With the rapid growth in the demand for plug-in electric vehicles (EVs), the corresponding charging infrastructures are expanding. These charging stations are located at various places and with different congestion levels. EV drivers face an important decision in choosing which charging station to go to in order to reduce their overall time costs. However, existing literature either assumes a flat charging rate and hence overlooks the physical characteristics of an EV battery where charging rate is typically reduced as the battery charges, or ignores the effect of other drivers on an EV's decision making process. In this paper, we consider both the predetermined exogenous wait cost and the endogenous congestion induced by other drivers' strategic decisions, and propose a differential equation based approach to find the optimal strategies. We analytically characterize the equilibrium strategies and find that co-located EVs may make different decisions depending on the charging rate and/or remaining battery levels. Through numerical experiments, we investigate the impact of charging rate characteristics, modeling parameters and the consideration of endogenous congestion levels on the optimal charging decisions. Finally, we conduct numerical studies on real-world data and find that some EV users with slower charging rates may benefit from the participation of fast-charging EVs.

翻译：随着插电式电动汽车需求的快速增长，相应的充电基础设施也在不断扩展。这些充电站分布于不同地点且拥堵程度各异。电动汽车驾驶员面临着一个重要决策——选择前往哪个充电站以降低总体时间成本。然而，现有文献要么假设恒定充电速率而忽略电动汽车电池的物理特性（随着电池充电量增加，充电速率通常会降低），要么忽略其他驾驶员对电动汽车决策过程的影响。本文同时考虑了预设的外生等待成本及其他驾驶员策略性决策所引发的内生拥堵，提出一种基于微分方程的方法来求解最优策略。我们通过解析方法刻画了均衡策略，发现同区域电动汽车可能因充电速率和/或剩余电量水平不同而做出差异化决策。通过数值实验，我们探究了充电速率特性、建模参数及内生拥堵水平对最优充电决策的影响。最后，基于真实数据开展数值研究，发现部分充电速率较慢的电动汽车用户可能从快速充电电动汽车的参与中获益。