Game Theoretic Energy Management for Electric Vehicles in Smart Grid

This paper presents a generalized Stackelberg game (GSG) for the management of electric vehicle (EV) charging activities in smart grid based on the non-cooperative game theory. On the one hand, the grid, as the leader of the game, sets the energy price to guide the charging behavior of EVs with the goal of improving its own income. On the other hand, as followers of the game, EVs weigh the benefits and costs of charging according to the energy price, and formulate reasonable charging strategies to maximize the benefits of charging. Their strategies also influence the set of energy price. Since the charging strategy of EV is related to other plays', the game between EVs is described as generalized Nash equilibrium problem (GNEP). In this paper, the existence of generalized Stackelberg equilibrium (GSE) is proved by using the theory of variational inequality (VI), and the variational equilibrium (VE) is obtained by using the projection algorithm with constant step (PACS)and the best response (BR) algorithm based on Gauss-Seidel. Finally, an EV charging example in a region is used to prove the effectiveness of the proposed model. The algorithm converges within the effective times, and the charging strategies of EVs as well as the energy price are obtained, providing a reference for EV charging management.