## 3 Results and Discussion
### Imbalance of Network Voltage Values between Phases
In this case, it can be seen that the values of the voltage imbalances in phase 2 with respect to the average production of the three phases fluctuate throughout the day with a greater incidence in the early hours of the day and in the afternoon, in the winter months, when the days are shorter. To see if this behaviour is related to the production of the plant, the imbalance, in absolute value, of the production in each of the phases (i), \(\Delta P_{AC\_grid\_phase\_i}\) versus the average value of the production of the three phases \(P_{AC\_grid\_phase\_i}\), with \(I=1\), 2 and 3, was determined in the same way as the imbalance of the voltage in the phases, by means of the Equation (2)  
\[\Delta P_{AC\_grid\_phase\_i}=\left|P_{AC\_grid\_phase\_i}-\left(\frac{\sum_{i= 1}^{3}P_{AC\_grid\_phase\_i}}{3}\right)\right| \tag{2}\]  
The results shown in Figure 27 were obtained in this way. It can be seen that during the first hours of the day, there was an imbalance in the grid voltage, but not in the production, so apparently this voltage imbalance was not caused by imbalances in the production of the PV plant between the phases. In the last hours of daily production, it is observed that there was an imbalance in both voltage and production values. With the data available, it is not possible to determine whether these voltage imbalances in the afternoon hours were a consequence of the production imbalances, or whether they were due to the same causes that deviated the voltage during the morning hours. It would be necessary to see if the state of the loads connected to the different phases changed throughout the day, which could make the network more sensitive to the presence of production imbalances between the three phases, but the authors did not have access to this information. Figure 27: PV production imbalance on phase 2 with respect to the production on the three phases, measured by inverter 2 in PV installation 4. This is why, if a study of the voltage imbalance between phases needs to be carried out with data from the inverters, it is recommended to have inverter models that can record the voltage 24 h a day, in order to have more complete information on what happens in the grid throughout the day, and thus be able to have a greater amount of voltage values from the grid when there is no injection of production in the PV installation. As far as possible, three-phase inverters, which measure simultaneously in all three phases, should be available, or at least the PV modules of the different strings associated with inverters feeding into different phases should be located in such a way that they do not receive unequal shading in the early or late hours of the day, so that all inverters start operating simultaneously. Three-phase inverters also help to ensure that there is no imbalance in production between the three phases and can, depending on the size of the plant, help to reduce the imbalance between the phases at that point in the grid. With respect to single-phase inverter measurements, it may also lead to errors in the interpretation of the phase-to-phase voltage imbalance data if there is a production failure in one or two of the inverters that are feeding into the different phases, and the rest of the inverters that have not failed to continue to produce electricity and record the grid voltage value. The failed inverters, not operating, will show zero voltage values, and therefore this apparent voltage imbalance between phases would be recorded for the whole period that the failure lasts, as it can be seen in Figure 28a for the case of installation 6. For example, on day 237 there is a fault in inverter 1, and therefore during the time that the fault lasts, the recording in this inverter of the grid voltage in phase 1, which is the phase in which it injects, is zero. As the rest of the inverters are working correctly and measure the grid voltage values in the other two phases, this apparent imbalance between the three phases appears.