Degradation-Aware Charger Deployment, Battery Sizing, and Charge Scheduling for Electric Bus Fleets

The transition to battery electric buses (BEBs) presents new challenges to the transportation and energy sectors, necessitating meticulous decision-making for a sustainable transition. This paper proposes an integrated optimization model to determine the required number of chargers, charger power, grid capacity upgrade, battery sizing, and charging schedules for a heterogeneous fleet of BEBs. The proposed battery-degradation-aware model captures the interdependencies of charger deployment, battery sizing, and battery degradation to determine the optimal decisions based on an assumed battery degradation behavior. To this end, we assume an arbitrary nonlinear degradation model and develop a tractable mixed-integer linear programming formulation using a decomposition approach and McCormick relaxation. We further account for the uncertainty of electricity prices to design a robust model. The model is then implemented for a real fleet of 78 buses with different trip schedules, and two empirical battery degradation models are employed. The results show that, considering the two degradation models, the degradation-aware model reduces the overall costs by 28.6% and 46.8% in comparison with the degradation-neutral model due to prolonging the estimated cycle life of batteries by 67% and 135% on average.