基于动态规划的混合动力有轨电车能量管理方法

针对传统动态规划算法在燃料电池混合动力系统能量分配中存在的误差累积问题，以及为进一步提高燃料电池混合动力有轨电车的耐久性和燃料经济性，提出了一种基于改进动态规划算法的燃料电池混合动力有轨电车能量管理方法；改进动态规划算法在传统动态规划的基础上调整了状态转移方程，通过只对系统状态量进行离散从而避免计算过程中的插值计算导致的误差累积；同时将系统等效氢耗、动力电池充电状态（SOC）约束和燃料电池加、减载带来的耐久性问题作为优化目标构成加权惩罚函数，使系统在获得良好燃料经济性的同时兼顾耐久性；将所提管理方法与功率跟随和传统动态规划进行对比分析. 研究结果表明:所提方法相较于功率跟随方法，使末态SOC值降低了13.3%，燃料经济性提高了78%；相较于基于传统动态规划算法的能量管理方法，使燃料经济性提高了3.5%，且SOC变化范围和燃料电池变载情况均具有显著改善. 

Energy Management Method for Hybrid Electric Tram Based on Dynamic Programming Algorithm

Aiming at the errors accumulation of traditional dynamic programming algorithm in energy distribution of the fuel cell hybrid electric system, an energy management method for the fuel cell hybrid electric tram was proposed based on improved dynamic programming algorithm, which aims to further improve the durability and fuel economy of the fuel cell hybrid electric tram. The improved dynamic programming algorithm adjusted the state transition equation based on the traditional dynamic programming by discretizing the system state quantities, which avoided the errors accumulation caused by interpolation calculation. At the same time, the equivalent hydrogen consumption of the system, the constraint of the state of charge (SOC) and the durability problems brought from loading and unloading of fuel cells were considered as optimization objectives to constitute a weighted penalty function, which made the system could take into account durability while achieved better fuel economy. The proposed management method was compared with power following and traditional dynamic programming. The results show that the proposed method reduces the final state SOC by 13.3% and the fuel economy by 78% compared with the power-following method. Moreover, the proposed method improves the fuel economy by 3.5%, and both the SOC variation range and the load-carrying condition of the fuel cell have significantly improved compared with the traditional dynamic programming algorithm.