# Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm
## 3 Results and Discussion
### aSi Cell
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Algorithm** & **Model** & \(I_{\mu}\)**(A) & \(I_{\mu}\)**(A) & \(n_{1}\)**(A) & \(n_{1}\)**(A) & \(R_{\alpha}\)**(A) & \(I_{\alpha}\)**(A) & \(n_{2}\)**(A) & \(n_{3}\)**(A) & \(n_{4}\)**(A) & \(n_{5}\)**(A) & \(n_{6}\)**(A) \\ \hline
**PSA** & **SDM** & **0.0113447220** & **0.736897291** & **3.346417** & **1.82123 \(\times\) 10\({}^{-14}\)** & **523.153423** & **-** & **-** & **4.64123 \(\times\) 10\({}^{-3}\)** & **-** & **-** & **-** \\ \hline BWOA & SOM & 0.011347220 & 0.736907259 & 3.336417 & 0.01 & 523.153416 & **-** & **-** & 4.64123 \(\times\) 10\({}^{-3}\) & 2.159064642 \(\times\) 10\({}^{-12}\) & 4.608524 \(\times\) 10\({}^{-5}\) \\ \hline SOA & SOM & 0.011344 & 0.741543 & 3.37156 & 1.1657 \(\times\) 10\({}^{-3}\) & 524.336 & **-** & **-** & 4.64127 \(\times\) 10\({}^{-3}\) & 3.66965627 \(\times\) 10\({}^{-7}\) & 4.605944 \(\times\) 10\({}^{-5}\) \\ \hline HSDA & SOM & 0.011347 & 0.7024526 & 3.353834 & 0.0040283 & 520.06510 & **-** & **-** & 4.64194 \(\times\) 10\({}^{-5}\) & 4.13377 \(\times\) 10\({}^{-7}\) & 4.61007 \(\times\) 10\({}^{-5}\) \\ \hline
**PSA** & **DDM** & **0.01133759** & **5.5097204** & **5.00009** & **0.8000000** & **0.606268** & **0.805810** & **2.71088634** & **4.0933 \(\times\) 10\({}^{-3}\)** & **3.678888895** \(\times\) 10\({}^{-4}\)** & **4.095979 \(\times\) 10\({}^{-5}\)** \\ \hline BWOA & DOM & 0.0113349013 & 3.49975120 & 4.9997203 & 0.380003610 & 584.641671 & 0.1561147 & 0.256719676 & 4.0943 \(\times\) 10\({}^{-3}\) & 9.3999975 \(\times\) 10\({}^{-3}\) & 4.248635 \(\times\) 10\({}^{-3}\) \\ \hline SOA & DOM & 0.01133334 & 0.164276 & 2.974484 & 0.347809 & 570.845 & 3.66266 & 4.99379 & 4.2596 \(\times\) 10\({}^{-5}\) & 2.60315 \(\times\) 10\({}^{-3}\) & 4.258692 \(\times\) 10\({}^{-5}\) \\ \hline HSDA & DOM & 0.01134914 & 0.222195 & 3.079462 & 0.1987938 & 528.1008 & 1.0065304 & 4.0091152 & 4.4673 \(\times\) 10\({}^{-5}\) & -4.003470528 \(\times\) 10\({}^{-7}\) & 4.486736 \(\times\) 10\({}^{-5}\) \\ \hline \hline \end{tabular}  
The results of PSA algorithm are highlighted in bold.  
\end{table} 
Table 7: RMSE of the \(a\)Si photovoltaic cell and the extracted parameters for different algorithms. Disparities between the observed current and the estimated current for both models are shown in Figure 10 as absolute errors, determined by the algorithm. The convergence curves of the PSA with a maximum of 1500 iterations and a population size of 100 are shown in Figure 11. On the graph, the minimum RMSE value is seen to have been reached at roughly 150 iterations at population 37. Additionally, the figure includes shaded regions representing the \(\pm\) standard deviation of RMSE values across the iterations. These bands serve to highlight the consistency and stability of the PSA throughout the optimization process. A narrow-shaded area indicates that the RMSE values remained closely clustered, reflecting robust convergence behavior, whereas wider regions would signify greater variability and less consistent performance. Figure 10: aSi SDM and DDM calculated absolute error. Figure 9: aSi SDM and DDM P–V characteristics. In addition to the RTC, the aSi photovoltaic cell benefited from the research that was performed. The original study looked at both models with a fixed number of iterations set to 100, and the population size was between 20 and 100. However, the highest results were obtained by setting both the population size and the number of iterations to 100; therefore, this strategy was not optimal. The investigation showed that the SDM took 0.6133 s to compute and had an RMSE of 4.72 \(\times\) 10\({}^{-5}\). The DDM, on the other hand, minimized the RMSE to 1.52113 \(\times\) 10\({}^{-4}\) in only 0.9482 s.  
In the next experiment, we kept the sample size the same while increasing the number of iterations by a factor of 200. By making this modification, we were able to find the algorithm's minimum RMSE.