Examples

The examples below demonstrate PyPSA's capabilities for energy system modeling. They cover a broad range of topics, including electricity markets, linear optimal power flow, unit commitment, capacity expansion, grid modelling, and more.

Operational Problems

• Electricity Market

  Demonstrates basic electricity market modeling with with multiple bidding zones, renewables and storage.

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• Demand and Supply Bids

  Demonstrates market-clearing with supply and demand bids in single and two-zone configurations.

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• Unit Commitment

  Models generator unit commitment with start-up and shut-down costs, ramping limits, minimum part loads, up and down times using binary variables.

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• Negative Prices in Linearized UC

  Shows how negative electricity prices emerge from linearized unit commitment constraints due to the trade-off between cycling costs and operating at minimum load.

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• Meshed AC-DC Networks

  Builds a stylized 3-node AC network coupled via AC-DC converters to a 3-node DC network.

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• SciGRID Network

  Performs linear optimal power flow on a high-resolution German grid model to analyze power flows and nodal prices.

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• Security-Constrained LOPF

  Implements N-1 security constraints in linear optimal power flow models to ensure grid reliability under line outage events.

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• Newton-Raphson Power Flow

  Solves non-linear AC power flow equations using the Newton-Raphson method to inspect voltage magnitudes and angles.

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• Negative LMPs from Line Congestion

  Explores how Kirchhoff's Voltage Law can lead to negative locational marginal prices when lines are congested.

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• Rolling-Horizon Optimization

  Explores how rolling-horizon optimization can be used to account for imperfect forecast horizons in reality.

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• Water Values

  Explores how water values, the marginal values of stored energy, can improve seasonal storage operation in rolling-horizon optimization.

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Planning Problems

• Single-Node Capacity Expansion

  Models investment decisions for generation and storage in a single-node system in the style of model.energy.

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• Three-Node Capacity Expansion

  Co-optimizes generation, storage and transmission investments in a stylized three-node network in Australia .

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• Pathway Planning

  Optimizes investment decisions across multiple investment periods for a long-term transition pathway with perfect foresight.

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• Myopic Pathway Planning

  Optimizes investment decisions across multiple investment periods for a long-term transition pathway with myopic foresight.

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• Stochastic Optimization

  Demonstrates investment planning under uncertainty with scenario-based two-stage stochastic optimization.

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• Modelling-to-Generate Alternatives

  Explores near-optimal solution diversity by generating alternative system designs with similar costs.

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• Exploring Near-Optimal Spaces

  Explores near-optimal space to understand flexibility in investment decisions while maintaining cost-effectiveness.

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• Modular Capacity Expansion

  Models discrete capacity additions with integer constraints on investment decisions considering predefined unit sizes.

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• Committable and Extendable Components

  Co-optimize capacity expansion and unit commitment using big-M linearization. Demonstrates continuous capacity decisions with start-up/shut-down costs, ramp limits, and minimum load constraints.

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• Modular and Committable Components

  Model discrete capacity blocks with unit commitment where status represents the number of committed modules. Shows modular gas turbines, HVDC links, and multi-module operational dynamics.

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Special Problems

• Redispatch

  Sketches how redispatch can be modelled by separating market clearing and congestion management.

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• Demand Elasticity

  Demonstrates modelling of price-responsive electricity demands and how they affect price formation.

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• Imperfect Competition

  Models oligopolistic behavior in energy markets using Cournot-Nash equilibrium with the fictitious objective approach, avoiding KKT conditions.

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• Screening Curves

  Determines optimal generation capacity mix based on screening curves.

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• Chained Hydro Reservoirs

  Models cascaded hydropower systems with water flow constraints between reservoirs.

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• Transformers

  Shows how transformers can be considered with varying tap ratios and phase shifts.

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• Reserve Constraints

  Implements operating reserve requirements in power system optimization.

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• Link Delay

  Demonstrates time-delayed energy transport through links, modeling pipeline or shipping delays with cyclic and non-cyclic boundary behavior.

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Sector Coupling

• Single-Node Sector-Coupling

  Extends the 1-node capacity expansion example with hydrogen, heat and transport demand.

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• Islanded Methanol Production

  Optimizes islanded renewable methanol production systems in Namibia or Argentina .

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• Electric Vehicles

  Demonstrates how to model flexible electric vehicle charging and discharging.

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• Backpressure CHPs

  Models combined heat and power plants with fixed heat-to-power ratios.

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• Extraction-Condensing CHPs

  Models combined heat and power plants with variable heat-to-power ratios.

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• Heat Pumps and Thermal Storage

  Models sector coupling with heat pumps and thermal energy storage.

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• Carbon Management

  Models carbon flows between atmosphere, biomass, and synthetic fuels.

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Complexity Management

• Time Series Aggregation

  Shows how model complexity can be reduced by aggregating snapshots.

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• Global Sensitivity Analysis

  Combines PyPSA with SALib's Sobol indices to understand how technology cost uncertainties affect optimal system design and total costs.

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• Storage Units as Links & Stores

  Shows how storage units can be replaced by more fundamental links and stores.

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• Tracing Infeasibilities

  Shows how to trace infeasibilities in the optimization problem using Irreducible Infeasible Subsets (IIS).

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