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目前对质子交换燃料电池动态性能的研究多针对于运行参数对系统的影响, 未涉及多时间尺度下电池的动态特性和相应多时间尺度模型的研究. 为探明质子交换膜燃料电池动态变化时系统内各因素在不同时间尺度下对输出性能的影响效力, 利用质量扩散方程及理想气体状态方程求得氧气和氢气有效分压, 根据能量守恒定律、热力学定律、电化学反应方程建立动态模型. 通过设置载荷突变(大、中、小时间尺度动态时长分别为0.6 s, 165 s, 16 min)研究负载电流突变时电压立即突变的机理, 从作用于动态性能时长的时间常数着手, 控制变量分析双层电荷层效应的电容C、燃料氧化剂的延迟时间常数τe、热力学特性(温度T)对动态性能的影响(变量初值为C = 4 F, τe = 80 s, T = 307.7 K), 明确其在不同时间尺度下的作用强度, 借助Matlab/Simulink平台仿真呈现研究结果并验证所建模型的正确性和有效性. 仿真结果表明: 负载突变时电压突变是由于开路电压和欧姆极化电阻的作用且欧姆电阻占主导(欧姆过电压变化值2 V, 开路电压变化0.05 V), 小时间尺度(ms)下C对动态性能起主导作用, 中时间尺度(s)下τe对动态特性影响较大, 大时间尺度(102—103 s)下T的作用较强, 并据此推导出了电池的多时间尺度模型. 本研究为后续电池能量管理、评价动态性能、精准控制提供参考依据及理论支撑.The current research on the dynamic performance of the proton exchange fuel cell is mostly aimed at the influence of operating parameters on the system, but does not involve with the dynamic characteristics of the cell on a multiple time scale nor the study of the corresponding multiple time scale model. In order to detect the dynamic changes of the proton exchange membrane fuel cell, the effects of various factors in the system on the output performance on different time scales are investigated. The effective partial pressure of oxygen and hydrogen are obtained by the mass diffusion equation and the ideal gas state equation, and the dynamic model is established according to the law of conservation of energy, the law of thermodynamics, and the electrochemical reaction equation. By setting the load mutations with a large/medium/small time scale dynamic duration of 0.6 s, 165 s, and16 min, respectively, the mechanism with which voltage suddenly changes when the load current changes abruptly is studied. Starting from the long time constant during which the dynamic performance takes effect, the control variable is used to analyze the double-layer charge. The influences of layer effect capacitance C, fuel oxidant delay time constant τe, and thermodynamic characteristics (temperature T) on the dynamic performance ( initial values of variables: C = 4 F, τe = 80 s, and T = 307.7 K) clarify the action intensities on different time scales. With the help of Matlab/Sumlink platform the simulation results are obtained and the correctness and effectiveness of the built model are verified. The simulation results show that the sudden change in voltage is due to the open circuit voltage and Ohmic polarization resistance, and the Ohmic resistance is dominant (the Ohmic overvoltage change value is 2 V, and the open circuit voltage change is 0.05 V), and the C pair dynamics on a small time scale (ms). The performance plays a leading role. Specifically, τe has a greater effect on the dynamic characteristics on a medium time scale (s), and T has a stronger effect on a large time scale (102–103 s). Based on the above deduction, a multi-time scale model of the battery is derived. The research provides the reference and theoretical support for subsequent battery energy management, evaluation of dynamic performance, and precise control.
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Keywords:
- proton exchange membrane fuel cell /
- multi-time scale analysis analysis /
- dynamic response characteristics /
- load mutation
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图 7 小时间尺度下负载阶跃变化时输出波形
Fig. 7. Output waveform when the load step changes in a small time scale.
图 8 小时间尺度下负载阶跃变化时的电压输出波形
Fig. 8. Voltage output waveform when the load step changes in a small time scale.
图 9 中时间尺度下负载阶跃变化时的输出波形
Fig. 9. Output waveform when the load step changes on the medium time scale.
图 10 中时间尺度下负载阶跃变化时的电压输出波形
Fig. 10. Voltage output waveform when the load step changes on the medium time scale.
图 11 大时间尺度下负载阶跃变化时的输出波形
Fig. 11. Output waveform when the load step changes on a large time scale.
图 12 大时间尺度下负载阶跃变化时的电压输出波形
Fig. 12. Voltage output waveform when the load step changes on a large time scale.
表 1 仿真参数值
Table 1. Simulation parameter values.
参数 数值 参数 数值 参数 数值 λe/Ω 0.00333 A/cm2 230 Pcathode/atm 1.0 τe/s 80.0 Mfc·Cfc/(J·K–1) 22000 初始温度Tinitial/K 307.7 N/个 48 Troom/K 307.7 J/(mA·cm–2) 5 h/(W·(m2·K)–1) 37.5 Panode/atm 1.5 电堆C/F 4.8 
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[1] 王季康, 李华, 彭宇飞, 李晓燕, 张新宇 2022 电子测量技术 45 22
Google Scholar
Wang J K, Li H, Pei Y F, Li X Y, Zhang X Y 2022 Elec. Mea. Tech. 45 22
Google Scholar
[2] 曲炳旺, 陈会翠, 邢夏杰, 章桐 2017 同济大学学报: 自然科学版 45 110
Google Scholar
Qu B W, Chen H C, Xing X J, Zhang T 2017 J. Tongji Univ.: Nat. Sci. Ed. 45 110
Google Scholar
[3] Wang X D, Xu J L, Yan W M, Lee D J, Ay S 2011 Int. J. Heat Mass Transf. 54 2375
Google Scholar
[4] Li H Y, Weng W C, Yan W M, Wang X D 2011 J. Power Sources 196 235
Google Scholar
[5] Ceraolo M, Miulli C, Pozio A 2003 J. Power Sources 113 131
Google Scholar
[6] Yan W M, Soong C Y, Chen F, Chu H S 2005 J. Power Sources 143 48
Google Scholar
[7] Chugh S, Chaudhari C, Sonkar K, Sharma A, Kapur G S, Ramakumar S S V 2020 Int. J. Hydrog. 45 8866
Google Scholar
[8] 皇甫宜耿, 任子俊, 张羽翔, 马睿 2020 电力电子技术 54 44
Google Scholar
Huangfu Y G, Ren Z J, Zhang Y X, Ma R 2020 Pow. Elec. 54 44
Google Scholar
[9] 肖燕, 常英杰, 张伟, 贾秋红 2018 电化学 24 166
Google Scholar
Xiao Y, Chang Y J, Zhang W, Jia Q H 2018 J. Electrochem. 24 166
Google Scholar
[10] 刘鹏程, 许思传 2021 化工进展 40 3172
Google Scholar
Liu P C, Xu S J 2021 Chem. Ind. Eng. Prog. 40 3172
Google Scholar
[11] Henning L B, Kevin S, Micchael D, Xin Y L, Amgad E, Michael W Thomas W, Brad R, Martha C 2020 Int. J. Hydrog. 45 861
Google Scholar
[12] 李威尔, 孙超, 霍为炜, 龚国庆 2021 电池 51 238
Google Scholar
Li W E, Su C, Huo W W, Gong G Q 2021 Battery 51 238
Google Scholar
[13] 闫飞宇, 李伟卓, 杨卫卫, 何雅玲 2019 中国科学: 技术科学 49 391
Google Scholar
Yan F Y, Li W Z, Yang W W, He Y L 2019 Sci. China Ser.: Technol. Sci 49 391
Google Scholar
[14] 肖伟强 2021 电池 51 429
Xiao W Q 2021 Battery 51 429
[15] Amanda L A, Imene Y, Jussara F F, Lucas F E, Fernando T 2020 Int. J. Hydrog. 45 30870
Google Scholar
[16] 柯超, 甘屹, 王胜佳, 何雅玲, 朱荣杰, 陈伟 2021 太阳能学报 42 488
Google Scholar
Ke C, Gan Q, Wang S S, Zhu R J 2021 Acta Energ. Solaris Sin. 42 488
Google Scholar
[17] Hashem M N, Wang C 2009 Modeling and Control of Fuel Cells: Distrbuted Generation Application (Hoboken: Wiley-IEEE Press) pp57–87
[18] Colleen S 2008 PEM Fuel Cell Modeling and Simulation Using Matlab (Amsterdam: Elsevier Press) pp99–125
[19] 戴海峰, 袁浩, 鱼乐, 魏学哲 2020 同济大学学报: 自然科学版 48 880
Google Scholar
Dai H F, Yan H, Yu L, Wei X Z 2020 J. Tongji Univ. :Nat. Sci. Ed. 48 880
Google Scholar
[20] 孙术发, 杨洁, 唐华林, 朱荣杰, 葛安华, 邢 涛, 马超 2019 哈尔滨工业大学学报 51 144
Google Scholar
Sun S F, Yang J, Tang H L, Ge A H, Xing T, Ma C 2019 J. Harbin. Inst. Technol. 51 144
Google Scholar
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