Optimal Scheduling of Virtual Power Plants Considering Willingness to Respond: A Stackelberg Game Approach

Abstract

With the global low-carbon transition and increasing wind and photovoltaic penetration, virtual power plant (VPP) scheduling increasingly requires coordinated low-carbon operation, resource management, and long-term stability. Existing studies often treat demand response (DR) resources as passive adjustable capacity, but insufficiently consider how satisfaction variation, fatigue accumulation, and scheduling experience under continuous dispatch feed back into subsequent response behavior. Meanwhile, the coordination among electricity, gas, carbon, and green certificate markets and market incentives reflecting the low-carbon value of power-to-gas (P2G) remain underexplored. To address these issues, this paper introduces a response-willingness feedback mechanism that feeds the satisfaction and fatigue accumulation of the demand response aggregator (DRA) back into subsequent deliverable DR capacity and scheduling behavior. A virtual power plant operator (VPPO)–DRA bi-level optimal scheduling model is then formulated under a Carbon–Green Certificate Coordinated P2G Incentive Mechanism, characterizing the Stackelberg interaction between the VPPO and the DRA. A hierarchical solution framework integrating CMA-ES, dynamic programming, and Gurobi is developed. Deterministic comparisons showed that the model maintained VPP profitability while improving DR sustainability and renewable accommodation. Under ex post stress testing, the fixed nominal day-ahead VPPO strategy maintained feasibility in all 200 cases and positive VPP profit in 94.0%.