Towards an efficient electric bus system: Multi-phase optimization model for incremental electrification of bus network with uncertain energy consumption

Abstract

Electrifying bus transit systems emerges as a practical solution to environmental degradation resulting from the unprecedented level of mobility nowadays. In the U.S., with the intensified efforts to expand EV infrastructure, a special emphasis is now placed on providing emission-free transit services. This initiative is central to America’s push towards a net-zero-emissions future. In response, a growing number of cities have started replacing diesel buses with battery electric buses (BEBs). However, technological, operational, and economic barriers related to charging infrastructure and power supplies make the electrification of bus systems a gradual process, where only a part of the system is electrified at each stage. Moreover, due to the limited battery capacities of BEBs and their stochastic discharge rates influenced by factors like weather, traffic, and road conditions, BEBs often require daytime charging to be able to continue operating throughout the day. Therefore, transit agencies need to develop an integrated strategy that can address various costs of electrification and minimize the planning and operational costs. This study proposes a framework to facilitate the incremental electrification of bus systems. We formulate the problem as a two-stage stochastic mixed-integer linear programming model. The first stage optimizes long-term strategical decisions related to fleet sizing, charging station siting, and charging-station-route assignments under random BEB charging demand and time-of-use electricity tariffs. The second-stage optimizes the charging operations of the BEB fleet for a realized charging demand scenario while maintaining the service schedule for passenger convenience. We also develop a Benders decomposition method to solve the problem with better computational efficiency than existing solvers. To validate the proposed model, we test it on a real-world bus network to design an incremental electrification plan. We show the efficacy of the solution approach and study the managerial insights including the deployment of fast charging and potential battery technology enhancement in the future.