## 3 Materials and Methods
The single-phase PV model, which can be seen in S1 in the Supplementary Material section, was adapted from the three-phase model available in the RSCAD library and connected to the network given by the RN in a single phase. Two models had to be designed given the scenarios tested: one with all of the PVs connected to the same phase (phase three) representing the PV unbalanced distribution scenario, and a second one with an even distribution of PV by all of the phases, representing the balanced case. When trying to simulate the amount of PV in a certain network, the scenarios have to be defined in regards to structural indicators. So, quantifying PV penetration relative to load is one important  
Figure 2: Real Time Simulator Computer Aided Design (RSCAD) overview model implementation. consideration. The literature also often refers to how important it is to quantify the amount of penetration relative to the power transformer capacity to the average power of each consumer or to the line length. However, the tendency in the literature as stated is to consider the comparison of PV power to the costumer's contracted one. The fact is that there is no single recommendation, which is possibly due to the diversity of network configurations in the EU and technical constraints. Nevertheless, the ratio will be considered so as to make a comparison between the simulation results and the literature. Four scenarios were considered, and the corresponding voltage unbalance was observed in each of the 12 buses. One refers to the unbalanced distribution of PVs, and the other one refers to a balanced distribution. In each of the simulations, two different load demand scenarios were considered. The first accounts for the maximum median load demand provided by the reference networks report (referred to herein as maximum), which corresponds to 4.19 kVA, of which there is 4.02 kW. It should be highlighted that the real-time simulation only considers a snapshot in time; hence, in a realistic situation, this would correspond to the peak hour, which is not likely to be coincident with the maximum PV generation. Starting with the unbalanced case with maximum load, several levels of PV power were injected in every bus. The V\({}_{\text{Unb}}\) was observed and the limits were recorded. The same was done with the minimum load scenarios. After the worst situations (buses with higher V\({}_{\text{Unb}}\)), were identified, the balanced model was run, and the maximum power injections were estimated. Figure 3 shows a representation of the runtime interface given by the RSCAD of the model, where the PVs and loads may be varied, connected, and disconnected, and all of the system values can be observed in real time and recorded. Empirically, when PV generation is higher, the residential load demand is more likely to be minimal. For such reason, there was a need to study what would be the impact of demand on the results. In order to do so, a minimum load of 200 W was considered per household, which could correspond to a fridge (or equivalent load). All of the results were compared against the EN 50160 [30] standard limits regarding voltage unbalance and nominal voltage limits, and conclusions were drawn regarding the limits of power injection in an unbalanced scenario first (all injection of PV power made in the same phase). The fifth and last simulation was carried out in order to identify which was the single-phase PV limit of power injection to the grid, but in a balanced scenario with minimum load demand. Several power levels (3.5 kW, 7 kW, 10.5 kW, and 14 kW) were chosen, and both voltage unbalance  
Figure 3: Representation of the runtime interface of the LV network model. and nominal value limits were observed. The first limit to be reached would indicate the maximum power injection.