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<p>The reduced-parameter semi-empirical modified Mann model for proton exchange membrane fuel cells (PEMFCs), as proposed by Perez et al. (Energy Conversion and Management, Vol. 331, pp. 119655, 2025), has recently gained attention as a promising approach due to its balance between simplicity and fitting accuracy. However, the inverse formulation of the modified Mann model, i.e., computing current as a function of voltage, is mathematically challenging due to its nonlinear and transcendental structure. This short communication proposes a hybrid numerical solver that combines an iterative Lambert W-based method with a fallback bisection strategy, which is activated if the Lambert W iteration fails to converge at high currents. The approach ensures fast, accurate, and numerically stable inversion across the entire operating range. Validation against experimental polarization data for two PEMFC systems is performed, and a comparison with the Newton–Raphson method is included, demonstrating both strong agreement and significantly improved computational robustness. This makes the method highly suitable for online control, diagnostics, and prognostics of PEMFC-based systems.</p>

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Innovative numerical inversion of the modified Mann PEMFC Model via Lambert W iterations with bisection backup

  • 期刊论文

  • 发表日期：

    2025年9月27日

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  • Martin Ćalasan

摘要

The reduced-parameter semi-empirical modified Mann model for proton exchange membrane fuel cells (PEMFCs), as proposed by Perez et al. (Energy Conversion and Management, Vol. 331, pp. 119655, 2025), has recently gained attention as a promising approach due to its balance between simplicity and fitting accuracy. However, the inverse formulation of the modified Mann model, i.e., computing current as a function of voltage, is mathematically challenging due to its nonlinear and transcendental structure. This short communication proposes a hybrid numerical solver that combines an iterative Lambert W-based method with a fallback bisection strategy, which is activated if the Lambert W iteration fails to converge at high currents. The approach ensures fast, accurate, and numerically stable inversion across the entire operating range. Validation against experimental polarization data for two PEMFC systems is performed, and a comparison with the Newton–Raphson method is included, demonstrating both strong agreement and significantly improved computational robustness. This makes the method highly suitable for online control, diagnostics, and prognostics of PEMFC-based systems.