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Plug-in hybrid electric vehicles (PHEVs) will be widely used in future transportation systems to reduce oil fuel consumption. Therefore, the electrical energy demand will be increased due to the charging of a large number of vehicles. Without intelligent control strategies, the charging process can easily overload the electricity grid at peak hours. In this paper, we consider a smart charging and discharging process for multiple PHEVs in a building’s garage to optimize the energy consumption profile of the building. We formulate a centralized optimization problem in which the building controller or planner aims to minimize the square Euclidean distance between the instantaneous energy demand and the average demand of the building by controlling the charging and discharging schedules of PHEVs (or ’users’). The PHEVs’ batteries will be charged during low-demand periods and discharged during high-demand periods in order to reduce the peak load of the building. In a decentralized system, we design an energy costsharing model and apply a non-cooperative approach to formulate an energy charging and discharging scheduling game, in which the players are the users, their strategies are the battery charging and discharging schedules, and the utility function of each user is de-fined as the negative total energy payment to the building. Based on the game theory setup, we also propose a distributed algorithm in which each PHEV independently selects its best strategy to maximize the utility function. The PHEVs update the building planner with their energy charging and discharging schedules. We also show that the PHEV owners will have an incentive to participate in the energy charging and discharging game. Simulation results verify that the proposed distributed algorithm will minimize the peak load and the total energy cost simultaneously.
