A Kepler optimization algorithm improved using a novel Lévy-Normal mechanism for optimal parameters selection of proton exchange membrane fuel cells: A comparative study

Abstract

Proton exchange membrane fuel cells (PEMFCs) are considered a promising renewable energy source and have sparked a lot of interest over the last few years due to their robust efficiency, low operating temperature, and longevity. The PEMFC's electrochemical model has seven unknown parameters, which are not given in the manufacturer's datasheets and need to be accurately estimated to present a more accurate model, leading to improved efficiency and performance of the PEMFC systems. The estimation of those unknown parameters has been dealt with as a complex and non-linear optimization problem that needs a powerful optimization algorithm to solve it. The existing optimization algorithms still have some disadvantages, such as falling into local minima and low convergence speed, which make them ineligible to solve this complicated problem with acceptable accuracy and low computational cost. Therefore, this study presents a new parameter estimation technique for estimating the unknown parameters of the PEMFC model more accurately, thereby achieving precise modeling of PEMFCs. This technique called IKOA is based on integrating the Kepler optimization algorithm (KOA) with a novel Lévy-Normal (LN) mechanism to strengthen its exploration and exploitation capabilities against this multimodal optimization problem. The Lévy flight in this mechanism aims to improve the KOA's exploitation operator to accelerate the convergence speed toward the near-optimal solution, thus minimizing the computational cost; meanwhile, the normal distribution is used to strengthen its exploration operator, thereby aiding in the escape of local minima. The proposed IKOA and KOA are herein evaluated against several rival algorithms using six well-known commercial PEMFC stacks to highlight their efficiency and effectiveness. Key performance metrics such as computational cost, fitness measures, and statistical validation through the Wilcoxon rank-sum test are herein used to highlight IKOA's effective performance in enhancing the predictive accuracy and operational efficiency of PEMFCs. The numerical findings show the high superiority of IKOA against all rival optimizers on all solved benchmarks.