A pontryagin minimum principle-based adaptive equivalent consumption minimum strategy for a plug-in hybrid electric bus on a fixed route

Abstract

When developing a real-time energy management strategy for a plug-in hybrid electric vehicle, it is still a challenge for the Equivalent Consumption Minimum Strategy to achieve near-optimal energy consumption, because the optimal equivalence factor is not readily available without the trip information. With the help of realistic speeding profiles sampled from a plug-in hybrid electric bus running on a fixed commuting line, this paper proposes a convenient and effective approach of determining the equivalence factor for an adaptive Equivalent Consumption Minimum Strategy. Firstly, with the adaptive law based on the feedback of battery SOC, the equivalence factor is described as a combination of the major component and tuning component. In particular, the major part defined as a constant is applied to the inherent consistency of regular speeding profiles, while the second part including a proportional and integral term can slightly tune the equivalence factor to satisfy the disparity of daily running cycles. Moreover, Pontryagin's Minimum Principle is employed and solved by using the shooting method to capture the co-state dynamics, in which the Secant method is introduced to adjust the initial co-state value. And then the initial co-state value in last shooting is taken as the optimal stable constant of equivalence factor. Finally, altogether ten successive driving profiles are selected with different initial SOC levels to evaluate the proposed method, and the results demonstrate the excellent fuel economy compared with the dynamic programming and PMP method.