A position allocation approach to the scheduling of battery-electric bus charging

Robust charging schedules for a growing market of battery-electric bus (BEB) fleets are critical to successful adoption. In this paper, we present a BEB charging scheduling framework that considers spatiotemporal schedule constraints, route schedules, fast and slow charging options, and battery dynamics, modeled as a mixed-integer linear program (MILP). The MILP is based on the berth allocation problem (BAP), a method that optimally assigns vessels for service, and is adapted in a modified form known as the position allocation problem (PAP), which assigns electric vehicles (EVs) for charging. Linear battery dynamics are included to model the charging of buses while at the station. To account for the BEB discharges over their respective routes, we assume that each BEB experiences an average kWh charge loss while in transit. The optimization coordinates BEB charging to ensure that each vehicle maintains a state-of-charge (SOC) above a specified level. The model also minimizes the total number of chargers utilized and prioritizes slow charging for battery health. The validity of the model is demonstrated using a set of routes sampled from the Utah Transit Authority (UTA) for 35 buses and 338 visits to the charging station. The model is also compared to a heuristic algorithm based on charge thresholds, referred to as the Qin-modified method. The results show that the MILP framework encourages battery health by assigning slow chargers to BEBs more readily than the Qin-modified method. The MILP utilized one fast charger and six slow chargers, whereas the Qin-modified method utilized four fast chargers and six slow chargers. Moreover, the MILP maintained a specified minimum SOC of 25% throughout the day and achieved the required minimum SOC of 70% at the end of the working day, whereas the Qin-modified method failed to maintain the SOC above 0% without any constraints applied. Furthermore, it is shown that the spatiotemporal constraints are met while considering the battery dynamics and minimizing both the charger count and consumption cost.