Benefiting from solar: Optimal scheduling for solar electric buses with onboard PV auxiliary power

Solar electric buses (SEBs), which install rooftop solar panels on battery electric buses (BEBs), harness photovoltaic (PV) electricity generated from solar radiation during in-motion and parking periods. The onboard PV system provides auxiliary power for SEBs in addition to the primary on-site charging. Particularly, varying PV gains greatly affect Li-ion battery consumption (LBC), requiring a schedule to avoid running out of Li-ion batteries while covering trips. Meanwhile, the schedule also affects PV gains in terms of parking periods and itinerary-specific deductions during in-motion processes. This study contributes to the vehicle scheduling problem (VSP) of SEBs, and a SEB-VSP model is developed on the basis of an underlying network, while quantitatively examining the operational benefits of installing solar panels. This model endogenously involves vehicle-trip assignment, varying PV gains, and on-site charging for Li-ion batteries. The branch-and-price algorithm is employed to solve this problem, wherein the pricing problem can be solved using a customized labeling algorithm. Heuristic approaches are applied over the branch-and-bound (B&B) tree to rapidly find high-quality integer solutions. The methodology is tested using real-world information on bus routes and solar radiation metrics in Hong Kong. The results show that more LBC is needed during the initial and end of operation periods. To collect more PV gains, SEBs favor serving trips with longer layovers in the scheduling phase. Additionally, the comparative findings underscore the operational benefits of adopting SEBs, mainly attributed to reduced charging detours.