Accurate Determination of Five Single-Diode Model Parameters for Solar Cells and PV Modules via a Five-Dimensional Newton–Raphson Approach

This study proposes a hybrid analytical–numerical method for accurately extracting five physically meaningful single-diode-model (SDM) parameters from measured illuminated I–V data. Five experimental data points are randomly selected to construct a system of five nonlinear implicit SDM equations. Hejri’s analytical method provides physically meaningful initial estimates, and an improved five-dimensional Newton–Raphson method is then used to solve the resulting equation system. When accurate characteristic-point data are unavailable, a metaheuristic fitting procedure is employed to determine the characteristic parameters required by initialization. The method is evaluated on the RTC cell, PWP 201 module, TOPCon cell, and TOPCon module and benchmarked against six state-of-the-art techniques: Ghani’s method, Hejri’s method, Kumar’s method, the artificial ecosystem-based optimization (AEO) algorithm, Phang’s method, and Villalva’s method. The proposed method achieves RMSE values of 8.31 × 10−4, 2.10 × 10−3, 2.40 × 10−2, and 2.36 × 10−2 A, respectively, consistently yielding the lowest RMSE among the four hybrid analytical–numerical methods. Its RMSE values are only 0.5–7.5% above the corresponding minima obtained by AEO. Moreover, in the equation-solving step, the proposed solver is approximately 30–2954 times faster than Ghani’s method and achieves higher convergence rates for three of the four devices. These results demonstrate that the proposed method enables accurate and efficient extraction of physically meaningful SDM parameters.