## 3 Results  
The proposed RBES has been tested considering an aerial LVEDN supplied by an EDS whose MV bus (20 kV) represents the CCP with the network of a Romanian DNO that carries out its distribution service in the respective area. Figure 4 shows the structure of the test LV EDN. Figure 4: The test 88-bus LV EDN. Localization of the network is in an area where the solar potential is high [44] (see Figure 6), so it is expected that the number of consumers who want to become PV prosumers will increase, considering the situation in Romania. According to the data presented in [45], about 50% of European Union citizens are expected to be able to produce their electricity by 2050. They also plan on meeting 45% of the energy requirements of the European Union. This information is strengthened by the last report of the Romanian Energy Regulatory Authority (RERA) published in 2022 [46], highlighting that the number of prosumers increased more than 6 times in 2021, from 2134 to 13,596. On the other hand, the reports of the RERA [47] regarding the evolution of energy consumption from 2020 to 2022 indicated a decrease at the residential consumer level by approximately 10%. This decrease was due to two factors associated with the pandemic crisis and the geopolitical situation (the war in Ukraine and the energy crisis). These data represented the basis of the assumptions regarding indicators used in the study. Thus, it has been considered that the number of prosumers will gradually increase to 50%. Regarding consumption, their trend will be associated with possible increases or decreases in the range \(\pm\)10%. Not least, the energy production of the prosumers will depend on solar radiation, which can have a high uncertainty modelled through a confidence interval characterised by statistical parameters (mean and standard deviation). Considering these assumptions, more scenarios have been considered with the following indicators: penetration degree, PD, PD \(\in\) {10%, 20%, 30%, 40, 50%}; consumption evolution, CEC, CEC \(\in\) {-10%, 5%, 0%, +5%, +10%}; and energy production of the PV systems from the month that includes the analysed day, EP\({}_{\text{PV}}\), EP\({}_{\text{PV}}\) \(\in\) {m\({}_{\text{PE}}^{\text{PV}}-2\times\) e\({}_{\text{PE}}^{\text{PV}}\),  
Figure 6: The location of the analysed LVEDN [44], (The World Bank, Source: Global Solar Atlas 2.0, Solar resource data: Solargis). m\({}_{\rm EP}^{\rm PV}\), m\({}_{\rm EP}^{\rm PV}\) + 2 \(\times\)\(\sigma_{\rm EP}^{\rm PV}\)}, where m\({}_{\rm EP}^{\rm PV}\) and \(\sigma_{\rm EP}^{\rm PV}\) represent the mean and standard deviation of the energy production (EP) associated with a PV system from the geographical area where the LVEDN is located (see Figure 6), having a certain installed capacity for a month from a year (in our case, June). Knowing the values m\({}_{\rm EP}^{\rm PV}\) and \(\sigma_{\rm EP}^{\rm PV}\), EP\({}_{\rm PV}\) with probability (confidence level) 0.95 belonging to the interval [m\({}_{\rm EP}^{\rm PV}\) - 2 \(\times\)\(\sigma_{\rm EP}^{\rm PV}\), m\({}_{\rm EP}^{\rm PV}\) + 2 \(\times\)\(\sigma_{\rm EP}^{\rm PV}\)] has been considered. This means that, in almost all cases, the frequency will not go beyond the specified interval. Even in 5% of cases, the errors will be minor [48]. The study analysed the penetration degrees considering the assumption that the consumers with the highest energy consumption are qualified and selected to become prosumers, maintaining their connection phase. Table 11 from Appendix A presents the allocation of the end-users. They were classified as consumers and prosumers, at each pillar associated with the five penetration degrees, PD \(\in\) {0%, 10%, 20%, 30%, 40, and 50%). Considering the energy consumption uploaded from the SMS, the PV systems were sized (having the installed capacities of 3 and 5 kWp). The sizing process was based on the generation profiles from the geographical location of the LVEDN uploaded from the PVGIS tool [49]. kWp (kilowatts peak) is associated with the peak power of a PV system.