Locating En-Route Charging Stations and Time Points for a Transit Route with Battery- Electric Buses

Abstract

While the acknowledged environmental benefits of battery-electric buses (BEBs) are widely recognized, their distinct differences from diesel buses necessitate adjustments in both route planning (including charging station placement) and operations (comprising schedule management and holding control). Overall, life cycle emissions of BEBs tend to be lower than those of diesel buses. However, the actual environmental impact depends on various factors, including the energy source for electricity generation, battery manufacturing practices, and disposal/recycling methods. Transitioning to electric buses, particularly in regions with a clean energy grid, holds significant potential for reducing greenhouse gas emissions and air pollution. The strategic placement of charging stations, their number, duration of charging, and station types all factor into the comprehensive planning process. These stations can be strategically situated at depots, termini, or even along the route. This study addresses the long-term planning and optimization challenge of revising formulations for dispatch policy, determining optimal en-route charging station locations and corresponding charging durations, and determining the location of the holding point and their slack time. This optimization endeavor aims to enhance passengers' waiting time, operational efficiency, and capital costs, all while mitigating the inherent variability arising from weather- induced ridership fluctuations and battery performance uncertainties intrinsic to BEBs while improving the reliability of the transit service. Two linear deterministic optimization models and a two-stage stochastic programming (SP) optimization process are developed to pursue these goals. These approaches facilitate the strategic placement of BEB charging stations along the route and calculate their associated charging times in addition to the placement of the time points. The application of these models encompasses both one-way and two-way operations. The practicality and efficacy of these methodologies are tested on two high-demand bus routes within Calgary's transit network. Additionally, the study evaluates the potential implications of charging station malfunctions, mainly focusing on scenarios where the maximum charging time is exceeded and its subsequent impact on operational schedules and BEB operation costs. Furthermore, the study explores the solution yielded by the stochastic model, using the expected value of perfect information as an evaluative metric.