# Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm
## 3 Results and Discussion
### PVM Panel
The evaluation of all PVM solar module parameters and the RMSE show that the PSA can choose the best solution and not become stuck in local minima. Figures 16 and 17 show the PSA's estimated and observed I-V and P-V for the SDMs and DDMs to show the difference between the measured current and the calculated current. The absolute errors acquired by the algorithm are shown in Figure 18, which illustrates the differences between the observed current and the predicted current for both the SDMs and DDMs. In the case of the DDM, the absolute errors are very low in comparison with the ones calculated with the SDM. Figure 16: PVM SDM and DDM I–V characteristics. The PSA's convergence curves for both models are shown in Figure 19. The algorithm's maximum iteration was set at 1500, with a population of 100. The graph shows which iterations the algorithm went through to reach the lowest RMSE value. The PSA began to evade the local minimum for the SDM around iteration 270 at 80 populations, arriving at the ideal RMSE value. For the DDM, on the other hand, this improvement started at iteration 370 at population 65, showing that it required a few more iterations to obtain the ideal RMSE value compared to the SDM. To provide a clearer view of performance consistency, the convergence curves are accompanied by shaded bands representing \(\pm\) standard deviation at each iteration. These bands indicate the degree of fluctuation in RMSE values and offer visual confirmation of the PSA's stability and reliability during the optimization process. Two tests were undertaken for both the SDMs and DDMs to find the appropriate combination of iteration size and population size for achieving the ideal RMSE in the case of PVM. Figure 17: PVM SDM and DDM P–V characteristics. Figure 18: PVM SDM and DDM calculated absolute error. The population size in the first experiment varied from 20 to 100, but the number of iterations remained constant at 100. This method, however, did not produce the best results, as the lowest RMSE value was found when both the population size and iteration were set to 100. This resulted in an RMSE of 2.2031 \(\times\) 10\({}^{-3}\) and a computation time of 0.6249 s for the SDM. Meanwhile, the DDM achieved a minimal RMSE of 5.9449 \(\times\) 10\({}^{-4}\) in 0.9250 s of computing time. In the second experiment, the number of iterations varied by 200 each time while the population size remained the same. The best RMSE value for the algorithm was calculated using this strategy. The SDM's optimum RMSE solution, computed with 1500 iterations and a population size of 50, took about 4.6392 s to complete. With a population size of 50, the optimal solution in the DDM was similarly discovered after 1500 iterations; however, this time the calculation took roughly 6.8158 s. Finding the ideal RMSE requires more iterations for the DDM than it does for the SDM since the DDM requires the extraction of seven parameters. The findings of the SDM analysis are shown in Table 16, while the DDM analysis results are shown in Table 17.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of** & **Population** & **Number of** & **RMSE** & **Run Time (s)** \\ \cline{2-5}
**Runs** & **Size** & **Iterations** & **RMSE** & **Run Time (s)** \\ \hline \hline \multirow{8}{*}{5} & 20 & 100 & \(3.6985\times 10^{-3}\) & 0.1184 \\ \cline{2-5}  & 30 & 100 & \(1.5959\times 10^{-2}\) & 0.1756 \\ \cline{2-5}  & 5  
In this experiment, summarized in Table 18, the performance of the SDMs and DDMs was evaluated in terms of CPU execution times across two processors: Intel Core i9 and AMD Ryzen 5 5600H. On the Intel Core i9, the DDM required 8.5112 s, significantly more than the 5.2231 s for the SDM. Similarly, on the AMD Ryzen 5, the DDM took 12.1566 s compared to 9.8966 s for the SDM. The differences in execution times between the processors also highlight the Intel Core i9's better efficiency in managing computational workloads, which is likely due to its optimized architecture and superior single-thread performance.