# Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm
## 3 Results and Discussion
### Multijunction Solar Cells (MJSC)
For the SDM, it achieved an RMSE of 7.538744 \(\times\) 10\({}^{-5}\), marking a significant improvement of 20.23% over BWOA and 25.99% over CSA. The parameters extracted by PSA, particularly \(I_{ph}\) and \(R_{s}\), remained stable and accurate despite the increased thermal stress. The differences in \(I_{ph}\) were slightly more pronounced, with PSA differing from BWOA by 0.10% and from CSA by 0.14%. These values reflect a slight increase in variability as temperature rises, which is expected due to the thermal impact on solar cell behavior. Additionally, the ideality factor (\(n1\)) showed reduced variation, ensuring reliable modeling under these conditions. In the DDM, PSA achieved an RMSE of 7.5161575 \(\times\) 10\({}^{-5}\), which was dramatically better than the BWOA and CSA, with improvements of 42.26% and 36.74%, respectively. The extracted parameters for \(I_{sd1}\) and \(R_{sh}\) were notably more consistent, avoiding the exaggerated deviations seen with CSA. Furthermore, PSA managed to align its \(R_{s}\) and \(n2\) values with expected trends, demonstrating its robustness in handling the complexity of the DDM. Under the most challenging conditions at 61.6 \({}^{\circ}\)C in Case C, PSA's ability to maintain accuracy was evident. For the SDM, it achieved an RMSE 6.7754050 \(\times\) 10\({}^{-5}\), a 30.01% improvement over BWOA and an impressive 88.11% over CSA. The extracted parameters, including \(I_{ph}\) and \(I_{sd1}\), remained highly accurate, and the differences in \(I_{ph}\) increased further, with PSA differing from BWOA by 0.20% and from CSA by 0.30%. These results highlight the challenges posed by high-temperature conditions, where thermal noise and variability in the dataset can affect parameter extraction, reflecting PSA's capability to handle the noise and variability introduced by higher temperatures. Additionally, \(R_{sh}\) and \(n1\) were extracted with significantly reduced deviations compared to CSA, ensuring a more precise representation of the solar cell's behavior. The best results obtained to extract the parameters of the MJSC for three temperatures are obtained using the PSA for both models by comparing the obtained results with the other algorithms in terms of RMSE, MBE, and STD. The reduction in RMSE between the temperatures is significant (Figure 24). At 51.3 \({}^{\circ}\)C, the RMSE improves by 3.68% compared to 41.5 \({}^{\circ}\)C. As the temperature increases to 61.6 \({}^{\circ}\)C, the RMSE further improves by 10.12% compared to 51.3 \({}^{\circ}\)C. Overall, the RMSE improves by 13.43% when comparing the highest temperature (61.6 \({}^{\circ}\)C) to the lowest (41.5 \({}^{\circ}\)C). Table 24 compares the performance of the SDM and DDM across three temperature scenarios--Case A (41.5 \({}^{\circ}\)C), Case B (51.3 \({}^{\circ}\)C), and Case C (61.6 \({}^{\circ}\)C)--on Intel Core i9 and AMD Ryzen 5 5600H processors. As temperature increases, run times vary slightly, with the SDM consistently requiring less time than the DDM. For example, in Case A, the SDM's run time is 3.1843 s compared to 4.099 s for the DDM, with similar trends in Cases B and C. The Intel Core i9 consistently outperforms the AMD Ryzen 5 in CPU execution times, completing tasks in as little as 2.9817 s (SDM, Case C) compared to Ryzen's 4.0331 s. Notably, the Intel Core i9's CPU execution times are slightly lower than the total run times due to its efficient handling of task overheads, while the AMD Ryzen 5's results are closer to the total run times, highlighting the i9's superior computational efficiency.