A Novel Mean Field Game-Based Strategy for Charging Electric Vehicles in Solar Powered Parking Lots

We develop a strategy, with concepts from Mean Field Games (MFG), to coordinate the charging of a large population of battery electric vehicles (BEVs) in a parking lot powered by solar energy and managed by an aggregator. A yearly parking fee is charged for each BEV irrespective of the amount of energy extracted. The goal is to share the energy available so as to minimize the standard deviation (STD) of the state of charge (SOC) of batteries when the BEVs are leaving the parking lot, while maintaining some fairness and decentralization criteria. The MFG charging laws correspond to the Nash equilibrium induced by quadratic cost functions based on an inverse Nash equilibrium concept and designed to favor the batteries with the lower SOCs upon arrival. While the MFG charging laws are strictly decentralized, they guarantee that a mean of instantaneous charging powers to the BEVs follows a trajectory based on the solar energy forecast for the day. That day ahead forecast is broadcasted to the BEVs which then gauge the necessary SOC upon leaving their home. We illustrate the advantages of the MFG strategy for the case of a typical sunny day and a typical cloudy day when compared to more straightforward strategies: first come first full/serve and equal sharing. The behavior of the charging strategies is contrasted under conditions of random arrivals and random departures of the BEVs in the parking lot