A Mean-Field Game Method for Decentralized Charging Coordination of a Large Population of Plug-in Electric Vehicles

Abstract

This paper develops a decentralized competitive charging coordination algorithm for a large population of plug-in electric vehicles (PEVs) using the concept of a mean-field (MF) game. The aim of each PEV is to find its optimal charging strategy by minimizing an objective function consisting of charging cost, battery degradation cost, and benefit from charging, subject to the input and state constraints. The strategy of a PEV affects the objective functions of other PEVs through the electricity price, and therefore, we can model the interactions among PEVs as a game problem. No information exchange is considered among the PEVs. Each PEV only sends its own control action value to a population coordinator, and the coordinator just broadcasts a common signal to all the PEVs. This common signal is an estimate of the average control actions of PEVs and is called the MF term. Utilizing an adjustment mechanism for the MF term, a decentralized MF-optimal control algorithm is proposed, and it is shown that the algorithm converges to the ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> -Nash equilibrium point of the game, with ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> uniformly converging to zero as the population sizes of the PEVs go to infinity. Simulation results and comparison with other methods are performed to clarify the advantages of the proposed method.