170 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 1, JANUARY 2003

A Wavelet-Based Technique for DiscriminationBetween Faults and Magnetizing Inrush

Currents in TransformersOmar A. S. Youssef, Member, IEEE

AbstractThis paper presents the development of a wavelet-based scheme, for distinguishing between transformer inrushcurrents and power system fault currents, which proved toprovide a reliable, fast, and computationally efficient tool. Theoperating time of the scheme is less than half the power frequencycycle (based on a 5-kHz sampling rate). In this work, a wavelettransform concept is presented. Feature extraction and method ofdiscrimination between transformer inrush and fault currents isderived. A 132/11-kV transformer connected to a 132-kV powersystem were simulated using the EMTP. The generated data wereused by the MATLAB to test the performance of the technique asto its speed of response, computational burden and reliability. Theproposed scheme proved to be reliable, accurate, and fast.

Index TermsDigital signal processors, protective relaying,transformers, transforms-transient analysis, wavelet transforms(WTs).

I. INTRODUCTION

T O AVOID the needless trip by magnetizing inrush cur-rent, the second harmonic component is commonly usedfor blocking differential relay in power transformers. The majordrawback of the differential protection of power transformer isthe possibility for false tripping caused by the magnetizing in-rush current during transformer energization. In this situation,the second harmonic component present in the inrush currentis used as a discrimination factor between fault and inrush cur-rents. In general, the major sources of harmonics in the inrushcurrents are

1) nonlinearities of transformer core;2) saturation of current transformers;3) overexcitation of the transformers due to dynamic over-

voltage condition;4) core residual magnetization;5) switching instant.Previous work on transformer protection includes trans-

former inductance during saturation [1], flux calculated fromthe integral of voltage, and the differential current [2], [3].New methods have been adopted which include ANN [4], andfuzzy logic [5]. Also, some techniques have been adopted toidentify the magnetizing inrush and internal faults. In [6], amodal analysis in conjunction with a microprocessor-basedsystem was used as a tool for this purpose. In [7], the active

Manuscript received January 16, 2002; revised March 22, 2002.The author is with the Faculty of Industrial Education, Suez Canal University,

Suez, Egypt.Digital Object Identifier 10.1109/TPWRD.2002.803797

power flowing into transformer is used as a discriminationfactor, which is almost zero in the case of energization. In [8],a wavelet-based system is used.

A wavelet-based signal processing technique [9], [10] is aneffective tool for power system transient analysis and featureextraction. Some applications of the technique have beenreported for power quality assessment [11], data compression[12], [13], protection [14], analysis for power quality problemsolution [15], [16], and fault detection [17].

This paper proposed a new wavelet-based method to iden-tify inrush currents and to distinguish it from power systemfaults. The second harmonic component is used as the char-acteristic component of the asymmetrical magnetization pecu-liar to the inrush. At first, the wavelet transform (WT) conceptis introduced. The property of multiresolution in time and fre-quency provided by wavelets is described, which allows accu-rate time location of transient components while simultaneouslyretaining information about the fundamental frequency and itslow-order harmonics, which facilitates the detection of trans-former inrush currents. The technique detects the inrush currentsby extracting the wavelet components contained in the threeline currents using data window less than half power frequencycycle. The results proved that the proposed technique is able tooffer the desired responses and could be used as a fast, reliablemethod to discriminate between inrush magnetizing and powerfrequency faults.

II. WAVELET TRANSFORMS

The waveforms associated with fast electromagnetic tran-sients are typically nonperiodic signals which contain bothhigh-frequency oscillations and localized impulses super-imposed on the power frequency and its harmonics. Thesecharacteristics present a problem for traditional discrete Fouriertransform (DFT) because its use assumes a periodic signal andthat the representation of a signal by the DFT is best reservedfor periodic signals. As power system disturbances are subjectto transient and nonperiodic components, the DFT alone can bean inadequate technique for signal analysis. If a signal is alteredin a localized time instant, the entire frequency spectrum canbe affected. To reduce the effect of nonperiodic signals onthe DFT, the short-time Fourier transform (STFT) is used. Itassumes local periodicity within a continuously translated timewindow. The time period of each window fixes the frequencyresolution . This, however, locates the start time of thetransient only to within one .

0885-8977/03$17.00 2003 IEEE

YOUSSEF: WAVELET-BASED TECHNIQUE FOR DISCRIMINATION 171

Fig. 1. Time-frequency tiles in DWT of two sinusoids.

A WT expands a signal not in terms of a trigonometric poly-nomial, but by wavelet, generated using the translation (shift intime) and dilation (compression in time) of a fixed wavelet func-tion called the mother wavelet. The wavelet function is local-ized in time and frequency yielding wavelet coefficients at dif-ferent scales (levels). This gives the WT much greater compactsupport for the analysis of signals with localized transient com-ponents. The discrete wavelet transform (DWT) output can berepresented in a two-dimensional (2-D) grid in a similar manneras the STFT, but with very different divisions in time and fre-quency, such that the windows are narrow at high frequenciesand wide at low frequencies. In contrast with the STFT, theWT can isolate transient components in the upper frequencyisolated in a shorter part of power frequency cycle. In discretewavelet analysis of a signal, a timefrequency picture of theanalyzed signal is set up. The timefrequency plane is a 2-Dspace useful for idealizing a two properties of transient signals,localization in time of transient phenomena, and presence ofspecific frequencies. The signal is decomposed into segmentscalled timefrequency tiles plotted on the plane. The position ofthe tiles indicate the nominal time, while the amplitude is indi-cated by shading. As shown in Fig. 1, two sinusoids with 50 Hz,500 Hz frequency, and a sampling rate 5 kHz, are plotted on thetop trace. The DWT is represented by the timefrequency tiles,and the mother wavelet function (db4) is dilated at low frequen-cies (level-6) and compressed at high frequencies (level-1) sothat large windows are used to obtain the low frequency compo-nents of the signal, while small windows reflect discontinuities.

The ability of WT to focus on short time intervals for high-fre-quency components and long intervals for low-frequency com-ponents improves the analysis of signals with localized impulsesand oscillations. For this reason, wavelet decomposition is idealfor studying transient signals and obtaining a much better cur-rent characterization and a more reliable discrimination.

It has been shown in a previous paper [18] that the single-leveldecomposition process in wavelet analysis of a signalsimplyconsists of passing through two complementary filters, i.e.,convolving the signal with filter coefficients, called low-passdecomposition (LD) and high-pass decomposition (HD) filters,

Fig. 2. Single level wavelet decomposition and reconstruction procedure.

Fig. 3. Four-Level wavelet decomposition of line currentI . HD; LD: HF,and LF decomposition coefficients respectively.L(HD I ): length of the HFdecomposition coefficients.

and by down-sampling the result they emerge as two compo-nents called low-frequency and high-frequency coefficients.Taking the appropriate length, up-sampling them and passingthe result through two filters, called low-pass and high-passreconstruction filters, they emerge as the two main componentsof (called the low-frequency and the high-frequency compo-nents of the original signal ). This is illustrated in Fig. 2.

The decomposition and reconstruction filters form quadra-ture mirror filters and are related to what is called the scalingfilter . In multilevel wavelet analysis, the decompositionprocess can be iterated, with successive low-frequency compo-nents being decomposed in turn, so that one signal is brokendown into many lower-resolution components. This is shown inFig. 3, while Fig. 4 shows a typical four-level wavelet analysisof line currents during simultaneous transformer inrushand BCG fault. Using wavelet function db4 with ten samples,data window, and noting that the filter and its LF decom-position ( ), HF decomposition ( ), LF reconstruction

172 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 1, JANUARY 2003

Fig. 4. Four-level wavelet analysis of line currentI . Simultaneous trans-former inrush and BCG fault.

TABLE IFREQUENCYALLOCATION IN WAVELET ANALYSIS

( ), and HF reconstruction (HR) filter coefficients, are givenby

The level-4 WT components of the three line currentscan be calculated as

where , and are 10 10matrices. Taking the mean value of the level4 transform ata particular sampling instant is equivalent to taking the meanvalue of the columns of and multiplying the resultingrow matrix by the 10 samples of the column matrix of line

Fig. 5. Model system under consideration.

current. The mean value of the columns of the four matricesare given by

Using the moving data window approach, and multiplying therow matrix by the 10 samples column matrix of linecurrent , we get a single output sample. Updating the datawindow by one sample, we get a new output sample, and so on.Based on the 5-kHz sampling rate, it should be noted that the fre-quency components are confined to wavelet analysis accordingto the scheme listed in Table I.

III. SYSTEM STUDIED

The system under consideration is the simplified one ma-chine model with a 11/132 kV transformer, with both sides starconnected with grounded neutrals. This is shown in Fig. 5. Thetransmission line is two 132-kV, 50-km sections. The systemis simulated using the EMTP [19], [20], in which the linewas simulated using the lumped parameters model, whilethe local-end source was simulated using lumped impedancemodel. The system parameters are given in the Appendix.

IV. DIGITAL SIMULATIONS

Digital simulations of the proposed algorithm are carriedout using the model system described earlier. The proposedtechnique is tested using simulated data from the EMTP. Thetransformer was simulated with 11-kV, Y-connected primary,132-kV, Y-connected secondary with both neutrals grounded.With the data given in Appendix, subroutine BCTRAN inEMTP is used to obtain transformer parameters. The simu-lations provide samples of currents in each phase when thetransformer is energized or when a fault occurs on the systemor when both occur simultaneously. The model transformerexhibited inrush phenomena which produced inrush currents inall three phases. Data from the simulations are used as input tothe algorithm to identify its response. A total of 108 fault cases

YOUSSEF: WAVELET-BASED TECHNIQUE FOR DISCRIMINATION 173

Fig. 6. Magnetizing inrush currents at 60 ms. No fault.

Fig. 7. BCG fault at BB2, 50 ms, andR = 0:001 .

and 12 energization cases were simulated to test the variousfeatures of the algorithm. The inrush currents used correspondto energization angles of 90, 180 , 270 , and 360 fromphase-a voltage zero-crossing. The fault resistance, consideredto simulate fault currents with the same energization angles,was 0.001 , 10.0 , and 100.0 . A sampling rate of 5.0 kHzhas been considered for the algorithm (100 samples per powerfrequency cycle based on 50 Hz). Simulations have been di-vided into three main categories: simultaneous fault and inrushconditions, magnetizing inrush conditions only, and faultyconditions (LG, LL, and 2LG) only. MATLAB has been usedto implement the algorithm using the three line currents derivedfrom the EMTP. In the fault tests, a total of 216 cases weresimulated. Those correspond to 108 cases for simultaneousinrush and fault conditions (three different source capacities,three different fault types, three different fault resistance, andfour different fault inception angles), and 108 cases for faultconditions without inrush currents. Figs. 611 show exampletest digital simulation results: the three line current waveforms

along with their resulting discrete wavelet analysis(absolute coefficients), and their frequency spectrum. In all ofthe tests, the magnetizing inrush current was characterized bythe presence of considerable second harmonic components.Observing DWT trace, the high-frequency impulse componentsin the line currents of the three phases, if present, appear inlevel

Fig. 8. Simultaneous magnetizing inrush current and AG fault at BB3, at60 ms, andR = 10 .

Fig. 9. Simultaneous magnetizing inrush current and BC fault at BB3, at55 ms, andR = 10 .

Fig. 10. Simultaneous magnetizing inrush current and BC fault at BB3, at60 ms, andR = 100 .

174 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 1, JANUARY 2003

Fig. 11. Simultaneous magnetizing inrush current and BCG fault at BB3, at60 ms, andR = 100 .

Fig. 12. Response in case of magnetizing inrush currents at 60 ms. No fault.

Fig. 13. Response in case of simultaneous magnetizing inrush current and AGfault at BB3, at 60 ms, andR = 10 .

Fig. 14. Response in case of simultaneous magnetizing inrush current and BCfault at BB3, at 55 ms, andR = 10 .

Fig. 15. Response in case of simultaneous magnetizing inrush current and BCfault at BB3, at 60 ms, andR = 100 .

1[12502500 Hz]. In successive scales, the relative amount ofenergy in each frequency band is shown by the magnitude andduration of the oscillations. The bulk of energy in the transientappears in level-4 (the lower frequency). The transient energyis filtered through successive stages.

V. FEATURE EXTRACTION SCHEME

By detecting two successive peak and bottom, or bottom andpeak of the three line current , and counting the numberof samples between them, the phase subjected to inrush currentcan be identified. Peak detection is carried out by computingthe difference between every two successive current samples. Achange in its sign from positive to negative indicate a peak whilechange from negative to positive indicate a bottom. In case ofinrush just after switching on, the second harmonic is predomi-nant (25 samples/half cycle), while faulty or healthy conditionsare characterized by 50 samples/half cycle. The algorithm issues

YOUSSEF: WAVELET-BASED TECHNIQUE FOR DISCRIMINATION 175

Fig. 16. Response in case of simultaneous magnetizing inrush current andBCG fault at BB3, at 60 ms, andR = 100 .

Fig. 17. Response in case of simultaneous magnetizing inrush current andBCG fault at BB2, at 50 ms, andR = 0:001 .

a zero output if the number of samples is greater than 30, whileit issues the actual computed number of sample if it is less than30 samples, which is translated to seconds/cycle (252/5000

0.01 s). This is explained in Figs. 1217 for different inrush,simultaneous inrush, and fault conditions. Two cases are shownin Figs. 6, 7 for magnetizing inrush only, and BCG fault at BB2with , respectively.

VI. CONCLUSION

The application of WT reveals that each waveform has dis-tinct features. Using features in the waveform signature, auto-mated recognition can be accomplished. The use of WTs as afeature extraction naturally emphasizes the difference betweenfault and inrush currents as generated by the EMTP, since theirfrequencies are very different. This paper demonstrates that thealgorithm successfully differentiates between magnetizing in-rush and fault conditions in less than half power frequency cycle.

The classification scheme is powerful yet the required calcula-tions are simple (10 multiplications and 10 additions each sam-pling interval) and that data window required for the algorithmis less than half the power frequency cycle (40 samples basedon 5 kHz sampling rate). It can actually be implemented in realtime.

In general, WTs used in analyzing power system transientsprovide valuable information for use in feature detection sys-tems.

APPENDIX

1) Source parameters, .

2) Transformer parametersThree phase 35.0 MVA, 50 Hz, 132/11 kV,Y/Y con-

nected windings with earthed neutrals and having the fol-lowing parameters

Y/Y connected windings kWkW

kWstand for positive and zero sequences respectively.

stands for losses, : stands for excitation.

3) T.L. parametersTwo cascaded -sections each with the following pa-

rameters:

REFERENCES

[1] K. Ingaki, M. Higaki, Y. Matsui, K. Kurita, M. Suzuki, K. Yoshida,and T. Maeda, Digital protection method for power transformers basedon an equivalent circuit composed of inverse inductance,IEEE Trans.Power Delivery, vol. 3, pp. 15011510, Oct. 1988.

[2] Y. Akimoto, S. Nishida, and T. Sakaguchi, Transformer protectionscheme based on a model including nonlinear magnetizing characteris-tics, Trans. Inst. Electr. Eng. Jpn. B, vol. 98, no. 8, pp. 703710, Aug.1978.

[3] A. G. Phadke and J. S. Thorp, A new computer-based flux-restrainedcurrent-differential relay for power transformer protection,IEEE Trans.Power App. Syst., vol. PAS-102, no. 11, pp. 36243629, Nov. 1983.

[4] L. G. Perez, A. J. Flechsig, J. L. Meador, and Z. Obradoviic, Trainingan artificial neural network to discriminate between magnetizing inrushand internal faults,IEEE Trans. Power Delivery, vol. 9, pp. 434441,Jan. 1994.

[5] A. Wiszniewski and B. Kasztenny, A multi-criteria differential trans-former relay based on fuzzy logic,IEEE Trans. Power Delivery, vol.10, pp. 17861792, Oct. 1995.

[6] T. S. Sidhu and M. S. Sachdev, On-line identification of magnetizing in-rush and internal faults in three-phase transformers,IEEE Trans. PowerDelivery, vol. 7, pp. 18851891, Oct. 1992.

[7] Y. Kukiaki, Power differential method for discrimination between faultand magnetizing inrush current in transformers,IEEE Trans. PowerDelivery, vol. 12, pp. 1109115, July 1997.

[8] M. G. Morante and D. W. Nicoletti, A wavelet-base differentialtransformer protection,IEEE Trans. Power Delivery, vol. 14, pp.13511358, Oct. 1999.

[9] I. Daubechies, S. Mallat, and A. S. Willsky, Eds.,IEEE Trans. Inform.Theory, Special Issue Wavelet Transforms Multires. Signal Anal., Mar.1992, vol. 38.

[10] Y. Meyer, Ed.,Wavelets and Applications. New York: Springer-Verlag,1992.

176 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 1, JANUARY 2003

[11] S. Santoso, E. J. Powers, W. M. Grady, and P. Hofmann, Power qualityassessment via wavelet transform analysis,IEEE Trans. Power De-livery, vol. 11, pp. 924930, Apr. 1996.

[12] S. Santoso, E. J. Powers, and W. M. Grady, Power quality disturbancedata compression using wavelet transform methods,IEEE Trans. PowerDelivery, vol. 12, pp. 12501257, Apr. 1997.

[13] T. B. Littler and D. J. Morrow, Wavelets for the analysis and compres-sion of power system disturbances,IEEE Trans. Power Delivery.

[14] O. Chaari, M. Meunier, and F. Brouaye, Wavelets: A new tool for theresonant grounded power distribution systems relaying,IEEE Trans.Power Delivery, vol. 11, pp. 13011308, July 1996.

[15] P. Pillay and A. Bhattacharjee, Application of wavelets to modelshort-term power system disturbances,IEEE Trans. Power Syst., vol.11, pp. 20312037, Nov. 1996.

[16] W. A. Wilkinson and M. D. Cox, Discrete wavelet analysis of powersystem transients,IEEE Trans. Power Syst., vol. 11, pp. 20382044,Nov. 1996.

[17] F. Jiang, Z. Q. Bo, and M. A. Redfern, A new generator fault detectionscheme using wavelet transform, inProc. 33rd Univ. Power Eng. Conf.,Edinburgh, U.K., Sept. 1998, pp. 360363.

[18] O. A. Youssef, New algorithm to phase selection based on wavelettransforms,IEEE Trans. Power Delivery, submitted for publication.

[19] Electromagnetic Transient Program (EMTP) Rule Book: EPRI EL6421-1, June 1989, vol. 1 and 2.

[20] A. K. Chaudhary, K. S. Tam, and A. G. Phadke, Protection systemrepresentation in the electromagnetic transient program,IEEE Trans.Power Delivery, vol. 9, pp. 701711, Apr. 1994.

Omar A. S. Youssef(M92) was born in Cairo, Egypt in 1945. He received theB.Sc., M.Sc., and Ph.D. degrees in electrical engineering from the University ofCairo, Faculty of Engineering, in 1966, 1976, and 1979, respectively.

Since 1966, he has undertaken lecturing or consulting assignments in Libya,Nigeria, Saudi Arabia, Iraq, and Qatar. In 1999, he was invited to be a VisitingResearch Fellow at University of Bath, Bath, U.K. He is currently the DeputyDean to Graduate Studies and Research, Faculty of Industrial Education, Uni-versity of Suez Canal, Suez, Egypt.

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