## 3 Results and Discussion
### Analysis of the Relationship between the Grid Voltage and the Power Generated by the Inverters
A summary of the maximum, minimum and average values of these parameters represented for each installation are shown in Tables 2-4. Figure 21: Weekly variation of the slope and the ordinate at the origin corresponding to the \(V_{AC}\) versus \(P_{AC}\) versus \(P_{AC}\) regressions in PV installation 6 during the three years monitored. Figure 22: Weekly variation of the determination coefficient corresponding to the \(V_{AC}\) versus \(P_{AC}\) regressions in the PV installations during the three years monitored. (**a**) Results for Installation 1, (**b**) Results for Installation 2, (**c**) Results for Installation 3, (**d**) Results for Installation 4, (**e**) Results for Installation 5 and (**f**) Results for Installation 6. In these Figures 16-22, the first year corresponds to the first 52 weeks, the second year ends at week 104 and the third year ends at week 256, which are the weeks indicated on the X-axis of these figures. The determination coefficients found, which have maximum values around 0.8 and lower average values (see Table 4), show that the grid voltage values have a certain dependence on the production of the plant injected into the grid, but that there are obviously more factors that are impacting in the values of this parameter, and that are external to the PV plants themselves. The variation of the value of this parameter over the monitored period also indicates that the impact of the production of PV installations on the grid voltage is not always constant, but also varies. It can also be observed that the values of the \(Y\)-axis intercept found, which would correspond to the voltage values of the grid without PV power production, have a margin of variation throughout the period analysed. Table 3 shows the difference between the maximum and minimum values found in the regression lines. The largest range of variation of the grid voltage with no injection of PV production is found in the grid into which installation 2 injects, which in turn is the one in which the highest value of the slope was found. This shows that plant 2 is the one that is injecting into the least resilient network. In fact, as can be seen in Figure 17, over the three years of monitoring, the value of grid voltage without the PV plant's production (value of the origin-axis intercept) increased by about 5 V, which shows that the state of the grid was modified independently of the operation of the PV installation. The most resilient grid would be those in which installation 6 injects (located in a residential area of a city), in which the voltage corresponding to the \(Y\)-axis \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Max Determination Coefficient** & **Min Determination Coefficient** & **Average Determination Coefficient** \\ \hline PV Installation 1 & 0.89 & 0.35 & 0.73 \\ PV Installation 2 & 0.84 & 0.51 & 0.72 \\ PV Installation 3 & 0.88 & 0.31 & 0.70 \\ PV Installation 4 & 0.74 & 0.04 & 0.44 \\ PV Installation 5 & 0.79 & \(-\)0.01 & 0.51 \\ PV Installation 6 & 0.63 & \(-\)0.26 & 0.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum, minimum, and average values of the determination coefficient R\({}^{2}\) obtained by correlating weekly over the three-year period the values of the grid voltage versus the power generated in the PV installations. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Max Slope** & **Min Slope** & **Average Slope** \\ \hline PV Installation 1 & 0.055 & 0.021 & 0.039 \\ PV Installation 2 & 0.13 & 0.050 & 0.078 \\ PV Installation 3 & 0.00074 & 0.00031 & 0.00050 \\ PV Installation 4 & 0.95 & 0.051 & 0.5 \\ PV Installation 5 & 0.00027 & \(-\)0.000031 & 0.00015 \\ PV Installation 6 & 0.00074 & \(-\)0.00030 & 0.00027 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum, minimum, and average values of the slope obtained by correlating weekly over the three-year period the values of the grid voltage versus the power generated in the PV installations.