# Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm
## 3 Results and Discussion
### PVM Panel  
PVM, short for PVM 752 GaAs thin-film photovoltaic panel, is the second photovoltaic panel being examined. The PVM I-V characteristic is being measured at 1000 W/m\({}^{2}\) irradiance and 25 \({}^{\circ}\)C. The result is observed [29], containing the measured data and current values derived using the SDMs and DDMs, together with the corresponding errors, and can be found in Table S4. The characteristics of the PVM photovoltaic panel that were derived using the PSA for the SDMs and DDMs are shown in Table 15. The SDM takes 5.3845 s to execute, whereas the DDM takes 8.5250 s. The performance of the algorithm, comprising BWOA, HSDA, AOS, OBEDO, and Supply-Demand-Based Optimization (SDO) [49], is \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of Runs** & **Population** & **Number of Iterations** & **RMSE** & **Run Time(s)** \\ \hline \multirow{5}{*}{5} & 20 & 100 & \(1.5243\times 10^{-3}\) & 0.1945 \\ \cline{2-5}  & 30 & 100 & \(3.4145\times 10^{-3}\) & 0.2907 \\ \cline{2-5}  & 50 & 100 & \(4.2702\times 10^{-3}\) & 0.4771 \\ \cline{2-5}  & 60 & 100 & \(3.6405\times 10^{-3}\) & 0.5735 \\ \cline{2-5}  & 80 & 100 & \(3.4981\times 10^{-3}\) & 0.7634 \\ \cline{2-5}  & 100 & 100 & \(1.3605\times 10^{-3}\) & 0.9482 \\ \cline{2-5}  & 50 & 300 & \(2.8906\times 10^{-3}\) & 1.4260 \\ \cline{2-5}  & 50 & 500 & \(9.9828\times 10^{-4}\) & 2.3688 \\ \cline{2-5}  & 50 & 700 & \(1.3823\times 10^{-3}\) & 3.3233 \\ \cline{2-5}  & 50 & 900 & \(5.0116\times 10^{-4}\) & 4.2179 \\ \cline{2-5}  & 50 & 1100 & \(5.2988\times 10^{-4}\) & 5.4857 \\ \cline{2-5}  & 50 & 1300 & \(4.7973\times 10^{-4}\) & 6.4356 \\ \cline{2-5}  & 50 & 1500 & \(2.6216\times 10^{-4}\) & 7.0822 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: mSi iteration vs. population size DDM case. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of Runs** & **Model** & \
\begin{tabular}{c} **Population Size/** \\ **Number of Iterations** \\ \end{tabular} & **RMSE** &
\begin{tabular}{c} **Intel Core i9 CPU** \\ **Execution Time (s)** \\ \end{tabular} & **AMD Ryzen 5 5600H** \\ \hline \multirow{2}{*}{5} & SDM & 100/1100 & 5.6309 \(\times\) 10\({}^{-4}\) & 3.7890 & 6.1665 \\ \cline{2-5}  & DDM & 100/1100 & 2.6216 \(\times\) 10\({}^{-4}\) & 5.2777 & 8.8891 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: mSi CPU execution time. Both the PSA and the BWOA provide the same RMSE values for the SDM, indicating that there is little difference between the two approaches. However, when HSDA and SDO are put up against PSA, the proposed algorithm performs much better, yielding a 3% advantage over both algorithms. On the other hand, the RMSE improvement using the PSA for the DDM is impressive: 1.19% better than BWOA and 22.18% better than HSDA. Despite this, for both models, the RMSE produced using the PSA method is still better than other algorithms. According to the RMSE values for the SDM, the PSA method achieves the same results as BWOA (2.2780 \(\times\) 10\({}^{-4}\)), with hardly any changes in the parameters that are found. However, as demonstrated in Table 15, when comparing it with other algorithms such as BWOA and HSDA, significant discrepancies are found. The PSA performs better than other algorithms in all statistical tests, as shown in particular by the DDM. AOS algorithms were unable to locate the lowest RMSE value because they were caught in local minima, which prevented them from obtaining the ideal RMSE. On the other hand, compared to other methods, substantial differences may be found when examining all obtained parameters using the PSA approach for both models. In the instance of SDM, the PSA produced significantly larger parameter value differences for the \(I_{sd1}\) of 3.778895 \(\times\) 10\({}^{-6}\) compared to BWOA with 3.7788 \(\times\) 10\({}^{-12}\), which resulted in a significantly lower RMSE value. Compared to BWOA and HSDA, the PSA improved the DDM the most by changing the reverse saturation for the recombination and generation processes and showing the most change in series and shunt resistance.