On the role of battery degradation in en-route charge scheduling for an electric bus system

Electric buses (EB) are widely promoted as a clean alternative to conventional fleets to mitigate greenhouse gas emissions from ground transportation. En-route charging that takes advantage of bus dwell time is an efficient and promising charging strategy to address mileage limitations and long energy replenishment time. However, the charging and discharging behavior of electric buses during operation has a vital impact on battery degradation, grid stability, and schedule robustness. The present study proposes an optimal electric bus charge scheduling model that addresses the grid and battery issues by introducing peak-to-average power ratio, time-of-use electricity price, and battery wear formulation while ensuring the original bus schedules. The model is formulated as a mixed-integer program that can be solved using off-the-shelf solvers even for large-scale problems. Extensive numerical studies based on real-world bus networks are introduced to demonstrate the performance and to gain insights from sensitive analysis. The result shows that the optimal schedule achieves a balanced spatial and temporal distribution of charging demand. Besides, it reveals that the battery wear costs have a greater impact on operations than charging costs, accounting for about 87.26% of total operating costs. However, this impact can be well controlled by controlling the battery state-of-charge (SOC) intervals.