IDEAS home Printed from https://ideas.repec.org/a/eee/energy/v264y2023ics0360544222030511.html
   My bibliography  Save this article

An innovative approach for mathematical modeling and parameter estimation of PEM fuel cells based on iterative Lambert W function

Author

Listed:
  • Ćalasan, Martin
  • Abdel Aleem, Shady H.E.
  • Hasanien, Hany M.
  • Alaas, Zuhair M.
  • Ali, Ziad M.

Abstract

In the literature, identifying the parameters of proton exchange membrane fuel cells (PEMFCs) relies on minimizing the difference between measured and simulated voltage values for different current values. In this regard, expressions representing the PEMFC voltage as a current function are usually used. Unlike literature approaches, in this work, a new mathematical expression of PEMFC current as a voltage function is derived and solved using the iterative Lambert W function for the first time in literature. The root-mean-square error (RMSE) and sum-of-squares error (SSE) between the measured and estimated current and voltage values are calculated, analyzed, and discussed using the parameters obtained from many optimization methods for two PEMFCs – Ballard-Mark-V 5 kW and BCS 500 W. An improved evaporation rate water cycle algorithm (ERWCA), named Chaotic ERWCA (ChERWCA), is employed to solve the new PEMFC parameter estimation problem based on minimizing SSE between the measured and estimated current values obtained using the new mathematical model. Moreover, SSE and RMSE of voltage and current measures were calculated for different recent methods presented in the literature. The results validate the effectiveness of the new mathematical model and show that the solutions obtained using ChERWCA outperformed those obtained by other methods presented for these fuel cells in the literature. The improvement of voltage SSE using the new mathematical formulation of the PEMFC model and the proposed algorithm is about 0.1% compared to the best result reported in the literature. Finally, this work lays the foundation for developing a novel mathematical model to investigate the operation of PEMFCs in modern power systems.

Suggested Citation

  • Ćalasan, Martin & Abdel Aleem, Shady H.E. & Hasanien, Hany M. & Alaas, Zuhair M. & Ali, Ziad M., 2023. "An innovative approach for mathematical modeling and parameter estimation of PEM fuel cells based on iterative Lambert W function," Energy, Elsevier, vol. 264(C).
    • Handle: RePEc:eee:energy:v:264:y:2023:i:c:s0360544222030511
    DOI: 10.1016/j.energy.2022.126165
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0360544222030511
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.energy.2022.126165?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Priya, K. & Sathishkumar, K. & Rajasekar, N., 2018. "A comprehensive review on parameter estimation techniques for Proton Exchange Membrane fuel cell modelling," Renewable and Sustainable Energy Reviews, Elsevier, vol. 93(C), pages 121-144.
    2. Song, Zhen & Pan, Yue & Chen, Huicui & Zhang, Tong, 2021. "Effects of temperature on the performance of fuel cell hybrid electric vehicles: A review," Applied Energy, Elsevier, vol. 302(C).
    3. Jerry L. Holechek & Hatim M. E. Geli & Mohammed N. Sawalhah & Raul Valdez, 2022. "A Global Assessment: Can Renewable Energy Replace Fossil Fuels by 2050?," Sustainability, MDPI, vol. 14(8), pages 1-22, April.
    4. Martin Ćalasan & Mujahed Al-Dhaifallah & Ziad M. Ali & Shady H. E. Abdel Aleem, 2022. "Comparative Analysis of Different Iterative Methods for Solving Current–Voltage Characteristics of Double and Triple Diode Models of Solar Cells," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    5. Fathy, Ahmed & Elaziz, Mohamed Abd & Alharbi, Abdullah G., 2020. "A novel approach based on hybrid vortex search algorithm and differential evolution for identifying the optimal parameters of PEM fuel cell," Renewable Energy, Elsevier, vol. 146(C), pages 1833-1845.
    6. Li, Jing & Zuo, Wei & E, Jiaqiang & Zhang, Yuntian & Li, Qingqing & Sun, Ke & Zhou, Kun & Zhang, Guangde, 2022. "Multi-objective optimization of mini U-channel cold plate with SiO2 nanofluid by RSM and NSGA-II," Energy, Elsevier, vol. 242(C).
    7. Pan, Mingzhang & Li, Chao & Liao, Jinyang & Lei, Han & Pan, Chengjie & Meng, Xianpan & Huang, Haozhong, 2020. "Design and modeling of PEM fuel cell based on different flow fields," Energy, Elsevier, vol. 207(C).
    8. Zhang, Xiaojie & Zhang, Tong & Chen, Huicui & Cao, Yinliang, 2021. "A review of online electrochemical diagnostic methods of on-board proton exchange membrane fuel cells," Applied Energy, Elsevier, vol. 286(C).
    9. Sharaf, Omar Z. & Orhan, Mehmet F., 2014. "An overview of fuel cell technology: Fundamentals and applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 32(C), pages 810-853.
    10. Zhang, Ziyu & Ding, Tao & Zhou, Quan & Sun, Yuge & Qu, Ming & Zeng, Ziyu & Ju, Yuntao & Li, Li & Wang, Kang & Chi, Fangde, 2021. "A review of technologies and applications on versatile energy storage systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 148(C).
    11. Abdollahipour, Armin & Sayyaadi, Hoseyn, 2022. "Optimal design of a hybrid power generation system based on integrating PEM fuel cell and PEM electrolyzer as a moderator for micro-renewable energy systems," Energy, Elsevier, vol. 260(C).
    12. Martin Ćalasan & Mihailo Micev & Ziad M. Ali & Ahmed F. Zobaa & Shady H. E. Abdel Aleem, 2020. "Parameter Estimation of Induction Machine Single-Cage and Double-Cage Models Using a Hybrid Simulated Annealing–Evaporation Rate Water Cycle Algorithm," Mathematics, MDPI, vol. 8(6), pages 1-29, June.
    13. Chadly, Assia & Azar, Elie & Maalouf, Maher & Mayyas, Ahmad, 2022. "Techno-economic analysis of energy storage systems using reversible fuel cells and rechargeable batteries in green buildings," Energy, Elsevier, vol. 247(C).
    14. Ijaodola, O.S. & El- Hassan, Zaki & Ogungbemi, E. & Khatib, F.N. & Wilberforce, Tabbi & Thompson, James & Olabi, A.G., 2019. "Energy efficiency improvements by investigating the water flooding management on proton exchange membrane fuel cell (PEMFC)," Energy, Elsevier, vol. 179(C), pages 246-267.
    15. Mohamed A. M. Shaheen & Hany M. Hasanien & Rania A. Turky & Martin Ćalasan & Ahmed F. Zobaa & Shady H. E. Abdel Aleem, 2021. "OPF of Modern Power Systems Comprising Renewable Energy Sources Using Improved CHGS Optimization Algorithm," Energies, MDPI, vol. 14(21), pages 1-21, October.
    16. Samuel Raafat Fahim & Hany M. Hasanien & Rania A. Turky & Abdulaziz Alkuhayli & Abdullrahman A. Al-Shamma’a & Abdullah M. Noman & Marcos Tostado-Véliz & Francisco Jurado, 2021. "Parameter Identification of Proton Exchange Membrane Fuel Cell Based on Hunger Games Search Algorithm," Energies, MDPI, vol. 14(16), pages 1-21, August.
    17. Zhang, Yuntian & Zuo, Wei & E, Jiaqiang & Li, Jing & Li, Qingqing & Sun, Ke & Zhou, Kun & Zhang, Guangde, 2022. "Performance comparison between straight channel cold plate and inclined channel cold plate for thermal management of a prismatic LiFePO4 battery," Energy, Elsevier, vol. 248(C).
    18. Rezk, Hegazy & Sayed, Enas Taha & Al-Dhaifallah, Mujahed & Obaid, M. & El-Sayed, Abou Hashema M. & Abdelkareem, Mohammad Ali & Olabi, A.G., 2019. "Fuel cell as an effective energy storage in reverse osmosis desalination plant powered by photovoltaic system," Energy, Elsevier, vol. 175(C), pages 423-433.
    19. Lyu, Zewei & Meng, Hao & Zhu, Jianzhong & Han, Minfang & Sun, Zaihong & Xue, Huaqing & Zhao, Yongming & Zhang, Fudong, 2020. "Comparison of off-gas utilization modes for solid oxide fuel cell stacks based on a semi-empirical parametric model," Applied Energy, Elsevier, vol. 270(C).
    20. Dimitrova, Zlatina & Nader, Wissam Bou, 2022. "PEM fuel cell as an auxiliary power unit for range extended hybrid electric vehicles," Energy, Elsevier, vol. 239(PA).
    21. Zuo, Wei & Zhang, Yuntian & E, Jiaqiang & Li, Jing & Li, Qingqing & Zhang, Guangde, 2022. "Performance comparison between single S-channel and double S-channel cold plate for thermal management of a prismatic LiFePO4 battery," Renewable Energy, Elsevier, vol. 192(C), pages 46-57.
    22. Kandidayeni, M. & Macias, A. & Khalatbarisoltani, A. & Boulon, L. & Kelouwani, S., 2019. "Benchmark of proton exchange membrane fuel cell parameters extraction with metaheuristic optimization algorithms," Energy, Elsevier, vol. 183(C), pages 912-925.
    23. Olabi, A.G. & Wilberforce, Tabbi & Abdelkareem, Mohammad Ali, 2021. "Fuel cell application in the automotive industry and future perspective," Energy, Elsevier, vol. 214(C).
    24. Rezk, Hegazy & Ferahtia, Seydali & Djeroui, Ali & Chouder, Aissa & Houari, Azeddine & Machmoum, Mohamed & Abdelkareem, Mohammad Ali, 2022. "Optimal parameter estimation strategy of PEM fuel cell using gradient-based optimizer," Energy, Elsevier, vol. 239(PC).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ziad M. Ali & Martin Calasan & Shady H. E. Abdel Aleem & Hany M. Hasanien, 2023. "On the Exact Analytical Formulas of Leakage Current-Based Supercapacitor Model Operating in Industrial Applications," Energies, MDPI, vol. 16(4), pages 1-22, February.
    2. Hassan Ali, Hossam & Fathy, Ahmed, 2024. "Reliable exponential distribution optimizer-based methodology for modeling proton exchange membrane fuel cells at different conditions," Energy, Elsevier, vol. 292(C).
    3. Ćalasan, Martin & Micev, Mihailo & Hasanien, Hany M. & Abdel Aleem, Shady H.E., 2024. "PEM fuel cells: Two novel approaches for mathematical modeling and parameter estimation," Energy, Elsevier, vol. 290(C).
    4. Ziad M. Ali & Martin Calasan & Shady H. E. Abdel Aleem & Francisco Jurado & Foad H. Gandoman, 2023. "Applications of Energy Storage Systems in Enhancing Energy Management and Access in Microgrids: A Review," Energies, MDPI, vol. 16(16), pages 1-41, August.
    5. Mohamed Ahmed Ali & Mohey Eldin Mandour & Mohammed Elsayed Lotfy, 2023. "Adaptive Estimation of Quasi-Empirical Proton Exchange Membrane Fuel Cell Models Based on Coot Bird Optimizer and Data Accumulation," Sustainability, MDPI, vol. 15(11), pages 1-20, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ćalasan, Martin & Micev, Mihailo & Hasanien, Hany M. & Abdel Aleem, Shady H.E., 2024. "PEM fuel cells: Two novel approaches for mathematical modeling and parameter estimation," Energy, Elsevier, vol. 290(C).
    2. Hasanien, Hany M. & Shaheen, Mohamed A.M. & Turky, Rania A. & Qais, Mohammed H. & Alghuwainem, Saad & Kamel, Salah & Tostado-Véliz, Marcos & Jurado, Francisco, 2022. "Precise modeling of PEM fuel cell using a novel Enhanced Transient Search Optimization algorithm," Energy, Elsevier, vol. 247(C).
    3. Zuo, Wei & Zhang, Yuntian & E, Jiaqiang & Huang, Yuhan & Li, Qingqing & Zhou, Kun & Zhang, Guangde, 2022. "Effects of multi-factors on performance of an improved multi-channel cold plate for thermal management of a prismatic LiFePO4 battery," Energy, Elsevier, vol. 261(PB).
    4. Ibrahim Alsaidan & Mohamed A. M. Shaheen & Hany M. Hasanien & Muhannad Alaraj & Abrar S. Alnafisah, 2021. "Proton Exchange Membrane Fuel Cells Modeling Using Chaos Game Optimization Technique," Sustainability, MDPI, vol. 13(14), pages 1-24, July.
    5. Zhang, Yuntian & Zuo, Wei & E, Jiaqiang & Li, Jing & Li, Qingqing & Sun, Ke & Zhou, Kun & Zhang, Guangde, 2022. "Performance comparison between straight channel cold plate and inclined channel cold plate for thermal management of a prismatic LiFePO4 battery," Energy, Elsevier, vol. 248(C).
    6. Rezk, Hegazy & Aly, Mokhtar & Fathy, Ahmed, 2021. "A novel strategy based on recent equilibrium optimizer to enhance the performance of PEM fuel cell system through optimized fuzzy logic MPPT," Energy, Elsevier, vol. 234(C).
    7. Rezk, Hegazy & Olabi, A.G. & Ferahtia, Seydali & Sayed, Enas Taha, 2022. "Accurate parameter estimation methodology applied to model proton exchange membrane fuel cell," Energy, Elsevier, vol. 255(C).
    8. Zuo, Wei & Wang, Zijie & E, Jiaqiang & Li, Qingqing & Cheng, Qianju & Wu, Yinkun & Zhou, Kun, 2023. "Numerical investigations on the performance of a hydrogen-fueled micro planar combustor with tube outlet for thermophotovoltaic applications," Energy, Elsevier, vol. 263(PC).
    9. Yang, Fan & Li, Yuehua & Chen, Dongfang & Hu, Song & Xu, Xiaoming, 2024. "Parameter identification of PEMFC steady-state model based on p-dimensional extremum seeking via simplex tuning optimization method," Energy, Elsevier, vol. 292(C).
    10. Liao, Shuxin & Qiu, Diankai & Yi, Peiyun & Peng, Linfa & Lai, Xinmin, 2022. "Modeling of a novel cathode flow field design with optimized sub-channels to improve drainage for proton exchange membrane fuel cells," Energy, Elsevier, vol. 261(PB).
    11. Najmi, Aezid-Ul-Hassan & Anyanwu, Ikechukwu S. & Xie, Xu & Liu, Zhi & Jiao, Kui, 2021. "Experimental investigation and optimization of proton exchange membrane fuel cell using different flow fields," Energy, Elsevier, vol. 217(C).
    12. Li, Yanju & Li, Dongxu & Ma, Zheshu & Zheng, Meng & Lu, Zhanghao & Song, Hanlin & Guo, Xinjia & Shao, Wei, 2022. "Performance analysis and optimization of a novel vehicular power system based on HT-PEMFC integrated methanol steam reforming and ORC," Energy, Elsevier, vol. 257(C).
    13. Zuo, Wei & Li, Dexin & Li, Qingqing & Cheng, Qianju & Huang, Yuhan, 2024. "Effects of intermittent pulsating flow on the performance of multi-channel cold plate in electric vehicle lithium-ion battery pack," Energy, Elsevier, vol. 294(C).
    14. Li, Jing & Zuo, Wei & E, Jiaqiang & Zhang, Yuntian & Li, Qingqing & Sun, Ke & Zhou, Kun & Zhang, Guangde, 2022. "Multi-objective optimization of mini U-channel cold plate with SiO2 nanofluid by RSM and NSGA-II," Energy, Elsevier, vol. 242(C).
    15. Fathy, Ahmed & Babu, Thanikanti Sudhakar & Abdelkareem, Mohammad Ali & Rezk, Hegazy & Yousri, Dalia, 2022. "Recent approach based heterogeneous comprehensive learning Archimedes optimization algorithm for identifying the optimal parameters of different fuel cells," Energy, Elsevier, vol. 248(C).
    16. Ángel Encalada-Dávila & Samir Echeverría & Jordy Santana-Villamar & Gabriel Cedeño & Mayken Espinoza-Andaluz, 2021. "Optimization Algorithms: Optimal Parameters Computation for Modeling the Polarization Curves of a PEFC Considering the Effect of the Relative Humidity," Energies, MDPI, vol. 14(18), pages 1-21, September.
    17. Andrew J. Riad & Hany M. Hasanien & Rania A. Turky & Ahmed H. Yakout, 2023. "Identifying the PEM Fuel Cell Parameters Using Artificial Rabbits Optimization Algorithm," Sustainability, MDPI, vol. 15(5), pages 1-17, March.
    18. Alaa A. Zaky & Rania M. Ghoniem & F. Selim, 2023. "Precise Modeling of Proton Exchange Membrane Fuel Cell Using the Modified Bald Eagle Optimization Algorithm," Sustainability, MDPI, vol. 15(13), pages 1-16, July.
    19. Li, Dexin & Zuo, Wei & Li, Qingqing & Zhang, Guangde & Zhou, Kun & E, Jiaqiang, 2023. "Effects of pulsating flow on the performance of multi-channel cold plate for thermal management of lithium-ion battery pack," Energy, Elsevier, vol. 273(C).
    20. Yang, Bo & Li, Danyang & Zeng, Chunyuan & Chen, Yijun & Guo, Zhengxun & Wang, Jingbo & Shu, Hongchun & Yu, Tao & Zhu, Jiawei, 2021. "Parameter extraction of PEMFC via Bayesian regularization neural network based meta-heuristic algorithms," Energy, Elsevier, vol. 228(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:energy:v:264:y:2023:i:c:s0360544222030511. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/energy .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.