## 3 Results and Discussion
In general, we can also observe that for the three studied distribution circuit, the minimum values of the coherence index appear in spring. These values evidence the presence of strong nonlinearities, so the blue block of Figure 1 suggests using HHT to study the electrical signals. HHT allows to outcome other frequency modes that the FFT is not able to find, being the Fourier analysis valid in the hypothesis of linear regime. In particular, the typical electrical signal analyzed here can exploit different working frequencies due to the non-linear and a-periodical working behavior. The results from the HHT analysis are proposed in Figure 5, where each plot is referred to single distribution circuit. Each diagram highlights the frequencies of the IMFs. Some IMFs, in the high-frequency as well as in low-frequency spectrum, could not be revealed by the FFT analysis. Moreover, a deeper analysis has been carried out, subdividing the whole dataset in three subsets, each one corresponding to a season: autumn, winter and spring (see Table 2). It is possible to observe that the number of the computed IMFs is directly related to the noise present in the electrical signal. The results are similar to the ones of Figure 5, but not all the IMFs are present in the current of each  
Figure 3: Time-domain waveforms of the currents flowing into the phase B of the three distribution circuits L1, L2, L3, for the whole analysis period. phase and of each distribution circuit. Observing the Figure 5 and the Table 2, it results that L3 is noisier than the other two, as highlighted by the largest number of IMFs obtained from the HHT analysis. This behavior depends on the typology of the connected users (we remind that L3 is the commercial distribution circuit). Now, in order to appreciate the usefulness of the proposed index PCref for suggesting the most suitable method to study the electrical signals, the FFT and the WA are applied to the same dataset, showing that only partial results would have been obtained with respect to the ones calculated by HHT. In fact, let us firstly consider the results from FFT (Figure 6). It can be noted that the main harmonics are located at the same frequencies, even if the amplitudes of the harmonics vary either for different phases of the same distribution circuit either for different distribution circuits. The main excited modes are related to the time periods 24 h and 12 h associated to the first and second frequency peak (11.63 uHz and 23.17 uHz, respectively). In addition, the higher order harmonics are also present but with a smaller peak amplitude. Comparing Figures 5 and 6, it is evident that HHT returns richer information than FFT, revealing operating modes that are not captured by the FFT. In fact, while the FFT evidences only the fundamental component and its higher harmonics, the HHT also shows non-multiple behaviors of the fundamental one. This happens because the dataset is nonlinear and nonstationary, with the consequence that only HHT can give the complete information, whereas FFT shows its limits. Lastly, let us apply the WA (Figure 7), which provides frequency vs time information. Basically, for the different cases reported, only two evident harmonics are excited, the fundamental one and the second one. However, a different temporal behavior is shown. In fact, it is easy to observe the fundamental component in all of the phases of the distribution circuits L1 and L2 (more evident in L1) for the whole period, whereas the first harmonic of the line L3 (\(f=11.63\) uH) has an intermittent behavior. Concerning the second harmonic (\(f=23.13\) uH), it is possible to observe that it is quite constant during the whole temporal window for L1, it is intermittent for L3, whereas the amplitude of L2 is quite small. With this in mind, it results that the presence of PV plant can influence the second harmonic behavior; in fact, the second harmonic is negligible for L2, which has a great amount of PV power, whereas it is quite constant for L1, which has no PV plant connected.