Optimizing charging station locations for mixed traffic of electric and gasoline vehicles: a stochastic user equilibrium approach

Charging station (CS) location planning is critical for accommodating the growing demand of electric vehicles (EVs). This paper develops a mixed-integer nonlinear programming (MINLP) model to address the charging station location and capacity problem in the road networks with mixed traffic of electric and gasoline vehicles, aiming to minimize both charging station investment costs and travel time costs. The main contributions of this study include: i) existing studies often assume that users are perfectly rational and cooperatively choose the shortest paths under the user equilibrium framework, overlooking perception errors and the stochastic nature of route choice. Thus, this model adopts a Stochastic User Equilibrium (SUE) framework to reflect users’ imperfect perceptions and decision-making variability in mixed traffic networks. ii) Inaccurate waiting time estimates are often overlooked during charging station location planning, leading to suboptimal and costly locations. Therefore, this study incorporates EV waiting time into the location decision and proposes a machine learning-based estimation model to improve prediction accuracy. Furthermore, this study proves the uniqueness of the SUE pattern through theoretical derivation, facilitating the joint application of the sparrow search algorithm, path-based method of successive averages, and random forest model to solve the MINLP. A case study is conducted on networks of varying sizes. Results from a realistic Eastern-Massachusetts highway network demonstrate that the accuracy of waiting time predictions will impact CS location-capacity results. Compared to the UE-based charging station location model, the SUE-based model produces a more dispersed traffic flow and less congestion on the shortest routes by integrating user perception errors and preference heterogeneity, thereby reducing travel time cost by 49.08% and total system cost by 48.83%. This study provides practical value for EV CS planning by addressing user perception errors and real-time waiting time prediction. Future research includes considering dynamic traffic demand and power grid interactions.