Selection of the Most Suitable Decomposition Filter for the Measurement of Fluctuating Harmonics

Abstract

Abstract-The proliferation of non-linear loads in both industrial and residential distribution grids leads to undesirable non-sinusoidal and fluctuating harmonic pollution on voltage and current waveforms. New analysis tools, such as wavelets, are being used to overcome the problems posed by the use of the Fourier Transform when analyzing complex waveforms. Nevertheless, the selection of the wavelet basis must be done carefully to minimize spectral leakage due to the non-exact frequency discrimination. In this context, this paper proposes an objective method for comparing different wavelet families for the measurement of harmonic contents. This methodology is applicable for determining the best filter among the 53 preselected structures according to the following requirements: frequency selectivity, computational complexity, convolution results and observed spectral leakage. With all these considerations, the Butterworth IIR filter of order 29 was found to be the best wavelet decomposition structure to achieve an effective harmonic analysis up to the 50 th order.

Wavelet Packet Decomposition for IEC Compliant Assessment of Harmonics under Stationary and Fluctuating Conditions

“…In this paper, it is shown that this can be achieved by an accurate study of the WPD implementation. The novel algorithm hereafter presented is the continuation of the work performed by the authors in [26], where a detailed study was conducted to define a methodology for the selection of the most suitable filter and convolution technique for WPD applied to power systems' harmonics. The methodology proposed in [26] is here employed to develop and characterize a complete measurement method.…”

“…The novel algorithm hereafter presented is the continuation of the work performed by the authors in [26], where a detailed study was conducted to define a methodology for the selection of the most suitable filter and convolution technique for WPD applied to power systems' harmonics. The methodology proposed in [26] is here employed to develop and characterize a complete measurement method. In order to obtain the IEC frequency bands, up to at least the 50th order, a sampling rate of 6400 Hz is necessary, and seven levels of decomposition must be implemented.…”

“…These necessary features set high requirements on the frequency selectivity of the decomposition filters. The work performed in [26] showed that a maximally-flat Butterworth Infinite Impulse Response (IIR) filter of order 29 was the most suitable choice, and for this reason, it was employed in this paper as the mother wavelet. Its superior behavior in frequency selectivity, number of coefficients, and spectral leakage under realistic conditions, compared with traditional mother wavelet functions (e.g., db20, db10, Vaidyanathan, etc.)…”

“…provides the high level of accuracy required to comply with the IEC standards in both stationary and non-stationary conditions. It must be noted that, although IIR filters have a non-linear phase, it does not represent a problem because the purpose of the method is to extract the RMS content of each frequency band, and the convolution technique presented in [26] allows preserving this information even with non-linear phase filtering.…”

“…On the other hand, it is for the first time compliant with the IEC 61000-4-7 standard. This result, never achieved before, is possible thanks to the accurate selection of the filtering implementation and to the uniform frequency bandwidth division of WPD, as studied by the authors in [26]. To assess the method's implementation and validate its superior performance within the IEC standard requirements, several voltage signals with known harmonic content, both in stationary and fluctuating conditions, were tested.…”