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Due to an ever-increasing market penetration of plug-in hybrid electric vehicles (PHEVs), the charging demand is expected to become a main determinant of the load in future distribution systems. In this paper, we investigate the problem of controlling in-home charging of PHEVs to accomplish peak load shifting while maximizing the revenue of the distribution service provider (DSP) and PHEV owners. A leader-follower game model is proposed to characterize the preference and revenue expectation of PHEV owners and DSP, respectively. The follower (PHEV owner) decides when to start charging based on the pricing schedule provided by the leader (DSP). The DSP can incentivize the charging of PHEV owners to avoid system peak load. The costs associated with power distribution, line loss, and voltage regulation are incorporated in the game model via power flow analysis. Based on a linear approximation of the power flow equations, the solution of sub-game perfect Nash equilibrium (SPNE) is obtained. A case study is performed based on the IEEE 13-bus test feeder and realistic PHEV charging statistics, and the results demonstrate that our proposed PHEV charging control scheme can significantly improve the power quality in distribution systems by reducing the peak load and voltage fluctuations

Game-theoretic control of PHEV charging with power flow analysis