A mean field game analysis of electric vehicles in the smart grid

In this article, we present an economical analysis of the integration of purely electrical vehicles (EV) in the smart grid energy market using tools from mean field game theory. Our main contribution consist in a formal description of the mean field equilibrium of the resulting competitive interaction when EV owners buy and sell electricity from their cars, selfishly but rationally, based on collective price incentives. We present a comprehensive set of numerical results, which allows a consistent analysis of the evolution of the price of electricity, of the timely demand, and possibly of the energy reserves in the grid.