## 4 Simulation Results
### Applications of RTC France PV
#### 4.1.2 Case 2: DD Model of RTC France PV  
In this instance, the recommended MGA is used to extract the R.T.C. France cell's DD model features. The seven unknown DD model parameters for various inspirational approaches that produced the greatest results in the experiment are listed in Table 3. The findings demonstrate that, in terms of competitiveness, the suggested MGA performs better than the comparable methods. This indicates that the optimal RMSE value of 9.8249 \(\times\) 10\({}^{-4}\) is achieved by the suggested MGA. Furthermore, this Table shows the PV-derived electrical parameters using the established optimization techniques; these include the Dwarf Mongoose Optimizer (DMO) [58], RIME [49], modified DMO [58], and modified RIME [49]. Moreover, this Table specifies the assessed parameters of the proposed MGA, which are 55.485441 \(\Omega\), 0.0367404 \(\Omega\), 0.7607811 A, 7.493 \(\times\) 10\({}^{-1}\) uA, 2.26\(\times\) 10\({}^{-1}\) uA, and 2, 1.4510 for the shunt resistance, series resistance, photo-current, saturation current for d1 and d2, and ideality factor for d1 and d2 respectively. Figure 4: (**a**) I–V and (**b**) P–V characteristics for the SD of the R.T.C. France cell using the suggested MGA. Figure 5: Overall discrepancies in currents and powers between the measured and simulated for the SD model of the R.T.C. France cell using MGA. Furthermore, Figure 6 illustrates fifty obtained RMSE objectives for the SD and DD of the R.T.C. France cell. This figure characterizes that the RMSE of MGA for the SD and DD models are 9.86022 \(\times\)\(10^{-4}\) and 9.82485 \(\times\)\(10^{-4}\). The worst values for the SD and DD models are the same value of 9.86022 \(\times\)\(10^{-4}\). The mean values for the SD and DD models are 9.86022 \(\times\)\(10^{-4}\) and 9.83096 \(\times\)\(10^{-4}\), respectively. The standard deviation for the SD and DD models are 1.49963 \(\times\)\(10^{-7}\) and 1.29387 \(\times\)\(10^{-6}\), respectively. These outcomes support the developed MGA's superiority for the R.T.C. France cell's SD and DD models. As a result, the recommended MGA produced the most significant value, showing that MGA ensures stability, precision, and effectiveness when comparing the parameters of the SD and DD models. The MGA's identification of the SD and DD models' validity is dependable. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Applied Algorithm** & **RIME** & **DMO** & **MRIME** & **MDMO** & **MGA** \\ \hline \(I_{\text{Pl}}\) (A) & 0.760864277 & 0.761086003 & 0.760780758 & 0.760777046 & 0.760781079 \\ \hline \(R_{\text{ss}}\) (\(\Omega\)) & 0.036173672 & 0.036452844 & 0.036767981 & 0.03658083 & 0.03674043 \\ \hline \(R_{\text{Sh}}\) (\(\Omega\)) & 53.58354831 & 56.0407128 & 55.64800559 & 54.7047585 & 55.48544096 \\ \hline \(I_{\text{S1}}\) (A) & \(4.3113\times 10^{-8}\) & \(3.81141\times 10^{-7}\) & \(8.0438\times 10^{-7}\) & \(4.27843\times 10^{-7}\) & \(7.49347\times 10^{-7}\) \\ \hline \(\eta_{1}\) & 1.827202939 & 1.83357911 & 1.999974446 & 1.991913976 & 2 \\ \hline \(I_{\text{S2}}\) (A) & 3.25421 \(\times\)\(10^{-7}\) & 2.38858 \(\times\)\(10^{-7}\) & 2.19744 \(\times\)\(10^{-7}\) & 2.63353 \(\times\)\(10^{-7}\) & 2.25974 \(\times\)\(10^{-7}\) \\ \hline \(\eta_{2}\) & 1.482783518 & 1.458364626 & 1.448694376 & 1.463888853 & 1.45101678 \\ \hline \(RMSE\) & \(9.9382\times 10^{-4}\) & \(1.028696\times 10^{-3}\) & \(9.8251\times 10^{-4}\) & \(9.83217\times 10^{-4}\) & \(9.82485\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Acquired parameters for the R.T.C. France PV module (DD model) using MGA compared to the reported results. Figure 6: Fifty obtained RMSE objectives for SD and DD models of the R.T.C. France cell. Figure 7a,b display the measured and simulated I-V and P-V characteristics for the DD model. It is demonstrable that the data generated by the MGA technique closely resemble the data acquired by experimentation, suggesting that the MGA technique was successful in producing power and current at a range of voltage levels.