The widespread adoption of renewable energy generation and diversified end-user equipment has significantly enhanced user benefits, attracting sustained attention from the research community. As energy systems become increasingly decentralized, traditional centralized optimization methods struggle to effectively capture the interactions among multiple agents. Achieving efficient interaction between diversified energy devices and load demands has emerged as a key challenge in current research. This study first outlines the system operation architecture and the involved game-theoretic agents, clarifying the roles of all participating entities. Subsequently, optimization models are established for the Virtual Power Plant (VPP) and the user aggregator, respectively, incorporating an integrated electro-thermal demand response mechanism under multi-device scenarios. By analyzing the Stackelberg game between the VPP and end-users, the existence of a unique equilibrium solution for this game is demonstrated. Simulations are conducted on the MATLAB R2021b platform using the YALMIP 20210331 toolbox and the CPLEX solver, with heuristic algorithms applied to further optimize the results. The proposed model effectively balances the interests of both parties while maintaining robust privacy protection for critical data.
Wang et al. (2026) studied this question.