## 3 Results
The internal test used the silhouette coefficient, and the algorithm identified the optimal number equal to 5 (for which the silhouette coefficient has the highest value, SC = 0.7168); see Figure 10. The representation of the silhouette coefficient for the optimal partition, K\({}_{\text{opt}}\) = 5, is given in Figure 11.  
Figure 11: The silhouette coefficient associated with the optimal partition, K\({}_{\text{opt}}\) = 5. Figure 9: The heatmap chart associated with correlation coefficients. Figure 12 highlights each class's percentage and the number of EDS it integrates. The analysis of the data indicates that the representative class is C5, containing 12 EDSs (30.77%), followed by classes C1 (10 EDSs, 25.64%), C2 (10 EDSs, 25.64%), C3 (5 EDSs, 12.82%), and C4 (2 EDSs, 5.13%). The allocation of the EDSs in each class can be observed in Figure 13. Two (Feeder 1 and Feeder 2) of three feeders have the EDSs associated with all classes, and one feeder (Feeder 3) contains the EDSs allocated to only three classes (C1, C2, and C5). Table 1 presents the statistical indicators corresponding to the quartiles (Q0-Q4), mean (M), and standard deviation (SD) for the obtained classes following the clustering process. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Class** & **Q0** & **Q1** & **Q2** & **Q3** & **Q4** & **M** & **SD** \\ \hline C1 & 0.69 & 0.71 & 0.73 & 0.75 & 0.8 & 0.74 & 0.04 \\ C2 & 0.51 & 0.57 & 0.595 & 0.68 & 0.71 & 0.62 & 0.07 \\ C3 & 0.57 & 0.59 & 0.63 & 0.64 & 0.65 & 0.62 & 0.03 \\ C4 & 0.40 & 0.40 & 0.40 & 0.40 & 0.40 & 0.40 & 0 \\ C5 & 0.75 & 0.77 & 0.79 & 0.81 & 0.82 & 0.79 & 0.02 \\ \hline \end{tabular}
\end{table} 
Table 1: The statistical indicators associated with the obtained classes for the optimal partition. Figure 12: The allocation of the EDSs in each class (cluster). Figure 13: The allocation of the EDSs to each class. The class with the values of the highest average correlation coefficient is C5, the range is [0.75, 0.82], and the smallest values are associated with C4 (0.4). The trend of the mean is the same, with the highest value recorded for class C5 (M = 0.79), followed by C1 (M = 0.74), C2 (M = 0.62), C3 (M = 0.62), and C4 (M = 0.4). The highest variation in the correlation coefficient belongs to class C2 (between 0.57 and 0.68), followed by C3 (between 0.59 and 0.64), C1 (between 0.71 and 0.75), and C5 (between 0.77 and 0.81); see Figure 14. The class C4 (having only two EDSs) was not taken into account, as it was unrepresentative for the analysis. Step 1 of the second layer aims to set the threshold for CC at 0.75 to choose the candidate classes. This value is widely used in the literature for the minimum threshold value. The only class that meets this condition for the average correlation coefficient is C5. Thus, the EDSs from this class, identified with blue in Figure 13, will represent the optimal locations to integrate the SCADA system. In the third step, the algorithm determines the multiple linear regression models to estimate the powers in the EDSs from the other classes not included in the set of the \"candidate\" classes. The models use as regressors the EDSs identified in the previous step. Table 2 and Figure 15 present the APEs obtained based on the previously determined regression models for each EDS without integration into the SCADA system. The APEs are equal to 0 for the EDSs from the candidate class (in our case, class C5), identified in bold in the table, because the system uploads the measurements from the SCADA system during the analysis period for these EDSs. The results obtained with the proposed hybrid clustering-multiple linear regression (C-MLR) method have been compared with two other methods from the literature to demonstrate the performance of the proposed approach: the simple linear regression (SLR) method and the typical load profiles (TLPs)-based method.