The rapid growth of electric vehicles (EVs) is driving the expansion of charging infrastructure globally. This expansion, however, places significant charging demand on the electricity grid, impacting grid operations and electricity pricing. While coordination among all charging stations is beneficial, it may not be always feasible. However, a subset of charging stations, which could be jointly operated by a company, could coordinate to decide their charging profile. In this paper we investigate whether such coalitions between charging stations is better than no coordination. We model EV charging as a non-cooperative aggregative game, where each station's cost is determined by both monetary payments tied to reactive electricity prices on the grid and its sensitivity to deviations from a nominal charging profile. We consider a solution concept that we call $\mathcal{C}$-Nash equilibrium, which is tied to a coalition $\mathcal{C}$ of charging stations coordinating to reduce their cumulative costs. We provide sufficient conditions, in terms of the demand and sensitivity of charging stations, to determine when independent (uncoordinated) operation of charging stations could result in lower overall costs to charging stations, the coalition, and charging stations outside the coalition. Somewhat counter to intuition, we demonstrate scenarios where allowing charging stations to operate independently is better than coordinating as a coalition. Jointly, these results provide operators of charging stations insights into how to coordinate their charging behavior, and open several research directions.

翻译：电动汽车（EV）的快速增长正推动全球充电基础设施的扩张。然而，这种扩张给电网带来了显著的充电需求，影响了电网运行和电价制定。尽管所有充电站之间的协调是有益的，但可能并不总是可行的。然而，由一家公司共同运营的充电站子集可以协调决定其充电曲线。本文研究充电站之间的这种联盟是否优于无协调情况。我们将电动汽车充电建模为非合作聚合博弈，其中每个充电站的成本由与电网响应性电价相关的货币支付以及其对标称充电曲线偏差的敏感度共同决定。我们考虑一种称为$\mathcal{C}$-纳什均衡的解概念，该均衡与协调以降低累计成本的充电站联盟$\mathcal{C}$相关联。我们根据充电站的需求和敏感度提供充分条件，以确定何时充电站的独立（非协调）运营能够为充电站、联盟以及联盟外的充电站带来更低的总体成本。与直觉稍显相悖的是，我们展示了允许充电站独立运营优于作为联盟进行协调的场景。综合来看，这些结果为充电站运营商提供了关于如何协调其充电行为的见解，并开辟了多个研究方向。