# Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm
## 3 Results and Discussion
### RTC France Cell
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Algorithm** & **Model** & \(I_{\mu_{A}}\) **(A)** & \(I_{\mu_{A}}\)**(A/A)** & \(m_{1}\) & \(R_{A}\)**(H)** & \(R_{A}\)**(H)** & \(L_{\mu_{B}}\)**(A/A)** & \(m_{2}\) & **RMSE** & **MSE** & **MSE** & **STD** \\ \hline ACS & DDM & 0.76078 & 0.22732 & 1.45151 & 0.036717 & 55.3951 & 0.72895 & 1.99879 & 9.8745 \(\times\) 10\({}^{-4}\) & 6.287730/9923 \(\times\) 10\({}^{-5}\) & 1.004967 \(\times\) 10\({}^{-3}\) \\ \hline BMOL & DOM & 0.760779169 & 0.766320100 & 2.0000000 & 0.026730850 & 55.667344 & 0.2251486 & 1.45077800 & 9.8252 \(\times\) 10\({}^{-4}\) & \(-\)2.6153864/1624 \(\times\) 10\({}^{-8}\) & 1.001984 \(\times\) 10\({}^{-3}\) \\ \hline HSDA & DOM & 0.76079412 & 0.2267302 & 1.451 & 0.03676287 & 55.996385 & 0.8284708 & 2.0030627 & 9.8217 \(\times\) 10\({}^{-4}\) & 3.302306/99231 \(\times\) 10\({}^{-4}\) & 1.001620 \(\times\) 10\({}^{-3}\) \\ \hline MSPS & DOM & 0.76078108 & 0.74934986 & 2.0000000 & 0.0267403 & 55.4854892 & 0.225940 & 1.45101648 & 9.8248 \(\times\) 10\({}^{-4}\) & 3.807620/992355 \(\times\) 10\({}^{-4}\) & 1.001924 \(\times\) 10\({}^{-3}\) \\ \hline GSC & DOM & 0.7608 & 0.2959 & 1.4627 & 0.0366 & 54.93037 & 4.07191 & 1.9939 & 9.8248 \(\times\) 10\({}^{-4}\) & 4.0382384/15 \(\times\) 10\({}^{-3}\) & 1.00134 \(\times\) 10\({}^{-3}\) \\ \hline MGCTO & DOM & 0.76087810 & 0.225974 & 1.4510167 & 0.0267404 & 55.485441 & 0.7493400 & 1.999999 & 9.8248 \(\times\) 10\({}^{-4}\) & 2.99270/69009 \(\times\) 10\({}^{-4}\) & 1.001924 \(\times\) 10\({}^{-3}\) \\ \hline LCJAPA & DOM & 0.7608 & 0.225976 & 1.4518 & 0.0387 & 55.4815 & 0.74640 & 2.000 & 3.0123 \(\times\) 10\({}^{-3}\) & 1.0052396/1538 \(\times\) 10\({}^{-3}\) & 2.997699 \(\times\) 10\({}^{-3}\) \\ \hline DE & DOM & 0.7605 & 0.423220 & 1.87579 & 0.02061 & 51.9945 & 0.18726 & 1.45062 & 3.086 \(\times\) 10\({}^{-2}\) & 1.18194/61538 \(\times\) 10\({}^{-2}\) & 2.97886 \(\times\) 10\({}^{-2}\) \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._Figure 4: RTC SDM and DDM I-V characteristics. Figure 5: RTC SDM and DDM P-V characteristics. Figure 6: RTC SDM and DDM calculated absolute error. The PSA's convergence curves for both models are shown in Figure 7, where the maximum iteration was 1500 and the population size was 100. The figure displays the iteration at which we began obtaining the least RMSE value, which is around 250 iterations at population 45 in the case of the SDM and population 93 in the case of the DDM. Additionally, shaded regions representing \(\pm\) standard deviation across the iterations are included to illustrate the algorithm's stability and convergence behavior over time. These bands reflect the variation in RMSE values and help assess the degree of fluctuation in the optimization process. Narrower bands indicate more consistent performance, while wider bands suggest increased variability. Another study focuses on how the RTC photovoltaic cell's RMSE and computation time change with iteration and population size. To find the best population size and iteration rate combination for minimizing the RMSE value, two studies were carried out. The population size ranged from 20 to 100, and both models were examined in the first study with a set number of iterations of 100. However, this method did not produce the best results because the smallest RMSE value was reached when the population size and iteration were both set to 100. The results of this analysis produced a SDM with an RMSE value of 2.0060 \(\times\) 10\({}^{-3}\) and a compute time of 0.3747 s. With a computation time of 0.5862 s, the DDM's minimal RMSE value was 4.5336 \(\times\) 10\({}^{-3}\). In the second study, the number of iterations was changed by a step of 200 while keeping the population size fixed. This method made it possible to determine the algorithm's lowest possible RMSE value. The optimum RMSE solution for the SDM needed a population size of 50 and 1100 iterations, which took around 2.056 s to compute. With a population size of 50 and 1500 iterations, the DDM took around 4.632 s to compute.