En-route charge scheduling for an electric bus network: Stochasticity and real-world practice

Bus electrification, with its high energy conversion efficiency and zero tailpipe emissions, has a significant impact on addressing the petroleum crisis and lowering carbon emissions in urban transportation. However, long charging times and uncertain operational risks hinder their wider adoption. This paper explores the robust en-route charge scheduling problem for electric buses to overcome uncertain energy consumption while ensuring charging accessibility. The problem is first described as a deterministic mixed-integer linear programming model that employs a time-of-use electricity price to balance the charging demand. Additionally, a robust counterpart model is formulated to account for stochastic energy. Numerical studies are designed to evaluate the proposed model in a real network, followed by a sensitivity analysis to investigate the impact of battery type, fleet composition, and depth of discharge on the charging schedule. The results show that the robust optimization model provides system feasibility against uncertainty with a comparable price and emissions.