## 3 Results and Discussion  
The case study is constituted by several real PDS, containing active and passive circuits. The active ones are characterized by bidirectional energy fluxes, due to the presence of distributed generators that inject relevant amount of power; instead, the passive ones are interested by energy flux along a unique direction. In particular, the attention is focused on three distribution circuits, named L1, L2, and L3, having different electrical behavior. L1 is a passive distribution circuit, whereas L2 and L3 are active (Table 1). L1 has a peak power of about 100 kW and no PV plant is connected. L2 has about 108 kW of PV power with a maximum peak of absorbed power of about 80 kW. L3 has only one 6-kWp grid-connected PV plant, with a peak-absorbed power of 50 kW. The three distribution circuits have about the same length. Moreover, the users of the L1 and L2 are almost exclusively residential, whereas L3 feeds commercial users. Regarding the acquisition system, the datalogger of DSO is set to store one sample every 10 minutes, then acquires 144 samples per day and covers the period from September 2013 to June 2014, corresponding to nine months with a total amount of about 40,000 samples. Following, the results coming from the application of the proposed methodology to the case under test are presented. Figure 3 reports the time-domain waveforms of the currents flowing in one of the three phases (specifically the phase B) for each considered distribution circuit L1, L2, and L3, during the whole period of investigation. The currents system is not symmetric (here not shown) and the maximum current values of the different circuits are different. L1 has a maximum current amplitude between 100 A and 150 A (depending on the phase), the peak amplitude of L2 is 100 A for the three phases, whereas L3 is less regular with peaks between 50 A and 80 A for the different phases. As it is evident, the distribution circuit L2 shows a more regular behavior during the whole period of acquisition than the other power distribution circuits. In addition, L3 is very noisy; this behavior can be ascribed to the typology of users that are connected to that distribution circuit. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Title** & **L1** & **L2** & **L3** \\ \hline Maximum absorbed power (kW) & 100 & 80 & 50 \\ PV power (kWp) &..... & 108 & 6 \\ Length (m) & 415 & 396 & 380 \\ Prevalent typology of end-user & residential & residential & commercial \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the PDS under investigation. Figure 2: Methods to analyze electrical signals of Power Distribution Systems (PDS) with PhotoVoltaic (PV) plants. (\(\times\) = not applicable; \(\sqrt{\) = applicable). Observing the flow-chart of Figure 1, the first step is the check on the linearity of the signal, based on the PC\({}_{\text{ref}}\) (it is worth mentioning that a coherence index equal to one means that the equivalent load is linear). As reference signal, a generic sinusoid with the same amplitude and frequency of the first harmonic of each line has been chosen. The analysis has been carried out during the different seasons, circuit by circuit, and phase by phase. Figure 4 shows that the value of PC\({}_{\text{ref}}\) of each line/phase/season is very different from one. Moreover, L3 is, on average, the less coherent than the other two PDS; in fact, the peak value 0.10 is never reached. The phases of L1, are, on average, the most coherent ones in the winter and the index follows the same trend for the three phases. The phases of L2 have very different behavior during all the seasons; also, in the spring, when the injected PV power has the maximum value and a minimum value of the index is expected, it is true for the phases B and C, whereas the phase A shows an opposite trend. This allows for affirming that the typology of the electrical loads and their utilization affect the electrical behavior of the distribution circuit more than the contribution of the injected PV power.