# 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  
#### 4.2.1 Single Diode Model  
Table 3 provides the optimal values of the control variables related to the best run for the compared algorithms. As shown, TFWO obtains the minimum _RMSE_ of 0.000986022 compared to the others. Based on TFWO, the photo-generated current is 0.760775529 A; the dark saturation current of the SDM is 0.323 uA; the diode ideality factor is 1.481183723; the series resistance is 0.036377085 \(\Omega\); the shunt resistance is 53.71858096 \(\Omega\). Figure 5 describes \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Published Year** & **Recent Applications** \\ \hline BSA [47] & 2013 & Reconfiguration in distribution networks (2020) [54], reactive power dispatch (2018) [55], parameter \\  & & optimization of the support vector machine (2020) [56]. \\ \hline GWO [48] & 2014 & Coordination of VAR compensators and distributed energy resources (2020) [57], allocation of distributed \\  & & generation in power systems (2020) [58], energy management, and battery size optimization (2020) [59]. \\ \hline CSO [49] & 2016 & Short-term wind speed forecasting (2020) [60], capacitor allocation in distribution networks (2017) [61], \\  & & emission economic dispatch [62] \\ \hline EO [50] & 2020 & Multi-thresholding image segmentation problems [63], operation of hybrid AC/DC grids (2020) [64]. \\ \hline MPA [51] & 2020 & Large-scale photovoltaic array reconfiguration (2020) [65], task scheduling in IoT-based fog computing \\  & & applications (2020) [66]. \\ \hline BSDE [52] & 2021 & Not applicable yet. \\ \hline MRFO [53] & 2020 & Fuel cell exergy analysis (2020) [67], optimal power flow (2020) [68], maximum power point (2020) [69]. \\ \hline TFWO [45] & 2021 & Not applicable yet. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Several recent applications of the compared algorithms. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & \(\mathbf{I_{ph}}\) **(A)** & \(\mathbf{I_{d1}}\) **(A)** & \(\mathbf{a_{1}}\) & \(\mathbf{R_{s}}\) **(\(\Omega\))** & \(\mathbf{R_{sh}}\) **(\(\Omega\))** & **RMSE** \\ \hline TFWO & 0.760775529 & 3.23 \(\times\)\(10^{-7}\) & 1.481183723 & 0.036377085 & 53.71858096 & 0.000986022 \\ MRFO & 0.760778817 & 3.22884 \(\times\)\(10^{-7}\) & 1.481141648 & 0.036380748 & 53.67819867 & 0.000986034 \\ BSDE & 0.760773529 & 3.23008 \(\times\)\(10^{-7}\) & 1.481179386 & 0.036378015 & 53.74364455 & 0.000986023 \\ MPA & 0.760846832 & 3.22991 \(\times\)\(10^{-7}\) & 1.48119268 & 0.036361364 & 52.76698061 & 0.000987369 \\ EO & 0.76077794 & 3.22162 \(\times\)\(10^{-7}\) & 1.480915424 & 0.036387935 & 53.64156933 & 0.000986035 \\ CSO & 0.760757142 & 3.24211 \(\times\)\(10^{-7}\) & 1.481546607 & 0.036366384 & 54.0990705 & 0.000986181 \\ GWO & 0.760695583 & 3.58429 \(\times\)\(10^{-7}\) & 1.491737687 & 0.035974121 & 57.26269608 & 0.001008231 \\ BSA & 0.760850914 & 3.11696 \(\times\)\(10^{-7}\) & 1.477614787 & 0.036510097 & 51.96067738 & 0.000989471 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parameters extracted for R.T.C. France SDM at the best root mean square error (_RMSE_). the convergence rates of the algorithms and shows that the capability of the proposed TFWO in finding the minimum \(RMSE\) is the fastest. Based on the extracted PV parameters using the TFWO, Figure 6 describes the I-V and P-V characteristic curves in comparison to the experimental data. This figure illustrates the great similarity between the extracted curves based on TFWO and the experimental results. Figure 7 shows this capability, where the error for each value of current and power is shown between the simulated and experimental data to measure the quality of the result. Table 4 records the minimum, maximum, mean, and standard deviation of the \(RMSE\) for the SDM. This table declares that TFWO presents the highest robustness characteristics.