Mean Field Game-based Decentralized Optimal Charging Control for large-scale of electric Vehicles

Abstract

In this paper, the online decentralized optimal charging control problem for large-scale electric vehicles is investigated. Massive concurrent charging, which often happens for the electric buses in a smart city, is devastating to the power grid's supply capacity due to the instant high load demand. Traditional strategies rely on a centralized dispatch center which suffers from the rising computational complexity and the data communication burden when the bus number is huge. In the novel design, a decentralized optimal charging control strategy is developed to tackle these challenges. By engaging the emerging Mean Field Games (MFG) theory with a novel Actor-Critic-Mass (ACM) reinforcement learning scheme, a probability density function (PDF) of the massive state of charge (SOC) is used to encode all electric vehicles’ charging demand information into a fix-dimension function. Moreover, the optimal charging control and the PDF of massive SOC can be solved through the coupled Fokker-Planck-Kolmogorov (FPK) and Hamilton-Jacobi-Bellman (HJB) equations in a decentralized manner. Eventually, the effectiveness of the proposed scheme is validated through a series of numerical simulations.