Battery sizing for plug-in hybrid electric buses considering variable route lengths

Abstract

For plug-in hybrid electric buses, optimizing the battery size is beneficial for lowering the capital cost and improving the efficiency of energy split between multiple power sources. In addition to the energy management strategy, the optimization of battery size is highly dependent on expected trip mileage. For a fleet of urban buses, the travel distance varies between different routes or even within the same route due to random events. The strategy proposed in this paper addresses uncertainty in route length by a method that coordinates the energy management strategy and battery aging to determine optimal battery size. The route length is assumed to follow a normal distribution, and the overall speed profile along the route is composed of basic driving cycles established using a Markov chain model. The co-optimization of battery size, energy management, and battery aging is formulated as a convex programming problem. The optimal battery size for a given expectation value of route length is identified by minimizing the total weighted cost of energy consumption and battery aging over the whole route length distribution. The results, when assuming a variable route length and calculating a weighted cost, are significantly different compared to the case when a fixed route length is used. When optimal depth-of-discharge is not considered, the weighted cost versus route length has a shallow parabolic shape, and an optimal battery size corresponding to minimum weighted cost can be identified. If the optimal depth-of-discharge is taken into account, the optimal battery size is roughly constant versus route length.