Balancing social utility with aggregator profit in electric vehicle charging

In this paper, we study the efficiency of equilibrium charging schedules of self-interested plug-in electric vehicles (PEVs) in an environment where a monopolistic aggregator sets time-dependent prices to maximize its own profit. Computing profit-maximizing prices is not only NP-hard, they can also lead to bad equilibrium charging schedules. In this work, we present a polynomially computable pricing policy that is efficient both in terms of social welfare (economic efficiency of the charging schedules) and seller profit (profit made the aggregator). We show that the economic efficiency and aggregator profit under the proposed pricing scheme (with respect to their maximum possible values) can be expressed in terms of a regularity (convexity) measure of the utility functions associated with the PEVs. Our numerical studies show that in practice these performance measures are within a small constant factor of the corresponding optimum values. Our pricing policy, which is time-dependent but non-discriminatory across users for any given time-slot, can thus be used to provide a good balance between system and aggregator objectives in PEV charging.