# A Multi-Objective Hybrid BESSA Optimization Scheme for Parameter Extraction from PV Modules
## 9 Discussion
When irradiance was fixed at 1000 W/m\({}^{2}\) with a temperature of 50 \({}^{\circ}\)C, the corresponding values of Y, %\(e_{P}\), %\(e_{V}\), and %\(e_{I}\) were 1.61 \(\times\) 10\({}^{5}\), 0, 0.476, and 0 for the modeling conducted with the Hybrid BESSA-based extracted parameters, whereas those same values were170,735.5, 0.101, 0.204, and 0 for the modeling conducted with the BES-based extracted parameters. The improvement in the combined objective function using the Hybrid BESSA-based extraction technique was 5.7% as compared to that of the BES. When irradiance was fixed at 1000 W/m\({}^{2}\) with a temperature of 70 \({}^{\circ}\)C, the corresponding values of Y, %\(e_{P}\), %\(e_{V}\), and %\(e_{I}\) were 1.26 \(\times\) 10\({}^{5}\), 0, 0.101, and 0 for the modeling conducted with the Hybrid BESSA-based extracted parameters, whereas those same values were 126,727.9, 0.088, 1.21, and 0 for the modeling conducted with the BES-based extracted parameters. The improvement in the combined objective function using the Hybrid BESSA-based extraction technique was 0.5% as compared to that of the BES. It can be seen from Table 11 that when the modeling of the PV cell was conducted with the Hybrid BESSA-based extracted parameters with irradiance at 1000 W/m\({}^{2}\) and a temperature of 25 \({}^{\circ}\)C, the combined objective function(Y) obtained was 2.108 \(\times\) 10\({}^{5}\), and the percentage error for the open circuit voltage (%\(e_{V}\)), percentage error of power (%\(e_{P}\)), and percentage error for the short circuit current (%\(e_{I}\))were 0, 0.01, and 0, respectively, whereas the parameters extracted using the Hybrid BESSA resulted in a combined objective function 211,863.1 and the %\(e_{V}\), %\(e_{P}\), and %\(e_{I}\) obtained were 0, 0.26, and 0, respectively. The improvement in the combined objective function using the Hybrid BESSA-based extraction technique was 0.5% as compared to that of the BES. When temperature was fixed at 25 \({}^{\circ}\)C with irradiance at 800 W/m\({}^{2}\), the corresponding values of Y, %\(e_{P}\), %\(e_{V}\), and %\(e_{I}\) were 1.3425 \(\times\) 10\({}^{5}\), 0, 0.424, 0.1 for the modeling conducted with the Hybrid BESSA-based extracted parameters, whereas they were 146,235.2, 0.1869, 0.612, and 0.1 for the modeling conducted with the BES-based extracted parameters. The improvement in the combined objective function using the Hybrid BESSA-based extraction technique was 8.1% as compared to that of the BES. When temperature was fixed at 25 \({}^{\circ}\)C with irradiance at 600 W/m\({}^{2}\), the corresponding values of Y, %\(e_{P}\), %\(e_{V}\), and %\(e_{I}\) were 7.64534 \(\times\) 10\({}^{4}\), 0, 0.969, and 0.01 for the modeling conducted with the Hybrid BESSA-based extracted parameters, whereas they were 76,846.52, 0.310, 1  
with the Hybrid BESSA-based extracted parameters, whereas they were 34,623.14, 0.81, 2.018, and 0.01 for the modeling conducted with the BES-based extracted parameters. The improvement in the combined objective function using the Hybrid BESSA-based extraction technique was 0.8% as compared to that of the BES. From the above analysis, it is evident that the combined objective function of \(\%ep\), \(\%e_{V}\), and \(\%e_{I}\) demonstrated significant improvements in the PV cell modeling conducted with the Hybrid BESSA-based extracted parameters as compared to the BES-based extracted parameters. This proves the robustness and high accuracy of the Hybrid BESSA technique. The modeling was simulated based on the practical hardware PV Module AS-M3607-S. The multi-objective parameter extraction scheme based on the Hybrid BESSA provided a more accurate modeling output as compared to that of the BES. This is evident from the lower percentage error of power, lower percentage error of the open circuit voltage, and lower percentage error of the short circuit current. The percentage error was calculated by comparing the results with the respective reference values.