# Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm
## 3 Results and Discussion
### RTC France Cell
In this instance, however, the PSA surpasses other algorithms across all statistical tests, as shown in Table 3. When all retrieved parameters are analyzed for both models using the PSA method, considerable differences can be detected when compared to other algorithms. In comparison to BWOA, the reverse saturation alteration for the diffusion mechanism is less in the DDM, varying by around 0.28%, but the difference for generation-recombination is high. As a result, it can be concluded that the DDM can accurately match the SDM in terms of parameter extraction and accuracy. Furthermore, the evaluation of all RTC photovoltaic cell parameters and the RMSE, MBE, and STD demonstrates the PSA's capability to find the optimal solution and avoid hitting local minima. In comparison to ISOA, both algorithms achieved the same RMSE of 9.8602 \(\times\) 10\({}^{-4}\); however, PSA yielded a significantly lower mean bias error (MBE) of 9.58 \(\times\) 10\({}^{-11}\) compared to ISOA's \(-\)1.57 \(\times\) 10\({}^{-8}\), indicating greater numerical stability. For the DDM, PSA achieved a better RMSE (9.7078 \(\times\) 10\({}^{-4}\)) than ISOA (9.8215 \(\times\) 10\({}^{-4}\)), as well as a notably reduced MBE (2.31 \(\times\) 10\({}^{-9}\) vs. \(-\)3.62 \(\times\) 10\({}^{-8}\)), confirming its consistency and precision. For both the SDMs and DDMs, Figure 4 shows how the PSA's estimated and observed I-V line up, and Figure 5 displays the P-V characteristics. The absolute errors that were calculated by the algorithm, which are the differences between the measured current and the calculated current for both models, are displayed in Figure 6.  
\begin{table}
\begin{tabular}{l l l l l l l l l l l l l} \hline \hline
**Algorithm** & **Model** & \(L_{H}\)**(**A**) & \(L_{H}\)**(**a**) & \(n\) & \(R_{A}\)**(**a**) & \(R_{A}\)**(**a**) & \(L_{H}\)**(**a**) & \(m_{2}\) & **RMSE** & **MSE** & **MSE** & **STD** \\ \hline
**PSA** & **SDM** & **0.76778530** & **0.323020790** & **1.48118538** & **0.043677929** & **5.7815283** & **-** & **-** & **9.802 \(\times 10^{-4}\)** & **9.58307902** \(\times 10^{-11}\)** & **1.005550 \(\times 10^{-3}\)** \\ \hline BWOA & SDM & 0.76778530 & 0.323020844 & 1.4811840 & 0.036779022 & 53.7182877 & **-** & **-** & 9.8402 \(\times 10^{-4}\)** & 9.6600008 \(\times 10^{-11}\) & 1.00550 \(\times 10^{-3}\) \\ \hline BOA & SDM & 0.7677751 & 0.323678 & 1.481385 & 0.0364688 & 53.76822 & **-** & **-** & 9.8602 \(\times 10^{-4}\) & \(-1.57692307647\times 10^{-8}\) & 1.005557 \(\times 10^{-3}\) \\ \hline ISHTS & SDM & 0.767078 & 0.32302 & 1.48118 & 0.036488 & 53.71853 & **-** & **-** & 9.8602 \(\times 10^{-4}\) & \(-3.7161583645\times 10^{-6}\) & 1.005500 \(\times 10^{-3}\) \\ \hline NCNDO & SDM & 0.767078 & 0.323020 & 1.48118 & 0.036488 & 53.71852 & **-** & **-** & 9.8602 \(\times 10^{-4}\) & \(-3.71709220769\times 10^{-4}\) & 1.005599 \(\times 10^{-3}\) \\ \hline DIVE/ISA & SDM & 0.767075 & 0.32302080 & 1.48118539 & 0.036770 & 53.718264 & **-** & **-** & 9.8602 \(\times 10^{-4}\) & \(-4.715836893\times 10^{-7}\) & 1.005594 \(\times 10^{-3}\) \\ \hline DIVIA/AIDA & SDM & 0.767075 & 0.323021 & 1.481183 & 0.036677 & 53.718265 & **-** & **-** & 9.8602 \(\times 10^{-4}\) & \(-1.7576923076\times 10^{-4}\) & 1.005551 \(\times 10^{-3}\) \\ \hline ONEDO & SDM & 0.76678 & 0.323 & 1.4812 & 0.0364 & 53.71852 & **-** & **-** & 9.8602 \(\times 10^{-4}\) & \(-1.26450