# A Multi-Objective Hybrid BESSA Optimization Scheme for Parameter Extraction from PV Modules
## 9 Discussion
For exactness and efficacy in evaluation, the lower bound and upper bound of the extracted parameters are specified in Table 7. Table 8 provide the values of the parameters extracted using the Hybrid BESSA and BES techniques for the PV Module AS-M3607-S (G1 CELLS) when keeping irradiance fixed at 1000 W/m\({}^{2}\) and varying temperature from \(-\)30 \({}^{\circ}\)C to 70 \({}^{\circ}\)C. Table 10 provides the parameters extracted by applying the Hybrid BESSA and BES techniques to the PV Module AS-M3607-S (G1 CELLS) when keeping temperature fixed at 25 \({}^{\circ}\)C and varying irradiance from 1000 W/m\({}^{2}\) to 800 W/m\({}^{2}\), 600 W/m\({}^{2}\), and 400 W/m\({}^{2}\). Tables 9 and 11 provide information about the reference values for power, current, and voltage, as well as the percentage error for the open circuit voltage, percentage error of power, and percentage error for the short circuit current of the PV Module AS-M3607-S when simulated using parameters extracted with the Hybrid BESSA and BES techniques, respectively, at different temperatures while keeping irradiance fixed at 1000 W/m\({}^{2}\). It can be seen from Table 9 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 temperature at \(-\)30 \({}^{\circ}\)C, the combined objective function (Y) obtained was 3.6199 \(\times\) 10\({}^{5}\) and the percentage error for the open circuit voltage (\(\%\)\(e\)\(\
u\)), percentage error of power(\(\%\)\(e\)\(\
u\)), and percentage error for the short circuit current (\(\%\)\(e\)\(\iota\))were 0.703, 0, and 0.01, respectively, whereas when the parameters extracted from the Hybrid BESSA resulted in a combined objective function of 3.654 \(\times\) 10\({}^{5}\), the obtained values for \(\%\)\(e\)\(\
u\), \(\%\)\(e\)\(\rho\), and \(\%\)\(e\)\(\iota\) were 1.49, 0.201, and 0, respectively. The improvement in the combined objective function using the Hybrid BESSA-based extraction technique was 0.9% as compared to that of the BES. When irradiance was fixed at 1000 W/m\({}^{2}\) with a temperature of 0 \({}^{\circ}\)C, the corresponding values of Y, %\(e_{P}\), %\(e_{V}\), and %\(e_{I}\) were 2.73 \(\times\) 10\({}^{5}\), 0, 0.378, and 0, respectively, for the modeling conducted with the Hybrid BESSA-based extracted parameters, whereas those same values were 298,578.7, 0.161, 0.738, and 0, respectively, 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 8.5% as compared to that of the BES. When irradiance was fixed at 1000 W/m\({}^{2}\) with a temperature of 25 \({}^{\circ}\)C, the corresponding values of Y, %\(e_{V}\), %\(e_{P}\), and %\(e_{I}\) were 2.12 \(\times\) 10\({}^{5}\), 0, 0, and 0 for the modeling conducted with the Hybrid BESSA-based extracted parameters, whereas those same values were 298,578.7, 0.025, 0, 0, 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 29.2% as compared to that of the BES. When irradiance was fixed at 1000 W/m\({}^{2}\) with a temperature of 30 \({}^{\circ}\)C, the corresponding values of Y, %\(e_{P}\), %\(e_{V}\), and %\(e_{I}\) were 2.01 \(\times\) 10\({}^{5}\), 0, 0.081, and 0 for the modeling conducted with the Hybrid BESSA-based extracted parameters, whereas those same values were 200,937.4, 0.204, 0.101, 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 0.03% as compared to that of the BES.