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

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

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We address the problem of charging plug-in electric vehicles (PEVs) in a decentralized way and under stochastic dynamics affecting the Twin Mattress 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 5 STAGE FILTER equilibrium, players do not pay any net total tax, nor receive any net total incentive.