Analyzing Electromagnetic Interferences in Power Applications by Using Time-Efficient Joint Analysis Based on DWT and WPT Trees

Abstract

Decompositions relying on trees used to implement the Wavelet Package Transform (WPT) provide numerous advantages but require a significant runtime. When the parameters of relatively narrows ranges of harmonic orders change, only few vectors from the final nodes and the vectors hosted by the associated "parent nodes" from upper levels are affected. The counterpart decomposition relying on a tree which implements the Discrete Wavelet Transform (DWT) with the same number of levels requires a 20 times smaller runtime. An estimation of the energetic sensitivity of all DWT details vectors to harmonic orders from the interval [2,256] was made. Both types of trees were connected by means of harmonic orders affecting the levels in the DWT tree and terminal nodes in the WPT tree. Through an original labeling of the WPT nodes, 18 topologies of WPT subtrees were deduced. These subtrees correspond to individual levels or to pairs/triplets of adjacent levels from the DWT tree. Tests on synthetic and real signals validated the DWT/WPT trees based algorithm used to perform faster identification of harmonic orders whose magnitudes change from one period to another. Runtime savings varying from 90% to 10% were obtained.

Optimized use of Wavelet Packet Trees for the analysis of electrical waveforms

“…Furthermore, the WT is a reversible transform, which makes the reconstruction or evaluation of certain signal components possible. WT is particularly useful for the transaction of 2 major tasks in signals of complex (transient and/or nonstationary) nature: de-noising and feature extraction [1,2]. Special capabilities related to "low-pass" filtering were revealed by some of the authors of this work in [3].…”

“…A tree segmentation in WPT subtrees was conceived and implemented, relying on the T7 terminal nodes' connection to the harmonic orders (HO) which affect their energies and also affect the energies of the vectors of details for various levels of an unbalanced DWT tree with 7 levels and relying on 'db14' [2]. Details on WPT and DWT trees implementation are provided in [6].…”

“…Deviations in the harmonic spectra involving relatively narrow ranges of harmonic orders (e.g. electromagnetic interferences -EMI) can be correctly detected and identified by means of a time-efficient joint analysis, relying on DWT and WPT trees [2]. The appropriate properties relative to adjacent harmonic ranges exhibited by the energies of DWT vectors of details allow for the identification of (combination of) levels with energy deviations.…”

“…Among other disadvantages, FFT lacks time localization and assumes that the 2-nd half period is symmetrical to the 1-st one. To address this problem, time-frequency representations were sought and developed [1,2].…”

“…An important fact observed when using wavelet mothers (WM) from the Daubechies family, was the overlap between the frequency bands (frequency aliasing) associated with the Discrete Wavelet Transform (DWT) decomposition of their signals [1,2]. The decompositions relying on Wavelet Packet Trees (WPT) reduce up to a certain extent this drawback [4].…”