Coordination of Plug-In Electric Vehicle Charging in a Stochastic Framework: A Decentralized Tax/Incentive-Based Mechanism to Reach Global Optimality

Abstract

We address the problem of charging plug-in electric vehicles (PEVs) in a decentralized way and under stochastic dynamics affecting the real-time electricity tariff. The model is formulated as a Nash equilibrium seeking problem, where players wish to minimize the costs for charging their own PEVs. For finite PEVs populations, the Nash equilibrium does not correspond to the social optimum, i.e., to a control strategy minimizing the total electricity costs at the aggregate level. We accordingly introduce some taxes/incentives on the price of electricity for charging PEVs and show that it is possible to tune them so that (a) the social optimum is reached as a Nash equilibrium, (b) in correspondence with this equilibrium, players do not pay any net total tax, nor receive any net total incentive.