Open Access


Optimal Parameter Estimation of Proton Exchange Membrane Fuel Cells

A. M. Abdullah1, Hegazy Rezk2,3,*, A. Hadad1, Mohamed K. Hassan1,4, A. F. Mohamed1,5
1 Mechanical Engineering Department, College of Engineering & Islamic Arch., Umm Al-Qura University, Makkah, Saudi Arabia
2 College of Engineering at Wadi Addawaser, Prince Sattam Bin Abdulaziz University, 11911 Al-Kharj, Saudi Arabia
3 Electrical Engineering Department, Faculty of Engineering, Minia University, 61517, Minia, Egypt
4 Production Engineering and Design Department, Faculty of Engineering, Minia University, 61517, Minia, Egypt
5 Mechanical Engineering Department, Faculty of Engineering, Sohag University, Sohag, Egypt
* Corresponding Author: Hegazy Rezk. Email:

Intelligent Automation & Soft Computing 2021, 29(2), 619-631.

Received 04 March 2021; Accepted 09 April 2021; Issue published 16 June 2021


The problem of parameter estimation of the proton exchange membrane fuel cell (PEMFC) model plays a significant role in the simulation and optimization of a PEMFC system. In the current research, a moth flame optimization algorithm (MFOA) is used to identify the best parameters of PEMFC. Two different PEMFCs, Nedstack PS6, 6 kW, and SR-12 PEM 500 W are used to demonstrate the accuracy of the MFOA. Throughout the optimization process, seven unidentified parameters (1, 2, 3, 4, λ, ℛ, and B) of PEMFC are appointed to be decision variables. The fitness function, which needed to be minimum, is represented by the root-mean-square error between the calculated voltage of the PEMFC and the experimental dataset. The results attained by the MFOA are compared with the sine cosine algorithm (SCA) and particle swarm optimization (PSO). The following metrics are considered in the comparison: best value, worst value, average value, standard deviation, and efficiency. The main findings verified the supremacy of the MFOA in estimating the best parameters of the PEMFC model in comparison with PSO and SCA. For the Nedstack PS6, the efficiency values are 24.50458%, 79.477%, and 38.84747% for MFOA, PSO and SCA, respectively. For PEMFC (SR-12 PEM), the average efficiency values are 14.965%, 79.933% and 31.87% for MFOA, PSO, and SCA, respectively.


Parameter estimation; fuel cell; optimization; renewable energy

Cite This Article

A. M. Abdullah, H. Rezk, A. Hadad, M. K. Hassan and A. F. Mohamed, "Optimal parameter estimation of proton exchange membrane fuel cells," Intelligent Automation & Soft Computing, vol. 29, no.2, pp. 619–631, 2021.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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