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A Guide to Concentration Alternating Frequency Response Analysis of Fuel Cells
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Advanced modeling and parameter estimation of PEM fuel cells using the g-function and self-adaptive differential

Martin Ćalasan1, Snežana Vujošević1, Mihailo Micev2

  • 1Faculty of Electrical Engineering, University of Montenegro, Džordža Vašingtona, Podgorica, 81000, Montenegro.

Scientific Reports
|December 22, 2025
PubMed
Summary

This study introduces a new method for modeling proton exchange membrane fuel cells (PEMFCs) using the g-function and a self-adaptive differential evolution (SaDE) algorithm for parameter estimation, improving accuracy and stability.

Keywords:
g-functionLambert W functionMathematical modelingMetaheuristic optimizationPEM fuel cellsParameter estimationRenewable energy

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Area of Science:

  • Energy Systems Engineering
  • Computational Modeling
  • Electrochemical Engineering

Background:

  • Proton exchange membrane fuel cells (PEMFCs) are crucial for sustainable energy, requiring accurate electrical characteristic models.
  • Traditional voltage-current models are insufficient for control systems; current-voltage models are needed.
  • Existing models face numerical limitations and require robust parameter estimation.

Purpose of the Study:

  • To develop a novel current-voltage model for PEMFCs using the g-function.
  • To introduce a self-adaptive differential evolution (SaDE) algorithm for efficient PEMFC parameter estimation.
  • To validate the proposed modeling and parameter estimation approach through comparative analysis.

Main Methods:

  • Utilized the g-function, a stable transformation of the Lambert W function, for PEMFC modeling.
  • Employed the self-adaptive differential evolution (SaDE) algorithm for parameter estimation.
  • Conducted comparative analysis and sensitivity analysis across three PEMFC systems (Ballard Mark V, BCS 500, NedStack PS6).

Main Results:

  • The proposed g-function model with SaDE parameter estimation demonstrated improved accuracy and numerical stability.
  • Achieved root mean square error (RMSE) reductions up to 6.65% and sum of squared errors (SSE) gains up to 12.87%.
  • The methodology showed robustness and transferability across different PEMFC types.

Conclusions:

  • The novel g-function based PEMFC model and SaDE algorithm offer enhanced accuracy and efficient parameter estimation.
  • The validated framework supports optimized PEMFC performance and integration into sustainable energy systems.
  • This approach advances PEMFC modeling for real-world applications.