Phase coherence index, HHT and wavelet analysis to extract features from active and passive distribution networks

The modern Power Distribution Systems (PDS) operate more and more often with distributed generators and the optimal operation of the utility distribution systems has to take into account the possibility of bi-directional energy flows, although this event may only occur for some of the PDS. For this reason, the analysis methods that are usually employed to investigate the electrical behavior of the PDS can be more or less effective, depending on the typology of electrical loads connected to the line and on the presence or absence of Renewable Energy Sources (RES). This paper proposes either a methodology to select the best performing mathematical tool to investigate the electrical behavior of the PDS-depending on their linearity and stationarity-either an index to discriminate the PDS on the basis of a different amount of PV penetration. The proposed approach is applied to three real cases of PDS with different characteristics: residential and commercial, in the presence or absence of PV plants. In addition, two indices that are able to characterize the PDS in terms of periodicity and disturbance of the electrical signal are considered, specifically the phase coherence between two arbitrary signals and the phase coherence between an arbitrary signal and a reference one. The combined use of these indices can give valuable information about the degree of non-linearity and can be a measure of the PV penetration in a distribution circuit.