## 5 Results and Discussion
### Experimentation Results  
In order to demonstrate that the proposed methodology delivers similar and uniform output data, it is necessary to perform a comparison with 2 sunny days and 2 cloudy days of the same month. In this sense, 4 days were randomly selected from the month of August, because in this month it is easy to find suitable days that match these characteristics (sunny and cloudy). The weights presented in Table 1 were used to estimate the delivered active power of these 4 days, and the results are presented in Figure 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Weight** & **S1** & **S2** & **S3** & **S4** \\ \hline \(u_{1}\) & \(-\)3.27 & \(-\)1.92 & 0.19 & 2.59 \\ \(u_{2}\) & 4.92 & 3.77 & \(-\)0.86 & 1.84 \\ \(u_{3}\) & 1.38 & 0.85 & \(-\)2.06 & \(-\)0.94 \\ \(u_{4}\) & \(-\)4.68 & 3.63 & \(-\)0.44 & 0.85 \\ \(u_{5}\) & 0.03 & \(-\)0.19 & \(-\)2.06 & \(-\)3.99 \\ \(u_{6}\) & 4.45 & \(-\)0.86 & 0.16 & \(-\)0.22 \\ \(u_{7}\) & \(-\)1.54 & 0.13 & 2.21 & \(-\)0.92 \\ \(u_{8}\) & 0.50 & 0.25 & 2.25 & \(-\)0.65 \\ \(u_{9}\) & \(-\)0.92 & \(-\)2.12 & \(-\)1.96 & \(-\)1.93 \\ \(u_{10}\) & \(-\)1.89 & \(-\)0.62 & \(-\)0.69 & \(-\)3.05 \\ \(u_{11}\) & 2.66 & 0.31 & \(-\)0.16 & \(-\)2.22 \\ \(u_{12}\) & \(-\)0.39 & \(-\)2.18 & 3.29 & 4.04 \\ \(u_{13}\) & \(-\)3.08 & \(-\)0.13 & 1.55 & \(-\)1.67 \\ \(u_{14}\) & \(-\)4.93 & 0.77 & 1.78 & \(-\)1.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Estimated weights for the four sections of the total harmonic distortion (THD) model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Weight** & **S1** & **S2** & **S3** & **S4** \\ \hline \(u_{1}\) & 34.23 & 25.13 & 7.57 & \(-\)1.92 \\ \(u_{2}\) & 7.14 & \(-\)55.62 & 75.85 & \(-\)24.83 \\ \(u_{3}\) & \(-\)1.19 & 1.06 & \(-\)6.25 & 0.98 \\ \(w_{4}\) & \(-\)63.16 & 37.39 & 103.43 & 120.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Estimated weights for the four sections of the active power model. Figure 2: Comparison of two sunny days: (**a**) 13 August and (**b**) 14 August; and two cloudy days: (**c**) 15 August and (**d**) 17 August; for the demonstration of data similarity and uniformity. From Figure 2, it is observed that when the days are sunny, the estimated and the real active power are very similar (see Figure 2a,b), reaching an estimation error of 0.1% for 13 August and 0.37% for 14 August. The difference between both errors is less than 0.3%, proving the consistency of the results delivered by the methodology. In the case of the cloudy days (Figure 2c,d), the cloudy nature of the days causes a high variability in the generated power. However, the methodology is able to follow most of the variations in a reasonable way reaching an error of 0.39% for 15 August and 0.56% for 17 August. This time the difference between both errors is even lower than in the previous case (<0.2%). In this way, it is possible to validate the similarity and uniformity of the resulting data for days with similar characteristics. As aforementioned, 8 days were used for experimentation with the proposed methodology in the piecewise approach. These days are presented in Figure 3 with the corresponding sections of the day (S1 to S4). The values of the irradiance are overall normalized in order to better appreciate the average tendency of every season of the year. It can be seen that the highest values are reached in spring, but they are sudden and last only a few minutes. The lowest values occur in winter; this situation is mainly due to the elevation of the sun in this season being the lowest of the year. Additionally, it is observed that there is a great variability between them because of the different environmental conditions. The first season presented in Figure 3 is summer, characterized by an abundance of sun and a few cloudy periods. The first day of this season is a completely sunny day (there is none irradiance variation), whereas the second day presents some unexpected variations (due to clouds) from the 12:00 to the 15:00 (see Figure 3a).