Integrated Mathematical and Hybrid Optimization Framework for Parametric Analysis of Single Diode Bifacial Photovoltaic Panels

Accurate and reliable parameter extraction is fundamental for single-diode modeling of bifacial photovoltaic (bPV) modules. While numerous extraction techniques have been reported, many rely solely on numerical optimization and provide limited insight into the mathematical role and sensitivity of model parameters. To address this limitation, this study presents a unified mathematical–optimization framework that integrates analytical formulation, hybrid optimization, and parametric sensitivity analysis for bPV modeling. A hybrid two-stage optimization strategy is employed, in which a real-coded genetic algorithm performs global exploration of the non-convex parameter space, followed by a gradient-based local optimizer to ensure stable convergence and high numerical accuracy. The bifacial behavior is incorporated through an equivalent irradiance formulation that accounts for rear-side contribution without modifying the single-diode structure. The proposed framework shows excellent agreement with manufacturer data and it shows 1.1% error. To assess parameter influence, a detailed sensitivity analysis is conducted revealing that series resistance predominantly affects the fill factor and maximum power whereas shunt resistance mainly impacts the low voltage region and partial shading conditions. Finally, the optimized model is applied under varying environmental conditions including temperature fluctuations, irradiance variations, and front rear asymmetry, highlighting nonlinear dependencies and the critical importance of accurate parameter extraction. This hybrid framework significantly enhances model fidelity and provides a reliable and versatile tool for performance prediction, diagnostic assessment, optimization, and design evaluation of bPV Modules under realistic operating scenarios.