In this paper, a bi-level programming model is established to address the planning issues of fast-charging stations in electrified transportation networks with the consideration of uncertain charging demands. The capacitated flow refueling location model is considered in the upper level to minimize the planning cost of fast-charging stations while the traffic assignment model is utilized in the lower level to determine the spatial and temporal distribution of plug-in electric vehicle flows over entire transportation networks. Such bi-level model unveils the inherent relationship among charging demands, electrical demands and the spatial and temporal distribution of plug-in electric vehicle flows. Robust chance constraints are formulated to characterize the service abilities of fast-charging stations under distribution-free uncertain charging demands, where the ambiguity set is constructed to estimate the potential values of the uncertainties based on their moment-based information, such that the robust chance constraints can exactly be reduced to mixed integer linear constraints. By introducing new variables, the bi-level model is then reformulated into a single-level mixed integer second-order cone programming model so as to be solved via off-the-shelf solvers, which guarantee the optimality of the solution. A case study is conducted to illustrate the effectiveness of the proposed planning model, which reveals three critical factors that significantly impact the planning outcomes.

在本文中，建立了一个双层规划模型来解决电气化交通网络中快速充电站的规划问题，同时考虑到不确定的充电需求。在上级中考虑了容量流加油位置模型，以最大程度地减少快速充电站的规划成本，而在下级中使用交通分配模型来确定整个运输过程中插电式电动汽车流量的时空分布网络。这种双层模型揭示了充电需求，电力需求以及插入式电动汽车流量的时空分布之间的内在联系。制定了鲁棒的机会约束来表征快速充电站在无分配不确定充电需求下的服务能力，在此基础上，模糊集被构造为基于其基于矩的信息来估计不确定性的潜在值，从而使鲁棒机会约束可以精确地简化为混合整数线性约束。通过引入新变量，将双层模型重新构造为单级混合整数二阶锥规划模型，以便通过现成的求解器进行求解，从而保证了求解的最优性。进行了一个案例研究，以说明所提议的计划模型的有效性，该模型揭示了三个对计划结果产生重大影响的关键因素。其中模糊度集被构造为基于不确定性的基于矩的信息来估计不确定性的潜在值，从而可以将鲁棒机会约束精确地减小为混合整数线性约束。通过引入新变量，将双层模型重新构造为单级混合整数二阶锥规划模型，以便通过现成的求解器进行求解，从而保证了求解的最优性。进行了一个案例研究，以说明所提议的计划模型的有效性，该模型揭示了三个对计划结果产生重大影响的关键因素。其中模糊度集被构造为基于其基于矩的信息来估计不确定性的潜在值，从而可以将鲁棒机会约束精确地减小为混合整数线性约束。通过引入新变量，将双层模型重新构造为单级混合整数二阶锥规划模型，以便通过现成的求解器进行求解，从而保证了求解的最优性。进行了一个案例研究，以说明所提议的计划模型的有效性，该模型揭示了三个对计划结果产生重大影响的关键因素。然后将双层模型重新构造为单层混合整数二阶锥规划模型，以便通过现成的求解器进行求解，从而保证了求解的最优性。进行了一个案例研究，以说明所提议的计划模型的有效性，该模型揭示了三个对计划结果产生重大影响的关键因素。然后将双层模型重新构造为单层混合整数二阶锥规划模型，以便通过现成的求解器进行求解，从而保证了求解的最优性。进行了一个案例研究，以说明所提议的计划模型的有效性，该模型揭示了三个对计划结果产生重大影响的关键因素。