## 4 Results and Discussion  
In this section, voltage unbalances are analysed both referring to all of the buses and to the distances to the power transformer (provided by the reference network report). The limits stated in the EN 50160 [30] standard for LV networks are \(\pm\)10% of voltage supply nominal value and \(\leq\)2% of V\({}_{\text{Unb}}\) or \(\leq\)3% (in some locations). Figure 4 shows the voltage unbalance for four different scenarios in an unbalanced situation (all PV connected to the same phase) with maximum load. As expected, without any PV generation, the system shows very low voltage unbalance that is very close to zero. Then, by inputting a generation of 1.7 kW per bus, the unbalance increases to approximately 1.00%. The limits of 2% and 3% of voltage unbalance stated in the EN 50160 [30] standard are reached with a power injection scenario of 3.5 kW and 4.6 kW, respectively. The more problematic buses tend to be the ones further away from the power transformer. Even though the standard states that the voltage unbalance limit can go up to 3% in some cases, we will pursue the conservative (2%) approach and consider the value of 3.5 kW as reference to deepen the analysis. Having verified the single-phase PV injection limit per bus, it is necessary to analyse this limit with respect to a minimum load situation, and examine how it behaves with a balanced distribution of the PV throughout the three phases. The minimum load simulation, which considers a minimum demand of 200 W per consumer, corresponds to a total of 21.4 kW power demand. For a balanced system simulation, a distributed single PV system of 3.5 kW is divided by the three phases in the following manner: Phase 1 (PVs on Bus 7, 12, 2, and 8); Phase 2 (PVs on Bus 5, 6, and 9); Phase 3 (PVs on Bus 11, 3, 4, and 10), corresponding to 36, 35, and 36 consumers, respectively, in each phase. Figure 5 shows the results of the voltage unbalance for the four scenarios. Figure 4: Voltage unbalance form an unbalanced distribution of a single-phase photovoltaic system (SPPS) with different power injection levels. Figure 5: Voltage unbalance with unbalanced and balanced photovoltaic (PV) distributions with minimum and maximum loads. When there is a balanced distribution of PVs, the minimum load case presents higher values of V\({}_{\text{Unb}}\) in all of the buses when compared to the minimum load case, as can be observed in Figure 5 (bottom two curves). This can be explained by there being a voltage rise in all of the phases, and the absolute value of the difference between them being higher than when the higher load case occurs due to the counter phenomena by the loads, which makes the voltage drop. On the contrary, when all of the PVs are connected in the same phase, the case of when higher loads are connected presents higher values of V\({}_{\text{Unb}}\). This is because the phase where all of the PVs are connected rises, whereas in the other phase, voltages decrease more than when compared to the minimum load case. Figure 6a presents the nominal voltage values variation, according to the distance of the bus from the power transformer. Both correspond to a 3.5-kW PV power injection balanced scenario, with maximum and minimum load power demand. The values shown are for phase 3, and it can be observed that the voltage decreases along the feeders when maximum loads are considered. The RNM base case (no PV and maximum load scenario) is also displayed for comparison. It can be seen that the voltage drop along the feeder is improved due to the PV power generation. Similarly, Figure 6b show the voltage variation in phase three with all of the PV injection made on this phase. One can observe that in regard to the case where no PV is connected, the difference of having all of the power in the same phase at the end of the feeder tends to be higher than in the beginning.