Abstract：The Pontryagin minimal principle (PMP) strategy, a widely used global optimization strategy, requires to know all working conditions in advance for energy management of the hybrid system of fuel cell trams. However, the actual operation of the tram is characterized by strong randomness and fluctuation, resulting in poor real-time and working condition adaptability of the energy allocation. In order to solve the problems, a coping strategy combining PMP and real-time working condition construction is proposed to achieve both global and transient optimal characteristics of energy management. Firstly, the minimization objective function of total hydrogen consumption for hybrid power system operation is derived based on the principle of minimal value, and the global optimal fuel cell reference power is solved offline. Secondly, the operating process is divided into five stages: idle traction, acceleration start, steady speed driving, deceleration braking and regenerative braking according to the real-time operating characteristics of the tram, and the corresponding state transfer probability matrices are constructed based on Markov chains to improve the adaptability of the energy management strategy to working conditions. At the same time, the fuel cell is classified into four modes: low efficiency, medium efficiency, high efficiency and super efficiency according to its power generation efficiency, and it is set not to start in the low efficiency mode, which can reduce the number of starts and stops of the fuel cell and improve its working efficiency, thus enhancing the engineering applicability of the proposed strategy. Finally, the results of the working condition construction are combined with the energy management, and the instantaneous optimal power allocation is updated online. The proposed strategy, traditional global PMP strategy and instantaneous equivalent consumption minimization strategy (ECMS) strategy are simulated under typical and atypical working conditions. The results show that: The hydrogen consumption of the proposed strategy is 3.76 kg under typical working conditions, which is reduced by 9.6% and 16.8%, respectively, compared with 4.13 kg under PMP strategy and 4.52 kg under ECMS strategy. Similarly, the hydrogen consumption of the proposed strategy is 5.25 kg under atypical working conditions. Compared with the consumption of 5.52 kg and 5.92 kg for PMP and ECMS, the consumption is reduced by 4.9% and 11.3%, respectively. The data indicating that the proposed strategy achieves the global optimal fuel economy. In terms of the calculation time of the optimization algorithm, the proposed strategy, PMP strategy and ECMS strategy are 37ms, 2 020 ms and 35 ms respectively under typical working conditions, and 32 ms, 1 820 ms and 29 ms respectively under atypical working conditions. Meanwhile, the proposed strategy can reduce the high power startup times and peak power fluctuation time of fuel cell, and further enhance the system rapidity on the basis of prolonging the service life of fuel cells. Combined with the simulation analysis, the core advantages of the proposed energy management strategy are: (1) overcoming the shortcomings of the global optimization strategy represented by the traditional minimum value principle in terms of real-time and working condition adaptability, and making the hybrid system power distribution both instantaneous and globally optimal. (2) Introducing the demand power prediction based on the identification of the operating state of the tram and dividing the fuel cell operating mode, which improves the working condition adaptability of the energy management strategy. (3) Compared with the traditional PMP strategy and ECMS strategy, the hydrogen consumption is reduced and the overall energy utilization efficiency of the system is improved under both typical and atypical working conditions, while the supercapacitor SOC and bus voltage fluctuation range are significantly improved.
高锋阳, 高翾宇, 张浩然, 杨凯文, 宋志翔. 全局与瞬时特性兼优的燃料电池有轨电车能量管理策略[J]. 电工技术学报, 2023, 38(21): 5923-5938.
Gao Fengyang, Gao Xuanyu, Zhang Haoran, Yang Kaiwen, Song Zhixiang. Management Strategy for Fuel Cell Trams with Both Global and Transient Characteristics. Transactions of China Electrotechnical Society, 2023, 38(21): 5923-5938.
[1] 张钢, 王运达, 刘志刚, 等. 城轨牵引供电系统多尺度和多物理域建模仿真方法[J]. 电工技术学报, 2022, 37(12): 3097-3107. Zhang Gang, Wang Yunda, Liu Zhigang, et al.Multi-scale and multi-physical domain modeling and simulation method for urban rail traction power supply system[J]. Transactions of China Electrotechnical Society, 2022, 37(12): 3097-3107. [2] 宋清超, 陈家伟, 蔡坤城, 等. 多电飞机用燃料电池-蓄电池-超级电容混合供电系统的高可靠动态功率分配技术[J]. 电工技术学报, 2022, 37(2): 445-458. Song Qingchao, Chen Jiawei, Cai Kuncheng, et al.A highly reliable power allocation technology for the fuel cell-battery-supercapacitor hybrid power supply system of a more electric aircraft[J]. Transactions of China Electrotechnical Society, 2022, 37(2): 445-458. [3] 莫浩楠, 杨中平, 林飞, 等. 有轨电车基于工况识别的强化学习能量管理策略[J]. 电工技术学报, 2021, 36(19): 4170-4182. Mo Haonan, Yang Zhongping, Lin Fei, et al.Reinforcement learning energy management strategy of tram based on condition identification[J]. Transactions of China Electrotechnical Society, 2021, 36(19): 4170-4182. [4] Njoya Motapon S, Dessaint L A, Al-Haddad K.A comparative study of energy management schemes for a fuel-cell hybrid emergency power system of more-electric aircraft[J]. IEEE Transactions on Industrial Electronics, 2014, 61(3): 1320-1334. [5] Fernandez L M, Garcia P, Garcia C A, et al.Hybrid electric system based on fuel cell and battery and integrating a single DC/DC converter for a tramway[J]. Energy Conversion and Management, 2011, 52(5): 2183-2192. [6] Li Chunyan, Liu Guoping.Optimal fuzzy power control and management of fuel cell/battery hybrid vehicles[J]. Journal of Power Sources, 2009, 192(2): 525-533. [7] Qin Feiyan, Xu Guoqing, Hu Yue, et al.Stochastic optimal control of parallel hybrid electric vehicles[J]. Energies, 2017, 10(2): 214. [8] Yan Fengjun, Wang Junmin, Huang Kaisheng.Hybrid electric vehicle model predictive control torque-split strategy incorporating engine transient characteristics[J]. IEEE Transactions on Vehicular Technology, 2012, 61(6): 2458-2467. [9] Guo Lulu, Ren Lina, Xiang Yu, et al.Performance analysis of a PHEV under optimal control strategy[C]//2013 IEEE Vehicle Power and Propulsion Conference (VPPC), Beijing, China, 2013: 1-6. [10] Luo Yugong, Chen Tao, Zhang Shuwei, et al.Intelligent hybrid electric vehicle ACC with coordinated control of tracking ability, fuel economy, and ride comfort[J]. IEEE Transactions on Intelligent Transportation Systems, 2015, 16(4): 2303-2308. [11] Boehme T J, Frank B, Schori M, et al.Multi-objective optimal powertrain design of parallel hybrid vehicles with respect to fuel consumption and driving performance[C]//2014 European Control Conference (ECC), Strasbourg, France, 2014: 1017-1023. [12] Zhang Yi, Liu Heping, Guo Qiang.Varying-domain optimal management strategy for parallel hybrid electric vehicles[J]. IEEE Transactions on Vehicular Technology, 2014, 63(2): 603-616. [13] Pisu P, Rizzoni G.A comparative study of supervisory control strategies for hybrid electric vehicles[J]. IEEE Transactions on Control Systems Technology, 2007, 15(3): 506-518. [14] 李峰, 杨中平, 王玙, 等. 基于庞特里亚金极小值原理的混合储能有轨电车能量管理策略[J]. 电工技术学报, 2019, 34(增刊2): 752-759. Li Feng, Yang Zhongping, Wang Yu, et al.Energy management strategy of tram with hybrid energy storage system based on Pontryagin’s minimum principle[J]. Transactions of China Electrotechnical Society, 2019, 34(S2): 752-759. [15] 陈泽宇, 方志远, 杨瑞鑫, 等. 基于深度强化学习的混合动力汽车能量管理策略[J]. 电工技术学报, 2022, 37(23): 6157-6168. Chen Zeyu, Fang Zhiyuan, Yang Ruixin, et al.Energy management strategy for hybrid electric vehicle based on the deep reinforcement learning method[J]. Transactions of China Electrotechnical Society, 2022, 37(23): 6157-6168. [16] 袁佳歆, 曲锴, 郑先锋, 等. 高速铁路混合储能系统容量优化研究[J]. 电工技术学报, 2021, 36(19): 4161-4169, 4182. Yuan Jiaxin, Qu Kai, Zheng Xianfeng, et al.Optimizing research on hybrid energy storage system of high speed railway[J]. Transactions of China Electrotechnical Society, 2021, 36(19): 4161-4169, 4182. [17] Yalcinoz T, Alam M S.Improved dynamic performance of hybrid PEM fuel cells and ultracapacitors for portable applications[J]. International Journal of Hydrogen Energy, 2008, 33(7): 1932-1940. [18] Hemi H, Ghouili J, Cheriti A.Combination of Markov chain and optimal control solved by Pontryagin’s minimum principle for a fuel cell/supercapacitor vehicle[J]. Energy Conversion and Management, 2015, 91: 387-393. [19] 武龙星, 庞辉, 晋佳敏, 等. 基于电化学模型的锂离子电池荷电状态估计方法综述[J]. 电工技术学报, 2022, 37(7): 1703-1725. Wu Longxing, Pang Hui, Jin Jiamin, et al.A review of SOC estimation methods for lithium-ion batteries based on electrochemical model[J]. Transactions of China Electrotechnical Society, 2022, 37(7): 1703-1725. [20] 吴铁洲, 王越洋, 许玉姗, 等. 基于PMP算法的HEV能量优化控制策略[J]. 自动化学报, 2018, 44(11): 2092-2102. Wu Tiezhou, Wang Yueyang, Xu Yushan, et al.Energy optimal control strategy of HEV with PMP algorithm[J]. Acta Automatica Sinica, 2018, 44(11): 2092-2102. [21] 丁强. 现代有轨电车交通概述[J]. 都市快轨交通, 2013, 26(6): 107-111. Ding Qiang.Overview of modern tram transportation[J]. Urban Rapid Rail Transit, 2013, 26(6): 107-111. [22] 何俊强, 师长立, 韦统振. 基于马尔科夫链的自适应储能需求功率预测模型[J]. 电工技术学报, 2021, 36(增刊2): 563-571. He Junqiang, Shi Changli, Wei Tongzhen.Adaptive power demand prediction model of energy storage based on Markov chain[J]. Transactions of China Electrotechnical Society, 2021, 36(S2): 563-571. [23] Ma Yan, Li Cheng, Wang Siyu.Multi-objective energy management strategy for fuel cell hybrid electric vehicle based on stochastic model predictive control[J]. ISA Transactions, 2022, 131: 178-196. [24] 赵秀春, 郭戈. 混合动力电动汽车能量管理策略研究综述[J]. 自动化学报, 2016, 42(3): 321-334. Zhao Xiuchun, Guo Ge.Survey on energy management strategies for hybrid electric vehicles[J]. Acta Automatica Sinica, 2016, 42(3): 321-334. [25] 高锋阳, 张浩然, 王文祥, 等. 氢燃料电池有轨电车混合储能系统的节能运行优化[J]. 电工技术学报, 2022, 37(3): 686-696. Gao Fengyang, Zhang Haoran, Wang Wenxiang, et al.Energy saving operation optimization of hybrid energy storage system for hydrogen fuel cell tram[J]. Transactions of China Electrotechnical Society, 2022, 37(3): 686-696.
2023, Vol. 38 
