Parameter estimation and sensitivity analysis of proton exchange membrane fuel cells based on electric eel foraging optimization algorithm

Fuel cells (FCs) offer a streamlined and eco-friendly solution for electricity generation by directly converting hydrogen energy into electrical energy. The accuracy of the mathematical models in simulating the electrochemical characteristics of FC stacks is vital to determine the accuracy of the simulations. Manufacturers don't offer detailed specifications, making it a challenge to accurately describe the behavior and features of proton exchange membrane fuel cells (PEM-FCs). Therefore, to accurately model the FC operation, it is essential to carefully estimate these unknown parameters. This paper introduces the electric eel foraging optimization (EEFO) technique to effectively identify unknown design parameters in four types of PEM-FC stacks: 250W, BCS 500W, SR-12 500W, and Temasek 1000W. The objective function calculates the total squared deviation to measure the difference between estimated and experimental cell voltages using several newly developed optimization algorithms including the squirrel search algorithm (SSA), spider wasp optimizer (SWO), particle swarm optimization (PSO), nutcracker optimization algorithm (NOA), moth-flame optimization algorithm (MFO), and other existing methods. A statistical analysis assesses the robustness of the results, confirming that the EEFO algorithm is the most reliable method for estimating parameters and optimizing the operation of PEM-FC. Also, the findings revealed that the EEFO algorithm has the lowest total squared deviation (TSD) and standard deviation across all studied FC types, confirming EEFO's superior stability and accuracy. The EEFO algorithm converges faster than SSA, SWO, PSO, NOA, and MFO. Moreover, the polarization curves generated by EEFO closely match the experimental data for all studied FC stacks, signifying its robustness and reliability. In addition, the impact of optimized parameter variations on the objective function is assessed through sensitivity analysis, providing critical insights for optimizing the PEM-FC performance. A reduced fourth-order PEM-FC model is introduced to enhance computational accuracy, from which the results demonstrate its effectiveness in improving convergence speed and reducing computational time while maintaining accuracy. The TSD values closely align with the complete model, making this reduced model a practical and efficient solution for real-time PEM-FC performance estimation.