A robust coordinated charging scheduling approach for hybrid electric bus charging systems

This paper proposes a coordinated electric bus (EB) charging scheduling approach for hybrid charging stations that support plug-in charging and battery-swapping simultaneously. To minimize the total charging cost under time-of-use electricity prices, both a deterministic optimization (DO) model and a robust optimization (RO) model are developed to design the EBs' charging schedule. In the deterministic model, the remaining capacity upon arrival at the station is assumed to be known. However, in practice, the remaining capacity of the EB is typically uncertain due to unpredictable traffic conditions. Therefore, this paper proposes an RO model to address this uncertainty, utilizing a budgeted uncertainty set and developing the affinely adjustable robust counterpart. The duality theorem is employed to convert the RO model into a computationally tractable formulation. The proposed approach is illustrated with two numerical examples, including a random instance and a real-world case study of Nanjingnan Station in Nanjing, China.