A Multi-stage Optimization of Battery Electric Bus Transit with Battery Degradation

Battery electric buses (BEBs) are appealing to transit operators for their elevated comfort, low noise, and zero tailpipe emissions. However, the degradation of BEB batteries over time challenges their performance and necessitates infrastructure adjustments. This study develops a generic multi-stage optimization model for BEB systems. The model addresses the dynamic influence of BEB battery degradation rates on the optimal BEB system configuration and operation, including component sizing, charging infrastructure allocation, BEB charging schedule, and battery replacement throughout the BEB usage lifecycle. A surrogate model-based space mapping (SMSM) algorithm is employed to address the inherent nonlinearity of incorporating battery degradation rates within the developed model. The model is tested on a real-world, multi-hub transit network, and the results highlight significant implications of battery degradation on the optimal spatiotemporal allocation of charging infrastructure, charging schedules, and battery replacement decisions throughout the 12-year BEB usage lifecycle. Sensitivity analysis highlights the influence of operational conditions on total system cost, indicating a 16.3% increase in cost with a 50% rise in both energy consumption rates and time-of-use (ToU) tariffs. Overall, the proposed model is a valuable decision-making tool for transit operators navigating BEB transit system planning.