A Stackelberg-based competition model for optimal participation of electric vehicle load aggregators in demand response programs

Plug-in electric vehicles are considered a flexible resource to participate in demand response programs via electric vehicle load aggregators. In practice, the aggregator often faces competition from other independent aggregators when the number of aggregated electric vehicles is limited. In this paper, a multi-leader multi-follower Stackelberg game is formulated to investigate the interactive behaviors between multiple aggregators and massive electric vehicles. In the game, aggregators act as leaders, setting the incentive price to aggregate demand response resources from electric vehicles for payoff maximization. Electric vehicle users act as followers, reducing the charging loads to achieve welfare maximization based on the aggregators' incentives. It is demonstrated that a unique Nash equilibrium solution always exists among multiple aggregators by utilizing the potential game. Moreover, for an exact potential game, the equilibrium solution is equivalent to maximizing the potential function of the game on its strategy set. The probabilistic models are adopted to capture a range of possible charging scenarios to address the charging uncertainty of electric vehicles. The proposed approach is assessed through simulation experiments and the numerical results indicate that aggregators can achieve total profit maximization by adopting the proposed equilibrium strategy. In addition, the factors affecting the Nash equilibrium, e.g., the expected demand response capacity of aggregators, and the available demand response capacity from electric vehicles, are also examined.