Optimal PEM Fuel Cell Model Using a Novel Circle Search Algorithm

Mohammed H. Qais, Hany M. Hasanien, Rania A. Turky, Saad Alghuwainem, Ka Hong Loo, Mohmmed Elgendy

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)


The aim of this article is to introduce a novel Circle Search Algorithm (CSA) with the purpose of obtaining a precise electrical model of a proton exchange membrane fuel cell (PEMFC). Current‐voltage and current‐power curves are used to characterize the performance of PEMFCs. A nonlinear model with seven unknown parameters is used to describe these polarization curves. Estimating these unknown parameters is a critical issue because they influence the dynamic analysis of fuel cells in a variety of applications such as transportation and smart grids. The suggested method is based on minimizing the fitness function (the sum of the squared errors (SSE)) between estimated and measured voltage values. The CSA is compared to the neural network algorithm (NNA), grey wolf optimization (GWO), and the sine cosine algorithm (SCA). The optimization results reveal that the simulation times of the CSA, NNA, GWO, and SCA are 5.2, 6, 5.8, and 5.75 s, respectively. Moreover, the CSA converges to the best minimum within the first 100 iterations, which is faster than the other algorithms. The robustness of the CSA is verified using 20 independent runs, where the CSA achieves the smallest average and standard deviation. In addition, the t‐ test proves the superiority of the CSA compared to the other algorithms, where all p‐values are less than 5%. The simulated I‐V and I‐P curves of the CSA‐PEMFC model match the measured curves very closely. Moreover, the efficacy of the CSA‐PEMFC model is evaluated under a variety of temperature and pressure conditions. Therefore, the suggested CSA‐PEMFC model has the potential to be an accurate and efficient model.

Original languageEnglish
Article number1808
Pages (from-to)1-21
Number of pages21
JournalElectronics (Switzerland)
Issue number12
Publication statusPublished - 1 Jun 2022


  • Circle Search Algorithm
  • fuel cell
  • optimization
  • parameters estimation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Hardware and Architecture
  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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