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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 1 PEMFC结构
Figure 1. PEMFC structure.
图 2 PEMFC等效电路
Figure 2. PEMFC equivalent circuit.
图 3 PEMFC 动态模型框图
Figure 3. PEMFC dynamic model block diagram.
图 4 PEMFC电压子模型
Figure 4. PEMFC voltage sub-model.
图 5 PEMFC模型U-I及P-I曲线
Figure 5. PEMFC model U-I and P-I curves.
图 6 负载阶跃变化时各输出电压波形
Figure 6. Each output voltage waveform when the load step changes.
图 7 小时间尺度下负载阶跃变化时输出波形
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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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