## 5 Experiments and Results
### Detailed Result Comparison of Three Studies
#### 5.1.2 Results on PV Cell of RTC France in DDM  
For the double-diode model on the PV cell of RTC France in Table 4, the best result of estimation parameters and RMSE for different algorithms are listed. It is clear that only the DLMVO and Rcr-JADE provide the best RMSE value (9.8248 \(\times\) 10\({}^{-4}\)) among all compared  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & \(I_{ph}\) **(A)** & \(I_{scl1}\) **(\(\mu\)A)** & \(R_{s}\) **(\(\Omega\))** & \(R_{sh}\) **(\(\Omega\))** & \(n_{1}\) & RMSE \\ \hline DLMVO & 0.7608 & 0.3230 & 0.0364 & 53.7185 & 1.4812 & **9.8602 \(\times\) 10\({}^{-4}\)** \\ MVO & 0.7599 & 0.3520 & 0.0361 & 91.1355 & 1.4900 & 1.1399 \(\times\) 10\({}^{-3}\) \\ QMVO & 0.7607 & 0.3176 & 0.0364 & 53.5931 & 1.4795 & 9.8750 \(\times\) 10\({}^{-4}\) \\ Rcr-JADE & 0.7608 & 0.3230 & 0.0364 & 53.7185 & 1.4812 & **9.8602 \(\times\) 10\({}^{-4}\)** \\ IWOA & 0.7608 & 0.3230 & 0.0364 & 53.7185 & 1.4812 & **9.8602 \(\times\) 10\({}^{-4}\)** \\ CLPSO & 0.7608 & 0.3330 & 0.0362 & 53.9788 & 1.4843 & 9.8879 \(\times\) 10\({}^{-4}\) \\ IJAYA & 0.7608 & 0.3228 & 0.0364 & 53.7595 & 1.4811 & 9.8603 \(\times\) 10\({}^{-4}\) \\ PGJAYA & 0.7608 & 0.3230 & 0.0364 & 53.7185 & 1.4812 & **9.8602 \(\times\) 10\({}^{-4}\)** \\ SATLBO & 0.7608 & 0.3230 & 0.0364 & 53.7185 & 1.4812 & **9.8602 \(\times\) 10\({}^{-4}\)** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Detailed results among different algorithms on SDM.  
Figure 6: Comparisons between measured data and simulated data obtained by DLMVO for SDM **(a)** I-V curves and **(b)** P-V curves.  
algorithms, and MVO still obtained the worst results. It is worth mentioning that IWOA, PGJAYA, and SATLBO, which can obtain the best results in parameter extraction of SDM, failed to obtain the best identification results in the parameter extraction experiment of DDM. This is because the DDM has seven unknowns, which requires a higher optimization solver than the parameter extraction of SDM. In addition, to demonstrate the accuracy of the DMM parameters extracted by the DLMVO, the I-V curves and P-V curves between measured and simulated data are shown in Figure 7, where the simulated data generated by the DLMVO also highly matched with the experimental data.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Algorithm** & \(I_{ph}\)**(A)** & \(I_{sd1}\)**(\(\mu\)A)** & \(I_{sd2}\)**(\(\mu\)A)** & \(R_{s}\)**(f)** & \(R_{sh}\)**(f)** & \(n_{1}\)** & \(n_{2}\) & \(RMSE\) \\ \hline DLMVO & 0.7608 & 0.7493 & 0.2260 & 0.0367 & 55.4854 & 2.0000 & 1.4510 & \(9.8248\times 10^{-4}\) \\ MVO & 0.7608 & 0.9689 & 0.0441 & 0.0373 & 57.6769 & 1.7347 & 1.3388 & \(1.0236\times 10^{-3}\) \\ QMVO & 0.7608 & 0.4753 & 0.2588 & 0.0366 & 54.7998 & 1.9999 & 1.4624 & \(9.8301\times 10^{-4}\) \\ Rcr-JADE & 0.7608 & 0.7493 & 0.2260 & 0.0367 & 55.4854 & 2.0000 & 1.4510 & \(9.8248\times 10^{-4}\) \\ IWOA & 0.7609 & 0.6771 & 0.2355 & 0.0367 & 55.4082 & 2.0000 & 1.4545 & \(9.8255\times 10^{-4}\) \\ CIPSO & 0.7606 & 0.0052 & 0.3380 & 0.0362 & 56.4635 & 1.4088 & 1.4893 & \(9.9492\times 10^{-4}\) \\ IJAYA & 0.7601 & 0.0050 & 0.7509 & 0.0376 & 77.8519 & 1.2186 & 1.6247 & \(9.8293\times 10^{-4}\) \\ PGJAYA & 0.7608 & 0.2103 & 0.8853 & 0.0368 & 55.8135 & 1.4450 & 2.0000 & \(9.8263\times 10^{-4}\) \\ SATLBO & 0.7608 & 0.2336 & 0.6849 & 0.0367 & 55.3382 & 1.4538 & 2.0000 & \(9.8252\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Detailed results among different algorithms on DDM.  
Figure 7: Comparisons between measured data and simulated data obtained by DLMVO for DDM (**a**) I-V curves and (**b**) P-V curves.