## 3 Results
Estimating the powers from the EDSs based on the SLR method proposed in [27] contains the linear regression models between the reference, considered the MV bus of the supply HV/MV EDS, and the MV/LV EDSs from the EDN. Regarding the second method [17], each EDS has assigned a typical active and reactive profile depending on the energy consumption category obtained through a clustering-based unsupervised learning process. The results indicate a substantial improvement in the estimation process of the APE values at the EDSs level with the proposed method compared to the SLR and TLPs methods. Table 3 and Figure 16, containing the statistical indicators associated with the quartiles Q0-Q4, confirms this conclusion with a decrease in the maximum value from 30.9% (calculated for SLR method) and 14.4% (calculated for TLPs method) to 6.3% and a median value (quartile Q2) from 11.8% (calculated for SLR method) and 9.0% (calculated for TLPs method) to 2.8%. The SLR method led to the highest variation in the APEs in the range of [4.1%, 30.9%], followed by the TLPs method with a range of [3.1%, 25.4%]. The proposed method has the least variation, in the range of [0.0%, 6.3%]. Regarding the MAPEs, Figure 17 presents the values of MAPEs calculated for the three methods. The value of MAPE decreases from 12.8% in the case of the SLR method to 9.9% in the case of the TLPs method and 2.6% (3% approximately) in the case of the proposed C-MLR method (10% approximately). In the following, Layer 3 of the methodology will use the results obtained with the proposed C-MLR method to estimate the state of the EDN associated with a day. Because the voltages calculated at the level of the EDSs with the Newton-Raphson method based on the estimated powers are very close to the real data, which are located between the allowable limits [+10%, -10%] compared with the nominal voltage, only the state variables obtained from the power flow calculations using the real and estimated active and reactive powers from the MV/LV EDSs associated with the injected active and reactive powers (P\({}_{\text{injected}}\) and Q\({}_{\text{injected}}\)) from the slack bus (the 20 kV bus of the HV/MV EDS), the requested active and reactive powers (P\({}_{\text{requested}}\) and Q\({}_{\text{requested}}\)) at the level of the MV/LV EDSs from the EDN, the active and reactive power losses (P\({}_{\text{loss}}\) and Q\({}_{\text{loss}}\)), and capacitive reactive power of the cables (Q\({}_{\text{capacitive}}\)) are analysed. Tables 15 and 16 from Appendix A present the hourly values obtained for these state variables. Table 4, Figures 18 and 19 integrates the hourly percentage errors calculated for each state variable. The data analysis highlights that higher errors than 1% are associated with 4 h (3, 7, 8, and 18) for all state variables (less capacitive reactive power of the cables, Q\({}_{\text{capacitive}}\)). However, the maximum value does not exceed 3% in the case of the active power loss at hour 7. Exceeding the 1% threshold is sporadically present, as other variables are, but they are tiny. However, all state variables have MAPEs below 1%, as seen in Figure 21, which means an outstanding performance of the estimation process. Finally, the proposed framework can offer the DNOs the state estimate synthesis based on the aggregated values quantified as energy amounts (W\({}_{\text{Pinjected}}\), W\({}_{\text{Qinjected}}\)--injected active and reactive powers in the EDN; W\({}_{\text{Prequested}}\), W\({}_{\text{Qrequested}}\)--requested active and reactive power in the EDN; W\({}_{\text{P loss}}\), W\({}_{\text{Q loss}}\)--active and reactive energy losses; and W\({}_{\text{Qcapacitive}}\)--capacitive reactive energy of the cables) for the analysed period. Table 6 presents the values of the state variables obtained in both cases (real and estimated) and Figure 22 shows the percentage errors. The information presented in the figure confirms again the accuracy of the estimation process where the state variables have errors below 0.5%.