Game Theoretic-Based Distributed Charging Strategy for PEVs in a Smart Charging Station

This article investigates the charging problem of plug-in electric vehicles (PEVs) in a smart charging station (SCS) under a new interaction mechanism that allows the interactions among PEVs. The target is to coordinate the charging strategies of all PEVs such that the energy cost of SCS is minimized without compromising a set of constraints for PEVs and SCS. To this end, we first construct a non-cooperative game framework, in which each player (i.e., PEV) expects to minimize its cost by choosing the optimal charging strategy over the entire charging horizon. Then, the existence andoptimality of Nash equilibrium (NE) for the formulated non-cooperative game is provided. Moreover, to find the unique generalized Nash equilibrium (GNE), we propose a distributed GNE-seeking algorithm based on the Newton fixed-point method. And a fast alternating direction multiplier method (fast-ADMM) framework is applied to determine the best response of PEVs. The convergence of the proposeddistributed GNE-seeking algorithm and PEVs' best response are also provided with theoretical analysis. Simulations are presented at last to validate the effectiveness of the proposed algorithm.