A Bilevel Programming Approach to Model the Charge Curve for EV Charging Scheduling at Capacity-Constrained Fast Charging Stations

DC fast charging is a key enabler for removing barriers to the widespread adoption of electric vehicles (EVs), offering rapid recharging solutions that alleviate range anxiety. However, at capacity-constrained fast charging stations (FCSs) with multiple ports, where the aggregate power is limited by technical or economic factors, it may not be possible to simultaneously charge all EVs at maximum power. This necessitates the implementation of EV charging scheduling schemes to distribute the available power capacity among connected EVs while ensuring high quality-of-service and fairness. Moreover, efficiently and accurately integrating the non-linear charge curve of EVs, which defines the maximum charging power as a function of state-of-charge, into an EV charging scheduling optimization problem remains a formidable challenge. In this work, we propose a modeling approach for EV charge curves using multi-segment piecewise linear (PWL) regression. We adopt a bilevel programming scheme to identify optimal breakpoints, slopes, and intercepts of the segments in the PWL model by minimizing the sum of absolute residuals error. The resulting PWL model is then efficiently integrated into a mixed-integer linear program to solve the charging scheduling problem. Case studies confirm the superiority of the framework, achieving up to 11.72% improvement over the best performing of three benchmark methods. Additionally, the solution time remains below 2.5 seconds for up to 200 simultaneously connected EVs, demonstrating its computational efficiency and scalability.