## 5 Results and Discussion
### Experimentation Results
The second season is autumn; here, the first day presents a few variations associated with cloud presence, whereas the second presents a storm during the second half of the day resulting in many abrupt irradiance variations (Figure 3b). The third season presented in the figure is winter; here, the first day (Figure 3c) presents a profile very similar to the first day of summer. However, it is observed that the total sunny hours are lower in winter. The highest irradiance level reached is also lower in winter than summer. The second day of winter shows a very irregular pattern because there is cloud presence during the entire day. Finally, the fourth and last presented season is spring. The first day presents a normal pattern of behavior for most of the day, but around the 17:00 it becomes cloudy and some variations in irradiance appear (Figure 3d). The second day of spring presents an erratic behavior since there are clouds all day. The weight values presented in Table 1 were substituted into (4) along with the irradiance, cell temperature, DC voltage, and DC current from every one of the sections. Figure 3: Days of analysis for (**a**) summer, (**b**) fall, (**c**) winter, and (**d**) spring, with normalized irradiance. Then, the estimation of the active power for the 8 days of analysis was carried out. In order to show the effectiveness of the proposed methodology, the performed estimation is compared with the estimation performed with an ANN, which is the most common technique for this purpose. The ANN was trained using the same 24 days that were used for estimating the parameterized model with the GA. Figure 4 shows the results of the active power estimation using these two techniques. It is observed that in the 8 days, the value estimated by the GA (red line) remains very close to the real value (blue line). Although there are days with many unexpected variations like 13 November (Figure 4d), 10 February (Figure 4f), and 21 March (Figure 4h), the obtained model can follow every variation reasonably. In the days where there are no abrupt changes, the difference between the estimated and the real value is almost imperceptible. When an ANN is used for the active power forecasting, the results are also good (yellow line). The prediction accurately follows the behavior shown by the real signal on most of the days. However, it is observed that for 9 January (Figure 4e), the estimation performed by the ANN presents a noticeable deviation from the real signal. In this sense, the estimation performed by the GA does not present this deviation making it a more reliable technique. On the other hand, the weights from Table 2 were substituted into (6) to obtain the mathematical model for the THD forecasting. Once again, the result of the estimation performed by the GA is compared with the estimation performed by an ANN. The results of using these models for estimating the THD through the day are depicted in Figure 5. In the days with almost no cloud presence (Figure 5a,c,e,g), the values estimated by the GA (red line) present just a few deviations from the real ones (blue line). In the days with severe cloud presence, the deviation between the estimated values and the real values is more noticeable, i.e., the error in the estimation increases. However, when an ANN is used for the THD prediction, it is noticeable that the network does not make a good estimation even on days when the sky is clear (yellow line). Thus, it can be inferred that the ANN presents problems for estimations where the relationship among the parameters is nonlinear. The error values for both techniques (GA and ANN) are summarized in Table 3. It is worth noting that the errors, for the case of the active power estimation, using the GA always remains in values lower than 1%. As expected, the estimation performed by the ANN presents the highest error on 9 January, but also 10 February, and 13 November present errors above 1%.