# Estimating Parameters of Photovoltaic Models Using Accurate Turbulent Flow of Water Optimizer
## 4 Simulation Results and Discussion
### Statistical Analysis for R.T.C. France Solar Cell
#### 4.2.2 Double Diode Model  
The proposed TFWO and the compared algorithms are applied for this model. Table 5 provides the optimal values of the control variables related to the best run, while Figure 9 describes their convergence rates. From both, it can be observed that the best _RMSE_ value (0.000982723) is achieved by the TFWO algorithm, while the second-best _RMSE_ (0.000983378) is achieved by MRFO, followed by CSO, EO, BSDE, BSA, GWO, and MPA.  
Figure 8: The RMS values of the 30 runs for R.T.C. France SDM.  
Figure 9: The convergence curves for R.T.C. France DDM.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Algorithm** & \(\mathbf{I_{ph}}\) **(A)** & \(\mathbf{R_{s}}\) **(T)** & \(\mathbf{R_{sh}}\) **(f)** & **RMSE** & \(\mathbf{I_{21}}\) **(A)** & \(\mathbf{a_{1}}\) & \(\mathbf{I_{42}}\) **(A)** & \(\mathbf{a_{2}}\) \\ \hline TFWO & 0.760782016 & 0.036839463 & 55.91920478 & 0.000982723 & \(2.06\times 10^{-7}\) & 1.443289469 & \(9.24\times 10^{-7}\) & 2 \\ MRFO & 0.760743575 & 0.036597626 & 54.95169271 & 0.000983378 & 4.37429 \(\times 10^{-7}\) & 1.998364786 & \(2.62887\times 10^{-7}\) & 1.463671024 \\ BSDE & 0.760782257 & 0.036991096 & 54.62889674 & 0.000989247 & 1.38431 \(\times 10^{-7}\) & 1.416972632 & \(5.71114\times 10^{-7}\) & 1.764756216 \\ MPA & 0.760918727 & 0.037865706 & 53.18011281 & 0.001026823 & 7.66125 \(\times 10^{-8}\) & 1.36857525 & \(9.99997\times 10^{-7}\) & 1.815337209 \\ EO & 0.760741801 & 0.036326616 & 54.628321228 & 0.0009866861 & 3.06281 \(\times 10^{-7}\) & 1.492481793 & \(2.85646\times 10^{-8}\) & 1.428997568 \\ CSO & 0.760756875 & 0.03652498 & 54.63222775 & 0.000983888 & 3.22867 \(\times 10^{-7}\) & 1.992580518 & \(2.7755\times 10^{-7}\) & 1.46831668 \\ GWO & 0.760583028 & 0.036533827 & 58.81767959 & 0.001003603 & \(3.2814\times 10^{-7}\) & 1.563347542 & \(8.25411\times 10^{-8}\) & 1.41082037 \\ BSA & 0.760980002 & 0.036723119 & 53.23192348 & 0.000993668 & 2.64414 \(\times 10^{-7}\) & 1.705891588 & \(1.99393\times 10^{-7}\) & 1.446025602 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The parameters extracted for R.T.C. France DDM.  
Based on the extracted PV parameters using the TFWO, Figure 10 describes the I-V and P-V characteristic curves in comparison to the experimental data, while Figure 11 displays the related errors. From both figures, the coincidence of the simulated data based on TFWO with the experimental data is very high.  
Figure 11: Error values for R.T.C. France DDM based on TFWO: (**a**) Current error values and (**b**) power error values.  
Figure 10: Characteristic curves for R.T.C. France DDM based on TFWO: (**a**) I-V ch/s and (**b**) P-V ch/s.  
Table 6 records the minimum, maximum, mean, and standard deviation of the _RMSE_ for the DDM. This table declares that TFWO presents the highest robustness characteristics. It gives the lowest values of the minimum, maximum, mean, and standard deviation of the _RMSE_ as 0.000982723, 0.0012, 0.00099392, and 3.9352 \(\times\) 10\({}^{-5}\), respectively. Figure 12 displays the _RMSE_ values of the 30 runs for the R.T.C. France DDM. The acquired values of the _RMSE_ based on the proposed TFWO are lower than their comparable values based on the others.