Energy-Efficient Parameter Estimation of Solid Oxide Fuel Cells under Varying Pressure Conditions Using the Black Widow Optimization Algorithm

Roshan Raman^1*Parminder Singh²Amanpreet Sandhu³Yunis Khan⁴Praveen Barmavatu⁵Aman Garg⁶

• ¹The Northcap University, Gurgaon, India
• ²Thapar Institute of Engineering and Technology (Deemed to be University), Indra Puri Colony, India
• ³Chitkara University, Rajpura, India
• ⁴Indian Institute of Technology (Indian School of Mines) Dhanbad, Dhanbad, India
• ⁵Universidad Tecnologica Metropolitana, Santiago, Chile
• ⁶Huazhong University of Science and Technology, Wuhan, China

Solid Oxide Fuel Cells (SOFCs) are highly efficient and fuel-flexible energy conversion devices, but accurate estimation of 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 the estimation of six critical SOFC parameters—open-circuit potential (E₀), Tafel slope (A), exchange current density (I₀), concentration loss coefficient (B), limiting current density (Iₗ), and ohmic resistance (Rₒₕₘ)—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 seconds, significantly outperforming benchmark metaheuristic algorithms such as Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), and 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 work will include real-time implementation under dynamic operating environments and integration with hybrid renewable energy systems to improve scalability, efficiency, and sustainability.