# Parameter Extraction of Solar Photovoltaic Model Based on Nutracker Optimization Algorithm
## 4 Experimental Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Algorithm** & \(R_{a}\) & \(R_{ab}\) & \(I_{pb}\) & \(I_{SDm}\) & \(I_{SD2}\) & \(I_{SD3}\) & \(n_{1}\) & \(n_{2}\) & \(n_{3}\) & **RMSE** \\ \hline NOA & 0.006564 & 5.210821 & 7.865464 & 2.9270 \(\times\) 10\({}^{-10}\) & 8.2069 \(\times\) 10\({}^{-7}\) & 9.1951 \(\times\) 10\({}^{-7}\) & 0.981139 & 8.745928 & 8.109913 & 6.23616 \(\times\) 10\({}^{-5}\) \\ PSO & 0.006739 & 100.00000 & 2.824180 & 0.000000 & 1.0000 \(\times\) 10\({}^{-6}\) & 1.4708 \(\times\) 10\({}^{-11}\) & 1.4708 \(\times\) 10\({}^{-11}\) & 1.69328 & 0.877124 & 0.013344 \\ FWA & 0.004407 & 62.99762 & 7.939448 & 0.00000 & 1.000 \(\times\) 10\({}^{-6}\) & 1.0000 \(\times\) 10\({}^{-6}\) & 0.556490 & 20.035365 & 1.483630 & 0.106027 \\ WOA & 0.006551 & 93.154950 & 7.813773 & 4.6284 \(\times\) 10\({}^{-10}\) & 9.3795 \(\times\) 10\({}^{-7}\) & 5.1560 \(\times\) 10\({}^{-9}\) & 1.000000 & 9.460711 & 9.315814 & 0.019484 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Test results for TDM. Figure 2: Convergence graph for (**a**) SDM, (**b**) DDM, (**c**) TDM. NOA's performance and probability distribution from its counterparts. Meanwhile, the h-value indicates whether the null hypothesis is accepted (h = 1) or rejected (h = 0). Any non-rejection of the null hypothesis would imply significant differences between NOA and a certain algorithm for a specific function, as per the Wilcoxon test. Through comparative analysis, it is evident that, although PSO, WOA, and FWA demonstrate remarkable performance in various optimization problems, their effectiveness is limited in this study. Upon reaching 50,000 iterations, the results of these algorithms still fail to achieve the desired optimal solution. This phenomenon can be primarily attributed to two aspects. First, the convergence behavior of these algorithms makes it difficult for them to escape local optima in a short time, ultimately obstructing their identification of global optimal values. Second, the insufficient compatibility between these algorithms and the unique characteristics of the Aleo Solar S79Y300 monocrystalline silicon solar cell, module parameter extraction problem leads to reduced efficiency in solving this specific issue. This implies that the problem features might not align well with the fundamental assumptions or heuristic methods employed by PSO, FWA, and WOA, resulting in suboptimal performance. By contrast, the NOA consistently outperforms popular algorithms (such as PSO, FWA, and WOA) in terms of accuracy and computational efficiency. The primary reason behind NOA's excellence is its dual search strategy approach, which expertly balances exploration and exploitation throughout the search process. As described in Section 3, the dual-strategy approach consists of two overall strategies: a foraging and storage strategy, and a caching and restoration strategy. These strategies work synergistically to facilitate a dynamic and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**NOA vs.** & **PSO** & **h** & **FWA** & **h** & **WOA** & **h** \\ \hline SDM & \(3.01985\times 10^{-11}\) & 1 & \(1.91209\times 10^{-9}\) & 1 & \(3.01985\times 10^{-11}\) & 1 \\ DDM & \(2.97473\times 10^{-11}\) & 1 & \(1.90126\times 10^{-9}\) & 1 & \(3.00270\times 10^{-11}\) & 1 \\ TDM & \(2.50779\times 10^{-11}\) & 1 & \(2.80032\times 10^{-11}\) & 1 & \(3.00098\times 10^{-11}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Wilcoxon rank test, comparative results. Figure 3: Simulated I-V curves of (a) SDM, (b) DDM, (c) TDM. adaptable search process that bypass local optima and quickly converge on the expected high-quality solution. The algorithm uses random numbers in each stage of various strategies during the optimization process, enhancing its adaptability and responsiveness to the search environment, which enables it to deal with complex multi-dimensional nonlinear optimization problems effectively.