6.1.2. PV Panel

The analyzed panels in this work were the Photowatt PWP-201 and STM6-40/36. The first one was investigated at 51 ◦C and 1000 W/m2, while the PWP-201 module was investigated at 45 ◦C and 1000 W/m2. The measured data for both considered panels are given in [54,77]. The fetched results for the DDMs of both panels are tabulated in Table 6. The proposed HGTO-BWO came in the first rank with the best RMSEs of 2.42508 × <sup>10</sup>−<sup>3</sup> for PWP-201 and 1.8032 × <sup>10</sup>−<sup>3</sup> for STM6-40/36, while the GTO approach was in the second rank with fitness values of 2.42511 × <sup>10</sup>−<sup>3</sup> and 1.88 × <sup>10</sup>−<sup>3</sup> for PWP-201 and STM6-40/36, respectively. The computed and measured *P*-*V* and *I*-*V* curves are shown in Figure 8. The obtained curves are completely consistent with the measured data, and this confirms the preference of the proposed method in obtaining an approved equivalent circuit that simulates reality. The mean ranking of the RMSE values is illustrated in

Figure 9. It is confirmed that the proposed HGTO-BWO has the greatest rank among the applied algorithms, while Figure 10 illustrates the bar chart of the statistical analysis of the DDM. Moreover, the TDM optimal parameters and statistical analysis achieved by the proposed HGTO-BWO and the others are presented in Table 7. It is observed that the best fitness values were attained by the proposed HGTO-BWO with values of 2.2068 × <sup>10</sup>−<sup>3</sup> for PWP-201 and 1.7435 × <sup>10</sup>−<sup>3</sup> for STM6-40/36, while the worst fitness values were obtained via BWO with 1.5132 × <sup>10</sup>−<sup>1</sup> and 2.4985 × <sup>10</sup>−<sup>1</sup> for PWP-201 and STM6-40/36, respectively. Figure 11 depicts the measured and computed *P-V* and *I-V* curves of the TDM; the computed data converge with the measured ones; this validates the competence of the proposed HGTO-BWO. The mean ranking of the RMSE values and the statistical analysis for the TDM are presented in Figures 12 and 13, respectively. The RMSE values in bold indicate the best solutions obtained by the proposed HGTO-BWO approach.

**Table 6.** The calculated parameters of DDM and statistical analysis for PWP-201 and STM6-40/36 panels.


**Figure 8.** *P-V* and *I-V* curves for DDM: (**a**) STM6-40/36 and (**b**) PWP-201.

**Figure 9.** The mean ranking RMSE DDM of the Friedman test: (**a**) STM6-40/36 panels and (**b**) PWP-201.

**Figure 10.** The statistical analysis for the DDM: (**a**) STM6-40/36 panels and (**b**) PWP-201.


**Table 7.** TDM optimal parameters and statistical analysis for PWP-201 and STM6-40/36 panels.

**Figure 11.** The *I-V* and *P-V* curves for TDM: (**a**) PWP-201 and (**b**) STM6-40/36.

**Figure 12.** The mean ranking RMSE TDM of the Friedman test: (**a**) STM6-40/36 panels and (**b**) PWP-201.

**Figure 13.** The statistical analysis for the TDM: (**a**) STM6-40/36 panels and (**b**) PWP-201.

#### *6.2. Case 2: Variable Weather Conditions*

The changes in temperature and solar radiation should be considered during the design of the PV system as they have great influence on the system's efficiency [78]. The proposed HGTO-BWO constructed the DDM of MSX60 and KC200GT PV panels at various weather situations with the aid of the data given in [79]. Table 8 displays the statistical analysis of KC200GT in case A and B, where case A was conducted by operating the panel at 1000 W/m<sup>2</sup> and at the different temperatures of 25 ◦C, 50 ◦C, and 75 ◦C. In case B, the panel was operated at 25 ◦C and at the various irradiances of 1000 W/m2, 800 W/m2, 600 W/m2, 400 W/m2, and 200 W/m2. The best RMSE values of 3.5092 × <sup>10</sup>−<sup>3</sup> and 1.6067 × <sup>10</sup>−<sup>3</sup> were obtained during operation at 25 ◦C and 50 ◦C via the proposed approach. Additionally, it achieved the minimum fitness values of 9.1596 × <sup>10</sup><sup>−</sup>4, 6.3910 × <sup>10</sup><sup>−</sup>4, 7.7891 × <sup>10</sup><sup>−</sup>4, and 2.3850 × <sup>10</sup>−<sup>4</sup> during operation at 800 W/m2, 600 W/m2, 400 W/m2, and 200 W/m2, respectively. Figure 14 illustrates the simulated and measured data of *I-V* and *P-V* curves. The statistical parameters of the approach during the establishment of the circuit of KC200GT at irradiances of 1000 W/m2 and a temperature of 25 ◦C are illustrated in Figure 15 while the statistical analyses of MSX60 during various temperature and irradiances are displayed in Table 9. The proposed approach achieved the best RMSE values for MSX60 of 1.0765 × <sup>10</sup><sup>−</sup>4, 1.9324× <sup>10</sup>−4, and 2.9790 × <sup>10</sup>−<sup>5</sup> at 1000 W/m<sup>2</sup> and temperatures of 25 ◦C, 50 ◦C, and <sup>75</sup> ◦C, respectively. Moreover, at 25 ◦C the fitness values were 1.1336 × <sup>10</sup>−<sup>3</sup> at 800 W/m2; 6.7775 × <sup>10</sup>−<sup>4</sup> at 600 W/m2; 2.4366 × <sup>10</sup>−<sup>5</sup> at 400 W/m2; and 5.9828 × <sup>10</sup>−<sup>5</sup> at 200 W/m2. The estimated and measured curves are shown in Figure 16. Moreover, the bar chart of the statistical analysis for MSX60 at 1000 W/m2 and 25 ◦C is given in Figure 17. The curves confirmed the efficiency and reliability of the suggested HGTO-BWO technique in establishing the PV panel equivalent circuit at different operating conditions.


**Table 8.** Statistical analysis of KC200GT obtained via the proposed approach and others.

**Figure 14.** *P-V* and *I-V* curves of KC200GT: (**a**) constant irradiance of 1000 W/m<sup>2</sup> and (**b**) constant temperature of 25 ◦C.

**Figure 15.** The statistical analysis for KC200Gt at 1000 W/m2 and 25 ◦C.


**Table 9.** Statistical parameters of MSX60 panel obtained via the proposed approach and others.

**Figure 16.** *I-V* and *P-V* curves of MSX60: (**a**) constant irradiance of 1000 W/m<sup>2</sup> and (**b**) constant temperature of 25 ◦C.

**Figure 17.** The statistical analysis for MSX60 at 1000 W/m2 and 25 ◦C.

The fetched results demonstrated that the proposed HGTO-BWO is efficient in finding the optimal parameters of various models for the PV cell/panel as it outperformed the other regarded methodologies in all considered cases.
