# Statistical Characterization of Supraharmonics in Low-Voltage Distribution Networks
## 4 Discussion and Conclusions  
The statistical characterization of supraharmonics is tackled in this paper to enable the generation of scenarios and to foster the probabilistic analysis of power systems accounting for emissions in the range 2-150 kHz. Several probability distribution families are considered to characterize supraharmonics within a detailed comparative scheme developed to generalize the approach and to suit different conditions and case studies. The numerical ex \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Component Frequency**} & \multirow{2}{*}{**Index**} & \multicolumn{6}{c}{**Individual Component Distribution**} \\ \cline{3-8}  & & **Norm** & **LogN** & **Weib** & **Burr** & **MixN C = 2** & **MixN C = 3** \\ \hline \multirow{2}{*}{6 kHz} & ADC (avg) & 0.9147 & 0.9692 & 0.9154 & 0.9707 & 0.9723 & **0.9985** \\  & ADC (peak) & 0.4665 & 0.7893 & 0.7141 & 0.9426 & **0.9448** & **0.9448** \\ \hline \multirow{2}{*}{26 kHz} & ADC (avg) & 0.9243 & 0.9591 & 0.9074 & 0.9863 & 0.9789 & **0.9910** \\  & ADC (peak) & 0.4409 & 0.6195 & 0.5927 & 0.7643 & **0.9720** & **0.9720** \\ \hline \multirow{2}{*}{50 kHz} & ADC (avg) & 0.9141 & 0.9416 & 0.8997 & 0.9660 & 0.9849 & **0.9930** \\  & ADC (peak) & 0.4530 & 0.5984 & 0.5834 & 0.7192 & **0.9840** & **0.9840** \\ \hline \multirow{2}{*}{120 kHz} & ADC (avg) & 0.9379 & 0.9364 & 0.9409 & 0.9408 & 0.9629 & **0.9636** \\  & ADC (peak) & 0.5683 & 0.8110 & 0.7380 & 0.9557 & **0.9560** & **0.9560** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Adjusted determination coefficient of the individual component distributions at Alameda. Bold values indicate the best fit. Figure 5: Q-Q plots of the: (**a**) 6-kHz; (**b**) 26-kHz; (**c**) 50-kHz; (**d**) 120-kHz peak voltage component at Alameda (CA). periments performed on public data collected at actual low-voltage distribution networks confirm that the time-varying nature of supraharmonics is prone to be analyzed within a probabilistic framework; moreover, the characterization is conveniently optimized using multimodal distributions that are able to catch and model different operation regimes that determine a different entity of supraharmonic components. Among the considered distributions, the MixN shows the best fitting results in characterizing both the overall supraharmonic content (through the TSHD) and individual supraharmonic components. Notably, the estimated quantiles of the MixN maintain statistical consistency with the empirical data quantiles even at low and high nominal coverages, as confirmed by the Q-Q plot inspection at left and right tails. Future research on this topic may follow several paths, such as the development of more appropriate probability distributions to model supraharmonics and the exploitation of the statistical characterization to generate scenarios and to implement probabilistic analysis with a specific focus on supraharmonic emissions (e.g., within probabilistic harmonic power flow studies). In perspective, this may also enable to take precise actions for the most impactful power system components, to determine the available remaining capacity of the network in terms of sustainable supraharmonic emissions, and to analyze the compensation (summing effects). The availability of wider datasets that are not burdened by the 2 kHz grouping may allow refining these procedures, accounting for a finer frequency resolution. Conceptualization, P.D.F. and P.V. ; methodology, P.D.F. and P.V. ; software, P.D.F. and P.V. ; validation, P.D.F. and P.V. ; formal analysis, P.D.F. and P.V. ; investigation, P.D.F. and P.V. ; data cu-ration, P.D.F. and P.V. ; writing--original draft preparation, P.D.F. and P.V. ; writing--review and editing, P.D.F. and P.V. ; visualization, P.D.F. and P.V. ; supervision, P.D.F. and P.V. All authors have read and agreed to the published version of the manuscript. This research received no external funding.