Abstract
This study presents a novel measurement-based method for modelling harmonic current injections of low-voltage power electronics equipment. The aim of the developed methodology is to accurately represent harmonic current phase angle in response to the applied harmonic background voltage at the terminals of modelled device. In this method, the harmonic angles are analysed with the techniques of circular statistics. The performed study proves the adequacy of representing phase angles as sets of directional data rather than linear. After graphical and quantitative analysis, the regression models with underlying von Mises distribution are derived in the form of algebraic equation. This algebraic equation features sine and cosine terms and explains relationship between independent variable – voltage harmonic angle and dependent variable – current harmonic angle. The subsequent analysis of the residuals allows to conclude that models developed by applying this technique can be used in commercial simulation packages and allow to account on any value of background harmonic voltage angle.
Highlights
Voltage and current harmonic distortions are taking nowadays place among power quality issues with rising amount of complaints by customers
The authors of this study proved that harmonic current is influenced significantly by applied harmonic voltage amplitudes and phase angles
We propose a novel method for modelling individual harmonic producing sources based on the foundations of circular statistics
Summary
Voltage and current harmonic distortions are taking nowadays place among power quality issues with rising amount of complaints by customers. The main advantage of the proposed approach is the possibility to reduce the model to an analytic dependency on the supplied voltage, which leads to the improvement of the iteration process in load-flow based solvers for harmonic analysis, as it avoids additional iterations in the simulations This will allow to exclude possible convergence problems with the algorithm in case of large system studies with a significant number of sources present. As it will be shown in this paper, an accurate modelling of harmonic angles cannot be performed on the basis of Gaussian distribution of linear data but rather needs to be tackled by approach of circular (directional) statistics.
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