IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v12y2020i19p8127-d422805.html
   My bibliography  Save this article

Fuel Cell Characteristic Curve Approximation Using the Bézier Curve Technique

Author

Listed:
  • Mohamed Louzazni

    (National School of Applied Sciences, Abdelmalek Essaadi University, Tetouan B.P. 2117, Morocco)

  • Sameer Al-Dahidi

    (Mechanical and Maintenance Engineering Department, School of Applied Technical Sciences, German Jordanian University, Amman 11180, Jordan)

  • Marco Mussetta

    (Dipartimento di Energia, Politecnico di Milano, Via Lambruschini 4, 20156 Milano, Italy)

Abstract

Accurate modelling of the fuel cell characteristics curve is essential for the simulation analysis, control management, performance evaluation, and fault detection of fuel cell power systems. However, the big challenge in fuel cell modelling is the multi-variable complexity of the characteristic curves. In this paper, we propose the implementation of a computer graphic technique called Bézier curve to approximate the characteristics curves of the fuel cell. Four different case studies are examined as follows: Ballard Systems, Horizon H-12 W stack, NedStackPS6, and 250 W proton exchange membrane fuel cells (PEMFC). The main objective is to minimize the absolute errors between experimental and calculated data by using the control points of the Bernstein–Bézier function and de Casteljau’s algorithm. The application of this technique entails subdividing the fuel cell curve to some segments, where each segment is approximated by a Bézier curve so that the approximation error is minimized. Further, the performance and accuracy of the proposed techniques are compared with recent results obtained by different metaheuristic algorithms and analytical methods. The comparison is carried out in terms of various statistical error indicators, such as Individual Absolute Error ( IAE ), Relative Error ( RE ), Root Mean Square Error ( RMSE ), Mean Bias Errors ( MBE ), and Autocorrelation Function ( ACF ). The results obtained by the Bézier curve technique show an excellent agreement with experimental data and are more accurate than those obtained by other comparative techniques.

Suggested Citation

  • Mohamed Louzazni & Sameer Al-Dahidi & Marco Mussetta, 2020. "Fuel Cell Characteristic Curve Approximation Using the Bézier Curve Technique," Sustainability, MDPI, vol. 12(19), pages 1-23, October.
    • Handle: RePEc:gam:jsusta:v:12:y:2020:i:19:p:8127-:d:422805
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/12/19/8127/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2071-1050/12/19/8127/
    Download Restriction: no
    ---><---

    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. Gong, Wenyin & Yan, Xuesong & Liu, Xiaobo & Cai, Zhihua, 2015. "Parameter extraction of different fuel cell models with transferred adaptive differential evolution," Energy, Elsevier, vol. 86(C), pages 139-151.
    3. El-Hay, E.A. & El-Hameed, M.A. & El-Fergany, A.A., 2019. "Optimized Parameters of SOFC for steady state and transient simulations using interior search algorithm," Energy, Elsevier, vol. 166(C), pages 451-461.
    4. Miao, Di & Chen, Wei & Zhao, Wei & Demsas, Tekle, 2020. "Parameter estimation of PEM fuel cells employing the hybrid grey wolf optimization method," Energy, Elsevier, vol. 193(C).
    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. Xu, Shuhui & Wang, Yong & Wang, Zhi, 2019. "Parameter estimation of proton exchange membrane fuel cells using eagle strategy based on JAYA algorithm and Nelder-Mead simplex method," Energy, Elsevier, vol. 173(C), pages 457-467.
    7. Ramadhani, F. & Hussain, M.A. & Mokhlis, H. & Hajimolana, S., 2017. "Optimization strategies for Solid Oxide Fuel Cell (SOFC) application: A literature survey," Renewable and Sustainable Energy Reviews, Elsevier, vol. 76(C), pages 460-484.
    8. Ahmed M. Agwa & Attia A. El-Fergany & Gamal M. Sarhan, 2019. "Steady-State Modeling of Fuel Cells Based on Atom Search Optimizer," Energies, MDPI, vol. 12(10), pages 1-14, May.
    9. Sun, Zhe & Wang, Ning & Bi, Yunrui & Srinivasan, Dipti, 2015. "Parameter identification of PEMFC model based on hybrid adaptive differential evolution algorithm," Energy, Elsevier, vol. 90(P2), pages 1334-1341.
    10. Ali, M. & El-Hameed, M.A. & Farahat, M.A., 2017. "Effective parameters’ identification for polymer electrolyte membrane fuel cell models using grey wolf optimizer," Renewable Energy, Elsevier, vol. 111(C), pages 455-462.
    11. Al-Baghdadi, Maher A.R. Sadiq, 2005. "Modelling of proton exchange membrane fuel cell performance based on semi-empirical equations," Renewable Energy, Elsevier, vol. 30(10), pages 1587-1599.
    12. 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.
    13. El-Fergany, Attia A., 2018. "Extracting optimal parameters of PEM fuel cells using Salp Swarm Optimizer," Renewable Energy, Elsevier, vol. 119(C), pages 641-648.
    14. Amith Khandakar & Muhammad E. H. Chowdhury & Monzure- Khoda Kazi & Kamel Benhmed & Farid Touati & Mohammed Al-Hitmi & Antonio Jr S. P. Gonzales, 2019. "Machine Learning Based Photovoltaics (PV) Power Prediction Using Different Environmental Parameters of Qatar," Energies, MDPI, vol. 12(14), pages 1-19, July.
    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. Mohammed Yousri Silaa & Mohamed Derbeli & Oscar Barambones & Cristian Napole & Ali Cheknane & José María Gonzalez De Durana, 2021. "An Efficient and Robust Current Control for Polymer Electrolyte Membrane Fuel Cell Power System," Sustainability, MDPI, vol. 13(4), pages 1-18, February.

    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. Gouda, Eid A. & Kotb, Mohamed F. & El-Fergany, Attia A., 2021. "Jellyfish search algorithm for extracting unknown parameters of PEM fuel cell models: Steady-state performance and analysis," Energy, Elsevier, vol. 221(C).
    2. Seleem, Sameh I. & Hasanien, Hany M. & El-Fergany, Attia A., 2021. "Equilibrium optimizer for parameter extraction of a fuel cell dynamic model," Renewable Energy, Elsevier, vol. 169(C), pages 117-128.
    3. Hachana, Oussama & El-Fergany, Attia A., 2022. "Efficient PEM fuel cells parameters identification using hybrid artificial bee colony differential evolution optimizer," Energy, Elsevier, vol. 250(C).
    4. 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.
    5. 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).
    6. 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.
    7. Abdel-Basset, Mohamed & Mohamed, Reda & El-Fergany, Attia & Chakrabortty, Ripon K. & Ryan, Michael J., 2021. "Adaptive and efficient optimization model for optimal parameters of proton exchange membrane fuel cells: A comprehensive analysis," Energy, Elsevier, vol. 233(C).
    8. 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.
    9. 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.
    10. El-Hay, E.A. & El-Hameed, M.A. & El-Fergany, A.A., 2019. "Optimized Parameters of SOFC for steady state and transient simulations using interior search algorithm," Energy, Elsevier, vol. 166(C), pages 451-461.
    11. Ahmed M. Agwa & Attia A. El-Fergany & Gamal M. Sarhan, 2019. "Steady-State Modeling of Fuel Cells Based on Atom Search Optimizer," Energies, MDPI, vol. 12(10), pages 1-14, May.
    12. 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).
    13. 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).
    14. 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.
    15. 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.
    16. Miao, Di & Chen, Wei & Zhao, Wei & Demsas, Tekle, 2020. "Parameter estimation of PEM fuel cells employing the hybrid grey wolf optimization method," Energy, Elsevier, vol. 193(C).
    17. Zhang, Bo & Wang, Rongjie & Jiang, Desong & Wang, Yichun & lin, Anhui & Wang, Jianfeng & Ruan, Bingcong, 2023. "Parameter identification of proton exchange membrane fuel cell based on swarm intelligence algorithm," Energy, Elsevier, vol. 283(C).
    18. 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.
    19. 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).
    20. Xu, Shuhui & Wang, Yong & Wang, Zhi, 2019. "Parameter estimation of proton exchange membrane fuel cells using eagle strategy based on JAYA algorithm and Nelder-Mead simplex method," Energy, Elsevier, vol. 173(C), pages 457-467.

    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:gam:jsusta:v:12:y:2020:i:19:p:8127-:d:422805. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.