使用连续小波变换在配电系统中故障定位_毕业论文(编辑修改稿)

使用连续小波变换在配电系统中故障定位_毕业论文(编辑修改稿)内容摘要：

one or more locations in the distribution system. Recent contributions to the subject are based on the use of the wavelet transform (., [1–4]), usually adopting the discretewavelet transform (DWT), due to its straightfor * Corresponding author. Tel.: +39 51 2093479。 fax: +39 51 2093470. Email address: (. Nucci). 01420615/$ see front matter 20xx Elsevier Ltd. All rights reserved. doi: ward implementation and the reduced putational time it requires. In this paper, use is made of the continuouswavelet transform (CWT) algorithm. As known, pared to the DWT algorithm, the CWT one allows performing a more detailed and continuous analysis of the spectrum energy of the fault transient. Such a feature is used to detect indi vidual frequencies that characterize the voltage transients generated by the fault. These frequencies can be used for inferring the location of the fault, being the work topol ogy, the wave propagation velocity along the lines and the fault type known. The proposed CWTbased fault location procedure is conceived to be bined with a measurement system aimed at acquiring both the starting time of the transient and the relevant waveforms. The paper is structured as follows. Section 3 introduces the proposed correlation between the results of the CWTanalysis and specific paths along the work covered by the traveling waves originated by the fault. 使用连续小波变换在配电系统中故障定位 A. Bhetti et al. / Electrical Power and Energy Systems 28 (20xx) 608–617 609 Section 4 presents the application to a distribution sys tem for both the case of symmetrical faults and nonsym metrical ones. It also presents the results obtained for Ch188。 Z254。 1 1 2 jW240。 x222。 j x dx 1 240。 3222。 different neutral grounding characteristics and fault loca tions. The CWTbased procedure is applied in such a sec tion to puter simulation results obtained with a detailed EMTP (electromagic transient program) model of the distribution system, whose characteristics and data are reported in Appendix. Section 5 describes the basic characteristics of the earlier mentioned measurement system with distributed architec ture for the acquisition of voltage transients. The conclusions summarize the results obtained with the proposed approach and identify the main aspects requiring Eq. (3) is satisfied by the two following conditions: • mean value of w(t) equal to zero。 • fast decrease to zero of w(t) for t ! 177。 1. Provided that the motherwavelet satisfies specific condi tions, in particular the orthogonality one, the signal can also be reconstructed from the transform coefficients. Several motherwavelet has been used in the literature (., [6–11]), in this paper, the socalled Morletwavelet is chosen as mother one w(t): additional research efforts. w240。 t222。 188。 et2=2ej2pF0t: 240。 4222。 2. Fault location information provided by continuous wavelet transform The CWT of a signal s(t) is the integral of the product between s(t) and the socalled daughterwavelets, which are time translated and scale expanded/pressed ver sions of a function having finite energy w(t), called motherwavelet. This process, equivalent to a scalar prod uct, produces wavelet coefficients C(a, b), which can be seen as ‘‘similarity indexes’’ between the signal and the socalled daughterwavelet located at position b (time shifting factor) and positive scale a: Z11 Unlike DWT, CWT can operate at any scale, specifically from that of the original signal up to some maximum scale. CWT is also continuous in terms of shifting: during putation, the analyzing wavelet is shifted smoothly over the full domain of the analyzed function. The CWTanalysis is performed in time domain on the voltage transients recorded after the fault in a bus of the distribution work. The analyzed part of the transient recorded signal s(t), which can correspond to a voltage or current fault transient, has a limited duration (few milliseconds) corre sponding to the product between the sampling time Ts and the number of samples N. The numerical implementa tion of the CWT to signal s(t) is a matrix C(a,b) defined as p wtb 240。 1222。 C240。 a。 b222。 188。 1 s240。 t222。 affiffiffi a dt follows: 1 where * denotes plex conjugation. Eq. (1) can be expressed also in frequency domain (., C240。 a。 iTs222。 188。 Ts pjffiffiffiffiffiffiajX1 n w240。 i222。 Ts a s240。 nTs222。 [5]): i 188。 0。 1。 . . .。 N : n188。 0 240。 5222。 F 240。 C240。 a。 b222。 222。 188。 pffiffiffiaW 240。 a x222。 S240。 x222。 240。 2222。 The sum of the squared values of all coefficients corre sponding to the same scale, which is henceforth called where F(C(a,b)), S(x) and W(x) are the Fourier transforms of C(a, b), s(t) and w(t), respectively. Eq. (2) shows that if the motherwavelet is a bandpass filter function in the frequencydomain, the use of CWT in the frequencydomain allows for the identification of the local features of the signal. According to the Fourier trans form theory, if the center frequency of the motherwavelet W(x) is F0, then the one of W(ax) is F0/a. Therefore, differ ent scales allows the extraction of different frequencies from the original signal – larger scale values corresponding to lower frequencies – given by the ratio between center fre quency and bandwidth. Opposite to the windowedFourier analysis where the frequency resolution is constant and depends on the width of the chosen window, in the wavelet approach the width of the window varies as a function of a, thus allowing a kind of timewindowed analysis, which is dependent to the values of scale a. As known, the use of CWT, allows the use of arbitrary motherwavelets which must satisfy the ‘admissibility condition’: 使用连续小波变换在配电系统中故障定位 CWTsignal energy ECWT(a), identifies a ‘scalogram’ which provides the weight of each fre。