Abstract
In this paper, noise propagation through a two-stage nonlinear algorithm for measurement of harmonic distortion in power systems according to IEC 61000-4-7 is analyzed. Noise generated in the instrument’s input circuitry is considered as an aggregated noise source without detailed characterization of its origin. The first stage of the measurement algorithm is the discrete Fourier transform (DFT) of the input signal. Noise propagation through the DFT is analyzed by means of probability theory. The result of this analysis, the probability density function (pdf) of the DFT spectrum amplitudes, is used for characterization of the second stage of the measurement algorithm – the root-sum-square grouping of several spectrum components into a single harmonic distortion index. In this way, pdfs of the most common harmonic indices are derived and analyzed. The study presented reveals that noise generated in the input stage produces, besides the already known variance of the results, an offset in the harmonic distortion indices. Analysis of the resulting pdfs implies that an increase in the number of components in the grouping procedure increases the offset error, whereas the standard deviations are essentially independent of the number of components included in the group. The validity of the model derived has been tested with a prototype of a low-cost portable instrument for three-phase power quality measurements.
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