Optimizing Demand Response in Virtual Power Plants: A Two-Stage Game-Programming Model

As an emerging intermediary between the supply and demand sides, virtual power plants (VPPs) aggregate and dispatch distributed resources such as energy storage systems and electric vehicles (EVs), facilitating efficient and flexible energy engineering management. Demand response (DR) is an effective means for demand-side management in VPPs. To further optimize the DR strategy, this study introduced a two stage game-programming model for the VPP that considers multiple uncertainties. In the day-ahead stage, the Stackelberg game is used to model hierarchical interactions among the main grid, the VPP operator, and end users. We proposed an integrated DR strategy combining both real-time pricing and dynamic subsidy at this stage. In the intra-day stage, a nonlinear programming method is applied to optimize the charging and discharging of energy storage systems, compensating for deviations between predicted and actual photovoltaic generation. We investigated demand response behaviors across users with differentiated electricity consumption preferences, considering the key role of EVs with vehicle-to-grid (V2G) capabilities in the VPP. To ensure research rigor, this study conducts a case study based on real-world data and validates the robustness of findings through multi-scenario comparisons and sensitivity analyses. Simulation results show that: (i) the introduction of the Vehicle to-Grid business model into the VPP can improve overall stakeholder benefits by 7.6%; (ii) to maximize customers' DR potential, incentive strategies should vary depending on their utility sensitivity and price sensitivity; and (iii) the proposed integrated DR strategy can simultaneously improve VPP operational economics, enhance user satisfaction, and strengthen grid stability.