Stackelberg Game Optimization Strategy of Virtual Power Plants and Electric Vehicles Based on Conditional Value-at-Risk - MA Qianxin, JIA Heping, GUO Yuchen, LI Peijun, YANG Ye, LIU Dunnan, ZHAO Zhenyu (Dianli jianshe, 2025)
[Objective] The large-scale integration of electric vehicles （EVs） presents potential flexibility and operational uncertainty in power systems. Virtual power plants （VPPs）， as efficient paradigms for aggregating distributed energy resources， offer a feasible approach for coordinating EV participation in grid operations. This study proposed a bi-level optimization strategy based on a Stackelberg game to manage the interaction between VPPs and EV users under uncertainty.[Methods] A bi-level Stackelberg game model was developed in which the VPP acts as the leader and the EV users as followers. The upper-level model maximized the VPP profit while managing EV-related uncertainties via the conditional value at risk （CVaR）. It sets risk-aware charging and discharging prices. The lower-level model minimized user costs by responding to these prices using a utility function that captures both cost satisfaction and charging experience. A particle swarm optimization algorithm was employed to solve the coupled model and identify the equilibrium strategies.[Results] A case study of a VPP system with wind， solar， storage， and 300 EVs demonstrated the effectiveness of the proposed approach. Compared to benchmark strategies， the model reduced the peak-valley load gap by up to 36.9%， lowered the average user cost by 28.79%， and enhanced profit stability under uncertainty.[Conclusions] The CVaR-based bi-level game framework effectively balances the VPP profit， EV user satisfaction， and system stability. It provides a risk-aware， market-oriented approach for flexible resource management and offers practical insights into future EV-grid integration strategies.