Mean Field Game-Based Algorithms for Charging in Solar-Powered Parking Lots and Discharging into Homes a Large Population of Heterogeneous Electric Vehicles

An optimal daily scheme is presented to coordinate a large population of heterogeneous battery electric vehicles when charging in daytime work solar-powered parking lots and discharging into homes during evening peak-demand hours. First, we develop a grid-to-vehicle strategy to share the solar energy available in a parking lot between vehicles where the statistics of their arrival states of charge are dictated by an aggregator. Then, we develop a vehicle-to-grid strategy so that vehicle owners with a satisfactory level of energy in their batteries could help to decongest the grid when they return by providing backup power to their homes at an aggregate level per vehicle based on a duration proposed by an aggregator. Both strategies, with concepts from Mean Field Games, would be implemented to reduce the standard deviation in the states of charge of batteries at the end of charging/discharging vehicles while maintaining some fairness and decentralization criteria. Realistic numerical results, based on deterministic data while considering the physical constraints of vehicle batteries, show, first, in the case of charging in a parking lot, a strong to slight decrease in the standard deviation in the states of charge at the end, respectively, for the sunniest day, an average day, and the cloudiest day; then, in the case of discharging into the grid, over three days, we observe at the end the same strong decrease in the standard deviation in the states of charge.