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 and optimality 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 proposed distributed 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.

中文翻译：

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智能充电站中基于博弈论的PEV分布式充电策略

本文研究了一种新的交互机制下允许电动汽车之间进行交互的智能充电站（SCS）中的插电式电动汽车（PEV）的充电问题。目标是协调所有PEV的充电策略，以使SCS的能源成本最小化而又不损害PEV和SCS的一组约束。为此，我们首先构建一个非合作游戏框架，其中每个玩家（即PEV）都希望通过在整个计费范围内选择最佳计费策略来最大程度地降低其成本。然后，为制定的非合作博弈提供了纳什均衡（NE）的存在性和最优性。此外，为了找到唯一的广义纳什均衡（GNE），我们提出了一种基于牛顿不动点法的分布式GNE寻找算法。并采用快速交替方向乘数法（fast-ADMM）框架来确定PEV的最佳响应。理论分析还提供了所提出的分布式GNE寻求算法的收敛性和PEV的最佳响应。最后通过仿真验证了所提算法的有效性。