Energy-efficient parameter estimation of solid oxide fuel cells under varying pressure conditions using the black widow optimization algorithm

Solid oxide fuel cells (SOFCs) are highly efficient and fuel-flexible energy conversion devices, but accurately estimating their governing parameters remains a challenge due to the nonlinear behavior of electrochemical processes. This study presents the first application of the black widow optimization (BWO) algorithm for estimating six critical SOFC parameters—open-circuit potential (E 0 ), Tafel slope (A), exchange current density (I 0 ), concentration loss coefficient (B), limiting current density (I l ), and ohmic resistance (R ohm )—under varying pressure conditions (1–5 atm). The objective was to minimize the mean squared error (MSE) between experimental and predicted polarization curves while ensuring computational efficiency. The proposed BWO framework achieved superior accuracy, with an MSE of 0.52 at 5 atm and convergence within 3.74 s, significantly outperforming benchmark metaheuristic algorithms such as particle swarm optimization (PSO), gray wolf optimization (GWO), and the whale optimization algorithm (WOA). Robustness was confirmed through cross-validation, where polarization curves predicted at unseen conditions deviated by less than 5% from experimental results. This demonstrates that the estimated parameters effectively capture intrinsic SOFC electrochemical behavior rather than overfitting specific datasets. Beyond numerical accuracy, the optimized parameters enhanced the predictive stability of voltage–current (V–I) and power–current (P–I) characteristics across all studied pressures, directly supporting improved operational reliability and long-term stack durability. The combination of higher precision, faster convergence, and strong generalizability positions BWO as a promising tool for real-time SOFC optimization. The findings establish a robust framework for parameter identification that not only reduces uncertainty in SOFC modeling but also contributes to practical advances in performance optimization and system longevity. Future extensions of this research will include real-time implementation under dynamic operating environments and integration with hybrid renewable energy systems to improve scalability, efficiency, and sustainability.