Discriminae 87..108

Journal of Engg. Research Vol. 1 - (3) December 2013 pp. 87-108, 2013

Discrimination of power transformer inrush and internal fault current using time to time transform and fault classi®cation using fuzzy clustering *

S. SENDILKUMAR **B. L. MATHUR AND ***MOHAMMED IMRAN

*

Dept of EEE,Panimalar Engineering College, [email protected], Chennai- 602103 ** Dept of Electrical Engineering, Jodhpur Institute of Technology, Jodhpur-342002 *** R&D Engineer,Nokia Solutions & Networks(NSN), Bangalore-560066.

ABSTRACT A new approach is attempted for the dierential protection of power transformer using advanced signal processing such as time to time transform along with Fuzzy clustering technique. The time-time representation is derived from inverse Fourier transform of Stransform, a method of representation of real time series as a set of complex, time local spectra. Here, TT-transform used to generate time-time TT contour from the samples of dierential current. Parseval's theorem extracts the features like energy and standard deviations. Later these features are used as inputs to the Fuzzy clustering to distinguish inrush current, external fault current and internal fault current. Simulation of the fault (with and without noise) was done using MATLAB/SIMULINK software taking 2 cycles of data from each 400 samples. The advantage of the proposed algorithm provides accurate results even in the presence of noise inputs (energy and standard deviations).

Keywords:

Inrush current; internal fault current; parseval's theorem; fault classi®cation; TT-transform; fuzzy clustering and wavelet transform.

INTRODUCTION Power transformers are essential and important equipment in the power system. Due to their size and variety, the protection approaches of power transformer dier, depending on the situation. For large transformer, dierential protection based on the circulating current principle is usually adopted. However, simple dierential protection is not sucient, because certain transient events such as magnetizing inrush currents cause the mal-operation of the dierential relay. Magnetizing inrush currents occur on the primary side of the transformer while switching it on. These inrush currents are of high magnitude but they will last only for a very few cycles. Therefore such inrush current will not damage the transformer. Thus, the processing of the dierential current is essential to discriminate the inrush current from internal faults.

88

S. Sendilkumar B. L. Mathur and Mohammed Imran

General discrimination methods Harmonic restrain techniques were used which discriminates inrush current from internal fault current using second harmonic component (Rahman & Jeyasurya, 1988). Sometimes, power transformer internal faults generate second harmonic component due to current transformer (CT) saturation or presence of a shunt capacitor or the distributive capacitance in a long extra high voltage transmission line to which the transformer may be connected (Sidhu et al., 1992; Bastard et al., 1995). In some situations inrush current has dominant second harmonic component to internal faults. However, with improved transformer design, this second harmonic component reduced more and complex to discriminate using harmonic restraint techniques (Liu et al., 1992). Later Arti®cial Neural Network and Fuzzy logic techniques were applied for power transformer protection.

Using soft computing techniques (Geethangali et al., 2008 & Coury et al., 2005) have used dierential current harmonics which have input to train neural network, require the large training set, and the large training time. In another approach, Fuzzy logic technique has been proposed. (Wiszniewski, 1995 & Shin et al., 2003) have used Fuzzy logic technique. The use of Fuzzy logic may not be the best choice as it lacks ¯exibility and hence suers from the hard threshold, and can hardly be adapted to the new functionalities added to the power system. In addition, much eort is needed to establish the inference rules to be used for decision making. Hence it requires modern signal processing techniques like Wavelet transform, HStransform and TT-transform.

Using signal processing techniques (Mao et al., 2000; Megahed et al., 2008; Sedighi et al., 2005; Youssef, 2003) have used discrete wavelet transform for dierential protection. In another approach, (Saleh & Rahman 2005) have used Wavelet packet algorithm they extracted the existence of the high frequency components to discriminate between faults and non-faults and results are compared for various mother wavelets. (Zabardast et al., 2008) have used maximum values of the wavelet coecients for decision making. For distinguishing the inrush current and fault current it is necessary to extract the features of dierential current. (Mao et al., 2001; Sudha et al., 2007) have extracted the features using the wavelet transform and neural network. (Monsef & Lot®fard, 2007) have used the wavelet transform for feature extraction and the Adaptive Neuro Fuzzy Inference System (ANFIS) for fault

Discrimination of power transformer inrush and internal fault current using time to time transform....

89

classi®cation. (Jazebi1 et al., 2009) have classi®ed faults using Gaussian mixture models and the wavelet transform. From the above speci®ed literature it is under stood that dierent authors have used the variations of the detailed coecients of the wavelet transform to distinguish magnetizing inrush and fault current. The wavelet transform speci®cally decomposes signals from high to low frequency bands through iterative procedure, which performs well for high frequency transients but not so well for low frequency transients that exit in the magnetizing inrush and fault currents. For this, appropriate mother wavelets have to be chosen. This task is very dicult as it increases the decomposition levels leading to a computational burden. Therefore, a suitable signal processing technique has been found to recognize the current signal patterns from a transformer. The main purpose of this paper is to bring the recent advances of using TT-transform to the application of dierential protection for distinguishing inrush currents and internal fault currents. TT-transform (Pinnegar & Mansinha, 2003) is an inverse Fourier transform of S-transform, it points to the possibility of ®ltering and signal to noise ratio improvement in the time domain. (Samantaray et al., 2008; Suja & Jovitha Jerome, 2010 & Biswal et al., 2009) have used the TT-transform for high impedance fault detection, power quality disturbances analysis and power signal classi®cation. Discriminate inrush and internal fault current of a transformer using the TTtransform along with Fuzzy clustering is presented in this paper. The simulated transients of inrush currents and internal fault currents are sampled for two power frequency cycles, yielding 800 samples. These samples processed to the TT-transform, which produces the TT-contour and TT-matrix. Features like energy and STD are calculated from the TT-contours, using Parseval's theorem. These extracted features processed to the Fuzzy clustering for distinguishing inrush current and internal fault currents. Simulation results analyzed through the two dierent relay algorithms such as TT-transform and wavelet transform to ensure the feasibility of the proposed algorithm.

This paper organized as follows . Mathematical background of the TT-transform is given in section transient analysis of the TT-transform. . In section use of Parseval's theorem, procedure for feature extraction and frequency contours are discussed. . System parameters for the simulink model and steps for relay algorithm are described in sections system studied and relay algorithm.

90


. Simulation results by TT-transform and Wavelet transform are given separately. . Data collection using TT-transform and Classi®cation using Fuzzy clustering followed by conclusion are discussed at the end of the paper

TRANSIENT ANALYSIS BASED ON TT-TRANSFORM The Short Time Fourier Transform (STFT) has the disadvantage of the ®xed width and height. This results in misinterpretation of signal components with periods longer than the window width. The ®nite width limits the time resolutions of high frequency signal components. Unlike STFT, the S-transform has a window whose height and width vary with frequency. The expression for the S-transform is scaled, its midpoint is = t. At any t and , the S-transform may be considered only the portion of primary function lying within a few wavelengths on either side of - t. The scaled contraction of w causes the relevant range of to become more strongly localized around t as f increases S may be expressed alternatively as The S-transform of a time series h (t) is de®ned as given in (Stockwell et al., 1996)

Z1 St; f

h wt ÿ ; exp2if d

1

ÿ1

Also it can be expressed through convolution sum as

Z1 H fW exp2itd

St; f

2

ÿ1

where W and H are Fourier transform of w and h respectively and the convolution variable has the same units as f Taking inverse Fourier transform of Equation (1) results

Z1 St; f exp2if df

h wt ÿ

3

ÿ1

For all values of `t' are considered the windowed function becomes a two dimensional function and is expressed as


91

Z1 STT t; f

St; f exp2if df

4

ÿ1

S (t, f) is the time-time distribution of STT (t,f). Similarly, another time-time distribution that can be obtained from the inverse Fourier transform of Stransform is given as follows where the S-transform (t, f) is de®ned as

Z1

St; f

H f exp ÿ1

22 2 exp2itd f2

5

Z1 St; f exp2if df

TTt;

6

ÿ1

The discrete TT-transform is obtained from the discrete form Equation (4) as TTjT; kT

nÿN=

h

n i 2ink exp S jT; NT NT 2

NX =2ÿ1

7

USE OF PARSEVAL'S THEOREM The Parseval's theorem states that energy of the signal i(t) remains the same, whether it is calculated in the signal domain (time) or in the transform domain (frequency). The Parseval's theorem mathematically expressed as ESignal

1 T

ZT

jitj 0

2

dt

N X

jinj

2

8

n0

where T and N are the time period and the length of the signal respectively, and i(n) 2 is the Fourier Transform of the signal. Using the Equation (8) in TTtransform the energy content of the signal is computed through TT-matrix and the corresponding STD is obtained to inrush currents, internal faults and external faults. (Gargoom et al., 2008). The feature extraction of the energy and STD of the TT-transform are derived by Energy a TT ÿ matrix a^2 TT-matrix a = TT-matrix of phase a and STD a = STD (abs (TT-matrix a))

9

(10)

92


STD a= standard deviation from the TT-matrix values for phase A, abs = absolute values from the TT-matrix

SYSTEM STUDIED In order to investigate the applicability of the proposed algorithm, a detailed simulation study has been carried on the power system model shown in the Figure 1. The system parameters are given in Table 1. The simulation model has been developed using SIMULINK software modules. The speci®cation for the load is 100 MW and 80 MVAR.

Table .1. System parameters Generator

500MVA, 50Hz, star connected with the solidly grounded neutral. X/R=50

Transformer Primary: 500kV, star connected with the grounded neutral Secondary: 230kV delta connected, Rpu = 0.0078, Xpu = 0.259 Sampling rate 20 kHz, i.e 400 samples per power cycle.

Fig. 1. Power system model

RELAYING ALGORITHM FOR TT-TRANSFORM Application of the TT-transform for the proposed scheme is given in Figure 1 and the steps followed as:


Step.1 Step.2 Step.3 Step.4 Step.5

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Obtain the samples i(t), the dierential current from the simulink model. Compute the TT-transform from inverse Fourier transform of Stransform. Compute the energy matrix and STD for all the values of TT-matrix using Parseval's theorem. Average the values to get energy vector. Relay operation is based on setting threshold value to relay. If energy vector is greater than the threshold value, the relay issues trip signal else it is retrained.

Table 2. Energy and Standard deviation for power transformer using TT-transform

Inrush/ Fault

WITHOUT NOISE Energy STD

WITHOUT LOAD WITH NOISE WITH NOISE WITHOUT (SNR= 0.5DB) (SNR=20DB) NOISE Energy STD Energy STD Energy STD

WITH LOAD WITH NOISE WITH NOISE (SNR= 0.5DB) (SNR=20DB) Energy STD Energy STD

Normal

0.00005292

0.0032

0.1053

0.0234

0.0029

0.0324

0.2317

0.2096

0.1255

0.0245

0.2355

0.2116

Inrush a

0.00005

0.0031

0.2508

0.3175

0.0034

0.351

0.2300

0.2081

0.3091

0.3126

0.2338

0.2108

Inrush b

0.000049

0.0031

0.1255

0.2186

0.0032

0.0339

0.2300

0.2089

0.3590

0.3350

0.2320

0.2139

Inrush c

0.000049

0.0031

0.2238

0.2914

0.0033

0.0350

0.2300

0.2089

0.4504

0.3729

0.2346

0.2155

Internal faults Fault a-g

2.0802

0.6987

2.1893

0.7336

2.0837

0.6974

1.7957

0.7127

2.2303

0.7401

1.7974

0,7139

Fault b-g

1.8825

0.6070

2.0866

0.7232

1.8844

0.6071

1.5219

0.5851

1.9800

0.6483

1.5244

0.5877

Fault c-g

1.8078

0.6128

1.9428

0.6664

1.8026

0.6120

1.3672

0.5378

1.9202

0.6667

1.3656

0.5385

Fault ab-g(a)

3.3873

0.866

3.5504

0.9189

3.3984

0.8669

3.3084

0.9011

3.5504

0.9189

3.3073

0.8986

Fault ab-g(b)

1.7964

0.5823

1.8934

0.6170

1.7962

0.5858

2.0506

0.6816

1.8934

0.6170

2.0400

0.6813

Fault bc-g(b)

3.0144

0.7596

3.1162

0.7935

3.0243

0.7612

2.8345

0.7540

3.1470

0.7947

2.8415

0.7560

Fault bc-g(c)

1.9655

0.6731

2.0202

0.7068

1.9577

0.6766

1.8202

0.6019

2.0834

0.7215

1.8220

0.6003

Fault ac-g(a)

2.0516

0.6931

2.2029

0.7464

2.0633

0.6939

2.2981

0.7791

2.1900

0.7288

2.3000

2.8550

Fault ac-g(c)

3.2555

0.8638

3.3081

0.8923

3.2564

0.8661

2.8534

0.7795

3.4224

0.9004

0.7818

0.7894

Fault abc-g(a)

3.3873

0.8665

3.5031

0.8939

3.4007

0.8696

3.6549

0.9504

3.5041

0.8982

3.6606

0.9507

Fault abc-g(b)

3.0144

0.7596

3.2062

0.8065

3.0184

0.7959

3.2069

0.8179

3.1535

0.7942

3.2250

0.8195

Fault abc-g(c)

3.2555

0.8638

3.4025

0.9099

3.2511

0.8654

3.0805

0.7927

3.3345

0.9047

3.0899

0.7966

External faults Fault a-g

0.0659

0.1454

0.0911

0.1798

0.0034

0.0352

0.2316

0.2096

0.1684

0.2437

0.2314

0.2137

Fault b-g

0.0137

0.1580

0.0967

0.1900

0.0032

0.0350

0.2318

0.2097

0.1638

0.2387

0.2357

0.2162

Fault c-g

0.00022

0.0104

0.2128

0.2783

0.0032

0.0346

0.2317

0.2096

0.1302

0.2161

0.2378

0.2162

Fault abc-g(a)

0.0002

0.2331

0.1073

0.2046

0.0036

0.0356

0.2316

0.2096

0.2073

0.2570

0.2300

0.2112

Fault abc-g(b)

0.0041

0.9529

0.0965

0.1897

0.0035

0.0346

0.2118

0.2097

0.1650

0.2261

0.2321

0.2132

Fault abc-g(c)

0.0043

0.9700

0.0940

0.1869

0.0037

0.0370

0.2317

0.2096

0.0977

0.1919

0.2359

0.2157

94


SIMULATION RESULTS USING THE TT-TRANSFORM The proposed simulation model given in the Figure 1 has been studied using the star to delta winding con®guration, and dierent cases such as inrush current, single line to ground fault, double line to ground fault, three phase fault and external faults are studied, with and without load. Noise of two dierent ratios such as SNR 5db and 20db are considered for both with and without load. Data given in the Table 2 is obtained from primary side of inrush current and internal fault current and Table 3 is obtained for secondary side fault current. In this paper using TT-transform following cases are presented 1) Magnetizing inrush current without load, 2) Single line to ground fault without load, 3) External single line to ground fault without load for SNR 20db 4) Magnetizing inrush current without load for SNR 5db

Case.1 Magnetizing inrush current without load

Fig.2a. Dierential current of phase A

Fig.2b. Exploded view of the ®rst two cycles of dierential current of Fig. 2(a)


95

Fig.2c. TT-contours Fig.2. Inrush current for an unloaded transformer Inrush current for phase A has been given in Figure 2. Figure 2a shows the inrush current of 5000 samples, with a simulation time of 0.25 sec for sampling frequency of 20 kHz. Figure 2b shows 400 samples yielding two cycles. Figure 2c Show the inverse of the frequency contours in which the contours are interrupted and present only for the ¯ow of inrush current. The energy and STD extracted from the inrush current are given in Table 2. The energy value computed for inrush current using TT-transform is found lesser than the threshold value, relay issues the restrain signal.

Case. 2 Single line to ground fault without load

Fig.3a. Dierential current of phase A

96



Fig.3c. TT-contours of phase A

Fig.3d. Trip signal of phase A- fault inception at time (a) and trip signal issued at time (b) Fig. 3. Single line to ground fault for an unloaded transformer Figure. 3 shows the single line to ground fault for phase A. After processing the fault current samples to TT-transform, the TT-contours are generated. The


97

energy and STD calculated for samples using the TT-matrix are given in the Table 2. Figure.3. (c) show the contours are regular throughout the time series, and there are no interruptions in the contours unlike in the inrush currents. A suitable threshold value is ®xed by energy values and trip signal is issued based on the energy values calculated from the TT-matrix, which consists of 800 rows and 400 columns.

Case. 3 Single line to ground fault for without load

Fig.4a. Dierential current of Phase A


98


Fig.4c. TT-contours of phase A Fig. 4. External single line to ground fault for an unloaded transformer Figure 4 shows the single line to ground fault with noise for phase A. The external fault is generated on the source side as well as on load side, and the dierential current iad is extracted at the relay point and SNR 20db added for the fault current samples of each phase then processed to TT-transform, which generate the TT-contours and the TT-matrix. Energy and STD is computed using TT-contours, will issue the restrain signal.

Case 4. Magnetizing inrush current without load for SNR 5 db

Fig.5a. Dierential current of Phase A


99


Fig.5c. TT-contours of phase A Fig.5 Inrush current for an unloaded transformer Figure. 5 shows the inrush current for unloaded transformer for phase A. Signals of Figure 5a and 5b are obtained from simulink model using Figure. 1. Figure 5c is the TT contour of the TT-matrix is obtained by polluting the signals using SNR 5db. The energy and STD calculated from the TT-contours; will issue the restrain signal.

SIMULATION RESULTS USING THE WAVELET TRANSFORM In this paper, using wavelet transform following cases are studied. 1.

Inrush current for the unloaded transformer for phase A

2.

Single line to ground fault for unloaded transformer

100


Case.1 Inrush current for the unloaded transformer

Fig.6a. Dierential current for inrush current for phase A

Fig.6b. Exploded view of the ®rst two cycles of dierential current of Fig.6. (a)

X- axis--Time (s), Y- axis--Amplitude (Hz)

Fig.6c. Amplitude of wavelet coecients for phase A Fig.6. Inrush current for the unloaded transformer for phase A


101

Figure 6 shows the inrush current for phase A. The dierential current signal of Iad for phase A generated on the source side is processed to the wavelet transform. Figure 6c shows the wavelet coecients have wide shapes and the relay restrains for the computed energy value, since the energy value is lesser than the threshold value.

Case.2 Single line to ground for unloaded transformer

Fig.7a. Dierential current for phase A

Fig.7b. Exploded view of the ®rst two cycles of the dierential current of Fig.(7)a

102


X- axis-Time (s), Y- axis-Amplitude (Hz) Fig.7c. Wavelet coecients for phase A Fig.7d. Trip signal of phase A

Fig.7. Single line to ground fault for an unloaded transformer Figure 7 shows the single line to ground fault for phase A. Two cycles of fault currents for 800 samples are processed to the wavelet transform. The original signal is divided into dierent scales of resolution, and the energy computed from each resolution of phase A is ED1+ED2+ ED3+ ED4+ED5. This computed energy value is compared with the threshold value; relay issues trip signal. Wavelet transform use the DB9 mother wavelet function that produce


103

series of wavelet coecients that translate and dilate to dierent frequencies unlike TT-transform. Frequency contours generated by TT-transform are inrush current and fault currents that are suitable for classi®cation by simple visual inception, but in wavelet transform, it is not possible. In this paper, simulation results of only two cases are given the other cases are expected to be similar to those using wavelet transform.

Table 3. Energy and Standard deviation for Power transformer using TT-transform

Without Noise Secondary Fault Energy STD Fault a-g

0.4273

0.3650

Fault b-g

0.5273

With Load With Noise SNR 20db With Noise SNR 5db Energy STD Energy STD 0.4372

0.3718

0.7137

0.4235

0.4281

0.5322

0.4297

0.7158

0.4218

Fault c-g

0.2973

0.2468

0.2934

0.2473

1.2061

0.5332

Fault abc-g(a)

2.1748

0.7616

2.1754

0.7635

2.2694

0.7859

Fault abc-g(b)

1.9076

0.6639

1.9006

0.6638

2.0646

0.7052

Fault abc-g(c)

1.7016

0.5830

1.7042

0.5834

1.8344

0.6458

DATA COLLECTION USING THE TT-TRANSFORM Dierential current samples for dierent operating conditions, obtained from two cycles of power frequency, are given as inputs to the TT-transform. The energy and STD calculated from the TT-contours using Parseval's theorem. These energy and STD values are tabulated in Table 2 and 3 Figure 8 shows the procedure for feature extraction and fault classi®cation.

Iad Ibd Icd

Feature extraction using TTtransform

Fault classification using Fuzzy clustering

Fig. 8. Feature extraction using TT-transform The features extracted from the TT-transform are the energy and STD of the TT-contour respectively, for two cycles of the fault current after the fault inception. Features processed to Fuzzy clustering for fault classi®cation. The TT-contours provide the frequency localization of the time- time series in the

104


time--time distribution. The TT-transform provides better time local properties of the time series, and thus helps in localizing the frequency components of the time series. Thus, the frequency information can be extracted from the TTcontours.

POWER TRANSFORMER FAULT CLASSIFICATION USING FUZZY CLUSTERING The purpose of the clustering to identify natural grouping of data from the large data set to produce a concise representation of systems behavior (B.Biswal et al., 2009).

Step.1 Step.2 Step.3 Step.4

Find cluster opens GUI to implement Fuzzy clustering. Data processed to GUI are obtained from Tables 2 and 3. The data obtained are a pair of energy and standard deviation values. Energy values are loaded in X axis and standard deviation values are loaded in Y-axis which include both data of with and without load. Fuzzy clustering starts with an initial guess for the clusters, which is intended to mark the mean location of each cluster. The initial guess for these cluster centers may be generally incorrect. Next, Fuzzy clustering assigns every data point a membership grade for each cluster. By iteratively updating the cluster centers and the member ship grades for each data point Fuzzy clustering iteratively moves the cluster centers to the correct location within a dataset, GUI performs clustering operation thereby classi®cation of inrush, and internal fault current is done by clusters.

Data of energy and standard deviation taken from Tables 2 and 3 are given as inputs to Fuzzy clustering. The output for Fuzzy clustering is shown in Figure 9. It clearly indicates that how all the three events namely inrush currents, internal fault currents and external fault currents are discriminated from each other. After calculating energy and standard deviation for inrush current, external fault current and internal fault current, thereby, classi®cation of inrush and internal fault current is done by clustering technique using Fuzzy logic tool box.


105

Fig.9. Fuzzy clustering to discriminate inrush and internal fault

CONCLUSIONS In the TT-transform, a new view of localizing the time features of a time series around a particular point on the time axis has been investigated. It diers from the windowed time series of S-transform that the degree of localization of the signal components is frequency-dependent rather than frequency invariant. Compared with the wavelet transform, the TT-transform provides better time local properties of time series and thus helps in localizing the frequency components of the time series. Using, time-time distributions dierent operating conditions are extracted using TT-transforms, which generate TT-contour. Dierent features like energy and standard deviations computed are processed to Fuzzy clustering to distinguish inrush and fault current.

REFERENCES

Bastard, P., Meunier, M., & Regal, H. 1995.

Neural Network-Based Algorithm For Power Transformer Dierential Relays. IET Generation Transmission & Distribution 142(4):386-392.

Biswal, B., Dash, P.K., & Panigrahi, B.K. 2009.

Non-Stationary Power Signal Processing For Pattern Recognition Using HS-Transform. Applied Soft Computing 9 (1): 107-111.

Biswal, B., Dash, P.K., Biswal, M.K. & Rao, M.V.N. 2009. TT-ACO Based Power Signal Classi®er. Proceedings of Nature & Biologically Inspired Computing 2009,1195-1200.

Coury, D.V. & Segatto, E.C. 2005. An Alternative Approach Using Arti®cial Neural Networks For Power Transformer Protection. European Transaction on Electrical Power 16(1):63-67.

106


Gargoom, A.M., Ertugrul, N. & Soong, W.L 2008. Automatic Classi®cation and Characterization of Power Quality Events. IEEE Transaction on Power Delivery 23(4):2417-2425. Geethanjali, M., Slochanal, S.M.R. & Bhavani, R. 2008. PSO Trained ANN-Based Dierential Protection Scheme For Power Transformers. Neurocomputing 71(4-6):904-918. Jazebi, S., Vahidi, B., Hosseinian, S.H. & Fai Z,J. 2009. Magnetizing Inrush Current Identi®cation

Using Wavelet Based Gaussian Mixture Models. Simulation Modelling Practice and Theory 17(6): 991-1010.

Liu, P., Malik, O.P., Chen, C., Hope, G.S. & Guo, Y. 1992. Improved Operation Of Dierential Protection Of Power Transformers For Internal Faults. IEEE.Transaction on Power Delivery 7(4):1912-1919.

Mao, P.L. & Aggarwal, R.K. 2000. A Wavelet Transform Based Decision Making Logic Method For Discrimination Between Internal Faults And Inrush Currents In Power Transformers. Electric Power System Research 22 (6):389-395.

Mao, P.L. & Aggarwal, R.K. 2001. A Novel Approach To The Classi®cation Of The Transient Phenomena In Power Transformers Using Combined Wavelet Transform And Neural Network. IEEE.Transaction on Power Delivery 16(4):654-660.

Megahed, A. I. Ramadan, A. & Mahdy, W. E. L. 2008. Power Transformer Dierential Relay Using Wavelet Transform Energies. Proceedings of the Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century,1-6.

Monsef, H. & Lot®fard, S. 2007.

Internal Fault Current Identi®cation Based On Wavelet Transform In Power Transformers. Electric Power System Research 77(12):1637-1645.

Pinnegar, C.R. & Mansinha.L. 2003. A Method Of Time -- Time Analysis: TT-Transform.Digital Signal Processing 13(4): 588-603. Rahman, M.A. & Jeyasurya, B.1988. A State-Of-The-Art Review Of Transformer Protection Algorithms. IEEE.Transaction on Power Delivery 3(2):534-544. Saleh, A. & Rahman, M.A. 2005. Modeling And Protection Of A Three Phase Power Transformer Using Wavelet Packet Transform. IEEE.Transaction on Power Delivery 20 (2):1273-1282. Samantaray, S.R., Panigrahi, B.K. & Dash, P.K. 2008. High Impedance Fault Detection In Power

Distribution Networks Using Time-Frequency Transform And Probabilistic Neural Network. IET Generation Transmission & Distribution 2(2):261-270.

Samantaray, S.R., Panigrahi, B.K., Dash, P.K. & Panda, G. 2007. Power Transformer Protection

Using S-Transform With Complex Window And Pattern Recognition Approach. IET Generation Transmission & Distribution 1(1):278-286.

Sedighi, A.R. & Haghifam, M.R. 2005. Detection Of Inrush Current In Distribution Transformer Using Wavelet Transform. International Journal Power & Energy System, 27 (5-6):361-370. Shin, M.C., Park, C.W., & Kim, J.H. 2003. Fuzzy logic-based relaying for large power transformer protection. IEEE.Transaction on Power Delivery 18(3): 713-718. Sidhu, T.S. Sachdev, M.S., Wood, H.C., & Nagpal, M. 1992. Design Implementation And Testing

Of A Micro-Processor-Based High-Speed Relay For Detecting Transformer Winding Faults. IEEE.Transaction on Power Delivery 7(1): 108-117.

Stockwell, R.G., Mansinha, L., & Lowe, R.P. 1996. Localization Of The Complex Spectrum: STransform. IEEE Transaction of Signal Processing 44(4):998-1001. Sudha, S. & Jeyakmar, A.E.2007. Wavelet And ANN Based Relaying For Power Transformer Protection. Journal of Computer Science 3eq6 : 454 ÿ 460 Suja. S. & Jerome. Jovitha. 2009. Pattern Recognition Of Power Signal Disturbances Using STransform And TT-Transform. Electric Power and Energy System 32(1):37-.53 Wiszniewski, A. & Kasztenny, B. 1995. A Multi-Criteria Dierential Transformer Relay Based On Fuzzy Logic. IEEE.Transaction on Power Delivery 10 (4):1786-1792. ;

:


107

Youssef, O.A.S. 2003.

A Wavelet-Based Technique For Discrimination Between Faults And Magnetizing Inrush Currents In Transformers. IEEE Transaction on Power Delivery, 18(1): 170 -176.

Zabardast, A., Feyzi, M. R. & Mehraein, A. 2008. Distinction Between Inrush Current Of Power Transformer And Fault Currents In Dierential Protection Using Wavelet Transformer, Proceedings of the Electrical Utility Deregulation and Restructuring and Power,1-6.

Submitted : 13/ March/2012 Revised : 13/ Oct/2012 Accepted : 17/Feb/2013

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