Price-driven charging of Plug-in Electric Vehicles: Nash equilibrium, social optimality and best-response convergence

As the number of charging Plugged-in Electric Vehicles (PEVs) increase, it is crucial to control the charging of PEVs in order to minimize energy generation and transmission costs, and ensure grid stability. In this work, we analyze the equilibrium properties of a natural price-driven charging control game in the distribution grid, between the utility (that sets the time-dependent energy usage price) and selfish PEVs (that choose their own charging schedules to minimize individual cost). We demonstrate through analysis and simulations that individual best-response strategies converge to socially optimal charging profiles (also equilibrium solutions) under fairly weak assumptions on the (asynchronous) charging profile update processes. We also discuss how the framework can be extended to consider the topology of the distribution tree and associated transmission line capacity constraints.