A Mean Field Game Theoretic Approach to Electric Vehicles Charging

Electric vehicles (EVs) provide environmentally friendly transport and they are considered to be an important component of distributed and mobile electric energy storage and supply system. It is possible that EVs can be used to store and transport energy from one geographical area to another as a supportive energy supply. Electricity consumption management should consider carefully the inclusion of EVs. One critical challenge in the consumption management for EVs is the optimization of battery charging. This paper provides a dynamic game theoretic optimization framework to formulate the optimal charging problem. The optimization considers a charging scenario where a large number of EVs charge simultaneously during a flexible period of time. Based on stochastic mean field game theory, the optimization will provide an optimal charging strategy for the EVs to proactively control their charging speed in order to minimize the cost of charging. Numerical results are presented to demonstrate the performance of the proposed framework.