# Statistical Characterization of Supraharmonics in Low-Voltage Distribution Networks
## 1 Introduction  
Power systems are undergoing a smart transition toward more sustainability and efficiency. This process passes through the widespread installation of distributed generation (e.g., renewables and small-scale generators), energy storage systems (fixed installations or mobile installations, such as electric vehicles), and high-efficiency loads [1, 2, 3]. These devices are typically interfaced to low-voltage distribution networks through electronic converters that introduce disturbances into voltage and current waveforms. The recent development of high-performance control systems determines emissions of spectral components that are beyond the classical 2 kHz milestone that individuates the low-frequency components, as they can reach up to 150 kHz for the common switching frequencies of the converters. The components in the range 2-150 kHz, typically labeled as supraharmonics in the relevant literature, have been studied much less than their low-frequency counterparts [4, 5]. This topic remains challenging since supraharmonics, especially in the context of modern smart grids [6] and modern household devices [7], may be responsible for severe malfunctioning and loss of efficiency [8]. They may: (i) bring disturbances affecting the performance of control systems or the measurements taken by smart meters, (ii) interfere with communication networks, (iii) add thermal stress to devices and equipment, reducing their useful life [9, 10]. Importantly, supraharmonics are not fully regulated yet [4, 11, 12], although in the very next years, they are expected to undergo specific regulations that willfix limits on the quality of the power supplied to the customers, as it is already common in the low-frequency range. Fixing these limits is still an ongoing process under discussion among regulators. Considering that supraharmonics are typically time-varying, the efficacy of steady-state analysis to evaluate their impact on distribution networks is very limited. To cope with the time variation, the IEC 61000-4-30 standard [12] suggests considering the minimum, average, and peak values of the rms voltage during each aggregation interval in order to determine, e.g., typical emissions (through the average values) or worst-case emissions (through the peak values). However, relying on point minimum, average and maximum values is far from being exhaustive [11] since a complete characterization of the supraharmonic emissions is preferable. Probabilistic harmonic analysis in the range 2-150 kHz may help in creating and studying scenarios to enable, e.g., taking precise actions for the most impactful components, determining the remaining available capacity of the network in terms of sustainable supraharmonic emissions (e.g., due to photovoltaics [13]), or compensation (e.g., through summing effect [14; 15]). In addition, since supraharmonics are detected from source as primary or secondary emissions [16], the statistical characterization may be helpful to individuate and characterize these two hidden regimes. The statistical characterization of supraharmonics is handy in any of these frameworks, but it is still unexplored (it is worth noting that the statistical characterization of the low-frequency harmonics has been extensively treated instead [17; 18; 19]). Related research on the statistical analysis of supraharmonics is in [11; 20; 21]. In [11; 20], the empirical distributions of the supraharmonic emissions in low-voltage distribution networks are evaluated, although without including characterization aspects. The correlation between voltage and currents grouped components is evaluated using a time series approach in [21]. This paper contributes to the state-of-the-art statistical characterization of supraharmonics in low-voltage distribution networks. The topic is tackled at a global level (i.e., characterizing the overall emissions in the entire supraharmonic range) and at an individual-component level (i.e., characterizing the magnitude of individual supraharmonic components).