Parametric harmonic analysis

Abstract

Harmonics in power systems is now a subject of wide ramifications. One particular aspect is that of capturing harmonic data at selected locations in a power network and processing it to identify harmonics and to quantify their magnitudes and arguments. Circumstances are encountered in practice for which the discrete Fourier transform (DFT) cannot be relied on to achieve valid harmonic component identification. These are where there are subharmonics, harmonics which are not integer multiples of the supply frequency, and where two or more harmonics have only small frequency separations between them. The paper reports a new procedure which fulfils the requirements of practical harmonic analysis. It avoids altogether the limitations of the DFT algorithm and is based on the nomination of a distorted waveform model expressed in terms of a sum of sinusoidal functions. Model parameters are the frequencies, magnitudes and arguments of the harmonics in the waveform it represents. The error between this model waveform and the actual one represented in captured form is minimised. At the minimum, the parameters of the model are those of the waveform for which harmonic analysis is required. A key advance in this parametric form of analysis is that of a partitioning of the data for the waveform to be analysed into a training set and a test set. This partitioned form of generalised parametric harmonic analysis is thus developed. Key concepts are clarified via a numerical example to illustrate how this approach can excel for the harmonic analysis in power systems.