## 4 Discussion  
The proposed expert system, including rule-based reasoning (RBES), applied in 75 scenarios had a success rate of 86.7% (65 out of 75 scenarios did not have the voltage issues anymore). For the remaining scenarios with voltage issues (S56-S60, and S71-S75), the maximum value of the phase voltage was reduced with the values between 0.12 p.u (9.5%) recorded for scenario S56 (PD = 40%, \(\mathrm{EP}^{\mathrm{H}}_{\mathrm{PV}}\), and CEC = \(-\)10%) and 0.15 p.u. (11.6%) associated with scenario S75 (PD = 50%, \(\mathrm{EP}^{\mathrm{H}}_{\mathrm{PV}}\), and CEC = +10%). Another voltage quality index can be used for these scenarios to quantify the unallowable voltage variations; see Table 7. This index calculated with relation (10) shows the percentage of the time slots in which the phase voltage deviations exceed the allowable limits. \[\mathrm{UVD}=\frac{\sum\limits_{\mathrm{e=1}}^{\mathrm{NE}}\sum\limits_{ \mathrm{s=0}}^{\mathrm{s}}\left(\sum\limits_{\mathrm{V}\in\{\gamma_{\mathrm{x }}\gamma_{\mathrm{y}}\gamma_{\mathrm{c}}\}}\left(\left|\frac{\mathrm{V}_{ \mathrm{g}}^{\{\{\mathrm{V}\}}}-\mathrm{V}_{\mathrm{r}}}{\mathrm{V}_{\mathrm{ r}}}\right|\right)\right)}{\mathrm{N}_{\gamma}\cdot\mathrm{NE}\cdot\mathrm{s}} \tag{10}\]  
where the signification of all variables has been indicated in Section 2. The values of UVD from Table 7 indicate that the phase voltages in the nodes (at the pillar level) of the LVEDN for all 10 scenarios are outside the range [\(-\)10%, +10], in a percentage between 1.73% and 4.98%. Higher percentages, between 4.49% and 4.98%, have been recorded for scenarios S71-S75. Thus, in at least 95% of the time slots, the voltages have been inside the range [\(-\)10%, +10%], according to the European Power Quality Standard. In these conditions, the DNOs should be very careful and take additional measures to improve the voltage level in the LVEDN, and one of them can be the phase load balancing [15], taking into account the higher unbalance degree emphasized in the base scenario, S0. Regarding the energy losses, lower values have been recorded for 58 scenarios (77.33% of the total number) than in the base scenario with PD = 0, CEC = 0, and \(\mathrm{EP}_{\mathrm{PV}}\) = 0 (\(\Delta\)W = 77.03 kWh). Higher values have been recorded for PD = 40%, 50%, \(\mathrm{EP}^{\mathrm{H}}_{\mathrm{PV}}\), and all considered possibilities of CEC, CEC \(\in\{-\)10, \(-\)5, 0, 5, 10\(\}\). In addition, the energy losses decrease in the columns top-down (from the smaller to higher CEC) and increase in the rows left to right (from the lower to higher PD and EPPV), aspects usually encountered in the LVEDNs. The minimum energy losses correspond to scenarios S31-S35 with a PD = 30%, all values of CEC, CEC \(\in\{-\)10, \(-\)5, 0, 5, 10\(\}\), and \(\mathrm{EP}^{\mathrm{L}}_{\mathrm{PV}}\). The obtained results have been compared with an efficient method, which proved its effectiveness in voltage control, having the same assumptions as in the proposed RBES to demonstrate the performance of the RBES. The control voltage has been treated as a multi-objective problem where the optimal tap positions of the OLTC in each time slot are determined to minimize the energy losses and voltage deviations in the presence of technical constraints associated with operating the LVEDN [6]. Combinatorial optimization has been used to solve the mathematical model using the Total Enumeration algorithm for rapid convergence. Thus, identification of the optimal tap position \(\alpha^{\star}\) has been made from the set of admissible solutions that contains all possible combinations. Finally, not all combinations are memorized, except the optimal position that minimizes both objectives and satisfies the technical constraints.