Applications of Wavelet Technique in Distributed Generation Rahul Pathak1 NIEC, New Delhi
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Mohit Kumar Katiyar2 M.Tech (C&I), DTU, New Delhi
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Abstract - Distributed generation is presently attracting increasing interest in all electrical stakeholders. Economical reasons, environmental concerns, technological advancements and market deregulation have brought distributed generation to forefront. Wavelet Transform is being used to develop new methods to sort out various issues related to economical, efficient and secure operation of distributed generation system. In this article, an attempt has been made to review application of wavelet transform in fault location, island detection and power quality issues in distributed generation. Keywords—Distributed generation; wavelet transform; fault location; islanding detection; power quality.
I. INTRODUCTION Distributed generation is recent innovation in power generation sector. Traditional power system characterized by centralized bulk power production is increasingly supported also by energy resources connected to distribution grid [1-3]. Distributed generation (DG) refers to any electric power production technology that is integrated within distribution system close to point of use. Distributed generators are connected to medium or low voltage grid [67]. DG has gain strong interest because of its capability of operating on broad range of renewable energy sources, along with cost effective, efficient, reliable and flexible on-site power alternative [4]. In era of DG integrated power system wavelet technique is proving effective way to address problems like fault location [7], islanding detection [5], power quality issues [6]. Wavelet technique was introduced to power system in 1994 by Robertson & Ribeiro. Since then, wavelet technique has found its way in almost all areas of power system like power quality improvement, transient analysis, load
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Priya Banga3 M.Tech (C&I), DTU, New Delhi
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forecasting, power system measurement, fault detection etc. Wavelet transform has been the evident signal processing development in recent year, as it has numerous applications. There are various types of transforms available; but the attention is subsequently focused on introducing wavelets in any application using the Fourier transform, has been more accurately localized sensual and frequency information (overview of wavelet analysis by HP Laboratories Japan, Daniel T. L. Lec and Akio Yamamoto). Because when a graph of captured signal is plotted in spite of amplitude versus time, information of frequency and phase also required for signal processing, now more significant is to know which type of processing to apply to solve the dataanalysis problem. Here the wavelet analysis comes in focus. Wavelet analysis is performed using a prototype function called a wavelet. The history of wavelet analysis is research of several decades, idea of approximation determined as Fourier analysis is not new, and it has existed since 1807 given by Joseph Fourier. However, in wavelet analysis, the fundamental idea is to analyze according to scale i.e. wavelet algorithms process data to different scales and resolutions [8], [9]. The elementary wavelet basis is the Haar basis. The first mention of wavelets appeared in an appendix to the thesis of Alfred Haar (1909) [10]. One property of the Haar wavelet is that it has compact support, which means that it vanishes outside a finite interval. Unfortunately, Haar wavelets are not continuously differentiable which somewhat limits their applications. In 1930 physicist Paul Levy investigated Haar basis function superior to the Fourier basis functions for studying small complicated details in the Brownian motion. In
1980, Grossman and Morlet, a physicist and an engineer, broadly defined wavelets in the context of quantum physics. They also proved that with nearly any wave shape they could recover the signal exactly from its transform [8]. In 1985, Stephane Mallat gave wavelets an additional jump-start through his work in digital signal processing. Then Y. Meyer constructed the first non-trivial wavelets. Unlike to Haar wavelets, the Meyer wavelets are continuously differentiable, but not have compact support. After sometime Daubechies construct a set of wavelet orthonormal basis functions, which is used in wavelet applications today [11]. In this article an attempt to review various applications of wavelet technique in DG system is done. II. WAVELET TECHNIQUE Wavelet multi-resolution analysis has drawn much consideration for its ability to analyze swiftly changing transient signals in both time and frequency domains. The term wavelet means a small wave. The smallness refers to the condition that this window function is of finite length. The ‘wave’ refers to the condition that this function is oscillatory [12]. There are several types of Wavelet transforms, mainly:
zero and must have an average value to zero. The mother wavelet is a band-pass filter and Ψ* is the complex conjugate form. The term translational refers to the location of window so is scale parameter is inversely proportional to frequency. In the definition of the wavelet transform, the scaling term is used in the denominator. So scales s1 compresses the signal as scale is inversely proportional to frequency. In practical applications [19], low scales (high frequencies) do not last for long, but they usually appear from time to time as short bursts. High scales (low frequencies) usually last for the entire duration of the signal. CWT is also continuous in terms of time shifting. During computation, the scaled mother wavelet is shifted smoothly over the full domain of the signal. Accordingly, a one-dimensional signal is translated into a two-dimensional time-frequency representation by the coefficient of CWT.
Continuous Wavelet transform
Discrete Wavelet transform Depending on the application one of these types of Wavelet transform may be selected. The Continuous Wavelet transform (CWT) [13] was developed as an alternative to Short Time Fourier Transform, to overcome the resolution problem and most suitable for signal analysis. The CWT is defined as: CWTxΨ (τ, s) = ΨxΨ (τ, s) = 1/√s ∫ x (t) Ψ*(t- τ /s) dt (1)
Where s>0 and -∞< τ
