基于极小值原理的增程式客车能量管理问题规律分析

Analysis for the Energy Management Problem of Extended-Range Electric City Buses Based on Pontryagin's Minimum Principle

为了提高增程式城市客车的燃油经济性,利用极小值原理设计在线能量管理策略是一种有效方法,然而难点在于如何避免协态变量的迭代计算。在对动力电池组的特性和输出功率进行合理假设的基础上,利用状态方程和协态方程推导出协态变量与动力电池组开路电压二者的关系方程。通过对该关系方程进行近似求解,得到了上述二者的比值可以视为常数的结论。将基于该结论所设计的在线能量管理策略应用于不同实际工况,并将结果与全局最优解对比,发现该策略的性能仅低于全局最优水平0.5%。由此可见,该策略是一种可以得到在线应用的最优能量管理策略。

In order to improve the fuel economy of extended-range electric city buses,using the Pontryagin＇s minimum principle to design on-line energy manage strategies is an effective solution,however,the challenge lies in how to avoid the iteration calculation of the co-state variable. Based on reasonable assumptions for battery characters and its output power,the state and adjoint equations areapplied to deduce the equation between the co-state variable and the battery open-circuit voltage.Through solving the equation approximately,it is concluded that the ratio of the two variables could be seemed constant. An on-line energy management strategy, which is designed based on such conclusion,is applied over different real-world driving cycles,the results show that the performance difference of this strategy is less than the 0. 5% compared with the global optimal level. Therefore,this strategy is an optimal energy management strategy for on-line applications.