Cost-Optimal Charging Strategies for Electric Bus Fleets Considering Battery Degradation and Nonlinear Charging

Electric buses are becoming increasingly popular in transit systems by virtue of their great potential in improving environmental sustainability. The electric bus charging scheduling problem (EBCSP) has been widely researched to minimize the operation cost by determining the charging strategies, including when and how much electricity to charge. However, few studies have considered both the battery degradation mechanism and the nonlinear charging. The former should be the implicit operational cost, while the latter should accurately estimate the electricity charged. Considering these two characteristics, this paper addresses the EBCSP with the goal of optimizing costs. First, a rigorous mathematical model is developed, constrained by the electricity quantity, preset timetable, charging facilities, and charging continuity. Then, the battery degradation cost is modeled by introducing the wear cost function, and the nonlinear charging profile is linearized by piecewise affine function. The model is further simplified to mixed integer linear programming with a reduced computational burden. Computational results suggest that the optimization can reduce battery degradation and total cost, especially for those bus routes with higher frequencies and longer travel distances. Finally, sensitive analysis indicates that a low initial state of charge can result in significant savings in degradation costs of about 19% and total costs of about 13%. Large fleet and battery sizes reduce charging costs while increasing battery degradation cost and total cost. Some solid managerial insights are provided for the application of electric transportation systems.