## 4 Experimental Results
### Comparison of Statistical Results  
For a clearer understanding of the comparison, the statistical results were also saved. We recorded the maximum (Max), the minimum (Min), the mean (Mean), and the standard deviation (SD) of the RMSE over 30 independent runs for each algorithm. By comparing the Min, Mean, and SD values of the RMSE, one can measure the accuracy, the average accuracy, and the robustness of the applied algorithms. Tables 7-9 present the statistical results for the 12 algorithms with \(n=40\) and \(n=80\) through 30 runs to identify the unknown parameters of the three PV models. A bold value indicates the algorithm that produced the best results. A Freidman test was used to determine the performance ranking of the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\pi\) & **Algorithm** & \(\mathbf{I_{p}(A)}\) & \(\mathbf{I(A)}\) & \(\mathbf{R_{sh}(\Omega)}\) & \(\mathbf{R_{s}(\Omega)}\) & \(\mathbf{u}\) & **RMSE** \\ \hline \multirow{8}{*}{80} & ICO & 1.03051 & \(3.48\times 10^{-6}\) & 27.277 & 0.0334 & 1.3512 & 2.42507486095010 \(\times 10^{-3}\) \\  & CO & 1.03051 & \(3.48\times 10^{-6}\) & 27.277 & 0.0334 & 1.3512 & 2.42507486094990 \(\times 10^{-3}\) \\  & DE & 1.02868 & \(2.27\times 10^{-5}\) & 1968.622 & 0.0264 & 1.5866 & 6.921126739647050 \(\times 10^{-3}\) \\  & PSO & 1.02664 & \(6.66\times 10^{-6}\) & 115.721 & 0.0314 & 1.4238 & 3.029451135597340 \(\times 10^{-3}\) \\  & GA & 1.03138 & \(2.87\times 10^{-5}\) & 2000.000 & 0.0252 & 1.6215 & 7.71296359673400 \(\times 10^{-3}\) \\  & TLDG & 1.02522 & \(5.63\times 10^{-6}\) & 881.405 & 0.0321 & 1.4034 & 3.2444520320505 \(\times 10^{-3}\) \\  & SEDE & 1.03013 & \(3.56\times 10^{-6}\) & 28.820 & 0.0333 & 1.3536 & 2.427162452872220 \(\times 10^{-3}\) \\  & JAYA & 1.02758 & \(1.51\times 10^{-5}\) & 1713.306 & 0.0277 & 1.5278 & 5.590303266807740 \(\times 10^{-3}\) \\  & PGJAYA & 1.02922 & \(4.29\times 10^{-6}\) & 33.745 & 0.0327 & 1.3739 & 2.518017787843970 \(\times 10^{-3}\) \\  & WSO & 1.03051 & \(3.48\times 10^{-6}\) & 27.277 & 0.0334 & 1.3512 & 2.425074860895060 \(\times 10^{-3}\) \\  & GWO & 1.07157 & \(5.00\times 10^{-5}\) & 5.528 & 0.0187 & 1.7213 & 2.019064583084870 \(\times 10^{-2}\) \\  & SSA & 1.06056 & \(4.31\times 10^{-5}\) & 12.652 & 0.0238 & 1.6888 & 1.554532543514840 \(\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: \(Cont.\)  
Figure 8: Estimated and measured data yielded by the ICO for the PV module model based on Photo Watt-PWP 201: (**a**) I–V, (**b**) P–V, (**c**) IAEI, and (**d**) IAEP. For the SDM, as shown in Table 7, when \(n=40\), the ICO, CO, and SEDE gave the best and average accuracy results in terms of the Min and Mean values. However, in terms of robustness, the ICO with an SD value of 3.091 \(\times\) 10\({}^{-17}\) showed the best performance among the competitive algorithms. PGJAYA and WSO showed the second- and third-best accuracies, respectively. According to the Friedman test, the CO showed the best performance, and the ICO had the second-best performance among the 12 algorithms. Aside from that, when \(n=80\), the ICO and CO showed the best accuracy, and WSO showed the second-best accuracy. However, in terms of reliability, the ICO and CO with SD values of 5.21 \(\times\) 10\({}^{-17}\) and 1.02 \(\times\) 10\({}^{-16}\) were the best and second-best among the competitive algorithms, respectively. Based on the [PERSON] signed rank test, there was no significant difference between the ICO and CO, while they obtained significantly superior results compared with the other competitive algorithms. When it comes to the DDM, as represented in Table 8, the CO resulted in the best accuracy, and the ICO obtained the best average accuracy among the tested algorithms. The ICO's accuracy in terms of the minimum value of the RMSE was very similar to the result of the CO, and other algorithms were unable to approach it. The ICO and CO rank first and second in terms of robustness, respectively.