Summation of Random Harmonic Currents

Abstract

This chapter deals with the probabilistic modeling of harmonic currents. After some definitions about single current injection models, the vectorial summation of random harmonic currents characterized by distributions independent of time is considered. The basic methods presented in literature for harmonic current summation modeling are discribed: the convolution method, the joint density method and Monte Carlo simulations. Applications of the methods to different case studies give an idea of the accuracy of the models considered.One aspect of assessing the harmonics tolerated by a power system is the estimation of the statistic figures of harmonics arising from the various time-varying/probabilistic sources. The assessment of harmonics is not exact or uniform, since there will be unpredictable variations in either the nonlinear sources and/or parameters of the system which affect the summation.The combination of a number of harmonic time-varying sources will generally lead to less than the arithmetic sum of the maximum values due to uncertainty of magnitude and phase angle. Hence the resulting summation is extremely difficult to estimate accurately.Before introducing the methods that can be adopted to solve the summation problem, it is necessary to introduce and discuss some basic concepts: random harmonic and interharmonic vectors, the harmonic summation principle and essential nomenclature. Time-Varying Waveform Distortions in Power Systems Edited by Paulo F. Ribeiro

Statistical Characterization of Supraharmonics in Low-Voltage Distribution Networks

“…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]).…”