Optimal charging scheduling of an electric bus fleet with photovoltaic-storage-charging stations

Replacing conventional diesel buses with widely acclaimed electric buses (EBs) for urban transit services can significantly reduce the operational costs and carbon emissions. However, if a bus fleet relies solely on the electricity grid as its energy supply, existing economic and environmental problems may not be fully overcome due to the grid’s overdependence on non-renewable energy sources such as fossil fuels. This study models and optimizes an emerging bus charging scenario where photovoltaic-storage-charging (PSC) stations and an electricity grid jointly supply electricity to an EB fleet. Each PSC station is equipped with photovoltaic (PV) panels to absorb solar power and a battery set to store electricity, which can either charge buses, supply electricity to the grid, or do both simultaneously when needed. Unlike previous studies, this research not only addresses when, where, and how much electricity each EB in the fleet should be charged but also determines the optimal internal allocation scheme of electricity within each PSC station that minimizes the total charging cost of the EB fleet in its daily operations. It introduces a mixed integer programming problem with time discretization across a time-expanded network. The charging cost of the fleet is calculated in terms of the sum of PV generation cost and time-of-use (TOU) electricity tariff minus the revenue of supplying electricity to the grid. To solve this problem, a Lagrangian relaxation procedure is designed, in which a dynamic programming algorithm implemented as a bi-criterion labeling procedure is developed for the decomposed single-bus charging scheduling subproblem. We collected relevant weather and operational data of an EB fleet operating in Jiading, Shanghai, to validate the model and algorithm and to gain managerial insights. A sensitivity analysis was conducted to examine how key model parameters such as charging demand and supply, PSC battery capacity, and electricity discharging price influence the charging schedule of the EB fleet. Finally, we compared our algorithm’s performance with a state-of-the-practice commercial solver, demonstrating that our algorithm achieves comparable solution optimality while significantly saving computing time.