Charging Station Location and Sizing for Electric Vehicles Under Congestion

This paper studies the problem of determining the strategic location of charging stations and their capacity levels under stochastic electric vehicle flows and charging times taking into account the route choice response of users. The problem is modeled using bilevel optimization, where the network planner or leader minimizes the total infrastructure cost of locating and sizing charging stations while ensuring a probabilistic service requirement on the waiting time to charge. Electric vehicle users or followers, on the other hand, minimize route length and may be cooperative or noncooperative. Their choice of route in turn determines the charging demand and waiting times at the charging stations and hence, the need to account for their decisions by the leader. The bilevel problem reduces to a single-level mixed-integer model using the optimality conditions of the follower's problem when the charging stations operate as M/M/c queues and the followers are cooperative. To solve the bilevel model, a decomposition-based solution methodology is developed that uses a new logic-based Benders algorithm for the location-only problem. Computational experiments are performed on benchmark and real-life highway networks, including a new eastern U.S. network. The impact of route choice response, service requirements, and deviation tolerance on the location and sizing decisions are analyzed. The analysis demonstrates that stringent service requirements increase the capacity levels at open charging stations rather than their number and that solutions allowing higher deviations are less costly. Moreover, the difference between solutions under cooperative and uncooperative route choices is more significant when the deviation tolerance is lower.