Lorenzo Zapparoli

Lorenzo Zapparoli, Blazhe Gjorgiev, Giovanni Sansavini

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.

Lorenzo Zapparoli, Paul Fäth, Blazhe Gjorgiev et al.

As the penetration of distributed energy resources (DERs) increases, harnessing their flexibility becomes critical for power system operations. Virtual power plants (VPPs) offer a promising solution. However, most existing scheduling tools rely on simplified DER or grid models and largely overlook local flexibility procurement mechanisms such as dynamic network tariffs. This paper proposes a two-stage stochastic optimization framework for VPP multi-market scheduling that integrates detailed device-level constraints, network limitations, and operational and market uncertainties. Conditional value-at-risk is incorporated to represent risk preferences, and Benders decomposition ensures tractability with extensive scenario sets. The model jointly optimizes bidding across energy and reserve markets while explicitly accounting for local flexibility procurement through dynamic network tariffs. The results from a realistic case study show that both risk-neutral and risk-averse strategies exploit arbitrage opportunities. However, risk aversion reduces profit volatility through closer alignment with physical dispatch. Dynamic tariffs unlock local flexibility by shifting demand across the day, though strong tariff signals reduce expected profitability by up to 65% with limited additional flexibility gains.