time_limit_seconds=30))
-
- # --- Analyze Results ---
- # Plotting through statistics accessor - returns PlotResult with .data and .figure
- flow_system.statistics.plot.heatmap('CHP(Q_th)') # Flow label - auto-resolves to flow_rate
- flow_system.statistics.plot.balance('Fernwärme')
- flow_system.statistics.plot.balance('Storage')
- flow_system.statistics.plot.heatmap('Storage') # Storage label - auto-resolves to charge_state
-
- # Access data as xarray Datasets
- print(flow_system.statistics.flow_rates)
- print(flow_system.statistics.charge_states)
diff --git a/examples/05_Two-stage-optimization/two_stage_optimization.py b/examples/05_Two-stage-optimization/two_stage_optimization.py
deleted file mode 100644
index 3f3278477..000000000
--- a/examples/05_Two-stage-optimization/two_stage_optimization.py
+++ /dev/null
@@ -1,186 +0,0 @@
-"""
-This script demonstrates how to use downsampling of a FlowSystem to effectively reduce the size of a model.
-This can be very useful when working with large models or during development,
-as it can drastically reduce the computational time.
-This leads to faster results and easier debugging.
-A common use case is to optimize the investments of a model with a downsampled version of the original model, and then fix the computed sizes when calculating the actual dispatch.
-While the final optimum might differ from the global optimum, the solving will be much faster.
-"""
-
-import logging
-import pathlib
-import timeit
-
-import numpy as np
-import pandas as pd
-import xarray as xr
-
-import flixopt as fx
-
-logger = logging.getLogger('flixopt')
-
-if __name__ == '__main__':
- fx.CONFIG.exploring()
-
- # Data Import
- data_import = pd.read_csv(
- pathlib.Path(__file__).parent.parent / 'resources' / 'Zeitreihen2020.csv', index_col=0
- ).sort_index()
- filtered_data = data_import[:500]
-
- filtered_data.index = pd.to_datetime(filtered_data.index)
- timesteps = filtered_data.index
-
- # Access specific columns and convert to 1D-numpy array
- electricity_demand = filtered_data['P_Netz/MW'].to_numpy()
- heat_demand = filtered_data['Q_Netz/MW'].to_numpy()
- electricity_price = filtered_data['Strompr.€/MWh'].to_numpy()
- gas_price = filtered_data['Gaspr.€/MWh'].to_numpy()
-
- flow_system = fx.FlowSystem(timesteps)
- # Carriers provide automatic color assignment in plots
- flow_system.add_elements(
- fx.Bus('Strom', carrier='electricity'),
- fx.Bus('Fernwärme', carrier='heat'),
- fx.Bus('Gas', carrier='gas'),
- fx.Bus('Kohle', carrier='fuel'),
- fx.Effect('costs', '€', 'Kosten', is_standard=True, is_objective=True),
- fx.Effect('CO2', 'kg', 'CO2_e-Emissionen'),
- fx.Effect('PE', 'kWh_PE', 'Primärenergie'),
- fx.linear_converters.Boiler(
- 'Kessel',
- thermal_efficiency=0.85,
- thermal_flow=fx.Flow(label='Q_th', bus='Fernwärme'),
- fuel_flow=fx.Flow(
- label='Q_fu',
- bus='Gas',
- size=fx.InvestParameters(
- effects_of_investment_per_size={'costs': 1_000}, minimum_size=10, maximum_size=600
- ),
- relative_minimum=0.2,
- previous_flow_rate=20,
- status_parameters=fx.StatusParameters(effects_per_startup=300),
- ),
- ),
- fx.linear_converters.CHP(
- 'BHKW2',
- thermal_efficiency=0.58,
- electrical_efficiency=0.22,
- status_parameters=fx.StatusParameters(effects_per_startup=1_000, min_uptime=10, min_downtime=10),
- electrical_flow=fx.Flow('P_el', bus='Strom'),
- thermal_flow=fx.Flow('Q_th', bus='Fernwärme'),
- fuel_flow=fx.Flow(
- 'Q_fu',
- bus='Kohle',
- size=fx.InvestParameters(
- effects_of_investment_per_size={'costs': 3_000}, minimum_size=10, maximum_size=500
- ),
- relative_minimum=0.3,
- previous_flow_rate=100,
- ),
- ),
- fx.Storage(
- 'Speicher',
- capacity_in_flow_hours=fx.InvestParameters(
- minimum_size=10, maximum_size=1000, effects_of_investment_per_size={'costs': 60}
- ),
- initial_charge_state='equals_final',
- eta_charge=1,
- eta_discharge=1,
- relative_loss_per_hour=0.001,
- prevent_simultaneous_charge_and_discharge=True,
- charging=fx.Flow('Q_th_load', size=200, bus='Fernwärme'),
- discharging=fx.Flow('Q_th_unload', size=200, bus='Fernwärme'),
- ),
- fx.Sink(
- 'Wärmelast', inputs=[fx.Flow('Q_th_Last', bus='Fernwärme', size=1, fixed_relative_profile=heat_demand)]
- ),
- fx.Source(
- 'Gastarif',
- outputs=[fx.Flow('Q_Gas', bus='Gas', size=1000, effects_per_flow_hour={'costs': gas_price, 'CO2': 0.3})],
- ),
- fx.Source(
- 'Kohletarif',
- outputs=[fx.Flow('Q_Kohle', bus='Kohle', size=1000, effects_per_flow_hour={'costs': 4.6, 'CO2': 0.3})],
- ),
- fx.Source(
- 'Einspeisung',
- outputs=[
- fx.Flow(
- 'P_el', bus='Strom', size=1000, effects_per_flow_hour={'costs': electricity_price + 0.5, 'CO2': 0.3}
- )
- ],
- ),
- fx.Sink(
- 'Stromlast',
- inputs=[fx.Flow('P_el_Last', bus='Strom', size=1, fixed_relative_profile=electricity_demand)],
- ),
- fx.Source(
- 'Stromtarif',
- outputs=[
- fx.Flow('P_el', bus='Strom', size=1000, effects_per_flow_hour={'costs': electricity_price, 'CO2': 0.3})
- ],
- ),
- )
-
- # Separate optimization of flow sizes and dispatch
- # Stage 1: Optimize sizes using downsampled (2h) data
- start = timeit.default_timer()
- calculation_sizing = fx.Optimization('Sizing', flow_system.resample('2h'))
- calculation_sizing.do_modeling()
- calculation_sizing.solve(fx.solvers.HighsSolver(0.1 / 100, 60))
- timer_sizing = timeit.default_timer() - start
-
- # Stage 2: Optimize dispatch with fixed sizes from Stage 1
- start = timeit.default_timer()
- calculation_dispatch = fx.Optimization('Dispatch', flow_system)
- calculation_dispatch.do_modeling()
- calculation_dispatch.fix_sizes(calculation_sizing.flow_system.solution)
- calculation_dispatch.solve(fx.solvers.HighsSolver(0.1 / 100, 60))
- timer_dispatch = timeit.default_timer() - start
-
- # Verify sizes were correctly fixed
- dispatch_sizes = calculation_dispatch.flow_system.statistics.sizes
- sizing_sizes = calculation_sizing.flow_system.statistics.sizes
- if np.allclose(dispatch_sizes.to_dataarray(), sizing_sizes.to_dataarray(), rtol=1e-5):
- logger.info('Sizes were correctly equalized')
- else:
- raise RuntimeError('Sizes were not correctly equalized')
-
- # Combined optimization: optimize both sizes and dispatch together
- start = timeit.default_timer()
- calculation_combined = fx.Optimization('Combined', flow_system)
- calculation_combined.do_modeling()
- calculation_combined.solve(fx.solvers.HighsSolver(0.1 / 100, 600))
- timer_combined = timeit.default_timer() - start
-
- # Comparison of results - access solutions from flow_system
- comparison = xr.concat(
- [calculation_combined.flow_system.solution, calculation_dispatch.flow_system.solution], dim='mode'
- ).assign_coords(mode=['Combined', 'Two-stage'])
- comparison['Duration [s]'] = xr.DataArray([timer_combined, timer_sizing + timer_dispatch], dims='mode')
-
- comparison_main = comparison[
- [
- 'Duration [s]',
- 'costs',
- 'costs(periodic)',
- 'costs(temporal)',
- 'BHKW2(Q_fu)|size',
- 'Kessel(Q_fu)|size',
- 'Speicher|size',
- ]
- ]
- comparison_main = xr.concat(
- [
- comparison_main,
- (
- (comparison_main.sel(mode='Two-stage') - comparison_main.sel(mode='Combined'))
- / comparison_main.sel(mode='Combined')
- * 100
- ).assign_coords(mode='Diff [%]'),
- ],
- dim='mode',
- )
-
- print(comparison_main.to_pandas().T.round(2))
diff --git a/examples/resources/Zeitreihen2020.csv b/examples/resources/Zeitreihen2020.csv
deleted file mode 100644
index 9b660ef9c..000000000
--- a/examples/resources/Zeitreihen2020.csv
+++ /dev/null
@@ -1,35137 +0,0 @@
-Zeit,P_Netz/MW,Q_Netz/MW,Strompr.€/MWh,Gaspr.€/MWh
-2020-01-01 00:00:00,58.39,127.059,7.461,32.459
-2020-01-01 00:15:00,58.36,122.156,7.461,32.459
-2020-01-01 00:30:00,58.11,124.412,7.461,32.459
-2020-01-01 00:45:00,57.71,127.713,7.461,32.459
-2020-01-01 01:00:00,55.53,130.69899999999998,2.65,32.459
-2020-01-01 01:15:00,56.24,132.166,2.65,32.459
-2020-01-01 01:30:00,55.17,132.394,2.65,32.459
-2020-01-01 01:45:00,54.5,132.431,2.65,32.459
-2020-01-01 02:00:00,52.95,134.403,-2.949,32.459
-2020-01-01 02:15:00,51.75,134.755,-2.949,32.459
-2020-01-01 02:30:00,50.7,135.631,-2.949,32.459
-2020-01-01 02:45:00,50.33,138.345,-2.949,32.459
-2020-01-01 03:00:00,47.11,141.071,-3.2680000000000002,32.459
-2020-01-01 03:15:00,49.35,141.319,-3.2680000000000002,32.459
-2020-01-01 03:30:00,48.33,143.024,-3.2680000000000002,32.459
-2020-01-01 03:45:00,48.73,144.697,-3.2680000000000002,32.459
-2020-01-01 04:00:00,46.6,152.569,-3.2680000000000002,32.459
-2020-01-01 04:15:00,47.33,160.688,-3.2680000000000002,32.459
-2020-01-01 04:30:00,47.5,161.673,-3.2680000000000002,32.459
-2020-01-01 04:45:00,48.62,163.165,-3.2680000000000002,32.459
-2020-01-01 05:00:00,49.18,176.398,-3.2680000000000002,32.459
-2020-01-01 05:15:00,50.0,184.233,-3.2680000000000002,32.459
-2020-01-01 05:30:00,50.1,181.12,-3.2680000000000002,32.459
-2020-01-01 05:45:00,50.36,179.642,-3.2680000000000002,32.459
-2020-01-01 06:00:00,50.32,196.364,-3.2680000000000002,32.459
-2020-01-01 06:15:00,50.22,215.918,-3.2680000000000002,32.459
-2020-01-01 06:30:00,52.17,211.0,-3.2680000000000002,32.459
-2020-01-01 06:45:00,54.2,206.111,-3.2680000000000002,32.459
-2020-01-01 07:00:00,55.6,202.635,-3.2680000000000002,32.459
-2020-01-01 07:15:00,55.35,207.093,-3.2680000000000002,32.459
-2020-01-01 07:30:00,55.44,211.667,-3.2680000000000002,32.459
-2020-01-01 07:45:00,55.15,215.882,-3.2680000000000002,32.459
-2020-01-01 08:00:00,56.21,219.793,-2.146,32.459
-2020-01-01 08:15:00,55.94,223.388,-2.146,32.459
-2020-01-01 08:30:00,58.2,226.081,-2.146,32.459
-2020-01-01 08:45:00,56.11,227.016,-2.146,32.459
-2020-01-01 09:00:00,61.62,222.30700000000002,1.7519999999999998,32.459
-2020-01-01 09:15:00,63.5,221.018,1.7519999999999998,32.459
-2020-01-01 09:30:00,64.24,219.09,1.7519999999999998,32.459
-2020-01-01 09:45:00,64.02,215.80700000000002,1.7519999999999998,32.459
-2020-01-01 10:00:00,61.38,212.231,4.19,32.459
-2020-01-01 10:15:00,62.05,209.50099999999998,4.19,32.459
-2020-01-01 10:30:00,61.84,206.963,4.19,32.459
-2020-01-01 10:45:00,65.9,204.111,4.19,32.459
-2020-01-01 11:00:00,67.33,203.37599999999998,5.517,32.459
-2020-01-01 11:15:00,68.34,200.575,5.517,32.459
-2020-01-01 11:30:00,67.43,198.755,5.517,32.459
-2020-01-01 11:45:00,68.73,197.22099999999998,5.517,32.459
-2020-01-01 12:00:00,74.2,191.555,4.27,32.459
-2020-01-01 12:15:00,69.91,191.37,4.27,32.459
-2020-01-01 12:30:00,68.83,190.28799999999998,4.27,32.459
-2020-01-01 12:45:00,70.01,189.851,4.27,32.459
-2020-01-01 13:00:00,69.02,188.09599999999998,3.484,32.459
-2020-01-01 13:15:00,68.68,189.604,3.484,32.459
-2020-01-01 13:30:00,68.45,188.61,3.484,32.459
-2020-01-01 13:45:00,68.18,188.303,3.484,32.459
-2020-01-01 14:00:00,68.94,187.555,2.523,32.459
-2020-01-01 14:15:00,66.1,188.747,2.523,32.459
-2020-01-01 14:30:00,70.61,189.53099999999998,2.523,32.459
-2020-01-01 14:45:00,70.58,189.93,2.523,32.459
-2020-01-01 15:00:00,73.81,189.581,5.667999999999999,32.459
-2020-01-01 15:15:00,69.6,191.454,5.667999999999999,32.459
-2020-01-01 15:30:00,68.66,194.55599999999998,5.667999999999999,32.459
-2020-01-01 15:45:00,71.32,197.227,5.667999999999999,32.459
-2020-01-01 16:00:00,73.3,197.49900000000002,12.109000000000002,32.459
-2020-01-01 16:15:00,77.24,199.38099999999997,12.109000000000002,32.459
-2020-01-01 16:30:00,83.2,202.511,12.109000000000002,32.459
-2020-01-01 16:45:00,86.91,205.047,12.109000000000002,32.459
-2020-01-01 17:00:00,89.85,207.06099999999998,22.824,32.459
-2020-01-01 17:15:00,90.61,208.69799999999998,22.824,32.459
-2020-01-01 17:30:00,92.03,209.25099999999998,22.824,32.459
-2020-01-01 17:45:00,93.49,210.672,22.824,32.459
-2020-01-01 18:00:00,95.17,211.632,21.656,32.459
-2020-01-01 18:15:00,94.51,211.645,21.656,32.459
-2020-01-01 18:30:00,93.87,209.94,21.656,32.459
-2020-01-01 18:45:00,93.48,208.489,21.656,32.459
-2020-01-01 19:00:00,92.14,209.826,19.749000000000002,32.459
-2020-01-01 19:15:00,90.85,207.487,19.749000000000002,32.459
-2020-01-01 19:30:00,89.81,204.959,19.749000000000002,32.459
-2020-01-01 19:45:00,88.14,202.29,19.749000000000002,32.459
-2020-01-01 20:00:00,84.73,200.835,24.274,32.459
-2020-01-01 20:15:00,83.37,197.709,24.274,32.459
-2020-01-01 20:30:00,82.23,194.57299999999998,24.274,32.459
-2020-01-01 20:45:00,80.34,191.52200000000002,24.274,32.459
-2020-01-01 21:00:00,78.43,188.843,23.044,32.459
-2020-01-01 21:15:00,77.95,186.56099999999998,23.044,32.459
-2020-01-01 21:30:00,77.04,186.183,23.044,32.459
-2020-01-01 21:45:00,76.57,184.824,23.044,32.459
-2020-01-01 22:00:00,72.56,178.928,25.155,32.459
-2020-01-01 22:15:00,72.48,174.81799999999998,25.155,32.459
-2020-01-01 22:30:00,70.04,170.76,25.155,32.459
-2020-01-01 22:45:00,67.68,167.32,25.155,32.459
-2020-01-01 23:00:00,59.3,159.845,20.101,32.459
-2020-01-01 23:15:00,63.51,156.17700000000002,20.101,32.459
-2020-01-01 23:30:00,61.08,153.764,20.101,32.459
-2020-01-01 23:45:00,60.81,150.845,20.101,32.459
-2020-01-02 00:00:00,72.56,131.099,38.399,32.641
-2020-01-02 00:15:00,75.51,130.822,38.399,32.641
-2020-01-02 00:30:00,76.2,132.15,38.399,32.641
-2020-01-02 00:45:00,79.94,133.753,38.399,32.641
-2020-01-02 01:00:00,76.22,136.549,36.94,32.641
-2020-01-02 01:15:00,75.52,136.971,36.94,32.641
-2020-01-02 01:30:00,69.71,137.433,36.94,32.641
-2020-01-02 01:45:00,72.15,137.96200000000002,36.94,32.641
-2020-01-02 02:00:00,68.46,139.933,35.275,32.641
-2020-01-02 02:15:00,68.93,141.73,35.275,32.641
-2020-01-02 02:30:00,69.13,142.344,35.275,32.641
-2020-01-02 02:45:00,71.05,144.38,35.275,32.641
-2020-01-02 03:00:00,77.24,147.17700000000002,35.329,32.641
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-2020-01-02 03:45:00,73.47,151.487,35.329,32.641
-2020-01-02 04:00:00,71.66,163.75,36.275,32.641
-2020-01-02 04:15:00,72.6,175.77599999999998,36.275,32.641
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-2020-01-02 05:00:00,80.9,217.042,42.193999999999996,32.641
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-2020-01-02 05:45:00,92.98,234.083,42.193999999999996,32.641
-2020-01-02 06:00:00,101.92,230.607,56.422,32.641
-2020-01-02 06:15:00,106.02,236.44099999999997,56.422,32.641
-2020-01-02 06:30:00,110.67,239.31400000000002,56.422,32.641
-2020-01-02 06:45:00,115.36,243.33,56.422,32.641
-2020-01-02 07:00:00,121.21,242.197,72.569,32.641
-2020-01-02 07:15:00,125.44,247.68200000000002,72.569,32.641
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-2020-01-02 07:45:00,129.3,252.55900000000003,72.569,32.641
-2020-01-02 08:00:00,131.83,251.364,67.704,32.641
-2020-01-02 08:15:00,129.92,251.618,67.704,32.641
-2020-01-02 08:30:00,130.03,249.708,67.704,32.641
-2020-01-02 08:45:00,129.65,246.764,67.704,32.641
-2020-01-02 09:00:00,130.4,240.053,63.434,32.641
-2020-01-02 09:15:00,132.18,236.87900000000002,63.434,32.641
-2020-01-02 09:30:00,133.68,234.63099999999997,63.434,32.641
-2020-01-02 09:45:00,133.99,231.472,63.434,32.641
-2020-01-02 10:00:00,133.44,226.187,61.88399999999999,32.641
-2020-01-02 10:15:00,135.64,221.955,61.88399999999999,32.641
-2020-01-02 10:30:00,134.92,218.68400000000003,61.88399999999999,32.641
-2020-01-02 10:45:00,136.65,216.98,61.88399999999999,32.641
-2020-01-02 11:00:00,136.01,214.97299999999998,61.481,32.641
-2020-01-02 11:15:00,135.6,213.702,61.481,32.641
-2020-01-02 11:30:00,135.49,212.15200000000002,61.481,32.641
-2020-01-02 11:45:00,136.56,210.945,61.481,32.641
-2020-01-02 12:00:00,136.24,205.8,59.527,32.641
-2020-01-02 12:15:00,135.89,205.143,59.527,32.641
-2020-01-02 12:30:00,133.92,205.12400000000002,59.527,32.641
-2020-01-02 12:45:00,134.1,205.96099999999998,59.527,32.641
-2020-01-02 13:00:00,130.94,204.35,58.794,32.641
-2020-01-02 13:15:00,129.98,203.88099999999997,58.794,32.641
-2020-01-02 13:30:00,129.31,203.575,58.794,32.641
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-2020-01-02 14:30:00,128.98,203.95,60.32,32.641
-2020-01-02 14:45:00,127.66,204.167,60.32,32.641
-2020-01-02 15:00:00,131.69,205.303,62.52,32.641
-2020-01-02 15:15:00,134.08,205.93900000000002,62.52,32.641
-2020-01-02 15:30:00,130.49,208.357,62.52,32.641
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-2020-01-02 16:30:00,137.68,215.345,64.199,32.641
-2020-01-02 16:45:00,138.3,216.87599999999998,64.199,32.641
-2020-01-02 17:00:00,141.23,219.28900000000002,68.19800000000001,32.641
-2020-01-02 17:15:00,140.55,219.918,68.19800000000001,32.641
-2020-01-02 17:30:00,141.63,220.68200000000002,68.19800000000001,32.641
-2020-01-02 17:45:00,141.55,220.424,68.19800000000001,32.641
-2020-01-02 18:00:00,140.02,221.84400000000002,67.899,32.641
-2020-01-02 18:15:00,138.28,218.955,67.899,32.641
-2020-01-02 18:30:00,137.19,217.683,67.899,32.641
-2020-01-02 18:45:00,137.6,217.707,67.899,32.641
-2020-01-02 19:00:00,134.26,217.453,64.72399999999999,32.641
-2020-01-02 19:15:00,133.22,213.481,64.72399999999999,32.641
-2020-01-02 19:30:00,134.64,210.797,64.72399999999999,32.641
-2020-01-02 19:45:00,136.88,207.28599999999997,64.72399999999999,32.641
-2020-01-02 20:00:00,130.24,203.518,64.062,32.641
-2020-01-02 20:15:00,119.33,197.062,64.062,32.641
-2020-01-02 20:30:00,118.31,192.979,64.062,32.641
-2020-01-02 20:45:00,112.7,191.03099999999998,64.062,32.641
-2020-01-02 21:00:00,107.44,188.12900000000002,57.971000000000004,32.641
-2020-01-02 21:15:00,112.86,185.61900000000003,57.971000000000004,32.641
-2020-01-02 21:30:00,111.93,183.535,57.971000000000004,32.641
-2020-01-02 21:45:00,108.29,181.894,57.971000000000004,32.641
-2020-01-02 22:00:00,98.52,174.86,53.715,32.641
-2020-01-02 22:15:00,94.85,168.98,53.715,32.641
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-2020-12-31 11:30:00,135.49,192.428,60.843,32.468
-2020-12-31 11:45:00,136.56,190.91299999999998,60.843,32.468
-2020-12-31 12:00:00,136.24,185.315,58.466,32.468
-2020-12-31 12:15:00,135.89,184.63299999999998,58.466,32.468
-2020-12-31 12:30:00,133.92,184.908,58.466,32.468
-2020-12-31 12:45:00,134.1,185.834,58.466,32.468
-2020-12-31 13:00:00,130.94,184.46,56.883,32.468
-2020-12-31 13:15:00,129.98,183.99,56.883,32.468
-2020-12-31 13:30:00,129.31,183.582,56.883,32.468
-2020-12-31 13:45:00,127.59,183.33599999999998,56.883,32.468
-2020-12-31 14:00:00,126.5,182.30700000000002,56.503,32.468
-2020-12-31 14:15:00,129.81,182.727,56.503,32.468
-2020-12-31 14:30:00,128.98,183.46099999999998,56.503,32.468
-2020-12-31 14:45:00,127.66,183.59,56.503,32.468
-2020-12-31 15:00:00,131.69,184.74,57.803999999999995,32.468
-2020-12-31 15:15:00,134.08,185.078,57.803999999999995,32.468
-2020-12-31 15:30:00,130.49,187.222,57.803999999999995,32.468
-2020-12-31 15:45:00,132.71,188.668,57.803999999999995,32.468
-2020-12-31 16:00:00,134.12,190.7,59.379,32.468
-2020-12-31 16:15:00,134.79,192.322,59.379,32.468
-2020-12-31 16:30:00,137.68,194.80599999999998,59.379,32.468
-2020-12-31 16:45:00,138.3,196.382,59.379,32.468
-2020-12-31 17:00:00,141.23,198.90900000000002,64.71600000000001,32.468
-2020-12-31 17:15:00,140.55,200.021,64.71600000000001,32.468
-2020-12-31 17:30:00,141.63,201.067,64.71600000000001,32.468
-2020-12-31 17:45:00,141.55,201.035,64.71600000000001,32.468
-2020-12-31 18:00:00,140.02,202.56799999999998,68.803,32.468
-2020-12-31 18:15:00,138.28,200.606,68.803,32.468
-2020-12-31 18:30:00,137.19,199.14700000000002,68.803,32.468
-2020-12-31 18:45:00,137.6,199.16,68.803,32.468
-2020-12-31 19:00:00,134.26,200.084,72.934,32.468
-2020-12-31 19:15:00,133.22,196.468,72.934,32.468
-2020-12-31 19:30:00,134.64,194.42700000000002,72.934,32.468
-2020-12-31 19:45:00,136.88,190.43900000000002,72.934,32.468
-2020-12-31 20:00:00,130.24,186.864,65.175,32.468
-2020-12-31 20:15:00,119.33,181.132,65.175,32.468
-2020-12-31 20:30:00,118.31,177.201,65.175,32.468
-2020-12-31 20:45:00,112.7,174.72400000000002,65.175,32.468
-2020-12-31 21:00:00,107.44,172.49,58.55,32.468
-2020-12-31 21:15:00,112.86,170.146,58.55,32.468
-2020-12-31 21:30:00,111.93,168.03,58.55,32.468
-2020-12-31 21:45:00,108.29,166.609,58.55,32.468
-2020-12-31 22:00:00,98.52,160.079,55.041000000000004,32.468
-2020-12-31 22:15:00,94.85,154.757,55.041000000000004,32.468
-2020-12-31 22:30:00,98.1,141.22899999999998,55.041000000000004,32.468
-2020-12-31 22:45:00,96.62,133.488,55.041000000000004,32.468
-2020-12-31 23:00:00,92.22,127.7,48.258,32.468
-2020-12-31 23:15:00,84.12,125.64200000000001,48.258,32.468
-2020-12-31 23:30:00,79.31,126.145,48.258,32.468
-2020-12-31 23:45:00,83.54,125.553,48.258,32.468
diff --git a/flixopt/config.py b/flixopt/config.py
index aaa3b34d2..a98d1dd6f 100644
--- a/flixopt/config.py
+++ b/flixopt/config.py
@@ -785,6 +785,44 @@ def browser_plotting(cls) -> type[CONFIG]:
return cls
+ @classmethod
+ def notebook(cls) -> type[CONFIG]:
+ """Configure for Jupyter notebook environments.
+
+ Optimizes settings for notebook usage:
+ - Sets plotly renderer to 'notebook' for inline display
+ - Disables automatic plot.show() calls (notebooks display via _repr_html_)
+ - Enables INFO-level console logging
+ - Disables solver console output (too verbose for notebooks)
+
+ Examples:
+ ```python
+ # At the start of your notebook
+ import flixopt as fx
+
+ fx.CONFIG.notebook()
+
+ # Now plots display inline automatically
+ flow_system.statistics.plot.balance('Heat') # Displays inline
+ ```
+ """
+ import plotly.io as pio
+
+ # Set plotly to render inline in notebooks
+ pio.renderers.default = 'notebook'
+
+ # Disable default show since notebooks render via _repr_html_
+ cls.Plotting.default_show = False
+
+ # Light logging - SUCCESS level without too much noise
+ cls.Logging.enable_console('SUCCESS')
+
+ # Disable solver console output (too verbose for notebooks)
+ cls.Solving.log_to_console = True
+ cls.Solving.log_main_results = True
+
+ return cls
+
@classmethod
def load_from_file(cls, config_file: str | Path) -> type[CONFIG]:
"""Load configuration from YAML file and apply it.
diff --git a/flixopt/flow_system.py b/flixopt/flow_system.py
index 0de7b6536..7a71efee9 100644
--- a/flixopt/flow_system.py
+++ b/flixopt/flow_system.py
@@ -16,6 +16,7 @@
import xarray as xr
from . import io as fx_io
+from .components import Storage
from .config import CONFIG, DEPRECATION_REMOVAL_VERSION
from .core import (
ConversionError,
@@ -507,6 +508,28 @@ def _update_period_metadata(
return dataset
+ @classmethod
+ def _update_scenario_metadata(cls, dataset: xr.Dataset) -> xr.Dataset:
+ """
+ Update scenario-related attributes and data variables in dataset based on its scenario index.
+
+ Recomputes or removes scenario weights. This ensures scenario metadata stays synchronized with the actual
+ scenarios after operations like selection.
+
+ This is analogous to _update_period_metadata() for time-related metadata.
+
+ Args:
+ dataset: Dataset to update (will be modified in place)
+
+ Returns:
+ The same dataset with updated scenario-related attributes and data variables
+ """
+ new_scenario_index = dataset.indexes.get('scenario')
+ if new_scenario_index is None or len(new_scenario_index) <= 1:
+ dataset.attrs.pop('scenario_weights')
+
+ return dataset
+
def _create_reference_structure(self) -> tuple[dict, dict[str, xr.DataArray]]:
"""
Override Interface method to handle FlowSystem-specific serialization.
@@ -1001,7 +1024,7 @@ def add_carriers(self, *carriers: Carrier) -> None:
CONFIG.Carriers defaults when resolving colors and units for buses.
Args:
- carrier: A Carrier object defining the carrier properties.
+ carriers: Carrier objects defining the carrier properties.
Raises:
RuntimeError: If the FlowSystem is locked (has a solution).
@@ -1657,6 +1680,18 @@ def flows(self) -> ElementContainer[Flow]:
self._flows_cache = ElementContainer(flows, element_type_name='flows', truncate_repr=10)
return self._flows_cache
+ @property
+ def storages(self) -> ElementContainer[Storage]:
+ """All storage components as an ElementContainer.
+
+ Returns:
+ ElementContainer containing all Storage components in the FlowSystem,
+ sorted by label for reproducibility.
+ """
+ storages = [c for c in self.components.values() if isinstance(c, Storage)]
+ storages = sorted(storages, key=lambda s: s.label_full.lower())
+ return ElementContainer(storages, element_type_name='storages', truncate_repr=10)
+
@property
def coords(self) -> dict[FlowSystemDimensions, pd.Index]:
active_coords = {'time': self.timesteps}
diff --git a/flixopt/interface.py b/flixopt/interface.py
index 7787eec18..0a9e9424c 100644
--- a/flixopt/interface.py
+++ b/flixopt/interface.py
@@ -10,6 +10,8 @@
import numpy as np
import pandas as pd
+import plotly.express as px
+import plotly.graph_objects as go
import xarray as xr
from .config import CONFIG
@@ -468,6 +470,93 @@ def transform_data(self) -> None:
for piecewise in self.piecewises.values():
piecewise.transform_data()
+ def plot(
+ self,
+ x_flow: str | None = None,
+ title: str = '',
+ ) -> go.Figure:
+ """Plot multi-flow piecewise conversion as X-Y scatter.
+
+ Visualizes the piecewise linear relationships between flows. One flow
+ is plotted on the X-axis, all others on the Y-axis. Each piece is shown
+ as a line segment. For data with periods/scenarios, uses faceting.
+
+ Note:
+ Requires FlowSystem to be connected and transformed (call
+ flow_system.connect_and_transform() first).
+
+ Args:
+ x_flow: Flow label to use for X-axis. Defaults to first flow in dict.
+ title: Plot title.
+
+ Returns:
+ Plotly Figure with X-Y scatter showing piecewise segments.
+
+ Examples:
+ >>> flow_system.connect_and_transform()
+ >>> chp.piecewise_conversion.plot(x_flow='Gas', title='CHP Curves')
+ """
+ if self._flow_system is None:
+ raise RuntimeError('Component must be part of a FlowSystem to plot.')
+ if not self._flow_system.connected_and_transformed:
+ logger.debug('Connecting flow_system for plotting PiecewiseConversion')
+ self.flow_system.connect_and_transform()
+
+ flow_labels = list(self.piecewises.keys())
+
+ # Use first flow as X-axis by default, or the specified one
+ x_label = x_flow if x_flow is not None else flow_labels[0]
+ if x_label not in flow_labels:
+ raise ValueError(f"x_flow '{x_label}' not found. Available: {flow_labels}")
+
+ y_flows = [label for label in flow_labels if label != x_label]
+ if not y_flows:
+ raise ValueError('Need at least two flows to plot')
+
+ x_piecewise = self.piecewises[x_label]
+
+ # Build xarray Dataset with all piece data, then convert to DataFrame for plotting
+ datasets = []
+ for y_label in y_flows:
+ y_piecewise = self.piecewises[y_label]
+ for i, (x_piece, y_piece) in enumerate(zip(x_piecewise, y_piecewise, strict=False)):
+ # Create Dataset with start and end points as a 'point' dimension
+ ds = xr.Dataset(
+ {
+ x_label: xr.concat([x_piece.start, x_piece.end], dim='point'),
+ 'output': xr.concat([y_piece.start, y_piece.end], dim='point'),
+ }
+ )
+ ds = ds.assign_coords(point=['start', 'end'])
+ ds['variable'] = y_label
+ ds['piece'] = i
+ datasets.append(ds)
+
+ combined = xr.concat(datasets, dim='trace')
+ combined['trace'] = range(len(datasets))
+
+ # Convert to DataFrame for plotting
+ df = combined.to_dataframe().reset_index()
+
+ # Determine faceting based on available dimensions
+ facet_col = 'scenario' if 'scenario' in df.columns and df['scenario'].nunique() > 1 else None
+ facet_row = 'period' if 'period' in df.columns and df['period'].nunique() > 1 else None
+
+ fig = px.line(
+ df,
+ x=x_label,
+ y='output',
+ color='variable',
+ line_group='trace',
+ facet_col=facet_col,
+ facet_row=facet_row,
+ title=title,
+ markers=True,
+ )
+
+ fig.update_layout(yaxis_title='Output' if len(y_flows) > 1 else y_flows[0])
+ return fig
+
@register_class_for_io
class PiecewiseEffects(Interface):
@@ -688,6 +777,81 @@ def transform_data(self) -> None:
for piecewise in self.piecewise_shares.values():
piecewise.transform_data()
+ def plot(self, title: str = '') -> go.Figure:
+ """Plot origin vs effect shares as X-Y scatter.
+
+ Visualizes the piecewise linear relationships between the origin variable
+ and its effect shares. Origin on X-axis, effect shares on Y-axis.
+ For data with periods/scenarios, uses faceting.
+
+ Note:
+ Requires FlowSystem to be connected and transformed (call
+ flow_system.connect_and_transform() first).
+
+ Args:
+ title: Plot title.
+
+ Returns:
+ Plotly Figure with X-Y scatter showing piecewise segments.
+
+ Examples:
+ >>> flow_system.connect_and_transform()
+ >>> invest_params.piecewise_effects_of_investment.plot(title='Investment Effects')
+ """
+ if self._flow_system is None:
+ raise RuntimeError('Component must be part of a FlowSystem to plot.')
+ if not self._flow_system.connected_and_transformed:
+ logger.debug('Connecting flow_system for plotting PiecewiseEffects')
+ self.flow_system.connect_and_transform()
+
+ effect_labels = list(self.piecewise_shares.keys())
+ if not effect_labels:
+ raise ValueError('Need at least one effect share to plot')
+
+ # Build xarray Dataset with all piece data, then convert to DataFrame for plotting
+ datasets = []
+ for effect_label in effect_labels:
+ y_piecewise = self.piecewise_shares[effect_label]
+ for i, (x_piece, y_piece) in enumerate(zip(self.piecewise_origin, y_piecewise, strict=False)):
+ ds = xr.Dataset(
+ {
+ 'origin': xr.concat([x_piece.start, x_piece.end], dim='point'),
+ 'share': xr.concat([y_piece.start, y_piece.end], dim='point'),
+ }
+ )
+ ds = ds.assign_coords(point=['start', 'end'])
+ ds['effect'] = effect_label
+ ds['piece'] = i
+ datasets.append(ds)
+
+ combined = xr.concat(datasets, dim='trace')
+ combined['trace'] = range(len(datasets))
+
+ # Convert to DataFrame for plotting
+ df = combined.to_dataframe().reset_index()
+
+ # Determine faceting based on available dimensions
+ facet_col = 'scenario' if 'scenario' in df.columns and df['scenario'].nunique() > 1 else None
+ facet_row = 'period' if 'period' in df.columns and df['period'].nunique() > 1 else None
+
+ fig = px.line(
+ df,
+ x='origin',
+ y='share',
+ color='effect',
+ line_group='trace',
+ facet_col=facet_col,
+ facet_row=facet_row,
+ title=title,
+ markers=True,
+ )
+
+ fig.update_layout(
+ xaxis_title='Origin',
+ yaxis_title='Effect Share' if len(effect_labels) > 1 else effect_labels[0],
+ )
+ return fig
+
@register_class_for_io
class InvestParameters(Interface):
diff --git a/flixopt/statistics_accessor.py b/flixopt/statistics_accessor.py
index 0cdd2f5ba..0ed790f44 100644
--- a/flixopt/statistics_accessor.py
+++ b/flixopt/statistics_accessor.py
@@ -178,6 +178,10 @@ class PlotResult:
data: xr.Dataset
figure: go.Figure
+ def _repr_html_(self) -> str:
+ """Return HTML representation for Jupyter notebook display."""
+ return self.figure.to_html(full_html=False, include_plotlyjs='cdn')
+
def show(self) -> PlotResult:
"""Display the figure. Returns self for chaining."""
self.figure.show()
@@ -364,6 +368,8 @@ def __init__(self, flow_system: FlowSystem) -> None:
# Cached data
self._flow_rates: xr.Dataset | None = None
self._flow_hours: xr.Dataset | None = None
+ self._flow_sizes: xr.Dataset | None = None
+ self._storage_sizes: xr.Dataset | None = None
self._sizes: xr.Dataset | None = None
self._charge_states: xr.Dataset | None = None
self._effect_share_factors: dict[str, dict] | None = None
@@ -413,16 +419,36 @@ def flow_hours(self) -> xr.Dataset:
return self._flow_hours
@property
- def sizes(self) -> xr.Dataset:
- """All flow sizes as a Dataset with flow labels as variable names."""
+ def flow_sizes(self) -> xr.Dataset:
+ """Flow sizes as a Dataset with flow labels as variable names."""
self._require_solution()
- if self._sizes is None:
- # Get flow labels to filter only flow sizes (not storage capacity sizes)
+ if self._flow_sizes is None:
flow_labels = set(self._fs.flows.keys())
size_vars = [
v for v in self._fs.solution.data_vars if v.endswith('|size') and v.replace('|size', '') in flow_labels
]
- self._sizes = xr.Dataset({v.replace('|size', ''): self._fs.solution[v] for v in size_vars})
+ self._flow_sizes = xr.Dataset({v.replace('|size', ''): self._fs.solution[v] for v in size_vars})
+ return self._flow_sizes
+
+ @property
+ def storage_sizes(self) -> xr.Dataset:
+ """Storage capacity sizes as a Dataset with storage labels as variable names."""
+ self._require_solution()
+ if self._storage_sizes is None:
+ storage_labels = set(self._fs.storages.keys())
+ size_vars = [
+ v
+ for v in self._fs.solution.data_vars
+ if v.endswith('|size') and v.replace('|size', '') in storage_labels
+ ]
+ self._storage_sizes = xr.Dataset({v.replace('|size', ''): self._fs.solution[v] for v in size_vars})
+ return self._storage_sizes
+
+ @property
+ def sizes(self) -> xr.Dataset:
+ """All investment sizes (flows and storage capacities) as a Dataset."""
+ if self._sizes is None:
+ self._sizes = xr.merge([self.flow_sizes, self.storage_sizes])
return self._sizes
@property
@@ -1057,7 +1083,7 @@ def flows(
for flow in self._fs.flows.values():
# Get bus label (could be string or Bus object)
bus_label = flow.bus
- comp_label = flow.component.label_full
+ comp_label = flow.component
# start/end filtering based on flow direction
if flow.is_input_in_component:
@@ -1715,3 +1741,189 @@ def effects(
fig.show()
return PlotResult(data=combined.to_dataset(name=aspect), figure=fig)
+
+ def charge_states(
+ self,
+ storages: str | list[str] | None = None,
+ *,
+ select: SelectType | None = None,
+ colors: ColorType | None = None,
+ facet_col: str | None = 'period',
+ facet_row: str | None = 'scenario',
+ show: bool | None = None,
+ **plotly_kwargs: Any,
+ ) -> PlotResult:
+ """Plot storage charge states over time.
+
+ Args:
+ storages: Storage label(s) to plot. If None, plots all storages.
+ select: xarray-style selection.
+ colors: Color specification (colorscale name, color list, or label-to-color dict).
+ facet_col: Dimension for column facets.
+ facet_row: Dimension for row facets.
+ show: Whether to display.
+
+ Returns:
+ PlotResult with charge state data.
+ """
+ self._stats._require_solution()
+ ds = self._stats.charge_states
+
+ if storages is not None:
+ if isinstance(storages, str):
+ storages = [storages]
+ ds = ds[[s for s in storages if s in ds]]
+
+ ds = _apply_selection(ds, select)
+ actual_facet_col, actual_facet_row = _resolve_facets(ds, facet_col, facet_row)
+
+ fig = _create_line(
+ ds,
+ colors=colors,
+ title='Storage Charge States',
+ facet_col=actual_facet_col,
+ facet_row=actual_facet_row,
+ **plotly_kwargs,
+ )
+ fig.update_yaxes(title_text='Charge State')
+
+ if show is None:
+ show = CONFIG.Plotting.default_show
+ if show:
+ fig.show()
+
+ return PlotResult(data=ds, figure=fig)
+
+ def storage(
+ self,
+ storage: str,
+ *,
+ select: SelectType | None = None,
+ unit: Literal['flow_rate', 'flow_hours'] = 'flow_rate',
+ colors: ColorType | None = None,
+ charge_state_color: str = 'black',
+ facet_col: str | None = 'period',
+ facet_row: str | None = 'scenario',
+ show: bool | None = None,
+ **plotly_kwargs: Any,
+ ) -> PlotResult:
+ """Plot storage operation: balance and charge state in vertically stacked subplots.
+
+ Creates two subplots sharing the x-axis:
+ - Top: Charging/discharging flows as stacked bars (inputs negative, outputs positive)
+ - Bottom: Charge state over time as a line
+
+ Args:
+ storage: Storage component label.
+ select: xarray-style selection.
+ unit: 'flow_rate' (power) or 'flow_hours' (energy).
+ colors: Color specification for flow bars.
+ charge_state_color: Color for the charge state line overlay.
+ facet_col: Dimension for column facets.
+ facet_row: Dimension for row facets.
+ show: Whether to display.
+
+ Returns:
+ PlotResult with combined balance and charge state data.
+
+ Raises:
+ KeyError: If storage component not found.
+ ValueError: If component is not a storage.
+ """
+ self._stats._require_solution()
+
+ # Get the storage component
+ if storage not in self._fs.components:
+ raise KeyError(f"'{storage}' not found in components")
+
+ component = self._fs.components[storage]
+
+ # Check if it's a storage by looking for charge_state variable
+ charge_state_var = f'{storage}|charge_state'
+ if charge_state_var not in self._fs.solution:
+ raise ValueError(f"'{storage}' is not a storage (no charge_state variable found)")
+
+ # Get flow data
+ input_labels = [f.label_full for f in component.inputs]
+ output_labels = [f.label_full for f in component.outputs]
+ all_labels = input_labels + output_labels
+
+ if unit == 'flow_rate':
+ ds = self._stats.flow_rates[[lbl for lbl in all_labels if lbl in self._stats.flow_rates]]
+ else:
+ ds = self._stats.flow_hours[[lbl for lbl in all_labels if lbl in self._stats.flow_hours]]
+
+ # Negate outputs for balance view (discharging shown as negative)
+ for label in output_labels:
+ if label in ds:
+ ds[label] = -ds[label]
+
+ # Get charge state and add to dataset
+ charge_state = self._fs.solution[charge_state_var].rename(storage)
+ ds['charge_state'] = charge_state
+
+ # Apply selection
+ ds = _apply_selection(ds, select)
+ actual_facet_col, actual_facet_row = _resolve_facets(ds, facet_col, facet_row)
+
+ # Build color map
+ flow_labels = [lbl for lbl in ds.data_vars if lbl != 'charge_state']
+ if colors is None:
+ colors = self._get_color_map_for_balance(storage, flow_labels)
+ color_map = process_colors(colors, flow_labels)
+ color_map['charge_state'] = 'black'
+
+ # Convert to long-form DataFrame
+ df = _dataset_to_long_df(ds)
+
+ # Create figure with facets using px.bar for flows, then add charge_state line
+ flow_df = df[df['variable'] != 'charge_state']
+ charge_df = df[df['variable'] == 'charge_state']
+
+ fig = px.bar(
+ flow_df,
+ x='time',
+ y='value',
+ color='variable',
+ facet_col=actual_facet_col,
+ facet_row=actual_facet_row,
+ color_discrete_map=color_map,
+ title=f'{storage} Operation ({unit})',
+ **plotly_kwargs,
+ )
+ fig.update_layout(bargap=0, bargroupgap=0)
+ fig.update_traces(marker_line_width=0)
+
+ # Add charge state as line on secondary y-axis using px.line, then merge traces
+ if not charge_df.empty:
+ line_fig = px.line(
+ charge_df,
+ x='time',
+ y='value',
+ facet_col=actual_facet_col,
+ facet_row=actual_facet_row,
+ )
+ # Update line traces and add to main figure
+ for trace in line_fig.data:
+ trace.name = 'charge_state'
+ trace.line = dict(color=charge_state_color, width=2)
+ trace.yaxis = 'y2'
+ trace.showlegend = True
+ fig.add_trace(trace)
+
+ # Add secondary y-axis
+ fig.update_layout(
+ yaxis2=dict(
+ title='Charge State',
+ overlaying='y',
+ side='right',
+ showgrid=False,
+ )
+ )
+
+ if show is None:
+ show = CONFIG.Plotting.default_show
+ if show:
+ fig.show()
+
+ return PlotResult(data=ds, figure=fig)
diff --git a/flixopt/transform_accessor.py b/flixopt/transform_accessor.py
index bf2a7ed5e..45a33c712 100644
--- a/flixopt/transform_accessor.py
+++ b/flixopt/transform_accessor.py
@@ -380,6 +380,9 @@ def _dataset_sel(
if 'period' in indexers:
result = FlowSystem._update_period_metadata(result)
+ if 'scenario' in indexers:
+ result = FlowSystem._update_scenario_metadata(result)
+
return result
@classmethod
@@ -427,6 +430,9 @@ def _dataset_isel(
if 'period' in indexers:
result = FlowSystem._update_period_metadata(result)
+ if 'scenario' in indexers:
+ result = FlowSystem._update_scenario_metadata(result)
+
return result
@classmethod
@@ -530,6 +536,125 @@ def _resample_by_dimension_groups(
return xr.merge(resampled_groups, combine_attrs='drop_conflicts')
+ def fix_sizes(
+ self,
+ sizes: xr.Dataset | dict[str, float] | None = None,
+ decimal_rounding: int | None = 5,
+ ) -> FlowSystem:
+ """
+ Create a new FlowSystem with investment sizes fixed to specified values.
+
+ This is useful for two-stage optimization workflows:
+ 1. Solve a sizing problem (possibly resampled for speed)
+ 2. Fix sizes and solve dispatch at full resolution
+
+ The returned FlowSystem has InvestParameters with fixed_size set,
+ making those sizes mandatory rather than decision variables.
+
+ Args:
+ sizes: The sizes to fix. Can be:
+ - None: Uses sizes from this FlowSystem's solution (must be solved)
+ - xr.Dataset: Dataset with size variables (e.g., from statistics.sizes)
+ - dict: Mapping of component names to sizes (e.g., {'Boiler(Q_fu)': 100})
+ decimal_rounding: Number of decimal places to round sizes to.
+ Rounding helps avoid numerical infeasibility. Set to None to disable.
+
+ Returns:
+ FlowSystem: New FlowSystem with fixed sizes (no solution).
+
+ Raises:
+ ValueError: If no sizes provided and FlowSystem has no solution.
+ KeyError: If a specified size doesn't match any InvestParameters.
+
+ Examples:
+ Two-stage optimization:
+
+ >>> # Stage 1: Size with resampled data
+ >>> fs_sizing = flow_system.transform.resample('2h')
+ >>> fs_sizing.optimize(solver)
+ >>>
+ >>> # Stage 2: Fix sizes and optimize at full resolution
+ >>> fs_dispatch = flow_system.transform.fix_sizes(fs_sizing.statistics.sizes)
+ >>> fs_dispatch.optimize(solver)
+
+ Using a dict:
+
+ >>> fs_fixed = flow_system.transform.fix_sizes(
+ ... {
+ ... 'Boiler(Q_fu)': 100,
+ ... 'Storage': 500,
+ ... }
+ ... )
+ >>> fs_fixed.optimize(solver)
+ """
+ from .flow_system import FlowSystem
+ from .interface import InvestParameters
+
+ # Get sizes from solution if not provided
+ if sizes is None:
+ if self._fs.solution is None:
+ raise ValueError(
+ 'No sizes provided and FlowSystem has no solution. '
+ 'Either provide sizes or optimize the FlowSystem first.'
+ )
+ sizes = self._fs.statistics.sizes
+
+ # Convert dict to Dataset format
+ if isinstance(sizes, dict):
+ sizes = xr.Dataset({k: xr.DataArray(v) for k, v in sizes.items()})
+
+ # Apply rounding
+ if decimal_rounding is not None:
+ sizes = sizes.round(decimal_rounding)
+
+ # Create copy of FlowSystem
+ if not self._fs.connected_and_transformed:
+ self._fs.connect_and_transform()
+
+ ds = self._fs.to_dataset()
+ new_fs = FlowSystem.from_dataset(ds)
+
+ # Fix sizes in the new FlowSystem's InvestParameters
+ # Note: statistics.sizes returns keys without '|size' suffix (e.g., 'Boiler(Q_fu)')
+ # but dicts may have either format
+ for size_var in sizes.data_vars:
+ # Normalize: strip '|size' suffix if present
+ base_name = size_var.replace('|size', '') if size_var.endswith('|size') else size_var
+ fixed_value = float(sizes[size_var].item())
+
+ # Find matching element with InvestParameters
+ found = False
+
+ # Check flows
+ for flow in new_fs.flows.values():
+ if flow.label_full == base_name and isinstance(flow.size, InvestParameters):
+ flow.size.fixed_size = fixed_value
+ flow.size.mandatory = True
+ found = True
+ logger.debug(f'Fixed size of {base_name} to {fixed_value}')
+ break
+
+ # Check storage capacity
+ if not found:
+ for component in new_fs.components.values():
+ if hasattr(component, 'capacity_in_flow_hours'):
+ if component.label == base_name and isinstance(
+ component.capacity_in_flow_hours, InvestParameters
+ ):
+ component.capacity_in_flow_hours.fixed_size = fixed_value
+ component.capacity_in_flow_hours.mandatory = True
+ found = True
+ logger.debug(f'Fixed size of {base_name} to {fixed_value}')
+ break
+
+ if not found:
+ logger.warning(
+ f'Size variable "{base_name}" not found as InvestParameters in FlowSystem. '
+ f'It may be a fixed-size component or the name may not match.'
+ )
+
+ return new_fs
+
# Future methods can be added here:
#
# def mga(self, alternatives: int = 5) -> FlowSystem:
diff --git a/mkdocs.yml b/mkdocs.yml
index 278081889..5ce16769e 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -51,16 +51,19 @@ nav:
- Roadmap: roadmap.md
- Examples:
- - Overview: examples/index.md
- - Basic Examples:
- - examples/00-Minimal Example.md
- - examples/01-Basic Example.md
- - Operational Optimization:
- - examples/02-Complex Example.md
- - examples/03-Optimization Modes.md
- - Planning & Investment:
- - examples/04-Scenarios.md
- - examples/05-Two-stage-optimization.md
+ - Overview: notebooks/index.md
+ - Getting Started:
+ - Quickstart: notebooks/01-quickstart.ipynb
+ - Heat System with Storage: notebooks/02-heat-system.ipynb
+ - Investment & Planning:
+ - Investment Optimization: notebooks/03-investment-optimization.ipynb
+ - Operational Constraints: notebooks/04-operational-constraints.ipynb
+ - Advanced Modeling:
+ - Multi-Carrier Systems: notebooks/05-multi-carrier-system.ipynb
+ - Piecewise Efficiency: notebooks/06-piecewise-efficiency.ipynb
+ - Scenarios & Scaling:
+ - Scenarios and Periods: notebooks/07-scenarios-and-periods.ipynb
+ - Large-Scale Optimization: notebooks/08-large-scale-optimization.ipynb
- API Reference: api-reference/
@@ -69,6 +72,7 @@ nav:
theme:
name: material
language: en
+ custom_dir: docs/overrides
palette:
# Palette toggle for automatic mode
@@ -215,6 +219,12 @@ plugins:
- search:
separator: '[\s\u200b\-_,:!=\[\]()"`/]+|\.(?!\d)|&[lg]t;|(?!\b)(?=[A-Z][a-z])'
+ - mkdocs-jupyter:
+ execute: true # Execute notebooks during build
+ allow_errors: false
+ include_source: true
+ include_requirejs: true
+
- plotly
- table-reader
diff --git a/pyproject.toml b/pyproject.toml
index bcd31f33c..88691e468 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -105,12 +105,14 @@ docs = [
"mkdocs-include-markdown-plugin==7.2.0",
"mkdocs-literate-nav==0.6.2",
"mkdocs-plotly-plugin==0.1.3",
+ "mkdocs-jupyter==0.25.1",
"markdown-include==0.8.1",
"pymdown-extensions==10.16.1",
"pygments==2.19.2",
"mike==2.1.3",
"mkdocs-git-revision-date-localized-plugin==1.5.0",
"mkdocs-minify-plugin==0.8.0",
+ "notebook>=7.5.0",
]
[project.urls]
diff --git a/tests/deprecated/test_examples.py b/tests/deprecated/test_examples.py
deleted file mode 100644
index 020670552..000000000
--- a/tests/deprecated/test_examples.py
+++ /dev/null
@@ -1,94 +0,0 @@
-import os
-import subprocess
-import sys
-from contextlib import contextmanager
-from pathlib import Path
-
-import pytest
-
-# Path to the examples directory
-EXAMPLES_DIR = Path(__file__).parent.parent / 'examples'
-
-# Examples that have dependencies and must run in sequence
-DEPENDENT_EXAMPLES = (
- '02_Complex/complex_example.py',
- '02_Complex/complex_example_results.py',
-)
-
-
-@contextmanager
-def working_directory(path):
- """Context manager for changing the working directory."""
- original_cwd = os.getcwd()
- try:
- os.chdir(path)
- yield
- finally:
- os.chdir(original_cwd)
-
-
-@pytest.mark.parametrize(
- 'example_script',
- sorted(
- [p for p in EXAMPLES_DIR.rglob('*.py') if str(p.relative_to(EXAMPLES_DIR)) not in DEPENDENT_EXAMPLES],
- key=lambda path: (str(path.parent), path.name),
- ),
- ids=lambda path: str(path.relative_to(EXAMPLES_DIR)).replace(os.sep, '/'),
-)
-@pytest.mark.examples
-def test_independent_examples(example_script):
- """
- Test independent example scripts.
- Ensures they run without errors.
- Changes the current working directory to the directory of the example script.
- Runs them alphabetically.
- This imitates behaviour of running the script directly.
- """
- with working_directory(example_script.parent):
- timeout = 800
- # Set environment variable to disable interactive plotting
- env = os.environ.copy()
- env['FLIXOPT_CI'] = 'true'
- try:
- result = subprocess.run(
- [sys.executable, example_script.name],
- capture_output=True,
- text=True,
- timeout=timeout,
- env=env,
- )
- except subprocess.TimeoutExpired:
- pytest.fail(f'Script {example_script} timed out after {timeout} seconds')
-
- assert result.returncode == 0, (
- f'Script {example_script} failed:\nSTDERR:\n{result.stderr}\nSTDOUT:\n{result.stdout}'
- )
-
-
-@pytest.mark.examples
-def test_dependent_examples():
- """Test examples that must run in order (complex_example.py generates data for complex_example_results.py)."""
- for script_path in DEPENDENT_EXAMPLES:
- script_full_path = EXAMPLES_DIR / script_path
-
- with working_directory(script_full_path.parent):
- timeout = 600
- # Set environment variable to disable interactive plotting
- env = os.environ.copy()
- env['FLIXOPT_CI'] = 'true'
- try:
- result = subprocess.run(
- [sys.executable, script_full_path.name],
- capture_output=True,
- text=True,
- timeout=timeout,
- env=env,
- )
- except subprocess.TimeoutExpired:
- pytest.fail(f'Script {script_path} timed out after {timeout} seconds')
-
- assert result.returncode == 0, f'{script_path} failed:\nSTDERR:\n{result.stderr}\nSTDOUT:\n{result.stdout}'
-
-
-if __name__ == '__main__':
- pytest.main(['-v', '--disable-warnings', '-m', 'examples'])
diff --git a/tests/test_examples.py b/tests/test_examples.py
deleted file mode 100644
index 020670552..000000000
--- a/tests/test_examples.py
+++ /dev/null
@@ -1,94 +0,0 @@
-import os
-import subprocess
-import sys
-from contextlib import contextmanager
-from pathlib import Path
-
-import pytest
-
-# Path to the examples directory
-EXAMPLES_DIR = Path(__file__).parent.parent / 'examples'
-
-# Examples that have dependencies and must run in sequence
-DEPENDENT_EXAMPLES = (
- '02_Complex/complex_example.py',
- '02_Complex/complex_example_results.py',
-)
-
-
-@contextmanager
-def working_directory(path):
- """Context manager for changing the working directory."""
- original_cwd = os.getcwd()
- try:
- os.chdir(path)
- yield
- finally:
- os.chdir(original_cwd)
-
-
-@pytest.mark.parametrize(
- 'example_script',
- sorted(
- [p for p in EXAMPLES_DIR.rglob('*.py') if str(p.relative_to(EXAMPLES_DIR)) not in DEPENDENT_EXAMPLES],
- key=lambda path: (str(path.parent), path.name),
- ),
- ids=lambda path: str(path.relative_to(EXAMPLES_DIR)).replace(os.sep, '/'),
-)
-@pytest.mark.examples
-def test_independent_examples(example_script):
- """
- Test independent example scripts.
- Ensures they run without errors.
- Changes the current working directory to the directory of the example script.
- Runs them alphabetically.
- This imitates behaviour of running the script directly.
- """
- with working_directory(example_script.parent):
- timeout = 800
- # Set environment variable to disable interactive plotting
- env = os.environ.copy()
- env['FLIXOPT_CI'] = 'true'
- try:
- result = subprocess.run(
- [sys.executable, example_script.name],
- capture_output=True,
- text=True,
- timeout=timeout,
- env=env,
- )
- except subprocess.TimeoutExpired:
- pytest.fail(f'Script {example_script} timed out after {timeout} seconds')
-
- assert result.returncode == 0, (
- f'Script {example_script} failed:\nSTDERR:\n{result.stderr}\nSTDOUT:\n{result.stdout}'
- )
-
-
-@pytest.mark.examples
-def test_dependent_examples():
- """Test examples that must run in order (complex_example.py generates data for complex_example_results.py)."""
- for script_path in DEPENDENT_EXAMPLES:
- script_full_path = EXAMPLES_DIR / script_path
-
- with working_directory(script_full_path.parent):
- timeout = 600
- # Set environment variable to disable interactive plotting
- env = os.environ.copy()
- env['FLIXOPT_CI'] = 'true'
- try:
- result = subprocess.run(
- [sys.executable, script_full_path.name],
- capture_output=True,
- text=True,
- timeout=timeout,
- env=env,
- )
- except subprocess.TimeoutExpired:
- pytest.fail(f'Script {script_path} timed out after {timeout} seconds')
-
- assert result.returncode == 0, f'{script_path} failed:\nSTDERR:\n{result.stderr}\nSTDOUT:\n{result.stdout}'
-
-
-if __name__ == '__main__':
- pytest.main(['-v', '--disable-warnings', '-m', 'examples'])
diff --git a/tests/test_solution_and_plotting.py b/tests/test_solution_and_plotting.py
index 88d92e91f..09f126613 100644
--- a/tests/test_solution_and_plotting.py
+++ b/tests/test_solution_and_plotting.py
@@ -170,7 +170,7 @@ class TestStatisticsAccessor:
"""Tests for flow_system.statistics accessor."""
def test_statistics_sizes_includes_all_flows(self, simple_flow_system, highs_solver):
- """Test that statistics.sizes includes all flow sizes (from InvestParameters)."""
+ """Test that statistics.sizes includes all flow and storage sizes (from InvestParameters)."""
simple_flow_system.optimize(highs_solver)
sizes = simple_flow_system.statistics.sizes
@@ -179,10 +179,12 @@ def test_statistics_sizes_includes_all_flows(self, simple_flow_system, highs_sol
# Should have sizes for flows with InvestParameters
assert len(sizes.data_vars) > 0
- # Check that all size labels are valid flow labels
+ # Check that all size labels are valid flow or storage labels
flow_labels = [f.label_full for f in simple_flow_system.flows.values()]
+ storage_labels = [s.label_full for s in simple_flow_system.storages.values()]
+ valid_labels = flow_labels + storage_labels
for label in sizes.data_vars:
- assert label in flow_labels, f'Size label {label} should be a valid flow'
+ assert label in valid_labels, f'Size label {label} should be a valid flow or storage'
def test_statistics_sizes_returns_correct_values(self, simple_flow_system, highs_solver):
"""Test that statistics.sizes returns correct size values."""
From 89d0aa2342a4e10e8c075e3a5ede16587567b46c Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Thu, 11 Dec 2025 09:00:27 +0100
Subject: [PATCH 28/49] Change default of Effect.description to ''
---
flixopt/effects.py | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/flixopt/effects.py b/flixopt/effects.py
index a7aae4bf4..cdac7ca7d 100644
--- a/flixopt/effects.py
+++ b/flixopt/effects.py
@@ -187,7 +187,7 @@ def __init__(
self,
label: str,
unit: str,
- description: str,
+ description: str = '',
meta_data: dict | None = None,
is_standard: bool = False,
is_objective: bool = False,
From ae7f0b06b7ccb7a56786a4a248418ee344ed1e8f Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Thu, 11 Dec 2025 09:47:30 +0100
Subject: [PATCH 29/49] Improve backwards compatability and allow saving the
solution directly
---
.pre-commit-config.yaml | 1 +
...tion-guide-v6.md => migration-guide-v5.md} | 80 +-
examples/00_Minmal/minimal_example.py | 36 +
examples/01_Simple/simple_example.py | 126 +
examples/02_Complex/complex_example.py | 207 +
.../02_Complex/complex_example_results.py | 38 +
.../example_optimization_modes.py | 245 +
examples/04_Scenarios/scenario_example.py | 214 +
.../two_stage_optimization.py | 186 +
examples/resources/Zeitreihen2020.csv | 35137 ++++++++++++++++
flixopt/flow_system.py | 73 +
flixopt/io.py | 226 +
flixopt/results.py | 89 +-
flixopt/structure.py | 48 +-
mkdocs.yml | 2 +-
tests/deprecated/test_examples.py | 94 +
.../v4-api/00_minimal--flow_system.nc4 | Bin 0 -> 46071 bytes
.../00_minimal--model_documentation.yaml | 213 +
.../v4-api/00_minimal--solution.nc4 | Bin 0 -> 42203 bytes
.../v4-api/00_minimal--summary.yaml | 46 +
.../v4-api/01_simple--flow_system.nc4 | Bin 0 -> 119706 bytes
.../01_simple--model_documentation.yaml | 848 +
.../ressources/v4-api/01_simple--solution.nc4 | Bin 0 -> 95968 bytes
.../ressources/v4-api/01_simple--summary.yaml | 51 +
.../v4-api/02_complex--flow_system.nc4 | Bin 0 -> 180475 bytes
.../02_complex--model_documentation.yaml | 1905 +
.../v4-api/02_complex--solution.nc4 | Bin 0 -> 181598 bytes
.../v4-api/02_complex--summary.yaml | 56 +
.../v4-api/04_scenarios--flow_system.nc4 | Bin 0 -> 62386 bytes
.../04_scenarios--model_documentation.yaml | 339 +
.../v4-api/04_scenarios--solution.nc4 | Bin 0 -> 64272 bytes
.../v4-api/04_scenarios--summary.yaml | 46 +
.../io_flow_system_base--flow_system.nc4 | Bin 0 -> 149245 bytes
...flow_system_base--model_documentation.yaml | 1758 +
.../v4-api/io_flow_system_base--solution.nc4 | Bin 0 -> 162802 bytes
.../v4-api/io_flow_system_base--summary.yaml | 56 +
.../io_flow_system_long--flow_system.nc4 | Bin 0 -> 161311 bytes
...flow_system_long--model_documentation.yaml | 1978 +
.../v4-api/io_flow_system_long--solution.nc4 | Bin 0 -> 183027 bytes
.../v4-api/io_flow_system_long--summary.yaml | 54 +
.../io_flow_system_segments--flow_system.nc4 | Bin 0 -> 181187 bytes
..._system_segments--model_documentation.yaml | 1914 +
.../io_flow_system_segments--solution.nc4 | Bin 0 -> 182466 bytes
.../io_flow_system_segments--summary.yaml | 56 +
.../io_simple_flow_system--flow_system.nc4 | Bin 0 -> 120032 bytes
...mple_flow_system--model_documentation.yaml | 944 +
.../io_simple_flow_system--solution.nc4 | Bin 0 -> 102763 bytes
.../io_simple_flow_system--summary.yaml | 51 +
...ple_flow_system_scenarios--flow_system.nc4 | Bin 0 -> 184035 bytes
...system_scenarios--model_documentation.yaml | 1375 +
...simple_flow_system_scenarios--solution.nc4 | Bin 0 -> 171583 bytes
...simple_flow_system_scenarios--summary.yaml | 51 +
tests/test_io_conversion.py | 773 +
53 files changed, 49264 insertions(+), 52 deletions(-)
rename docs/user-guide/{migration-guide-v6.md => migration-guide-v5.md} (85%)
create mode 100644 examples/00_Minmal/minimal_example.py
create mode 100644 examples/01_Simple/simple_example.py
create mode 100644 examples/02_Complex/complex_example.py
create mode 100644 examples/02_Complex/complex_example_results.py
create mode 100644 examples/03_Optimization_modes/example_optimization_modes.py
create mode 100644 examples/04_Scenarios/scenario_example.py
create mode 100644 examples/05_Two-stage-optimization/two_stage_optimization.py
create mode 100644 examples/resources/Zeitreihen2020.csv
create mode 100644 tests/deprecated/test_examples.py
create mode 100644 tests/ressources/v4-api/00_minimal--flow_system.nc4
create mode 100644 tests/ressources/v4-api/00_minimal--model_documentation.yaml
create mode 100644 tests/ressources/v4-api/00_minimal--solution.nc4
create mode 100644 tests/ressources/v4-api/00_minimal--summary.yaml
create mode 100644 tests/ressources/v4-api/01_simple--flow_system.nc4
create mode 100644 tests/ressources/v4-api/01_simple--model_documentation.yaml
create mode 100644 tests/ressources/v4-api/01_simple--solution.nc4
create mode 100644 tests/ressources/v4-api/01_simple--summary.yaml
create mode 100644 tests/ressources/v4-api/02_complex--flow_system.nc4
create mode 100644 tests/ressources/v4-api/02_complex--model_documentation.yaml
create mode 100644 tests/ressources/v4-api/02_complex--solution.nc4
create mode 100644 tests/ressources/v4-api/02_complex--summary.yaml
create mode 100644 tests/ressources/v4-api/04_scenarios--flow_system.nc4
create mode 100644 tests/ressources/v4-api/04_scenarios--model_documentation.yaml
create mode 100644 tests/ressources/v4-api/04_scenarios--solution.nc4
create mode 100644 tests/ressources/v4-api/04_scenarios--summary.yaml
create mode 100644 tests/ressources/v4-api/io_flow_system_base--flow_system.nc4
create mode 100644 tests/ressources/v4-api/io_flow_system_base--model_documentation.yaml
create mode 100644 tests/ressources/v4-api/io_flow_system_base--solution.nc4
create mode 100644 tests/ressources/v4-api/io_flow_system_base--summary.yaml
create mode 100644 tests/ressources/v4-api/io_flow_system_long--flow_system.nc4
create mode 100644 tests/ressources/v4-api/io_flow_system_long--model_documentation.yaml
create mode 100644 tests/ressources/v4-api/io_flow_system_long--solution.nc4
create mode 100644 tests/ressources/v4-api/io_flow_system_long--summary.yaml
create mode 100644 tests/ressources/v4-api/io_flow_system_segments--flow_system.nc4
create mode 100644 tests/ressources/v4-api/io_flow_system_segments--model_documentation.yaml
create mode 100644 tests/ressources/v4-api/io_flow_system_segments--solution.nc4
create mode 100644 tests/ressources/v4-api/io_flow_system_segments--summary.yaml
create mode 100644 tests/ressources/v4-api/io_simple_flow_system--flow_system.nc4
create mode 100644 tests/ressources/v4-api/io_simple_flow_system--model_documentation.yaml
create mode 100644 tests/ressources/v4-api/io_simple_flow_system--solution.nc4
create mode 100644 tests/ressources/v4-api/io_simple_flow_system--summary.yaml
create mode 100644 tests/ressources/v4-api/io_simple_flow_system_scenarios--flow_system.nc4
create mode 100644 tests/ressources/v4-api/io_simple_flow_system_scenarios--model_documentation.yaml
create mode 100644 tests/ressources/v4-api/io_simple_flow_system_scenarios--solution.nc4
create mode 100644 tests/ressources/v4-api/io_simple_flow_system_scenarios--summary.yaml
create mode 100644 tests/test_io_conversion.py
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 76c32d069..cfe4d0770 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -7,6 +7,7 @@ repos:
- id: check-yaml
exclude: ^mkdocs\.yml$ # Skip mkdocs.yml
- id: check-added-large-files
+ exclude: ^examples/resources/Zeitreihen2020\.csv$
- repo: https://github.com/astral-sh/ruff-pre-commit
rev: v0.12.4
diff --git a/docs/user-guide/migration-guide-v6.md b/docs/user-guide/migration-guide-v5.md
similarity index 85%
rename from docs/user-guide/migration-guide-v6.md
rename to docs/user-guide/migration-guide-v5.md
index 164ff5a28..856571a61 100644
--- a/docs/user-guide/migration-guide-v6.md
+++ b/docs/user-guide/migration-guide-v5.md
@@ -1,4 +1,4 @@
-# Migration Guide: v5.x → v6.0.0
+# Migration Guide: v4.x → v5.0.0
!!! tip "Quick Start"
```bash
@@ -10,9 +10,9 @@
## Overview
-v6.0.0 introduces a streamlined API for optimization and results access. The key changes are:
+v5.0.0 introduces a streamlined API for optimization and results access. The key changes are:
-| Aspect | Old API (v5.x) | New API (v6.0.0) |
+| Aspect | Old API (v4.x) | New API (v5.0.0) |
|--------|----------------|------------------|
| **Optimization** | `fx.Optimization` class | `FlowSystem.optimize()` method |
| **Results access** | `element.submodel.variable.solution` | `flow_system.solution['variable_name']` |
@@ -20,13 +20,13 @@ v6.0.0 introduces a streamlined API for optimization and results access. The key
---
-## 💥 Breaking Changes in v6.0.0
+## 💥 Breaking Changes in v5.0.0
### Optimization API
The `Optimization` class is removed. Use `FlowSystem.optimize()` directly.
-=== "v5.x (Old)"
+=== "v4.x (Old)"
```python
import flixopt as fx
@@ -44,7 +44,7 @@ The `Optimization` class is removed. Use `FlowSystem.optimize()` directly.
costs = results.model['costs'].solution.item()
```
-=== "v6.0.0 (New)"
+=== "v5.0.0 (New)"
```python
import flixopt as fx
@@ -74,7 +74,7 @@ Results are now accessed via `flow_system.solution`, which is an `xarray.Dataset
#### Effect Values
-=== "v5.x (Old)"
+=== "v4.x (Old)"
```python
# Via element reference
costs = flow_system.effects['costs']
@@ -84,7 +84,7 @@ Results are now accessed via `flow_system.solution`, which is an `xarray.Dataset
total_costs = optimization.results.model['costs'].solution.item()
```
-=== "v6.0.0 (New)"
+=== "v5.0.0 (New)"
```python
# Direct access via solution Dataset
total_costs = flow_system.solution['costs'].item()
@@ -97,27 +97,27 @@ Results are now accessed via `flow_system.solution`, which is an `xarray.Dataset
#### Flow Rates
-=== "v5.x (Old)"
+=== "v4.x (Old)"
```python
boiler = flow_system.components['Boiler']
flow_rate = boiler.thermal_flow.submodel.flow_rate.solution.values
```
-=== "v6.0.0 (New)"
+=== "v5.0.0 (New)"
```python
flow_rate = flow_system.solution['Boiler(Q_th)|flow_rate'].values
```
#### Investment Variables
-=== "v5.x (Old)"
+=== "v4.x (Old)"
```python
boiler = flow_system.components['Boiler']
size = boiler.thermal_flow.submodel.investment.size.solution.item()
invested = boiler.thermal_flow.submodel.investment.invested.solution.item()
```
-=== "v6.0.0 (New)"
+=== "v5.0.0 (New)"
```python
size = flow_system.solution['Boiler(Q_th)|size'].item()
invested = flow_system.solution['Boiler(Q_th)|invested'].item()
@@ -125,7 +125,7 @@ Results are now accessed via `flow_system.solution`, which is an `xarray.Dataset
#### Status Variables
-=== "v5.x (Old)"
+=== "v4.x (Old)"
```python
boiler = flow_system.components['Boiler']
status = boiler.thermal_flow.submodel.status.status.solution.values
@@ -133,7 +133,7 @@ Results are now accessed via `flow_system.solution`, which is an `xarray.Dataset
shutdown = boiler.thermal_flow.submodel.status.shutdown.solution.values
```
-=== "v6.0.0 (New)"
+=== "v5.0.0 (New)"
```python
status = flow_system.solution['Boiler(Q_th)|status'].values
startup = flow_system.solution['Boiler(Q_th)|startup'].values
@@ -142,14 +142,14 @@ Results are now accessed via `flow_system.solution`, which is an `xarray.Dataset
#### Storage Variables
-=== "v5.x (Old)"
+=== "v4.x (Old)"
```python
storage = flow_system.components['Speicher']
charge_state = storage.submodel.charge_state.solution.values
netto_discharge = storage.submodel.netto_discharge.solution.values
```
-=== "v6.0.0 (New)"
+=== "v5.0.0 (New)"
```python
charge_state = flow_system.solution['Speicher|charge_state'].values
netto_discharge = flow_system.solution['Speicher|netto_discharge'].values
@@ -214,12 +214,12 @@ boiler_vars = [v for v in flow_system.solution.data_vars if 'Boiler' in v]
### Saving Results
-=== "v5.x (Old)"
+=== "v4.x (Old)"
```python
optimization.results.to_file(folder='results', name='my_model')
```
-=== "v6.0.0 (New)"
+=== "v5.0.0 (New)"
```python
# Save entire FlowSystem with solution
flow_system.to_netcdf('results/my_model.nc4')
@@ -230,12 +230,12 @@ boiler_vars = [v for v in flow_system.solution.data_vars if 'Boiler' in v]
### Loading Results
-=== "v5.x (Old)"
+=== "v4.x (Old)"
```python
results = fx.results.Results.from_file('results', 'my_model')
```
-=== "v6.0.0 (New)"
+=== "v5.0.0 (New)"
```python
import xarray as xr
@@ -246,6 +246,35 @@ boiler_vars = [v for v in flow_system.solution.data_vars if 'Boiler' in v]
solution = xr.open_dataset('results/solution.nc4')
```
+### Migrating Old Result Files
+
+If you have result files saved with the old API (v4.x), you can migrate them to the new format using `FlowSystem.from_old_results()`. This method:
+
+- Loads the old multi-file format (`*--flow_system.nc4`, `*--solution.nc4`)
+- Renames deprecated parameters in the FlowSystem structure (e.g., `on_off_parameters` → `status_parameters`)
+- Attaches the solution data to the FlowSystem
+
+```python
+# Load old results
+flow_system = fx.FlowSystem.from_old_results('results_folder', 'my_model')
+
+# Access basic solution data (flow rates, sizes, charge states, etc.)
+flow_system.solution['Boiler(Q_th)|flow_rate'].plot()
+
+# Save in new single-file format
+flow_system.to_netcdf('results/my_model_migrated.nc4')
+```
+
+!!! warning "Limitations"
+ This is a best-effort migration for accessing old results:
+
+ - **Solution variable names are NOT renamed** - only basic variables work
+ (flow rates, sizes, charge states, effect totals)
+ - Advanced variable access may require using the original variable names
+ - Summary metadata (solver info, timing) is not loaded
+
+ For full compatibility, re-run optimizations with the new API.
+
---
## Working with xarray Dataset
@@ -278,7 +307,7 @@ df = flow_system.solution.to_dataframe()
The new API also applies to advanced optimization modes:
-=== "v5.x (Old)"
+=== "v4.x (Old)"
```python
calc = fx.SegmentedOptimization('model', flow_system,
timesteps_per_segment=96)
@@ -286,7 +315,7 @@ The new API also applies to advanced optimization modes:
results = calc.results
```
-=== "v6.0.0 (New)"
+=== "v5.0.0 (New)"
```python
# Use transform accessor for segmented optimization
flow_system.transform.segment(timesteps_per_segment=96)
@@ -343,8 +372,9 @@ stats.total_effects['costs'].groupby('component_type').sum()
| **Replace Optimization class** | Use `flow_system.optimize(solver)` instead |
| **Update results access** | Use `flow_system.solution['var_name']` pattern |
| **Update I/O code** | Use `to_netcdf()` / `from_netcdf()` |
+| **Migrate old result files** | Use `FlowSystem.from_old_results(folder, name)` |
| **Update transform methods** | Use `flow_system.transform.sel/isel/resample()` instead |
-| **Test thoroughly** | Verify results match v5.x outputs |
+| **Test thoroughly** | Verify results match v4.x outputs |
| **Remove deprecated imports** | Remove `fx.Optimization`, `fx.Results` |
---
@@ -382,8 +412,8 @@ The `sel()`, `isel()`, and `resample()` methods have been moved from `FlowSystem
| Version | Status |
|---------|--------|
-| v5.x | `Optimization` class deprecated with warning |
-| v6.0.0 | `Optimization` class removed, `sel/isel/resample` methods deprecated |
+| v4.x | `Optimization` and `Results` classes available |
+| v5.0.0 | `Optimization` and `Results` deprecated, new API available |
!!! warning "Update your code"
The `Optimization` and `Results` classes are deprecated and will be removed in a future version.
diff --git a/examples/00_Minmal/minimal_example.py b/examples/00_Minmal/minimal_example.py
new file mode 100644
index 000000000..207faa9a9
--- /dev/null
+++ b/examples/00_Minmal/minimal_example.py
@@ -0,0 +1,36 @@
+"""
+This script shows how to use the flixopt framework to model a super minimalistic energy system in the most concise way possible.
+THis can also be used to create proposals for new features, bug reports etc
+"""
+
+import numpy as np
+import pandas as pd
+
+import flixopt as fx
+
+if __name__ == '__main__':
+ fx.CONFIG.silent()
+ flow_system = fx.FlowSystem(pd.date_range('2020-01-01', periods=3, freq='h'))
+
+ flow_system.add_elements(
+ fx.Bus('Heat'),
+ fx.Bus('Gas'),
+ fx.Effect('Costs', '€', 'Cost', is_standard=True, is_objective=True),
+ fx.linear_converters.Boiler(
+ 'Boiler',
+ thermal_efficiency=0.5,
+ thermal_flow=fx.Flow(label='Heat', bus='Heat', size=50),
+ fuel_flow=fx.Flow(label='Gas', bus='Gas'),
+ ),
+ fx.Sink(
+ 'Sink',
+ inputs=[fx.Flow(label='Demand', bus='Heat', size=1, fixed_relative_profile=np.array([30, 0, 20]))],
+ ),
+ fx.Source(
+ 'Source',
+ outputs=[fx.Flow(label='Gas', bus='Gas', size=1000, effects_per_flow_hour=0.04)],
+ ),
+ )
+
+ flow_system.optimize(fx.solvers.HighsSolver(0.01, 60))
+ flow_system.statistics.plot.balance('Heat')
diff --git a/examples/01_Simple/simple_example.py b/examples/01_Simple/simple_example.py
new file mode 100644
index 000000000..b63260ece
--- /dev/null
+++ b/examples/01_Simple/simple_example.py
@@ -0,0 +1,126 @@
+"""
+This script shows how to use the flixopt framework to model a simple energy system.
+"""
+
+import numpy as np
+import pandas as pd
+
+import flixopt as fx
+
+if __name__ == '__main__':
+ fx.CONFIG.exploring()
+
+ # --- Create Time Series Data ---
+ # Heat demand profile (e.g., kW) over time and corresponding power prices
+ heat_demand_per_h = np.array([30, 0, 90, 110, 110, 20, 20, 20, 20])
+ power_prices = 1 / 1000 * np.array([80, 80, 80, 80, 80, 80, 80, 80, 80])
+
+ # Create datetime array starting from '2020-01-01' for the given time period
+ timesteps = pd.date_range('2020-01-01', periods=len(heat_demand_per_h), freq='h')
+ flow_system = fx.FlowSystem(timesteps=timesteps)
+
+ # --- Define Energy Buses ---
+ # These represent nodes, where the used medias are balanced (electricity, heat, and gas)
+ # Carriers provide automatic color assignment in plots (yellow for electricity, red for heat, etc.)
+ flow_system.add_elements(
+ fx.Bus(label='Strom', carrier='electricity'),
+ fx.Bus(label='Fernwärme', carrier='heat'),
+ fx.Bus(label='Gas', carrier='gas'),
+ )
+
+ # --- Define Effects (Objective and CO2 Emissions) ---
+ # Cost effect: used as the optimization objective --> minimizing costs
+ costs = fx.Effect(
+ label='costs',
+ unit='€',
+ description='Kosten',
+ is_standard=True, # standard effect: no explicit value needed for costs
+ is_objective=True, # Minimizing costs as the optimization objective
+ share_from_temporal={'CO2': 0.2},
+ )
+
+ # CO2 emissions effect with an associated cost impact
+ CO2 = fx.Effect(
+ label='CO2',
+ unit='kg',
+ description='CO2_e-Emissionen',
+ maximum_per_hour=1000, # Max CO2 emissions per hour
+ )
+
+ # --- Define Flow System Components ---
+ # Boiler: Converts fuel (gas) into thermal energy (heat)
+ boiler = fx.linear_converters.Boiler(
+ label='Boiler',
+ thermal_efficiency=0.5,
+ thermal_flow=fx.Flow(label='Q_th', bus='Fernwärme', size=50, relative_minimum=0.1, relative_maximum=1),
+ fuel_flow=fx.Flow(label='Q_fu', bus='Gas'),
+ )
+
+ # Combined Heat and Power (CHP): Generates both electricity and heat from fuel
+ chp = fx.linear_converters.CHP(
+ label='CHP',
+ thermal_efficiency=0.5,
+ electrical_efficiency=0.4,
+ electrical_flow=fx.Flow('P_el', bus='Strom', size=60, relative_minimum=5 / 60),
+ thermal_flow=fx.Flow('Q_th', bus='Fernwärme'),
+ fuel_flow=fx.Flow('Q_fu', bus='Gas'),
+ )
+
+ # Storage: Energy storage system with charging and discharging capabilities
+ storage = fx.Storage(
+ label='Storage',
+ charging=fx.Flow('Q_th_load', bus='Fernwärme', size=1000),
+ discharging=fx.Flow('Q_th_unload', bus='Fernwärme', size=1000),
+ capacity_in_flow_hours=fx.InvestParameters(effects_of_investment=20, fixed_size=30, mandatory=True),
+ initial_charge_state=0, # Initial storage state: empty
+ relative_maximum_charge_state=1 / 100 * np.array([80, 70, 80, 80, 80, 80, 80, 80, 80]),
+ relative_maximum_final_charge_state=0.8,
+ eta_charge=0.9,
+ eta_discharge=1, # Efficiency factors for charging/discharging
+ relative_loss_per_hour=0.08, # 8% loss per hour. Absolute loss depends on current charge state
+ prevent_simultaneous_charge_and_discharge=True, # Prevent charging and discharging at the same time
+ )
+
+ # Heat Demand Sink: Represents a fixed heat demand profile
+ heat_sink = fx.Sink(
+ label='Heat Demand',
+ inputs=[fx.Flow(label='Q_th_Last', bus='Fernwärme', size=1, fixed_relative_profile=heat_demand_per_h)],
+ )
+
+ # Gas Source: Gas tariff source with associated costs and CO2 emissions
+ gas_source = fx.Source(
+ label='Gastarif',
+ outputs=[
+ fx.Flow(label='Q_Gas', bus='Gas', size=1000, effects_per_flow_hour={costs.label: 0.04, CO2.label: 0.3})
+ ],
+ )
+
+ # Power Sink: Represents the export of electricity to the grid
+ power_sink = fx.Sink(
+ label='Einspeisung', inputs=[fx.Flow(label='P_el', bus='Strom', effects_per_flow_hour=-1 * power_prices)]
+ )
+
+ # --- Build the Flow System ---
+ # Add all defined components and effects to the flow system
+ flow_system.add_elements(costs, CO2, boiler, storage, chp, heat_sink, gas_source, power_sink)
+
+ # Visualize the flow system for validation purposes
+ flow_system.topology.plot()
+
+ # --- Define and Solve Optimization ---
+ flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0, time_limit_seconds=30))
+
+ # --- Analyze Results ---
+ # Plotting through statistics accessor - returns PlotResult with .data and .figure
+ flow_system.statistics.plot.balance('Fernwärme')
+ flow_system.statistics.plot.balance('Storage')
+ flow_system.statistics.plot.heatmap('CHP(Q_th)')
+ flow_system.statistics.plot.heatmap('Storage')
+
+ # Access data as xarray Datasets
+ print(flow_system.statistics.flow_rates)
+ print(flow_system.statistics.charge_states)
+
+ # Duration curve and effects analysis
+ flow_system.statistics.plot.duration_curve('Boiler(Q_th)')
+ print(flow_system.statistics.temporal_effects)
diff --git a/examples/02_Complex/complex_example.py b/examples/02_Complex/complex_example.py
new file mode 100644
index 000000000..3f38ff954
--- /dev/null
+++ b/examples/02_Complex/complex_example.py
@@ -0,0 +1,207 @@
+"""
+This script shows how to use the flixopt framework to model a more complex energy system.
+"""
+
+import numpy as np
+import pandas as pd
+
+import flixopt as fx
+
+if __name__ == '__main__':
+ fx.CONFIG.exploring()
+
+ # --- Experiment Options ---
+ # Configure options for testing various parameters and behaviors
+ check_penalty = False
+ imbalance_penalty = 1e5
+ use_chp_with_piecewise_conversion = True
+
+ # --- Define Demand and Price Profiles ---
+ # Input data for electricity and heat demands, as well as electricity price
+ electricity_demand = np.array([70, 80, 90, 90, 90, 90, 90, 90, 90])
+ heat_demand = (
+ np.array([30, 0, 90, 110, 2000, 20, 20, 20, 20])
+ if check_penalty
+ else np.array([30, 0, 90, 110, 110, 20, 20, 20, 20])
+ )
+ electricity_price = np.array([40, 40, 40, 40, 40, 40, 40, 40, 40])
+
+ # --- Define the Flow System, that will hold all elements, and the time steps you want to model ---
+ timesteps = pd.date_range('2020-01-01', periods=len(heat_demand), freq='h')
+ flow_system = fx.FlowSystem(timesteps) # Create FlowSystem
+
+ # --- Define Energy Buses ---
+ # Represent node balances (inputs=outputs) for the different energy carriers (electricity, heat, gas) in the system
+ # Carriers provide automatic color assignment in plots (yellow for electricity, red for heat, blue for gas)
+ flow_system.add_elements(
+ fx.Bus('Strom', carrier='electricity', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Fernwärme', carrier='heat', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Gas', carrier='gas', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ )
+
+ # --- Define Effects ---
+ # Specify effects related to costs, CO2 emissions, and primary energy consumption
+ Costs = fx.Effect('costs', '€', 'Kosten', is_standard=True, is_objective=True, share_from_temporal={'CO2': 0.2})
+ CO2 = fx.Effect('CO2', 'kg', 'CO2_e-Emissionen')
+ PE = fx.Effect('PE', 'kWh_PE', 'Primärenergie', maximum_total=3.5e3)
+
+ # --- Define Components ---
+ # 1. Define Boiler Component
+ # A gas boiler that converts fuel into thermal output, with investment and on-inactive parameters
+ Gaskessel = fx.linear_converters.Boiler(
+ 'Kessel',
+ thermal_efficiency=0.5, # Efficiency ratio
+ status_parameters=fx.StatusParameters(
+ effects_per_active_hour={Costs.label: 0, CO2.label: 1000}
+ ), # CO2 emissions per hour
+ thermal_flow=fx.Flow(
+ label='Q_th', # Thermal output
+ bus='Fernwärme', # Linked bus
+ size=fx.InvestParameters(
+ effects_of_investment=1000, # Fixed investment costs
+ fixed_size=50, # Fixed size
+ mandatory=True, # Forced investment
+ effects_of_investment_per_size={Costs.label: 10, PE.label: 2}, # Specific costs
+ ),
+ load_factor_max=1.0, # Maximum load factor (50 kW)
+ load_factor_min=0.1, # Minimum load factor (5 kW)
+ relative_minimum=5 / 50, # Minimum part load
+ relative_maximum=1, # Maximum part load
+ previous_flow_rate=50, # Previous flow rate
+ flow_hours_max=1e6, # Total energy flow limit
+ status_parameters=fx.StatusParameters(
+ active_hours_min=0, # Minimum operating hours
+ active_hours_max=1000, # Maximum operating hours
+ max_uptime=10, # Max consecutive operating hours
+ min_uptime=np.array([1, 1, 1, 1, 1, 2, 2, 2, 2]), # min consecutive operation hours
+ max_downtime=10, # Max consecutive inactive hours
+ effects_per_startup={Costs.label: 0.01}, # Cost per startup
+ startup_limit=1000, # Max number of starts
+ ),
+ ),
+ fuel_flow=fx.Flow(label='Q_fu', bus='Gas', size=200),
+ )
+
+ # 2. Define CHP Unit
+ # Combined Heat and Power unit that generates both electricity and heat from fuel
+ bhkw = fx.linear_converters.CHP(
+ 'BHKW2',
+ thermal_efficiency=0.5,
+ electrical_efficiency=0.4,
+ status_parameters=fx.StatusParameters(effects_per_startup={Costs.label: 0.01}),
+ electrical_flow=fx.Flow('P_el', bus='Strom', size=60, relative_minimum=5 / 60),
+ thermal_flow=fx.Flow('Q_th', bus='Fernwärme', size=1e3),
+ fuel_flow=fx.Flow('Q_fu', bus='Gas', size=1e3, previous_flow_rate=20), # The CHP was ON previously
+ )
+
+ # 3. Define CHP with Piecewise Conversion
+ # This CHP unit uses piecewise conversion for more dynamic behavior over time
+ P_el = fx.Flow('P_el', bus='Strom', size=60, previous_flow_rate=20)
+ Q_th = fx.Flow('Q_th', bus='Fernwärme')
+ Q_fu = fx.Flow('Q_fu', bus='Gas')
+ piecewise_conversion = fx.PiecewiseConversion(
+ {
+ P_el.label: fx.Piecewise([fx.Piece(5, 30), fx.Piece(40, 60)]),
+ Q_th.label: fx.Piecewise([fx.Piece(6, 35), fx.Piece(45, 100)]),
+ Q_fu.label: fx.Piecewise([fx.Piece(12, 70), fx.Piece(90, 200)]),
+ }
+ )
+
+ bhkw_2 = fx.LinearConverter(
+ 'BHKW2',
+ inputs=[Q_fu],
+ outputs=[P_el, Q_th],
+ piecewise_conversion=piecewise_conversion,
+ status_parameters=fx.StatusParameters(effects_per_startup={Costs.label: 0.01}),
+ )
+
+ # 4. Define Storage Component
+ # Storage with variable size and piecewise investment effects
+ segmented_investment_effects = fx.PiecewiseEffects(
+ piecewise_origin=fx.Piecewise([fx.Piece(5, 25), fx.Piece(25, 100)]),
+ piecewise_shares={
+ Costs.label: fx.Piecewise([fx.Piece(50, 250), fx.Piece(250, 800)]),
+ PE.label: fx.Piecewise([fx.Piece(5, 25), fx.Piece(25, 100)]),
+ },
+ )
+
+ speicher = fx.Storage(
+ 'Speicher',
+ charging=fx.Flow('Q_th_load', bus='Fernwärme', size=1e4),
+ discharging=fx.Flow('Q_th_unload', bus='Fernwärme', size=1e4),
+ capacity_in_flow_hours=fx.InvestParameters(
+ piecewise_effects_of_investment=segmented_investment_effects, # Investment effects
+ mandatory=True, # Forced investment
+ minimum_size=0,
+ maximum_size=1000, # Optimizing between 0 and 1000 kWh
+ ),
+ initial_charge_state=0, # Initial charge state
+ maximal_final_charge_state=10, # Maximum final charge state
+ eta_charge=0.9,
+ eta_discharge=1, # Charge/discharge efficiency
+ relative_loss_per_hour=0.08, # Energy loss per hour, relative to current charge state
+ prevent_simultaneous_charge_and_discharge=True, # Prevent simultaneous charge/discharge
+ )
+
+ # 5. Define Sinks and Sources
+ # 5.a) Heat demand profile
+ Waermelast = fx.Sink(
+ 'Wärmelast',
+ inputs=[
+ fx.Flow(
+ 'Q_th_Last', # Heat sink
+ bus='Fernwärme', # Linked bus
+ size=1,
+ fixed_relative_profile=heat_demand, # Fixed demand profile
+ )
+ ],
+ )
+
+ # 5.b) Gas tariff
+ Gasbezug = fx.Source(
+ 'Gastarif',
+ outputs=[
+ fx.Flow(
+ 'Q_Gas',
+ bus='Gas', # Gas source
+ size=1000, # Nominal size
+ effects_per_flow_hour={Costs.label: 0.04, CO2.label: 0.3},
+ )
+ ],
+ )
+
+ # 5.c) Feed-in of electricity
+ Stromverkauf = fx.Sink(
+ 'Einspeisung',
+ inputs=[
+ fx.Flow(
+ 'P_el',
+ bus='Strom', # Feed-in tariff for electricity
+ effects_per_flow_hour=-1 * electricity_price, # Negative price for feed-in
+ )
+ ],
+ )
+
+ # --- Build FlowSystem ---
+ # Select components to be included in the flow system
+ flow_system.add_elements(Costs, CO2, PE, Gaskessel, Waermelast, Gasbezug, Stromverkauf, speicher)
+ flow_system.add_elements(bhkw_2) if use_chp_with_piecewise_conversion else flow_system.add_elements(bhkw)
+
+ print(flow_system) # Get a string representation of the FlowSystem
+ try:
+ flow_system.topology.start_app() # Start the network app
+ except ImportError as e:
+ print(f'Network app requires extra dependencies: {e}')
+
+ # --- Solve FlowSystem ---
+ flow_system.optimize(fx.solvers.HighsSolver(0.01, 60))
+
+ # --- Results ---
+ # Save the flow system with solution to file for later analysis
+ flow_system.to_netcdf('results/complex_example.nc')
+
+ # Plot results using the statistics accessor
+ flow_system.statistics.plot.heatmap('BHKW2(Q_th)') # Flow label - auto-resolves to flow_rate
+ flow_system.statistics.plot.balance('BHKW2')
+ flow_system.statistics.plot.heatmap('Speicher') # Storage label - auto-resolves to charge_state
+ flow_system.statistics.plot.balance('Fernwärme')
diff --git a/examples/02_Complex/complex_example_results.py b/examples/02_Complex/complex_example_results.py
new file mode 100644
index 000000000..6978caff1
--- /dev/null
+++ b/examples/02_Complex/complex_example_results.py
@@ -0,0 +1,38 @@
+"""
+This script shows how to load results of a prior optimization and how to analyze them.
+"""
+
+import flixopt as fx
+
+if __name__ == '__main__':
+ fx.CONFIG.exploring()
+
+ # --- Load FlowSystem with Solution ---
+ try:
+ flow_system = fx.FlowSystem.from_netcdf('results/complex_example.nc')
+ except FileNotFoundError as e:
+ raise FileNotFoundError(
+ f"Results file not found ('results/complex_example.nc'). "
+ f"Please ensure that the file is generated by running 'complex_example.py'. "
+ f'Original error: {e}'
+ ) from e
+
+ # --- Basic overview ---
+ flow_system.topology.plot()
+ flow_system.statistics.plot.balance('Fernwärme')
+
+ # --- Detailed Plots ---
+ # In-depth plot for individual flow rates
+ flow_system.statistics.plot.heatmap('Wärmelast(Q_th_Last)|flow_rate')
+
+ # Plot balances for all buses
+ for bus in flow_system.buses.values():
+ flow_system.statistics.plot.balance(bus.label).to_html(f'results/{bus.label}--balance.html')
+
+ # --- Plotting internal variables manually ---
+ flow_system.statistics.plot.heatmap('BHKW2(Q_th)|status')
+ flow_system.statistics.plot.heatmap('Kessel(Q_th)|status')
+
+ # Access data as DataFrames:
+ print(flow_system.statistics.flow_rates.to_dataframe())
+ print(flow_system.solution.to_dataframe())
diff --git a/examples/03_Optimization_modes/example_optimization_modes.py b/examples/03_Optimization_modes/example_optimization_modes.py
new file mode 100644
index 000000000..1f9968357
--- /dev/null
+++ b/examples/03_Optimization_modes/example_optimization_modes.py
@@ -0,0 +1,245 @@
+"""
+This script demonstrates how to use the different calculation types in the flixopt framework
+to model the same energy system. The results will be compared to each other.
+"""
+
+import pathlib
+
+import pandas as pd
+import xarray as xr
+
+import flixopt as fx
+
+
+# Get solutions for plotting for different optimizations
+def get_solutions(optimizations: list, variable: str) -> xr.Dataset:
+ dataarrays = []
+ for optimization in optimizations:
+ if optimization.name == 'Segmented':
+ # SegmentedOptimization requires special handling to remove overlaps
+ dataarrays.append(optimization.results.solution_without_overlap(variable).rename(optimization.name))
+ else:
+ # For Full and Clustered, access solution from the flow_system
+ dataarrays.append(optimization.flow_system.solution[variable].rename(optimization.name))
+ return xr.merge(dataarrays, join='outer')
+
+
+if __name__ == '__main__':
+ fx.CONFIG.exploring()
+
+ # Calculation Types
+ full, segmented, aggregated = True, True, True
+
+ # Segmented Properties
+ segment_length, overlap_length = 96, 1
+
+ # Aggregated Properties
+ clustering_parameters = fx.ClusteringParameters(
+ hours_per_period=6,
+ nr_of_periods=4,
+ fix_storage_flows=False,
+ aggregate_data_and_fix_non_binary_vars=True,
+ percentage_of_period_freedom=0,
+ penalty_of_period_freedom=0,
+ )
+ keep_extreme_periods = True
+ imbalance_penalty = 1e5 # or set to None if not needed
+
+ # Data Import
+ data_import = pd.read_csv(
+ pathlib.Path(__file__).parent.parent / 'resources' / 'Zeitreihen2020.csv', index_col=0
+ ).sort_index()
+ filtered_data = data_import['2020-01-01':'2020-01-07 23:45:00']
+ # filtered_data = data_import[0:500] # Alternatively filter by index
+
+ filtered_data.index = pd.to_datetime(filtered_data.index)
+ timesteps = filtered_data.index
+
+ # Access specific columns and convert to 1D-numpy array
+ electricity_demand = filtered_data['P_Netz/MW'].to_numpy()
+ heat_demand = filtered_data['Q_Netz/MW'].to_numpy()
+ electricity_price = filtered_data['Strompr.€/MWh'].to_numpy()
+ gas_price = filtered_data['Gaspr.€/MWh'].to_numpy()
+
+ # TimeSeriesData objects
+ TS_heat_demand = fx.TimeSeriesData(heat_demand)
+ TS_electricity_demand = fx.TimeSeriesData(electricity_demand, clustering_weight=0.7)
+ TS_electricity_price_sell = fx.TimeSeriesData(-(electricity_price - 0.5), clustering_group='p_el')
+ TS_electricity_price_buy = fx.TimeSeriesData(electricity_price + 0.5, clustering_group='p_el')
+
+ flow_system = fx.FlowSystem(timesteps)
+ flow_system.add_elements(
+ fx.Bus('Strom', carrier='electricity', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Fernwärme', carrier='heat', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Gas', carrier='gas', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ fx.Bus('Kohle', carrier='fuel', imbalance_penalty_per_flow_hour=imbalance_penalty),
+ )
+
+ # Effects
+ costs = fx.Effect('costs', '€', 'Kosten', is_standard=True, is_objective=True)
+ CO2 = fx.Effect('CO2', 'kg', 'CO2_e-Emissionen')
+ PE = fx.Effect('PE', 'kWh_PE', 'Primärenergie')
+
+ # Component Definitions
+
+ # 1. Boiler
+ a_gaskessel = fx.linear_converters.Boiler(
+ 'Kessel',
+ thermal_efficiency=0.85,
+ thermal_flow=fx.Flow(label='Q_th', bus='Fernwärme'),
+ fuel_flow=fx.Flow(
+ label='Q_fu',
+ bus='Gas',
+ size=95,
+ relative_minimum=12 / 95,
+ previous_flow_rate=20,
+ status_parameters=fx.StatusParameters(effects_per_startup=1000),
+ ),
+ )
+
+ # 2. CHP
+ a_kwk = fx.linear_converters.CHP(
+ 'BHKW2',
+ thermal_efficiency=0.58,
+ electrical_efficiency=0.22,
+ status_parameters=fx.StatusParameters(effects_per_startup=24000),
+ electrical_flow=fx.Flow('P_el', bus='Strom', size=200),
+ thermal_flow=fx.Flow('Q_th', bus='Fernwärme', size=200),
+ fuel_flow=fx.Flow('Q_fu', bus='Kohle', size=288, relative_minimum=87 / 288, previous_flow_rate=100),
+ )
+
+ # 3. Storage
+ a_speicher = fx.Storage(
+ 'Speicher',
+ capacity_in_flow_hours=684,
+ initial_charge_state=137,
+ minimal_final_charge_state=137,
+ maximal_final_charge_state=158,
+ eta_charge=1,
+ eta_discharge=1,
+ relative_loss_per_hour=0.001,
+ prevent_simultaneous_charge_and_discharge=True,
+ charging=fx.Flow('Q_th_load', size=137, bus='Fernwärme'),
+ discharging=fx.Flow('Q_th_unload', size=158, bus='Fernwärme'),
+ )
+
+ # 4. Sinks and Sources
+ # Heat Load Profile
+ a_waermelast = fx.Sink(
+ 'Wärmelast', inputs=[fx.Flow('Q_th_Last', bus='Fernwärme', size=1, fixed_relative_profile=TS_heat_demand)]
+ )
+
+ # Electricity Feed-in
+ a_strom_last = fx.Sink(
+ 'Stromlast', inputs=[fx.Flow('P_el_Last', bus='Strom', size=1, fixed_relative_profile=TS_electricity_demand)]
+ )
+
+ # Gas Tariff
+ a_gas_tarif = fx.Source(
+ 'Gastarif',
+ outputs=[
+ fx.Flow('Q_Gas', bus='Gas', size=1000, effects_per_flow_hour={costs.label: gas_price, CO2.label: 0.3})
+ ],
+ )
+
+ # Coal Tariff
+ a_kohle_tarif = fx.Source(
+ 'Kohletarif',
+ outputs=[fx.Flow('Q_Kohle', bus='Kohle', size=1000, effects_per_flow_hour={costs.label: 4.6, CO2.label: 0.3})],
+ )
+
+ # Electricity Tariff and Feed-in
+ a_strom_einspeisung = fx.Sink(
+ 'Einspeisung', inputs=[fx.Flow('P_el', bus='Strom', size=1000, effects_per_flow_hour=TS_electricity_price_sell)]
+ )
+
+ a_strom_tarif = fx.Source(
+ 'Stromtarif',
+ outputs=[
+ fx.Flow(
+ 'P_el',
+ bus='Strom',
+ size=1000,
+ effects_per_flow_hour={costs.label: TS_electricity_price_buy, CO2.label: 0.3},
+ )
+ ],
+ )
+
+ # Flow System Setup
+ flow_system.add_elements(costs, CO2, PE)
+ flow_system.add_elements(
+ a_gaskessel,
+ a_waermelast,
+ a_strom_last,
+ a_gas_tarif,
+ a_kohle_tarif,
+ a_strom_einspeisung,
+ a_strom_tarif,
+ a_kwk,
+ a_speicher,
+ )
+ flow_system.topology.plot()
+
+ # Optimizations
+ optimizations: list[fx.Optimization | fx.ClusteredOptimization | fx.SegmentedOptimization] = []
+
+ if full:
+ optimization = fx.Optimization('Full', flow_system.copy())
+ optimization.do_modeling()
+ optimization.solve(fx.solvers.HighsSolver(0.01 / 100, 60))
+ optimizations.append(optimization)
+
+ if segmented:
+ optimization = fx.SegmentedOptimization('Segmented', flow_system.copy(), segment_length, overlap_length)
+ optimization.do_modeling_and_solve(fx.solvers.HighsSolver(0.01 / 100, 60))
+ optimizations.append(optimization)
+
+ if aggregated:
+ if keep_extreme_periods:
+ clustering_parameters.time_series_for_high_peaks = [TS_heat_demand]
+ clustering_parameters.time_series_for_low_peaks = [TS_electricity_demand, TS_heat_demand]
+ optimization = fx.ClusteredOptimization('Aggregated', flow_system.copy(), clustering_parameters)
+ optimization.do_modeling()
+ optimization.solve(fx.solvers.HighsSolver(0.01 / 100, 60))
+ optimizations.append(optimization)
+
+ # --- Plotting for comparison ---
+ fx.plotting.with_plotly(
+ get_solutions(optimizations, 'Speicher|charge_state'),
+ mode='line',
+ title='Charge State Comparison',
+ ylabel='Charge state',
+ xlabel='Time in h',
+ ).write_html('results/Charge State.html')
+
+ fx.plotting.with_plotly(
+ get_solutions(optimizations, 'BHKW2(Q_th)|flow_rate'),
+ mode='line',
+ title='BHKW2(Q_th) Flow Rate Comparison',
+ ylabel='Flow rate',
+ xlabel='Time in h',
+ ).write_html('results/BHKW2 Thermal Power.html')
+
+ fx.plotting.with_plotly(
+ get_solutions(optimizations, 'costs(temporal)|per_timestep'),
+ mode='line',
+ title='Operation Cost Comparison',
+ ylabel='Costs [€]',
+ xlabel='Time in h',
+ ).write_html('results/Operation Costs.html')
+
+ fx.plotting.with_plotly(
+ get_solutions(optimizations, 'costs(temporal)|per_timestep').sum('time'),
+ mode='stacked_bar',
+ title='Total Cost Comparison',
+ ylabel='Costs [€]',
+ ).update_layout(barmode='group').write_html('results/Total Costs.html')
+
+ fx.plotting.with_plotly(
+ pd.DataFrame(
+ [calc.durations for calc in optimizations], index=[calc.name for calc in optimizations]
+ ).to_xarray(),
+ mode='stacked_bar',
+ ).update_layout(title='Duration Comparison', xaxis_title='Optimization type', yaxis_title='Time (s)').write_html(
+ 'results/Speed Comparison.html'
+ )
diff --git a/examples/04_Scenarios/scenario_example.py b/examples/04_Scenarios/scenario_example.py
new file mode 100644
index 000000000..820336e93
--- /dev/null
+++ b/examples/04_Scenarios/scenario_example.py
@@ -0,0 +1,214 @@
+"""
+This script shows how to use the flixopt framework to model a simple energy system.
+"""
+
+import numpy as np
+import pandas as pd
+
+import flixopt as fx
+
+if __name__ == '__main__':
+ fx.CONFIG.exploring()
+
+ # Create datetime array starting from '2020-01-01' for one week
+ timesteps = pd.date_range('2020-01-01', periods=24 * 7, freq='h')
+ scenarios = pd.Index(['Base Case', 'High Demand'])
+ periods = pd.Index([2020, 2021, 2022])
+
+ # --- Create Time Series Data ---
+ # Realistic daily patterns: morning/evening peaks, night/midday lows
+ np.random.seed(42)
+ n_hours = len(timesteps)
+
+ # Heat demand: 24-hour patterns (kW) for Base Case and High Demand scenarios
+ base_daily_pattern = np.array(
+ [22, 20, 18, 18, 20, 25, 40, 70, 95, 110, 85, 65, 60, 58, 62, 68, 75, 88, 105, 125, 130, 122, 95, 35]
+ )
+ high_daily_pattern = np.array(
+ [28, 25, 22, 22, 24, 30, 52, 88, 118, 135, 105, 80, 75, 72, 75, 82, 92, 108, 128, 148, 155, 145, 115, 48]
+ )
+
+ # Tile and add variation
+ base_demand = np.tile(base_daily_pattern, n_hours // 24 + 1)[:n_hours] * (
+ 1 + np.random.uniform(-0.05, 0.05, n_hours)
+ )
+ high_demand = np.tile(high_daily_pattern, n_hours // 24 + 1)[:n_hours] * (
+ 1 + np.random.uniform(-0.07, 0.07, n_hours)
+ )
+
+ heat_demand_per_h = pd.DataFrame({'Base Case': base_demand, 'High Demand': high_demand}, index=timesteps)
+
+ # Power prices: hourly factors (night low, peak high) and period escalation (2020-2022)
+ hourly_price_factors = np.array(
+ [
+ 0.70,
+ 0.65,
+ 0.62,
+ 0.60,
+ 0.62,
+ 0.70,
+ 0.95,
+ 1.15,
+ 1.30,
+ 1.25,
+ 1.10,
+ 1.00,
+ 0.95,
+ 0.90,
+ 0.88,
+ 0.92,
+ 1.00,
+ 1.10,
+ 1.25,
+ 1.40,
+ 1.35,
+ 1.20,
+ 0.95,
+ 0.80,
+ ]
+ )
+ period_base_prices = np.array([0.075, 0.095, 0.135]) # €/kWh for 2020, 2021, 2022
+
+ price_series = np.zeros((n_hours, 3))
+ for period_idx, base_price in enumerate(period_base_prices):
+ price_series[:, period_idx] = (
+ np.tile(hourly_price_factors, n_hours // 24 + 1)[:n_hours]
+ * base_price
+ * (1 + np.random.uniform(-0.03, 0.03, n_hours))
+ )
+
+ power_prices = price_series.mean(axis=0)
+
+ # Scenario weights: probability of each scenario occurring
+ # Base Case: 60% probability, High Demand: 40% probability
+ scenario_weights = np.array([0.6, 0.4])
+
+ flow_system = fx.FlowSystem(
+ timesteps=timesteps, periods=periods, scenarios=scenarios, scenario_weights=scenario_weights
+ )
+
+ # --- Define Energy Buses ---
+ # These represent nodes, where the used medias are balanced (electricity, heat, and gas)
+ # Carriers provide automatic color assignment in plots (yellow for electricity, red for heat, blue for gas)
+ flow_system.add_elements(
+ fx.Bus(label='Strom', carrier='electricity'),
+ fx.Bus(label='Fernwärme', carrier='heat'),
+ fx.Bus(label='Gas', carrier='gas'),
+ )
+
+ # --- Define Effects (Objective and CO2 Emissions) ---
+ # Cost effect: used as the optimization objective --> minimizing costs
+ costs = fx.Effect(
+ label='costs',
+ unit='€',
+ description='Kosten',
+ is_standard=True, # standard effect: no explicit value needed for costs
+ is_objective=True, # Minimizing costs as the optimization objective
+ share_from_temporal={'CO2': 0.2}, # Carbon price: 0.2 €/kg CO2 (e.g., carbon tax)
+ )
+
+ # CO2 emissions effect with constraint
+ # Maximum of 1000 kg CO2/hour represents a regulatory or voluntary emissions limit
+ CO2 = fx.Effect(
+ label='CO2',
+ unit='kg',
+ description='CO2_e-Emissionen',
+ maximum_per_hour=1000, # Regulatory emissions limit: 1000 kg CO2/hour
+ )
+
+ # --- Define Flow System Components ---
+ # Boiler: Converts fuel (gas) into thermal energy (heat)
+ # Modern condensing gas boiler with realistic efficiency
+ boiler = fx.linear_converters.Boiler(
+ label='Boiler',
+ thermal_efficiency=0.92, # Realistic efficiency for modern condensing gas boiler (92%)
+ thermal_flow=fx.Flow(
+ label='Q_th',
+ bus='Fernwärme',
+ size=100,
+ relative_minimum=0.1,
+ relative_maximum=1,
+ status_parameters=fx.StatusParameters(),
+ ),
+ fuel_flow=fx.Flow(label='Q_fu', bus='Gas'),
+ )
+
+ # Combined Heat and Power (CHP): Generates both electricity and heat from fuel
+ # Modern CHP unit with realistic efficiencies (total efficiency ~88%)
+ chp = fx.linear_converters.CHP(
+ label='CHP',
+ thermal_efficiency=0.48, # Realistic thermal efficiency (48%)
+ electrical_efficiency=0.40, # Realistic electrical efficiency (40%)
+ electrical_flow=fx.Flow(
+ 'P_el', bus='Strom', size=80, relative_minimum=5 / 80, status_parameters=fx.StatusParameters()
+ ),
+ thermal_flow=fx.Flow('Q_th', bus='Fernwärme'),
+ fuel_flow=fx.Flow('Q_fu', bus='Gas'),
+ )
+
+ # Storage: Thermal energy storage system with charging and discharging capabilities
+ # Realistic thermal storage parameters (e.g., insulated hot water tank)
+ storage = fx.Storage(
+ label='Storage',
+ charging=fx.Flow('Q_th_load', bus='Fernwärme', size=1000),
+ discharging=fx.Flow('Q_th_unload', bus='Fernwärme', size=1000),
+ capacity_in_flow_hours=fx.InvestParameters(effects_of_investment=20, fixed_size=30, mandatory=True),
+ initial_charge_state=0, # Initial storage state: empty
+ relative_maximum_final_charge_state=np.array([0.8, 0.5, 0.1]),
+ eta_charge=0.95, # Realistic charging efficiency (~95%)
+ eta_discharge=0.98, # Realistic discharging efficiency (~98%)
+ relative_loss_per_hour=np.array([0.008, 0.015]), # Realistic thermal losses: 0.8-1.5% per hour
+ prevent_simultaneous_charge_and_discharge=True, # Prevent charging and discharging at the same time
+ )
+
+ # Heat Demand Sink: Represents a fixed heat demand profile
+ heat_sink = fx.Sink(
+ label='Heat Demand',
+ inputs=[fx.Flow(label='Q_th_Last', bus='Fernwärme', size=1, fixed_relative_profile=heat_demand_per_h)],
+ )
+
+ # Gas Source: Gas tariff source with associated costs and CO2 emissions
+ # Realistic gas prices varying by period (reflecting 2020-2022 energy crisis)
+ # 2020: 0.04 €/kWh, 2021: 0.06 €/kWh, 2022: 0.11 €/kWh
+ gas_prices_per_period = np.array([0.04, 0.06, 0.11])
+
+ # CO2 emissions factor for natural gas: ~0.202 kg CO2/kWh (realistic value)
+ gas_co2_emissions = 0.202
+
+ gas_source = fx.Source(
+ label='Gastarif',
+ outputs=[
+ fx.Flow(
+ label='Q_Gas',
+ bus='Gas',
+ size=1000,
+ effects_per_flow_hour={costs.label: gas_prices_per_period, CO2.label: gas_co2_emissions},
+ )
+ ],
+ )
+
+ # Power Sink: Represents the export of electricity to the grid
+ power_sink = fx.Sink(
+ label='Einspeisung', inputs=[fx.Flow(label='P_el', bus='Strom', effects_per_flow_hour=-1 * power_prices)]
+ )
+
+ # --- Build the Flow System ---
+ # Add all defined components and effects to the flow system
+ flow_system.add_elements(costs, CO2, boiler, storage, chp, heat_sink, gas_source, power_sink)
+
+ # Visualize the flow system for validation purposes
+ flow_system.topology.plot()
+
+ # --- Define and Solve Optimization ---
+ flow_system.optimize(fx.solvers.HighsSolver(mip_gap=0, time_limit_seconds=30))
+
+ # --- Analyze Results ---
+ # Plotting through statistics accessor - returns PlotResult with .data and .figure
+ flow_system.statistics.plot.heatmap('CHP(Q_th)') # Flow label - auto-resolves to flow_rate
+ flow_system.statistics.plot.balance('Fernwärme')
+ flow_system.statistics.plot.balance('Storage')
+ flow_system.statistics.plot.heatmap('Storage') # Storage label - auto-resolves to charge_state
+
+ # Access data as xarray Datasets
+ print(flow_system.statistics.flow_rates)
+ print(flow_system.statistics.charge_states)
diff --git a/examples/05_Two-stage-optimization/two_stage_optimization.py b/examples/05_Two-stage-optimization/two_stage_optimization.py
new file mode 100644
index 000000000..3f3278477
--- /dev/null
+++ b/examples/05_Two-stage-optimization/two_stage_optimization.py
@@ -0,0 +1,186 @@
+"""
+This script demonstrates how to use downsampling of a FlowSystem to effectively reduce the size of a model.
+This can be very useful when working with large models or during development,
+as it can drastically reduce the computational time.
+This leads to faster results and easier debugging.
+A common use case is to optimize the investments of a model with a downsampled version of the original model, and then fix the computed sizes when calculating the actual dispatch.
+While the final optimum might differ from the global optimum, the solving will be much faster.
+"""
+
+import logging
+import pathlib
+import timeit
+
+import numpy as np
+import pandas as pd
+import xarray as xr
+
+import flixopt as fx
+
+logger = logging.getLogger('flixopt')
+
+if __name__ == '__main__':
+ fx.CONFIG.exploring()
+
+ # Data Import
+ data_import = pd.read_csv(
+ pathlib.Path(__file__).parent.parent / 'resources' / 'Zeitreihen2020.csv', index_col=0
+ ).sort_index()
+ filtered_data = data_import[:500]
+
+ filtered_data.index = pd.to_datetime(filtered_data.index)
+ timesteps = filtered_data.index
+
+ # Access specific columns and convert to 1D-numpy array
+ electricity_demand = filtered_data['P_Netz/MW'].to_numpy()
+ heat_demand = filtered_data['Q_Netz/MW'].to_numpy()
+ electricity_price = filtered_data['Strompr.€/MWh'].to_numpy()
+ gas_price = filtered_data['Gaspr.€/MWh'].to_numpy()
+
+ flow_system = fx.FlowSystem(timesteps)
+ # Carriers provide automatic color assignment in plots
+ flow_system.add_elements(
+ fx.Bus('Strom', carrier='electricity'),
+ fx.Bus('Fernwärme', carrier='heat'),
+ fx.Bus('Gas', carrier='gas'),
+ fx.Bus('Kohle', carrier='fuel'),
+ fx.Effect('costs', '€', 'Kosten', is_standard=True, is_objective=True),
+ fx.Effect('CO2', 'kg', 'CO2_e-Emissionen'),
+ fx.Effect('PE', 'kWh_PE', 'Primärenergie'),
+ fx.linear_converters.Boiler(
+ 'Kessel',
+ thermal_efficiency=0.85,
+ thermal_flow=fx.Flow(label='Q_th', bus='Fernwärme'),
+ fuel_flow=fx.Flow(
+ label='Q_fu',
+ bus='Gas',
+ size=fx.InvestParameters(
+ effects_of_investment_per_size={'costs': 1_000}, minimum_size=10, maximum_size=600
+ ),
+ relative_minimum=0.2,
+ previous_flow_rate=20,
+ status_parameters=fx.StatusParameters(effects_per_startup=300),
+ ),
+ ),
+ fx.linear_converters.CHP(
+ 'BHKW2',
+ thermal_efficiency=0.58,
+ electrical_efficiency=0.22,
+ status_parameters=fx.StatusParameters(effects_per_startup=1_000, min_uptime=10, min_downtime=10),
+ electrical_flow=fx.Flow('P_el', bus='Strom'),
+ thermal_flow=fx.Flow('Q_th', bus='Fernwärme'),
+ fuel_flow=fx.Flow(
+ 'Q_fu',
+ bus='Kohle',
+ size=fx.InvestParameters(
+ effects_of_investment_per_size={'costs': 3_000}, minimum_size=10, maximum_size=500
+ ),
+ relative_minimum=0.3,
+ previous_flow_rate=100,
+ ),
+ ),
+ fx.Storage(
+ 'Speicher',
+ capacity_in_flow_hours=fx.InvestParameters(
+ minimum_size=10, maximum_size=1000, effects_of_investment_per_size={'costs': 60}
+ ),
+ initial_charge_state='equals_final',
+ eta_charge=1,
+ eta_discharge=1,
+ relative_loss_per_hour=0.001,
+ prevent_simultaneous_charge_and_discharge=True,
+ charging=fx.Flow('Q_th_load', size=200, bus='Fernwärme'),
+ discharging=fx.Flow('Q_th_unload', size=200, bus='Fernwärme'),
+ ),
+ fx.Sink(
+ 'Wärmelast', inputs=[fx.Flow('Q_th_Last', bus='Fernwärme', size=1, fixed_relative_profile=heat_demand)]
+ ),
+ fx.Source(
+ 'Gastarif',
+ outputs=[fx.Flow('Q_Gas', bus='Gas', size=1000, effects_per_flow_hour={'costs': gas_price, 'CO2': 0.3})],
+ ),
+ fx.Source(
+ 'Kohletarif',
+ outputs=[fx.Flow('Q_Kohle', bus='Kohle', size=1000, effects_per_flow_hour={'costs': 4.6, 'CO2': 0.3})],
+ ),
+ fx.Source(
+ 'Einspeisung',
+ outputs=[
+ fx.Flow(
+ 'P_el', bus='Strom', size=1000, effects_per_flow_hour={'costs': electricity_price + 0.5, 'CO2': 0.3}
+ )
+ ],
+ ),
+ fx.Sink(
+ 'Stromlast',
+ inputs=[fx.Flow('P_el_Last', bus='Strom', size=1, fixed_relative_profile=electricity_demand)],
+ ),
+ fx.Source(
+ 'Stromtarif',
+ outputs=[
+ fx.Flow('P_el', bus='Strom', size=1000, effects_per_flow_hour={'costs': electricity_price, 'CO2': 0.3})
+ ],
+ ),
+ )
+
+ # Separate optimization of flow sizes and dispatch
+ # Stage 1: Optimize sizes using downsampled (2h) data
+ start = timeit.default_timer()
+ calculation_sizing = fx.Optimization('Sizing', flow_system.resample('2h'))
+ calculation_sizing.do_modeling()
+ calculation_sizing.solve(fx.solvers.HighsSolver(0.1 / 100, 60))
+ timer_sizing = timeit.default_timer() - start
+
+ # Stage 2: Optimize dispatch with fixed sizes from Stage 1
+ start = timeit.default_timer()
+ calculation_dispatch = fx.Optimization('Dispatch', flow_system)
+ calculation_dispatch.do_modeling()
+ calculation_dispatch.fix_sizes(calculation_sizing.flow_system.solution)
+ calculation_dispatch.solve(fx.solvers.HighsSolver(0.1 / 100, 60))
+ timer_dispatch = timeit.default_timer() - start
+
+ # Verify sizes were correctly fixed
+ dispatch_sizes = calculation_dispatch.flow_system.statistics.sizes
+ sizing_sizes = calculation_sizing.flow_system.statistics.sizes
+ if np.allclose(dispatch_sizes.to_dataarray(), sizing_sizes.to_dataarray(), rtol=1e-5):
+ logger.info('Sizes were correctly equalized')
+ else:
+ raise RuntimeError('Sizes were not correctly equalized')
+
+ # Combined optimization: optimize both sizes and dispatch together
+ start = timeit.default_timer()
+ calculation_combined = fx.Optimization('Combined', flow_system)
+ calculation_combined.do_modeling()
+ calculation_combined.solve(fx.solvers.HighsSolver(0.1 / 100, 600))
+ timer_combined = timeit.default_timer() - start
+
+ # Comparison of results - access solutions from flow_system
+ comparison = xr.concat(
+ [calculation_combined.flow_system.solution, calculation_dispatch.flow_system.solution], dim='mode'
+ ).assign_coords(mode=['Combined', 'Two-stage'])
+ comparison['Duration [s]'] = xr.DataArray([timer_combined, timer_sizing + timer_dispatch], dims='mode')
+
+ comparison_main = comparison[
+ [
+ 'Duration [s]',
+ 'costs',
+ 'costs(periodic)',
+ 'costs(temporal)',
+ 'BHKW2(Q_fu)|size',
+ 'Kessel(Q_fu)|size',
+ 'Speicher|size',
+ ]
+ ]
+ comparison_main = xr.concat(
+ [
+ comparison_main,
+ (
+ (comparison_main.sel(mode='Two-stage') - comparison_main.sel(mode='Combined'))
+ / comparison_main.sel(mode='Combined')
+ * 100
+ ).assign_coords(mode='Diff [%]'),
+ ],
+ dim='mode',
+ )
+
+ print(comparison_main.to_pandas().T.round(2))
diff --git a/examples/resources/Zeitreihen2020.csv b/examples/resources/Zeitreihen2020.csv
new file mode 100644
index 000000000..9b660ef9c
--- /dev/null
+++ b/examples/resources/Zeitreihen2020.csv
@@ -0,0 +1,35137 @@
+Zeit,P_Netz/MW,Q_Netz/MW,Strompr.€/MWh,Gaspr.€/MWh
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+2020-12-31 18:45:00,137.6,199.16,68.803,32.468
+2020-12-31 19:00:00,134.26,200.084,72.934,32.468
+2020-12-31 19:15:00,133.22,196.468,72.934,32.468
+2020-12-31 19:30:00,134.64,194.42700000000002,72.934,32.468
+2020-12-31 19:45:00,136.88,190.43900000000002,72.934,32.468
+2020-12-31 20:00:00,130.24,186.864,65.175,32.468
+2020-12-31 20:15:00,119.33,181.132,65.175,32.468
+2020-12-31 20:30:00,118.31,177.201,65.175,32.468
+2020-12-31 20:45:00,112.7,174.72400000000002,65.175,32.468
+2020-12-31 21:00:00,107.44,172.49,58.55,32.468
+2020-12-31 21:15:00,112.86,170.146,58.55,32.468
+2020-12-31 21:30:00,111.93,168.03,58.55,32.468
+2020-12-31 21:45:00,108.29,166.609,58.55,32.468
+2020-12-31 22:00:00,98.52,160.079,55.041000000000004,32.468
+2020-12-31 22:15:00,94.85,154.757,55.041000000000004,32.468
+2020-12-31 22:30:00,98.1,141.22899999999998,55.041000000000004,32.468
+2020-12-31 22:45:00,96.62,133.488,55.041000000000004,32.468
+2020-12-31 23:00:00,92.22,127.7,48.258,32.468
+2020-12-31 23:15:00,84.12,125.64200000000001,48.258,32.468
+2020-12-31 23:30:00,79.31,126.145,48.258,32.468
+2020-12-31 23:45:00,83.54,125.553,48.258,32.468
diff --git a/flixopt/flow_system.py b/flixopt/flow_system.py
index 7a71efee9..e28e37368 100644
--- a/flixopt/flow_system.py
+++ b/flixopt/flow_system.py
@@ -754,6 +754,79 @@ def from_netcdf(cls, path: str | pathlib.Path) -> FlowSystem:
flow_system.name = path.stem
return flow_system
+ @classmethod
+ def from_old_results(cls, folder: str | pathlib.Path, name: str) -> FlowSystem:
+ """
+ Load a FlowSystem from old-format Results files (pre-v5 API).
+
+ This method loads results saved with the deprecated Results API
+ (which used multiple files: ``*--flow_system.nc4``, ``*--solution.nc4``)
+ and converts them to a FlowSystem with the solution attached.
+
+ The method performs the following:
+
+ - Loads the old multi-file format
+ - Renames deprecated parameters in the FlowSystem structure
+ (e.g., ``on_off_parameters`` → ``status_parameters``)
+ - Attaches the solution data to the FlowSystem
+
+ Args:
+ folder: Directory containing the saved result files
+ name: Base name of the saved files (without extensions)
+
+ Returns:
+ FlowSystem instance with solution attached
+
+ Warning:
+ This is a best-effort migration for accessing old results:
+
+ - **Solution variable names are NOT renamed** - only basic variables
+ work (flow rates, sizes, charge states, effect totals)
+ - Advanced variable access may require using the original names
+ - Summary metadata (solver info, timing) is not loaded
+
+ For full compatibility, re-run optimizations with the new API.
+
+ Examples:
+ ```python
+ # Load old results
+ fs = FlowSystem.from_old_results('results_folder', 'my_optimization')
+
+ # Access basic solution data
+ fs.solution['Boiler(Q_th)|flow_rate'].plot()
+
+ # Save in new single-file format
+ fs.to_netcdf('my_optimization.nc')
+ ```
+ """
+ import json
+
+ from flixopt.io import convert_old_dataset, load_dataset_from_netcdf
+
+ folder = pathlib.Path(folder)
+
+ # Load datasets directly (old format used --flow_system.nc4 and --solution.nc4)
+ flow_system_path = folder / f'{name}--flow_system.nc4'
+ solution_path = folder / f'{name}--solution.nc4'
+
+ flow_system_data = load_dataset_from_netcdf(flow_system_path)
+ solution = load_dataset_from_netcdf(solution_path)
+
+ # Convert flow_system_data to new parameter names
+ convert_old_dataset(flow_system_data)
+
+ # Reconstruct FlowSystem
+ flow_system = cls.from_dataset(flow_system_data)
+ flow_system.name = name
+
+ # Attach solution (convert attrs from dicts to JSON strings for consistency)
+ for key in ['Components', 'Buses', 'Effects', 'Flows']:
+ if key in solution.attrs and isinstance(solution.attrs[key], dict):
+ solution.attrs[key] = json.dumps(solution.attrs[key])
+ flow_system.solution = solution
+
+ return flow_system
+
def copy(self) -> FlowSystem:
"""Create a copy of the FlowSystem without optimization state.
diff --git a/flixopt/io.py b/flixopt/io.py
index 27bc242ff..0994b841d 100644
--- a/flixopt/io.py
+++ b/flixopt/io.py
@@ -597,6 +597,232 @@ def load_dataset_from_netcdf(path: str | pathlib.Path) -> xr.Dataset:
return ds
+# Parameter rename mappings for backwards compatibility conversion
+# Format: {old_name: new_name}
+PARAMETER_RENAMES = {
+ # Effect parameters
+ 'minimum_operation': 'minimum_temporal',
+ 'maximum_operation': 'maximum_temporal',
+ 'minimum_invest': 'minimum_periodic',
+ 'maximum_invest': 'maximum_periodic',
+ 'minimum_investment': 'minimum_periodic',
+ 'maximum_investment': 'maximum_periodic',
+ 'minimum_operation_per_hour': 'minimum_per_hour',
+ 'maximum_operation_per_hour': 'maximum_per_hour',
+ # InvestParameters
+ 'fix_effects': 'effects_of_investment',
+ 'specific_effects': 'effects_of_investment_per_size',
+ 'divest_effects': 'effects_of_retirement',
+ 'piecewise_effects': 'piecewise_effects_of_investment',
+ # Flow/OnOffParameters
+ 'flow_hours_total_max': 'flow_hours_max',
+ 'flow_hours_total_min': 'flow_hours_min',
+ 'on_hours_total_max': 'on_hours_max',
+ 'on_hours_total_min': 'on_hours_min',
+ 'switch_on_total_max': 'switch_on_max',
+ # Bus
+ 'excess_penalty_per_flow_hour': 'imbalance_penalty_per_flow_hour',
+ # Component parameters (Source/Sink)
+ 'source': 'outputs',
+ 'sink': 'inputs',
+ 'prevent_simultaneous_sink_and_source': 'prevent_simultaneous_flow_rates',
+ # LinearConverter flow/efficiency parameters (pre-v4 files)
+ # These are needed for very old files that use short flow names
+ 'Q_fu': 'fuel_flow',
+ 'P_el': 'electrical_flow',
+ 'Q_th': 'thermal_flow',
+ 'Q_ab': 'heat_source_flow',
+ 'eta': 'thermal_efficiency',
+ 'eta_th': 'thermal_efficiency',
+ 'eta_el': 'electrical_efficiency',
+ 'COP': 'cop',
+ # Storage
+ # Note: 'lastValueOfSim' → 'equals_final' is a value change, not a key change
+ # Class renames (v4.2.0)
+ 'FullCalculation': 'Optimization',
+ 'AggregatedCalculation': 'ClusteredOptimization',
+ 'SegmentedCalculation': 'SegmentedOptimization',
+ 'CalculationResults': 'Results',
+ 'SegmentedCalculationResults': 'SegmentedResults',
+ 'Aggregation': 'Clustering',
+ 'AggregationParameters': 'ClusteringParameters',
+ 'AggregationModel': 'ClusteringModel',
+ # OnOffParameters → StatusParameters (class and attribute names)
+ 'OnOffParameters': 'StatusParameters',
+ 'on_off_parameters': 'status_parameters',
+ # StatusParameters attribute renames (applies to both Flow-level and Component-level)
+ 'effects_per_switch_on': 'effects_per_startup',
+ 'effects_per_running_hour': 'effects_per_active_hour',
+ 'consecutive_on_hours_min': 'min_uptime',
+ 'consecutive_on_hours_max': 'max_uptime',
+ 'consecutive_off_hours_min': 'min_downtime',
+ 'consecutive_off_hours_max': 'max_downtime',
+ # TimeSeriesData
+ 'agg_group': 'aggregation_group',
+ 'agg_weight': 'aggregation_weight',
+}
+
+# Value renames (for specific parameter values that changed)
+VALUE_RENAMES = {
+ 'initial_charge_state': {'lastValueOfSim': 'equals_final'},
+}
+
+
+# Keys that should NOT have their child keys renamed (they reference flow labels)
+_FLOW_LABEL_REFERENCE_KEYS = {'piecewises', 'conversion_factors'}
+
+# Keys that ARE flow parameters on components (should be renamed)
+_FLOW_PARAMETER_KEYS = {'Q_fu', 'P_el', 'Q_th', 'Q_ab', 'eta', 'eta_th', 'eta_el', 'COP'}
+
+
+def _rename_keys_recursive(
+ obj: Any,
+ key_renames: dict[str, str],
+ value_renames: dict[str, dict],
+ skip_flow_renames: bool = False,
+) -> Any:
+ """Recursively rename keys and values in nested data structures.
+
+ Args:
+ obj: The object to process (dict, list, or scalar)
+ key_renames: Mapping of old key names to new key names
+ value_renames: Mapping of key names to {old_value: new_value} dicts
+ skip_flow_renames: If True, skip renaming flow parameter keys (for inside piecewises)
+
+ Returns:
+ The processed object with renamed keys and values
+ """
+ if isinstance(obj, dict):
+ new_dict = {}
+ for key, value in obj.items():
+ # Determine if we should skip flow renames for children
+ child_skip_flow_renames = skip_flow_renames or key in _FLOW_LABEL_REFERENCE_KEYS
+
+ # Rename the key if needed (skip flow params if in reference context)
+ if skip_flow_renames and key in _FLOW_PARAMETER_KEYS:
+ new_key = key # Don't rename flow labels inside piecewises etc.
+ else:
+ new_key = key_renames.get(key, key)
+
+ # Process the value recursively
+ new_value = _rename_keys_recursive(value, key_renames, value_renames, child_skip_flow_renames)
+
+ # Check if this key has value renames
+ if key in value_renames and isinstance(new_value, str):
+ new_value = value_renames[key].get(new_value, new_value)
+
+ # Handle __class__ values - rename class names
+ if key == '__class__' and isinstance(new_value, str):
+ new_value = key_renames.get(new_value, new_value)
+
+ new_dict[new_key] = new_value
+ return new_dict
+
+ elif isinstance(obj, list):
+ return [_rename_keys_recursive(item, key_renames, value_renames, skip_flow_renames) for item in obj]
+
+ else:
+ return obj
+
+
+def convert_old_dataset(
+ ds: xr.Dataset,
+ key_renames: dict[str, str] | None = None,
+ value_renames: dict[str, dict] | None = None,
+) -> xr.Dataset:
+ """Convert an old FlowSystem dataset to use new parameter names.
+
+ This function updates the reference structure in a dataset's attrs to use
+ the current parameter naming conventions. This is useful for loading
+ FlowSystem files saved with older versions of flixopt.
+
+ Args:
+ ds: The dataset to convert (will be modified in place)
+ key_renames: Custom key renames to apply. If None, uses PARAMETER_RENAMES.
+ value_renames: Custom value renames to apply. If None, uses VALUE_RENAMES.
+
+ Returns:
+ The converted dataset (same object, modified in place)
+
+ Examples:
+ Convert an old netCDF file to new format:
+
+ ```python
+ from flixopt import io
+
+ # Load old file
+ ds = io.load_dataset_from_netcdf('old_flow_system.nc4')
+
+ # Convert parameter names
+ ds = io.convert_old_dataset(ds)
+
+ # Now load as FlowSystem
+ from flixopt import FlowSystem
+
+ fs = FlowSystem.from_dataset(ds)
+ ```
+ """
+ if key_renames is None:
+ key_renames = PARAMETER_RENAMES
+ if value_renames is None:
+ value_renames = VALUE_RENAMES
+
+ # Convert the attrs (reference_structure)
+ ds.attrs = _rename_keys_recursive(ds.attrs, key_renames, value_renames)
+
+ return ds
+
+
+def convert_old_netcdf(
+ input_path: str | pathlib.Path,
+ output_path: str | pathlib.Path | None = None,
+ compression: int = 0,
+) -> xr.Dataset:
+ """Load an old FlowSystem netCDF file and convert to new parameter names.
+
+ This is a convenience function that combines loading, conversion, and
+ optionally saving the converted dataset.
+
+ Args:
+ input_path: Path to the old netCDF file
+ output_path: If provided, save the converted dataset to this path.
+ If None, only returns the converted dataset without saving.
+ compression: Compression level (0-9) for saving. Only used if output_path is provided.
+
+ Returns:
+ The converted dataset
+
+ Examples:
+ Convert and save to new file:
+
+ ```python
+ from flixopt import io
+
+ # Convert old file to new format
+ ds = io.convert_old_netcdf('old_system.nc4', 'new_system.nc')
+ ```
+
+ Convert and load as FlowSystem:
+
+ ```python
+ from flixopt import FlowSystem, io
+
+ ds = io.convert_old_netcdf('old_system.nc4')
+ fs = FlowSystem.from_dataset(ds)
+ ```
+ """
+ # Load and convert
+ ds = load_dataset_from_netcdf(input_path)
+ ds = convert_old_dataset(ds)
+
+ # Optionally save
+ if output_path is not None:
+ save_dataset_to_netcdf(ds, output_path, compression=compression)
+ logger.info(f'Converted {input_path} -> {output_path}')
+
+ return ds
+
+
@dataclass
class ResultsPaths:
"""Container for all paths related to saving Results."""
diff --git a/flixopt/results.py b/flixopt/results.py
index edcbb7a87..16d88743a 100644
--- a/flixopt/results.py
+++ b/flixopt/results.py
@@ -2,6 +2,7 @@
import copy
import datetime
+import json
import logging
import pathlib
import warnings
@@ -47,6 +48,18 @@ def load_mapping_from_file(path: pathlib.Path) -> dict[str, str | list[str]]:
return fx_io.load_config_file(path)
+def _get_solution_attr(solution: xr.Dataset, key: str) -> dict:
+ """Get an attribute from solution, decoding JSON if necessary.
+
+ Solution attrs are stored as JSON strings for netCDF compatibility.
+ This helper handles both JSON strings and dicts (for backward compatibility).
+ """
+ value = solution.attrs.get(key, {})
+ if isinstance(value, str):
+ return json.loads(value)
+ return value
+
+
class _FlowSystemRestorationError(Exception):
"""Exception raised when a FlowSystem cannot be restored from dataset."""
@@ -225,7 +238,8 @@ def __init__(
warnings.warn(
f'Results is deprecated and will be removed in v{DEPRECATION_REMOVAL_VERSION}. '
'Access results directly via FlowSystem.solution after optimization, or use the '
- '.plot accessor on FlowSystem and its components (e.g., flow_system.plot.heatmap(...)).',
+ '.plot accessor on FlowSystem and its components (e.g., flow_system.plot.heatmap(...)). '
+ 'To load old result files, use FlowSystem.from_old_results(folder, name).',
DeprecationWarning,
stacklevel=2,
)
@@ -239,19 +253,25 @@ def __init__(
# Create ResultsContainers for better access patterns
components_dict = {
- label: ComponentResults(self, **infos) for label, infos in self.solution.attrs['Components'].items()
+ label: ComponentResults(self, **infos)
+ for label, infos in _get_solution_attr(self.solution, 'Components').items()
}
self.components = ResultsContainer(
elements=components_dict, element_type_name='component results', truncate_repr=10
)
- buses_dict = {label: BusResults(self, **infos) for label, infos in self.solution.attrs['Buses'].items()}
+ buses_dict = {
+ label: BusResults(self, **infos) for label, infos in _get_solution_attr(self.solution, 'Buses').items()
+ }
self.buses = ResultsContainer(elements=buses_dict, element_type_name='bus results', truncate_repr=10)
- effects_dict = {label: EffectResults(self, **infos) for label, infos in self.solution.attrs['Effects'].items()}
+ effects_dict = {
+ label: EffectResults(self, **infos) for label, infos in _get_solution_attr(self.solution, 'Effects').items()
+ }
self.effects = ResultsContainer(elements=effects_dict, element_type_name='effect results', truncate_repr=10)
- if 'Flows' not in self.solution.attrs:
+ flows_attr = _get_solution_attr(self.solution, 'Flows')
+ if not flows_attr:
warnings.warn(
'No Data about flows found in the results. This data is only included since v2.2.0. Some functionality '
'is not availlable. We recommend to evaluate your results with a version <2.2.0.',
@@ -260,9 +280,7 @@ def __init__(
flows_dict = {}
self._has_flow_data = False
else:
- flows_dict = {
- label: FlowResults(self, **infos) for label, infos in self.solution.attrs.get('Flows', {}).items()
- }
+ flows_dict = {label: FlowResults(self, **infos) for label, infos in flows_attr.items()}
self._has_flow_data = True
self.flows = ResultsContainer(elements=flows_dict, element_type_name='flow results', truncate_repr=10)
@@ -1111,6 +1129,61 @@ def plot_network(
path = self.folder / f'{self.name}--network.html'
return self.flow_system.plot_network(controls=controls, path=path, show=show)
+ def to_flow_system(self) -> FlowSystem:
+ """Convert Results to a FlowSystem with solution attached.
+
+ This method migrates results from the deprecated Results format to the
+ new FlowSystem-based format, enabling use of the modern API.
+
+ Note:
+ For loading old results files directly, consider using
+ ``FlowSystem.from_old_results(folder, name)`` instead.
+
+ Returns:
+ FlowSystem: A FlowSystem instance with the solution data attached.
+
+ Caveats:
+ - The linopy model is NOT attached (only the solution data)
+ - Element submodels are NOT recreated (no re-optimization without
+ calling build_model() first)
+ - Variable/constraint names on elements are NOT restored
+
+ Examples:
+ Convert loaded Results to FlowSystem:
+
+ ```python
+ # Load old results
+ results = Results.from_file('results', 'my_optimization')
+
+ # Convert to FlowSystem
+ flow_system = results.to_flow_system()
+
+ # Use new API
+ flow_system.plot.heatmap()
+ flow_system.solution.to_netcdf('solution.nc')
+
+ # Save in new single-file format
+ flow_system.to_netcdf('my_optimization.nc')
+ ```
+ """
+ from flixopt.io import convert_old_dataset
+
+ # Convert flow_system_data to new parameter names
+ convert_old_dataset(self.flow_system_data)
+
+ # Reconstruct FlowSystem from stored data
+ flow_system = FlowSystem.from_dataset(self.flow_system_data)
+
+ # Convert solution attrs from dicts to JSON strings for consistency with new format
+ # The _get_solution_attr helper handles both formats, but we normalize here
+ solution = self.solution.copy()
+ for key in ['Components', 'Buses', 'Effects', 'Flows']:
+ if key in solution.attrs and isinstance(solution.attrs[key], dict):
+ solution.attrs[key] = json.dumps(solution.attrs[key])
+
+ flow_system.solution = solution
+ return flow_system
+
def to_file(
self,
folder: str | pathlib.Path | None = None,
diff --git a/flixopt/structure.py b/flixopt/structure.py
index 63d028660..536b2a697 100644
--- a/flixopt/structure.py
+++ b/flixopt/structure.py
@@ -6,6 +6,7 @@
from __future__ import annotations
import inspect
+import json
import logging
import pathlib
import re
@@ -169,25 +170,36 @@ def solution(self):
"""Build solution dataset, reindexing to timesteps_extra for consistency."""
solution = super().solution
solution['objective'] = self.objective.value
+ # Store attrs as JSON strings for netCDF compatibility
solution.attrs = {
- 'Components': {
- comp.label_full: comp.submodel.results_structure()
- for comp in sorted(
- self.flow_system.components.values(), key=lambda component: component.label_full.upper()
- )
- },
- 'Buses': {
- bus.label_full: bus.submodel.results_structure()
- for bus in sorted(self.flow_system.buses.values(), key=lambda bus: bus.label_full.upper())
- },
- 'Effects': {
- effect.label_full: effect.submodel.results_structure()
- for effect in sorted(self.flow_system.effects.values(), key=lambda effect: effect.label_full.upper())
- },
- 'Flows': {
- flow.label_full: flow.submodel.results_structure()
- for flow in sorted(self.flow_system.flows.values(), key=lambda flow: flow.label_full.upper())
- },
+ 'Components': json.dumps(
+ {
+ comp.label_full: comp.submodel.results_structure()
+ for comp in sorted(
+ self.flow_system.components.values(), key=lambda component: component.label_full.upper()
+ )
+ }
+ ),
+ 'Buses': json.dumps(
+ {
+ bus.label_full: bus.submodel.results_structure()
+ for bus in sorted(self.flow_system.buses.values(), key=lambda bus: bus.label_full.upper())
+ }
+ ),
+ 'Effects': json.dumps(
+ {
+ effect.label_full: effect.submodel.results_structure()
+ for effect in sorted(
+ self.flow_system.effects.values(), key=lambda effect: effect.label_full.upper()
+ )
+ }
+ ),
+ 'Flows': json.dumps(
+ {
+ flow.label_full: flow.submodel.results_structure()
+ for flow in sorted(self.flow_system.flows.values(), key=lambda flow: flow.label_full.upper())
+ }
+ ),
}
# Ensure solution is always indexed by timesteps_extra for consistency.
# Variables without extra timestep data will have NaN at the final timestep.
diff --git a/mkdocs.yml b/mkdocs.yml
index 5ce16769e..f414c1ab4 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -45,7 +45,7 @@ nav:
- Troubleshooting: user-guide/troubleshooting.md
- Community: user-guide/support.md
- Migration & Updates:
- - Migration Guide v6: user-guide/migration-guide-v6.md
+ - Migration Guide v5: user-guide/migration-guide-v5.md
- Migration Guide v3: user-guide/migration-guide-v3.md
- Release Notes: changelog.md
- Roadmap: roadmap.md
diff --git a/tests/deprecated/test_examples.py b/tests/deprecated/test_examples.py
new file mode 100644
index 000000000..020670552
--- /dev/null
+++ b/tests/deprecated/test_examples.py
@@ -0,0 +1,94 @@
+import os
+import subprocess
+import sys
+from contextlib import contextmanager
+from pathlib import Path
+
+import pytest
+
+# Path to the examples directory
+EXAMPLES_DIR = Path(__file__).parent.parent / 'examples'
+
+# Examples that have dependencies and must run in sequence
+DEPENDENT_EXAMPLES = (
+ '02_Complex/complex_example.py',
+ '02_Complex/complex_example_results.py',
+)
+
+
+@contextmanager
+def working_directory(path):
+ """Context manager for changing the working directory."""
+ original_cwd = os.getcwd()
+ try:
+ os.chdir(path)
+ yield
+ finally:
+ os.chdir(original_cwd)
+
+
+@pytest.mark.parametrize(
+ 'example_script',
+ sorted(
+ [p for p in EXAMPLES_DIR.rglob('*.py') if str(p.relative_to(EXAMPLES_DIR)) not in DEPENDENT_EXAMPLES],
+ key=lambda path: (str(path.parent), path.name),
+ ),
+ ids=lambda path: str(path.relative_to(EXAMPLES_DIR)).replace(os.sep, '/'),
+)
+@pytest.mark.examples
+def test_independent_examples(example_script):
+ """
+ Test independent example scripts.
+ Ensures they run without errors.
+ Changes the current working directory to the directory of the example script.
+ Runs them alphabetically.
+ This imitates behaviour of running the script directly.
+ """
+ with working_directory(example_script.parent):
+ timeout = 800
+ # Set environment variable to disable interactive plotting
+ env = os.environ.copy()
+ env['FLIXOPT_CI'] = 'true'
+ try:
+ result = subprocess.run(
+ [sys.executable, example_script.name],
+ capture_output=True,
+ text=True,
+ timeout=timeout,
+ env=env,
+ )
+ except subprocess.TimeoutExpired:
+ pytest.fail(f'Script {example_script} timed out after {timeout} seconds')
+
+ assert result.returncode == 0, (
+ f'Script {example_script} failed:\nSTDERR:\n{result.stderr}\nSTDOUT:\n{result.stdout}'
+ )
+
+
+@pytest.mark.examples
+def test_dependent_examples():
+ """Test examples that must run in order (complex_example.py generates data for complex_example_results.py)."""
+ for script_path in DEPENDENT_EXAMPLES:
+ script_full_path = EXAMPLES_DIR / script_path
+
+ with working_directory(script_full_path.parent):
+ timeout = 600
+ # Set environment variable to disable interactive plotting
+ env = os.environ.copy()
+ env['FLIXOPT_CI'] = 'true'
+ try:
+ result = subprocess.run(
+ [sys.executable, script_full_path.name],
+ capture_output=True,
+ text=True,
+ timeout=timeout,
+ env=env,
+ )
+ except subprocess.TimeoutExpired:
+ pytest.fail(f'Script {script_path} timed out after {timeout} seconds')
+
+ assert result.returncode == 0, f'{script_path} failed:\nSTDERR:\n{result.stderr}\nSTDOUT:\n{result.stdout}'
+
+
+if __name__ == '__main__':
+ pytest.main(['-v', '--disable-warnings', '-m', 'examples'])
diff --git a/tests/ressources/v4-api/00_minimal--flow_system.nc4 b/tests/ressources/v4-api/00_minimal--flow_system.nc4
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diff --git a/tests/ressources/v4-api/00_minimal--model_documentation.yaml b/tests/ressources/v4-api/00_minimal--model_documentation.yaml
new file mode 100644
index 000000000..f398d484d
--- /dev/null
+++ b/tests/ressources/v4-api/00_minimal--model_documentation.yaml
@@ -0,0 +1,213 @@
+objective: |-
+ Objective:
+ ----------
+ LinearExpression: +1 Costs + 1 Penalty
+ Sense: min
+ Value: 4.0
+termination_condition: optimal
+status: ok
+nvars: 40
+nvarsbin: 0
+nvarscont: 40
+ncons: 25
+variables:
+ Costs(periodic): |-
+ Variable
+ --------
+ Costs(periodic) ∈ [-inf, inf]
+ Costs(temporal): |-
+ Variable
+ --------
+ Costs(temporal) ∈ [-inf, inf]
+ "Costs(temporal)|per_timestep": |-
+ Variable (time: 3)
+ ------------------
+ [2020-01-01 00:00:00]: Costs(temporal)|per_timestep[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Costs(temporal)|per_timestep[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Costs(temporal)|per_timestep[2020-01-01 02:00:00] ∈ [-inf, inf]
+ Costs: |-
+ Variable
+ --------
+ Costs ∈ [-inf, inf]
+ Penalty: |-
+ Variable
+ --------
+ Penalty ∈ [-inf, inf]
+ "Boiler(Gas)|flow_rate": |-
+ Variable (time: 3)
+ ------------------
+ [2020-01-01 00:00:00]: Boiler(Gas)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1e+07]
+ [2020-01-01 01:00:00]: Boiler(Gas)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1e+07]
+ [2020-01-01 02:00:00]: Boiler(Gas)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1e+07]
+ "Boiler(Gas)|total_flow_hours": |-
+ Variable
+ --------
+ Boiler(Gas)|total_flow_hours ∈ [0, inf]
+ "Boiler(Heat)|flow_rate": |-
+ Variable (time: 3)
+ ------------------
+ [2020-01-01 00:00:00]: Boiler(Heat)|flow_rate[2020-01-01 00:00:00] ∈ [0, 50]
+ [2020-01-01 01:00:00]: Boiler(Heat)|flow_rate[2020-01-01 01:00:00] ∈ [0, 50]
+ [2020-01-01 02:00:00]: Boiler(Heat)|flow_rate[2020-01-01 02:00:00] ∈ [0, 50]
+ "Boiler(Heat)|total_flow_hours": |-
+ Variable
+ --------
+ Boiler(Heat)|total_flow_hours ∈ [0, inf]
+ "Sink(Demand)|flow_rate": |-
+ Variable (time: 3)
+ ------------------
+ [2020-01-01 00:00:00]: Sink(Demand)|flow_rate[2020-01-01 00:00:00] ∈ [30, 30]
+ [2020-01-01 01:00:00]: Sink(Demand)|flow_rate[2020-01-01 01:00:00] ∈ [0, 0]
+ [2020-01-01 02:00:00]: Sink(Demand)|flow_rate[2020-01-01 02:00:00] ∈ [20, 20]
+ "Sink(Demand)|total_flow_hours": |-
+ Variable
+ --------
+ Sink(Demand)|total_flow_hours ∈ [0, inf]
+ "Source(Gas)|flow_rate": |-
+ Variable (time: 3)
+ ------------------
+ [2020-01-01 00:00:00]: Source(Gas)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1000]
+ [2020-01-01 01:00:00]: Source(Gas)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1000]
+ [2020-01-01 02:00:00]: Source(Gas)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1000]
+ "Source(Gas)|total_flow_hours": |-
+ Variable
+ --------
+ Source(Gas)|total_flow_hours ∈ [0, inf]
+ "Source(Gas)->Costs(temporal)": |-
+ Variable (time: 3)
+ ------------------
+ [2020-01-01 00:00:00]: Source(Gas)->Costs(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Source(Gas)->Costs(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Source(Gas)->Costs(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ "Heat|excess_input": |-
+ Variable (time: 3)
+ ------------------
+ [2020-01-01 00:00:00]: Heat|excess_input[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Heat|excess_input[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Heat|excess_input[2020-01-01 02:00:00] ∈ [0, inf]
+ "Heat|excess_output": |-
+ Variable (time: 3)
+ ------------------
+ [2020-01-01 00:00:00]: Heat|excess_output[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Heat|excess_output[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Heat|excess_output[2020-01-01 02:00:00] ∈ [0, inf]
+ "Heat->Penalty": |-
+ Variable
+ --------
+ Heat->Penalty ∈ [-inf, inf]
+ "Gas|excess_input": |-
+ Variable (time: 3)
+ ------------------
+ [2020-01-01 00:00:00]: Gas|excess_input[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Gas|excess_input[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Gas|excess_input[2020-01-01 02:00:00] ∈ [0, inf]
+ "Gas|excess_output": |-
+ Variable (time: 3)
+ ------------------
+ [2020-01-01 00:00:00]: Gas|excess_output[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Gas|excess_output[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Gas|excess_output[2020-01-01 02:00:00] ∈ [0, inf]
+ "Gas->Penalty": |-
+ Variable
+ --------
+ Gas->Penalty ∈ [-inf, inf]
+constraints:
+ Costs(periodic): |-
+ Constraint `Costs(periodic)`
+ ----------------------------
+ +1 Costs(periodic) = -0.0
+ Costs(temporal): |-
+ Constraint `Costs(temporal)`
+ ----------------------------
+ +1 Costs(temporal) - 1 Costs(temporal)|per_timestep[2020-01-01 00:00:00] - 1 Costs(temporal)|per_timestep[2020-01-01 01:00:00] - 1 Costs(temporal)|per_timestep[2020-01-01 02:00:00] = -0.0
+ "Costs(temporal)|per_timestep": |-
+ Constraint `Costs(temporal)|per_timestep`
+ [time: 3]:
+ ----------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Costs(temporal)|per_timestep[2020-01-01 00:00:00] - 1 Source(Gas)->Costs(temporal)[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Costs(temporal)|per_timestep[2020-01-01 01:00:00] - 1 Source(Gas)->Costs(temporal)[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Costs(temporal)|per_timestep[2020-01-01 02:00:00] - 1 Source(Gas)->Costs(temporal)[2020-01-01 02:00:00] = -0.0
+ Costs: |-
+ Constraint `Costs`
+ ------------------
+ +1 Costs - 1 Costs(temporal) - 1 Costs(periodic) = -0.0
+ Penalty: |-
+ Constraint `Penalty`
+ --------------------
+ +1 Penalty - 1 Heat->Penalty - 1 Gas->Penalty = -0.0
+ "Boiler(Gas)|total_flow_hours": |-
+ Constraint `Boiler(Gas)|total_flow_hours`
+ -----------------------------------------
+ +1 Boiler(Gas)|total_flow_hours - 1 Boiler(Gas)|flow_rate[2020-01-01 00:00:00] - 1 Boiler(Gas)|flow_rate[2020-01-01 01:00:00] - 1 Boiler(Gas)|flow_rate[2020-01-01 02:00:00] = -0.0
+ "Boiler(Heat)|total_flow_hours": |-
+ Constraint `Boiler(Heat)|total_flow_hours`
+ ------------------------------------------
+ +1 Boiler(Heat)|total_flow_hours - 1 Boiler(Heat)|flow_rate[2020-01-01 00:00:00] - 1 Boiler(Heat)|flow_rate[2020-01-01 01:00:00] - 1 Boiler(Heat)|flow_rate[2020-01-01 02:00:00] = -0.0
+ "Boiler|conversion_0": |-
+ Constraint `Boiler|conversion_0`
+ [time: 3]:
+ -------------------------------------------
+ [2020-01-01 00:00:00]: +0.5 Boiler(Gas)|flow_rate[2020-01-01 00:00:00] - 1 Boiler(Heat)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +0.5 Boiler(Gas)|flow_rate[2020-01-01 01:00:00] - 1 Boiler(Heat)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +0.5 Boiler(Gas)|flow_rate[2020-01-01 02:00:00] - 1 Boiler(Heat)|flow_rate[2020-01-01 02:00:00] = -0.0
+ "Sink(Demand)|total_flow_hours": |-
+ Constraint `Sink(Demand)|total_flow_hours`
+ ------------------------------------------
+ +1 Sink(Demand)|total_flow_hours - 1 Sink(Demand)|flow_rate[2020-01-01 00:00:00] - 1 Sink(Demand)|flow_rate[2020-01-01 01:00:00] - 1 Sink(Demand)|flow_rate[2020-01-01 02:00:00] = -0.0
+ "Source(Gas)|total_flow_hours": |-
+ Constraint `Source(Gas)|total_flow_hours`
+ -----------------------------------------
+ +1 Source(Gas)|total_flow_hours - 1 Source(Gas)|flow_rate[2020-01-01 00:00:00] - 1 Source(Gas)|flow_rate[2020-01-01 01:00:00] - 1 Source(Gas)|flow_rate[2020-01-01 02:00:00] = -0.0
+ "Source(Gas)->Costs(temporal)": |-
+ Constraint `Source(Gas)->Costs(temporal)`
+ [time: 3]:
+ ----------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Source(Gas)->Costs(temporal)[2020-01-01 00:00:00] - 0.04 Source(Gas)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Source(Gas)->Costs(temporal)[2020-01-01 01:00:00] - 0.04 Source(Gas)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Source(Gas)->Costs(temporal)[2020-01-01 02:00:00] - 0.04 Source(Gas)|flow_rate[2020-01-01 02:00:00] = -0.0
+ "Heat|balance": |-
+ Constraint `Heat|balance`
+ [time: 3]:
+ ------------------------------------
+ [2020-01-01 00:00:00]: +1 Boiler(Heat)|flow_rate[2020-01-01 00:00:00] - 1 Sink(Demand)|flow_rate[2020-01-01 00:00:00] + 1 Heat|excess_input[2020-01-01 00:00:00] - 1 Heat|excess_output[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Boiler(Heat)|flow_rate[2020-01-01 01:00:00] - 1 Sink(Demand)|flow_rate[2020-01-01 01:00:00] + 1 Heat|excess_input[2020-01-01 01:00:00] - 1 Heat|excess_output[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Boiler(Heat)|flow_rate[2020-01-01 02:00:00] - 1 Sink(Demand)|flow_rate[2020-01-01 02:00:00] + 1 Heat|excess_input[2020-01-01 02:00:00] - 1 Heat|excess_output[2020-01-01 02:00:00] = -0.0
+ "Heat->Penalty": |-
+ Constraint `Heat->Penalty`
+ --------------------------
+ +1 Heat->Penalty - 1e+05 Heat|excess_input[2020-01-01 00:00:00] - 1e+05 Heat|excess_input[2020-01-01 01:00:00]... -1e+05 Heat|excess_output[2020-01-01 00:00:00] - 1e+05 Heat|excess_output[2020-01-01 01:00:00] - 1e+05 Heat|excess_output[2020-01-01 02:00:00] = -0.0
+ "Gas|balance": |-
+ Constraint `Gas|balance`
+ [time: 3]:
+ -----------------------------------
+ [2020-01-01 00:00:00]: +1 Source(Gas)|flow_rate[2020-01-01 00:00:00] - 1 Boiler(Gas)|flow_rate[2020-01-01 00:00:00] + 1 Gas|excess_input[2020-01-01 00:00:00] - 1 Gas|excess_output[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Source(Gas)|flow_rate[2020-01-01 01:00:00] - 1 Boiler(Gas)|flow_rate[2020-01-01 01:00:00] + 1 Gas|excess_input[2020-01-01 01:00:00] - 1 Gas|excess_output[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Source(Gas)|flow_rate[2020-01-01 02:00:00] - 1 Boiler(Gas)|flow_rate[2020-01-01 02:00:00] + 1 Gas|excess_input[2020-01-01 02:00:00] - 1 Gas|excess_output[2020-01-01 02:00:00] = -0.0
+ "Gas->Penalty": |-
+ Constraint `Gas->Penalty`
+ -------------------------
+ +1 Gas->Penalty - 1e+05 Gas|excess_input[2020-01-01 00:00:00] - 1e+05 Gas|excess_input[2020-01-01 01:00:00]... -1e+05 Gas|excess_output[2020-01-01 00:00:00] - 1e+05 Gas|excess_output[2020-01-01 01:00:00] - 1e+05 Gas|excess_output[2020-01-01 02:00:00] = -0.0
+binaries: []
+integers: []
+continuous:
+ - Costs(periodic)
+ - Costs(temporal)
+ - "Costs(temporal)|per_timestep"
+ - Costs
+ - Penalty
+ - "Boiler(Gas)|flow_rate"
+ - "Boiler(Gas)|total_flow_hours"
+ - "Boiler(Heat)|flow_rate"
+ - "Boiler(Heat)|total_flow_hours"
+ - "Sink(Demand)|flow_rate"
+ - "Sink(Demand)|total_flow_hours"
+ - "Source(Gas)|flow_rate"
+ - "Source(Gas)|total_flow_hours"
+ - "Source(Gas)->Costs(temporal)"
+ - "Heat|excess_input"
+ - "Heat|excess_output"
+ - "Heat->Penalty"
+ - "Gas|excess_input"
+ - "Gas|excess_output"
+ - "Gas->Penalty"
+infeasible_constraints: ''
diff --git a/tests/ressources/v4-api/00_minimal--solution.nc4 b/tests/ressources/v4-api/00_minimal--solution.nc4
new file mode 100644
index 0000000000000000000000000000000000000000..86f94e3b5da04a5462d9d845e10f61d591f8f976
GIT binary patch
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diff --git a/tests/ressources/v4-api/00_minimal--summary.yaml b/tests/ressources/v4-api/00_minimal--summary.yaml
new file mode 100644
index 000000000..598c501ed
--- /dev/null
+++ b/tests/ressources/v4-api/00_minimal--summary.yaml
@@ -0,0 +1,46 @@
+Name: 00_minimal
+Number of timesteps: 3
+Calculation Type: FullCalculation
+Constraints: 25
+Variables: 40
+Main Results:
+ Objective: 4.0
+ Penalty: -0.0
+ Effects:
+ Costs [€]:
+ temporal: 4.0
+ periodic: -0.0
+ total: 4.0
+ Invest-Decisions:
+ Invested: {}
+ Not invested: {}
+ Buses with excess: []
+Durations:
+ modeling: 0.39
+ solving: 0.17
+ saving: 0.0
+Config:
+ config_name: flixopt
+ logging:
+ level: INFO
+ file: null
+ console: false
+ max_file_size: 10485760
+ backup_count: 5
+ verbose_tracebacks: false
+ modeling:
+ big: 10000000
+ epsilon: 1.0e-05
+ big_binary_bound: 100000
+ solving:
+ mip_gap: 0.01
+ time_limit_seconds: 300
+ log_to_console: false
+ log_main_results: false
+ plotting:
+ default_show: false
+ default_engine: plotly
+ default_dpi: 300
+ default_facet_cols: 3
+ default_sequential_colorscale: turbo
+ default_qualitative_colorscale: plotly
diff --git a/tests/ressources/v4-api/01_simple--flow_system.nc4 b/tests/ressources/v4-api/01_simple--flow_system.nc4
new file mode 100644
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diff --git a/tests/ressources/v4-api/01_simple--model_documentation.yaml b/tests/ressources/v4-api/01_simple--model_documentation.yaml
new file mode 100644
index 000000000..947ddea6f
--- /dev/null
+++ b/tests/ressources/v4-api/01_simple--model_documentation.yaml
@@ -0,0 +1,848 @@
+objective: |-
+ Objective:
+ ----------
+ LinearExpression: +1 costs + 1 Penalty
+ Sense: min
+ Value: 83.88394666666667
+termination_condition: optimal
+status: ok
+nvars: 259
+nvarsbin: 18
+nvarscont: 241
+ncons: 215
+variables:
+ costs(periodic): |-
+ Variable
+ --------
+ costs(periodic) ∈ [-inf, inf]
+ costs(temporal): |-
+ Variable
+ --------
+ costs(temporal) ∈ [-inf, inf]
+ "costs(temporal)|per_timestep": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: costs(temporal)|per_timestep[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: costs(temporal)|per_timestep[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: costs(temporal)|per_timestep[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: costs(temporal)|per_timestep[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: costs(temporal)|per_timestep[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: costs(temporal)|per_timestep[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: costs(temporal)|per_timestep[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: costs(temporal)|per_timestep[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: costs(temporal)|per_timestep[2020-01-01 08:00:00] ∈ [-inf, inf]
+ costs: |-
+ Variable
+ --------
+ costs ∈ [-inf, inf]
+ CO2(periodic): |-
+ Variable
+ --------
+ CO2(periodic) ∈ [-inf, inf]
+ CO2(temporal): |-
+ Variable
+ --------
+ CO2(temporal) ∈ [-inf, inf]
+ "CO2(temporal)|per_timestep": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: CO2(temporal)|per_timestep[2020-01-01 00:00:00] ∈ [-inf, 1000]
+ [2020-01-01 01:00:00]: CO2(temporal)|per_timestep[2020-01-01 01:00:00] ∈ [-inf, 1000]
+ [2020-01-01 02:00:00]: CO2(temporal)|per_timestep[2020-01-01 02:00:00] ∈ [-inf, 1000]
+ [2020-01-01 03:00:00]: CO2(temporal)|per_timestep[2020-01-01 03:00:00] ∈ [-inf, 1000]
+ [2020-01-01 04:00:00]: CO2(temporal)|per_timestep[2020-01-01 04:00:00] ∈ [-inf, 1000]
+ [2020-01-01 05:00:00]: CO2(temporal)|per_timestep[2020-01-01 05:00:00] ∈ [-inf, 1000]
+ [2020-01-01 06:00:00]: CO2(temporal)|per_timestep[2020-01-01 06:00:00] ∈ [-inf, 1000]
+ [2020-01-01 07:00:00]: CO2(temporal)|per_timestep[2020-01-01 07:00:00] ∈ [-inf, 1000]
+ [2020-01-01 08:00:00]: CO2(temporal)|per_timestep[2020-01-01 08:00:00] ∈ [-inf, 1000]
+ CO2: |-
+ Variable
+ --------
+ CO2 ∈ [-inf, inf]
+ Penalty: |-
+ Variable
+ --------
+ Penalty ∈ [-inf, inf]
+ "CO2(temporal)->costs(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Boiler(Q_fu)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Boiler(Q_fu)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1e+07]
+ [2020-01-01 01:00:00]: Boiler(Q_fu)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1e+07]
+ [2020-01-01 02:00:00]: Boiler(Q_fu)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1e+07]
+ [2020-01-01 03:00:00]: Boiler(Q_fu)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1e+07]
+ [2020-01-01 04:00:00]: Boiler(Q_fu)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1e+07]
+ [2020-01-01 05:00:00]: Boiler(Q_fu)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1e+07]
+ [2020-01-01 06:00:00]: Boiler(Q_fu)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1e+07]
+ [2020-01-01 07:00:00]: Boiler(Q_fu)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1e+07]
+ [2020-01-01 08:00:00]: Boiler(Q_fu)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1e+07]
+ "Boiler(Q_fu)|total_flow_hours": |-
+ Variable
+ --------
+ Boiler(Q_fu)|total_flow_hours ∈ [0, inf]
+ "Boiler(Q_th)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Boiler(Q_th)|flow_rate[2020-01-01 00:00:00] ∈ [5, 50]
+ [2020-01-01 01:00:00]: Boiler(Q_th)|flow_rate[2020-01-01 01:00:00] ∈ [5, 50]
+ [2020-01-01 02:00:00]: Boiler(Q_th)|flow_rate[2020-01-01 02:00:00] ∈ [5, 50]
+ [2020-01-01 03:00:00]: Boiler(Q_th)|flow_rate[2020-01-01 03:00:00] ∈ [5, 50]
+ [2020-01-01 04:00:00]: Boiler(Q_th)|flow_rate[2020-01-01 04:00:00] ∈ [5, 50]
+ [2020-01-01 05:00:00]: Boiler(Q_th)|flow_rate[2020-01-01 05:00:00] ∈ [5, 50]
+ [2020-01-01 06:00:00]: Boiler(Q_th)|flow_rate[2020-01-01 06:00:00] ∈ [5, 50]
+ [2020-01-01 07:00:00]: Boiler(Q_th)|flow_rate[2020-01-01 07:00:00] ∈ [5, 50]
+ [2020-01-01 08:00:00]: Boiler(Q_th)|flow_rate[2020-01-01 08:00:00] ∈ [5, 50]
+ "Boiler(Q_th)|total_flow_hours": |-
+ Variable
+ --------
+ Boiler(Q_th)|total_flow_hours ∈ [0, inf]
+ "Storage(Q_th_load)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Storage(Q_th_load)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1000]
+ [2020-01-01 01:00:00]: Storage(Q_th_load)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1000]
+ [2020-01-01 02:00:00]: Storage(Q_th_load)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1000]
+ [2020-01-01 03:00:00]: Storage(Q_th_load)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1000]
+ [2020-01-01 04:00:00]: Storage(Q_th_load)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1000]
+ [2020-01-01 05:00:00]: Storage(Q_th_load)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1000]
+ [2020-01-01 06:00:00]: Storage(Q_th_load)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1000]
+ [2020-01-01 07:00:00]: Storage(Q_th_load)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1000]
+ [2020-01-01 08:00:00]: Storage(Q_th_load)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1000]
+ "Storage(Q_th_load)|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Storage(Q_th_load)|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: Storage(Q_th_load)|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: Storage(Q_th_load)|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: Storage(Q_th_load)|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: Storage(Q_th_load)|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: Storage(Q_th_load)|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: Storage(Q_th_load)|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: Storage(Q_th_load)|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: Storage(Q_th_load)|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "Storage(Q_th_load)|on_hours_total": |-
+ Variable
+ --------
+ Storage(Q_th_load)|on_hours_total ∈ [0, inf]
+ "Storage(Q_th_load)|total_flow_hours": |-
+ Variable
+ --------
+ Storage(Q_th_load)|total_flow_hours ∈ [0, inf]
+ "Storage(Q_th_unload)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Storage(Q_th_unload)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1000]
+ [2020-01-01 01:00:00]: Storage(Q_th_unload)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1000]
+ [2020-01-01 02:00:00]: Storage(Q_th_unload)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1000]
+ [2020-01-01 03:00:00]: Storage(Q_th_unload)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1000]
+ [2020-01-01 04:00:00]: Storage(Q_th_unload)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1000]
+ [2020-01-01 05:00:00]: Storage(Q_th_unload)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1000]
+ [2020-01-01 06:00:00]: Storage(Q_th_unload)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1000]
+ [2020-01-01 07:00:00]: Storage(Q_th_unload)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1000]
+ [2020-01-01 08:00:00]: Storage(Q_th_unload)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1000]
+ "Storage(Q_th_unload)|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Storage(Q_th_unload)|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: Storage(Q_th_unload)|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: Storage(Q_th_unload)|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: Storage(Q_th_unload)|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: Storage(Q_th_unload)|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: Storage(Q_th_unload)|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: Storage(Q_th_unload)|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: Storage(Q_th_unload)|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: Storage(Q_th_unload)|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "Storage(Q_th_unload)|on_hours_total": |-
+ Variable
+ --------
+ Storage(Q_th_unload)|on_hours_total ∈ [0, inf]
+ "Storage(Q_th_unload)|total_flow_hours": |-
+ Variable
+ --------
+ Storage(Q_th_unload)|total_flow_hours ∈ [0, inf]
+ "Storage|charge_state": |-
+ Variable (time: 10)
+ -------------------
+ [2020-01-01 00:00:00]: Storage|charge_state[2020-01-01 00:00:00] ∈ [0, 8e+06]
+ [2020-01-01 01:00:00]: Storage|charge_state[2020-01-01 01:00:00] ∈ [0, 7e+06]
+ [2020-01-01 02:00:00]: Storage|charge_state[2020-01-01 02:00:00] ∈ [0, 8e+06]
+ [2020-01-01 03:00:00]: Storage|charge_state[2020-01-01 03:00:00] ∈ [0, 8e+06]
+ [2020-01-01 04:00:00]: Storage|charge_state[2020-01-01 04:00:00] ∈ [0, 8e+06]
+ [2020-01-01 05:00:00]: Storage|charge_state[2020-01-01 05:00:00] ∈ [0, 8e+06]
+ [2020-01-01 06:00:00]: Storage|charge_state[2020-01-01 06:00:00] ∈ [0, 8e+06]
+ [2020-01-01 07:00:00]: Storage|charge_state[2020-01-01 07:00:00] ∈ [0, 8e+06]
+ [2020-01-01 08:00:00]: Storage|charge_state[2020-01-01 08:00:00] ∈ [0, 8e+06]
+ [2020-01-01 09:00:00]: Storage|charge_state[2020-01-01 09:00:00] ∈ [0, 8e+06]
+ "Storage|netto_discharge": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Storage|netto_discharge[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Storage|netto_discharge[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Storage|netto_discharge[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Storage|netto_discharge[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Storage|netto_discharge[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Storage|netto_discharge[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Storage|netto_discharge[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Storage|netto_discharge[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Storage|netto_discharge[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Storage|size": |-
+ Variable
+ --------
+ Storage|size ∈ [30, 30]
+ "Storage->costs(periodic)": |-
+ Variable
+ --------
+ Storage->costs(periodic) ∈ [-inf, inf]
+ "CHP(Q_fu)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: CHP(Q_fu)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1e+07]
+ [2020-01-01 01:00:00]: CHP(Q_fu)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1e+07]
+ [2020-01-01 02:00:00]: CHP(Q_fu)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1e+07]
+ [2020-01-01 03:00:00]: CHP(Q_fu)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1e+07]
+ [2020-01-01 04:00:00]: CHP(Q_fu)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1e+07]
+ [2020-01-01 05:00:00]: CHP(Q_fu)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1e+07]
+ [2020-01-01 06:00:00]: CHP(Q_fu)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1e+07]
+ [2020-01-01 07:00:00]: CHP(Q_fu)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1e+07]
+ [2020-01-01 08:00:00]: CHP(Q_fu)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1e+07]
+ "CHP(Q_fu)|total_flow_hours": |-
+ Variable
+ --------
+ CHP(Q_fu)|total_flow_hours ∈ [0, inf]
+ "CHP(Q_th)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: CHP(Q_th)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1e+07]
+ [2020-01-01 01:00:00]: CHP(Q_th)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1e+07]
+ [2020-01-01 02:00:00]: CHP(Q_th)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1e+07]
+ [2020-01-01 03:00:00]: CHP(Q_th)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1e+07]
+ [2020-01-01 04:00:00]: CHP(Q_th)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1e+07]
+ [2020-01-01 05:00:00]: CHP(Q_th)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1e+07]
+ [2020-01-01 06:00:00]: CHP(Q_th)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1e+07]
+ [2020-01-01 07:00:00]: CHP(Q_th)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1e+07]
+ [2020-01-01 08:00:00]: CHP(Q_th)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1e+07]
+ "CHP(Q_th)|total_flow_hours": |-
+ Variable
+ --------
+ CHP(Q_th)|total_flow_hours ∈ [0, inf]
+ "CHP(P_el)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: CHP(P_el)|flow_rate[2020-01-01 00:00:00] ∈ [5, 60]
+ [2020-01-01 01:00:00]: CHP(P_el)|flow_rate[2020-01-01 01:00:00] ∈ [5, 60]
+ [2020-01-01 02:00:00]: CHP(P_el)|flow_rate[2020-01-01 02:00:00] ∈ [5, 60]
+ [2020-01-01 03:00:00]: CHP(P_el)|flow_rate[2020-01-01 03:00:00] ∈ [5, 60]
+ [2020-01-01 04:00:00]: CHP(P_el)|flow_rate[2020-01-01 04:00:00] ∈ [5, 60]
+ [2020-01-01 05:00:00]: CHP(P_el)|flow_rate[2020-01-01 05:00:00] ∈ [5, 60]
+ [2020-01-01 06:00:00]: CHP(P_el)|flow_rate[2020-01-01 06:00:00] ∈ [5, 60]
+ [2020-01-01 07:00:00]: CHP(P_el)|flow_rate[2020-01-01 07:00:00] ∈ [5, 60]
+ [2020-01-01 08:00:00]: CHP(P_el)|flow_rate[2020-01-01 08:00:00] ∈ [5, 60]
+ "CHP(P_el)|total_flow_hours": |-
+ Variable
+ --------
+ CHP(P_el)|total_flow_hours ∈ [0, inf]
+ "Heat Demand(Q_th_Last)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Heat Demand(Q_th_Last)|flow_rate[2020-01-01 00:00:00] ∈ [30, 30]
+ [2020-01-01 01:00:00]: Heat Demand(Q_th_Last)|flow_rate[2020-01-01 01:00:00] ∈ [0, 0]
+ [2020-01-01 02:00:00]: Heat Demand(Q_th_Last)|flow_rate[2020-01-01 02:00:00] ∈ [90, 90]
+ [2020-01-01 03:00:00]: Heat Demand(Q_th_Last)|flow_rate[2020-01-01 03:00:00] ∈ [110, 110]
+ [2020-01-01 04:00:00]: Heat Demand(Q_th_Last)|flow_rate[2020-01-01 04:00:00] ∈ [110, 110]
+ [2020-01-01 05:00:00]: Heat Demand(Q_th_Last)|flow_rate[2020-01-01 05:00:00] ∈ [20, 20]
+ [2020-01-01 06:00:00]: Heat Demand(Q_th_Last)|flow_rate[2020-01-01 06:00:00] ∈ [20, 20]
+ [2020-01-01 07:00:00]: Heat Demand(Q_th_Last)|flow_rate[2020-01-01 07:00:00] ∈ [20, 20]
+ [2020-01-01 08:00:00]: Heat Demand(Q_th_Last)|flow_rate[2020-01-01 08:00:00] ∈ [20, 20]
+ "Heat Demand(Q_th_Last)|total_flow_hours": |-
+ Variable
+ --------
+ Heat Demand(Q_th_Last)|total_flow_hours ∈ [0, inf]
+ "Gastarif(Q_Gas)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1000]
+ [2020-01-01 01:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1000]
+ [2020-01-01 02:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1000]
+ [2020-01-01 03:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1000]
+ [2020-01-01 04:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1000]
+ [2020-01-01 05:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1000]
+ [2020-01-01 06:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1000]
+ [2020-01-01 07:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1000]
+ [2020-01-01 08:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1000]
+ "Gastarif(Q_Gas)|total_flow_hours": |-
+ Variable
+ --------
+ Gastarif(Q_Gas)|total_flow_hours ∈ [0, inf]
+ "Gastarif(Q_Gas)->costs(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Gastarif(Q_Gas)->CO2(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Einspeisung(P_el)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1e+07]
+ [2020-01-01 01:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1e+07]
+ [2020-01-01 02:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1e+07]
+ [2020-01-01 03:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1e+07]
+ [2020-01-01 04:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1e+07]
+ [2020-01-01 05:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1e+07]
+ [2020-01-01 06:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1e+07]
+ [2020-01-01 07:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1e+07]
+ [2020-01-01 08:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1e+07]
+ "Einspeisung(P_el)|total_flow_hours": |-
+ Variable
+ --------
+ Einspeisung(P_el)|total_flow_hours ∈ [0, inf]
+ "Einspeisung(P_el)->costs(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Strom|excess_input": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Strom|excess_input[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Strom|excess_input[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Strom|excess_input[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Strom|excess_input[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Strom|excess_input[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Strom|excess_input[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Strom|excess_input[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Strom|excess_input[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Strom|excess_input[2020-01-01 08:00:00] ∈ [0, inf]
+ "Strom|excess_output": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Strom|excess_output[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Strom|excess_output[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Strom|excess_output[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Strom|excess_output[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Strom|excess_output[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Strom|excess_output[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Strom|excess_output[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Strom|excess_output[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Strom|excess_output[2020-01-01 08:00:00] ∈ [0, inf]
+ "Strom->Penalty": |-
+ Variable
+ --------
+ Strom->Penalty ∈ [-inf, inf]
+ "Fernwärme|excess_input": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Fernwärme|excess_input[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Fernwärme|excess_input[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Fernwärme|excess_input[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Fernwärme|excess_input[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Fernwärme|excess_input[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Fernwärme|excess_input[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Fernwärme|excess_input[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Fernwärme|excess_input[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Fernwärme|excess_input[2020-01-01 08:00:00] ∈ [0, inf]
+ "Fernwärme|excess_output": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Fernwärme|excess_output[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Fernwärme|excess_output[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Fernwärme|excess_output[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Fernwärme|excess_output[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Fernwärme|excess_output[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Fernwärme|excess_output[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Fernwärme|excess_output[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Fernwärme|excess_output[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Fernwärme|excess_output[2020-01-01 08:00:00] ∈ [0, inf]
+ "Fernwärme->Penalty": |-
+ Variable
+ --------
+ Fernwärme->Penalty ∈ [-inf, inf]
+ "Gas|excess_input": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Gas|excess_input[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Gas|excess_input[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Gas|excess_input[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Gas|excess_input[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Gas|excess_input[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Gas|excess_input[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Gas|excess_input[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Gas|excess_input[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Gas|excess_input[2020-01-01 08:00:00] ∈ [0, inf]
+ "Gas|excess_output": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Gas|excess_output[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Gas|excess_output[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Gas|excess_output[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Gas|excess_output[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Gas|excess_output[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Gas|excess_output[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Gas|excess_output[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Gas|excess_output[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Gas|excess_output[2020-01-01 08:00:00] ∈ [0, inf]
+ "Gas->Penalty": |-
+ Variable
+ --------
+ Gas->Penalty ∈ [-inf, inf]
+constraints:
+ costs(periodic): |-
+ Constraint `costs(periodic)`
+ ----------------------------
+ +1 costs(periodic) - 1 Storage->costs(periodic) = -0.0
+ costs(temporal): |-
+ Constraint `costs(temporal)`
+ ----------------------------
+ +1 costs(temporal) - 1 costs(temporal)|per_timestep[2020-01-01 00:00:00] - 1 costs(temporal)|per_timestep[2020-01-01 01:00:00]... -1 costs(temporal)|per_timestep[2020-01-01 06:00:00] - 1 costs(temporal)|per_timestep[2020-01-01 07:00:00] - 1 costs(temporal)|per_timestep[2020-01-01 08:00:00] = -0.0
+ "costs(temporal)|per_timestep": |-
+ Constraint `costs(temporal)|per_timestep`
+ [time: 9]:
+ ----------------------------------------------------
+ [2020-01-01 00:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 00:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 00:00:00] - 1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 00:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 01:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 01:00:00] - 1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 01:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 02:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 02:00:00] - 1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 02:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 03:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 03:00:00] - 1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 03:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 04:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 04:00:00] - 1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 04:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 05:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 05:00:00] - 1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 05:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 06:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 06:00:00] - 1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 06:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 07:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 07:00:00] - 1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 07:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 08:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 08:00:00] - 1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 08:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 08:00:00] = -0.0
+ costs: |-
+ Constraint `costs`
+ ------------------
+ +1 costs - 1 costs(temporal) - 1 costs(periodic) = -0.0
+ CO2(periodic): |-
+ Constraint `CO2(periodic)`
+ --------------------------
+ +1 CO2(periodic) = -0.0
+ CO2(temporal): |-
+ Constraint `CO2(temporal)`
+ --------------------------
+ +1 CO2(temporal) - 1 CO2(temporal)|per_timestep[2020-01-01 00:00:00] - 1 CO2(temporal)|per_timestep[2020-01-01 01:00:00]... -1 CO2(temporal)|per_timestep[2020-01-01 06:00:00] - 1 CO2(temporal)|per_timestep[2020-01-01 07:00:00] - 1 CO2(temporal)|per_timestep[2020-01-01 08:00:00] = -0.0
+ "CO2(temporal)|per_timestep": |-
+ Constraint `CO2(temporal)|per_timestep`
+ [time: 9]:
+ --------------------------------------------------
+ [2020-01-01 00:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 00:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 01:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 02:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 03:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 04:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 05:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 06:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 07:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 08:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 08:00:00] = -0.0
+ CO2: |-
+ Constraint `CO2`
+ ----------------
+ +1 CO2 - 1 CO2(temporal) - 1 CO2(periodic) = -0.0
+ Penalty: |-
+ Constraint `Penalty`
+ --------------------
+ +1 Penalty - 1 Strom->Penalty - 1 Fernwärme->Penalty - 1 Gas->Penalty = -0.0
+ "CO2(temporal)->costs(temporal)": |-
+ Constraint `CO2(temporal)->costs(temporal)`
+ [time: 9]:
+ ------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 00:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 01:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 02:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 03:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 04:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 05:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 06:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 07:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 08:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 08:00:00] = -0.0
+ "Boiler(Q_fu)|total_flow_hours": |-
+ Constraint `Boiler(Q_fu)|total_flow_hours`
+ ------------------------------------------
+ +1 Boiler(Q_fu)|total_flow_hours - 1 Boiler(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 01:00:00]... -1 Boiler(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Boiler(Q_th)|total_flow_hours": |-
+ Constraint `Boiler(Q_th)|total_flow_hours`
+ ------------------------------------------
+ +1 Boiler(Q_th)|total_flow_hours - 1 Boiler(Q_th)|flow_rate[2020-01-01 00:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 01:00:00]... -1 Boiler(Q_th)|flow_rate[2020-01-01 06:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 07:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Boiler|conversion_0": |-
+ Constraint `Boiler|conversion_0`
+ [time: 9]:
+ -------------------------------------------
+ [2020-01-01 00:00:00]: +0.5 Boiler(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +0.5 Boiler(Q_fu)|flow_rate[2020-01-01 01:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +0.5 Boiler(Q_fu)|flow_rate[2020-01-01 02:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +0.5 Boiler(Q_fu)|flow_rate[2020-01-01 03:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +0.5 Boiler(Q_fu)|flow_rate[2020-01-01 04:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +0.5 Boiler(Q_fu)|flow_rate[2020-01-01 05:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +0.5 Boiler(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +0.5 Boiler(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +0.5 Boiler(Q_fu)|flow_rate[2020-01-01 08:00:00] - 1 Boiler(Q_th)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Storage(Q_th_load)|on_hours_total": |-
+ Constraint `Storage(Q_th_load)|on_hours_total`
+ ----------------------------------------------
+ +1 Storage(Q_th_load)|on_hours_total - 1 Storage(Q_th_load)|on[2020-01-01 00:00:00] - 1 Storage(Q_th_load)|on[2020-01-01 01:00:00]... -1 Storage(Q_th_load)|on[2020-01-01 06:00:00] - 1 Storage(Q_th_load)|on[2020-01-01 07:00:00] - 1 Storage(Q_th_load)|on[2020-01-01 08:00:00] = -0.0
+ "Storage(Q_th_load)|flow_rate|ub": |-
+ Constraint `Storage(Q_th_load)|flow_rate|ub`
+ [time: 9]:
+ -------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 00:00:00] - 1000 Storage(Q_th_load)|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 01:00:00] - 1000 Storage(Q_th_load)|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 02:00:00] - 1000 Storage(Q_th_load)|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 03:00:00] - 1000 Storage(Q_th_load)|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 04:00:00] - 1000 Storage(Q_th_load)|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 05:00:00] - 1000 Storage(Q_th_load)|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 06:00:00] - 1000 Storage(Q_th_load)|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 07:00:00] - 1000 Storage(Q_th_load)|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 08:00:00] - 1000 Storage(Q_th_load)|on[2020-01-01 08:00:00] ≤ -0.0
+ "Storage(Q_th_load)|flow_rate|lb": |-
+ Constraint `Storage(Q_th_load)|flow_rate|lb`
+ [time: 9]:
+ -------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 00:00:00] - 1e-05 Storage(Q_th_load)|on[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 01:00:00] - 1e-05 Storage(Q_th_load)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 02:00:00] - 1e-05 Storage(Q_th_load)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 03:00:00] - 1e-05 Storage(Q_th_load)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 04:00:00] - 1e-05 Storage(Q_th_load)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 05:00:00] - 1e-05 Storage(Q_th_load)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 06:00:00] - 1e-05 Storage(Q_th_load)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 07:00:00] - 1e-05 Storage(Q_th_load)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 Storage(Q_th_load)|flow_rate[2020-01-01 08:00:00] - 1e-05 Storage(Q_th_load)|on[2020-01-01 08:00:00] ≥ -0.0
+ "Storage(Q_th_load)|total_flow_hours": |-
+ Constraint `Storage(Q_th_load)|total_flow_hours`
+ ------------------------------------------------
+ +1 Storage(Q_th_load)|total_flow_hours - 1 Storage(Q_th_load)|flow_rate[2020-01-01 00:00:00] - 1 Storage(Q_th_load)|flow_rate[2020-01-01 01:00:00]... -1 Storage(Q_th_load)|flow_rate[2020-01-01 06:00:00] - 1 Storage(Q_th_load)|flow_rate[2020-01-01 07:00:00] - 1 Storage(Q_th_load)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Storage(Q_th_unload)|on_hours_total": |-
+ Constraint `Storage(Q_th_unload)|on_hours_total`
+ ------------------------------------------------
+ +1 Storage(Q_th_unload)|on_hours_total - 1 Storage(Q_th_unload)|on[2020-01-01 00:00:00] - 1 Storage(Q_th_unload)|on[2020-01-01 01:00:00]... -1 Storage(Q_th_unload)|on[2020-01-01 06:00:00] - 1 Storage(Q_th_unload)|on[2020-01-01 07:00:00] - 1 Storage(Q_th_unload)|on[2020-01-01 08:00:00] = -0.0
+ "Storage(Q_th_unload)|flow_rate|ub": |-
+ Constraint `Storage(Q_th_unload)|flow_rate|ub`
+ [time: 9]:
+ ---------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 00:00:00] - 1000 Storage(Q_th_unload)|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 01:00:00] - 1000 Storage(Q_th_unload)|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 02:00:00] - 1000 Storage(Q_th_unload)|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 03:00:00] - 1000 Storage(Q_th_unload)|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 04:00:00] - 1000 Storage(Q_th_unload)|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 05:00:00] - 1000 Storage(Q_th_unload)|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 06:00:00] - 1000 Storage(Q_th_unload)|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 07:00:00] - 1000 Storage(Q_th_unload)|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 08:00:00] - 1000 Storage(Q_th_unload)|on[2020-01-01 08:00:00] ≤ -0.0
+ "Storage(Q_th_unload)|flow_rate|lb": |-
+ Constraint `Storage(Q_th_unload)|flow_rate|lb`
+ [time: 9]:
+ ---------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 00:00:00] - 1e-05 Storage(Q_th_unload)|on[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 01:00:00] - 1e-05 Storage(Q_th_unload)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 02:00:00] - 1e-05 Storage(Q_th_unload)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 03:00:00] - 1e-05 Storage(Q_th_unload)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 04:00:00] - 1e-05 Storage(Q_th_unload)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 05:00:00] - 1e-05 Storage(Q_th_unload)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 06:00:00] - 1e-05 Storage(Q_th_unload)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 07:00:00] - 1e-05 Storage(Q_th_unload)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 Storage(Q_th_unload)|flow_rate[2020-01-01 08:00:00] - 1e-05 Storage(Q_th_unload)|on[2020-01-01 08:00:00] ≥ -0.0
+ "Storage(Q_th_unload)|total_flow_hours": |-
+ Constraint `Storage(Q_th_unload)|total_flow_hours`
+ --------------------------------------------------
+ +1 Storage(Q_th_unload)|total_flow_hours - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 00:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 01:00:00]... -1 Storage(Q_th_unload)|flow_rate[2020-01-01 06:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 07:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Storage|prevent_simultaneous_use": |-
+ Constraint `Storage|prevent_simultaneous_use`
+ [time: 9]:
+ --------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Storage(Q_th_load)|on[2020-01-01 00:00:00] + 1 Storage(Q_th_unload)|on[2020-01-01 00:00:00] ≤ 1.0
+ [2020-01-01 01:00:00]: +1 Storage(Q_th_load)|on[2020-01-01 01:00:00] + 1 Storage(Q_th_unload)|on[2020-01-01 01:00:00] ≤ 1.0
+ [2020-01-01 02:00:00]: +1 Storage(Q_th_load)|on[2020-01-01 02:00:00] + 1 Storage(Q_th_unload)|on[2020-01-01 02:00:00] ≤ 1.0
+ [2020-01-01 03:00:00]: +1 Storage(Q_th_load)|on[2020-01-01 03:00:00] + 1 Storage(Q_th_unload)|on[2020-01-01 03:00:00] ≤ 1.0
+ [2020-01-01 04:00:00]: +1 Storage(Q_th_load)|on[2020-01-01 04:00:00] + 1 Storage(Q_th_unload)|on[2020-01-01 04:00:00] ≤ 1.0
+ [2020-01-01 05:00:00]: +1 Storage(Q_th_load)|on[2020-01-01 05:00:00] + 1 Storage(Q_th_unload)|on[2020-01-01 05:00:00] ≤ 1.0
+ [2020-01-01 06:00:00]: +1 Storage(Q_th_load)|on[2020-01-01 06:00:00] + 1 Storage(Q_th_unload)|on[2020-01-01 06:00:00] ≤ 1.0
+ [2020-01-01 07:00:00]: +1 Storage(Q_th_load)|on[2020-01-01 07:00:00] + 1 Storage(Q_th_unload)|on[2020-01-01 07:00:00] ≤ 1.0
+ [2020-01-01 08:00:00]: +1 Storage(Q_th_load)|on[2020-01-01 08:00:00] + 1 Storage(Q_th_unload)|on[2020-01-01 08:00:00] ≤ 1.0
+ "Storage|netto_discharge": |-
+ Constraint `Storage|netto_discharge`
+ [time: 9]:
+ -----------------------------------------------
+ [2020-01-01 00:00:00]: +1 Storage|netto_discharge[2020-01-01 00:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 00:00:00] + 1 Storage(Q_th_load)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Storage|netto_discharge[2020-01-01 01:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 01:00:00] + 1 Storage(Q_th_load)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Storage|netto_discharge[2020-01-01 02:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 02:00:00] + 1 Storage(Q_th_load)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Storage|netto_discharge[2020-01-01 03:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 03:00:00] + 1 Storage(Q_th_load)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Storage|netto_discharge[2020-01-01 04:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 04:00:00] + 1 Storage(Q_th_load)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Storage|netto_discharge[2020-01-01 05:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 05:00:00] + 1 Storage(Q_th_load)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Storage|netto_discharge[2020-01-01 06:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 06:00:00] + 1 Storage(Q_th_load)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Storage|netto_discharge[2020-01-01 07:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 07:00:00] + 1 Storage(Q_th_load)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Storage|netto_discharge[2020-01-01 08:00:00] - 1 Storage(Q_th_unload)|flow_rate[2020-01-01 08:00:00] + 1 Storage(Q_th_load)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Storage|charge_state": |-
+ Constraint `Storage|charge_state`
+ [time: 9]:
+ --------------------------------------------
+ [2020-01-01 01:00:00]: +1 Storage|charge_state[2020-01-01 01:00:00] - 0.92 Storage|charge_state[2020-01-01 00:00:00] - 0.9 Storage(Q_th_load)|flow_rate[2020-01-01 00:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Storage|charge_state[2020-01-01 02:00:00] - 0.92 Storage|charge_state[2020-01-01 01:00:00] - 0.9 Storage(Q_th_load)|flow_rate[2020-01-01 01:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Storage|charge_state[2020-01-01 03:00:00] - 0.92 Storage|charge_state[2020-01-01 02:00:00] - 0.9 Storage(Q_th_load)|flow_rate[2020-01-01 02:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Storage|charge_state[2020-01-01 04:00:00] - 0.92 Storage|charge_state[2020-01-01 03:00:00] - 0.9 Storage(Q_th_load)|flow_rate[2020-01-01 03:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Storage|charge_state[2020-01-01 05:00:00] - 0.92 Storage|charge_state[2020-01-01 04:00:00] - 0.9 Storage(Q_th_load)|flow_rate[2020-01-01 04:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Storage|charge_state[2020-01-01 06:00:00] - 0.92 Storage|charge_state[2020-01-01 05:00:00] - 0.9 Storage(Q_th_load)|flow_rate[2020-01-01 05:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Storage|charge_state[2020-01-01 07:00:00] - 0.92 Storage|charge_state[2020-01-01 06:00:00] - 0.9 Storage(Q_th_load)|flow_rate[2020-01-01 06:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Storage|charge_state[2020-01-01 08:00:00] - 0.92 Storage|charge_state[2020-01-01 07:00:00] - 0.9 Storage(Q_th_load)|flow_rate[2020-01-01 07:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 09:00:00]: +1 Storage|charge_state[2020-01-01 09:00:00] - 0.92 Storage|charge_state[2020-01-01 08:00:00] - 0.9 Storage(Q_th_load)|flow_rate[2020-01-01 08:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Storage->costs(periodic)": |-
+ Constraint `Storage->costs(periodic)`
+ -------------------------------------
+ +1 Storage->costs(periodic) = 20.0
+ "Storage|charge_state|ub": |-
+ Constraint `Storage|charge_state|ub`
+ [time: 10]:
+ ------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Storage|charge_state[2020-01-01 00:00:00] - 0.8 Storage|size ≤ -0.0
+ [2020-01-01 01:00:00]: +1 Storage|charge_state[2020-01-01 01:00:00] - 0.7 Storage|size ≤ -0.0
+ [2020-01-01 02:00:00]: +1 Storage|charge_state[2020-01-01 02:00:00] - 0.8 Storage|size ≤ -0.0
+ [2020-01-01 03:00:00]: +1 Storage|charge_state[2020-01-01 03:00:00] - 0.8 Storage|size ≤ -0.0
+ [2020-01-01 04:00:00]: +1 Storage|charge_state[2020-01-01 04:00:00] - 0.8 Storage|size ≤ -0.0
+ [2020-01-01 05:00:00]: +1 Storage|charge_state[2020-01-01 05:00:00] - 0.8 Storage|size ≤ -0.0
+ [2020-01-01 06:00:00]: +1 Storage|charge_state[2020-01-01 06:00:00] - 0.8 Storage|size ≤ -0.0
+ [2020-01-01 07:00:00]: +1 Storage|charge_state[2020-01-01 07:00:00] - 0.8 Storage|size ≤ -0.0
+ [2020-01-01 08:00:00]: +1 Storage|charge_state[2020-01-01 08:00:00] - 0.8 Storage|size ≤ -0.0
+ [2020-01-01 09:00:00]: +1 Storage|charge_state[2020-01-01 09:00:00] - 0.8 Storage|size ≤ -0.0
+ "Storage|charge_state|lb": |-
+ Constraint `Storage|charge_state|lb`
+ [time: 10]:
+ ------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Storage|charge_state[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 Storage|charge_state[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 Storage|charge_state[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 Storage|charge_state[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 Storage|charge_state[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 Storage|charge_state[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 Storage|charge_state[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 Storage|charge_state[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 Storage|charge_state[2020-01-01 08:00:00] ≥ -0.0
+ [2020-01-01 09:00:00]: +1 Storage|charge_state[2020-01-01 09:00:00] ≥ -0.0
+ "Storage|initial_charge_state": |-
+ Constraint `Storage|initial_charge_state`
+ -----------------------------------------
+ +1 Storage|charge_state[2020-01-01 00:00:00] = -0.0
+ "CHP(Q_fu)|total_flow_hours": |-
+ Constraint `CHP(Q_fu)|total_flow_hours`
+ ---------------------------------------
+ +1 CHP(Q_fu)|total_flow_hours - 1 CHP(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 01:00:00]... -1 CHP(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "CHP(Q_th)|total_flow_hours": |-
+ Constraint `CHP(Q_th)|total_flow_hours`
+ ---------------------------------------
+ +1 CHP(Q_th)|total_flow_hours - 1 CHP(Q_th)|flow_rate[2020-01-01 00:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 01:00:00]... -1 CHP(Q_th)|flow_rate[2020-01-01 06:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 07:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "CHP(P_el)|total_flow_hours": |-
+ Constraint `CHP(P_el)|total_flow_hours`
+ ---------------------------------------
+ +1 CHP(P_el)|total_flow_hours - 1 CHP(P_el)|flow_rate[2020-01-01 00:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 01:00:00]... -1 CHP(P_el)|flow_rate[2020-01-01 06:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 07:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "CHP|conversion_0": |-
+ Constraint `CHP|conversion_0`
+ [time: 9]:
+ ----------------------------------------
+ [2020-01-01 00:00:00]: +0.5 CHP(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +0.5 CHP(Q_fu)|flow_rate[2020-01-01 01:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +0.5 CHP(Q_fu)|flow_rate[2020-01-01 02:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +0.5 CHP(Q_fu)|flow_rate[2020-01-01 03:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +0.5 CHP(Q_fu)|flow_rate[2020-01-01 04:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +0.5 CHP(Q_fu)|flow_rate[2020-01-01 05:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +0.5 CHP(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +0.5 CHP(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +0.5 CHP(Q_fu)|flow_rate[2020-01-01 08:00:00] - 1 CHP(Q_th)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "CHP|conversion_1": |-
+ Constraint `CHP|conversion_1`
+ [time: 9]:
+ ----------------------------------------
+ [2020-01-01 00:00:00]: +0.4 CHP(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +0.4 CHP(Q_fu)|flow_rate[2020-01-01 01:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +0.4 CHP(Q_fu)|flow_rate[2020-01-01 02:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +0.4 CHP(Q_fu)|flow_rate[2020-01-01 03:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +0.4 CHP(Q_fu)|flow_rate[2020-01-01 04:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +0.4 CHP(Q_fu)|flow_rate[2020-01-01 05:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +0.4 CHP(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +0.4 CHP(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +0.4 CHP(Q_fu)|flow_rate[2020-01-01 08:00:00] - 1 CHP(P_el)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Heat Demand(Q_th_Last)|total_flow_hours": |-
+ Constraint `Heat Demand(Q_th_Last)|total_flow_hours`
+ ----------------------------------------------------
+ +1 Heat Demand(Q_th_Last)|total_flow_hours - 1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 00:00:00] - 1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 01:00:00]... -1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 06:00:00] - 1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 07:00:00] - 1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Gastarif(Q_Gas)|total_flow_hours": |-
+ Constraint `Gastarif(Q_Gas)|total_flow_hours`
+ ---------------------------------------------
+ +1 Gastarif(Q_Gas)|total_flow_hours - 1 Gastarif(Q_Gas)|flow_rate[2020-01-01 00:00:00] - 1 Gastarif(Q_Gas)|flow_rate[2020-01-01 01:00:00]... -1 Gastarif(Q_Gas)|flow_rate[2020-01-01 06:00:00] - 1 Gastarif(Q_Gas)|flow_rate[2020-01-01 07:00:00] - 1 Gastarif(Q_Gas)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Gastarif(Q_Gas)->costs(temporal)": |-
+ Constraint `Gastarif(Q_Gas)->costs(temporal)`
+ [time: 9]:
+ --------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 00:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 01:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 02:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 03:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 04:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 05:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 06:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 07:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 08:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Gastarif(Q_Gas)->CO2(temporal)": |-
+ Constraint `Gastarif(Q_Gas)->CO2(temporal)`
+ [time: 9]:
+ ------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 00:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 01:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 02:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 03:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 04:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 05:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 06:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 07:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 08:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Einspeisung(P_el)|total_flow_hours": |-
+ Constraint `Einspeisung(P_el)|total_flow_hours`
+ -----------------------------------------------
+ +1 Einspeisung(P_el)|total_flow_hours - 1 Einspeisung(P_el)|flow_rate[2020-01-01 00:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 01:00:00]... -1 Einspeisung(P_el)|flow_rate[2020-01-01 06:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 07:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Einspeisung(P_el)->costs(temporal)": |-
+ Constraint `Einspeisung(P_el)->costs(temporal)`
+ [time: 9]:
+ ----------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 00:00:00] + 0.08 Einspeisung(P_el)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 01:00:00] + 0.08 Einspeisung(P_el)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 02:00:00] + 0.08 Einspeisung(P_el)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 03:00:00] + 0.08 Einspeisung(P_el)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 04:00:00] + 0.08 Einspeisung(P_el)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 05:00:00] + 0.08 Einspeisung(P_el)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 06:00:00] + 0.08 Einspeisung(P_el)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 07:00:00] + 0.08 Einspeisung(P_el)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 08:00:00] + 0.08 Einspeisung(P_el)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Strom|balance": |-
+ Constraint `Strom|balance`
+ [time: 9]:
+ -------------------------------------
+ [2020-01-01 00:00:00]: +1 CHP(P_el)|flow_rate[2020-01-01 00:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 00:00:00] + 1 Strom|excess_input[2020-01-01 00:00:00] - 1 Strom|excess_output[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 CHP(P_el)|flow_rate[2020-01-01 01:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 01:00:00] + 1 Strom|excess_input[2020-01-01 01:00:00] - 1 Strom|excess_output[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 CHP(P_el)|flow_rate[2020-01-01 02:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 02:00:00] + 1 Strom|excess_input[2020-01-01 02:00:00] - 1 Strom|excess_output[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 CHP(P_el)|flow_rate[2020-01-01 03:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 03:00:00] + 1 Strom|excess_input[2020-01-01 03:00:00] - 1 Strom|excess_output[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 CHP(P_el)|flow_rate[2020-01-01 04:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 04:00:00] + 1 Strom|excess_input[2020-01-01 04:00:00] - 1 Strom|excess_output[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 CHP(P_el)|flow_rate[2020-01-01 05:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 05:00:00] + 1 Strom|excess_input[2020-01-01 05:00:00] - 1 Strom|excess_output[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 CHP(P_el)|flow_rate[2020-01-01 06:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 06:00:00] + 1 Strom|excess_input[2020-01-01 06:00:00] - 1 Strom|excess_output[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 CHP(P_el)|flow_rate[2020-01-01 07:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 07:00:00] + 1 Strom|excess_input[2020-01-01 07:00:00] - 1 Strom|excess_output[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 CHP(P_el)|flow_rate[2020-01-01 08:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 08:00:00] + 1 Strom|excess_input[2020-01-01 08:00:00] - 1 Strom|excess_output[2020-01-01 08:00:00] = -0.0
+ "Strom->Penalty": |-
+ Constraint `Strom->Penalty`
+ ---------------------------
+ +1 Strom->Penalty - 1e+05 Strom|excess_input[2020-01-01 00:00:00] - 1e+05 Strom|excess_input[2020-01-01 01:00:00]... -1e+05 Strom|excess_output[2020-01-01 06:00:00] - 1e+05 Strom|excess_output[2020-01-01 07:00:00] - 1e+05 Strom|excess_output[2020-01-01 08:00:00] = -0.0
+ "Fernwärme|balance": |-
+ Constraint `Fernwärme|balance`
+ [time: 9]:
+ -----------------------------------------
+ [2020-01-01 00:00:00]: +1 Boiler(Q_th)|flow_rate[2020-01-01 00:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 00:00:00] + 1 CHP(Q_th)|flow_rate[2020-01-01 00:00:00]... -1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 00:00:00] + 1 Fernwärme|excess_input[2020-01-01 00:00:00] - 1 Fernwärme|excess_output[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Boiler(Q_th)|flow_rate[2020-01-01 01:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 01:00:00] + 1 CHP(Q_th)|flow_rate[2020-01-01 01:00:00]... -1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 01:00:00] + 1 Fernwärme|excess_input[2020-01-01 01:00:00] - 1 Fernwärme|excess_output[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Boiler(Q_th)|flow_rate[2020-01-01 02:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 02:00:00] + 1 CHP(Q_th)|flow_rate[2020-01-01 02:00:00]... -1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 02:00:00] + 1 Fernwärme|excess_input[2020-01-01 02:00:00] - 1 Fernwärme|excess_output[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Boiler(Q_th)|flow_rate[2020-01-01 03:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 03:00:00] + 1 CHP(Q_th)|flow_rate[2020-01-01 03:00:00]... -1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 03:00:00] + 1 Fernwärme|excess_input[2020-01-01 03:00:00] - 1 Fernwärme|excess_output[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Boiler(Q_th)|flow_rate[2020-01-01 04:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 04:00:00] + 1 CHP(Q_th)|flow_rate[2020-01-01 04:00:00]... -1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 04:00:00] + 1 Fernwärme|excess_input[2020-01-01 04:00:00] - 1 Fernwärme|excess_output[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Boiler(Q_th)|flow_rate[2020-01-01 05:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 05:00:00] + 1 CHP(Q_th)|flow_rate[2020-01-01 05:00:00]... -1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 05:00:00] + 1 Fernwärme|excess_input[2020-01-01 05:00:00] - 1 Fernwärme|excess_output[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Boiler(Q_th)|flow_rate[2020-01-01 06:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 06:00:00] + 1 CHP(Q_th)|flow_rate[2020-01-01 06:00:00]... -1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 06:00:00] + 1 Fernwärme|excess_input[2020-01-01 06:00:00] - 1 Fernwärme|excess_output[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Boiler(Q_th)|flow_rate[2020-01-01 07:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 07:00:00] + 1 CHP(Q_th)|flow_rate[2020-01-01 07:00:00]... -1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 07:00:00] + 1 Fernwärme|excess_input[2020-01-01 07:00:00] - 1 Fernwärme|excess_output[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Boiler(Q_th)|flow_rate[2020-01-01 08:00:00] + 1 Storage(Q_th_unload)|flow_rate[2020-01-01 08:00:00] + 1 CHP(Q_th)|flow_rate[2020-01-01 08:00:00]... -1 Heat Demand(Q_th_Last)|flow_rate[2020-01-01 08:00:00] + 1 Fernwärme|excess_input[2020-01-01 08:00:00] - 1 Fernwärme|excess_output[2020-01-01 08:00:00] = -0.0
+ "Fernwärme->Penalty": |-
+ Constraint `Fernwärme->Penalty`
+ -------------------------------
+ +1 Fernwärme->Penalty - 1e+05 Fernwärme|excess_input[2020-01-01 00:00:00] - 1e+05 Fernwärme|excess_input[2020-01-01 01:00:00]... -1e+05 Fernwärme|excess_output[2020-01-01 06:00:00] - 1e+05 Fernwärme|excess_output[2020-01-01 07:00:00] - 1e+05 Fernwärme|excess_output[2020-01-01 08:00:00] = -0.0
+ "Gas|balance": |-
+ Constraint `Gas|balance`
+ [time: 9]:
+ -----------------------------------
+ [2020-01-01 00:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 00:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 00:00:00] + 1 Gas|excess_input[2020-01-01 00:00:00] - 1 Gas|excess_output[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 01:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 01:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 01:00:00] + 1 Gas|excess_input[2020-01-01 01:00:00] - 1 Gas|excess_output[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 02:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 02:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 02:00:00] + 1 Gas|excess_input[2020-01-01 02:00:00] - 1 Gas|excess_output[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 03:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 03:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 03:00:00] + 1 Gas|excess_input[2020-01-01 03:00:00] - 1 Gas|excess_output[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 04:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 04:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 04:00:00] + 1 Gas|excess_input[2020-01-01 04:00:00] - 1 Gas|excess_output[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 05:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 05:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 05:00:00] + 1 Gas|excess_input[2020-01-01 05:00:00] - 1 Gas|excess_output[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 06:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 06:00:00] + 1 Gas|excess_input[2020-01-01 06:00:00] - 1 Gas|excess_output[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 07:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 07:00:00] + 1 Gas|excess_input[2020-01-01 07:00:00] - 1 Gas|excess_output[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 08:00:00] - 1 Boiler(Q_fu)|flow_rate[2020-01-01 08:00:00] - 1 CHP(Q_fu)|flow_rate[2020-01-01 08:00:00] + 1 Gas|excess_input[2020-01-01 08:00:00] - 1 Gas|excess_output[2020-01-01 08:00:00] = -0.0
+ "Gas->Penalty": |-
+ Constraint `Gas->Penalty`
+ -------------------------
+ +1 Gas->Penalty - 1e+05 Gas|excess_input[2020-01-01 00:00:00] - 1e+05 Gas|excess_input[2020-01-01 01:00:00]... -1e+05 Gas|excess_output[2020-01-01 06:00:00] - 1e+05 Gas|excess_output[2020-01-01 07:00:00] - 1e+05 Gas|excess_output[2020-01-01 08:00:00] = -0.0
+binaries:
+ - "Storage(Q_th_load)|on"
+ - "Storage(Q_th_unload)|on"
+integers: []
+continuous:
+ - costs(periodic)
+ - costs(temporal)
+ - "costs(temporal)|per_timestep"
+ - costs
+ - CO2(periodic)
+ - CO2(temporal)
+ - "CO2(temporal)|per_timestep"
+ - CO2
+ - Penalty
+ - "CO2(temporal)->costs(temporal)"
+ - "Boiler(Q_fu)|flow_rate"
+ - "Boiler(Q_fu)|total_flow_hours"
+ - "Boiler(Q_th)|flow_rate"
+ - "Boiler(Q_th)|total_flow_hours"
+ - "Storage(Q_th_load)|flow_rate"
+ - "Storage(Q_th_load)|on_hours_total"
+ - "Storage(Q_th_load)|total_flow_hours"
+ - "Storage(Q_th_unload)|flow_rate"
+ - "Storage(Q_th_unload)|on_hours_total"
+ - "Storage(Q_th_unload)|total_flow_hours"
+ - "Storage|charge_state"
+ - "Storage|netto_discharge"
+ - "Storage|size"
+ - "Storage->costs(periodic)"
+ - "CHP(Q_fu)|flow_rate"
+ - "CHP(Q_fu)|total_flow_hours"
+ - "CHP(Q_th)|flow_rate"
+ - "CHP(Q_th)|total_flow_hours"
+ - "CHP(P_el)|flow_rate"
+ - "CHP(P_el)|total_flow_hours"
+ - "Heat Demand(Q_th_Last)|flow_rate"
+ - "Heat Demand(Q_th_Last)|total_flow_hours"
+ - "Gastarif(Q_Gas)|flow_rate"
+ - "Gastarif(Q_Gas)|total_flow_hours"
+ - "Gastarif(Q_Gas)->costs(temporal)"
+ - "Gastarif(Q_Gas)->CO2(temporal)"
+ - "Einspeisung(P_el)|flow_rate"
+ - "Einspeisung(P_el)|total_flow_hours"
+ - "Einspeisung(P_el)->costs(temporal)"
+ - "Strom|excess_input"
+ - "Strom|excess_output"
+ - "Strom->Penalty"
+ - "Fernwärme|excess_input"
+ - "Fernwärme|excess_output"
+ - "Fernwärme->Penalty"
+ - "Gas|excess_input"
+ - "Gas|excess_output"
+ - "Gas->Penalty"
+infeasible_constraints: ''
diff --git a/tests/ressources/v4-api/01_simple--solution.nc4 b/tests/ressources/v4-api/01_simple--solution.nc4
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diff --git a/tests/ressources/v4-api/01_simple--summary.yaml b/tests/ressources/v4-api/01_simple--summary.yaml
new file mode 100644
index 000000000..87984de57
--- /dev/null
+++ b/tests/ressources/v4-api/01_simple--summary.yaml
@@ -0,0 +1,51 @@
+Name: 01_simple
+Number of timesteps: 9
+Calculation Type: FullCalculation
+Constraints: 215
+Variables: 259
+Main Results:
+ Objective: 83.88
+ Penalty: 0.0
+ Effects:
+ CO2 [kg]:
+ temporal: 255.33
+ periodic: -0.0
+ total: 255.33
+ costs [€]:
+ temporal: 63.88
+ periodic: 20.0
+ total: 83.88
+ Invest-Decisions:
+ Invested:
+ Storage: 30.0
+ Not invested: {}
+ Buses with excess: []
+Durations:
+ modeling: 0.65
+ solving: 0.38
+ saving: 0.0
+Config:
+ config_name: flixopt
+ logging:
+ level: INFO
+ file: null
+ console: false
+ max_file_size: 10485760
+ backup_count: 5
+ verbose_tracebacks: false
+ modeling:
+ big: 10000000
+ epsilon: 1.0e-05
+ big_binary_bound: 100000
+ solving:
+ mip_gap: 0.01
+ time_limit_seconds: 300
+ log_to_console: false
+ log_main_results: false
+ plotting:
+ default_show: false
+ default_engine: plotly
+ default_dpi: 300
+ default_facet_cols: 3
+ default_sequential_colorscale: turbo
+ default_qualitative_colorscale: plotly
diff --git a/tests/ressources/v4-api/02_complex--flow_system.nc4 b/tests/ressources/v4-api/02_complex--flow_system.nc4
new file mode 100644
index 0000000000000000000000000000000000000000..107f10a7959515ca682ad7a040e45a94fe6849e4
GIT binary patch
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diff --git a/tests/ressources/v4-api/02_complex--model_documentation.yaml b/tests/ressources/v4-api/02_complex--model_documentation.yaml
new file mode 100644
index 000000000..d77ed31f6
--- /dev/null
+++ b/tests/ressources/v4-api/02_complex--model_documentation.yaml
@@ -0,0 +1,1905 @@
+objective: |-
+ Objective:
+ ----------
+ LinearExpression: +1 costs + 1 Penalty
+ Sense: min
+ Value: -10711.526565761338
+termination_condition: optimal
+status: ok
+nvars: 507
+nvarsbin: 146
+nvarscont: 361
+ncons: 589
+variables:
+ costs(periodic): |-
+ Variable
+ --------
+ costs(periodic) ∈ [-inf, inf]
+ costs(temporal): |-
+ Variable
+ --------
+ costs(temporal) ∈ [-inf, inf]
+ "costs(temporal)|per_timestep": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: costs(temporal)|per_timestep[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: costs(temporal)|per_timestep[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: costs(temporal)|per_timestep[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: costs(temporal)|per_timestep[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: costs(temporal)|per_timestep[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: costs(temporal)|per_timestep[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: costs(temporal)|per_timestep[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: costs(temporal)|per_timestep[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: costs(temporal)|per_timestep[2020-01-01 08:00:00] ∈ [-inf, inf]
+ costs: |-
+ Variable
+ --------
+ costs ∈ [-inf, inf]
+ CO2(periodic): |-
+ Variable
+ --------
+ CO2(periodic) ∈ [-inf, inf]
+ CO2(temporal): |-
+ Variable
+ --------
+ CO2(temporal) ∈ [-inf, inf]
+ "CO2(temporal)|per_timestep": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: CO2(temporal)|per_timestep[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: CO2(temporal)|per_timestep[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: CO2(temporal)|per_timestep[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: CO2(temporal)|per_timestep[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: CO2(temporal)|per_timestep[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: CO2(temporal)|per_timestep[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: CO2(temporal)|per_timestep[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: CO2(temporal)|per_timestep[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: CO2(temporal)|per_timestep[2020-01-01 08:00:00] ∈ [-inf, inf]
+ CO2: |-
+ Variable
+ --------
+ CO2 ∈ [-inf, inf]
+ PE(periodic): |-
+ Variable
+ --------
+ PE(periodic) ∈ [-inf, inf]
+ PE(temporal): |-
+ Variable
+ --------
+ PE(temporal) ∈ [-inf, inf]
+ "PE(temporal)|per_timestep": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: PE(temporal)|per_timestep[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: PE(temporal)|per_timestep[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: PE(temporal)|per_timestep[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: PE(temporal)|per_timestep[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: PE(temporal)|per_timestep[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: PE(temporal)|per_timestep[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: PE(temporal)|per_timestep[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: PE(temporal)|per_timestep[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: PE(temporal)|per_timestep[2020-01-01 08:00:00] ∈ [-inf, inf]
+ PE: |-
+ Variable
+ --------
+ PE ∈ [-inf, 3500]
+ Penalty: |-
+ Variable
+ --------
+ Penalty ∈ [-inf, inf]
+ "CO2(temporal)->costs(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: CO2(temporal)->costs(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Kessel(Q_fu)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel(Q_fu)|flow_rate[2020-01-01 00:00:00] ∈ [0, 200]
+ [2020-01-01 01:00:00]: Kessel(Q_fu)|flow_rate[2020-01-01 01:00:00] ∈ [0, 200]
+ [2020-01-01 02:00:00]: Kessel(Q_fu)|flow_rate[2020-01-01 02:00:00] ∈ [0, 200]
+ [2020-01-01 03:00:00]: Kessel(Q_fu)|flow_rate[2020-01-01 03:00:00] ∈ [0, 200]
+ [2020-01-01 04:00:00]: Kessel(Q_fu)|flow_rate[2020-01-01 04:00:00] ∈ [0, 200]
+ [2020-01-01 05:00:00]: Kessel(Q_fu)|flow_rate[2020-01-01 05:00:00] ∈ [0, 200]
+ [2020-01-01 06:00:00]: Kessel(Q_fu)|flow_rate[2020-01-01 06:00:00] ∈ [0, 200]
+ [2020-01-01 07:00:00]: Kessel(Q_fu)|flow_rate[2020-01-01 07:00:00] ∈ [0, 200]
+ [2020-01-01 08:00:00]: Kessel(Q_fu)|flow_rate[2020-01-01 08:00:00] ∈ [0, 200]
+ "Kessel(Q_fu)|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel(Q_fu)|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: Kessel(Q_fu)|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: Kessel(Q_fu)|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: Kessel(Q_fu)|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: Kessel(Q_fu)|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: Kessel(Q_fu)|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: Kessel(Q_fu)|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: Kessel(Q_fu)|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: Kessel(Q_fu)|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "Kessel(Q_fu)|on_hours_total": |-
+ Variable
+ --------
+ Kessel(Q_fu)|on_hours_total ∈ [0, inf]
+ "Kessel(Q_fu)|total_flow_hours": |-
+ Variable
+ --------
+ Kessel(Q_fu)|total_flow_hours ∈ [0, inf]
+ "Kessel(Q_th)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel(Q_th)|flow_rate[2020-01-01 00:00:00] ∈ [0, 50]
+ [2020-01-01 01:00:00]: Kessel(Q_th)|flow_rate[2020-01-01 01:00:00] ∈ [0, 50]
+ [2020-01-01 02:00:00]: Kessel(Q_th)|flow_rate[2020-01-01 02:00:00] ∈ [0, 50]
+ [2020-01-01 03:00:00]: Kessel(Q_th)|flow_rate[2020-01-01 03:00:00] ∈ [0, 50]
+ [2020-01-01 04:00:00]: Kessel(Q_th)|flow_rate[2020-01-01 04:00:00] ∈ [0, 50]
+ [2020-01-01 05:00:00]: Kessel(Q_th)|flow_rate[2020-01-01 05:00:00] ∈ [0, 50]
+ [2020-01-01 06:00:00]: Kessel(Q_th)|flow_rate[2020-01-01 06:00:00] ∈ [0, 50]
+ [2020-01-01 07:00:00]: Kessel(Q_th)|flow_rate[2020-01-01 07:00:00] ∈ [0, 50]
+ [2020-01-01 08:00:00]: Kessel(Q_th)|flow_rate[2020-01-01 08:00:00] ∈ [0, 50]
+ "Kessel(Q_th)|size": |-
+ Variable
+ --------
+ Kessel(Q_th)|size ∈ [50, 50]
+ "Kessel(Q_th)->costs(periodic)": |-
+ Variable
+ --------
+ Kessel(Q_th)->costs(periodic) ∈ [-inf, inf]
+ "Kessel(Q_th)->PE(periodic)": |-
+ Variable
+ --------
+ Kessel(Q_th)->PE(periodic) ∈ [-inf, inf]
+ "Kessel(Q_th)|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel(Q_th)|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: Kessel(Q_th)|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: Kessel(Q_th)|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: Kessel(Q_th)|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: Kessel(Q_th)|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: Kessel(Q_th)|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: Kessel(Q_th)|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: Kessel(Q_th)|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: Kessel(Q_th)|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "Kessel(Q_th)|off": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel(Q_th)|off[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: Kessel(Q_th)|off[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: Kessel(Q_th)|off[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: Kessel(Q_th)|off[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: Kessel(Q_th)|off[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: Kessel(Q_th)|off[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: Kessel(Q_th)|off[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: Kessel(Q_th)|off[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: Kessel(Q_th)|off[2020-01-01 08:00:00] ∈ {0, 1}
+ "Kessel(Q_th)|on_hours_total": |-
+ Variable
+ --------
+ Kessel(Q_th)|on_hours_total ∈ [0, 1000]
+ "Kessel(Q_th)|switch|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel(Q_th)|switch|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: Kessel(Q_th)|switch|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: Kessel(Q_th)|switch|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: Kessel(Q_th)|switch|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: Kessel(Q_th)|switch|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: Kessel(Q_th)|switch|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: Kessel(Q_th)|switch|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: Kessel(Q_th)|switch|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: Kessel(Q_th)|switch|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "Kessel(Q_th)|switch|off": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel(Q_th)|switch|off[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: Kessel(Q_th)|switch|off[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: Kessel(Q_th)|switch|off[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: Kessel(Q_th)|switch|off[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: Kessel(Q_th)|switch|off[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: Kessel(Q_th)|switch|off[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: Kessel(Q_th)|switch|off[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: Kessel(Q_th)|switch|off[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: Kessel(Q_th)|switch|off[2020-01-01 08:00:00] ∈ {0, 1}
+ "Kessel(Q_th)|switch|count": |-
+ Variable
+ --------
+ Kessel(Q_th)|switch|count ∈ [0, 1000]
+ "Kessel(Q_th)|consecutive_on_hours": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel(Q_th)|consecutive_on_hours[2020-01-01 00:00:00] ∈ [0, 10]
+ [2020-01-01 01:00:00]: Kessel(Q_th)|consecutive_on_hours[2020-01-01 01:00:00] ∈ [0, 10]
+ [2020-01-01 02:00:00]: Kessel(Q_th)|consecutive_on_hours[2020-01-01 02:00:00] ∈ [0, 10]
+ [2020-01-01 03:00:00]: Kessel(Q_th)|consecutive_on_hours[2020-01-01 03:00:00] ∈ [0, 10]
+ [2020-01-01 04:00:00]: Kessel(Q_th)|consecutive_on_hours[2020-01-01 04:00:00] ∈ [0, 10]
+ [2020-01-01 05:00:00]: Kessel(Q_th)|consecutive_on_hours[2020-01-01 05:00:00] ∈ [0, 10]
+ [2020-01-01 06:00:00]: Kessel(Q_th)|consecutive_on_hours[2020-01-01 06:00:00] ∈ [0, 10]
+ [2020-01-01 07:00:00]: Kessel(Q_th)|consecutive_on_hours[2020-01-01 07:00:00] ∈ [0, 10]
+ [2020-01-01 08:00:00]: Kessel(Q_th)|consecutive_on_hours[2020-01-01 08:00:00] ∈ [0, 10]
+ "Kessel(Q_th)|consecutive_off_hours": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel(Q_th)|consecutive_off_hours[2020-01-01 00:00:00] ∈ [0, 10]
+ [2020-01-01 01:00:00]: Kessel(Q_th)|consecutive_off_hours[2020-01-01 01:00:00] ∈ [0, 10]
+ [2020-01-01 02:00:00]: Kessel(Q_th)|consecutive_off_hours[2020-01-01 02:00:00] ∈ [0, 10]
+ [2020-01-01 03:00:00]: Kessel(Q_th)|consecutive_off_hours[2020-01-01 03:00:00] ∈ [0, 10]
+ [2020-01-01 04:00:00]: Kessel(Q_th)|consecutive_off_hours[2020-01-01 04:00:00] ∈ [0, 10]
+ [2020-01-01 05:00:00]: Kessel(Q_th)|consecutive_off_hours[2020-01-01 05:00:00] ∈ [0, 10]
+ [2020-01-01 06:00:00]: Kessel(Q_th)|consecutive_off_hours[2020-01-01 06:00:00] ∈ [0, 10]
+ [2020-01-01 07:00:00]: Kessel(Q_th)|consecutive_off_hours[2020-01-01 07:00:00] ∈ [0, 10]
+ [2020-01-01 08:00:00]: Kessel(Q_th)|consecutive_off_hours[2020-01-01 08:00:00] ∈ [0, 10]
+ "Kessel(Q_th)->costs(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel(Q_th)->costs(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Kessel(Q_th)->costs(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Kessel(Q_th)->costs(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Kessel(Q_th)->costs(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Kessel(Q_th)->costs(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Kessel(Q_th)->costs(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Kessel(Q_th)->costs(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Kessel(Q_th)->costs(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Kessel(Q_th)->costs(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Kessel(Q_th)|total_flow_hours": |-
+ Variable
+ --------
+ Kessel(Q_th)|total_flow_hours ∈ [0, 1e+06]
+ "Kessel|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: Kessel|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: Kessel|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: Kessel|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: Kessel|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: Kessel|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: Kessel|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: Kessel|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: Kessel|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "Kessel|on_hours_total": |-
+ Variable
+ --------
+ Kessel|on_hours_total ∈ [0, inf]
+ "Kessel->costs(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel->costs(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Kessel->costs(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Kessel->costs(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Kessel->costs(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Kessel->costs(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Kessel->costs(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Kessel->costs(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Kessel->costs(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Kessel->costs(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Kessel->CO2(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Kessel->CO2(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Kessel->CO2(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Kessel->CO2(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Kessel->CO2(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Kessel->CO2(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Kessel->CO2(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Kessel->CO2(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Kessel->CO2(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Kessel->CO2(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Wärmelast(Q_th_Last)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Wärmelast(Q_th_Last)|flow_rate[2020-01-01 00:00:00] ∈ [30, 30]
+ [2020-01-01 01:00:00]: Wärmelast(Q_th_Last)|flow_rate[2020-01-01 01:00:00] ∈ [0, 0]
+ [2020-01-01 02:00:00]: Wärmelast(Q_th_Last)|flow_rate[2020-01-01 02:00:00] ∈ [90, 90]
+ [2020-01-01 03:00:00]: Wärmelast(Q_th_Last)|flow_rate[2020-01-01 03:00:00] ∈ [110, 110]
+ [2020-01-01 04:00:00]: Wärmelast(Q_th_Last)|flow_rate[2020-01-01 04:00:00] ∈ [110, 110]
+ [2020-01-01 05:00:00]: Wärmelast(Q_th_Last)|flow_rate[2020-01-01 05:00:00] ∈ [20, 20]
+ [2020-01-01 06:00:00]: Wärmelast(Q_th_Last)|flow_rate[2020-01-01 06:00:00] ∈ [20, 20]
+ [2020-01-01 07:00:00]: Wärmelast(Q_th_Last)|flow_rate[2020-01-01 07:00:00] ∈ [20, 20]
+ [2020-01-01 08:00:00]: Wärmelast(Q_th_Last)|flow_rate[2020-01-01 08:00:00] ∈ [20, 20]
+ "Wärmelast(Q_th_Last)|total_flow_hours": |-
+ Variable
+ --------
+ Wärmelast(Q_th_Last)|total_flow_hours ∈ [0, inf]
+ "Gastarif(Q_Gas)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1000]
+ [2020-01-01 01:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1000]
+ [2020-01-01 02:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1000]
+ [2020-01-01 03:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1000]
+ [2020-01-01 04:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1000]
+ [2020-01-01 05:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1000]
+ [2020-01-01 06:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1000]
+ [2020-01-01 07:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1000]
+ [2020-01-01 08:00:00]: Gastarif(Q_Gas)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1000]
+ "Gastarif(Q_Gas)|total_flow_hours": |-
+ Variable
+ --------
+ Gastarif(Q_Gas)|total_flow_hours ∈ [0, inf]
+ "Gastarif(Q_Gas)->costs(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Gastarif(Q_Gas)->costs(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Gastarif(Q_Gas)->CO2(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Einspeisung(P_el)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1e+07]
+ [2020-01-01 01:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1e+07]
+ [2020-01-01 02:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1e+07]
+ [2020-01-01 03:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1e+07]
+ [2020-01-01 04:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1e+07]
+ [2020-01-01 05:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1e+07]
+ [2020-01-01 06:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1e+07]
+ [2020-01-01 07:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1e+07]
+ [2020-01-01 08:00:00]: Einspeisung(P_el)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1e+07]
+ "Einspeisung(P_el)|total_flow_hours": |-
+ Variable
+ --------
+ Einspeisung(P_el)|total_flow_hours ∈ [0, inf]
+ "Einspeisung(P_el)->costs(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Einspeisung(P_el)->costs(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Speicher(Q_th_load)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Speicher(Q_th_load)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1e+04]
+ [2020-01-01 01:00:00]: Speicher(Q_th_load)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1e+04]
+ [2020-01-01 02:00:00]: Speicher(Q_th_load)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1e+04]
+ [2020-01-01 03:00:00]: Speicher(Q_th_load)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1e+04]
+ [2020-01-01 04:00:00]: Speicher(Q_th_load)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1e+04]
+ [2020-01-01 05:00:00]: Speicher(Q_th_load)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1e+04]
+ [2020-01-01 06:00:00]: Speicher(Q_th_load)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1e+04]
+ [2020-01-01 07:00:00]: Speicher(Q_th_load)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1e+04]
+ [2020-01-01 08:00:00]: Speicher(Q_th_load)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1e+04]
+ "Speicher(Q_th_load)|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Speicher(Q_th_load)|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: Speicher(Q_th_load)|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: Speicher(Q_th_load)|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: Speicher(Q_th_load)|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: Speicher(Q_th_load)|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: Speicher(Q_th_load)|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: Speicher(Q_th_load)|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: Speicher(Q_th_load)|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: Speicher(Q_th_load)|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "Speicher(Q_th_load)|on_hours_total": |-
+ Variable
+ --------
+ Speicher(Q_th_load)|on_hours_total ∈ [0, inf]
+ "Speicher(Q_th_load)|total_flow_hours": |-
+ Variable
+ --------
+ Speicher(Q_th_load)|total_flow_hours ∈ [0, inf]
+ "Speicher(Q_th_unload)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Speicher(Q_th_unload)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1e+04]
+ [2020-01-01 01:00:00]: Speicher(Q_th_unload)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1e+04]
+ [2020-01-01 02:00:00]: Speicher(Q_th_unload)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1e+04]
+ [2020-01-01 03:00:00]: Speicher(Q_th_unload)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1e+04]
+ [2020-01-01 04:00:00]: Speicher(Q_th_unload)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1e+04]
+ [2020-01-01 05:00:00]: Speicher(Q_th_unload)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1e+04]
+ [2020-01-01 06:00:00]: Speicher(Q_th_unload)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1e+04]
+ [2020-01-01 07:00:00]: Speicher(Q_th_unload)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1e+04]
+ [2020-01-01 08:00:00]: Speicher(Q_th_unload)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1e+04]
+ "Speicher(Q_th_unload)|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Speicher(Q_th_unload)|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: Speicher(Q_th_unload)|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: Speicher(Q_th_unload)|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: Speicher(Q_th_unload)|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: Speicher(Q_th_unload)|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: Speicher(Q_th_unload)|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: Speicher(Q_th_unload)|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: Speicher(Q_th_unload)|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: Speicher(Q_th_unload)|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "Speicher(Q_th_unload)|on_hours_total": |-
+ Variable
+ --------
+ Speicher(Q_th_unload)|on_hours_total ∈ [0, inf]
+ "Speicher(Q_th_unload)|total_flow_hours": |-
+ Variable
+ --------
+ Speicher(Q_th_unload)|total_flow_hours ∈ [0, inf]
+ "Speicher|charge_state": |-
+ Variable (time: 10)
+ -------------------
+ [2020-01-01 00:00:00]: Speicher|charge_state[2020-01-01 00:00:00] ∈ [0, 1000]
+ [2020-01-01 01:00:00]: Speicher|charge_state[2020-01-01 01:00:00] ∈ [0, 1000]
+ [2020-01-01 02:00:00]: Speicher|charge_state[2020-01-01 02:00:00] ∈ [0, 1000]
+ [2020-01-01 03:00:00]: Speicher|charge_state[2020-01-01 03:00:00] ∈ [0, 1000]
+ [2020-01-01 04:00:00]: Speicher|charge_state[2020-01-01 04:00:00] ∈ [0, 1000]
+ [2020-01-01 05:00:00]: Speicher|charge_state[2020-01-01 05:00:00] ∈ [0, 1000]
+ [2020-01-01 06:00:00]: Speicher|charge_state[2020-01-01 06:00:00] ∈ [0, 1000]
+ [2020-01-01 07:00:00]: Speicher|charge_state[2020-01-01 07:00:00] ∈ [0, 1000]
+ [2020-01-01 08:00:00]: Speicher|charge_state[2020-01-01 08:00:00] ∈ [0, 1000]
+ [2020-01-01 09:00:00]: Speicher|charge_state[2020-01-01 09:00:00] ∈ [0, 1000]
+ "Speicher|netto_discharge": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Speicher|netto_discharge[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: Speicher|netto_discharge[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: Speicher|netto_discharge[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: Speicher|netto_discharge[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: Speicher|netto_discharge[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: Speicher|netto_discharge[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: Speicher|netto_discharge[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: Speicher|netto_discharge[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: Speicher|netto_discharge[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "Speicher|size": |-
+ Variable
+ --------
+ Speicher|size ∈ [0, 1000]
+ "Speicher|PiecewiseEffects|costs": |-
+ Variable
+ --------
+ Speicher|PiecewiseEffects|costs ∈ [-inf, inf]
+ "Speicher|PiecewiseEffects|PE": |-
+ Variable
+ --------
+ Speicher|PiecewiseEffects|PE ∈ [-inf, inf]
+ "Speicher|Piece_0|inside_piece": |-
+ Variable
+ --------
+ Speicher|Piece_0|inside_piece ∈ {0, 1}
+ "Speicher|Piece_0|lambda0": |-
+ Variable
+ --------
+ Speicher|Piece_0|lambda0 ∈ [0, 1]
+ "Speicher|Piece_0|lambda1": |-
+ Variable
+ --------
+ Speicher|Piece_0|lambda1 ∈ [0, 1]
+ "Speicher|Piece_1|inside_piece": |-
+ Variable
+ --------
+ Speicher|Piece_1|inside_piece ∈ {0, 1}
+ "Speicher|Piece_1|lambda0": |-
+ Variable
+ --------
+ Speicher|Piece_1|lambda0 ∈ [0, 1]
+ "Speicher|Piece_1|lambda1": |-
+ Variable
+ --------
+ Speicher|Piece_1|lambda1 ∈ [0, 1]
+ "Speicher->costs(periodic)": |-
+ Variable
+ --------
+ Speicher->costs(periodic) ∈ [-inf, inf]
+ "Speicher->PE(periodic)": |-
+ Variable
+ --------
+ Speicher->PE(periodic) ∈ [-inf, inf]
+ "BHKW2(Q_fu)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2(Q_fu)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1e+07]
+ [2020-01-01 01:00:00]: BHKW2(Q_fu)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1e+07]
+ [2020-01-01 02:00:00]: BHKW2(Q_fu)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1e+07]
+ [2020-01-01 03:00:00]: BHKW2(Q_fu)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1e+07]
+ [2020-01-01 04:00:00]: BHKW2(Q_fu)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1e+07]
+ [2020-01-01 05:00:00]: BHKW2(Q_fu)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1e+07]
+ [2020-01-01 06:00:00]: BHKW2(Q_fu)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1e+07]
+ [2020-01-01 07:00:00]: BHKW2(Q_fu)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1e+07]
+ [2020-01-01 08:00:00]: BHKW2(Q_fu)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1e+07]
+ "BHKW2(Q_fu)|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2(Q_fu)|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: BHKW2(Q_fu)|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: BHKW2(Q_fu)|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: BHKW2(Q_fu)|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: BHKW2(Q_fu)|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: BHKW2(Q_fu)|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: BHKW2(Q_fu)|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: BHKW2(Q_fu)|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: BHKW2(Q_fu)|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "BHKW2(Q_fu)|on_hours_total": |-
+ Variable
+ --------
+ BHKW2(Q_fu)|on_hours_total ∈ [0, inf]
+ "BHKW2(Q_fu)|total_flow_hours": |-
+ Variable
+ --------
+ BHKW2(Q_fu)|total_flow_hours ∈ [0, inf]
+ "BHKW2(P_el)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2(P_el)|flow_rate[2020-01-01 00:00:00] ∈ [0, 60]
+ [2020-01-01 01:00:00]: BHKW2(P_el)|flow_rate[2020-01-01 01:00:00] ∈ [0, 60]
+ [2020-01-01 02:00:00]: BHKW2(P_el)|flow_rate[2020-01-01 02:00:00] ∈ [0, 60]
+ [2020-01-01 03:00:00]: BHKW2(P_el)|flow_rate[2020-01-01 03:00:00] ∈ [0, 60]
+ [2020-01-01 04:00:00]: BHKW2(P_el)|flow_rate[2020-01-01 04:00:00] ∈ [0, 60]
+ [2020-01-01 05:00:00]: BHKW2(P_el)|flow_rate[2020-01-01 05:00:00] ∈ [0, 60]
+ [2020-01-01 06:00:00]: BHKW2(P_el)|flow_rate[2020-01-01 06:00:00] ∈ [0, 60]
+ [2020-01-01 07:00:00]: BHKW2(P_el)|flow_rate[2020-01-01 07:00:00] ∈ [0, 60]
+ [2020-01-01 08:00:00]: BHKW2(P_el)|flow_rate[2020-01-01 08:00:00] ∈ [0, 60]
+ "BHKW2(P_el)|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2(P_el)|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: BHKW2(P_el)|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: BHKW2(P_el)|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: BHKW2(P_el)|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: BHKW2(P_el)|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: BHKW2(P_el)|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: BHKW2(P_el)|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: BHKW2(P_el)|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: BHKW2(P_el)|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "BHKW2(P_el)|on_hours_total": |-
+ Variable
+ --------
+ BHKW2(P_el)|on_hours_total ∈ [0, inf]
+ "BHKW2(P_el)|total_flow_hours": |-
+ Variable
+ --------
+ BHKW2(P_el)|total_flow_hours ∈ [0, inf]
+ "BHKW2(Q_th)|flow_rate": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2(Q_th)|flow_rate[2020-01-01 00:00:00] ∈ [0, 1e+07]
+ [2020-01-01 01:00:00]: BHKW2(Q_th)|flow_rate[2020-01-01 01:00:00] ∈ [0, 1e+07]
+ [2020-01-01 02:00:00]: BHKW2(Q_th)|flow_rate[2020-01-01 02:00:00] ∈ [0, 1e+07]
+ [2020-01-01 03:00:00]: BHKW2(Q_th)|flow_rate[2020-01-01 03:00:00] ∈ [0, 1e+07]
+ [2020-01-01 04:00:00]: BHKW2(Q_th)|flow_rate[2020-01-01 04:00:00] ∈ [0, 1e+07]
+ [2020-01-01 05:00:00]: BHKW2(Q_th)|flow_rate[2020-01-01 05:00:00] ∈ [0, 1e+07]
+ [2020-01-01 06:00:00]: BHKW2(Q_th)|flow_rate[2020-01-01 06:00:00] ∈ [0, 1e+07]
+ [2020-01-01 07:00:00]: BHKW2(Q_th)|flow_rate[2020-01-01 07:00:00] ∈ [0, 1e+07]
+ [2020-01-01 08:00:00]: BHKW2(Q_th)|flow_rate[2020-01-01 08:00:00] ∈ [0, 1e+07]
+ "BHKW2(Q_th)|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2(Q_th)|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: BHKW2(Q_th)|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: BHKW2(Q_th)|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: BHKW2(Q_th)|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: BHKW2(Q_th)|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: BHKW2(Q_th)|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: BHKW2(Q_th)|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: BHKW2(Q_th)|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: BHKW2(Q_th)|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "BHKW2(Q_th)|on_hours_total": |-
+ Variable
+ --------
+ BHKW2(Q_th)|on_hours_total ∈ [0, inf]
+ "BHKW2(Q_th)|total_flow_hours": |-
+ Variable
+ --------
+ BHKW2(Q_th)|total_flow_hours ∈ [0, inf]
+ "BHKW2|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: BHKW2|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: BHKW2|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: BHKW2|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: BHKW2|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: BHKW2|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: BHKW2|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: BHKW2|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: BHKW2|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "BHKW2|on_hours_total": |-
+ Variable
+ --------
+ BHKW2|on_hours_total ∈ [0, inf]
+ "BHKW2|switch|on": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2|switch|on[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: BHKW2|switch|on[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: BHKW2|switch|on[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: BHKW2|switch|on[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: BHKW2|switch|on[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: BHKW2|switch|on[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: BHKW2|switch|on[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: BHKW2|switch|on[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: BHKW2|switch|on[2020-01-01 08:00:00] ∈ {0, 1}
+ "BHKW2|switch|off": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2|switch|off[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: BHKW2|switch|off[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: BHKW2|switch|off[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: BHKW2|switch|off[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: BHKW2|switch|off[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: BHKW2|switch|off[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: BHKW2|switch|off[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: BHKW2|switch|off[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: BHKW2|switch|off[2020-01-01 08:00:00] ∈ {0, 1}
+ "BHKW2->costs(temporal)": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2->costs(temporal)[2020-01-01 00:00:00] ∈ [-inf, inf]
+ [2020-01-01 01:00:00]: BHKW2->costs(temporal)[2020-01-01 01:00:00] ∈ [-inf, inf]
+ [2020-01-01 02:00:00]: BHKW2->costs(temporal)[2020-01-01 02:00:00] ∈ [-inf, inf]
+ [2020-01-01 03:00:00]: BHKW2->costs(temporal)[2020-01-01 03:00:00] ∈ [-inf, inf]
+ [2020-01-01 04:00:00]: BHKW2->costs(temporal)[2020-01-01 04:00:00] ∈ [-inf, inf]
+ [2020-01-01 05:00:00]: BHKW2->costs(temporal)[2020-01-01 05:00:00] ∈ [-inf, inf]
+ [2020-01-01 06:00:00]: BHKW2->costs(temporal)[2020-01-01 06:00:00] ∈ [-inf, inf]
+ [2020-01-01 07:00:00]: BHKW2->costs(temporal)[2020-01-01 07:00:00] ∈ [-inf, inf]
+ [2020-01-01 08:00:00]: BHKW2->costs(temporal)[2020-01-01 08:00:00] ∈ [-inf, inf]
+ "BHKW2|Piece_0|inside_piece": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2|Piece_0|inside_piece[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: BHKW2|Piece_0|inside_piece[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: BHKW2|Piece_0|inside_piece[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: BHKW2|Piece_0|inside_piece[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: BHKW2|Piece_0|inside_piece[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: BHKW2|Piece_0|inside_piece[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: BHKW2|Piece_0|inside_piece[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: BHKW2|Piece_0|inside_piece[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: BHKW2|Piece_0|inside_piece[2020-01-01 08:00:00] ∈ {0, 1}
+ "BHKW2|Piece_0|lambda0": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2|Piece_0|lambda0[2020-01-01 00:00:00] ∈ [0, 1]
+ [2020-01-01 01:00:00]: BHKW2|Piece_0|lambda0[2020-01-01 01:00:00] ∈ [0, 1]
+ [2020-01-01 02:00:00]: BHKW2|Piece_0|lambda0[2020-01-01 02:00:00] ∈ [0, 1]
+ [2020-01-01 03:00:00]: BHKW2|Piece_0|lambda0[2020-01-01 03:00:00] ∈ [0, 1]
+ [2020-01-01 04:00:00]: BHKW2|Piece_0|lambda0[2020-01-01 04:00:00] ∈ [0, 1]
+ [2020-01-01 05:00:00]: BHKW2|Piece_0|lambda0[2020-01-01 05:00:00] ∈ [0, 1]
+ [2020-01-01 06:00:00]: BHKW2|Piece_0|lambda0[2020-01-01 06:00:00] ∈ [0, 1]
+ [2020-01-01 07:00:00]: BHKW2|Piece_0|lambda0[2020-01-01 07:00:00] ∈ [0, 1]
+ [2020-01-01 08:00:00]: BHKW2|Piece_0|lambda0[2020-01-01 08:00:00] ∈ [0, 1]
+ "BHKW2|Piece_0|lambda1": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2|Piece_0|lambda1[2020-01-01 00:00:00] ∈ [0, 1]
+ [2020-01-01 01:00:00]: BHKW2|Piece_0|lambda1[2020-01-01 01:00:00] ∈ [0, 1]
+ [2020-01-01 02:00:00]: BHKW2|Piece_0|lambda1[2020-01-01 02:00:00] ∈ [0, 1]
+ [2020-01-01 03:00:00]: BHKW2|Piece_0|lambda1[2020-01-01 03:00:00] ∈ [0, 1]
+ [2020-01-01 04:00:00]: BHKW2|Piece_0|lambda1[2020-01-01 04:00:00] ∈ [0, 1]
+ [2020-01-01 05:00:00]: BHKW2|Piece_0|lambda1[2020-01-01 05:00:00] ∈ [0, 1]
+ [2020-01-01 06:00:00]: BHKW2|Piece_0|lambda1[2020-01-01 06:00:00] ∈ [0, 1]
+ [2020-01-01 07:00:00]: BHKW2|Piece_0|lambda1[2020-01-01 07:00:00] ∈ [0, 1]
+ [2020-01-01 08:00:00]: BHKW2|Piece_0|lambda1[2020-01-01 08:00:00] ∈ [0, 1]
+ "BHKW2|Piece_1|inside_piece": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2|Piece_1|inside_piece[2020-01-01 00:00:00] ∈ {0, 1}
+ [2020-01-01 01:00:00]: BHKW2|Piece_1|inside_piece[2020-01-01 01:00:00] ∈ {0, 1}
+ [2020-01-01 02:00:00]: BHKW2|Piece_1|inside_piece[2020-01-01 02:00:00] ∈ {0, 1}
+ [2020-01-01 03:00:00]: BHKW2|Piece_1|inside_piece[2020-01-01 03:00:00] ∈ {0, 1}
+ [2020-01-01 04:00:00]: BHKW2|Piece_1|inside_piece[2020-01-01 04:00:00] ∈ {0, 1}
+ [2020-01-01 05:00:00]: BHKW2|Piece_1|inside_piece[2020-01-01 05:00:00] ∈ {0, 1}
+ [2020-01-01 06:00:00]: BHKW2|Piece_1|inside_piece[2020-01-01 06:00:00] ∈ {0, 1}
+ [2020-01-01 07:00:00]: BHKW2|Piece_1|inside_piece[2020-01-01 07:00:00] ∈ {0, 1}
+ [2020-01-01 08:00:00]: BHKW2|Piece_1|inside_piece[2020-01-01 08:00:00] ∈ {0, 1}
+ "BHKW2|Piece_1|lambda0": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2|Piece_1|lambda0[2020-01-01 00:00:00] ∈ [0, 1]
+ [2020-01-01 01:00:00]: BHKW2|Piece_1|lambda0[2020-01-01 01:00:00] ∈ [0, 1]
+ [2020-01-01 02:00:00]: BHKW2|Piece_1|lambda0[2020-01-01 02:00:00] ∈ [0, 1]
+ [2020-01-01 03:00:00]: BHKW2|Piece_1|lambda0[2020-01-01 03:00:00] ∈ [0, 1]
+ [2020-01-01 04:00:00]: BHKW2|Piece_1|lambda0[2020-01-01 04:00:00] ∈ [0, 1]
+ [2020-01-01 05:00:00]: BHKW2|Piece_1|lambda0[2020-01-01 05:00:00] ∈ [0, 1]
+ [2020-01-01 06:00:00]: BHKW2|Piece_1|lambda0[2020-01-01 06:00:00] ∈ [0, 1]
+ [2020-01-01 07:00:00]: BHKW2|Piece_1|lambda0[2020-01-01 07:00:00] ∈ [0, 1]
+ [2020-01-01 08:00:00]: BHKW2|Piece_1|lambda0[2020-01-01 08:00:00] ∈ [0, 1]
+ "BHKW2|Piece_1|lambda1": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: BHKW2|Piece_1|lambda1[2020-01-01 00:00:00] ∈ [0, 1]
+ [2020-01-01 01:00:00]: BHKW2|Piece_1|lambda1[2020-01-01 01:00:00] ∈ [0, 1]
+ [2020-01-01 02:00:00]: BHKW2|Piece_1|lambda1[2020-01-01 02:00:00] ∈ [0, 1]
+ [2020-01-01 03:00:00]: BHKW2|Piece_1|lambda1[2020-01-01 03:00:00] ∈ [0, 1]
+ [2020-01-01 04:00:00]: BHKW2|Piece_1|lambda1[2020-01-01 04:00:00] ∈ [0, 1]
+ [2020-01-01 05:00:00]: BHKW2|Piece_1|lambda1[2020-01-01 05:00:00] ∈ [0, 1]
+ [2020-01-01 06:00:00]: BHKW2|Piece_1|lambda1[2020-01-01 06:00:00] ∈ [0, 1]
+ [2020-01-01 07:00:00]: BHKW2|Piece_1|lambda1[2020-01-01 07:00:00] ∈ [0, 1]
+ [2020-01-01 08:00:00]: BHKW2|Piece_1|lambda1[2020-01-01 08:00:00] ∈ [0, 1]
+ "Strom|excess_input": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Strom|excess_input[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Strom|excess_input[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Strom|excess_input[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Strom|excess_input[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Strom|excess_input[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Strom|excess_input[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Strom|excess_input[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Strom|excess_input[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Strom|excess_input[2020-01-01 08:00:00] ∈ [0, inf]
+ "Strom|excess_output": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Strom|excess_output[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Strom|excess_output[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Strom|excess_output[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Strom|excess_output[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Strom|excess_output[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Strom|excess_output[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Strom|excess_output[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Strom|excess_output[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Strom|excess_output[2020-01-01 08:00:00] ∈ [0, inf]
+ "Strom->Penalty": |-
+ Variable
+ --------
+ Strom->Penalty ∈ [-inf, inf]
+ "Fernwärme|excess_input": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Fernwärme|excess_input[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Fernwärme|excess_input[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Fernwärme|excess_input[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Fernwärme|excess_input[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Fernwärme|excess_input[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Fernwärme|excess_input[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Fernwärme|excess_input[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Fernwärme|excess_input[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Fernwärme|excess_input[2020-01-01 08:00:00] ∈ [0, inf]
+ "Fernwärme|excess_output": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Fernwärme|excess_output[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Fernwärme|excess_output[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Fernwärme|excess_output[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Fernwärme|excess_output[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Fernwärme|excess_output[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Fernwärme|excess_output[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Fernwärme|excess_output[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Fernwärme|excess_output[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Fernwärme|excess_output[2020-01-01 08:00:00] ∈ [0, inf]
+ "Fernwärme->Penalty": |-
+ Variable
+ --------
+ Fernwärme->Penalty ∈ [-inf, inf]
+ "Gas|excess_input": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Gas|excess_input[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Gas|excess_input[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Gas|excess_input[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Gas|excess_input[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Gas|excess_input[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Gas|excess_input[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Gas|excess_input[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Gas|excess_input[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Gas|excess_input[2020-01-01 08:00:00] ∈ [0, inf]
+ "Gas|excess_output": |-
+ Variable (time: 9)
+ ------------------
+ [2020-01-01 00:00:00]: Gas|excess_output[2020-01-01 00:00:00] ∈ [0, inf]
+ [2020-01-01 01:00:00]: Gas|excess_output[2020-01-01 01:00:00] ∈ [0, inf]
+ [2020-01-01 02:00:00]: Gas|excess_output[2020-01-01 02:00:00] ∈ [0, inf]
+ [2020-01-01 03:00:00]: Gas|excess_output[2020-01-01 03:00:00] ∈ [0, inf]
+ [2020-01-01 04:00:00]: Gas|excess_output[2020-01-01 04:00:00] ∈ [0, inf]
+ [2020-01-01 05:00:00]: Gas|excess_output[2020-01-01 05:00:00] ∈ [0, inf]
+ [2020-01-01 06:00:00]: Gas|excess_output[2020-01-01 06:00:00] ∈ [0, inf]
+ [2020-01-01 07:00:00]: Gas|excess_output[2020-01-01 07:00:00] ∈ [0, inf]
+ [2020-01-01 08:00:00]: Gas|excess_output[2020-01-01 08:00:00] ∈ [0, inf]
+ "Gas->Penalty": |-
+ Variable
+ --------
+ Gas->Penalty ∈ [-inf, inf]
+constraints:
+ costs(periodic): |-
+ Constraint `costs(periodic)`
+ ----------------------------
+ +1 costs(periodic) - 1 Kessel(Q_th)->costs(periodic) - 1 Speicher->costs(periodic) = -0.0
+ costs(temporal): |-
+ Constraint `costs(temporal)`
+ ----------------------------
+ +1 costs(temporal) - 1 costs(temporal)|per_timestep[2020-01-01 00:00:00] - 1 costs(temporal)|per_timestep[2020-01-01 01:00:00]... -1 costs(temporal)|per_timestep[2020-01-01 06:00:00] - 1 costs(temporal)|per_timestep[2020-01-01 07:00:00] - 1 costs(temporal)|per_timestep[2020-01-01 08:00:00] = -0.0
+ "costs(temporal)|per_timestep": |-
+ Constraint `costs(temporal)|per_timestep`
+ [time: 9]:
+ ----------------------------------------------------
+ [2020-01-01 00:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 00:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 00:00:00] - 1 Kessel(Q_th)->costs(temporal)[2020-01-01 00:00:00]... -1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 00:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 00:00:00] - 1 BHKW2->costs(temporal)[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 01:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 01:00:00] - 1 Kessel(Q_th)->costs(temporal)[2020-01-01 01:00:00]... -1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 01:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 01:00:00] - 1 BHKW2->costs(temporal)[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 02:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 02:00:00] - 1 Kessel(Q_th)->costs(temporal)[2020-01-01 02:00:00]... -1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 02:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 02:00:00] - 1 BHKW2->costs(temporal)[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 03:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 03:00:00] - 1 Kessel(Q_th)->costs(temporal)[2020-01-01 03:00:00]... -1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 03:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 03:00:00] - 1 BHKW2->costs(temporal)[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 04:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 04:00:00] - 1 Kessel(Q_th)->costs(temporal)[2020-01-01 04:00:00]... -1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 04:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 04:00:00] - 1 BHKW2->costs(temporal)[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 05:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 05:00:00] - 1 Kessel(Q_th)->costs(temporal)[2020-01-01 05:00:00]... -1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 05:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 05:00:00] - 1 BHKW2->costs(temporal)[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 06:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 06:00:00] - 1 Kessel(Q_th)->costs(temporal)[2020-01-01 06:00:00]... -1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 06:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 06:00:00] - 1 BHKW2->costs(temporal)[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 07:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 07:00:00] - 1 Kessel(Q_th)->costs(temporal)[2020-01-01 07:00:00]... -1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 07:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 07:00:00] - 1 BHKW2->costs(temporal)[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 costs(temporal)|per_timestep[2020-01-01 08:00:00] - 1 CO2(temporal)->costs(temporal)[2020-01-01 08:00:00] - 1 Kessel(Q_th)->costs(temporal)[2020-01-01 08:00:00]... -1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 08:00:00] - 1 Einspeisung(P_el)->costs(temporal)[2020-01-01 08:00:00] - 1 BHKW2->costs(temporal)[2020-01-01 08:00:00] = -0.0
+ costs: |-
+ Constraint `costs`
+ ------------------
+ +1 costs - 1 costs(temporal) - 1 costs(periodic) = -0.0
+ CO2(periodic): |-
+ Constraint `CO2(periodic)`
+ --------------------------
+ +1 CO2(periodic) = -0.0
+ CO2(temporal): |-
+ Constraint `CO2(temporal)`
+ --------------------------
+ +1 CO2(temporal) - 1 CO2(temporal)|per_timestep[2020-01-01 00:00:00] - 1 CO2(temporal)|per_timestep[2020-01-01 01:00:00]... -1 CO2(temporal)|per_timestep[2020-01-01 06:00:00] - 1 CO2(temporal)|per_timestep[2020-01-01 07:00:00] - 1 CO2(temporal)|per_timestep[2020-01-01 08:00:00] = -0.0
+ "CO2(temporal)|per_timestep": |-
+ Constraint `CO2(temporal)|per_timestep`
+ [time: 9]:
+ --------------------------------------------------
+ [2020-01-01 00:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 00:00:00] - 1 Kessel->CO2(temporal)[2020-01-01 00:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 01:00:00] - 1 Kessel->CO2(temporal)[2020-01-01 01:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 02:00:00] - 1 Kessel->CO2(temporal)[2020-01-01 02:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 03:00:00] - 1 Kessel->CO2(temporal)[2020-01-01 03:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 04:00:00] - 1 Kessel->CO2(temporal)[2020-01-01 04:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 05:00:00] - 1 Kessel->CO2(temporal)[2020-01-01 05:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 06:00:00] - 1 Kessel->CO2(temporal)[2020-01-01 06:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 07:00:00] - 1 Kessel->CO2(temporal)[2020-01-01 07:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 CO2(temporal)|per_timestep[2020-01-01 08:00:00] - 1 Kessel->CO2(temporal)[2020-01-01 08:00:00] - 1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 08:00:00] = -0.0
+ CO2: |-
+ Constraint `CO2`
+ ----------------
+ +1 CO2 - 1 CO2(temporal) - 1 CO2(periodic) = -0.0
+ PE(periodic): |-
+ Constraint `PE(periodic)`
+ -------------------------
+ +1 PE(periodic) - 1 Kessel(Q_th)->PE(periodic) - 1 Speicher->PE(periodic) = -0.0
+ PE(temporal): |-
+ Constraint `PE(temporal)`
+ -------------------------
+ +1 PE(temporal) - 1 PE(temporal)|per_timestep[2020-01-01 00:00:00] - 1 PE(temporal)|per_timestep[2020-01-01 01:00:00]... -1 PE(temporal)|per_timestep[2020-01-01 06:00:00] - 1 PE(temporal)|per_timestep[2020-01-01 07:00:00] - 1 PE(temporal)|per_timestep[2020-01-01 08:00:00] = -0.0
+ "PE(temporal)|per_timestep": |-
+ Constraint `PE(temporal)|per_timestep`
+ [time: 9]:
+ -------------------------------------------------
+ [2020-01-01 00:00:00]: +1 PE(temporal)|per_timestep[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 PE(temporal)|per_timestep[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 PE(temporal)|per_timestep[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 PE(temporal)|per_timestep[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 PE(temporal)|per_timestep[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 PE(temporal)|per_timestep[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 PE(temporal)|per_timestep[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 PE(temporal)|per_timestep[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 PE(temporal)|per_timestep[2020-01-01 08:00:00] = -0.0
+ PE: |-
+ Constraint `PE`
+ ---------------
+ +1 PE - 1 PE(temporal) - 1 PE(periodic) = -0.0
+ Penalty: |-
+ Constraint `Penalty`
+ --------------------
+ +1 Penalty - 1 Strom->Penalty - 1 Fernwärme->Penalty - 1 Gas->Penalty = -0.0
+ "CO2(temporal)->costs(temporal)": |-
+ Constraint `CO2(temporal)->costs(temporal)`
+ [time: 9]:
+ ------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 00:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 01:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 02:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 03:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 04:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 05:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 06:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 07:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 CO2(temporal)->costs(temporal)[2020-01-01 08:00:00] - 0.2 CO2(temporal)|per_timestep[2020-01-01 08:00:00] = -0.0
+ "Kessel(Q_fu)|on_hours_total": |-
+ Constraint `Kessel(Q_fu)|on_hours_total`
+ ----------------------------------------
+ +1 Kessel(Q_fu)|on_hours_total - 1 Kessel(Q_fu)|on[2020-01-01 00:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 01:00:00]... -1 Kessel(Q_fu)|on[2020-01-01 06:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 07:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 08:00:00] = -0.0
+ "Kessel(Q_fu)|flow_rate|ub": |-
+ Constraint `Kessel(Q_fu)|flow_rate|ub`
+ [time: 9]:
+ -------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 00:00:00] - 200 Kessel(Q_fu)|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 01:00:00] - 200 Kessel(Q_fu)|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 02:00:00] - 200 Kessel(Q_fu)|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 03:00:00] - 200 Kessel(Q_fu)|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 04:00:00] - 200 Kessel(Q_fu)|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 05:00:00] - 200 Kessel(Q_fu)|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 06:00:00] - 200 Kessel(Q_fu)|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 07:00:00] - 200 Kessel(Q_fu)|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 08:00:00] - 200 Kessel(Q_fu)|on[2020-01-01 08:00:00] ≤ -0.0
+ "Kessel(Q_fu)|flow_rate|lb": |-
+ Constraint `Kessel(Q_fu)|flow_rate|lb`
+ [time: 9]:
+ -------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1e-05 Kessel(Q_fu)|on[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 01:00:00] - 1e-05 Kessel(Q_fu)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 02:00:00] - 1e-05 Kessel(Q_fu)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 03:00:00] - 1e-05 Kessel(Q_fu)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 04:00:00] - 1e-05 Kessel(Q_fu)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 05:00:00] - 1e-05 Kessel(Q_fu)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1e-05 Kessel(Q_fu)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1e-05 Kessel(Q_fu)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_fu)|flow_rate[2020-01-01 08:00:00] - 1e-05 Kessel(Q_fu)|on[2020-01-01 08:00:00] ≥ -0.0
+ "Kessel(Q_fu)|total_flow_hours": |-
+ Constraint `Kessel(Q_fu)|total_flow_hours`
+ ------------------------------------------
+ +1 Kessel(Q_fu)|total_flow_hours - 1 Kessel(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 01:00:00]... -1 Kessel(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Kessel(Q_th)->costs(periodic)": |-
+ Constraint `Kessel(Q_th)->costs(periodic)`
+ ------------------------------------------
+ +1 Kessel(Q_th)->costs(periodic) - 10 Kessel(Q_th)|size = 1000.0
+ "Kessel(Q_th)->PE(periodic)": |-
+ Constraint `Kessel(Q_th)->PE(periodic)`
+ ---------------------------------------
+ +1 Kessel(Q_th)->PE(periodic) - 2 Kessel(Q_th)|size = -0.0
+ "Kessel(Q_th)|complementary": |-
+ Constraint `Kessel(Q_th)|complementary`
+ [time: 9]:
+ --------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_th)|on[2020-01-01 00:00:00] + 1 Kessel(Q_th)|off[2020-01-01 00:00:00] = 1.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|on[2020-01-01 01:00:00] + 1 Kessel(Q_th)|off[2020-01-01 01:00:00] = 1.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|on[2020-01-01 02:00:00] + 1 Kessel(Q_th)|off[2020-01-01 02:00:00] = 1.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|on[2020-01-01 03:00:00] + 1 Kessel(Q_th)|off[2020-01-01 03:00:00] = 1.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|on[2020-01-01 04:00:00] + 1 Kessel(Q_th)|off[2020-01-01 04:00:00] = 1.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|on[2020-01-01 05:00:00] + 1 Kessel(Q_th)|off[2020-01-01 05:00:00] = 1.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|on[2020-01-01 06:00:00] + 1 Kessel(Q_th)|off[2020-01-01 06:00:00] = 1.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|on[2020-01-01 07:00:00] + 1 Kessel(Q_th)|off[2020-01-01 07:00:00] = 1.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|on[2020-01-01 08:00:00] + 1 Kessel(Q_th)|off[2020-01-01 08:00:00] = 1.0
+ "Kessel(Q_th)|on_hours_total": |-
+ Constraint `Kessel(Q_th)|on_hours_total`
+ ----------------------------------------
+ +1 Kessel(Q_th)|on_hours_total - 1 Kessel(Q_th)|on[2020-01-01 00:00:00] - 1 Kessel(Q_th)|on[2020-01-01 01:00:00]... -1 Kessel(Q_th)|on[2020-01-01 06:00:00] - 1 Kessel(Q_th)|on[2020-01-01 07:00:00] - 1 Kessel(Q_th)|on[2020-01-01 08:00:00] = -0.0
+ "Kessel(Q_th)|switch|transition": |-
+ Constraint `Kessel(Q_th)|switch|transition`
+ [time: 8]:
+ ------------------------------------------------------
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 01:00:00] - 1 Kessel(Q_th)|switch|off[2020-01-01 01:00:00] - 1 Kessel(Q_th)|on[2020-01-01 01:00:00] + 1 Kessel(Q_th)|on[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 02:00:00] - 1 Kessel(Q_th)|switch|off[2020-01-01 02:00:00] - 1 Kessel(Q_th)|on[2020-01-01 02:00:00] + 1 Kessel(Q_th)|on[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 03:00:00] - 1 Kessel(Q_th)|switch|off[2020-01-01 03:00:00] - 1 Kessel(Q_th)|on[2020-01-01 03:00:00] + 1 Kessel(Q_th)|on[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 04:00:00] - 1 Kessel(Q_th)|switch|off[2020-01-01 04:00:00] - 1 Kessel(Q_th)|on[2020-01-01 04:00:00] + 1 Kessel(Q_th)|on[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 05:00:00] - 1 Kessel(Q_th)|switch|off[2020-01-01 05:00:00] - 1 Kessel(Q_th)|on[2020-01-01 05:00:00] + 1 Kessel(Q_th)|on[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 06:00:00] - 1 Kessel(Q_th)|switch|off[2020-01-01 06:00:00] - 1 Kessel(Q_th)|on[2020-01-01 06:00:00] + 1 Kessel(Q_th)|on[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 07:00:00] - 1 Kessel(Q_th)|switch|off[2020-01-01 07:00:00] - 1 Kessel(Q_th)|on[2020-01-01 07:00:00] + 1 Kessel(Q_th)|on[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 08:00:00] - 1 Kessel(Q_th)|switch|off[2020-01-01 08:00:00] - 1 Kessel(Q_th)|on[2020-01-01 08:00:00] + 1 Kessel(Q_th)|on[2020-01-01 07:00:00] = -0.0
+ "Kessel(Q_th)|switch|initial": |-
+ Constraint `Kessel(Q_th)|switch|initial`
+ ----------------------------------------
+ +1 Kessel(Q_th)|switch|on[2020-01-01 00:00:00] - 1 Kessel(Q_th)|switch|off[2020-01-01 00:00:00] - 1 Kessel(Q_th)|on[2020-01-01 00:00:00] = -1.0
+ "Kessel(Q_th)|switch|mutex": |-
+ Constraint `Kessel(Q_th)|switch|mutex`
+ [time: 9]:
+ -------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 00:00:00] + 1 Kessel(Q_th)|switch|off[2020-01-01 00:00:00] ≤ 1.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 01:00:00] + 1 Kessel(Q_th)|switch|off[2020-01-01 01:00:00] ≤ 1.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 02:00:00] + 1 Kessel(Q_th)|switch|off[2020-01-01 02:00:00] ≤ 1.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 03:00:00] + 1 Kessel(Q_th)|switch|off[2020-01-01 03:00:00] ≤ 1.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 04:00:00] + 1 Kessel(Q_th)|switch|off[2020-01-01 04:00:00] ≤ 1.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 05:00:00] + 1 Kessel(Q_th)|switch|off[2020-01-01 05:00:00] ≤ 1.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 06:00:00] + 1 Kessel(Q_th)|switch|off[2020-01-01 06:00:00] ≤ 1.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 07:00:00] + 1 Kessel(Q_th)|switch|off[2020-01-01 07:00:00] ≤ 1.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|switch|on[2020-01-01 08:00:00] + 1 Kessel(Q_th)|switch|off[2020-01-01 08:00:00] ≤ 1.0
+ "Kessel(Q_th)|switch|count": |-
+ Constraint `Kessel(Q_th)|switch|count`
+ --------------------------------------
+ +1 Kessel(Q_th)|switch|count - 1 Kessel(Q_th)|switch|on[2020-01-01 00:00:00] - 1 Kessel(Q_th)|switch|on[2020-01-01 01:00:00]... -1 Kessel(Q_th)|switch|on[2020-01-01 06:00:00] - 1 Kessel(Q_th)|switch|on[2020-01-01 07:00:00] - 1 Kessel(Q_th)|switch|on[2020-01-01 08:00:00] = -0.0
+ "Kessel(Q_th)|consecutive_on_hours|ub": |-
+ Constraint `Kessel(Q_th)|consecutive_on_hours|ub`
+ [time: 9]:
+ ------------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 00:00:00] - 10 Kessel(Q_th)|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 01:00:00] - 10 Kessel(Q_th)|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 02:00:00] - 10 Kessel(Q_th)|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 03:00:00] - 10 Kessel(Q_th)|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 04:00:00] - 10 Kessel(Q_th)|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 05:00:00] - 10 Kessel(Q_th)|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 06:00:00] - 10 Kessel(Q_th)|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 07:00:00] - 10 Kessel(Q_th)|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 08:00:00] - 10 Kessel(Q_th)|on[2020-01-01 08:00:00] ≤ -0.0
+ "Kessel(Q_th)|consecutive_on_hours|forward": |-
+ Constraint `Kessel(Q_th)|consecutive_on_hours|forward`
+ [time: 8]:
+ -----------------------------------------------------------------
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 01:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 00:00:00] ≤ 1.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 02:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 01:00:00] ≤ 1.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 03:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 02:00:00] ≤ 1.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 04:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 03:00:00] ≤ 1.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 05:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 04:00:00] ≤ 1.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 06:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 05:00:00] ≤ 1.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 07:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 06:00:00] ≤ 1.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 08:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 07:00:00] ≤ 1.0
+ "Kessel(Q_th)|consecutive_on_hours|backward": |-
+ Constraint `Kessel(Q_th)|consecutive_on_hours|backward`
+ [time: 8]:
+ ------------------------------------------------------------------
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 01:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 00:00:00] - 10 Kessel(Q_th)|on[2020-01-01 01:00:00] ≥ -9.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 02:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 01:00:00] - 10 Kessel(Q_th)|on[2020-01-01 02:00:00] ≥ -9.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 03:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 02:00:00] - 10 Kessel(Q_th)|on[2020-01-01 03:00:00] ≥ -9.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 04:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 03:00:00] - 10 Kessel(Q_th)|on[2020-01-01 04:00:00] ≥ -9.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 05:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 04:00:00] - 10 Kessel(Q_th)|on[2020-01-01 05:00:00] ≥ -9.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 06:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 05:00:00] - 10 Kessel(Q_th)|on[2020-01-01 06:00:00] ≥ -9.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 07:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 06:00:00] - 10 Kessel(Q_th)|on[2020-01-01 07:00:00] ≥ -9.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 08:00:00] - 1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 07:00:00] - 10 Kessel(Q_th)|on[2020-01-01 08:00:00] ≥ -9.0
+ "Kessel(Q_th)|consecutive_on_hours|initial": |-
+ Constraint `Kessel(Q_th)|consecutive_on_hours|initial`
+ ------------------------------------------------------
+ +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 00:00:00] - 2 Kessel(Q_th)|on[2020-01-01 00:00:00] = -0.0
+ "Kessel(Q_th)|consecutive_on_hours|lb": |-
+ Constraint `Kessel(Q_th)|consecutive_on_hours|lb`
+ [time: 9]:
+ ------------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 00:00:00] - 1 Kessel(Q_th)|on[2020-01-01 00:00:00] + 1 Kessel(Q_th)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 01:00:00] - 1 Kessel(Q_th)|on[2020-01-01 01:00:00] + 1 Kessel(Q_th)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 02:00:00] - 1 Kessel(Q_th)|on[2020-01-01 02:00:00] + 1 Kessel(Q_th)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 03:00:00] - 1 Kessel(Q_th)|on[2020-01-01 03:00:00] + 1 Kessel(Q_th)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 04:00:00] - 1 Kessel(Q_th)|on[2020-01-01 04:00:00] + 1 Kessel(Q_th)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 05:00:00] - 2 Kessel(Q_th)|on[2020-01-01 05:00:00] + 2 Kessel(Q_th)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 06:00:00] - 2 Kessel(Q_th)|on[2020-01-01 06:00:00] + 2 Kessel(Q_th)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 07:00:00] - 2 Kessel(Q_th)|on[2020-01-01 07:00:00] + 2 Kessel(Q_th)|on[2020-01-01 08:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|consecutive_on_hours[2020-01-01 08:00:00] ≥ -0.0
+ "Kessel(Q_th)|consecutive_off_hours|ub": |-
+ Constraint `Kessel(Q_th)|consecutive_off_hours|ub`
+ [time: 9]:
+ -------------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 00:00:00] - 9 Kessel(Q_th)|off[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 01:00:00] - 9 Kessel(Q_th)|off[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 02:00:00] - 9 Kessel(Q_th)|off[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 03:00:00] - 9 Kessel(Q_th)|off[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 04:00:00] - 9 Kessel(Q_th)|off[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 05:00:00] - 9 Kessel(Q_th)|off[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 06:00:00] - 9 Kessel(Q_th)|off[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 07:00:00] - 9 Kessel(Q_th)|off[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 08:00:00] - 9 Kessel(Q_th)|off[2020-01-01 08:00:00] ≤ -0.0
+ "Kessel(Q_th)|consecutive_off_hours|forward": |-
+ Constraint `Kessel(Q_th)|consecutive_off_hours|forward`
+ [time: 8]:
+ ------------------------------------------------------------------
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 01:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 00:00:00] ≤ 1.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 02:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 01:00:00] ≤ 1.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 03:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 02:00:00] ≤ 1.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 04:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 03:00:00] ≤ 1.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 05:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 04:00:00] ≤ 1.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 06:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 05:00:00] ≤ 1.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 07:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 06:00:00] ≤ 1.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 08:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 07:00:00] ≤ 1.0
+ "Kessel(Q_th)|consecutive_off_hours|backward": |-
+ Constraint `Kessel(Q_th)|consecutive_off_hours|backward`
+ [time: 8]:
+ -------------------------------------------------------------------
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 01:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 00:00:00] - 9 Kessel(Q_th)|off[2020-01-01 01:00:00] ≥ -8.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 02:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 01:00:00] - 9 Kessel(Q_th)|off[2020-01-01 02:00:00] ≥ -8.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 03:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 02:00:00] - 9 Kessel(Q_th)|off[2020-01-01 03:00:00] ≥ -8.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 04:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 03:00:00] - 9 Kessel(Q_th)|off[2020-01-01 04:00:00] ≥ -8.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 05:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 04:00:00] - 9 Kessel(Q_th)|off[2020-01-01 05:00:00] ≥ -8.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 06:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 05:00:00] - 9 Kessel(Q_th)|off[2020-01-01 06:00:00] ≥ -8.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 07:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 06:00:00] - 9 Kessel(Q_th)|off[2020-01-01 07:00:00] ≥ -8.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 08:00:00] - 1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 07:00:00] - 9 Kessel(Q_th)|off[2020-01-01 08:00:00] ≥ -8.0
+ "Kessel(Q_th)|consecutive_off_hours|initial": |-
+ Constraint `Kessel(Q_th)|consecutive_off_hours|initial`
+ -------------------------------------------------------
+ +1 Kessel(Q_th)|consecutive_off_hours[2020-01-01 00:00:00] - 1 Kessel(Q_th)|off[2020-01-01 00:00:00] = -0.0
+ "Kessel(Q_th)->costs(temporal)": |-
+ Constraint `Kessel(Q_th)->costs(temporal)`
+ [time: 9]:
+ -----------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_th)->costs(temporal)[2020-01-01 00:00:00] - 0.01 Kessel(Q_th)|switch|on[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)->costs(temporal)[2020-01-01 01:00:00] - 0.01 Kessel(Q_th)|switch|on[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)->costs(temporal)[2020-01-01 02:00:00] - 0.01 Kessel(Q_th)|switch|on[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)->costs(temporal)[2020-01-01 03:00:00] - 0.01 Kessel(Q_th)|switch|on[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)->costs(temporal)[2020-01-01 04:00:00] - 0.01 Kessel(Q_th)|switch|on[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)->costs(temporal)[2020-01-01 05:00:00] - 0.01 Kessel(Q_th)|switch|on[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)->costs(temporal)[2020-01-01 06:00:00] - 0.01 Kessel(Q_th)|switch|on[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)->costs(temporal)[2020-01-01 07:00:00] - 0.01 Kessel(Q_th)|switch|on[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)->costs(temporal)[2020-01-01 08:00:00] - 0.01 Kessel(Q_th)|switch|on[2020-01-01 08:00:00] = -0.0
+ "Kessel(Q_th)|flow_rate|lb2": |-
+ Constraint `Kessel(Q_th)|flow_rate|lb2`
+ [time: 9]:
+ --------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 00:00:00] - 5 Kessel(Q_th)|on[2020-01-01 00:00:00] - 0.1 Kessel(Q_th)|size ≥ -5.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 01:00:00] - 5 Kessel(Q_th)|on[2020-01-01 01:00:00] - 0.1 Kessel(Q_th)|size ≥ -5.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 02:00:00] - 5 Kessel(Q_th)|on[2020-01-01 02:00:00] - 0.1 Kessel(Q_th)|size ≥ -5.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 03:00:00] - 5 Kessel(Q_th)|on[2020-01-01 03:00:00] - 0.1 Kessel(Q_th)|size ≥ -5.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 04:00:00] - 5 Kessel(Q_th)|on[2020-01-01 04:00:00] - 0.1 Kessel(Q_th)|size ≥ -5.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 05:00:00] - 5 Kessel(Q_th)|on[2020-01-01 05:00:00] - 0.1 Kessel(Q_th)|size ≥ -5.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 06:00:00] - 5 Kessel(Q_th)|on[2020-01-01 06:00:00] - 0.1 Kessel(Q_th)|size ≥ -5.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 07:00:00] - 5 Kessel(Q_th)|on[2020-01-01 07:00:00] - 0.1 Kessel(Q_th)|size ≥ -5.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 08:00:00] - 5 Kessel(Q_th)|on[2020-01-01 08:00:00] - 0.1 Kessel(Q_th)|size ≥ -5.0
+ "Kessel(Q_th)|flow_rate|ub2": |-
+ Constraint `Kessel(Q_th)|flow_rate|ub2`
+ [time: 9]:
+ --------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 00:00:00] - 1 Kessel(Q_th)|size ≤ -0.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 01:00:00] - 1 Kessel(Q_th)|size ≤ -0.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 02:00:00] - 1 Kessel(Q_th)|size ≤ -0.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 03:00:00] - 1 Kessel(Q_th)|size ≤ -0.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 04:00:00] - 1 Kessel(Q_th)|size ≤ -0.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 05:00:00] - 1 Kessel(Q_th)|size ≤ -0.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 06:00:00] - 1 Kessel(Q_th)|size ≤ -0.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 07:00:00] - 1 Kessel(Q_th)|size ≤ -0.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 08:00:00] - 1 Kessel(Q_th)|size ≤ -0.0
+ "Kessel(Q_th)|flow_rate|ub1": |-
+ Constraint `Kessel(Q_th)|flow_rate|ub1`
+ [time: 9]:
+ --------------------------------------------------
+ [2020-01-01 00:00:00]: +50 Kessel(Q_th)|on[2020-01-01 00:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +50 Kessel(Q_th)|on[2020-01-01 01:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +50 Kessel(Q_th)|on[2020-01-01 02:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +50 Kessel(Q_th)|on[2020-01-01 03:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +50 Kessel(Q_th)|on[2020-01-01 04:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +50 Kessel(Q_th)|on[2020-01-01 05:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +50 Kessel(Q_th)|on[2020-01-01 06:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +50 Kessel(Q_th)|on[2020-01-01 07:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +50 Kessel(Q_th)|on[2020-01-01 08:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 08:00:00] ≥ -0.0
+ "Kessel(Q_th)|flow_rate|lb1": |-
+ Constraint `Kessel(Q_th)|flow_rate|lb1`
+ [time: 9]:
+ --------------------------------------------------
+ [2020-01-01 00:00:00]: +5 Kessel(Q_th)|on[2020-01-01 00:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +5 Kessel(Q_th)|on[2020-01-01 01:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +5 Kessel(Q_th)|on[2020-01-01 02:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +5 Kessel(Q_th)|on[2020-01-01 03:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +5 Kessel(Q_th)|on[2020-01-01 04:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +5 Kessel(Q_th)|on[2020-01-01 05:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +5 Kessel(Q_th)|on[2020-01-01 06:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +5 Kessel(Q_th)|on[2020-01-01 07:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +5 Kessel(Q_th)|on[2020-01-01 08:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 08:00:00] ≤ -0.0
+ "Kessel(Q_th)|total_flow_hours": |-
+ Constraint `Kessel(Q_th)|total_flow_hours`
+ ------------------------------------------
+ +1 Kessel(Q_th)|total_flow_hours - 1 Kessel(Q_th)|flow_rate[2020-01-01 00:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 01:00:00]... -1 Kessel(Q_th)|flow_rate[2020-01-01 06:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 07:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Kessel(Q_th)|load_factor_max": |-
+ Constraint `Kessel(Q_th)|load_factor_max`
+ -----------------------------------------
+ +1 Kessel(Q_th)|total_flow_hours - 9 Kessel(Q_th)|size ≤ -0.0
+ "Kessel(Q_th)|load_factor_min": |-
+ Constraint `Kessel(Q_th)|load_factor_min`
+ -----------------------------------------
+ +1 Kessel(Q_th)|total_flow_hours - 0.9 Kessel(Q_th)|size ≥ -0.0
+ "Kessel|on|ub": |-
+ Constraint `Kessel|on|ub`
+ [time: 9]:
+ ------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel|on[2020-01-01 00:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 00:00:00] - 1 Kessel(Q_th)|on[2020-01-01 00:00:00] ≤ 1e-05
+ [2020-01-01 01:00:00]: +1 Kessel|on[2020-01-01 01:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 01:00:00] - 1 Kessel(Q_th)|on[2020-01-01 01:00:00] ≤ 1e-05
+ [2020-01-01 02:00:00]: +1 Kessel|on[2020-01-01 02:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 02:00:00] - 1 Kessel(Q_th)|on[2020-01-01 02:00:00] ≤ 1e-05
+ [2020-01-01 03:00:00]: +1 Kessel|on[2020-01-01 03:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 03:00:00] - 1 Kessel(Q_th)|on[2020-01-01 03:00:00] ≤ 1e-05
+ [2020-01-01 04:00:00]: +1 Kessel|on[2020-01-01 04:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 04:00:00] - 1 Kessel(Q_th)|on[2020-01-01 04:00:00] ≤ 1e-05
+ [2020-01-01 05:00:00]: +1 Kessel|on[2020-01-01 05:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 05:00:00] - 1 Kessel(Q_th)|on[2020-01-01 05:00:00] ≤ 1e-05
+ [2020-01-01 06:00:00]: +1 Kessel|on[2020-01-01 06:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 06:00:00] - 1 Kessel(Q_th)|on[2020-01-01 06:00:00] ≤ 1e-05
+ [2020-01-01 07:00:00]: +1 Kessel|on[2020-01-01 07:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 07:00:00] - 1 Kessel(Q_th)|on[2020-01-01 07:00:00] ≤ 1e-05
+ [2020-01-01 08:00:00]: +1 Kessel|on[2020-01-01 08:00:00] - 1 Kessel(Q_fu)|on[2020-01-01 08:00:00] - 1 Kessel(Q_th)|on[2020-01-01 08:00:00] ≤ 1e-05
+ "Kessel|on|lb": |-
+ Constraint `Kessel|on|lb`
+ [time: 9]:
+ ------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel|on[2020-01-01 00:00:00] - 0.5 Kessel(Q_fu)|on[2020-01-01 00:00:00] - 0.5 Kessel(Q_th)|on[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 Kessel|on[2020-01-01 01:00:00] - 0.5 Kessel(Q_fu)|on[2020-01-01 01:00:00] - 0.5 Kessel(Q_th)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 Kessel|on[2020-01-01 02:00:00] - 0.5 Kessel(Q_fu)|on[2020-01-01 02:00:00] - 0.5 Kessel(Q_th)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 Kessel|on[2020-01-01 03:00:00] - 0.5 Kessel(Q_fu)|on[2020-01-01 03:00:00] - 0.5 Kessel(Q_th)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 Kessel|on[2020-01-01 04:00:00] - 0.5 Kessel(Q_fu)|on[2020-01-01 04:00:00] - 0.5 Kessel(Q_th)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 Kessel|on[2020-01-01 05:00:00] - 0.5 Kessel(Q_fu)|on[2020-01-01 05:00:00] - 0.5 Kessel(Q_th)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 Kessel|on[2020-01-01 06:00:00] - 0.5 Kessel(Q_fu)|on[2020-01-01 06:00:00] - 0.5 Kessel(Q_th)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 Kessel|on[2020-01-01 07:00:00] - 0.5 Kessel(Q_fu)|on[2020-01-01 07:00:00] - 0.5 Kessel(Q_th)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 Kessel|on[2020-01-01 08:00:00] - 0.5 Kessel(Q_fu)|on[2020-01-01 08:00:00] - 0.5 Kessel(Q_th)|on[2020-01-01 08:00:00] ≥ -0.0
+ "Kessel|on_hours_total": |-
+ Constraint `Kessel|on_hours_total`
+ ----------------------------------
+ +1 Kessel|on_hours_total - 1 Kessel|on[2020-01-01 00:00:00] - 1 Kessel|on[2020-01-01 01:00:00]... -1 Kessel|on[2020-01-01 06:00:00] - 1 Kessel|on[2020-01-01 07:00:00] - 1 Kessel|on[2020-01-01 08:00:00] = -0.0
+ "Kessel->costs(temporal)": |-
+ Constraint `Kessel->costs(temporal)`
+ [time: 9]:
+ -----------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel->costs(temporal)[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Kessel->costs(temporal)[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Kessel->costs(temporal)[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Kessel->costs(temporal)[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Kessel->costs(temporal)[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Kessel->costs(temporal)[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Kessel->costs(temporal)[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Kessel->costs(temporal)[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Kessel->costs(temporal)[2020-01-01 08:00:00] = -0.0
+ "Kessel->CO2(temporal)": |-
+ Constraint `Kessel->CO2(temporal)`
+ [time: 9]:
+ ---------------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel->CO2(temporal)[2020-01-01 00:00:00] - 1000 Kessel|on[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Kessel->CO2(temporal)[2020-01-01 01:00:00] - 1000 Kessel|on[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Kessel->CO2(temporal)[2020-01-01 02:00:00] - 1000 Kessel|on[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Kessel->CO2(temporal)[2020-01-01 03:00:00] - 1000 Kessel|on[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Kessel->CO2(temporal)[2020-01-01 04:00:00] - 1000 Kessel|on[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Kessel->CO2(temporal)[2020-01-01 05:00:00] - 1000 Kessel|on[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Kessel->CO2(temporal)[2020-01-01 06:00:00] - 1000 Kessel|on[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Kessel->CO2(temporal)[2020-01-01 07:00:00] - 1000 Kessel|on[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Kessel->CO2(temporal)[2020-01-01 08:00:00] - 1000 Kessel|on[2020-01-01 08:00:00] = -0.0
+ "Kessel|conversion_0": |-
+ Constraint `Kessel|conversion_0`
+ [time: 9]:
+ -------------------------------------------
+ [2020-01-01 00:00:00]: +0.5 Kessel(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +0.5 Kessel(Q_fu)|flow_rate[2020-01-01 01:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +0.5 Kessel(Q_fu)|flow_rate[2020-01-01 02:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +0.5 Kessel(Q_fu)|flow_rate[2020-01-01 03:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +0.5 Kessel(Q_fu)|flow_rate[2020-01-01 04:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +0.5 Kessel(Q_fu)|flow_rate[2020-01-01 05:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +0.5 Kessel(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +0.5 Kessel(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +0.5 Kessel(Q_fu)|flow_rate[2020-01-01 08:00:00] - 1 Kessel(Q_th)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Wärmelast(Q_th_Last)|total_flow_hours": |-
+ Constraint `Wärmelast(Q_th_Last)|total_flow_hours`
+ --------------------------------------------------
+ +1 Wärmelast(Q_th_Last)|total_flow_hours - 1 Wärmelast(Q_th_Last)|flow_rate[2020-01-01 00:00:00] - 1 Wärmelast(Q_th_Last)|flow_rate[2020-01-01 01:00:00]... -1 Wärmelast(Q_th_Last)|flow_rate[2020-01-01 06:00:00] - 1 Wärmelast(Q_th_Last)|flow_rate[2020-01-01 07:00:00] - 1 Wärmelast(Q_th_Last)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Gastarif(Q_Gas)|total_flow_hours": |-
+ Constraint `Gastarif(Q_Gas)|total_flow_hours`
+ ---------------------------------------------
+ +1 Gastarif(Q_Gas)|total_flow_hours - 1 Gastarif(Q_Gas)|flow_rate[2020-01-01 00:00:00] - 1 Gastarif(Q_Gas)|flow_rate[2020-01-01 01:00:00]... -1 Gastarif(Q_Gas)|flow_rate[2020-01-01 06:00:00] - 1 Gastarif(Q_Gas)|flow_rate[2020-01-01 07:00:00] - 1 Gastarif(Q_Gas)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Gastarif(Q_Gas)->costs(temporal)": |-
+ Constraint `Gastarif(Q_Gas)->costs(temporal)`
+ [time: 9]:
+ --------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 00:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 01:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 02:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 03:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 04:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 05:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 06:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 07:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Gastarif(Q_Gas)->costs(temporal)[2020-01-01 08:00:00] - 0.04 Gastarif(Q_Gas)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Gastarif(Q_Gas)->CO2(temporal)": |-
+ Constraint `Gastarif(Q_Gas)->CO2(temporal)`
+ [time: 9]:
+ ------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 00:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 01:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 02:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 03:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 04:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 05:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 06:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 07:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Gastarif(Q_Gas)->CO2(temporal)[2020-01-01 08:00:00] - 0.3 Gastarif(Q_Gas)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Einspeisung(P_el)|total_flow_hours": |-
+ Constraint `Einspeisung(P_el)|total_flow_hours`
+ -----------------------------------------------
+ +1 Einspeisung(P_el)|total_flow_hours - 1 Einspeisung(P_el)|flow_rate[2020-01-01 00:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 01:00:00]... -1 Einspeisung(P_el)|flow_rate[2020-01-01 06:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 07:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Einspeisung(P_el)->costs(temporal)": |-
+ Constraint `Einspeisung(P_el)->costs(temporal)`
+ [time: 9]:
+ ----------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 00:00:00] + 40 Einspeisung(P_el)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 01:00:00] + 40 Einspeisung(P_el)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 02:00:00] + 40 Einspeisung(P_el)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 03:00:00] + 40 Einspeisung(P_el)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 04:00:00] + 40 Einspeisung(P_el)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 05:00:00] + 40 Einspeisung(P_el)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 06:00:00] + 40 Einspeisung(P_el)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 07:00:00] + 40 Einspeisung(P_el)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Einspeisung(P_el)->costs(temporal)[2020-01-01 08:00:00] + 40 Einspeisung(P_el)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Speicher(Q_th_load)|on_hours_total": |-
+ Constraint `Speicher(Q_th_load)|on_hours_total`
+ -----------------------------------------------
+ +1 Speicher(Q_th_load)|on_hours_total - 1 Speicher(Q_th_load)|on[2020-01-01 00:00:00] - 1 Speicher(Q_th_load)|on[2020-01-01 01:00:00]... -1 Speicher(Q_th_load)|on[2020-01-01 06:00:00] - 1 Speicher(Q_th_load)|on[2020-01-01 07:00:00] - 1 Speicher(Q_th_load)|on[2020-01-01 08:00:00] = -0.0
+ "Speicher(Q_th_load)|flow_rate|ub": |-
+ Constraint `Speicher(Q_th_load)|flow_rate|ub`
+ [time: 9]:
+ --------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 00:00:00] - 1e+04 Speicher(Q_th_load)|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 01:00:00] - 1e+04 Speicher(Q_th_load)|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 02:00:00] - 1e+04 Speicher(Q_th_load)|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 03:00:00] - 1e+04 Speicher(Q_th_load)|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 04:00:00] - 1e+04 Speicher(Q_th_load)|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 05:00:00] - 1e+04 Speicher(Q_th_load)|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 06:00:00] - 1e+04 Speicher(Q_th_load)|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 07:00:00] - 1e+04 Speicher(Q_th_load)|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 08:00:00] - 1e+04 Speicher(Q_th_load)|on[2020-01-01 08:00:00] ≤ -0.0
+ "Speicher(Q_th_load)|flow_rate|lb": |-
+ Constraint `Speicher(Q_th_load)|flow_rate|lb`
+ [time: 9]:
+ --------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 00:00:00] - 1e-05 Speicher(Q_th_load)|on[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 01:00:00] - 1e-05 Speicher(Q_th_load)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 02:00:00] - 1e-05 Speicher(Q_th_load)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 03:00:00] - 1e-05 Speicher(Q_th_load)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 04:00:00] - 1e-05 Speicher(Q_th_load)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 05:00:00] - 1e-05 Speicher(Q_th_load)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 06:00:00] - 1e-05 Speicher(Q_th_load)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 07:00:00] - 1e-05 Speicher(Q_th_load)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 Speicher(Q_th_load)|flow_rate[2020-01-01 08:00:00] - 1e-05 Speicher(Q_th_load)|on[2020-01-01 08:00:00] ≥ -0.0
+ "Speicher(Q_th_load)|total_flow_hours": |-
+ Constraint `Speicher(Q_th_load)|total_flow_hours`
+ -------------------------------------------------
+ +1 Speicher(Q_th_load)|total_flow_hours - 1 Speicher(Q_th_load)|flow_rate[2020-01-01 00:00:00] - 1 Speicher(Q_th_load)|flow_rate[2020-01-01 01:00:00]... -1 Speicher(Q_th_load)|flow_rate[2020-01-01 06:00:00] - 1 Speicher(Q_th_load)|flow_rate[2020-01-01 07:00:00] - 1 Speicher(Q_th_load)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Speicher(Q_th_unload)|on_hours_total": |-
+ Constraint `Speicher(Q_th_unload)|on_hours_total`
+ -------------------------------------------------
+ +1 Speicher(Q_th_unload)|on_hours_total - 1 Speicher(Q_th_unload)|on[2020-01-01 00:00:00] - 1 Speicher(Q_th_unload)|on[2020-01-01 01:00:00]... -1 Speicher(Q_th_unload)|on[2020-01-01 06:00:00] - 1 Speicher(Q_th_unload)|on[2020-01-01 07:00:00] - 1 Speicher(Q_th_unload)|on[2020-01-01 08:00:00] = -0.0
+ "Speicher(Q_th_unload)|flow_rate|ub": |-
+ Constraint `Speicher(Q_th_unload)|flow_rate|ub`
+ [time: 9]:
+ ----------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 00:00:00] - 1e+04 Speicher(Q_th_unload)|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 01:00:00] - 1e+04 Speicher(Q_th_unload)|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 02:00:00] - 1e+04 Speicher(Q_th_unload)|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 03:00:00] - 1e+04 Speicher(Q_th_unload)|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 04:00:00] - 1e+04 Speicher(Q_th_unload)|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 05:00:00] - 1e+04 Speicher(Q_th_unload)|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 06:00:00] - 1e+04 Speicher(Q_th_unload)|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 07:00:00] - 1e+04 Speicher(Q_th_unload)|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 08:00:00] - 1e+04 Speicher(Q_th_unload)|on[2020-01-01 08:00:00] ≤ -0.0
+ "Speicher(Q_th_unload)|flow_rate|lb": |-
+ Constraint `Speicher(Q_th_unload)|flow_rate|lb`
+ [time: 9]:
+ ----------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 00:00:00] - 1e-05 Speicher(Q_th_unload)|on[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 01:00:00] - 1e-05 Speicher(Q_th_unload)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 02:00:00] - 1e-05 Speicher(Q_th_unload)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 03:00:00] - 1e-05 Speicher(Q_th_unload)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 04:00:00] - 1e-05 Speicher(Q_th_unload)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 05:00:00] - 1e-05 Speicher(Q_th_unload)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 06:00:00] - 1e-05 Speicher(Q_th_unload)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 07:00:00] - 1e-05 Speicher(Q_th_unload)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 Speicher(Q_th_unload)|flow_rate[2020-01-01 08:00:00] - 1e-05 Speicher(Q_th_unload)|on[2020-01-01 08:00:00] ≥ -0.0
+ "Speicher(Q_th_unload)|total_flow_hours": |-
+ Constraint `Speicher(Q_th_unload)|total_flow_hours`
+ ---------------------------------------------------
+ +1 Speicher(Q_th_unload)|total_flow_hours - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 00:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 01:00:00]... -1 Speicher(Q_th_unload)|flow_rate[2020-01-01 06:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 07:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Speicher|prevent_simultaneous_use": |-
+ Constraint `Speicher|prevent_simultaneous_use`
+ [time: 9]:
+ ---------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Speicher(Q_th_load)|on[2020-01-01 00:00:00] + 1 Speicher(Q_th_unload)|on[2020-01-01 00:00:00] ≤ 1.0
+ [2020-01-01 01:00:00]: +1 Speicher(Q_th_load)|on[2020-01-01 01:00:00] + 1 Speicher(Q_th_unload)|on[2020-01-01 01:00:00] ≤ 1.0
+ [2020-01-01 02:00:00]: +1 Speicher(Q_th_load)|on[2020-01-01 02:00:00] + 1 Speicher(Q_th_unload)|on[2020-01-01 02:00:00] ≤ 1.0
+ [2020-01-01 03:00:00]: +1 Speicher(Q_th_load)|on[2020-01-01 03:00:00] + 1 Speicher(Q_th_unload)|on[2020-01-01 03:00:00] ≤ 1.0
+ [2020-01-01 04:00:00]: +1 Speicher(Q_th_load)|on[2020-01-01 04:00:00] + 1 Speicher(Q_th_unload)|on[2020-01-01 04:00:00] ≤ 1.0
+ [2020-01-01 05:00:00]: +1 Speicher(Q_th_load)|on[2020-01-01 05:00:00] + 1 Speicher(Q_th_unload)|on[2020-01-01 05:00:00] ≤ 1.0
+ [2020-01-01 06:00:00]: +1 Speicher(Q_th_load)|on[2020-01-01 06:00:00] + 1 Speicher(Q_th_unload)|on[2020-01-01 06:00:00] ≤ 1.0
+ [2020-01-01 07:00:00]: +1 Speicher(Q_th_load)|on[2020-01-01 07:00:00] + 1 Speicher(Q_th_unload)|on[2020-01-01 07:00:00] ≤ 1.0
+ [2020-01-01 08:00:00]: +1 Speicher(Q_th_load)|on[2020-01-01 08:00:00] + 1 Speicher(Q_th_unload)|on[2020-01-01 08:00:00] ≤ 1.0
+ "Speicher|netto_discharge": |-
+ Constraint `Speicher|netto_discharge`
+ [time: 9]:
+ ------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Speicher|netto_discharge[2020-01-01 00:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 00:00:00] + 1 Speicher(Q_th_load)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Speicher|netto_discharge[2020-01-01 01:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 01:00:00] + 1 Speicher(Q_th_load)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Speicher|netto_discharge[2020-01-01 02:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 02:00:00] + 1 Speicher(Q_th_load)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Speicher|netto_discharge[2020-01-01 03:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 03:00:00] + 1 Speicher(Q_th_load)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Speicher|netto_discharge[2020-01-01 04:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 04:00:00] + 1 Speicher(Q_th_load)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Speicher|netto_discharge[2020-01-01 05:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 05:00:00] + 1 Speicher(Q_th_load)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Speicher|netto_discharge[2020-01-01 06:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 06:00:00] + 1 Speicher(Q_th_load)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Speicher|netto_discharge[2020-01-01 07:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 07:00:00] + 1 Speicher(Q_th_load)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Speicher|netto_discharge[2020-01-01 08:00:00] - 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 08:00:00] + 1 Speicher(Q_th_load)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Speicher|charge_state": |-
+ Constraint `Speicher|charge_state`
+ [time: 9]:
+ ---------------------------------------------
+ [2020-01-01 01:00:00]: +1 Speicher|charge_state[2020-01-01 01:00:00] - 0.92 Speicher|charge_state[2020-01-01 00:00:00] - 0.9 Speicher(Q_th_load)|flow_rate[2020-01-01 00:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Speicher|charge_state[2020-01-01 02:00:00] - 0.92 Speicher|charge_state[2020-01-01 01:00:00] - 0.9 Speicher(Q_th_load)|flow_rate[2020-01-01 01:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Speicher|charge_state[2020-01-01 03:00:00] - 0.92 Speicher|charge_state[2020-01-01 02:00:00] - 0.9 Speicher(Q_th_load)|flow_rate[2020-01-01 02:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Speicher|charge_state[2020-01-01 04:00:00] - 0.92 Speicher|charge_state[2020-01-01 03:00:00] - 0.9 Speicher(Q_th_load)|flow_rate[2020-01-01 03:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Speicher|charge_state[2020-01-01 05:00:00] - 0.92 Speicher|charge_state[2020-01-01 04:00:00] - 0.9 Speicher(Q_th_load)|flow_rate[2020-01-01 04:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Speicher|charge_state[2020-01-01 06:00:00] - 0.92 Speicher|charge_state[2020-01-01 05:00:00] - 0.9 Speicher(Q_th_load)|flow_rate[2020-01-01 05:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Speicher|charge_state[2020-01-01 07:00:00] - 0.92 Speicher|charge_state[2020-01-01 06:00:00] - 0.9 Speicher(Q_th_load)|flow_rate[2020-01-01 06:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Speicher|charge_state[2020-01-01 08:00:00] - 0.92 Speicher|charge_state[2020-01-01 07:00:00] - 0.9 Speicher(Q_th_load)|flow_rate[2020-01-01 07:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 09:00:00]: +1 Speicher|charge_state[2020-01-01 09:00:00] - 0.92 Speicher|charge_state[2020-01-01 08:00:00] - 0.9 Speicher(Q_th_load)|flow_rate[2020-01-01 08:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "Speicher|Piece_0|inside_piece": |-
+ Constraint `Speicher|Piece_0|inside_piece`
+ ------------------------------------------
+ +1 Speicher|Piece_0|inside_piece - 1 Speicher|Piece_0|lambda0 - 1 Speicher|Piece_0|lambda1 = -0.0
+ "Speicher|Piece_1|inside_piece": |-
+ Constraint `Speicher|Piece_1|inside_piece`
+ ------------------------------------------
+ +1 Speicher|Piece_1|inside_piece - 1 Speicher|Piece_1|lambda0 - 1 Speicher|Piece_1|lambda1 = -0.0
+ "Speicher|PiecewiseEffects|Speicher|size|lambda": |-
+ Constraint `Speicher|PiecewiseEffects|Speicher|size|lambda`
+ -----------------------------------------------------------
+ +1 Speicher|size - 5 Speicher|Piece_0|lambda0 - 25 Speicher|Piece_0|lambda1 - 25 Speicher|Piece_1|lambda0 - 100 Speicher|Piece_1|lambda1 = -0.0
+ "Speicher|PiecewiseEffects|Speicher|size|single_segment": |-
+ Constraint `Speicher|PiecewiseEffects|Speicher|size|single_segment`
+ -------------------------------------------------------------------
+ +1 Speicher|Piece_0|inside_piece + 1 Speicher|Piece_1|inside_piece ≤ 1.0
+ "Speicher|PiecewiseEffects|Speicher|PiecewiseEffects|costs|lambda": |-
+ Constraint `Speicher|PiecewiseEffects|Speicher|PiecewiseEffects|costs|lambda`
+ -----------------------------------------------------------------------------
+ +1 Speicher|PiecewiseEffects|costs - 50 Speicher|Piece_0|lambda0 - 250 Speicher|Piece_0|lambda1 - 250 Speicher|Piece_1|lambda0 - 800 Speicher|Piece_1|lambda1 = -0.0
+ "Speicher|PiecewiseEffects|Speicher|PiecewiseEffects|costs|single_segment": |-
+ Constraint `Speicher|PiecewiseEffects|Speicher|PiecewiseEffects|costs|single_segment`
+ -------------------------------------------------------------------------------------
+ +1 Speicher|Piece_0|inside_piece + 1 Speicher|Piece_1|inside_piece ≤ 1.0
+ "Speicher|PiecewiseEffects|Speicher|PiecewiseEffects|PE|lambda": |-
+ Constraint `Speicher|PiecewiseEffects|Speicher|PiecewiseEffects|PE|lambda`
+ --------------------------------------------------------------------------
+ +1 Speicher|PiecewiseEffects|PE - 5 Speicher|Piece_0|lambda0 - 25 Speicher|Piece_0|lambda1 - 25 Speicher|Piece_1|lambda0 - 100 Speicher|Piece_1|lambda1 = -0.0
+ "Speicher|PiecewiseEffects|Speicher|PiecewiseEffects|PE|single_segment": |-
+ Constraint `Speicher|PiecewiseEffects|Speicher|PiecewiseEffects|PE|single_segment`
+ ----------------------------------------------------------------------------------
+ +1 Speicher|Piece_0|inside_piece + 1 Speicher|Piece_1|inside_piece ≤ 1.0
+ "Speicher->costs(periodic)": |-
+ Constraint `Speicher->costs(periodic)`
+ --------------------------------------
+ +1 Speicher->costs(periodic) - 1 Speicher|PiecewiseEffects|costs = -0.0
+ "Speicher->PE(periodic)": |-
+ Constraint `Speicher->PE(periodic)`
+ -----------------------------------
+ +1 Speicher->PE(periodic) - 1 Speicher|PiecewiseEffects|PE = -0.0
+ "Speicher|charge_state|ub": |-
+ Constraint `Speicher|charge_state|ub`
+ [time: 10]:
+ -------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Speicher|charge_state[2020-01-01 00:00:00] - 1 Speicher|size ≤ -0.0
+ [2020-01-01 01:00:00]: +1 Speicher|charge_state[2020-01-01 01:00:00] - 1 Speicher|size ≤ -0.0
+ [2020-01-01 02:00:00]: +1 Speicher|charge_state[2020-01-01 02:00:00] - 1 Speicher|size ≤ -0.0
+ [2020-01-01 03:00:00]: +1 Speicher|charge_state[2020-01-01 03:00:00] - 1 Speicher|size ≤ -0.0
+ [2020-01-01 04:00:00]: +1 Speicher|charge_state[2020-01-01 04:00:00] - 1 Speicher|size ≤ -0.0
+ [2020-01-01 05:00:00]: +1 Speicher|charge_state[2020-01-01 05:00:00] - 1 Speicher|size ≤ -0.0
+ [2020-01-01 06:00:00]: +1 Speicher|charge_state[2020-01-01 06:00:00] - 1 Speicher|size ≤ -0.0
+ [2020-01-01 07:00:00]: +1 Speicher|charge_state[2020-01-01 07:00:00] - 1 Speicher|size ≤ -0.0
+ [2020-01-01 08:00:00]: +1 Speicher|charge_state[2020-01-01 08:00:00] - 1 Speicher|size ≤ -0.0
+ [2020-01-01 09:00:00]: +1 Speicher|charge_state[2020-01-01 09:00:00] - 1 Speicher|size ≤ -0.0
+ "Speicher|charge_state|lb": |-
+ Constraint `Speicher|charge_state|lb`
+ [time: 10]:
+ -------------------------------------------------
+ [2020-01-01 00:00:00]: +1 Speicher|charge_state[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 Speicher|charge_state[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 Speicher|charge_state[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 Speicher|charge_state[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 Speicher|charge_state[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 Speicher|charge_state[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 Speicher|charge_state[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 Speicher|charge_state[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 Speicher|charge_state[2020-01-01 08:00:00] ≥ -0.0
+ [2020-01-01 09:00:00]: +1 Speicher|charge_state[2020-01-01 09:00:00] ≥ -0.0
+ "Speicher|initial_charge_state": |-
+ Constraint `Speicher|initial_charge_state`
+ ------------------------------------------
+ +1 Speicher|charge_state[2020-01-01 00:00:00] = -0.0
+ "Speicher|final_charge_max": |-
+ Constraint `Speicher|final_charge_max`
+ --------------------------------------
+ +1 Speicher|charge_state[2020-01-01 09:00:00] ≤ 10.0
+ "BHKW2(Q_fu)|on_hours_total": |-
+ Constraint `BHKW2(Q_fu)|on_hours_total`
+ ---------------------------------------
+ +1 BHKW2(Q_fu)|on_hours_total - 1 BHKW2(Q_fu)|on[2020-01-01 00:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 01:00:00]... -1 BHKW2(Q_fu)|on[2020-01-01 06:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 07:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 08:00:00] = -0.0
+ "BHKW2(Q_fu)|flow_rate|ub": |-
+ Constraint `BHKW2(Q_fu)|flow_rate|ub`
+ [time: 9]:
+ ------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1e+07 BHKW2(Q_fu)|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 01:00:00] - 1e+07 BHKW2(Q_fu)|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 02:00:00] - 1e+07 BHKW2(Q_fu)|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 03:00:00] - 1e+07 BHKW2(Q_fu)|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 04:00:00] - 1e+07 BHKW2(Q_fu)|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 05:00:00] - 1e+07 BHKW2(Q_fu)|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1e+07 BHKW2(Q_fu)|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1e+07 BHKW2(Q_fu)|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 08:00:00] - 1e+07 BHKW2(Q_fu)|on[2020-01-01 08:00:00] ≤ -0.0
+ "BHKW2(Q_fu)|flow_rate|lb": |-
+ Constraint `BHKW2(Q_fu)|flow_rate|lb`
+ [time: 9]:
+ ------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1e-05 BHKW2(Q_fu)|on[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 01:00:00] - 1e-05 BHKW2(Q_fu)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 02:00:00] - 1e-05 BHKW2(Q_fu)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 03:00:00] - 1e-05 BHKW2(Q_fu)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 04:00:00] - 1e-05 BHKW2(Q_fu)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 05:00:00] - 1e-05 BHKW2(Q_fu)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1e-05 BHKW2(Q_fu)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1e-05 BHKW2(Q_fu)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 08:00:00] - 1e-05 BHKW2(Q_fu)|on[2020-01-01 08:00:00] ≥ -0.0
+ "BHKW2(Q_fu)|total_flow_hours": |-
+ Constraint `BHKW2(Q_fu)|total_flow_hours`
+ -----------------------------------------
+ +1 BHKW2(Q_fu)|total_flow_hours - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 01:00:00]... -1 BHKW2(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "BHKW2(P_el)|on_hours_total": |-
+ Constraint `BHKW2(P_el)|on_hours_total`
+ ---------------------------------------
+ +1 BHKW2(P_el)|on_hours_total - 1 BHKW2(P_el)|on[2020-01-01 00:00:00] - 1 BHKW2(P_el)|on[2020-01-01 01:00:00]... -1 BHKW2(P_el)|on[2020-01-01 06:00:00] - 1 BHKW2(P_el)|on[2020-01-01 07:00:00] - 1 BHKW2(P_el)|on[2020-01-01 08:00:00] = -0.0
+ "BHKW2(P_el)|flow_rate|ub": |-
+ Constraint `BHKW2(P_el)|flow_rate|ub`
+ [time: 9]:
+ ------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 00:00:00] - 60 BHKW2(P_el)|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 01:00:00] - 60 BHKW2(P_el)|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 02:00:00] - 60 BHKW2(P_el)|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 03:00:00] - 60 BHKW2(P_el)|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 04:00:00] - 60 BHKW2(P_el)|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 05:00:00] - 60 BHKW2(P_el)|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 06:00:00] - 60 BHKW2(P_el)|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 07:00:00] - 60 BHKW2(P_el)|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 08:00:00] - 60 BHKW2(P_el)|on[2020-01-01 08:00:00] ≤ -0.0
+ "BHKW2(P_el)|flow_rate|lb": |-
+ Constraint `BHKW2(P_el)|flow_rate|lb`
+ [time: 9]:
+ ------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 00:00:00] - 1e-05 BHKW2(P_el)|on[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 01:00:00] - 1e-05 BHKW2(P_el)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 02:00:00] - 1e-05 BHKW2(P_el)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 03:00:00] - 1e-05 BHKW2(P_el)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 04:00:00] - 1e-05 BHKW2(P_el)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 05:00:00] - 1e-05 BHKW2(P_el)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 06:00:00] - 1e-05 BHKW2(P_el)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 07:00:00] - 1e-05 BHKW2(P_el)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 08:00:00] - 1e-05 BHKW2(P_el)|on[2020-01-01 08:00:00] ≥ -0.0
+ "BHKW2(P_el)|total_flow_hours": |-
+ Constraint `BHKW2(P_el)|total_flow_hours`
+ -----------------------------------------
+ +1 BHKW2(P_el)|total_flow_hours - 1 BHKW2(P_el)|flow_rate[2020-01-01 00:00:00] - 1 BHKW2(P_el)|flow_rate[2020-01-01 01:00:00]... -1 BHKW2(P_el)|flow_rate[2020-01-01 06:00:00] - 1 BHKW2(P_el)|flow_rate[2020-01-01 07:00:00] - 1 BHKW2(P_el)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "BHKW2(Q_th)|on_hours_total": |-
+ Constraint `BHKW2(Q_th)|on_hours_total`
+ ---------------------------------------
+ +1 BHKW2(Q_th)|on_hours_total - 1 BHKW2(Q_th)|on[2020-01-01 00:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 01:00:00]... -1 BHKW2(Q_th)|on[2020-01-01 06:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 07:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 08:00:00] = -0.0
+ "BHKW2(Q_th)|flow_rate|ub": |-
+ Constraint `BHKW2(Q_th)|flow_rate|ub`
+ [time: 9]:
+ ------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 00:00:00] - 1e+07 BHKW2(Q_th)|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 01:00:00] - 1e+07 BHKW2(Q_th)|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 02:00:00] - 1e+07 BHKW2(Q_th)|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 03:00:00] - 1e+07 BHKW2(Q_th)|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 04:00:00] - 1e+07 BHKW2(Q_th)|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 05:00:00] - 1e+07 BHKW2(Q_th)|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 06:00:00] - 1e+07 BHKW2(Q_th)|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 07:00:00] - 1e+07 BHKW2(Q_th)|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 08:00:00] - 1e+07 BHKW2(Q_th)|on[2020-01-01 08:00:00] ≤ -0.0
+ "BHKW2(Q_th)|flow_rate|lb": |-
+ Constraint `BHKW2(Q_th)|flow_rate|lb`
+ [time: 9]:
+ ------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 00:00:00] - 1e-05 BHKW2(Q_th)|on[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 01:00:00] - 1e-05 BHKW2(Q_th)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 02:00:00] - 1e-05 BHKW2(Q_th)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 03:00:00] - 1e-05 BHKW2(Q_th)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 04:00:00] - 1e-05 BHKW2(Q_th)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 05:00:00] - 1e-05 BHKW2(Q_th)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 06:00:00] - 1e-05 BHKW2(Q_th)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 07:00:00] - 1e-05 BHKW2(Q_th)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 08:00:00] - 1e-05 BHKW2(Q_th)|on[2020-01-01 08:00:00] ≥ -0.0
+ "BHKW2(Q_th)|total_flow_hours": |-
+ Constraint `BHKW2(Q_th)|total_flow_hours`
+ -----------------------------------------
+ +1 BHKW2(Q_th)|total_flow_hours - 1 BHKW2(Q_th)|flow_rate[2020-01-01 00:00:00] - 1 BHKW2(Q_th)|flow_rate[2020-01-01 01:00:00]... -1 BHKW2(Q_th)|flow_rate[2020-01-01 06:00:00] - 1 BHKW2(Q_th)|flow_rate[2020-01-01 07:00:00] - 1 BHKW2(Q_th)|flow_rate[2020-01-01 08:00:00] = -0.0
+ "BHKW2|on|ub": |-
+ Constraint `BHKW2|on|ub`
+ [time: 9]:
+ -----------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2|on[2020-01-01 00:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 00:00:00] - 1 BHKW2(P_el)|on[2020-01-01 00:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 00:00:00] ≤ 1e-05
+ [2020-01-01 01:00:00]: +1 BHKW2|on[2020-01-01 01:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 01:00:00] - 1 BHKW2(P_el)|on[2020-01-01 01:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 01:00:00] ≤ 1e-05
+ [2020-01-01 02:00:00]: +1 BHKW2|on[2020-01-01 02:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 02:00:00] - 1 BHKW2(P_el)|on[2020-01-01 02:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 02:00:00] ≤ 1e-05
+ [2020-01-01 03:00:00]: +1 BHKW2|on[2020-01-01 03:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 03:00:00] - 1 BHKW2(P_el)|on[2020-01-01 03:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 03:00:00] ≤ 1e-05
+ [2020-01-01 04:00:00]: +1 BHKW2|on[2020-01-01 04:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 04:00:00] - 1 BHKW2(P_el)|on[2020-01-01 04:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 04:00:00] ≤ 1e-05
+ [2020-01-01 05:00:00]: +1 BHKW2|on[2020-01-01 05:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 05:00:00] - 1 BHKW2(P_el)|on[2020-01-01 05:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 05:00:00] ≤ 1e-05
+ [2020-01-01 06:00:00]: +1 BHKW2|on[2020-01-01 06:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 06:00:00] - 1 BHKW2(P_el)|on[2020-01-01 06:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 06:00:00] ≤ 1e-05
+ [2020-01-01 07:00:00]: +1 BHKW2|on[2020-01-01 07:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 07:00:00] - 1 BHKW2(P_el)|on[2020-01-01 07:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 07:00:00] ≤ 1e-05
+ [2020-01-01 08:00:00]: +1 BHKW2|on[2020-01-01 08:00:00] - 1 BHKW2(Q_fu)|on[2020-01-01 08:00:00] - 1 BHKW2(P_el)|on[2020-01-01 08:00:00] - 1 BHKW2(Q_th)|on[2020-01-01 08:00:00] ≤ 1e-05
+ "BHKW2|on|lb": |-
+ Constraint `BHKW2|on|lb`
+ [time: 9]:
+ -----------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2|on[2020-01-01 00:00:00] - 0.3333 BHKW2(Q_fu)|on[2020-01-01 00:00:00] - 0.3333 BHKW2(P_el)|on[2020-01-01 00:00:00] - 0.3333 BHKW2(Q_th)|on[2020-01-01 00:00:00] ≥ -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2|on[2020-01-01 01:00:00] - 0.3333 BHKW2(Q_fu)|on[2020-01-01 01:00:00] - 0.3333 BHKW2(P_el)|on[2020-01-01 01:00:00] - 0.3333 BHKW2(Q_th)|on[2020-01-01 01:00:00] ≥ -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2|on[2020-01-01 02:00:00] - 0.3333 BHKW2(Q_fu)|on[2020-01-01 02:00:00] - 0.3333 BHKW2(P_el)|on[2020-01-01 02:00:00] - 0.3333 BHKW2(Q_th)|on[2020-01-01 02:00:00] ≥ -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2|on[2020-01-01 03:00:00] - 0.3333 BHKW2(Q_fu)|on[2020-01-01 03:00:00] - 0.3333 BHKW2(P_el)|on[2020-01-01 03:00:00] - 0.3333 BHKW2(Q_th)|on[2020-01-01 03:00:00] ≥ -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2|on[2020-01-01 04:00:00] - 0.3333 BHKW2(Q_fu)|on[2020-01-01 04:00:00] - 0.3333 BHKW2(P_el)|on[2020-01-01 04:00:00] - 0.3333 BHKW2(Q_th)|on[2020-01-01 04:00:00] ≥ -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2|on[2020-01-01 05:00:00] - 0.3333 BHKW2(Q_fu)|on[2020-01-01 05:00:00] - 0.3333 BHKW2(P_el)|on[2020-01-01 05:00:00] - 0.3333 BHKW2(Q_th)|on[2020-01-01 05:00:00] ≥ -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2|on[2020-01-01 06:00:00] - 0.3333 BHKW2(Q_fu)|on[2020-01-01 06:00:00] - 0.3333 BHKW2(P_el)|on[2020-01-01 06:00:00] - 0.3333 BHKW2(Q_th)|on[2020-01-01 06:00:00] ≥ -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2|on[2020-01-01 07:00:00] - 0.3333 BHKW2(Q_fu)|on[2020-01-01 07:00:00] - 0.3333 BHKW2(P_el)|on[2020-01-01 07:00:00] - 0.3333 BHKW2(Q_th)|on[2020-01-01 07:00:00] ≥ -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2|on[2020-01-01 08:00:00] - 0.3333 BHKW2(Q_fu)|on[2020-01-01 08:00:00] - 0.3333 BHKW2(P_el)|on[2020-01-01 08:00:00] - 0.3333 BHKW2(Q_th)|on[2020-01-01 08:00:00] ≥ -0.0
+ "BHKW2|on_hours_total": |-
+ Constraint `BHKW2|on_hours_total`
+ ---------------------------------
+ +1 BHKW2|on_hours_total - 1 BHKW2|on[2020-01-01 00:00:00] - 1 BHKW2|on[2020-01-01 01:00:00]... -1 BHKW2|on[2020-01-01 06:00:00] - 1 BHKW2|on[2020-01-01 07:00:00] - 1 BHKW2|on[2020-01-01 08:00:00] = -0.0
+ "BHKW2|switch|transition": |-
+ Constraint `BHKW2|switch|transition`
+ [time: 8]:
+ -----------------------------------------------
+ [2020-01-01 01:00:00]: +1 BHKW2|switch|on[2020-01-01 01:00:00] - 1 BHKW2|switch|off[2020-01-01 01:00:00] - 1 BHKW2|on[2020-01-01 01:00:00] + 1 BHKW2|on[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2|switch|on[2020-01-01 02:00:00] - 1 BHKW2|switch|off[2020-01-01 02:00:00] - 1 BHKW2|on[2020-01-01 02:00:00] + 1 BHKW2|on[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2|switch|on[2020-01-01 03:00:00] - 1 BHKW2|switch|off[2020-01-01 03:00:00] - 1 BHKW2|on[2020-01-01 03:00:00] + 1 BHKW2|on[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2|switch|on[2020-01-01 04:00:00] - 1 BHKW2|switch|off[2020-01-01 04:00:00] - 1 BHKW2|on[2020-01-01 04:00:00] + 1 BHKW2|on[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2|switch|on[2020-01-01 05:00:00] - 1 BHKW2|switch|off[2020-01-01 05:00:00] - 1 BHKW2|on[2020-01-01 05:00:00] + 1 BHKW2|on[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2|switch|on[2020-01-01 06:00:00] - 1 BHKW2|switch|off[2020-01-01 06:00:00] - 1 BHKW2|on[2020-01-01 06:00:00] + 1 BHKW2|on[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2|switch|on[2020-01-01 07:00:00] - 1 BHKW2|switch|off[2020-01-01 07:00:00] - 1 BHKW2|on[2020-01-01 07:00:00] + 1 BHKW2|on[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2|switch|on[2020-01-01 08:00:00] - 1 BHKW2|switch|off[2020-01-01 08:00:00] - 1 BHKW2|on[2020-01-01 08:00:00] + 1 BHKW2|on[2020-01-01 07:00:00] = -0.0
+ "BHKW2|switch|initial": |-
+ Constraint `BHKW2|switch|initial`
+ ---------------------------------
+ +1 BHKW2|switch|on[2020-01-01 00:00:00] - 1 BHKW2|switch|off[2020-01-01 00:00:00] - 1 BHKW2|on[2020-01-01 00:00:00] = -1.0
+ "BHKW2|switch|mutex": |-
+ Constraint `BHKW2|switch|mutex`
+ [time: 9]:
+ ------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2|switch|on[2020-01-01 00:00:00] + 1 BHKW2|switch|off[2020-01-01 00:00:00] ≤ 1.0
+ [2020-01-01 01:00:00]: +1 BHKW2|switch|on[2020-01-01 01:00:00] + 1 BHKW2|switch|off[2020-01-01 01:00:00] ≤ 1.0
+ [2020-01-01 02:00:00]: +1 BHKW2|switch|on[2020-01-01 02:00:00] + 1 BHKW2|switch|off[2020-01-01 02:00:00] ≤ 1.0
+ [2020-01-01 03:00:00]: +1 BHKW2|switch|on[2020-01-01 03:00:00] + 1 BHKW2|switch|off[2020-01-01 03:00:00] ≤ 1.0
+ [2020-01-01 04:00:00]: +1 BHKW2|switch|on[2020-01-01 04:00:00] + 1 BHKW2|switch|off[2020-01-01 04:00:00] ≤ 1.0
+ [2020-01-01 05:00:00]: +1 BHKW2|switch|on[2020-01-01 05:00:00] + 1 BHKW2|switch|off[2020-01-01 05:00:00] ≤ 1.0
+ [2020-01-01 06:00:00]: +1 BHKW2|switch|on[2020-01-01 06:00:00] + 1 BHKW2|switch|off[2020-01-01 06:00:00] ≤ 1.0
+ [2020-01-01 07:00:00]: +1 BHKW2|switch|on[2020-01-01 07:00:00] + 1 BHKW2|switch|off[2020-01-01 07:00:00] ≤ 1.0
+ [2020-01-01 08:00:00]: +1 BHKW2|switch|on[2020-01-01 08:00:00] + 1 BHKW2|switch|off[2020-01-01 08:00:00] ≤ 1.0
+ "BHKW2->costs(temporal)": |-
+ Constraint `BHKW2->costs(temporal)`
+ [time: 9]:
+ ----------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2->costs(temporal)[2020-01-01 00:00:00] - 0.01 BHKW2|switch|on[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2->costs(temporal)[2020-01-01 01:00:00] - 0.01 BHKW2|switch|on[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2->costs(temporal)[2020-01-01 02:00:00] - 0.01 BHKW2|switch|on[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2->costs(temporal)[2020-01-01 03:00:00] - 0.01 BHKW2|switch|on[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2->costs(temporal)[2020-01-01 04:00:00] - 0.01 BHKW2|switch|on[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2->costs(temporal)[2020-01-01 05:00:00] - 0.01 BHKW2|switch|on[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2->costs(temporal)[2020-01-01 06:00:00] - 0.01 BHKW2|switch|on[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2->costs(temporal)[2020-01-01 07:00:00] - 0.01 BHKW2|switch|on[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2->costs(temporal)[2020-01-01 08:00:00] - 0.01 BHKW2|switch|on[2020-01-01 08:00:00] = -0.0
+ "BHKW2|Piece_0|inside_piece": |-
+ Constraint `BHKW2|Piece_0|inside_piece`
+ [time: 9]:
+ --------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 00:00:00] - 1 BHKW2|Piece_0|lambda0[2020-01-01 00:00:00] - 1 BHKW2|Piece_0|lambda1[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 01:00:00] - 1 BHKW2|Piece_0|lambda0[2020-01-01 01:00:00] - 1 BHKW2|Piece_0|lambda1[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 02:00:00] - 1 BHKW2|Piece_0|lambda0[2020-01-01 02:00:00] - 1 BHKW2|Piece_0|lambda1[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 03:00:00] - 1 BHKW2|Piece_0|lambda0[2020-01-01 03:00:00] - 1 BHKW2|Piece_0|lambda1[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 04:00:00] - 1 BHKW2|Piece_0|lambda0[2020-01-01 04:00:00] - 1 BHKW2|Piece_0|lambda1[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 05:00:00] - 1 BHKW2|Piece_0|lambda0[2020-01-01 05:00:00] - 1 BHKW2|Piece_0|lambda1[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 06:00:00] - 1 BHKW2|Piece_0|lambda0[2020-01-01 06:00:00] - 1 BHKW2|Piece_0|lambda1[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 07:00:00] - 1 BHKW2|Piece_0|lambda0[2020-01-01 07:00:00] - 1 BHKW2|Piece_0|lambda1[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 08:00:00] - 1 BHKW2|Piece_0|lambda0[2020-01-01 08:00:00] - 1 BHKW2|Piece_0|lambda1[2020-01-01 08:00:00] = -0.0
+ "BHKW2|Piece_1|inside_piece": |-
+ Constraint `BHKW2|Piece_1|inside_piece`
+ [time: 9]:
+ --------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2|Piece_1|inside_piece[2020-01-01 00:00:00] - 1 BHKW2|Piece_1|lambda0[2020-01-01 00:00:00] - 1 BHKW2|Piece_1|lambda1[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2|Piece_1|inside_piece[2020-01-01 01:00:00] - 1 BHKW2|Piece_1|lambda0[2020-01-01 01:00:00] - 1 BHKW2|Piece_1|lambda1[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2|Piece_1|inside_piece[2020-01-01 02:00:00] - 1 BHKW2|Piece_1|lambda0[2020-01-01 02:00:00] - 1 BHKW2|Piece_1|lambda1[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2|Piece_1|inside_piece[2020-01-01 03:00:00] - 1 BHKW2|Piece_1|lambda0[2020-01-01 03:00:00] - 1 BHKW2|Piece_1|lambda1[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2|Piece_1|inside_piece[2020-01-01 04:00:00] - 1 BHKW2|Piece_1|lambda0[2020-01-01 04:00:00] - 1 BHKW2|Piece_1|lambda1[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2|Piece_1|inside_piece[2020-01-01 05:00:00] - 1 BHKW2|Piece_1|lambda0[2020-01-01 05:00:00] - 1 BHKW2|Piece_1|lambda1[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2|Piece_1|inside_piece[2020-01-01 06:00:00] - 1 BHKW2|Piece_1|lambda0[2020-01-01 06:00:00] - 1 BHKW2|Piece_1|lambda1[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2|Piece_1|inside_piece[2020-01-01 07:00:00] - 1 BHKW2|Piece_1|lambda0[2020-01-01 07:00:00] - 1 BHKW2|Piece_1|lambda1[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2|Piece_1|inside_piece[2020-01-01 08:00:00] - 1 BHKW2|Piece_1|lambda0[2020-01-01 08:00:00] - 1 BHKW2|Piece_1|lambda1[2020-01-01 08:00:00] = -0.0
+ "BHKW2|BHKW2(P_el)|flow_rate|lambda": |-
+ Constraint `BHKW2|BHKW2(P_el)|flow_rate|lambda`
+ [time: 9]:
+ ----------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 00:00:00] - 5 BHKW2|Piece_0|lambda0[2020-01-01 00:00:00] - 30 BHKW2|Piece_0|lambda1[2020-01-01 00:00:00] - 40 BHKW2|Piece_1|lambda0[2020-01-01 00:00:00] - 60 BHKW2|Piece_1|lambda1[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 01:00:00] - 5 BHKW2|Piece_0|lambda0[2020-01-01 01:00:00] - 30 BHKW2|Piece_0|lambda1[2020-01-01 01:00:00] - 40 BHKW2|Piece_1|lambda0[2020-01-01 01:00:00] - 60 BHKW2|Piece_1|lambda1[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 02:00:00] - 5 BHKW2|Piece_0|lambda0[2020-01-01 02:00:00] - 30 BHKW2|Piece_0|lambda1[2020-01-01 02:00:00] - 40 BHKW2|Piece_1|lambda0[2020-01-01 02:00:00] - 60 BHKW2|Piece_1|lambda1[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 03:00:00] - 5 BHKW2|Piece_0|lambda0[2020-01-01 03:00:00] - 30 BHKW2|Piece_0|lambda1[2020-01-01 03:00:00] - 40 BHKW2|Piece_1|lambda0[2020-01-01 03:00:00] - 60 BHKW2|Piece_1|lambda1[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 04:00:00] - 5 BHKW2|Piece_0|lambda0[2020-01-01 04:00:00] - 30 BHKW2|Piece_0|lambda1[2020-01-01 04:00:00] - 40 BHKW2|Piece_1|lambda0[2020-01-01 04:00:00] - 60 BHKW2|Piece_1|lambda1[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 05:00:00] - 5 BHKW2|Piece_0|lambda0[2020-01-01 05:00:00] - 30 BHKW2|Piece_0|lambda1[2020-01-01 05:00:00] - 40 BHKW2|Piece_1|lambda0[2020-01-01 05:00:00] - 60 BHKW2|Piece_1|lambda1[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 06:00:00] - 5 BHKW2|Piece_0|lambda0[2020-01-01 06:00:00] - 30 BHKW2|Piece_0|lambda1[2020-01-01 06:00:00] - 40 BHKW2|Piece_1|lambda0[2020-01-01 06:00:00] - 60 BHKW2|Piece_1|lambda1[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 07:00:00] - 5 BHKW2|Piece_0|lambda0[2020-01-01 07:00:00] - 30 BHKW2|Piece_0|lambda1[2020-01-01 07:00:00] - 40 BHKW2|Piece_1|lambda0[2020-01-01 07:00:00] - 60 BHKW2|Piece_1|lambda1[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 08:00:00] - 5 BHKW2|Piece_0|lambda0[2020-01-01 08:00:00] - 30 BHKW2|Piece_0|lambda1[2020-01-01 08:00:00] - 40 BHKW2|Piece_1|lambda0[2020-01-01 08:00:00] - 60 BHKW2|Piece_1|lambda1[2020-01-01 08:00:00] = -0.0
+ "BHKW2|BHKW2(P_el)|flow_rate|single_segment": |-
+ Constraint `BHKW2|BHKW2(P_el)|flow_rate|single_segment`
+ [time: 9]:
+ ------------------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 00:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 00:00:00] - 1 BHKW2|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 01:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 01:00:00] - 1 BHKW2|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 02:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 02:00:00] - 1 BHKW2|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 03:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 03:00:00] - 1 BHKW2|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 04:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 04:00:00] - 1 BHKW2|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 05:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 05:00:00] - 1 BHKW2|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 06:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 06:00:00] - 1 BHKW2|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 07:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 07:00:00] - 1 BHKW2|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 08:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 08:00:00] - 1 BHKW2|on[2020-01-01 08:00:00] ≤ -0.0
+ "BHKW2|BHKW2(Q_th)|flow_rate|lambda": |-
+ Constraint `BHKW2|BHKW2(Q_th)|flow_rate|lambda`
+ [time: 9]:
+ ----------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 00:00:00] - 6 BHKW2|Piece_0|lambda0[2020-01-01 00:00:00] - 35 BHKW2|Piece_0|lambda1[2020-01-01 00:00:00] - 45 BHKW2|Piece_1|lambda0[2020-01-01 00:00:00] - 100 BHKW2|Piece_1|lambda1[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 01:00:00] - 6 BHKW2|Piece_0|lambda0[2020-01-01 01:00:00] - 35 BHKW2|Piece_0|lambda1[2020-01-01 01:00:00] - 45 BHKW2|Piece_1|lambda0[2020-01-01 01:00:00] - 100 BHKW2|Piece_1|lambda1[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 02:00:00] - 6 BHKW2|Piece_0|lambda0[2020-01-01 02:00:00] - 35 BHKW2|Piece_0|lambda1[2020-01-01 02:00:00] - 45 BHKW2|Piece_1|lambda0[2020-01-01 02:00:00] - 100 BHKW2|Piece_1|lambda1[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 03:00:00] - 6 BHKW2|Piece_0|lambda0[2020-01-01 03:00:00] - 35 BHKW2|Piece_0|lambda1[2020-01-01 03:00:00] - 45 BHKW2|Piece_1|lambda0[2020-01-01 03:00:00] - 100 BHKW2|Piece_1|lambda1[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 04:00:00] - 6 BHKW2|Piece_0|lambda0[2020-01-01 04:00:00] - 35 BHKW2|Piece_0|lambda1[2020-01-01 04:00:00] - 45 BHKW2|Piece_1|lambda0[2020-01-01 04:00:00] - 100 BHKW2|Piece_1|lambda1[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 05:00:00] - 6 BHKW2|Piece_0|lambda0[2020-01-01 05:00:00] - 35 BHKW2|Piece_0|lambda1[2020-01-01 05:00:00] - 45 BHKW2|Piece_1|lambda0[2020-01-01 05:00:00] - 100 BHKW2|Piece_1|lambda1[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 06:00:00] - 6 BHKW2|Piece_0|lambda0[2020-01-01 06:00:00] - 35 BHKW2|Piece_0|lambda1[2020-01-01 06:00:00] - 45 BHKW2|Piece_1|lambda0[2020-01-01 06:00:00] - 100 BHKW2|Piece_1|lambda1[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 07:00:00] - 6 BHKW2|Piece_0|lambda0[2020-01-01 07:00:00] - 35 BHKW2|Piece_0|lambda1[2020-01-01 07:00:00] - 45 BHKW2|Piece_1|lambda0[2020-01-01 07:00:00] - 100 BHKW2|Piece_1|lambda1[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2(Q_th)|flow_rate[2020-01-01 08:00:00] - 6 BHKW2|Piece_0|lambda0[2020-01-01 08:00:00] - 35 BHKW2|Piece_0|lambda1[2020-01-01 08:00:00] - 45 BHKW2|Piece_1|lambda0[2020-01-01 08:00:00] - 100 BHKW2|Piece_1|lambda1[2020-01-01 08:00:00] = -0.0
+ "BHKW2|BHKW2(Q_th)|flow_rate|single_segment": |-
+ Constraint `BHKW2|BHKW2(Q_th)|flow_rate|single_segment`
+ [time: 9]:
+ ------------------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 00:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 00:00:00] - 1 BHKW2|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 01:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 01:00:00] - 1 BHKW2|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 02:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 02:00:00] - 1 BHKW2|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 03:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 03:00:00] - 1 BHKW2|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 04:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 04:00:00] - 1 BHKW2|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 05:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 05:00:00] - 1 BHKW2|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 06:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 06:00:00] - 1 BHKW2|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 07:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 07:00:00] - 1 BHKW2|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 08:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 08:00:00] - 1 BHKW2|on[2020-01-01 08:00:00] ≤ -0.0
+ "BHKW2|BHKW2(Q_fu)|flow_rate|lambda": |-
+ Constraint `BHKW2|BHKW2(Q_fu)|flow_rate|lambda`
+ [time: 9]:
+ ----------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 00:00:00] - 12 BHKW2|Piece_0|lambda0[2020-01-01 00:00:00] - 70 BHKW2|Piece_0|lambda1[2020-01-01 00:00:00] - 90 BHKW2|Piece_1|lambda0[2020-01-01 00:00:00] - 200 BHKW2|Piece_1|lambda1[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 01:00:00] - 12 BHKW2|Piece_0|lambda0[2020-01-01 01:00:00] - 70 BHKW2|Piece_0|lambda1[2020-01-01 01:00:00] - 90 BHKW2|Piece_1|lambda0[2020-01-01 01:00:00] - 200 BHKW2|Piece_1|lambda1[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 02:00:00] - 12 BHKW2|Piece_0|lambda0[2020-01-01 02:00:00] - 70 BHKW2|Piece_0|lambda1[2020-01-01 02:00:00] - 90 BHKW2|Piece_1|lambda0[2020-01-01 02:00:00] - 200 BHKW2|Piece_1|lambda1[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 03:00:00] - 12 BHKW2|Piece_0|lambda0[2020-01-01 03:00:00] - 70 BHKW2|Piece_0|lambda1[2020-01-01 03:00:00] - 90 BHKW2|Piece_1|lambda0[2020-01-01 03:00:00] - 200 BHKW2|Piece_1|lambda1[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 04:00:00] - 12 BHKW2|Piece_0|lambda0[2020-01-01 04:00:00] - 70 BHKW2|Piece_0|lambda1[2020-01-01 04:00:00] - 90 BHKW2|Piece_1|lambda0[2020-01-01 04:00:00] - 200 BHKW2|Piece_1|lambda1[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 05:00:00] - 12 BHKW2|Piece_0|lambda0[2020-01-01 05:00:00] - 70 BHKW2|Piece_0|lambda1[2020-01-01 05:00:00] - 90 BHKW2|Piece_1|lambda0[2020-01-01 05:00:00] - 200 BHKW2|Piece_1|lambda1[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 06:00:00] - 12 BHKW2|Piece_0|lambda0[2020-01-01 06:00:00] - 70 BHKW2|Piece_0|lambda1[2020-01-01 06:00:00] - 90 BHKW2|Piece_1|lambda0[2020-01-01 06:00:00] - 200 BHKW2|Piece_1|lambda1[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 07:00:00] - 12 BHKW2|Piece_0|lambda0[2020-01-01 07:00:00] - 70 BHKW2|Piece_0|lambda1[2020-01-01 07:00:00] - 90 BHKW2|Piece_1|lambda0[2020-01-01 07:00:00] - 200 BHKW2|Piece_1|lambda1[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2(Q_fu)|flow_rate[2020-01-01 08:00:00] - 12 BHKW2|Piece_0|lambda0[2020-01-01 08:00:00] - 70 BHKW2|Piece_0|lambda1[2020-01-01 08:00:00] - 90 BHKW2|Piece_1|lambda0[2020-01-01 08:00:00] - 200 BHKW2|Piece_1|lambda1[2020-01-01 08:00:00] = -0.0
+ "BHKW2|BHKW2(Q_fu)|flow_rate|single_segment": |-
+ Constraint `BHKW2|BHKW2(Q_fu)|flow_rate|single_segment`
+ [time: 9]:
+ ------------------------------------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 00:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 00:00:00] - 1 BHKW2|on[2020-01-01 00:00:00] ≤ -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 01:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 01:00:00] - 1 BHKW2|on[2020-01-01 01:00:00] ≤ -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 02:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 02:00:00] - 1 BHKW2|on[2020-01-01 02:00:00] ≤ -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 03:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 03:00:00] - 1 BHKW2|on[2020-01-01 03:00:00] ≤ -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 04:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 04:00:00] - 1 BHKW2|on[2020-01-01 04:00:00] ≤ -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 05:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 05:00:00] - 1 BHKW2|on[2020-01-01 05:00:00] ≤ -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 06:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 06:00:00] - 1 BHKW2|on[2020-01-01 06:00:00] ≤ -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 07:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 07:00:00] - 1 BHKW2|on[2020-01-01 07:00:00] ≤ -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2|Piece_0|inside_piece[2020-01-01 08:00:00] + 1 BHKW2|Piece_1|inside_piece[2020-01-01 08:00:00] - 1 BHKW2|on[2020-01-01 08:00:00] ≤ -0.0
+ "Strom|balance": |-
+ Constraint `Strom|balance`
+ [time: 9]:
+ -------------------------------------
+ [2020-01-01 00:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 00:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 00:00:00] + 1 Strom|excess_input[2020-01-01 00:00:00] - 1 Strom|excess_output[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 01:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 01:00:00] + 1 Strom|excess_input[2020-01-01 01:00:00] - 1 Strom|excess_output[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 02:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 02:00:00] + 1 Strom|excess_input[2020-01-01 02:00:00] - 1 Strom|excess_output[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 03:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 03:00:00] + 1 Strom|excess_input[2020-01-01 03:00:00] - 1 Strom|excess_output[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 04:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 04:00:00] + 1 Strom|excess_input[2020-01-01 04:00:00] - 1 Strom|excess_output[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 05:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 05:00:00] + 1 Strom|excess_input[2020-01-01 05:00:00] - 1 Strom|excess_output[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 06:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 06:00:00] + 1 Strom|excess_input[2020-01-01 06:00:00] - 1 Strom|excess_output[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 07:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 07:00:00] + 1 Strom|excess_input[2020-01-01 07:00:00] - 1 Strom|excess_output[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 BHKW2(P_el)|flow_rate[2020-01-01 08:00:00] - 1 Einspeisung(P_el)|flow_rate[2020-01-01 08:00:00] + 1 Strom|excess_input[2020-01-01 08:00:00] - 1 Strom|excess_output[2020-01-01 08:00:00] = -0.0
+ "Strom->Penalty": |-
+ Constraint `Strom->Penalty`
+ ---------------------------
+ +1 Strom->Penalty - 1e+05 Strom|excess_input[2020-01-01 00:00:00] - 1e+05 Strom|excess_input[2020-01-01 01:00:00]... -1e+05 Strom|excess_output[2020-01-01 06:00:00] - 1e+05 Strom|excess_output[2020-01-01 07:00:00] - 1e+05 Strom|excess_output[2020-01-01 08:00:00] = -0.0
+ "Fernwärme|balance": |-
+ Constraint `Fernwärme|balance`
+ [time: 9]:
+ -----------------------------------------
+ [2020-01-01 00:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 00:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 00:00:00] + 1 BHKW2(Q_th)|flow_rate[2020-01-01 00:00:00]... -1 Speicher(Q_th_load)|flow_rate[2020-01-01 00:00:00] + 1 Fernwärme|excess_input[2020-01-01 00:00:00] - 1 Fernwärme|excess_output[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 01:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 01:00:00] + 1 BHKW2(Q_th)|flow_rate[2020-01-01 01:00:00]... -1 Speicher(Q_th_load)|flow_rate[2020-01-01 01:00:00] + 1 Fernwärme|excess_input[2020-01-01 01:00:00] - 1 Fernwärme|excess_output[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 02:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 02:00:00] + 1 BHKW2(Q_th)|flow_rate[2020-01-01 02:00:00]... -1 Speicher(Q_th_load)|flow_rate[2020-01-01 02:00:00] + 1 Fernwärme|excess_input[2020-01-01 02:00:00] - 1 Fernwärme|excess_output[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 03:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 03:00:00] + 1 BHKW2(Q_th)|flow_rate[2020-01-01 03:00:00]... -1 Speicher(Q_th_load)|flow_rate[2020-01-01 03:00:00] + 1 Fernwärme|excess_input[2020-01-01 03:00:00] - 1 Fernwärme|excess_output[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 04:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 04:00:00] + 1 BHKW2(Q_th)|flow_rate[2020-01-01 04:00:00]... -1 Speicher(Q_th_load)|flow_rate[2020-01-01 04:00:00] + 1 Fernwärme|excess_input[2020-01-01 04:00:00] - 1 Fernwärme|excess_output[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 05:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 05:00:00] + 1 BHKW2(Q_th)|flow_rate[2020-01-01 05:00:00]... -1 Speicher(Q_th_load)|flow_rate[2020-01-01 05:00:00] + 1 Fernwärme|excess_input[2020-01-01 05:00:00] - 1 Fernwärme|excess_output[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 06:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 06:00:00] + 1 BHKW2(Q_th)|flow_rate[2020-01-01 06:00:00]... -1 Speicher(Q_th_load)|flow_rate[2020-01-01 06:00:00] + 1 Fernwärme|excess_input[2020-01-01 06:00:00] - 1 Fernwärme|excess_output[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 07:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 07:00:00] + 1 BHKW2(Q_th)|flow_rate[2020-01-01 07:00:00]... -1 Speicher(Q_th_load)|flow_rate[2020-01-01 07:00:00] + 1 Fernwärme|excess_input[2020-01-01 07:00:00] - 1 Fernwärme|excess_output[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Kessel(Q_th)|flow_rate[2020-01-01 08:00:00] + 1 Speicher(Q_th_unload)|flow_rate[2020-01-01 08:00:00] + 1 BHKW2(Q_th)|flow_rate[2020-01-01 08:00:00]... -1 Speicher(Q_th_load)|flow_rate[2020-01-01 08:00:00] + 1 Fernwärme|excess_input[2020-01-01 08:00:00] - 1 Fernwärme|excess_output[2020-01-01 08:00:00] = -0.0
+ "Fernwärme->Penalty": |-
+ Constraint `Fernwärme->Penalty`
+ -------------------------------
+ +1 Fernwärme->Penalty - 1e+05 Fernwärme|excess_input[2020-01-01 00:00:00] - 1e+05 Fernwärme|excess_input[2020-01-01 01:00:00]... -1e+05 Fernwärme|excess_output[2020-01-01 06:00:00] - 1e+05 Fernwärme|excess_output[2020-01-01 07:00:00] - 1e+05 Fernwärme|excess_output[2020-01-01 08:00:00] = -0.0
+ "Gas|balance": |-
+ Constraint `Gas|balance`
+ [time: 9]:
+ -----------------------------------
+ [2020-01-01 00:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 00:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 00:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 00:00:00] + 1 Gas|excess_input[2020-01-01 00:00:00] - 1 Gas|excess_output[2020-01-01 00:00:00] = -0.0
+ [2020-01-01 01:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 01:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 01:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 01:00:00] + 1 Gas|excess_input[2020-01-01 01:00:00] - 1 Gas|excess_output[2020-01-01 01:00:00] = -0.0
+ [2020-01-01 02:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 02:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 02:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 02:00:00] + 1 Gas|excess_input[2020-01-01 02:00:00] - 1 Gas|excess_output[2020-01-01 02:00:00] = -0.0
+ [2020-01-01 03:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 03:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 03:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 03:00:00] + 1 Gas|excess_input[2020-01-01 03:00:00] - 1 Gas|excess_output[2020-01-01 03:00:00] = -0.0
+ [2020-01-01 04:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 04:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 04:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 04:00:00] + 1 Gas|excess_input[2020-01-01 04:00:00] - 1 Gas|excess_output[2020-01-01 04:00:00] = -0.0
+ [2020-01-01 05:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 05:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 05:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 05:00:00] + 1 Gas|excess_input[2020-01-01 05:00:00] - 1 Gas|excess_output[2020-01-01 05:00:00] = -0.0
+ [2020-01-01 06:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 06:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 06:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 06:00:00] + 1 Gas|excess_input[2020-01-01 06:00:00] - 1 Gas|excess_output[2020-01-01 06:00:00] = -0.0
+ [2020-01-01 07:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 07:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 07:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 07:00:00] + 1 Gas|excess_input[2020-01-01 07:00:00] - 1 Gas|excess_output[2020-01-01 07:00:00] = -0.0
+ [2020-01-01 08:00:00]: +1 Gastarif(Q_Gas)|flow_rate[2020-01-01 08:00:00] - 1 Kessel(Q_fu)|flow_rate[2020-01-01 08:00:00] - 1 BHKW2(Q_fu)|flow_rate[2020-01-01 08:00:00] + 1 Gas|excess_input[2020-01-01 08:00:00] - 1 Gas|excess_output[2020-01-01 08:00:00] = -0.0
+ "Gas->Penalty": |-
+ Constraint `Gas->Penalty`
+ -------------------------
+ +1 Gas->Penalty - 1e+05 Gas|excess_input[2020-01-01 00:00:00] - 1e+05 Gas|excess_input[2020-01-01 01:00:00]... -1e+05 Gas|excess_output[2020-01-01 06:00:00] - 1e+05 Gas|excess_output[2020-01-01 07:00:00] - 1e+05 Gas|excess_output[2020-01-01 08:00:00] = -0.0
+binaries:
+ - "Kessel(Q_fu)|on"
+ - "Kessel(Q_th)|on"
+ - "Kessel(Q_th)|off"
+ - "Kessel(Q_th)|switch|on"
+ - "Kessel(Q_th)|switch|off"
+ - "Kessel|on"
+ - "Speicher(Q_th_load)|on"
+ - "Speicher(Q_th_unload)|on"
+ - "Speicher|Piece_0|inside_piece"
+ - "Speicher|Piece_1|inside_piece"
+ - "BHKW2(Q_fu)|on"
+ - "BHKW2(P_el)|on"
+ - "BHKW2(Q_th)|on"
+ - "BHKW2|on"
+ - "BHKW2|switch|on"
+ - "BHKW2|switch|off"
+ - "BHKW2|Piece_0|inside_piece"
+ - "BHKW2|Piece_1|inside_piece"
+integers: []
+continuous:
+ - costs(periodic)
+ - costs(temporal)
+ - "costs(temporal)|per_timestep"
+ - costs
+ - CO2(periodic)
+ - CO2(temporal)
+ - "CO2(temporal)|per_timestep"
+ - CO2
+ - PE(periodic)
+ - PE(temporal)
+ - "PE(temporal)|per_timestep"
+ - PE
+ - Penalty
+ - "CO2(temporal)->costs(temporal)"
+ - "Kessel(Q_fu)|flow_rate"
+ - "Kessel(Q_fu)|on_hours_total"
+ - "Kessel(Q_fu)|total_flow_hours"
+ - "Kessel(Q_th)|flow_rate"
+ - "Kessel(Q_th)|size"
+ - "Kessel(Q_th)->costs(periodic)"
+ - "Kessel(Q_th)->PE(periodic)"
+ - "Kessel(Q_th)|on_hours_total"
+ - "Kessel(Q_th)|switch|count"
+ - "Kessel(Q_th)|consecutive_on_hours"
+ - "Kessel(Q_th)|consecutive_off_hours"
+ - "Kessel(Q_th)->costs(temporal)"
+ - "Kessel(Q_th)|total_flow_hours"
+ - "Kessel|on_hours_total"
+ - "Kessel->costs(temporal)"
+ - "Kessel->CO2(temporal)"
+ - "Wärmelast(Q_th_Last)|flow_rate"
+ - "Wärmelast(Q_th_Last)|total_flow_hours"
+ - "Gastarif(Q_Gas)|flow_rate"
+ - "Gastarif(Q_Gas)|total_flow_hours"
+ - "Gastarif(Q_Gas)->costs(temporal)"
+ - "Gastarif(Q_Gas)->CO2(temporal)"
+ - "Einspeisung(P_el)|flow_rate"
+ - "Einspeisung(P_el)|total_flow_hours"
+ - "Einspeisung(P_el)->costs(temporal)"
+ - "Speicher(Q_th_load)|flow_rate"
+ - "Speicher(Q_th_load)|on_hours_total"
+ - "Speicher(Q_th_load)|total_flow_hours"
+ - "Speicher(Q_th_unload)|flow_rate"
+ - "Speicher(Q_th_unload)|on_hours_total"
+ - "Speicher(Q_th_unload)|total_flow_hours"
+ - "Speicher|charge_state"
+ - "Speicher|netto_discharge"
+ - "Speicher|size"
+ - "Speicher|PiecewiseEffects|costs"
+ - "Speicher|PiecewiseEffects|PE"
+ - "Speicher|Piece_0|lambda0"
+ - "Speicher|Piece_0|lambda1"
+ - "Speicher|Piece_1|lambda0"
+ - "Speicher|Piece_1|lambda1"
+ - "Speicher->costs(periodic)"
+ - "Speicher->PE(periodic)"
+ - "BHKW2(Q_fu)|flow_rate"
+ - "BHKW2(Q_fu)|on_hours_total"
+ - "BHKW2(Q_fu)|total_flow_hours"
+ - "BHKW2(P_el)|flow_rate"
+ - "BHKW2(P_el)|on_hours_total"
+ - "BHKW2(P_el)|total_flow_hours"
+ - "BHKW2(Q_th)|flow_rate"
+ - "BHKW2(Q_th)|on_hours_total"
+ - "BHKW2(Q_th)|total_flow_hours"
+ - "BHKW2|on_hours_total"
+ - "BHKW2->costs(temporal)"
+ - "BHKW2|Piece_0|lambda0"
+ - "BHKW2|Piece_0|lambda1"
+ - "BHKW2|Piece_1|lambda0"
+ - "BHKW2|Piece_1|lambda1"
+ - "Strom|excess_input"
+ - "Strom|excess_output"
+ - "Strom->Penalty"
+ - "Fernwärme|excess_input"
+ - "Fernwärme|excess_output"
+ - "Fernwärme->Penalty"
+ - "Gas|excess_input"
+ - "Gas|excess_output"
+ - "Gas->Penalty"
+infeasible_constraints: ''
diff --git a/tests/ressources/v4-api/02_complex--solution.nc4 b/tests/ressources/v4-api/02_complex--solution.nc4
new file mode 100644
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