This paper presents the equilibrium analysis of a game composed of heterogeneous electric vehicles (EVs) and a power distribution system operator (DSO) as the players, and charging station operators (CSOs) and a transportation network operator (TNO) as coordinators. Each EV tries to pick a charging station as its destination and a route to get there at the same time. However, the traffic and electrical load congestion on the roads and charging stations lead to the interdependencies between the optimal decisions of EVs. CSOs and the TNO need to apply some tolling to control such congestion. On the other hand, the pricing at charging stations depends on real-time distributional locational marginal pricing, which is determined by the DSO after solving the optimal power flow over the power distribution network. This paper also takes into account the local and the coupling/infrastructure constraints of EVs, transportation and distribution networks. This problem is modeled as a generalized aggregative game, and then a decentralized learning method is proposed to obtain an equilibrium point of the game, which is known as variational generalized Wardrop equilibrium. The existence of such an equilibrium point and the convergence of the proposed algorithm to it are proven. We undertake numerical studies on the Savannah city model and the IEEE 33-bus distribution network and investigate the impact of various characteristics on demand and prices.

翻译：本文针对由异构电动汽车（EV）与电力配电系统运营商（DSO）作为博弈参与者，充电站运营商（CSO）与交通网络运营商（TNO）作为协调者的博弈问题展开均衡分析。每辆电动汽车需同时选择目标充电站及其行驶路径。然而，交通拥堵与充电站电气负荷过载导致电动汽车最优决策间存在相互依存关系。CSO与TNO需通过收费机制管控此类拥堵状况。另一方面，充电站定价基于实时配电网边际电价，该电价由DSO在求解配电网络最优潮流后确定。本文同时考虑了电动汽车、交通网络与配电网络的本地约束及耦合/基础设施限制。该问题被建模为广义聚合博弈，进而提出一种分散式学习方法以获取博弈均衡点——即变分广义Wardrop均衡。本文证明了该均衡点的存在性及所提算法的收敛性。通过在萨凡纳城市模型与IEEE 33节点配电系统上的数值研究，我们分析了不同特征参数对需求与价格的影响。