## 3 Results
The following notations have been used for the indicator EP\({}_{\text{PV}}\): low energy production--EP\({}^{\text{LP}}_{\text{PV}}\) (EP\({}^{\text{LP}}_{\text{PV}}\) = m\({}^{\text{PV}}_{\text{EP}}\)\(-\) 2 \(\times\) \({}^{\text{PV}}_{\text{EP}}\)), average energy production--EP\({}^{\text{AP}}_{\text{PV}}\) (EP\({}^{\text{AP}}_{\text{PV}}\) = m\({}^{\text{PV}}_{\text{EP}}\)), and high energy production--EP\({}^{\text{PH}}_{\text{PV}}\) (EP\({}^{\text{PH}}_{\text{PV}}\) = m\({}^{\text{PV}}_{\text{EP}}\)\(+\) 2 \(\times\) \({}^{\text{PV}}_{\text{EP}}\)). The analysis of the results presented in Table 3 highlighted that in 40 scenarios (53.3%) from the total number, the phase voltage exceeded the upper allowable value (1.1 p.u.). All values over 1.1 p.u. are highlighted in the table in bold. These situations were recorded in the phases \(\gamma_{\text{a}}\) and \(\gamma_{\text{c}}\), where the requested power of the consumers was small, and the injected power of the prosumers was high. The increases were between 0.005 p.u. (scenario S30, with PD = 20%, CEC = 10 %, and EP\({}^{\text{PH}}_{\text{PV}}\)) and 0.185 p.u. (scenario with PD = 50%, CEC = \(-10\) %, and EP\({}^{\text{PH}}\)). Regarding the energy losses, the values are lower for 58 scenarios (77.33% of the total number) than in the base scenario, S0 (\(\Delta\)W = 77.03 kWh). The higher values, highlighted with bold font in the table, have been recorded for PD = 40%, 50%, EP\({}^{\text{HP}}_{\text{PV}}\), 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 EP\({}_{\text{PV}}\)), 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 EP\({}^{\text{LP}}_{\text{PV}}\). Figure 11: The phase voltages at the level of the end pillar (P88). A scenarios-based voltage quality matrix can be available to the DNO, indicating possible future values of the maximum phase voltage in the LVEDNs and highlighting the worst scenarios (bold font and larger size); see Figure 12. The rows of the matrix are associated with the CEC possibilities that go top-down (from small to high). The columns correspond to various alternatives for the EP\({}_{\text{PV}}\) and PG following one another from left to right. It is clear that if the RBES-based voltage control is not used, the DNO can have issues with the integration in the LVEDN of an increasing number of prosumers. These issues can be more complicated if there are changes in energy consumption at the level of consumers. Thus, the proposed RBES-based voltage control has been applied only in the scenarios with voltage issues. Tables 5 and 6 present the data associated with these scenarios in bold font. For the scenarios without voltage issues, the maximum voltage corresponds to the steady state without applying the RBES-based voltage control. The voltage issues have been removed for 30 of 40 scenarios where the maximum values of the phase voltage exceeded the upper allowable limit. The remaining scenarios with voltage issues, (S56-S60, and S71-S75), identified with bold font and larger size in Table 5 and the scenarios-based voltage quality matrix represented in Figure 13, are associated with PD \(\in\) (40%, 50%), EP\({}^{\text{H}}\)\({}_{\text{PV}}\), and CEC \(\in\) {-10%, -5%, 0%, 5%, 10%]. Figure 12: The scenarios-based voltage quality matrix indicating possible future values of the maximum phase voltage recorded for each scenario associated with the LV EDN. The energy losses in the conductors for the scenarios (S26-S30) and (S36-S40) are slightly lower between 0.21% (S26 and S36) and 5.16% (S30); see Table 6. For all other scenarios (S41-S45 and S51-S75) the values are higher, especially for S56-S60.