## 3 Results and Discussion
### Grid Voltage Values Recorded at Each PV Installation during the Monitoring Period
Voltage values without PV production are only recorded in the early morning hours, when the inverter starts operating but is still trying to synchronise with the grid, and in the later hours of the day, when the inverter stops producing electricity until it shuts down. Since these inverter models are not measuring 24 h a day, the occurrences reflected in these graphs for the case of no plant production are much lower than in the case where there is PV production. In Figures 3, 5, 7, 9, 11 and 13, there was a general shift to the right and therefore an increase in voltage values when PV installations were feeding energy into the grid. The exception was, as seen previously, in installation 6 (Figure 13), where the voltage values hardly increased when the installation was producing electricity and injecting it into the grid. This is, as already indicated, a grid located within a city, and it is more resilient to the impact of the plant's production, given that, as can be seen in Figure 12, the voltage values hardly increased during the hours when the PV installation was generating at its maximum. It can be seen in Figure 7 (installation 3) and in Figures 11 and 13 (installations 5 and 6) that certain grid voltage values appeared with a marked increase in probability with respect to the rest of the values, e.g., with a higher frequency of appearance, which suggests that in these cases, the behaviour of the statistical distribution was multimodal, unlike the rest of the installations where a monomodal trend can be seen. On the other hand, it can be seen in these cases (installations 3, 5 and 6) that the pattern of the statistical distribution of voltage values was maintained regardless of whether the PV plant injects energy, so it can be deduced that the origin of this behaviour was unrelated to the PV installations, indicating that the explanation for this behaviour was related exclusively to the state of the distribution network. In this sense, the hypothesis considered to explain this multimodal behaviour is that the loads in the areas served by these installations could have a tendency towards some specific consumption values, more likely than others, which condition the values of the network voltage. Given that the histograms in Figures 7, 11 and 13 represent data frequency, it could be analysed how these voltage values were distributed over time by means of Figures 6, 10 and 12. In this way, it could be seen whether the most probable consumptions of the loads that cause this behaviour appear daily or at certain times of the year, which could be useful for the management of the electricity system itself. This detailed analysis was not carried out in the present work, but it will be carried out in future research. Figure 14 plots the distribution of the grid voltage values recorded in the six PV plants, to show the data of all installations together. The non-zero \(V_{AC}\) grid voltage data recorded by the inverters are plotted in box plots, showing the mean voltage for each installation (red line inside the box), the 75 th percentile (the upper side of the box) and the 25 th percentile (lower side of the box). The distance between these last two values is the inter quartile  
range. Since each PV installation injects into different distribution lines, the average voltage values in each of them were different, as they will depend on the specific point of the grid where they are located, and the distance from the transformer.