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Optimal Parameter Estimation of Proton Exchange Membrane Fuel Cell Based on Improved Particle Swarm Optimization Algorithm
DOI: 10.12677/AEPE.2021.95025, PDF, HTML, XML, 下载: 500  浏览: 765  科研立项经费支持

Abstract: Precise modeling of proton exchange membrane fuel cell (PEMFC) is helpful to predict its perfor-mance more accurately. In this paper, the mathematical modeling of the proton exchange mem-brane fuel cell is firstly carried out, proposing an Improved Particle Swarm Optimization (IPSO) al-gorithm, by comparing the improved particle swarm optimization (IPSO) algorithm, the basic parti-cle swarm algorithm (PSO) and genetic algorithm (GA) for the parameter estimation. The results show that the improved particle swarm optimization (IPSO) algorithm to the results of the proton exchange membrane model parameter estimation algorithm is more accurate than the other two. The polarization curves of fuel cells at different temperatures and pressures can be predicted by using the improved particle swarm optimization algorithm (IPSO). The results show that the im-proved particle swarm optimization algorithm (IPSO) has a strong searching ability and accurate searching results.

1. 引言

2. PEMFC的数学模型

PEMFC是一种高效、清洁的能量转换装置，与其他种类的燃料电池比较，它的内部反应相对简单，它将氢气和氧气的化学能转化为电能。PEMFC的简化结构如图1所示，如图为质子交换膜燃料电池的整体结构，图2为质子交换膜燃料电池的膜电极，图3为最常用的内部流道，通常为蛇形流道。PEMFC由阳极和阴极还有膜电极构成，膜电极将PEMFC阴极阳极隔开，它允许质子通过，不允许电子通过。在阳极通入氢气，在催化剂的作用下，一个氢分子被转化为两个质子并生成两个电子，如式(1)，质子可以穿过中间膜，电子则通过外部电路到达阴极。质子在阴极催化环境下，与通入的氧气形成水和热，如式(2)，总反应式(3)。如果将一个个PEMFC单体串联起来，那么就可以获得更大的功率。

Figure 1. Simplified structure of PEMFC

Figure 2. Membrane electrode for PEMFC

Figure 3. Common flow channel of PEMFC

${\text{H}}_{2}\to 2{\text{H}}^{+}+2{\text{e}}^{-}$ (1)

${O}_{2}+4{H}^{+}+4{e}^{-}\to 2{H}_{2}O+Heat$ (2)

$2{H}_{2}+{O}_{2}\to 2{H}_{2}O+Heat+Electricity$ (3)

$E=n×\left({E}_{N}-{E}_{act}-{E}_{\Omega }-{E}_{con}\right)$ (4)

${E}_{N}=1.229-8.5×{10}^{-4}\left({T}_{PEM}-298.15\right)+4.31×{10}^{-5}×{T}_{PEM}×\mathrm{ln}\left({P}_{{H}_{2}}\sqrt{{P}_{{O}_{2}}}\right)$ (5)

${P}_{{H}_{2}}=\frac{{R}_{ha}×{P}_{{H}_{2}O}}{2}×\left[\frac{1}{\frac{{R}_{ha}×{P}_{{H}_{2}O}}{{P}_{a}}×{\text{e}}^{\frac{1.635{I}_{PEM}/A}{{T}_{PEM}^{1.334}}}}-1\right]$ (6)

${P}_{{O}_{2}}={R}_{hc}×{P}_{{H}_{2}O}×\left[\frac{1}{\frac{{R}_{hc}×{P}_{{H}_{2}O}}{{P}_{c}}×{\text{e}}^{\frac{1.635{I}_{PEM}/A}{{T}_{PEM}^{1.334}}}}-1\right]$ (7)

$\begin{array}{c}{\mathrm{log}}_{10}\left({P}_{{H}_{2}O}\right)=2.95×{10}^{-2}\left({T}_{PEM}-273.15\right)-9.18×{10}^{-5}{\left({T}_{PEM}-273.15\right)}^{2}\\ \text{\hspace{0.17em}}\text{ }+1.44×{10}^{-7}{\left({T}_{PEM}-273.15\right)}^{3}-2.18\end{array}$ (8)

${E}_{act}=-\left[{\beta }_{1}+{\beta }_{2}×{T}_{PEM}+{\beta }_{3}×{T}_{PEM}×\mathrm{ln}\left({C}_{{O}_{2}}\right)+{\beta }_{4}×{T}_{PEM}×\mathrm{ln}\left({I}_{PEM}\right)\right]$ (9)

${\beta }_{2}=2.86×{10}^{-3}+2×{10}^{-4}×\mathrm{ln}\left(A\right)+4.3×{10}^{-5}×\mathrm{ln}\left({C}_{{H}_{2}}\right)$ (10)

${C}_{{O}_{2}}=\frac{{P}_{{O}_{2}}}{5.08×{10}^{6}}×{\text{e}}^{\frac{498}{{T}_{PEM}}}$ (11)

${C}_{{H}_{2}}=\frac{{P}_{{H}_{2}}}{1.09×{10}^{6}}×{\text{e}}^{-\frac{77}{{T}_{PEM}}}$ (12)

${E}_{\Omega }={I}_{PEM}×\left({R}_{m}+{R}_{c}\right)$ (13)

${R}_{m}=\frac{{\rho }_{m}×l}{A}$ (14)

${\rho }_{m}=\frac{181.6×\left[1+0.03\left(\frac{{I}_{PEM}}{A}\right)+0.062×{\left(\frac{{T}_{PEM}}{303}\right)}^{2}×{\left(\frac{{I}_{PEM}}{A}\right)}^{2.5}\right]}{\left[\lambda -0.634-3\left(\frac{{I}_{PEM}}{A}\right)\right]×{\text{e}}^{4.18×\frac{{T}_{PEM-303}}{{T}_{PEM}}}}$ (15)

${E}_{con}=-\beta ×\mathrm{ln}\left(\frac{{J}_{\mathrm{max}}-J}{{J}_{\mathrm{max}}}\right)$ (16)

Econ表示浓度压降，β为参数系数，J为实际电流密度(Acm−2)，Jmax为电流密度的最大值(Acm−2)。

Table 1. Upper and lower limits of model parameters

3. 目标函数

PEMFC的模型参数由以上六个未知数构成，将由算法分别优化每一个参数，在解决这个优化问题的时候，模型的准确性可由下述的公式验证，如公式(17)，使用MATLAB软件建模，目的是最小化实验电压和估计电压误差平方和SSE，SSE的值越小，说明模型确精确。

$Min\left(SSE\right)=Min\underset{k=1}{\overset{N}{\sum }}{\left({V}_{k}^{est}-{V}_{k}^{exp}\right)}^{2}$ (17)

4. 改进的粒子群算法

4.1. 基本粒子群算法

${v}_{id}^{k}=\omega \ast {v}_{id}^{k-1}+{c}_{1}\ast {r}_{1}\ast \left(pbes{t}_{id}-{x}_{id}^{k-1}\right)+{c}_{2}\ast {r}_{2}\ast \left(gbes{t}_{d}-{x}_{id}^{k-1}\right)$ (18)

${x}_{id}^{k}={x}_{id}^{k-1}+{v}_{id}^{k}$ (19)

4.2. 改进的粒子群算法

${\omega }_{id}=\left\{\begin{array}{l}{\omega }_{\mathrm{min}}+\left({\omega }_{\mathrm{max}}-{\omega }_{\text{average}}\right)\ast {\text{e}}^{\frac{f\left({x}_{id}\right)-1}{{f}_{\text{average}}^{d}-{f}_{\mathrm{min}}^{d}}},f\left({x}_{id}\right)\le {f}_{\text{average}}^{d}\\ {\omega }_{\mathrm{max}},\text{else}\end{array}$ (20)

5. 仿真结果

Table 2. Specific parameters of BCS 500-W fuel cell

Table 3. SSE validation of BCS 500-W fuel cell

Figure 4. Polarization curves of BCS 500-W fuel cell

Figure 5. Polarization curves of BCS 500-W PEMFC at different partial pressures

Figure 6. Polarization curves of BCS 500-W PEMFC at different temperatures

6. 结论

 [1] 叶可. 燃料电池供给系统关键参数对其性能影响的研究[D]: [硕士学位论文]. 长春: 吉林大学, 2020. [2] 梅明鋆, 赵博. 改善大气环境和能源危机的太阳能潜力分析[J]. 技术市场, 2021, 28(2): 128-129. [3] 曹继雷. 氢能支撑的风-燃气耦合低碳微网容量优化配置研究[D]: [硕士学位论文]. 大连: 大连理工大学, 2021. [4] 赵俊杰, 涂正凯. 高温车用燃料电池的发展及现状综述[J]. 化工进展, 2020, 39(5): 1722-1733. [5] Sharaf, O.Z. and Orhan, M.F. (2014) An Overview of Fuel Cell Technology: Fundamentals and Applications. Renewable and Sustainable Energy Reviews, 32, 810-853. https://doi.org/10.1016/j.rser.2014.01.012 [6] 陈怡萍. 布谷鸟算法及应用研究[D]: [硕士学位论文]. 杭州: 浙江大学, 2019. [7] 吕慧珍. DNA遗传算法及其在燃料电池中的应用研究[D]: [硕士学位论文]. 杭州: 浙江工业大学, 2015. [8] 谢宏远, 刘逸, 候权, 徐心海. 基于粒子滤波和遗传算法的氢燃料电池剩余使用寿命预测[J]. 东北电力大学学报, 2021, 41(1): 56-64. [9] 李奇, 陈维荣, 刘述奎, 林川, 贾俊波. 基于自适应聚焦粒子群算法的质子交换膜燃料电池机理建模[J]. 中国电机工程学报, 2009, 29(20): 119-124. [10] Kennedy, J. and Eberhart, R. (1995) Particle Swarm Optimization. Proceedings of ICNN’95-International Conference on Neural Networks, Perth, Australia, 27 November-1 December 1995, 1942-1948. [11] Omran, A., Luc-chesi, A., Smith, D., et al. (2021) Mathematical Model of a Proton-Exchange Membrane (PEM) Fuel Cell. International Journal of Thermofluids, 11, Article No. 100110. https://doi.org/10.1016/j.ijft.2021.100110 [12] El-Fergany, A.A. (2018) Extracting Optimal Parameters of PEM Fuel Cells Using Salp Swarm Optimizer. Renewable Energy, 119, 641-648. https://doi.org/10.1016/j.renene.2017.12.051