# Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm
## 3 Results and Discussion
### mSi Cell
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**Algorithm** & **Model** & \(I_{\mu}\)**(A) & \(I_{\mu}\)**(A/A) & \(n_{1}\)** & \(R_{\mu}\)**(A/B) & \(R_{\mu}\)**(A/B) & \(I_{\mu}\)**(A/B) & \(n_{2}\)** & **RMSE** & **MSE** & **MSE** & **STD** \\ \hline
**PSA** & **SDM** & **0.425750202** & **0.517217783** & **1.47956503** & **0.091302173** & **99.1799271** & - & - & **5.63906 \(\times\) 10\({}^{-4}\)** & **1.025410758621 \(\times\) 10\({}^{-7}\)** & **5.533625 \(\times\) 10\({}^{-2}\)** \\ \hline BOA & SDM & 0.425745 & 0.523619 & 1.68107 & 0.0911642 & 99.8127 & - & - & 5.5854 \(\times\) 10\({}^{-4}\) & 7.0257503483 \(\times\) 10\({}^{-5}\) & 5.53362 \(\times\) 10\({}^{-2}\) \\ \hline HSDA & SDM & 0.425753 & 0.516241 & 1.679334 & 0.0913289 & 99.07598 & - & - & 5.63098 \(\times\) 10\({}^{-4}\) & 3.80064 \(\times\) 10\({}^{-7}\) & 5.533616 \(\times\) 10\({}^{-2}\) \\ \hline MOA & SDM & 0.426020 & 0.54433 & 1.4429 & 0.11186 & 50.305 & - & - & 1.8456 \(\times\) 10\({}^{-3}\) & 5.53840 \(\times\) 10\({}^{-1}\) & 1.290548 \(\times\) 10\({}^{-6}\) \\ \hline
**PSA** & **DDM** & **0.42511171** & **2.9925786** & **2.0093446** & **0.11383041** & **200.0** & **2.29042278 \(\times\) 10\({}^{-8}\)** & **1.000** & **2.26166 \(\times\) 10\({}^{-4}\)** & **2.0283182724 \(\times\) 10\({}^{-8}\)** & **5.527190 \(\times\) 10\({}^{-2}\)** \\ \hline BOA & DDM & 0.425579 & 0.313003 & 1.53882 & 0.0806953 & 130.184 & 7.18119 & 2.57289 & 4.4308 \(\times\) 10\({}^{-1}\) & 1.0256313971 \(\times\) 10\({}^{-7}\) & 5.535605 \(\times\) 10\({}^{-2}\) \\ \hline HSDA & DDM & 0.425748 & 0.2402586 & 1.879334 & 0.0913289 & 105.075 & 1.0031352 & 2.091868 & 5.3057 \(\times\) 10\({}^{-4}\) & -5.75799 \(\times\) 10\({}^{-7}\) & 7.307780 \(\times\) 10\({}^{-2}\) \\ \hline BMOA & DDM & 0.425731 & 0.056095 & 1.4532 & 0.10822 & 53.106 & 0.35674 & 2.0685 & 1.3754 \(\times\) 10\({}^{-3}\) & 2.40771 \(\times\) 10\({}^{-4}\) & 5.535128 \(\times\) 10\({}^{-2}\) \\ \hline \end{tabular}
\end{table} 
Table 11: mSI photovoltaic cell RMSE and extracted parameters for various algorithms. In terms of the SDM, the RMSE value achieved by the PSA is not exceeded by ISOA; however, it does vary slightly from HSDA. In the instance of the DDM, the RMSE value improves by 40.9% when compared to ISOA and 50.58% when compared to HSDA. Despite these gains, the RMSE for both models generated by the BMOW algorithm is still greater than that achieved by the PSA. The SDM's RMSE findings show that the PSA was below ISOA's RMSE value, with the discrepancies in the extracted parameters being very small. But there are notable differences when compared to other algorithms like BMOA and HSDA. In contrast, the PSA surpasses all other algorithms in the DDM with a high improvement, as seen in Table 11.  
The performance of the BMOA was poor, since it became stuck in a local minimum and could not achieve the optimal results. When comparing the PSA findings to those of other algorithms, significant discrepancies were found after assessing all of the obtained parameters for both models. The PSA's parameters, specifically in the SDM, exhibited only minor variations in values compared to ISOA, resulting in a greater RMSE value than that attained by ISOA, where ISOA obtained 5.5854 \(\times\) 10\({}^{-4}\) while PSA obtained 5.63096 \(\times\) 10\({}^{-4}\). The PSA, however, produced significant improvements in the DDM, notably in reverse saturation for the recombination and generation processes, as well as changes in series and shunt resistance. In terms of RMSE, PSA obtained 2.6216 \(\times\) 10\({}^{-4}\) while ISOA obtained 4.4383 \(\times\) 10\({}^{-4}\), representing an improvement of around 40.9% by PSA in this case. When compared to ISOA and HSDA, these improvements produced a greater overall improvement. Importantly, the PSA's capability to locate the ideal solution and avoid being trapped in local minima is shown by the assessment of all mSi photovoltaic cell characteristics and the RMSE.