## 3 Results and Discussion
### IPIF Model's Results  
Based on the results in Section 3.1.5, the 15-neuron FFNN model was used as a baseline to develop our proposed IPIF described in Section 2.2. The total number of \(\beta^{*}\) parameters \((L)\) in the chosen FFNN was computed as \(L=Mx(I+2)+1=1501\), where \(M\) is the number of neurons in the hidden layer and \(I\) refers to the system's number of inputs, i.e., 15 neurons and 98 inputs, respectively. Therefore, \(F\), which represents a set of the training database used to fit the PPF model, is the last parameter to be defined in the proposed IPIF model. Thus, \(F\) parameter must satisfy the following condition \(35040>F>1501\), where 35040 is the length of the database used to fit the PPF model and 1501 is the total number of \(\beta^{*}\) parameters. In addition, it must be reminded that for each \(F\) set, parameters present in Equations (12)-(14) must be recomputed. To be able to select the \(F\) parameter that maximizes the IPIF's accuracy, a sensitivity analysis was performed, in which several \(F\) sets were examined for different \(\alpha\) error rates. Table 9 shows the PICP\({}_{\alpha}\) results for each computed scenario \((F,\ \alpha)\) on randomly chosen days. Remember that the condition PICP\({}_{\alpha}>(1-\alpha)\) must be fulfilled in order for the proposed IPIF model to be considered valid and \(N=96\) represents the number of predicted values during each day. From the results shown in Table 9, it can be concluded, for bigger \(F\) values, that when the \(\alpha\) error rate increases the IPIF's PICP\({}_{\alpha}\) accuracy value decreases (see Table 9 columns \(F=1560\) or \(F=1552\)). However, this relationship has a weaker effect or completely disappears when lower \(F\) values are chosen (see Table 9 columns \(F=1538\) or \(F=1536\)). In addition, all the analyzed scenarios presented in Table 9 satisfy the PICP\({}_{\alpha}>(1-\alpha)\) requirement, so all \(F\) sets can continue being examined. The next step was based on analyzing each scenario's sharpness error metrics; for this purpose, the NPIAW\({}_{\alpha}\) parameter was calculated for the scenarios from the previous table (see Table 10). To compute the NPIAW\({}_{\alpha}\) error metric, parameter \(P\) takes the training database's average value, 3546 kW. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multicolumn{1}{c}{} & \multicolumn{5}{c}{\(F\)} \\ \hline
**Error Metric** & **Date** & **1560** & **1552** & **1546** & **1540** & **1538** & **1536** \\ \hline \multirow{4}{*}{\(100\times\) PICP\({}_{0.05}\)} & 08/02/2017 & 98.96 & 100.00 & 100.00 & 100.00 & 100.00 \\  & 04/05/2017 & 95.83 & 95.83 & 96.87 & 97.91 & 97.91 & 97.91 \\ (N = 96) & 25/07/2017 & 98.96 & 100.00 & 100.00 & 100.00 & 100.00 \\  & 16/08/2017 & 95.83 & 97.91 & 97.91 & 97.91 & 100.00 & 100.00 \\ \hline \multirow{4}{*}{\(100\times\) PICP\({}_{0.10}\)} & 08/02/2017 & 94.79 & 97.91 & 98.95 & 100.00 & 100.00 & 100.00 \\  & 04/05/2017 & 92.71 & 92.71 & 95.83 & 95.83 & 97.91 & 97.91 \\ (N = 96) & 25/07/2017 & 94.79 & 97.91 & 100.00 & 98.5 & 100.00 & 100.00 \\  & 16/08/2017 & 90.63 & 92.71 & 95.83 & 96.88 & 100.00 & 100.00 \\ \hline \multirow{4}{*}{\(100\times\) PICP\({}_{0.15}\)} & 08/02/2017 & 93.75 & 97.91 & 97.91 & 97.91 & 100.00 & 100.00 \\  & 04/05/2017 & 88.54 & 90.63 & 94.79 & 93.75 & 97.91 & 97.91 \\ (N = 96) & 25/07/2017 & 92.71 & 93.75 & 95.83 & 97.92 & 98.95 & 100.00 \\  & 16/08/2017 & 85.41 & 87.50 & 92.71 & 92.71 & 97.91 & 100.00 \\ \hline \end{tabular}
\end{table} 
Table 9: **PICP\({}_{\alpha}\)** results for computed scenarios \((\mathbf{F},\ \alpha)\). Based on the results presented in Table 10, it can be concluded that, considering the same \(\alpha\) error rate, the lower F value is the bigger the NPIAW\({}_{\alpha}\) error metric is. This means that the interval width increases as the F value decreases. However, if the F value holds constant and the \(\alpha\) error rate changes, then the bigger the \(\alpha\) error rate is, the narrower the predicted interval is.