research paper

Topics: Wavelet, Discrete Fourier transform, Fourier transform Pages: 8 (2324 words) Published: August 18, 2014
Wavelet-Transform-Based Algorithm for Harmonic Analysis of Power System Waveforms

Javid Akhtar, Md Imran Ali Baig
Ghousia College of Engineering
 The concept is to develop an approach based on wavelet transform for the evaluation of harmonic contents of power system waveforms. This new algorithmic approach can simultaneously identify all harmonics including integer, non-integer and sub-harmonics. This algorithm presents features that characterize the power quality disturbances from recorded voltage waveforms using wavelet transform. The discrete wavelet transform has been used to detect and analyze power quality disturbances. The disturbances of interest include sag, swell, outage and transient. Waveforms at strategic points can be obtained for analysis, which includes different power quality disturbances. The wavelet has been chosen to perform feature extraction. The outputs of the feature extraction are the wavelet coefficients representing the power quality disturbance signal. Wavelet coefficients at different levels reveal the time localizing information about the variation of the signal. A wavelet packet transform (WPT) method is introduced as a useful tool for detecting, classifying and quantifying the RMS of testing waveform and harmonic ratio value. The proposed approach can measure the distribution of the RMS of testing waveform with respect to individual frequency bands directly from the wavelet transform coefficients. The harmonic ratio value relative to basic frequency band can be calculated as well. The method is evaluated by its application to both analytical waveform and actual testing waveform data.  

Keywords: wavelet packet transform (WPT), Discrete Fourier Transform (DFT), Fourier Series (FS), Discrete Wavelet Packet Transform (DWPT), Multi-Resolution Analysis (MRA)

1. Introduction
Mathematical transformation are applied to signals to obtain a further information from that signal that is not readily available in the raw signal Raw signal - Time domain signal
Processed Signal – Signal that has been “Transformed” by any of the available mathematical transformation as a processed signal Transformation tools :
Fourier transformation
Fast Fourier transformation
Wavelet transformation
1.1 Wavelets
Wavelets are a set of non-linear bases. When projecting (or approximating) a function in terms of wavelets, the wavelet basis functions is chosen according to the function being proximate. Hence, unlike families of linear bases where the same, static set of basic functions are used for every input function, wavelets employ a dynamic set of basic functions that represents the input function in the most efficient way. Thus wavelets are able to provide a great deal of compression and are therefore very popular in the fields of image and signal processing. 1.2 Wavelet Transform

Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. Wavelets were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, and earthquake prediction. This introduces wavelets to the interested technical person outside of the digital signal processing field. It describe the history of wavelets beginning with Fourier, compare wavelet transforms with Fourier transforms, state properties and other special aspects of wavelets, and finish with some interesting applications such as image compression, musical tones, and de-noising noisy data.

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