## 3 Results  
A real urban MV EDN has been used to test the proposed framework. The END, supplied from an HV/MV (110/20 kV) EDS, contains 3 MV feeders with 39 MV/LV (20/0.4 kV) EDSs. Figure 4 presents the topology of the test MV EDN. Figure 4: The topology of the test 39-bus MV EDN. Table 12 from Appendix A includes each branch's length between two EDSs associated with each feeder. The EDN has the cross-section of the first branch (EDS-1, EDS-14, and EDS-29), with a size of 185 [mm\({}^{2}\)] (r\({}_{0}\) = 0.157 [\(\Omega\)/km] and x\({}_{0}\) = 0.112 [\(\Omega\)/km]), which is different from the other branches, equal to 150 [mm\({}^{2}\)] ((r\({}_{0}\) = 0.194 [\(\Omega\)/km] and x\({}_{0}\) = 0.115 [\(\Omega\)/km]). Also, the branch length is in the range of [0.1-0.5] km, with a total length for the second feeder of 6.07 km higher than the other two feeders (3.36 km for the first feeder and 3.54 km for the third feeder, respectively). Figure 5 presents the synthesis of this information. The rated power of the transformers, denoted with S\({}_{r}\), from the EDSs supplied by the three feeders, is between 400 and 1000 kVA (see Table 13 from Appendix A). The total installed powers (calculated as the sum of the rated powers of the distribution transformers supplied by each feeder) are 7.15 MVA for the first feeder, 12.21 MVA for the second feeder, and 9.52 MVA for the third feeder, resulting in the total power of the EDN at 28.88 MVA (see Figure 6). Step 1 of the first layer from the proposed methodology considers the building of a database with the active and reactive power profiles recorded in the matrix form, as seen in the relationships (1), based on a measurement campaign performed by the DNO during a week in the most loaded period. Figures 7 and 8 present the boxplots of the active and reactive powers associated with the measurement campaign. Figure 5: The total length of each feeder from the test 39-bus MV EDN. Figure 6: The total installed power of each feeder from the test 39-bus MV EDN. A boxplot is a method that shows the locality, skewness, and spread groups of data through their respective quartiles. In addition to the box, there are also whiskers, which are lines that extend from the box to indicate variability outside the lower and upper limits of the range. These are referred to as box-and-whiskers and box-and-whiskers, respectively [36; 37]. Tables A3 and A4, from Appendix A, show the quartiles associated with the boxplot representation and two other statistical indicators (mean and standard deviation). The analysis of the information highlights that there are 14 EDSs with a high variation in the powers (9, 10, 12, 14, 17, 22, 27, 29, 30, 31, 33, 34, 38, and 39), 7 EDSs with slight variations (1, 2, 3, 4, 23, 24, and 25), and 18 EDSs with normal variations. Step 2 of the first layer involves the calculation of the correlation coefficient between each of the two EDSs from the analysed EDN, which is recorded in the matrix [CC] and has a size of [39 \(\times\) 39]. Figure 9 presents the heatmap chart associated with matrix [CC] containing the values between \(-\)0.1 and 0.99. The vast majority of values are above 0.6. Still, there are also values close to 0 or even negative, which means that as one variable increases, the other decreases proportionally. Application of the K-means algorithm-based clustering process included in the last step of the first layer led to the classes corresponding to the EDSs with similar features of the correlation coefficients. Figure 8: The boxplots of the reactive powers from the EDSs. Figure 7: The boxplots of the active powers from the EDSs. The maximum number of the clusters (named classes in the following) corresponded to a partition in six clusters.