Enhancing the analytical modeling of proton-exchange membrane fuel cells for optimal parameter extraction with the Ali Baba and the forty thieves algorithm

Abstract

Background:

This research presents an improvement in the analytical modeling of the equivalent electrical circuit of Proton-Exchange Membrane Fuel Cells (PEMFC). This enhancement is based on a more generalized theoretical framework than existing approaches, providing a more accurate representation of the fuel cell’s electrical behavior.

Methods:

A new expression for the activation voltage has been developed from an improved solution to the Butler–Volmer equation, providing a more accurate representation of electrochemical kinetics without resorting to the Tafel approximation. Additionally, a generalized formulation of the reversible voltage, accounting for the presence of water vapor, along with adjustments to the concentration voltage, has been integrated to optimize the model’s accuracy. The Ali Baba and The Forty Thieves (AFT) metaheuristic algorithm is employed for parameter extraction, ensuring efficient and robust model optimization.

Significant Results:

The proposed model demonstrates significantly higher accuracy, with Total Sum of Squares (SSE) values of $3.9083e^{-08},5.9158e^{-08}$, and $8.0147e^{-10}$ for the commercial fuel cells NedStack, BCS 500, and Ballard, respectively. These values are considerably lower than the best results reported in the literature ($2.2881\times 10^{-2},1.1364e^{-2},0.1486$), demonstrating the enhanced reliability and precision of the proposed model.