Optimal locations and sizes of layover charging stations for electric buses

Public transit agencies across the world are rapidly converting their bus fleets from diesel or hybrid powertrains to battery-electric propulsion systems. To realize the benefits of the transition to battery-electric buses (BEBs) while retaining acceptable quality of service and limiting capital costs, agencies must intelligently decide where to locate recharging infrastructure. While most agencies electrifying their fleets plan to install chargers at bases where buses are kept overnight, a question faced by many fleet operators is where to install layover chargers that provide additional energy while buses are in operation during the day. To address this challenge, this work presents a mixed-integer linear programming model, referred to as BEB-OCL (BEB Optimal Charger Location), that optimizes the tradeoff between upfront charging infrastructure costs and operational performance. The key decision variables include the locations at which to install chargers, the number of chargers installed at each chosen location, and the location, duration, and sequence of charger visits for each bus. We also introduce a second optimization model, referred to as BEB-BRP (BEB Block Revision Problem), that revises vehicle schedules by dispatching backup buses to serve some trips so that buses do not run out of battery and all passenger trips are still completed as scheduled. The models are applied to a case study of the highest-ridership bus routes in King County, WA, USA, where an electric bus deployment is currently underway.