綠能系統逐漸成為二十一世紀發電儲電主流，為達成有效設計與控制系統的效能，參數鑑定是一項至關重要工作，然而目前商用綠能系統難以直接從製造廠商獲得詳細之內部參數數據。本研究將探討三種主流的綠色能源系統，包含光伏太陽電池、質子交換膜燃料電池及鋰離子電池等。應用強健性高之群體智慧演算法預測這三種系統之模型參數，以辨識並取得高精確度的參數值有效地提供預測各系統模組在不同工作條件下的效能。
本論文提出一種使用廣義增量規則來更新粒子速度以求得全域最佳值的動量形式粒子群體智慧演算法並應用於綠能系統之參數辨識問題上。首先本研究以拉伸/壓縮彈簧、壓力容器、焊接組合鋼樑三種基準範例工程最佳化問題執行演算法之強健度測試以確認演算法之有效性後再進行前述之三種能源模組參數辨識。分析解包含有目標函數值的收斂率、解答精確性及平均絕對誤差與標準差。本論文之光伏太陽電池使用二極體電路模型，而質子交換膜燃料電池及鋰離子電池均使用電化學模型。透過動量型式粒子群體智慧演算法最佳化計算獲得這些綠能系統內之模組參數後將可掌控系統內之電池電極、電解質與隔離膜之間的化學反應機制。
由三種工程最佳化的問題之參數最佳化結果顯示出動量型粒子群體智慧演算法具有相當好的最佳化函數值求解能力和演算法穩健性。進一步在能源系統的參數最佳化結果顯示光伏太陽電池電壓的均方根誤差為8.839E-4 V，而質子交換膜燃料電池電壓的平方誤差和為2.0656 V。在鋰離子電池動態負載模型分析上，本論文亦建置了鋰離子電池實驗平台進行實驗，以提供模組分析之效能比對驗證。由實驗與分析結果比對後，鋰離子電池的電壓平均絕對誤差為3.6350 mV，預測1 C充放電的SOC為0.0139 %。將參數套入2C、0.5C以及路況動態效能驗證中，鋰離子電池端電壓的誤差小於0.5 %，電池之SOC小於0.8 %。從計算結果顯示動量粒子群體演算法可以有效率地計算出電池模組之待定參數的最佳化值，相當適合應用在需要高精準度之綠能系統的電池動態負載模型效能預測上。

Green energy systems have gradually become the mainstream of power generation and storage in the 21st century. In order to achieve effective design and control system performance, parameter identification is a vital task. However, it is difficult for commercial green energy systems to obtain detailed data of internal parameters directly from manufacturers. This thesis will investigate three mainstream green energy systems, including photovoltaic solar cells, proton exchange membrane fuel cells, and lithium-ion batteries. The use of highly robust swarm intelligence algorithm to predict the model parameters of these three systems can identify and obtain high-precision values of parameters to effectively predict the performance of each system model under different working conditions.
This thesis proposes a momentum particle swarm intelligence algorithm that uses the generalized delta rule to update the particle’s velocity to obtain the global optimal value and applies it to the parameter identification problem of the green energy system. First, in this study, three benchmark engineering optimization problems of tension/compression springs, pressure vessels, and welded composite steel beams were used to perform the robustness test of the algorithm to confirm the effectiveness of the algorithm, and then parameter identifications were performed of the aforementioned three energy modules. The analyzed solution includes the convergence rate of the objective function value, the accuracy of the solution, and the average absolute error and standard deviation. The photovoltaic solar cell in this study uses the diode circuit model, while the proton exchange membrane fuel cell and lithium ion battery both use the electrochemical model. After obtaining these module parameters in the green energy system through the optimization calculation using the momentum-type particle swarm intelligent algorithm, the chemical reaction mechanism between the battery electrodes, electrolyte and separator in the system can be controlled.
The parameter optimization results of the three engineering optimization problems show that the momentum-type particle swarm intelligence algorithm has a very good capability to achieve the optimal function value and the robustness of the algorithm. Moreover, the parameter optimization results in the energy system show that the root mean square error of photovoltaic solar cells is 8.839E-4 V, while the sum of square errors of proton exchange membrane fuel cells is 2.0656 V. In the analysis of the dynamic load model of lithium-ion battery, this thesis also built a lithium-ion battery experimental platform for experiments to provide performance comparison verification for module analysis. After comparing the experimental and analytical results, the average absolute error of the voltage of the lithium-ion battery is 3.6350 mV, and the SOC of 1C charge and discharge is predicted to be 0.0139%. Applying the parameters to 2C, 0.5C and dynamic performance verification on road conditions, the error of the lithium-ion battery terminal voltage is less than 0.5%, and the battery SOC is less than 0.8%. The calculation results show that the momentum particle swarm algorithm can efficiently calculate the optimal value of the undetermined parameters of the battery module, so it is quite suitable for application in the performance prediction of the battery dynamic load model of the green energy system that requires high accuracy.

摘要 I
Abstract III

目錄 V
圖目錄 VII
表目錄 IX
符號列表 X
1 緒論 1
1.1 研究背景 1
1.2 研究動機 3
1.3 研究流程 3
1.4 文獻回顧 5
1.4.1 群體智慧演算法 5
1.4.4 氫能燃料電池 11
1.4.5 鋰離子電池 13
1.4.6 全球調和輕型車輛測試程序 17
2 系統模組建立 18
2.1 動量型粒子群體智慧演算法 18
2.2 多限制式之工程最佳化設計問題 22
2.3 光伏太陽電池模組 26
2.4 質子交換膜燃料電池 27
2.5 鋰離子電池模組 33
3 系統參數設定與電池實驗平台建置 39
3.1 研究流程 39
3.1.1 非線性工程最佳化問題參數設定 40
3.1.2 光伏太陽電池參數設定 41
3.1.3 氫能燃料電池參數設定 42
3.2 鋰離子電池參數設定與實驗平台建置 44
3.2.1 鋰離子電池待定參數設定 44
3.2.2 鋰離子電池實驗平台建置 45
4 結果與討論 48
4.1 動量型粒子群體智慧演算法強健性測試 48
4.1.1 拉伸/壓縮彈簧設計最佳化問題 48
4.1.2 壓力容器設計最佳化問題 49
4.1.3 焊接組合鋼樑設計最佳化問題 51
4.2 光伏太陽電池參數最佳化 53
4.3 氫能燃料電池參數最佳化 58
5 結論與未來研究方向 73
5.1 結論 73
5.2 未來研究方向 74
參考文獻 76
附錄A　 光伏打太陽電池之終端電流計算值及參數解與實驗值及其他演算法之結果比較 88
附錄B　 PEMFC電池之堆棧電壓計算值及參數解與實驗值及其他演算法之結果比較 90

[1] C. Le Quéré et al., “Temporary reduction in daily global CO 2 emissions during the COVID-19 forced confinement,” Nature Climate Change, vol. 10, no. 7, pp. 647-653, 2020.
[2] J. Moor, “The Dartmouth College artificial intelligence conference: The next fifty years,” Ai Magazine, vol. 27, no. 4, pp. 87-87, 2006.
[3] M. Dorigo, M. Birattari, and T. Stutzle, “Ant colony optimization,” IEEE computational intelligence magazine, vol. 1, no. 4, pp. 28-39, 2006.
[4] D. Karaboga and B. Basturk, "On the performance of artificial bee colony (ABC) algorithm," Applied soft computing, vol. 8, no. 1, pp. 687-697, 2008.
[5] J. Y. Liu, M. Z. Guo, and C. Deng, “GeesePSO: An efficient improvement to particle swarm optimization,” Computer Science, vol. 33, no. 11, pp. 166-168, 2006.
[6] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN'95-international conference on neural networks, 1995, vol. 4, pp. 1942-1948: IEEE.
[7] S. Mirjalili and A. Lewis, “The whale optimization algorithm,” Advances in engineering software, vol. 95, pp. 51-67, 2016.
[8]D. Whitley, “A genetic algorithm tutorial,” Statistics and computing, vol. 4, no. 2, pp. 65-85, 1994.
[9] R. C. Eberhart and Y. Shi, “Comparing inertia weights and constriction factors in particle swarm optimization,” in Proceedings of the 2000 congress on evolutionary computation. CEC00 (Cat. No. 00TH8512), 2000, vol. 1, pp. 84-88: IEEE.
[10] K. E. Parsopoulos and M. N. Vrahatis, “UPSO: A unified particle swarm optimization scheme,” in International Conference of Computational Methods in Sciences and Engineering 2004 (ICCMSE 2004), 2019, pp. 868-873: CRC Press.
[11] F. J. Toledo, J. M. Blanes, and V. Galiano, “Two-step linear least-squares method for photovoltaic single-diode model parameters extraction,” IEEE Transactions on Industrial Electronics, vol. 65, no. 8, pp. 6301-6308, 2018.
[12] F. Dkhichi, B. Oukarfi, A. Fakkar, and N. Belbounaguia, “Parameter identification of solar cell model using Levenberg–Marquardt algorithm combined with simulated annealing,” Solar Energy, vol. 110, pp. 781-788, 2014.
[13] H. Andrei, T. Ivanovici, G. Predusca, E. Diaconu, and P. Andrei, “Curve fitting method for modeling and analysis of photovoltaic cells characteristics,” in Proceedings of 2012 IEEE International Conference on Automation, Quality and Testing, Robotics, 2012, pp. 307-312: IEEE.
[14] Y.-P. Huang and S.-Y. Hsu, “A performance evaluation model of a high concentration photovoltaic module with a fractional open circuit voltage-based maximum power point tracking algorithm,” Computers & Electrical Engineering, vol. 51, pp. 331-342, 2016.
[15] B. Cortés, R. T. Sánchez, and J. J. Flores, “Characterization of a polycrystalline photovoltaic cell using artificial neural networks,” Solar Energy, vol. 196, pp. 157-167, 2020.
[16] A. Khare and S. Rangnekar, “A review of particle swarm optimization and its applications in solar photovoltaic system,” Applied Soft Computing, vol. 13, no. 5, pp. 2997-3006, 2013.
[17] D. Oliva, E. Cuevas, and G. Pajares, “Parameter identification of solar cells using artificial bee colony optimization,” Energy, vol. 72, pp. 93-102, 2014.
[18] S. Gude and K. C. Jana, “Parameter extraction of photovoltaic cell using an improved cuckoo search optimization,” Solar Energy, vol. 204, pp. 280-293, 2020.
[19] D. Oliva, M. Abd El Aziz, and A. E. Hassanien, “Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm,” Applied energy, vol. 200, pp. 141-154, 2017.
[20] M. Louzazni, A. Khouya, K. Amechnoue, A. Gandelli, M. Mussetta, and A. Crăciunescu, “Metaheuristic algorithm for photovoltaic parameters: comparative study and prediction with a firefly algorithm,” Applied Sciences, vol. 8, no. 3, p. 339, 2018.
[21] D. F. Alam, D. A. Yousri, and M. B. Eteiba, “Flower pollination algorithm based solar PV parameter estimation,” Energy Conversion and Management, vol. 101, pp. 410-422, 2015.
[22] J. Larminie, A. Dicks, and M. S. McDonald, Fuel cell systems explained. J. Wiley Chichester, UK, 2003.
[23] Y. Jiang, Z. Yang, K. Jiao, and Q. Du, "Sensitivity analysis of uncertain parameters based on an improved proton exchange membrane fuel cell analytical model," Energy Conversion and Management, vol. 164, pp. 639-654, 2018.
[24] D. Cheddie and N. Munroe, “Review and comparison of approaches to proton exchange membrane fuel cell modeling,” Journal of Power Sources, vol. 147, no. 1-2, pp. 72-84, 2005.
[25] J. J. Giner-Sanz, E. M. Ortega, and V. Pérez-Herranz, "Mechanistic equivalent circuit modelling of a commercial polymer electrolyte membrane fuel cell," Journal of Power Sources, vol. 379, pp. 328-337, 2018.
[26] D. Ouellette, C. O. Colpan, E. Matida, and C. A. Cruickshank, “A single domain approach to modeling the multiphase flow within a flowing electrolyte–direct methanol fuel cell,” International Journal of Hydrogen Energy, vol. 40, no. 24, pp. 7817-7828, 2015.
[27] B. Blunier and A. Miraoui, “Modelling of fuel cells using multi-domain VHDL-AMS language,” Journal of Power Sources, vol. 177, no. 2, pp. 434-450, 2008.
[28]Y. Song et al., “Review on current research of materials, fabrication and application for bipolar plate in proton exchange membrane fuel cell,” International Journal of Hydrogen Energy, vol. 45, no. 54, pp. 29832-29847, 2020
[29] S. Wu, X. Peng, L. Mao, A. Liu, L. Dong, and T. Wang, “On-line Fault Diagnosis of Proton Exchange Membrane Membrane Fuel Cell Using Polarization Curve,” in 2020 International Conference on Sensing, Measurement & Data Analytics in the era of Artificial Intelligence (ICSMD), 2020, pp. 7-10: IEEE.
[30] T. Wilberforce and A. G. Olabi, “Proton exchange membrane fuel cell performance prediction using artificial neural network,” International Journal of Hydrogen Energy, vol. 46, no. 8, pp. 6037-6050, 2021
[31] M. M. Savrun and M. İnci, “Adaptive neuro-fuzzy inference system combined with genetic algorithm to improve power extraction capability in fuel cell applications,” Journal of Cleaner Production, vol. 299, p. 126944, 2021.
[32] W. Zou, D. Froning, Y. Shi, and W. Lehnert, “Working zone for a least-squares support vector machine for modeling polymer electrolyte fuel cell voltage,” Applied Energy, vol. 283, p. 116191, 2021
[33] J. Wishart, Z. Dong, and M. Secanell, “Optimization of a PEM fuel cell system based on empirical data and a generalized electrochemical semi-empirical model,” Journal of Power Sources, vol. 161, no. 2, pp. 1041-1055, 2006.
[34] A. P. Sasmito and A. S. Mujumdar, “Performance evaluation of a polymer electrolyte fuel cell with a dead-end anode: A computational fluid dynamic study,” International Journal of Hydrogen Energy, vol. 36, no. 17, pp. 10917-10933, 2011.
[35] P. E. Almeida and M. G. Simoes, “Neural optimal control of PEM-fuel cells with parametric CMAC networks,” in 38th IAS Annual Meeting on Conference Record of the Industry Applications Conference, 2003., 2003, vol. 2, pp. 723-730: IEEE.
[36] Z.-d. Zhong, H.-b. Huo, X.-j. Zhu, G.-y. Cao, and Y. Ren, “Adaptive maximum power point tracking control of fuel cell power plants,” Journal of Power Sources, vol. 176, no. 1, pp. 259-269, 2008
[37] W.-L. Yu, S.-J. Wu, and S.-W. Shiah, “Parametric analysis of the proton exchange membrane fuel cell performance using design of experiments,” International journal of hydrogen energy, vol. 33, no. 9, pp. 2311-2322, 2008.
[38] N. Chatrattanawet, T. Hakhen, S. Kheawhom, and A. Arpornwichanop, “Control structure design and robust model predictive control for controlling a proton exchange membrane fuel cell,” Journal of Cleaner Production, vol. 148, pp. 934-947, 2017
[39] P. Dobson, C. Lei, T. Navessin, and M. Secanell, “Characterization of the PEM fuel cell catalyst layer microstructure by nonlinear least-squares parameter estimation,” Journal of the Electrochemical Society, vol. 159, no. 5, p. B514, 2012.
[40] W.-Y. Chang, “Application of current switching method to estimate the model parameters of proton exchange membrane fuel cell,” Simulation Modelling Practice and Theory, vol. 18, no. 1, pp. 35-50, 2010.
[41] D. Kashyap et al., “Application of electrochemical impedance spectroscopy in bio-fuel cell characterization: A review,” International Journal of Hydrogen Energy, vol. 39, no. 35, pp. 20159-20170, 2014.
[42] I. Mohamed and N. Jenkins, “Proton exchange membrane (PEM) fuel cell stack configuration using genetic algorithms,” Journal of Power Sources, vol. 131, no. 1-2, pp. 142-146, 2004.
[43] M. Ye, X. Wang, and Y. Xu, “Parameter identification for proton exchange membrane fuel cell model using particle swarm optimization,” International Journal of hydrogen energy, vol. 34, no. 2, pp. 981-989, 2009.
[44] W. Zhang, N. Wang, and S. Yang, “Hybrid artificial bee colony algorithm for parameter estimation of proton exchange membrane fuel cell,” International journal of hydrogen energy, vol. 38, no. 14, pp. 5796-5806, 2013.
[45] A. A. El-Fergany, H. M. Hasanien, and A. M. Agwa, “Semi-empirical PEM fuel cells model using whale optimization algorithm,” Energy Conversion and Management, vol. 201, p. 112197, 2019.
[46] M. Ali, M. A. El-Hameed, and M. A. Farahat, “Effective parameters’ identification for polymer electrolyte membrane fuel cell models using grey wolf optimizer,” Renewable energy, vol. 111, pp. 455-462, 2017.
[47] B. G. Carkhuff, P. A. Demirev, and R. Srinivasan, “Impedance-based battery management system for safety monitoring of lithium-ion batteries,” IEEE Transactions on Industrial Electronics, vol. 65, no. 8, pp. 6497-6504, 2018.
[48] T. Feng, L. Yang, X. Zhao, H. Zhang, and J. Qiang, “Online identification of lithium-ion battery parameters based on an improved equivalent-circuit model and its implementation on battery state-of-power prediction,” Journal of Power Sources, vol. 281, pp. 192-203, 2015.
[49] S. Pramanik and S. Anwar, “Electrochemical model based charge optimization for lithium-ion batteries,” Journal of Power Sources, vol. 313, pp. 164-177, 2016.
[50] Y. Guo, Z. Zhao, and L. Huang, “SoC estimation of Lithium battery based on improved BP neural network,” Energy Procedia, vol. 105, pp. 4153-4158, 2017.
[51] H. He, R. Xiong, and J. Fan, “Evaluation of lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach,” energies, vol. 4, no. 4, pp. 582-598, 2011.
[52] S. Nejad, D. T. Gladwin, and D. A. Stone, “A systematic review of lumped-parameter equivalent circuit models for real-time estimation of lithium-ion battery states,” Journal of Power Sources, vol. 316, pp. 183-196, 2016.
[53] A. Jokar, B. Rajabloo, M. Désilets, and M. Lacroix, “Review of simplified Pseudo-two-Dimensional models of lithium-ion batteries,” Journal of Power Sources, vol. 327, pp. 44-55, 2016.
[54] X. Han, M. Ouyang, L. Lu, and J. Li, “Simplification of physics-based electrochemical model for lithium ion battery on electric vehicle. Part I: Diffusion simplification and single particle model,” Journal of Power Sources, vol. 278, pp. 802-813, 2015.
[55] L. Oca et al., "Physico-chemical parameter measurement and model response evaluation for a pseudo-two-dimensional model of a commercial lithium-ion battery," Electrochimica Acta, vol. 382, p. 138287, 2021.
[56] S. Piller, M. Perrin, and A. Jossen, "Methods for state-of-charge determination and their applications," Journal of power sources, vol. 96, no. 1, pp. 113-120, 2001.
[57] X. Dang, L. Yan, K. Xu, X. Wu, H. Jiang, and H. Sun, “Open-circuit voltage-based state of charge estimation of lithium-ion battery using dual neural network fusion battery model,” Electrochimica Acta, vol. 188, pp. 356-366, 2016.
[58] K. S. Ng, C.-S. Moo, Y.-P. Chen, and Y.-C. Hsieh, “Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries,” Applied energy, vol. 86, no. 9, pp. 1506-1511, 2009.
[59] M. Charkhgard and M. Farrokhi, “State-of-charge estimation for lithium-ion batteries using neural networks and EKF,” IEEE transactions on industrial electronics, vol. 57, no. 12, pp. 4178-4187, 2010.
[60] S. Sato and A. Kawamura, "A new estimation method of state of charge using terminal voltage and internal resistance for lead acid battery," in Proceedings of the Power Conversion Conference-Osaka 2002 (Cat. No. 02TH8579), 2002, vol. 2, pp. 565-570: IEEE.
[61] M. Tutuianu et al., “Development of a World-wide Worldwide harmonized Light duty driving Test Cycle (WLTC),” Technical Report, 2013.
[62] J.-L. Liu and J.-H. Lin, "Evolutionary computation of unconstrained and constrained problems using a novel momentum-type particle swarm optimization," Engineering Optimization, vol. 39, no. 3, pp. 287-305, 2007.
[63] S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey wolf optimizer,” Advances in engineering software, vol. 69, pp. 46-61, 2014.
[64] A. F. Nematollahi, A. Rahiminejad, and B. Vahidi, “A novel physical based meta-heuristic optimization method known as Lightning Attachment Procedure Optimization,” Applied Soft Computing, vol. 59, pp. 596-621, 2017.
[65] H. Zheng and Y. Zhou, “A Cooperative Coevolutionary Cuckoo Search Algorithm for Optimization Problem,” Journal of Applied Mathematics, vol. 2013, p. 912056, 2013/08/27 2013.
[66] A. Rowe and X. Li, “Mathematical modeling of proton exchange membrane fuel cells,” Journal of power sources, vol. 102, no. 1-2, pp. 82-96, 2001.
[67] T. E. Springer, T. A. Zawodzinski, and S. Gottesfeld, “Polymer electrolyte fuel cell model,” Journal of the electrochemical society, vol. 138, no. 8, p. 2334, 1991.
[68] K. Broka and P. Ekdunge, “Oxygen and hydrogen permeation properties and water uptake of Nafion® 117 membrane and recast film for PEM fuel cell,” Journal of applied electrochemistry, vol. 27, no. 2, pp. 117-123, 1997.
[69] M. Doyle, T. F. Fuller, and J. Newman, “Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell,” Journal of the Electrochemical society, vol. 140, no. 6, p. 1526, 1993.
[70] D.-W. Chung, M. Ebner, D. R. Ely, V. Wood, and R. E. García, “Validity of the Bruggeman relation for porous electrodes,” Modelling and Simulation in Materials Science and Engineering, vol. 21, no. 7, p. 074009, 2013.
[71] J. Li, X. Gao, Y. Cui, J. Hu, G. Xu, and Z. Zhang, “Accurate, efficient and reliable parameter extraction of PEM fuel cells using shuffled multi-simplexes search algorithm,” Energy Conversion and Management, vol. 206, p. 112501, 2020.
[72] R. F. Mann, J. C. Amphlett, M. A. I. Hooper, H. M. Jensen, B. A. Peppley, and P. R. Roberge, “Development and application of a generalised steady-state electrochemical model for a PEM fuel cell,” Journal of power sources, vol. 86, no. 1-2, pp. 173-180, 2000.
[73] Z. J. Mo, X. J. Zhu, L. Y. Wei, and G. Y. Cao, “Parameter optimization for a PEMFC model with a hybrid genetic algorithm,” International Journal of Energy Research, vol. 30, no. 8, pp. 585-597, 2006.
[74] M. Xu, Z. Zhang, X. Wang, L. Jia, and L. Yang, “A pseudo three-dimensional electrochemical–thermal model of a prismatic LiFePO4 battery during discharge process,” Energy, vol. 80, pp. 303-317, 2015.
[75] J. Chiew, C. S. Chin, W. D. Toh, Z. Gao, J. Jia, and C. Z. Zhang, “A pseudo three-dimensional electrochemical-thermal model of a cylindrical LiFePO4/graphite battery,” Applied Thermal Engineering, vol. 147, pp. 450-463, 2019.
[76] M. Farkhondeh et al., “Full-range simulation of a commercial LiFePO4 electrode accounting for bulk and surface effects: A comparative analysis,” Journal of The Electrochemical Society, vol. 161, no. 3, p. A201, 2013.
[77] M. M. Majdabadi, S. Farhad, M. Farkhondeh, R. A. Fraser, and M. Fowler, “Simplified electrochemical multi-particle model for LiFePO4 cathodes in lithium-ion batteries,” Journal of Power Sources, vol. 275, pp. 633-643, 2015.
[78] E. H. Houssein, M. R. Saad, F. A. Hashim, H. Shaban, and M. Hassaballah, “Lévy flight distribution: A new metaheuristic algorithm for solving engineering optimization problems,” Engineering Applications of Artificial Intelligence, vol. 94, p. 103731, 2020.
[79] Z. Meng, G. Li, X. Wang, S. M. Sait, and A. R. Yıldız, “A comparative study of metaheuristic algorithms for reliability-based design optimization problems,” Archives of Computational Methods in Engineering, vol. 28, pp. 1853-1869, 2021.
[80] T. Easwarakhanthan, J. Bottin, I. Bouhouch, and C. Boutrit, “Nonlinear minimization algorithm for determining the solar cell parameters with microcomputers,” International journal of solar energy, vol. 4, no. 1, pp. 1-12, 1986.
[81] N. Pourmousa, S. M. Ebrahimi, M. Malekzadeh, and M. Alizadeh, “Parameter estimation of photovoltaic cells using improved Lozi map based chaotic optimization Algorithm,” Solar Energy, vol. 180, pp. 180-191, 2019.
[82] N. T. Tong and W. Pora, “A parameter extraction technique exploiting intrinsic properties of solar cells,” Applied energy, vol. 176, pp. 104-115, 2016.
[83] W. Gong and Z. Cai, “Parameter extraction of solar cell models using repaired adaptive differential evolution,” Solar Energy, vol. 94, pp. 209-220, 2013.
[84] M. F. AlHajri, K. M. El-Naggar, M. R. AlRashidi, and A. K. Al-Othman, “Optimal extraction of solar cell parameters using pattern search,” Renewable Energy, vol. 44, pp. 238-245, 2012.
[85] K. M. El-Naggar, M. R. AlRashidi, M. F. AlHajri, and A. K. Al-Othman, “Simulated annealing algorithm for photovoltaic parameters identification,” Solar Energy, vol. 86, no. 1, pp. 266-274, 2012.
[86] J. Li, X. Gao, Y. Cui, J. Hu, G. Xu, and Z. Zhang, “Accurate, efficient and reliable parameter extraction of PEM fuel cells using shuffled multi-simplexes search algorithm,” Energy Conversion and Management, vol. 206, p. 112501, 2020.
[87] M. Kandidayeni, A. Macias, A. Khalatbarisoltani, L. Boulon, and S. Kelouwani, “Benchmark of proton exchange membrane fuel cell parameters extraction with metaheuristic optimization algorithms,” Energy, vol. 183, pp. 912-925, 2019.
[88] A. A. El-Fergany, “Extracting optimal parameters of PEM fuel cells using salp swarm optimizer,” Renewable Energy, vol. 119, pp. 641-648, 2018.
[89] Y. Cao, X. Kou, Y. Wu, K. Jermsittiparsert, and A. Yildizbasi, “PEM fuel cells model parameter identification based on a new improved fluid search optimization algorithm,” Energy Reports, vol. 6, pp. 813-823, 2020.
[90] E. A. Gouda, M. F. Kotb, and A. A. El-Fergany, “Jellyfish search algorithm for extracting unknown parameters of PEM fuel cell models: Steady-state performance and analysis,” Energy, vol. 221, p. 119836, 2021.