Price Coordination for Electric Vehicle Fleet Using Mean Field Game Theory

This paper proposes an advanced approach to control and coordinate a large number of electric vehicles to optimize their charging and discharging strategies using mean field game theory. Due to high-dimensional complexity, studying a system with a swarm of agents is computationally expensive. Therefore, the system can be structured as a game using mean field game theory to handle this complexity. Mean field game facilitates the interactions between players by considering the collective behavior of all agents. The finite difference method integrated with Bayesian optimization is utilized to solve the mean field game system, which consists of coupled Hamilton-Jacobi-Bellman and Kolmogorov forward equations. Those formulas guide electric vehicle owners' decisions to avoid penalties. This paper aims to determine the optimal parameters that enhance the numerical stability and accuracy of the finite difference method. Then, these parameters are utilized to solve the system of mean field game to control the actions of electric vehicle owners and analyze the impact of the estimated mass function of the entire population on their decision-making process. In addition, the reliability is evaluated to assess the effectiveness of price coordination in enhancing energy management. Comprehensive economic analyses for a fleet of electric vehicles are also conducted through a numerical example to validate the efficiency of the proposed method.