Fast Convergence in Electric Vehicle Smart Charging

Abstract

We address the problem to control the charging schedules in a large population of plug-in electric vehicles, considered as heterogeneous noncooperative agents, with different strongly convex cost functions weakly coupled by a common pricing signal, convex charging constraints, e.g. plug-in times, deadlines and capacity limits. We assume a minimal information structure through which a central control unit can broadcast incentive signals to coordinate the decentralized optimal responses of the agents. We propose a dynamic control that, based on fixed-point operator theory, ensures global exponential convergence to an aggregative equilibrium, independently on the population size. We illustrate the benefits of the proposed control via numerical simulations, in scenarios where the aggregate charging demand tends to fill the overnight demand valley. Finally, we touch upon the a generalized setup with convex, separable, joint constraints, e.g. transmission line constraints and shared network resources.