Charging Scheduling for Battery Electric Buses Under Limited Depot Resources

With the electrification of urban bus fleets, the sustainability of public transport operation increasingly depends on resource-efficient energy management at bus depots. Under time-of-use electricity pricing and limited depot resources, shifting many charging tasks to low-price periods may increase depot-level peak load and charger competition, thereby affecting vehicle time windows and departure state-of-charge (SOC) requirements. This study formulates a multi-objective nighttime centralized charging scheduling model that minimizes an economic objective while controlling depot-level peak load. The model combines staged charging characteristics with an interval-overlap-based load calculation method to link SOC evolution, time-window occupancy, and depot load formation. For the resulting constrained discrete scheduling task, a problem-specific SPEA2-based solution framework, named DCS-SPEA2, is developed with vehicle-block encoding, repair-coupled decoding, and archive-based Pareto search. A case study using Shanghai bus route 71 shows that the compromise solution achieves a 100% minimum departure SOC compliance rate, reduces the depot-level peak load to 562.74 kW, and decreases the economic objective by 17.97% and 16.30% compared with first-come-first-served charging and valley-price-priority charging, respectively. Compared with standard SPEA2, DCS-SPEA2 increases the average hypervolume from 0.5783 to 0.6620 and reduces the average inverted generational distance from 0.2505 to 0.1993. These results indicate that coordinated charging scheduling can improve resource use efficiency and operational reliability at electric bus depots, thereby supporting sustainable public transport operation under limited depot resources.