A position allocation approach to the scheduling of battery-electric bus charging - Brown, Alexander; Droge, Greg; Gunther, Jacob (Frontiers in Energy Research, 2024)
Robust charging schedules in a growing market of Battery-Electric Bus (BEB) fleets are a critical component to successful adoption. In this paper, a BEB charging scheduling framework that considers spatiotemporal schedule constraints, route schedules, fast and slow charging, and battery dynamics is modeled as a Mixed Integer Linear Program (MILP). The MILP is modeled after the Berth Allocation Problem (BAP), a method of optimally assigning vessels to be serviced, in a modified form known as the Position Allocation Problem (PAP), which assigns Electric Vehicels (EVs) to be charged. Linear battery dynamics are included to model the charging of buses while at the station. To model the BEB discharges over their respective routes, it is assumed each BEB has an average kWh charge loss while on route. The optimization coordinates BEB charging to ensure that each vehicle remains above a specified State-Of-Charge (SOC). The model also minimizes the total number of chargers utilized and prioritizes slow charging for battery health. The model validity is demonstrated with 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 presented show that the MILP framework encourages battery health by assigning BEBs slow chargers more readily than the Qin-Modified. The MILP utilizied one fast charger and six slow chargers whereas the Qin-Modified utilized four fast chargers and six slow. Moreover, the MILP was able to maintain a specified minimum SOC of 25% throughout the day and meeting a reqired minimum SOC at the end of the working day of 70% whereas the Qin-Modifed was unable to keep the SOC above 0% without any constraints applied. Furthermore, it is shown that the spatiotemporal constraints are met while considering the battery dynamics while minimizing both the charger count and consumption cost.