## 3 Results and Discussion
So, it results that WA gives more information than FFT in the case of non-stationary signals, because WA can extract the frequency components for many temporal windows inside the total investigation time. Nevertheless, also, the frequency components  
Figure 4: Coherence degree between each current signal and a generic sinusoid (as a reference), PCref, for each phase of each distribution circuit for the different seasons. (**a**) L1; (**b**) L2; and, (**c**) L3. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **L1** & **L2** & **L3** \\ \hline \multicolumn{4}{c}{**Autumn**} \\ \hline Phase A & 13 & 13 & 13 \\ Phase B & 13 & 13 & 13 \\ Phase C & 13 & 12 & 13 \\ \hline \multicolumn{4}{c}{**Winter**} \\ \hline Phase A & 12 & 13 & 12 \\ Phase B & 12 & 13 & 13 \\ Phase C & 13 & 13 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of Intrinsic Mode Function (IMFs) for each current, for each distribution circuit, for each season. Figure 6: FFT of the currents flowing into the distribution circuits L1, L2, L3 for the whole period. (a) L1; (b) L2; and, (c) L3. Figure 7: Wavelet of the currents flowing in L1, L2, L3 for the entire period. (a–c) phases of the line L1; (d–f) phases of the line L2; (g–i) phases of the line L3. Finally, to estimate the PV penetration, the PC\({}_{\rm sigs}\) for the three possible combinations among the three distribution circuits under investigation have been calculated, choosing just one phase of each distribution circuit (the phase B in this case, but similar behaviors have been found for the other phases): current of L1 versus current of L2, current of L1 versus current of L3, current of L2 versus current of L3. The three indices are calculated for the three seasons (Figure 8). It results that the distribution circuit L2 and L3 (both fed also by the PV generators) are the most coherent ones during the autumn and winter, instead L1 and L2 are the less coherent ones, because L1 is a passive distribution circuit, whereas L2 has the larger amount of PV power. The coherence degree between the distribution circuits L1 and L3 has an intermediate value. In spring, the great amount of current that is injected in L2 by the 108 kWp-PV generators completely modifies the mutual interactions. However, in general, the comparison of the coherence degrees of distinct active distribution circuits with respect to a common passive one can provide useful qualitative information about the presence of PV plants. From all the previous analyses, it results that the main key findings of the proposed methodology are two. The first one regards the PC\({}_{\rm sigs}\) index that allows to distinguish the distribution circuits with different PV penetration, simply calculating an index. The monitoring of the PC\({}_{\rm sigs}\) can be useful to prevent the major disturbances in distribution systems, as the voltage variation and the harmonic distortion. Secondly, the proposed procedure allows to select the best analysis method among HHT/FFT/WA. In fact, even if the FFT is the simplest and fastest method to use, nevertheless, as evidenced above, the extraction of all the operating modes in presence of strongly nonlinear signals is possible only by using HHT. In fact, in the case study, several operating modes are not detected correctly by the FFT neither by the WA, but it is necessary to use mathematical methods (like the HHT) that are able to extract the main features of a non-linear, non-stationary, and non-periodic electrical signal. \begin{table}
\begin{tabular}{l c c c} \hline  & **L1** & **L2** & **L3** \\ \hline \multicolumn{4}{c}{**Spring**} \\ \hline Phase A & 13 & 12 & 14 \\ Phase B & 12 & 13 & 13 \\ Phase C & 13 & 12 & 13 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 8: Coherence degree between two lines PC\({}_{\rm sigs}\), based on the currents flowing into a fixed and arbitrary phase.