## 4 Discussion
Table 8 presents the errors associated with the energy losses between the two methods calculated with the relation:  
\[\delta\Delta\mathrm{W}=\left(\frac{\Delta\mathrm{W}_{\mathrm{MM}}-\mathrm{W}_{ \mathrm{RBE}}}{\Delta\mathrm{W}_{\mathrm{MM}}}\right)\ \cdot 100\,\ [\%] \tag{11}\]  
where \(\Delta\mathrm{W}_{\mathrm{MM}}\) represents the energy losses calculated with the multi-objective method (MM), and \(\Delta\mathrm{W}_{\mathrm{RBED}}\) corresponds to the energy losses determined with the proposed RBES. The analysis of the data highlighted that the energy losses are slightly smaller in the case of RBES compared with the MM method, with differences between 0.85% (PD = 50%, EP\({}^{A}\)PV, and CEC = 10%) and 3.54% (PD = 20%, EP\({}^{A}\)PV, and CEC = \(-\)10%). The similar values of the maximum phase voltage have been obtained in 47 scenarios (62.7%) highlighted through null values of the errors; see Table 9. However, the maximum values are slightly higher in the other scenarios (28) for the RBES compared with the MM method, between 0.08% (PD = 10%, EP\({}^{I}\)PV, and CEC = \(-\)10%) and 2.62% (PD = 40%, EP\({}^{I}\)PV, and CEC = \(-\)10%). In addition, the voltage issues have not been solved fully for scenarios S56-S60 and S71-S75, but in at least 95% of the time slots, the voltages were inside the range [\(-\)10%, +10%], according to the European Power Quality Standard, and for the rest of the time slots, up to 100% were very close to the limits of the range. The highest differences have been identified at the level of the optimization variables (the tap positions). A comparison between methods has been made only for the scenarios with voltage issues highlighted with bold font in the tables. The total number of tap position changes is higher in the MM method than in the RBES, which makes RB more efficient; see Table 10. Tables 11 and 12 from Appendix A present the tap position changes for the two methods. Table 11 shows the average computational time (ACT) required to get the optimal solution in a time slot. The algorithms were developed using a Matlab implementation and were run on a computer with an Intel Core i7, 3.10 GHz processor, 4 GB RAM, and a 64-bit Windows 10 operating system. The ACT is very close between the methods (the error is 4.7%). However, due to the other advantages regarding the smaller energy losses and the total number of tap position changes, the RBES method can represent a better alternative for DNOs. If the sampling step of smart meters to send information to the data concentrator has smaller values (15 or 30 min), then the total number of tap position changes increases. However, the technical constraint regarding the total number of tap changes from a day will not be violated, as shown in [53]. The maximum number considered in this research was 96, according to [41]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{CEC} & \multicolumn{3}{c}{**10**} & \multicolumn{3}{c}{**20**} & \multicolumn{3}{c}{**30**} & \multicolumn{3}{c}{**40**} & \multicolumn{3}{c}{**50**} \\ \cline{2-13}  & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** & **mF\({}^{2}\)** \\ \hline \hline \multirow{2}{*}{\(-\)10} & 0.00 & 0.