On the price of being selfish in large populations of plug-in electric vehicles

We consider the problem of optimally scheduling the flexible electricity demand of a fleet of plug-in electric vehicles (PEVs). More specifically, we analyze the solutions of the following charging optimization problems: a) the welfare-optimal problem, where the overall system cost is minimized; b) the fleet-optimal problem, where the charging cost of the fleet as a whole is minimized by a central agent, that is the PEV aggregator; c) the selfish-optimal problem, where the noncooperative PEVs aim at minimizing their individual charging cost. For a homogenous PEV fleet and a simplified problem setup, we show that the solutions of the three different approaches correspond to different valley-filling results. A main insight is that, as the population of PEVs grows, the selfish-optimal solution converges to the welfare-optimal solution. On the other hand, we show that the centralized fleet-optimal solution of the PEV aggregation can be recovered via decentralized selfish-optimal solutions with respect to an appropriate price signal as the population size grows. Finally, we demonstrate our technical results on a realistic PEV fleet case study.