## 3 Results and Discussion  
### Hermosillo Site  
Figure 3 shows the geographical zone where Hermosillo Site (HS) is located. This site covers a period data of 6 months. Figures 4-7 depict the dispersion graphic and fitted curve for each input variable against the electric power. In Tables 2 and 3, the monthly and total results of the characteristic equations for each fitted curve and their determination coefficients are described, respectively. Equation (7) is applied in order to calculate the values of \(\theta_{k}\) for Hermosillo by using the Matlab(r) software. The optimal values found for \(\theta\) are mentioned in Table 4 and substituted into Equation (4), thereby obtaining its mathematical representation given by Equation (9). Figure 8 is obtained by implementing six months of gathered data into Equation (9). It describes the behavior of the statistical estimation (red) against the real data (green) obtained by the PV system in Hermosillo. For a better appreciation of these results, Figure 9 shows a close-up from 24 November to 24 December 2018. A tracing practically coincident with the rise and fall times for each day as a satisfactory reach of the maximum and minimum values is observed. \[h_{\theta}=0.0044+2.2387x_{1}+0.1156x_{2}+0.0154x_{3}+0.0022x_{4} \tag{9}\]Figure 4: The Power vs. Solar radiation of HS. Figure 5: The Power vs. Temperature of HS. Figure 3: The geographical location of the Hermosillo Site (HS) [49] (29.0843293 N, \(-\)110.9583558 W). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Month** & \multicolumn{2}{c}{**Input Variables**} \\ \hline \multicolumn{3}{c}{Solar radiation} & Temperature \\ Aug & \(f\left(x\right)=2.245x+92.59\) & \(f\left(x\right)=-17.98x^{2}+1274x-20,920\) \\ Sep & \(f\left(x\right)=2.308x+28.45\) & \(f\left(x\right)=-11.43x^{2}+796.7x-12,210\) \\ Oct & \(f\left(x\right)=2.276x+50.32\) & \(f\left(x\right)=-8.751x^{2}+556.5x-7217\) \\ Nov & \(f\left(x\right)=2.326x-29.48\) & \(f\left(x\right)=-6.074x^{2}+354.8x-3505\) \\ Dec & \(f\left(x\right)=2.25x-36.17\) & \(f\left(x\right)=0.08391x^{2}+45.57x+219.1\) \\ Jan & \(f\left(x\right)=2.398x+8.88\) & \(f\left(x\right)=-2.016x^{2}+144.8x-752.7\) \\ TOTAL & \(f\left(x\right)=2.296x-1.747\) & \(f\left(x\right)=-1.751x^{2}+124.2x-581.9\) \\ \hline \multicolumn{3}{c}{Wind speed} & Hour \\ Aug & \(f\left(x\right)=-60.94x^{2}+438.2x+753.3\) & \(f\left(x\right)=-43,250x^{2}+44,070x-8893\) \\ Sep & \(f\left(x\right)=-21.89x^{2}+111.6x+1352\) & \(f\left(x\right)=-42,970x^{2}+43,290x-8593\) \\ Oct & \(f\left(x\right)=-20.63x^{2}+118.4x+1292\) & \(f\left(x\right)=-46,940x^{2}+46,740x-9314\) \\ Nov & \(f\left(x\right)=4.208x^{2}+12.31x+1348\) & \(f\left(x\right)=-50,610x^{2}+50,160x-10,180\) \\ Dec & \(f\left(x\right)=-11.68x^{2}+120.2x+1005\) & \(f\left(x\right)=-51,600x^{2}+51,860x-10,900\) \\ Jan & \(f\left(x\right)=-14.18x^{2}+206.8x+886.7\) & \(f\left(x\right)=-55,500x^{2}+56,360x-11,960\) \\ TOTAL & \(f\left(x\right)=-14.47x^{2}+138.7x+1096\) & \(f\left(x\right)=-49,950x^{2}+50,110x-10,360\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The fitted curve characteristic equation of every input from HS. Figure 6: The Power vs. Wind speed of HS. Figure 7: The Power vs. Time of HS. \begin{table}
\begin{tabular}{c c} \hline \(\theta_{k}\) & HS \\ \hline \(\theta_{0}\) & 0.0044 \\ \(\theta_{1}\) & 2.2387 \\ \(\theta_{2}\) & 0.1156 \\ \(\theta_{3}\) & 0.0154 \\ \(\theta_{4}\) & 0.0022 \\ \hline \end{tabular}
\end{table} 
Table 4: The values of \(\theta_{k}\) from HS by gradient descent. Figure 8: The results obtained from HS by gradient descent. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Month** & **Solar Radiation** & **Temperature** & **Wind Speed** & **Hour** \\ \hline Aug & 0.9917 & 0.1679 & 0.0541 & 0.9825 \\ Sep & 0.9981 & 0.1502 & 0.0242 & 0.9968 \\ Oct & 0.9523 & 0.1664 & 0.0380 & 0.9850 \\ Nov & 0.9708 & 0.1955 & 0.0135 & 0.9962 \\ Dec & 0.9851 & 0.0965 & 0.0136 & 0.8865 \\ Jan & 0.9609 & 0.1390 & 0.0565 & 0.9760 \\ TOTAL & 0.9532 & 0.1077 & 0.0140 & 0.8098 \\ \hline \hline \end{tabular}
\end{table}