A Comparative Review of Modeling and Metaheuristic Parameter Identification Strategies for Zero-Dimensional PEMFC Polarization Models

Fang, Yesheng; Yang, Fuyong; Xing, Yanfeng; Zhang, Xiaobing; Wang, Wei; Lin, Shengyao

doi:10.3390/en19061438

Open AccessReview

A Comparative Review of Modeling and Metaheuristic Parameter Identification Strategies for Zero-Dimensional PEMFC Polarization Models

by

Yesheng Fang

,

Fuyong Yang

^*

,

Yanfeng Xing

,

Xiaobing Zhang

,

Wei Wang

and

Shengyao Lin

School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China

^*

Author to whom correspondence should be addressed.

Energies 2026, 19(6), 1438; https://doi.org/10.3390/en19061438

Submission received: 8 February 2026 / Revised: 3 March 2026 / Accepted: 6 March 2026 / Published: 12 March 2026

(This article belongs to the Topic AI and Computational Methods for Modelling, Simulations and Optimizing of Advanced Systems: Innovations in Complexity, 2nd Edition)

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Abstract

Proton exchange membrane fuel cells (PEMFCs) are promising energy conversion de-vices owing to high efficiency and zero local emissions. Accurate PEMFC performance assessment and control require well-posed models, whose predictive accuracy is largely determined by the correct calibration of key parameters. Metaheuristic algorithms (MHAs) have therefore been widely applied to PEMFC stack parameter estimation, but their rapid proliferation calls for a more systematic and fine-grained synthesis. This review refines the taxonomy of PEMFC mathematical modeling approaches and summarizes Zero-Dimensional PEMFC modeling methods, key parameters, and representative improvement directions aimed at reducing identification difficulty while retaining physical meaning. Newly developed MHAs and enhanced variants of existing methods are then surveyed, and over 40 distinctive optimization approaches are selected for systematic comparison. Modeling approaches and parameter identification methodologies are summarized. In addition, an algorithm selection guide and 26 representative algorithms with their variants are compiled and benchmarked across the five most widely used commercial PEMFC models to enable cross-model comparison.

Keywords: proton exchange membrane fuel cell; steady-state polarization modeling; zero-dimensional modelling; parameter identification; model calibration; electrochemical loss; optimization algorithms; metaheuristic algorithms

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MDPI and ACS Style

Fang, Y.; Yang, F.; Xing, Y.; Zhang, X.; Wang, W.; Lin, S. A Comparative Review of Modeling and Metaheuristic Parameter Identification Strategies for Zero-Dimensional PEMFC Polarization Models. Energies 2026, 19, 1438. https://doi.org/10.3390/en19061438

AMA Style

Fang Y, Yang F, Xing Y, Zhang X, Wang W, Lin S. A Comparative Review of Modeling and Metaheuristic Parameter Identification Strategies for Zero-Dimensional PEMFC Polarization Models. Energies. 2026; 19(6):1438. https://doi.org/10.3390/en19061438

Chicago/Turabian Style

Fang, Yesheng, Fuyong Yang, Yanfeng Xing, Xiaobing Zhang, Wei Wang, and Shengyao Lin. 2026. "A Comparative Review of Modeling and Metaheuristic Parameter Identification Strategies for Zero-Dimensional PEMFC Polarization Models" Energies 19, no. 6: 1438. https://doi.org/10.3390/en19061438

APA Style

Fang, Y., Yang, F., Xing, Y., Zhang, X., Wang, W., & Lin, S. (2026). A Comparative Review of Modeling and Metaheuristic Parameter Identification Strategies for Zero-Dimensional PEMFC Polarization Models. Energies, 19(6), 1438. https://doi.org/10.3390/en19061438

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A Comparative Review of Modeling and Metaheuristic Parameter Identification Strategies for Zero-Dimensional PEMFC Polarization Models

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