Adaptively coordinated optimization of battery aging and energy management in plug-in hybrid electric buses

Plug-in hybrid electric buses with large battery packs exhibit salient advantages in increasing fuel economy and reducing toxic emissions. However, they may be subject to expensive battery replacement caused by battery aging. This paper designs an online, coordinated optimization approach, based on Pontryagin's minimum principle, for a single-shaft parallel plug-in hybrid electric bus, aiming at minimizing the total cost of energy consumption and battery degradation. Specifically, three key contributions are delivered to complement the relevant literature. First, a capacity loss model for lithium ion batteries emulating dynamics of both cycle life and calendar life is exploited in the optimization framework, in order to highlight the importance of considering calendar life and its implication to overall energy management performance in real bus operations. Second, the online adaptive mechanism of the optimization method with respect to varying driving conditions is achieved by tracking two reference trajectories to adjust the state of charge and effective ampere-hour throughput of the battery. Finally, to verify the effectiveness of the proposed scheme, various comparative studies are carried out, accounting for different driving scenarios. Simulation results show that the maximum control errors between the proposed strategy and Pontryagin's minimum principle are only 0.4% in the battery capacity loss and 2.7% in fuel economy under four random driving cycles, which indicates the prominent adaptability and optimization performance of the designed strategy.