Customized Mean Field Game Method of Virtual Power Plant for Real-Time Peak Regulation

This paper proposes a customized incentive compatible mean field game (MFG) method for virtual power plant (VPP) with a large number of self-interest heterogeneous distributed energy resources (DERs) to participate in the real-time peak regulation. Firstly, an optimal chance-constrained peak-regulation bidding model of VPP considering the stochastic power flexibility is formulated, where inscribed pyramid approximation method is utilized to form a compact and concise dispatch region. Secondly, a customized MFG method with dynamic granulation division is proposed for encouraging very large-scale DERs to spontaneously respond to the peak regulation instructions from VPP while achieving dynamic allocation of peak-regulation revenue. Brouwer fixed-point theorem and contraction mapping theorem are used to prove the existence and uniqueness of the mean field equilibrium (MFE) of the formulated MFG, and ϵ-Nash property of MFE is validated based on the Lipschitz continuity condition. Furthermore, an accelerated decentralized solution algorithm is developed to rapidly search MFE, exhibiting good scalability. Comparative studies have validated the superiority of the proposed methodology on incentive compatibility and decomposition efficiency of the VPP's peak-regulation instructions.