Nonlinear pricing for social optimality of PEV charging under uncertain user preferences

In this paper, we analyze a framework of charging Plug-in Electric Vehicles (PEVs) where the electric utility (or aggregator) sets time-dependent prices for charging, and the PEVs choose their charging profiles so as to minimize their individual charging costs (maximize individual profits). We show that there exists pricing policies that results in social optimality (i.e., minimize the network-wide charging cost, or maximize the total economic surplus) under individually rational (selfish) decision-making by the PEVs. The pricing policy is non-linear and can differ across PEVs, and takes into account the uncertainty in the user (PEV-owner) charging preferences which are in general not known to the utility, but can possibly be stochastically estimated (predicted) through observations over time. We evaluate the proposed pricing policy through simulations, in terms of the mean and variance of the total electric load on a sample distribution network.