# Statistical Characterization of Supraharmonics in Low-Voltage Distribution Networks
## 3 Results
### Individual Supraharmonic Component Characterization  
The individual components evaluated at the eight locations are characterized through the Norm, LogN, Weib, Burr, and MixN distributions. Only for the sake of conciseness, the  
Figure 2: Q-Q plots of the: (**a**) \(\text{TSHD}_{\text{avg}}\) at Alameda (CA); (**b**) \(\text{TSHD}_{\text{peak}}\) at Alameda (CA); (**c**) \(\text{TSHD}_{\text{avg}}\) at Wohlen (Switzerland); (**d**) \(\text{TSHD}_{\text{peak}}\) at Wohlen (Switzerland).  
results presented below refer to four individual components (6, 26, 50, and 120 kHz) at Alameda; similar considerations arise from the analysis performed at the other locations. The 6-, 26-, 50-, and 120-kHz components are investigated as they are representative of the ranges 2-9, 9-30, 30-90, and 90-150 kHz, which are typically the object of interest in supraharmonic analysis [11]. Both the avg and the peak values are considered in the experiments.  
The estimated CDFs of the four avg individual components and of the four peak individual components are illustrated in Figures 3 and 4, respectively. The empirical CDF shapes of the avg individual components strongly differ from the empirical CDF shapes of the peak individual components: at a higher frequency, the CDFs of the avg components appear to follow a stepwise pattern, denoting regions of quasi-continuous avg supraharmonic emissions, whereas CDFs of the peak components appear to follow a continuous, slightly oscillating pattern, with distributed regions of peak supraharmonic emissions. The regimes identified for the peak individual components can be adequately modeled only through the multimodal MixN distribution. It appears instead that the benefit of applying the multimodal MixN distribution is reduced while considering the avg individual components at a higher frequency.  
Figure 3: Estimated and empirical CDFs of the: (**a**) 6-kHz; (**b**) 26-kHz; (**c**) 50-kHz; (**d**) 120-kHz avg voltage component at Alameda (CA).  
The quantitative assessment of the GOF is reported in Table 2 through the ADC. Bold values indicate the best fit. The MixN distribution with \(C=3\) components is the best pick in all the considered scenarios, as the ADC values are the greatest ones. As guessed by the graphical inspection, the use of a multimodal distribution has the most impact in characterizing the peak individual components as the unimodal components are particularly poor, whereas the gap between unimodal and multimodal distribution is more reduced in characterizing the avg individual components.  
The Q-Q plot of the peak individual components at Alameda and Wohlen are illustrated in Figure 5; for the sake of clarity, only the Burr distribution and the MixN distribution with \(C=3\) components are considered in the Q-Q plots. The Q-Q plots of the MixN distribution with \(C=3\) components are closer to resemble the bisector line, compared to the Q-Q plots of the Burr distribution, which cannot even be assimilated to a straight line.  
Figure 4: Estimated and empirical CDFs of the: (**a**) 6-kHz; (**b**) 26-kHz; (**c**) 50-kHz; (**d**) 120-kHz peak voltage component at Alameda (CA).