Integrated charging scheduling and operational control for an electric bus network

The last few years have seen the massive deployment of electric buses in many existing transit networks. However, the planning and operation of an electric bus system differ from that of a bus system with conventional vehicles, and some key problems have not yet been studied in the literature. In this work, we address the integrated operational control and charging scheduling problem for a network of electric buses with a limited opportunity charging capacity. Operational control is carried out through speed control of the vehicles and bus holding at the terminal. We propose a hierarchical control framework to solve this integrated problem, where the charging and operational decisions are taken jointly by solving a mixed-integer linear program in the high-level control layer. Since this optimization problem might become very large as more bus lines are considered, we propose to apply Lagrangian relaxation in such a way as to exploit the structure of the problem and enable a decomposition into independent subproblems. A local search heuristic is then deployed in order to generate good feasible solutions to the original problem. This entire Lagrangian heuristic procedure is shown to scale much better on transit networks with an increasing number of bus lines than trying to solve the original problem with an off-the-shelf solver. The proposed procedure is then tested in the high-fidelity microscopic traffic environment Vissim on a bus network constructed from an openly available dataset of the city of Chicago. The results show the benefits of combining the charging scheduling decisions with the real-time operational control of the vehicles as the proposed control framework manages to achieve both a better level of service and lower charging costs over control baselines with predetermined charging schedules.