As the number of electric vehicles (EVs) continues to rise, it is essential to consider appropriate management strategies for coordinating EVs connected to different buses in the power networks. In light of this, this paper proposes a stochastic two-stage bi-level model for coordinating EVs in a distribution network with charging stations under alternating current optimal power flow (ACOPF) constraints. The scheduling problem is considered to independently minimize the costs of the distribution system operator (DSO) and EVs parked at different charging stations located at various buses of the network. In the proposed model, the DSO as the leader, and all EVs as independent followers, are individual entities who try to follow their priorities and objectives. The amount and price of exchanged power between the DSO and EVs are optimally determined in the proposed model. The proposed bi-level model has been converted to a single-level model using the Karush–Kuhn–Tucker (KKT) conditions. Afterwards, the Big M method is used to convert the non-linear equations that appear due to utilizing the KKT approach. The scenario-based uncertainty modeling is used to model the uncertainty in input data such as day-ahead and real-time market prices, EVs’ initial state of charge (SOC), and arrival/departure time. The centralized unilateral form of the model has also been developed to validate the proposed model. The results indicate that the bi-level model can lead to cost reduction for the EVs.

随着电动汽车 (EV) 数量的不断增加，必须考虑适当的管理策略来协调连接到电网中不同总线的电动汽车。鉴于此，本文提出了一种随机两阶段双层模型，用于在交流最优功率流 (ACOPF) 约束下协调带充电站的配电网中的电动汽车。调度问题被认为是独立地最小化配电系统运营商 (DSO) 和停在位于网络的各种总线的不同充电站的 EV 的成本。在提议的模型中，作为领导者的 DSO，以及作为独立追随者的所有 EV，都是试图遵循其优先事项和目标的个体实体。DSO 和 EV 之间交换电力的数量和价格在所提出的模型中得到最佳确定。使用 Karush–Kuhn–Tucker (KKT) 条件，已将拟议的双层模型转换为单层模型。随后，大M方法用于转换由于使用KKT方法而出现的非线性方程。基于场景的不确定性建模用于对输入数据的不确定性进行建模，例如日前和实时市场价格、EV 的初始充电状态 (SOC) 和到达/离开时间。还开发了模型的集中式单边形式来验证所提出的模型。结果表明，双层模型可以降低电动汽车的成本。