EV Charging in Smart Grids: Mean Field Equilibrium and Approximate Non-Cooperative and Cooperative Strategies

We study the optimal charging strategies for large-scale electric vehicles in smart grids within a finite-horizon mean field game framework. We first establish the existence and uniqueness of the solution to the consistency condition equation, which characterizes the optimal charging behavior in the mean field limit. Building on this result, we construct approximate optimal charging strategies for a finite population of vehicles in both non-cooperative and cooperative settings. Finally, we provide numerical analyses that illustrate and compare the approximate strategies in the non-cooperative and cooperative games.