Scalable co-optimization of virtual power plants in frequency regulation markets: Integrating stochastic bidding and mean field games

The paper proposes a multi-objective optimization strategy for an aggregator of a Virtual Power Plant (VPP) which aggregates different types of Distributed Energy Resources (DERs), such as Electric Vehicles (EVs), Photovoltaics (PVs), and Temperature-Controlled Loads (TCLs), to provide flexible bids to real-time frequency regulation markets. A two-stage stochastic optimization model is formulated for hourly bidding, incorporating chance-constrained flexibility aggregation to handle uncertainties in DER availability and forecast errors. The aggregated flexibility is represented using an inscribed pyramid approximation for computational tractability. To address the real-time dispatch challenge for large-scale fleets, a customized mean field game (MFG) is developed with dynamic granulation clustering, incentive-compatible cost functions, and coupled Hamilton-Jacobi-Bellman and Fokker-Planck equations. Theoretical guarantees are provided, including uniqueness of the mean field equilibrium via contraction mapping, ε-Nash equilibrium for incentive compatibility, and dual consistency linking bidding and dispatch stages. An accelerated online algorithm enables decentralized power allocation within stringent time constraints 4 s. Numerical simulations based on PJM RegD market data and a fleet of 360 DERs demonstrate superior profitability (lift over benchmarks), high-fidelity signal tracking, and robustness to hyperparameters.