Mean Field Optimal Energy Management of Plug-In Hybrid Electric Vehicles

This paper addresses the problem of energy consumption management of a large population of plug-in hybrid electric vehicles (PHEVs). A PHEV can be derived either on its gasoline or the battery modes while traveling, and can be either charged from or discharged to the grid while parking at home, respectively. This feature is the main novel consideration in our system model, besides taking into account the constraints like traveling time and distance, and the bounds on the charging power and state of charge of the battery. On the basis of the proposed model of PHEV, the optimal battery-gasoline energy management strategy is obtained in order to minimize the cost of energy and battery degradation for each user. Such a strategy can also compensate the peak load. Since the strategy of each PHEV affects other users' cost through the electricity price, we model such an interaction as a game problem and we prove that there exist a unique Nash equilibrium point of the game. Then, due to the fact that the effect of a single PHEV of a large population on the other users' costs is negligible, the theory of mean filed (MF) game is utilized to develop a decentralized control strategy for PHEVs. The lightweight information exchange of the proposed MF algorithm ensures a low computational cost and communication overhead. The proof of convergence for the proposed algorithm is given and it is shown that as the number of PHEVs goes to infinity the MF optimal strategy of the players converges to the unique Nash equilibrium point of the game. In simulation results, the effectiveness of the proposed method in terms of demand side management, peak shaving, convergence rate, and robustness is studied.