We study the traffic patterns as well as the charging patterns of a population of cost-minimizing EV owners traveling and charging within a transportation network equipped with fast charging stations (FCSs). Specifically, we study how the charging network operator (CNO) can influence where EV users charge in order to optimize the utilization of fast charging stations. These charging decisions of private EV owners affect aggregate congestion at stations (i.e., waiting time) as well as the aggregate EV charging load across the network. In this work, we capture the resulting equilibrium wait times and electricity load through a so-called \textit{traffic and charge assignment problem} (TCAP) in a fast charging station network. Our formulation allows us to: 1) Study the expected station wait times as well as the probability distribution of aggregate charging load of EVs in a FCS network in a mobility-aware fashion (an aspect unique to our work), while accounting for heterogeneities in users' travel patterns, energy demands, and geographically variant electricity prices. 2) Analytically characterize the special threshold-based structure that determines how EV owners choose where to charge their vehicle at equilibrium, in response to the FCS's charging price structure, users' energy demands, and users' mobility patterns. 3) Provide a convex optimization problem formulation to identify the network's unique equilibrium. Furthermore, we illustrate how to induce a socially optimal charging behavior by deriving the socially optimal plug-in fees and electricity prices at the charging stations.

中文翻译：

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具有地域价格变化的移动感知电动汽车快速充电负载模型

我们研究了在配备快速充电站 (FCS) 的交通网络中出行和充电的成本最低的 EV 车主的交通模式以及充电模式。具体而言，我们研究充电网络运营商 (CNO) 如何影响电动汽车用户充电的位置，以优化快速充电站的利用率。私人电动车车主的这些充电决定会影响车站的总体拥堵（即等待时间）以及整个网络的电动车充电总负荷。在这项工作中，我们通过快速充电站网络中所谓的\textit{交通和充电分配问题}（TCAP）来捕获由此产生的平衡等待时间和电力负载。我们的配方使我们能够：1) 以移动感知方式研究 FCS 网络中电动汽车的预期车站等待时间以及总充电负载的概率分布（我们工作的一个独特方面），同时考虑用户出行模式、能源的异质性需求，以及不同地区的电价。2) 分析表征基于阈值的特殊结构，该结构决定了电动车车主如何选择平衡充电的位置，以响应 FCS 的充电价格结构、用户的能源需求和用户的移动模式。3) 提供凸优化问题公式来确定网络的唯一均衡。此外，