Optimal charging facility location and capacity for electric vehicles considering route choice and charging time equilibrium

In this study, the optimal design of location and capacity of charging facilities for electric vehicles (EVs) is investigated. A bi-level mathematical model is proposed to derive optimal design considering the equilibrium of route choice and waiting time for charging. The objective is to minimize the joint cost of facility constructions and EV drivers’ travel and waiting time over the network. The upper-level model allocates the facilities and their capacity, while the lower-level model characterizes equilibrium behavior of drivers’ route and charging facility choices. In particular, we model drivers at each charging facility as the M(t)/M/n queue and approximate the average queuing time and probability of waiting time as functions of facility capacity and demand arrival rate. The bi-level model is then converted into a single-level model, and the solution algorithm is proposed for iteratively solving the relaxed problems. Comprehensive experiments are conducted on three networks to evaluate algorithm performances, assess solution robustness and understand the scalability of the solution approach on large networks.