Efficient Multi-Market Scheduling of Virtual Power Plants via Spectral Representation of Uncertainty

TL;DR

This paper introduces a spectral uncertainty representation for multi-market virtual power plant scheduling, significantly reducing computational effort while maintaining decision accuracy.

Contribution

It proposes an intrusive Polynomial Chaos Expansion-based spectral framework that efficiently reformulates stochastic VPP scheduling problems, outperforming traditional scenario-based methods.

Findings

Spectral approach achieves up to 137 times reduction in computational effort.

Solution quality comparable to scenario-based benchmarks.

Open-source tool for spectral reformulation of stochastic programs.

Abstract

As the penetration of distributed energy resources increases, harnessing their flexibility becomes critical for power system operations. Virtual power plants (VPPs) offer a promising solution. However, existing VPP market scheduling tools exhibit a tradeoff between economic performance and tractability. Stochastic formulations provide probabilistically optimal decisions but are computationally intractable for large systems due to scenario explosion. Robust approaches are more tractable but often yield conservative decisions. This paper addresses this gap by proposing a stochastic multi-market VPP scheduling framework that represents uncertainty in the spectral domain via intrusive Polynomial Chaos Expansion (PCE). The resulting reformulation yields a low-dimensional deterministic spectral counterpart that preserves the stochastic structure and can be solved efficiently with standard optimization tools. The proposed spectral approach is demonstrated on a DER-based VPP operating on a realistic Swiss low-voltage grid and benchmarked against a state-of-the-art scenario-based solution. Results show that intrusive PCE achieves solution quality comparable to the scenario-based benchmark, with up to a 137 times reduction in computational effort, while yielding highly accurate bidding decisions. Finally, to facilitate adoption and reproducibility, we release an open-source, application-agnostic projection tool that automates the spectral reformulation for generic single- and two-stage stochastic programs.