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Discrimination between faults and magnetising inrush currents in transformers based on wavelet transforms
Electric Power Systems Research 63 (2002) 87 /94 www.elsevier.com/locate/epsr
Discrimination between faults and magnetising inrush currents in transformers based on wavelet transforms Omar A.S. Youssef * Faculty of Industrial Education, Suez Canal University, Suez, Egypt Received 22 August 2001; received in revised form 24 January 2002; accepted 21 February 2002
Abstract This paper presents the development of a wavelet-based scheme, for distinguishing between transformer inrush currents and power system fault currents, which proved to provide a reliable, fast and computationally efficient tool. The operating time of the scheme is less than half power frequency cycle (based on 5 kHz sampling rate). In this work wavelet transform concept is presented. Feature extraction and method of discrimination between transformer inrush and fault currents is derived. A 132/11 kV, transformer connected to a 132 kV power system were simulated using the EMTP. The generated data were used by the MATALB to test the performance of the technique as to its speed of response, computational burden and reliability. The proposed scheme proved to be reliable, accurate and fast. # 2002 Published by Elsevier Science B.V. Keywords: Wavelet transforms; Protective relaying; Digital signal processors; Protective relaying; Transforms; Transient analysis; Transformers
1. Introduction To avoid the needless trip by magnetising inrush current, the second harmonic component is commonly used for blocking differential relay in power transformers. The major drawback of the differential protection of power transformer is the possibility for false tripping caused by the magnetising inrush current during transformer energisation. In this situation, the 2nd harmonic component present in the inrush current is used as a discrimination factor between fault and inrush currents. In general, the major sources of harmonics in the inrush currents are: 1) Non-linearities of transformer core. 2) Saturation of current transformers. 3) Over-excitation of the transformers due to dynamic over-voltage condition. 4) Core residual magnetisation. 5) Switching instant.
* Present address: 8 El-Heussain Ebn Ali St.-West Heliopolis, Cairo 11351, Egypt. Tel.: /20-2-635-9384; fax: /20-2-637-6596 E-mail address: [email protected] (O.A.S. Youssef).
Previous work on transformer protection include transformer inductance during saturation [1], flux calculated from the integral of voltage and the differential current [2,3]. New methods have been adopted which include ANN [4], fuzzy logic [5]. Also, some techniques have been adopted to identify the magnetising inrush and internal faults. In [6] a modal analysis in conjunction with a microprocessor-based system was used as a tool for this purpose. In [7] the active power flowing into transformer is used as a discrimination factor which is almost zero in case of energisation. In [8] wavelet-based system is used. A wavelet-based signal processing technique [9,10] is an effective tool for power system transient analysis and feature extraction. Some applications of the technique have been reported for power quality assessment [11], data compression [12,13], protection [14], analysis for power quality problem solution [15,16], and fault detection [17]. This paper proposed a new wavelet-based method to identify inrush currents and to distinguish it from power system faults. The second harmonic component is used as the characteristic component of the asymmetrical magnetisation peculiar to the inrush. At first, wavelet transform concept is introduced. The property of multiresolution in time and frequency provided by wavelets is
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described, which allows accurate time location of transient components while simultaneously retaining information about the fundamental frequency and its low-order harmonics, which facilitates the detection of transformer inrush currents. The technique detects the inrush currents by extracting the wavelet components contained in the three line currents using data window less than half power frequency cycle. The results proved that the proposed technique is able to offer the desired responses and could be used as a fast, reliable method to discriminate between inrush magnetising and power frequency faults.
2. Wavelet transforms The waveforms associated with fast electromagnetic transients are typically non-periodic signals which contain both high-frequency oscillations and localised impulses superimposed on the power frequency and its harmonics. These characteristics present a problem for traditional discrete Fourier transform (DFT) because its use assumes a periodic signal and that the representation of a signal by the DFT is best reserved for periodic signals. As power system disturbances are subject to transient and non-periodic components, the DFT alone can be an inadequate technique for signal analysis. If a signal is altered in a localised time instant, the entire frequency spectrum can be affected. To reduce the effect of non-periodic signals on the DFT, the short-time Fourier transform (STFT) is used. It assumes local periodicity within a continuously translated time window. The time period of each window fixes the frequency resolution Df. This however locates the start time of the transient only to within one DF . A wavelet transform (WT) expands a signal not in terms of a trigonometric polynomial but by wavelet, generated using the translation (shift in time) and dilation (compression in time) of a fixed wavelet function called the mother wavelet. The wavelet function is localised in time and frequency yielding wavelet coefficients at different scales (levels). This gives the wavelet transform much greater compact support for the analysis of signals with localised transient components. The discrete wavelet transform (DWT) output can be represented in a two dimensional (2-D) grid in a similar manner as the STFT but with very different divisions in time and frequency such that the windows are narrow at high frequencies and wide at low frequencies. In contrast with the STFT, the wavelet transform can isolate transient components in the upper frequency isolated in a shorter part of power frequency cycle. In discrete wavelet analysis of a signal a timefrequency picture of the analysed signal is set up. The time-frequency plane is a 2-D space useful for idealising two properties of transient signals; localisation in time
of transient phenomena and presence of specific frequencies. The signal is decomposed into segments called time-frequency tiles plotted on the plane. The position of the tiles indicate the nominal time and while the amplitude is indicated by shading. As shown in Fig. 1, two sinusoids with 50 Hz, and 500 Hz frequency, and sampling rate 5 kHz, are plotted on the top trace. The DWT is represented by the time-frequency tiles, the mother wavelet function (db4) is dilated at low frequencies (level-6) and compressed at high frequencies (level1), so that large windows are used to obtain the low frequency components of the signal, while small windows reflect discontinuities. The ability of wavelet transform to focus on short time intervals for high-frequency components and long intervals for low-frequency components improves the analysis of signals with localised impulses and oscillations. For this reason wavelet decomposition is ideal for studying transient signals and obtaining a much better current characterisation and a more reliable discrimination. It has been shown in a previous paper [18] that the single-level decomposition process in wavelet analysis of a signal Ia simply consists of passing Ia through two complementary filters, i.e. convolving the signal with filter coefficients, called low-pass decomposition (LD), and high-pass decomposition (HD) filters and by downsampling the result they emerge as two components called low-frequency and high-frequency coefficients. Taking the appropriate length, up-sampling them and passing the result through two filters, called low-pass and high-pass reconstruction filters, they emerge as the two main components of Ia (called the low-frequency and the high-frequency components of the original signal Ia). This is illustrated in Fig. 2. The decomposition and reconstruction filters form a quadrature mirror filters and related to what is called the scaling filter W. In multi-level wavelet analysis, the decomposition process can be iterated, with successive
Fig. 1. Time-frequency tiles in DWT of two sinusoids.
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Fig. 2. Single level wavelet decomposition and reconstruction procedure.
low-frequency components being decomposed in turn, so that one signal is broken down into many lowerresolution components. This is shown in Fig. 3, while Fig. 4 shows a typical 4-level wavelet analysis of line currents Ia,b,c during simultaneous transformer inrush and BCG fault. Using wavelet function db4 with ten samples data window, and noting that the filter W and its LF decomposition (LD), HF decomposition (HD), LF reconstruction (LR), and HF reconstruction (HR) filter coefficients are given by:
Fig. 3. 4-level wavelet decomposition of line current Ia. HD, LD: HF, and LF decomposition coefficients respectively. L (HD2 Ia), length of the HF decomposition coefficients.
0:0058 0:0113 0:0075 0:0039 0:0029]
[W] [0:1629 0:5055 0:4461 0:0198 0:1323 0:0218 0:0233 0:0075] [LD] [ 0:0106 0:0329 0:0308 0:1870 0:0280 0:6309 0:7148 0:2304] [HD] [ 0:2304 0:7148 0:6309 0:0280 0:1870 0:0308 0:0329 0:0106] [LR] [0:2304 0:7148 0:6309 0:0280 0:1870 0:0308 0:0329 0:0106] [HR] [ 0:0106 0:0329 0:0308 0:1870 0:0280 0:6309 0:7148 0:2304] The level-4 wavelet transform components of the three line currents Ia,b,c can be calculated as W4 Ia;b;c [coef4][Ia;b;c ];
W3 Ia;b;c [coef3][Ia;b;c ]
W2 Ia;b;c [coef2][Ia;b;c ];
W1 Ia;b;c [coef1][Ia;b;c ]
where [coef4], [coef3], [coef2], and [coef1] are 10 /10 matrices. Taking the mean value of the level-4 transform at a particular sampling instant is equivalent to taking the mean value of the columns of [coef4] and multiplying the resulting row matrix by the ten samples of the column matrix of line current. The mean value of the columns of the four matrices are given by: [mcoef1] [0:0352 0:0007 0:0126 0:0013 0:0036 0:0006 0:0017 0:0096 0:0019 0:0338] [mcoef2] [0:0121 0:0129 0:0056 0:0138 0:0196 0:0121 0:0028 0:0139 0:0203 0:0147] [mcoef3] [0:0011 0:0155 0:0206 0:0149 0:0074
[coef4] [ 0:0249 0:0164 0:0077 0:0009 0:0134 0:0289 0:0370 0:0372 0:0338 0:0240] Using moving data window approach, and multiplying the row matrix [mcoef4] by the ten samples column matrix of line current Ia we get a single output sample. Updating the data window by one sample we get a new output sample and so on. Based on 5 kHz sampling rate, it should be noted that the frequency components are confined to wavelet analysis according to the scheme listed in Table 1.
3. System studied The system under consideration is the simplified one machine model with a 11/132 kV transformer, with both sides star connected with grounded neutrals. This is shown in Fig. 5. The transmission line is two 132 kV, 50 km sections. The system is simulated using the EMTP Table 1 Frequency allocation in wavelet analysis Wavelet analysis
Frequency components, Hz
Level Level Level Level Level
1250 /2500 625 /1250 312.5 /625 156.25 /312.5 78.125 /156.25
1 2 3 4 5
(scale 2) (scale) (scale 8) (scale 16) (scale 32)
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Fig. 6. Magnetising inrush currents at 60 ms. No fault. Fig. 4. 4-level wavelet analysis of line current Ia. Simultaneous transformer inrush and B /C /G fault.
[19,20], and in which the line was simulated using the lumped p parameters model, while the local-end source was simulated using lumped impedance model. The system parameters are given in Appendix A.
4. Digital simulations Digital simulations of the proposed algorithm are carried out using the model system described earlier. The proposed technique is tested using simulated data from the EMTP. The transformer was simulated with 11 kV, Y-connected primary, 132 kV, Y-connected secondary with both neutrals grounded. With the data given in Appendix A, subroutine BCTRAN in EMTP is used to obtain transformer parameters. The simulations provide samples of currents in each phase when the transformer is energised or when a fault occurs on the system or when both occur simultaneously. The model transformer exhibited inrush phenomena which produced inrush currents in all three phases. Data from the simulations are used as input to the algorithm to identify its response. A total of 108 fault cases and 12 energisation cases were simulated to test the various features of the algorithm. The inrush currents used correspond to energisation angles of 90, 180, 270, and 3608 from phase-a voltage zero-crossing. The fault resistance considered to simulate fault currents with the same
Fig. 5. Model system under consideration.
energisation angles were 0.001, 10.0 and 100.0 V. Sampling rate of 5.0 kHz has been considered for the algorithm (100 samples per power frequency cycle based on 50 Hz). Simulations have been divided into three main categories; simultaneous fault and inrush conditions, magnetising inrush conditions only, and faulty conditions (LG, LL, and 2LG) only. MATLAB has been used to implement the algorithm using the three line currents derived from the EMTP. In the fault tests a total of 216 cases were simulated. Those correspond to 108 cases for simultaneous inrush and fault conditions (three different source capacities, three different fault types, three different fault resistance, and four different fault inception angles), and 108 cases for fault conditions without inrush currents. Figs. 6 /11 show example test digital simulation results. The three line current waveforms Ia,b,c along with their resulting discrete wavelet analysis (absolute coefficients), and their frequency spectrum. In all of the tests the magnetising inrush current was characterised by the presence of considerable second harmonic components. Observing DWT trace, the high-frequency impulse components in
Fig. 7. BCG fault at BB2, 50 ms, Rf /0.001 V.
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Fig. 8. Simultaneous magnetising inrush current and A /G fault at BB3 at 60 ms, and Rf /10 V.
Fig. 9. Simultaneous magnetising inrush current and B /C fault at BB3 at 55 ms, and Rf /10 V.
the line currents of the three phases if present appear in level 1 [1250 2500 Hz]. In successive scales, the relative amount of energy in each frequency band is shown by the magnitude and duration of the oscillations. The bulk of energy in the transient appears in level-4, (the lower frequency). The transient energy is filtered through successive stages.
5. Feature extraction scheme By detecting two successive peak and bottom, or bottom and peak of the three line current Ia,b,c, and counting the number of samples between them, the phase subjected to inrush current can be identified. Peak detection is carried out by computing the difference
91
Fig. 10. Simultaneous magnetising inrush current and B /C fault at BB3 at 60 ms, and Rf /100 V.
Fig. 11. Simultaneous magnetising inrush current and B /C /G fault at BB3 at 60 ms, and Rf /100 V.
between every two successive current samples. A change in its sign from positive to negative indicate a peak while change from negative to positive indicate a bottom. In case of inrush just after switching on, the second harmonic is predominant (25 samples/half cycle), while faulty or healthy conditions are characterised by 50 samples/half cycle. The algorithm issues a zero output if the number of samples is greater than 30 while it issues the actual computed number of samples if it is less than 30 samples, which is translated to seconds/cycle (25 /2/ 5000 /0.01 s). This is explained in Figs. 12 /17 for different inrush, simultaneous inrush and fault conditions. Two cases are shown in Figs. 6 and 7 for magnetising inrush only, and BCG fault at BB2 with Rf /0.001 V, respectively.
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Fig. 12. Response in case of magnetising inrush currents at 60 ms. No fault.
Fig. 15. Response in case of simultaneous magnetising inrush current and B /C fault at BB3 at 60 ms, and Rf /100 V.
Fig. 13. Response in case of simultaneous magnetising inrush current and AG fault at BB3 at 60 ms, and Rf /10 V. Fig. 16. Response in case of simultaneous magnetising inrush current and B /C /G fault at BB3 at 60 ms, and Rf /100 V.
6. Conclusion
Fig. 14. Response in case of simultaneous magnetising inrush current and B /C fault at BB3 at 55 ms, and Rf /10 V.
The application of wavelet transform reveals that each waveform has distinct features. Using features in the waveform signature automated recognition can be accomplished. The use of wavelet transforms as a feature extraction naturally emphasises the difference between fault and inrush currents as generated by the EMTP, since their frequencies are very different. This paper demonstrates that the algorithm successfully differentiates between magnetising inrush and fault conditions in less than half power frequency cycle. The classification scheme is powerful yet the required calculations are simple (ten multiplications and ten additions each sampling interval) and that data window required for the algorithm is less than half power
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Z0 1:16j13:3 V Z1 /0.665/j7.5 V
References
Fig. 17. Response in case of simultaneous magnetising inrush current and B /C /G fault at BB2 at 50 ms, and Rf /0.001 V.
frequency cycle (40 samples based on 5 kHz sampling rate). It can actually be implemented in real time. In general, wavelet transforms used in analysing power system transients provide valuable information for use in feature detection systems.
Appendix A A.1 Source parameters Z0 1:16j13:3 V;
Z1 0:6550j7:50 V
A.2 Transformer parameters Three phase 35.0 MVA, 50 Hz, 132/11 kV, Y/Y connected windings with earthed neutrals and having the following parameters Y/Y connected windings WZ. exc. /3353 kW Ip exc. /0.1316% WSC. p /192 kW IZ. exc. /49.15% Zp. SC. /26% Wp exc. / 18.2 kW ZZ. SC. /24% p, z stand for positive and zero sequences respectively; W stands for losses; exc. stands for excitation. A.3 T.L. parameters Two cascaded p-sections each with the following parameters:
[1] K. Ingaki, M. Higaki, Y. Matsui, K. Kurita, M. Suzuki, K. Yoshida, T Maeda, Digital protection method for power transformers based on an equivalent circuit composed of inverse inductance, IEEE Transactions on Power Delivery 3 (4) (1988) 1501 /1510. [2] Y. Akimoto, S. Nishida, T. Sakaguchi, Transformer protection scheme based on a model including nonlinear magnetizing characteristics, IEEJ Transactions 98-B (8) (1978) 703 /710. [3] A.G. Phadke, J.S. Thorp, A new computer-based flux-restrained current-differential relay for power transformer protection, IEEE Transactions on Power Apparatus and Systems PAS-102 (11) (1983) 3624 /3629. [4] L.G. Perez, A.J. Flechsig, J.L. Meador, Z. Obradoviic, Training an artificial neural network to discriminate between magnetizing inrush and internal faults, IEEE Transactions on Power Delivery 9 (1) (1994) 434 /441. [5] A. Wiszniewski, B. Kasztenny, A multi-criteria differential transformer relay based on fuzzy logic, IEEE Transactions on Power Delivery 10 (4) (1995) 1786 /1792. [6] T.S. Sidhu, M.S. Sachdev, On-line identification of magnetizing inrush and internal faults in three-phase transformers, IEEE Transactions on Power Delivery 7 (4) (1992) 1885 /1891. [7] K. Yabe, Power differential method for discrimination between fault and magnetizing inrush current in transformers, IEEE Transactions on Power Delivery 12 (3) (1997) 1109 /1115. [8] M.G. Morante, D.W. Nicoletti, A wavelet-base differential transformer protection, IEEE Transactions on Power Delivery 14 (4) (1999) 1351 /1358. [9] I. Daubechies, S. Mallat, A.S. Willsky (Eds.), IEEE Transactions of Information Theory, Special Issue on Wavelet Transforms on Multi-resolution Signal Analysis, Vol. 38, No. 2, March 1992. [10] Y. Meyer (Ed.), Wavelets and Applications, Springer-Verlag, New York, 1992. [11] S. Santoso, E.J. Powers, W.M. Grady, P. Hofmann, Power quality assessment via wavelet transform analysis, IEEE Transactions on Power Delivery 11 (2) (1996) 924 /930. [12] S. Santoso, E.J. Powers, W.M. Grady, Power quality disturbance data compression using wavelet transform methods, IEEE Transactions on Power Delivery 12 (3) (1997) 1250 /1257. [13] T.B. Littler and D.J. Morrow, Wavelets for the analysis and compression of power system disturbances, IEEE Preprint number PE-425-PWRD-0-05-1998. To be published in IEEE Transactions on Power Delivery. [14] O. Chaari, M. Meunier, F. Brouaye, Wavelets: a new tool for the resonant grounded power distribution systems relaying, IEEE Transactions on Power Delivery 11 (3) (1996) 1301 /1308. [15] P. Pillay, A. Bhattacharjee, Application of wavelets to model short-term power system disturbances, IEEE Transactions on Power Systems 11 (4) (1996) 2031 /2037. [16] W.A. Wilkinson, M.D. Cox, Discrete wavelet analysis of power system transients, IEEE Transactions on Power Systems 11 (4) (1996) 2038 /2044. [17] F. Jiang, Z.Q. Bo, M.A. Redfern, A New Generator Fault Detection Scheme Using Wavelet Transform, Proc. 33rd Universities Power Engineering Conference (UPEC’ 98), Edinburgh, UK, September 1998, pp. 360 /363. [18] O.A. Youssef, New algorithm to phase selection based on wavelet transforms, submitted for publication in the IEEE Transactions on Power Delivery.
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[19] Electromagnetic Transient Program (EMTP) Rule Book, EPRI EL 6421-1, Vol. 1 and 2, June 1989. [20] A.K. Chaudhary, K.S. Tam, A.G. Phadke, Protection system representation in the Electromagnetic Transient Program, IEEE Transactions on Power Delivery 9 (2) (1994) 701 /711.
Biography Omar Youssef (M’92) was born in Cairo, Egypt in 1945. He received the B.Sc., M.Sc., and Ph.D. in
Electrical Engineering from University of Cairo, Faculty of Engineering in 1966, 1976, and 1979 respectively. From 1966 he has undertaken lecturing or consulting assignments in Libya, Nigeria, Saudi Arabia, Iraq, Qatar. In 1999 he was invited as a Visiting Research Fellow at University of Bath, U.K. He is currently the Deputy Dean to Graduate Studies and Research, Faculty of Industrial Education, University of Suez Canal, Suez, Egypt.
Discrimination between faults and magnetising inrush currents in transformers based on wavelet transforms Omar A.S. Youssef * Faculty of Industrial Education, Suez Canal University, Suez, Egypt Received 22 August 2001; received in revised form 24 January 2002; accepted 21 February 2002
Abstract This paper presents the development of a wavelet-based scheme, for distinguishing between transformer inrush currents and power system fault currents, which proved to provide a reliable, fast and computationally efficient tool. The operating time of the scheme is less than half power frequency cycle (based on 5 kHz sampling rate). In this work wavelet transform concept is presented. Feature extraction and method of discrimination between transformer inrush and fault currents is derived. A 132/11 kV, transformer connected to a 132 kV power system were simulated using the EMTP. The generated data were used by the MATALB to test the performance of the technique as to its speed of response, computational burden and reliability. The proposed scheme proved to be reliable, accurate and fast. # 2002 Published by Elsevier Science B.V. Keywords: Wavelet transforms; Protective relaying; Digital signal processors; Protective relaying; Transforms; Transient analysis; Transformers
1. Introduction To avoid the needless trip by magnetising inrush current, the second harmonic component is commonly used for blocking differential relay in power transformers. The major drawback of the differential protection of power transformer is the possibility for false tripping caused by the magnetising inrush current during transformer energisation. In this situation, the 2nd harmonic component present in the inrush current is used as a discrimination factor between fault and inrush currents. In general, the major sources of harmonics in the inrush currents are: 1) Non-linearities of transformer core. 2) Saturation of current transformers. 3) Over-excitation of the transformers due to dynamic over-voltage condition. 4) Core residual magnetisation. 5) Switching instant.
* Present address: 8 El-Heussain Ebn Ali St.-West Heliopolis, Cairo 11351, Egypt. Tel.: /20-2-635-9384; fax: /20-2-637-6596 E-mail address: [email protected] (O.A.S. Youssef).
Previous work on transformer protection include transformer inductance during saturation [1], flux calculated from the integral of voltage and the differential current [2,3]. New methods have been adopted which include ANN [4], fuzzy logic [5]. Also, some techniques have been adopted to identify the magnetising inrush and internal faults. In [6] a modal analysis in conjunction with a microprocessor-based system was used as a tool for this purpose. In [7] the active power flowing into transformer is used as a discrimination factor which is almost zero in case of energisation. In [8] wavelet-based system is used. A wavelet-based signal processing technique [9,10] is an effective tool for power system transient analysis and feature extraction. Some applications of the technique have been reported for power quality assessment [11], data compression [12,13], protection [14], analysis for power quality problem solution [15,16], and fault detection [17]. This paper proposed a new wavelet-based method to identify inrush currents and to distinguish it from power system faults. The second harmonic component is used as the characteristic component of the asymmetrical magnetisation peculiar to the inrush. At first, wavelet transform concept is introduced. The property of multiresolution in time and frequency provided by wavelets is
0378-7796/02/$ - see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 3 7 8 - 7 7 9 6 ( 0 2 ) 0 0 0 8 5 - 8
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O.A.S. Youssef / Electric Power Systems Research 63 (2002) 87 /94
described, which allows accurate time location of transient components while simultaneously retaining information about the fundamental frequency and its low-order harmonics, which facilitates the detection of transformer inrush currents. The technique detects the inrush currents by extracting the wavelet components contained in the three line currents using data window less than half power frequency cycle. The results proved that the proposed technique is able to offer the desired responses and could be used as a fast, reliable method to discriminate between inrush magnetising and power frequency faults.
2. Wavelet transforms The waveforms associated with fast electromagnetic transients are typically non-periodic signals which contain both high-frequency oscillations and localised impulses superimposed on the power frequency and its harmonics. These characteristics present a problem for traditional discrete Fourier transform (DFT) because its use assumes a periodic signal and that the representation of a signal by the DFT is best reserved for periodic signals. As power system disturbances are subject to transient and non-periodic components, the DFT alone can be an inadequate technique for signal analysis. If a signal is altered in a localised time instant, the entire frequency spectrum can be affected. To reduce the effect of non-periodic signals on the DFT, the short-time Fourier transform (STFT) is used. It assumes local periodicity within a continuously translated time window. The time period of each window fixes the frequency resolution Df. This however locates the start time of the transient only to within one DF . A wavelet transform (WT) expands a signal not in terms of a trigonometric polynomial but by wavelet, generated using the translation (shift in time) and dilation (compression in time) of a fixed wavelet function called the mother wavelet. The wavelet function is localised in time and frequency yielding wavelet coefficients at different scales (levels). This gives the wavelet transform much greater compact support for the analysis of signals with localised transient components. The discrete wavelet transform (DWT) output can be represented in a two dimensional (2-D) grid in a similar manner as the STFT but with very different divisions in time and frequency such that the windows are narrow at high frequencies and wide at low frequencies. In contrast with the STFT, the wavelet transform can isolate transient components in the upper frequency isolated in a shorter part of power frequency cycle. In discrete wavelet analysis of a signal a timefrequency picture of the analysed signal is set up. The time-frequency plane is a 2-D space useful for idealising two properties of transient signals; localisation in time
of transient phenomena and presence of specific frequencies. The signal is decomposed into segments called time-frequency tiles plotted on the plane. The position of the tiles indicate the nominal time and while the amplitude is indicated by shading. As shown in Fig. 1, two sinusoids with 50 Hz, and 500 Hz frequency, and sampling rate 5 kHz, are plotted on the top trace. The DWT is represented by the time-frequency tiles, the mother wavelet function (db4) is dilated at low frequencies (level-6) and compressed at high frequencies (level1), so that large windows are used to obtain the low frequency components of the signal, while small windows reflect discontinuities. The ability of wavelet transform to focus on short time intervals for high-frequency components and long intervals for low-frequency components improves the analysis of signals with localised impulses and oscillations. For this reason wavelet decomposition is ideal for studying transient signals and obtaining a much better current characterisation and a more reliable discrimination. It has been shown in a previous paper [18] that the single-level decomposition process in wavelet analysis of a signal Ia simply consists of passing Ia through two complementary filters, i.e. convolving the signal with filter coefficients, called low-pass decomposition (LD), and high-pass decomposition (HD) filters and by downsampling the result they emerge as two components called low-frequency and high-frequency coefficients. Taking the appropriate length, up-sampling them and passing the result through two filters, called low-pass and high-pass reconstruction filters, they emerge as the two main components of Ia (called the low-frequency and the high-frequency components of the original signal Ia). This is illustrated in Fig. 2. The decomposition and reconstruction filters form a quadrature mirror filters and related to what is called the scaling filter W. In multi-level wavelet analysis, the decomposition process can be iterated, with successive
Fig. 1. Time-frequency tiles in DWT of two sinusoids.
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Fig. 2. Single level wavelet decomposition and reconstruction procedure.
low-frequency components being decomposed in turn, so that one signal is broken down into many lowerresolution components. This is shown in Fig. 3, while Fig. 4 shows a typical 4-level wavelet analysis of line currents Ia,b,c during simultaneous transformer inrush and BCG fault. Using wavelet function db4 with ten samples data window, and noting that the filter W and its LF decomposition (LD), HF decomposition (HD), LF reconstruction (LR), and HF reconstruction (HR) filter coefficients are given by:
Fig. 3. 4-level wavelet decomposition of line current Ia. HD, LD: HF, and LF decomposition coefficients respectively. L (HD2 Ia), length of the HF decomposition coefficients.
0:0058 0:0113 0:0075 0:0039 0:0029]
[W] [0:1629 0:5055 0:4461 0:0198 0:1323 0:0218 0:0233 0:0075] [LD] [ 0:0106 0:0329 0:0308 0:1870 0:0280 0:6309 0:7148 0:2304] [HD] [ 0:2304 0:7148 0:6309 0:0280 0:1870 0:0308 0:0329 0:0106] [LR] [0:2304 0:7148 0:6309 0:0280 0:1870 0:0308 0:0329 0:0106] [HR] [ 0:0106 0:0329 0:0308 0:1870 0:0280 0:6309 0:7148 0:2304] The level-4 wavelet transform components of the three line currents Ia,b,c can be calculated as W4 Ia;b;c [coef4][Ia;b;c ];
W3 Ia;b;c [coef3][Ia;b;c ]
W2 Ia;b;c [coef2][Ia;b;c ];
W1 Ia;b;c [coef1][Ia;b;c ]
where [coef4], [coef3], [coef2], and [coef1] are 10 /10 matrices. Taking the mean value of the level-4 transform at a particular sampling instant is equivalent to taking the mean value of the columns of [coef4] and multiplying the resulting row matrix by the ten samples of the column matrix of line current. The mean value of the columns of the four matrices are given by: [mcoef1] [0:0352 0:0007 0:0126 0:0013 0:0036 0:0006 0:0017 0:0096 0:0019 0:0338] [mcoef2] [0:0121 0:0129 0:0056 0:0138 0:0196 0:0121 0:0028 0:0139 0:0203 0:0147] [mcoef3] [0:0011 0:0155 0:0206 0:0149 0:0074
[coef4] [ 0:0249 0:0164 0:0077 0:0009 0:0134 0:0289 0:0370 0:0372 0:0338 0:0240] Using moving data window approach, and multiplying the row matrix [mcoef4] by the ten samples column matrix of line current Ia we get a single output sample. Updating the data window by one sample we get a new output sample and so on. Based on 5 kHz sampling rate, it should be noted that the frequency components are confined to wavelet analysis according to the scheme listed in Table 1.
3. System studied The system under consideration is the simplified one machine model with a 11/132 kV transformer, with both sides star connected with grounded neutrals. This is shown in Fig. 5. The transmission line is two 132 kV, 50 km sections. The system is simulated using the EMTP Table 1 Frequency allocation in wavelet analysis Wavelet analysis
Frequency components, Hz
Level Level Level Level Level
1250 /2500 625 /1250 312.5 /625 156.25 /312.5 78.125 /156.25
1 2 3 4 5
(scale 2) (scale) (scale 8) (scale 16) (scale 32)
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Fig. 6. Magnetising inrush currents at 60 ms. No fault. Fig. 4. 4-level wavelet analysis of line current Ia. Simultaneous transformer inrush and B /C /G fault.
[19,20], and in which the line was simulated using the lumped p parameters model, while the local-end source was simulated using lumped impedance model. The system parameters are given in Appendix A.
4. Digital simulations Digital simulations of the proposed algorithm are carried out using the model system described earlier. The proposed technique is tested using simulated data from the EMTP. The transformer was simulated with 11 kV, Y-connected primary, 132 kV, Y-connected secondary with both neutrals grounded. With the data given in Appendix A, subroutine BCTRAN in EMTP is used to obtain transformer parameters. The simulations provide samples of currents in each phase when the transformer is energised or when a fault occurs on the system or when both occur simultaneously. The model transformer exhibited inrush phenomena which produced inrush currents in all three phases. Data from the simulations are used as input to the algorithm to identify its response. A total of 108 fault cases and 12 energisation cases were simulated to test the various features of the algorithm. The inrush currents used correspond to energisation angles of 90, 180, 270, and 3608 from phase-a voltage zero-crossing. The fault resistance considered to simulate fault currents with the same
Fig. 5. Model system under consideration.
energisation angles were 0.001, 10.0 and 100.0 V. Sampling rate of 5.0 kHz has been considered for the algorithm (100 samples per power frequency cycle based on 50 Hz). Simulations have been divided into three main categories; simultaneous fault and inrush conditions, magnetising inrush conditions only, and faulty conditions (LG, LL, and 2LG) only. MATLAB has been used to implement the algorithm using the three line currents derived from the EMTP. In the fault tests a total of 216 cases were simulated. Those correspond to 108 cases for simultaneous inrush and fault conditions (three different source capacities, three different fault types, three different fault resistance, and four different fault inception angles), and 108 cases for fault conditions without inrush currents. Figs. 6 /11 show example test digital simulation results. The three line current waveforms Ia,b,c along with their resulting discrete wavelet analysis (absolute coefficients), and their frequency spectrum. In all of the tests the magnetising inrush current was characterised by the presence of considerable second harmonic components. Observing DWT trace, the high-frequency impulse components in
Fig. 7. BCG fault at BB2, 50 ms, Rf /0.001 V.
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Fig. 8. Simultaneous magnetising inrush current and A /G fault at BB3 at 60 ms, and Rf /10 V.
Fig. 9. Simultaneous magnetising inrush current and B /C fault at BB3 at 55 ms, and Rf /10 V.
the line currents of the three phases if present appear in level 1 [1250 2500 Hz]. In successive scales, the relative amount of energy in each frequency band is shown by the magnitude and duration of the oscillations. The bulk of energy in the transient appears in level-4, (the lower frequency). The transient energy is filtered through successive stages.
5. Feature extraction scheme By detecting two successive peak and bottom, or bottom and peak of the three line current Ia,b,c, and counting the number of samples between them, the phase subjected to inrush current can be identified. Peak detection is carried out by computing the difference
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Fig. 10. Simultaneous magnetising inrush current and B /C fault at BB3 at 60 ms, and Rf /100 V.
Fig. 11. Simultaneous magnetising inrush current and B /C /G fault at BB3 at 60 ms, and Rf /100 V.
between every two successive current samples. A change in its sign from positive to negative indicate a peak while change from negative to positive indicate a bottom. In case of inrush just after switching on, the second harmonic is predominant (25 samples/half cycle), while faulty or healthy conditions are characterised by 50 samples/half cycle. The algorithm issues a zero output if the number of samples is greater than 30 while it issues the actual computed number of samples if it is less than 30 samples, which is translated to seconds/cycle (25 /2/ 5000 /0.01 s). This is explained in Figs. 12 /17 for different inrush, simultaneous inrush and fault conditions. Two cases are shown in Figs. 6 and 7 for magnetising inrush only, and BCG fault at BB2 with Rf /0.001 V, respectively.
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Fig. 12. Response in case of magnetising inrush currents at 60 ms. No fault.
Fig. 15. Response in case of simultaneous magnetising inrush current and B /C fault at BB3 at 60 ms, and Rf /100 V.
Fig. 13. Response in case of simultaneous magnetising inrush current and AG fault at BB3 at 60 ms, and Rf /10 V. Fig. 16. Response in case of simultaneous magnetising inrush current and B /C /G fault at BB3 at 60 ms, and Rf /100 V.
6. Conclusion
Fig. 14. Response in case of simultaneous magnetising inrush current and B /C fault at BB3 at 55 ms, and Rf /10 V.
The application of wavelet transform reveals that each waveform has distinct features. Using features in the waveform signature automated recognition can be accomplished. The use of wavelet transforms as a feature extraction naturally emphasises the difference between fault and inrush currents as generated by the EMTP, since their frequencies are very different. This paper demonstrates that the algorithm successfully differentiates between magnetising inrush and fault conditions in less than half power frequency cycle. The classification scheme is powerful yet the required calculations are simple (ten multiplications and ten additions each sampling interval) and that data window required for the algorithm is less than half power
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Z0 1:16j13:3 V Z1 /0.665/j7.5 V
References
Fig. 17. Response in case of simultaneous magnetising inrush current and B /C /G fault at BB2 at 50 ms, and Rf /0.001 V.
frequency cycle (40 samples based on 5 kHz sampling rate). It can actually be implemented in real time. In general, wavelet transforms used in analysing power system transients provide valuable information for use in feature detection systems.
Appendix A A.1 Source parameters Z0 1:16j13:3 V;
Z1 0:6550j7:50 V
A.2 Transformer parameters Three phase 35.0 MVA, 50 Hz, 132/11 kV, Y/Y connected windings with earthed neutrals and having the following parameters Y/Y connected windings WZ. exc. /3353 kW Ip exc. /0.1316% WSC. p /192 kW IZ. exc. /49.15% Zp. SC. /26% Wp exc. / 18.2 kW ZZ. SC. /24% p, z stand for positive and zero sequences respectively; W stands for losses; exc. stands for excitation. A.3 T.L. parameters Two cascaded p-sections each with the following parameters:
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Biography Omar Youssef (M’92) was born in Cairo, Egypt in 1945. He received the B.Sc., M.Sc., and Ph.D. in
Electrical Engineering from University of Cairo, Faculty of Engineering in 1966, 1976, and 1979 respectively. From 1966 he has undertaken lecturing or consulting assignments in Libya, Nigeria, Saudi Arabia, Iraq, Qatar. In 1999 he was invited as a Visiting Research Fellow at University of Bath, U.K. He is currently the Deputy Dean to Graduate Studies and Research, Faculty of Industrial Education, University of Suez Canal, Suez, Egypt.