## 4 Experimental Results
### Results of Parameter Extraction Based on the DDM  
The best solutions found by competitive algorithms for the DDMs with \(n=40\) and \(n=80\), including the PV parameters and optimal RMSE values, are represented in Table 5. From the table, it can be seen that the CO obtained the best RMSE value of 9.824848822723 \(\times\) 10\({}^{-4}\) for \(n=40\), followed by the ICO with an RMSE of 9.824860991382 \(\times\) 10\({}^{-4}\). Additionally, for \(n=80\), these optimizers obtained the best results out of the 12 algorithms. Conversely, SSA and GWO produced the worst results. Figure 7a,b illustrates the I-V and P-V curves, respectively, using the measured and estimated data for the DDM model. The corresponding IAEI and IAEP are illustrated in Figure 7c,d, respectively, indicating that the CO and ICO were incredibly accurate in estimating the DDM parameters. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \(n\) & **Algorithm** & \(I_{p}\)**(A)** & **I(A)** & \(R_{sh}\)**(\(\Omega\))** & \(R_{s}\)**(\(\Omega\))** & \(u\)** & **RMSE** \\ \hline \multirow{9}{*}{40} & ICO & 0.761 & 3.23 \(\times\) 10\({}^{-7}\) & 53.719 & 0.0364 & 1.4812 & 9.860218778914 \(\times\) 10\({}^{-4}\) \\  & CO & 0.761 & 3.23 \(\times\) 10\({}^{-7}\) & 53.719 & 0.0364 & 1.4812 & 9.860218778914 \(\times\) 10\({}^{-4}\) \\  & DE & 0.763 & 3.18 \(\times\) 10\({}^{-6}\) & 100.000 & 0.0243 & 1.7547 & 5.274028415510 \(\times\) 10\({}^{-3}\) \\  & PSO & 0.761 & 2.67 \(\times\) 10\({}^{-7}\) & 48.768 & 0.0371 & 1.4623 & 1.049908843005 \(\times\) 10\({}^{-3}\) \\  & GA & 0.764 & 2.63 \(\times\) 10\({}^{-6}\) & 70.532 & 0.0257 & 1.7285 & 5.028715197625 \(\times\) 10\({}^{-3}\) \\  & TLBO & 0.761 & 3.77 \(\times\) 10\({}^{-7}\) & 63.546 & 0.0358 & 1.4967 & 1.061394487359 \(\times\) 10\({}^{-3}\) \\  & SEDE & 0.761 & 3.23 \(\times\) 10\({}^{-7}\) & 53.719 & 0.0364 & 1.4812 & 9.860218778915 \(\times\) 10\({}^{-4}\) \\  & JAYA & 0.761 & 6.08 \(\times\) 10\({}^{-7}\) & 70.138 & 0.0337 & 1.5478 & 1.596303826167 \(\times\) 10\({}^{-3}\) \\  & PGJAYA & 0.761 & 3.23 \(\times\) 10\({}^{-7}\) & 53.713 & 0.0364 & 1.4812 & 9.860219332331 \(\times\) 10\({}^{-4}\) \\  & WSO & 0.761 & 3.23 \(\times\) 10\({}^{-7}\) & 53.719 & 0.0364 & 1.4812 & 9.860219332331 \(\times\) 10\({}^{-4}\) \\  & GWO & 0.838 & 0.0000000 & 1.139 & 0.0000 & 2.0000 & 2.228699161204 \(\times\) 10\({}^{-1}\) \\  & SSA & 0.835 & 0.0000000 & 1.162 & 0.0000 & 1.0000 & 2.228762271791 \(\times\) 10\({}^{-1}\) \\ \hline \multirow{9}{*}{80} & ICO & 0.761 & 3.23 \(\times\) 10\({}^{-7}\) & 53.719 & 0.0364 & 1.4812 & 9.860218778914 \(\times\) 10\({}^{-4}\) \\  & CO & 0.761 & 3.23 \(\times\) 10\({}^{-7}\) & 53.719 & 0.0364 & 1.4812 & 9.860218778914 \(\times\) 10\({}^{-4}\) \\  & DE & 0.763 & 1.54 \(\times\) 10\({}^{-6}\) & 99.600 & 0.0296 & 1.6569 & 3.541687987531 \(\times\) 10\({}^{-3}\) \\  & PSO & 0.761 & 3.54 \(\times\) 10\({}^{-7}\) & 56.556 & 0.0360 & 1.4903 & 1.001530647734 \(\times\) 10\({}^{-3}\) \\  & GA & 0.759 & 1.29 \(\times\) 10\({}^{-7}\) & 46.427 & 0.0399 & 1.3938 & 2.24830938365 \(\times\) 10\({}^{-3}\) \\  & TLBO & 0.761 & 3.40 \(\times\) 10\({}^{-7}\) & 55.608 & 0.0362 & 1.4865 & 9.917684200620 \(\times\) 10\({}^{-4}\) \\  & SEDE & 0.761 & 3.36 \(\times\) 10\({}^{-7}\) & 54.054 & 0.0362 & 1.4852 & 9.902825250634 \(\times\) 10\({}^{-4}\) \\  & JAYA & 0.762 & 9.73 \(\times\) 10\({}^{-7}\) & 88.523 & 0.0312 & 1.6013 & 2.589835639165 \(\times\) 10\({}^{-3}\) \\  & PGJAYA & 0.761 & 3.23 \(\times\) 10\({}^{-7}\) & 53.722 & 0.0364 & 1.4812 & 9.860220454267 \(\times\) 10\({}^{-4}\) \\  & WSO & 0.761 & 3.23 \(\times\) 10\({}^{-7}\) & 53.719 & 0.0364 & 1.4812 & 9.860218778915 \(\times\) 10\({}^{-4}\) \\  & GWO & 0.769 & 4.43 \(\times\) 10\({}^{-6}\) & 24.455 & 0.0200 & 1.8059 & 9.281563258264 \(\times\) 10\({}^{-3}\) \\  & SSA & 1.000 & 8.72 \(\times\) 10\({}^{-7}\) & 1.098 & 0.0007 & 1.6512 & 1.525312427660 \(\times\) 10\({}^{-1}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Optimal parameters of SDM obtained by different algorithms with \(n=40\).