A Discrete

IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERINGIEEJ Trans 2014; 9: 302314Published online in Wiley Online Library (wileyonlinelibrary.com). DOI:10.1002/tee.21971

Paper

A Discrete Wavelet Transform Approach to Discriminating among InrushCurrent, External Fault, and Internal Fault in Power Transformer using

Low-Frequency Components Differential Current Only

Atthapol Ngaopitakkula, Non-memberChaiyan Jettanasen, Non-member

This paper proposes an algorithm based on discrete wavelet transform (DWT) for discriminating among inrush current,internal fault, and external fault in power transformers. Fault conditions are simulated using the Alternative TransientsProgram/Electromagnetic Transients Program (ATP/EMTP). Daubechies4 (db4) is employed as the mother wavelet to decomposelow-frequency components from fault signals. The ratio between per unit (p.u.) differential current and p.u. time is suggested asan index. The numerator of the ratio is the difference between the maximum differential current and the minimum differentialcurrent in terms of p.u. with a base value selected at the transformer-rated current. The ratio is calculated for all three phases,and from a trial and error process the indices for the separation among the internal fault condition, the external fault condition,and inrush condition are defined. The results obtained from the proposed technique show good accuracy for discriminating faultsin the considered system. In addition, the proposed algorithm uses data of the differential current with a time of quarter cycleunder the analysis. 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Keywords: interturn fault, power transformer, discrete wavelet transforms, inrush current

Received 15 January 2013 Revised 20 June 2013

1. Introduction

A reliable supply of electric power is essential, and a failureof any part of the installed equipment is expensive not onlyfor utilities but also for the manufacturing industry. A powerutility may lose revenues and incur penalties for nondelivery,while the failure of an industrial transformer, for example, maylead to lengthy and therefore costly downtime. The differentialrelaying principle is used for the protection of medium andlarge power transformers. In the literature for fault detection,several decision algorithms [142] have been developed to beemployed in the protective relay for preventing maloperationof the protective equipment under different nonfault conditions,including magnetizing inrush current, ratio mismatch, through-fault current, etc. There are many techniques [142] for detectingfaults, such as artificial neural networks (ANNs) [12,30,39,40],transient-based protection [13,1820], finite element [14], fuzzylogic [35], hybrid systems [14,32], and so on. An algorithm forprotecting a transformer with three windings using the incrementsof flux linkages (IFLs) has been proposed by Kang et al . [2]. Ninedetectors and a rule are suggested for fault detection, the faultedphase, and winding identification. Mathematical morphology hasbeen proposed to identify the inrush current [3]. It is able todiscriminate between inrush and internal fault currents even inthe case of an inrush with a low second-harmonic component andan internal fault current with a high second-harmonic component.A novel technique to distinguish the inrush currents from internalfaults in a power transformer is proposed by Ma et al . [4] usingthe normalized grille curve (NGC). NGC is an effective tool fortransient signal analysis. The NGC calculation method is first

a Correspondence to: Atthapol Ngaopitakkul. E-mail:[email protected]

Faculty of Engineering, King Mongkuts Institute of Technology Ladkra-bang, Bangkok 10520, Thailand

derived. Then, the criteria to extract features of the inrush currentand the internal fault in the respective time and frequency domainsare developed in detail. This technique is able to identify inrushcurrents rapidly and can be implemented with only a small amountof computation. A method for distinguishing the fault-originatedtransients from the switching transients has been developed [6].The decision trees (DTs), hidden Markov models (HMM), andprobabilistic neural network (PNN) techniques were compared, andthe PNN classifier gave the best classification results. In Ref. [7],an index is proposed to discriminate external faults, incipientfaults, inrush currents, and internal faults by using the hyperbolicS-transform-based method. This method has two steps; in the firststep, external faults are discriminated from other disturbances. Ifan internal disturbance is detected, then the absolute deviationof the S-transform matrix values will be applied. In Ref. [30],a support vector machine (SVM) classification technique for thedetection of minor internal turn-to-turn faults was presented. Thediscrimination between internal turn-to-turn fault, external fault,and the inrush condition can be made within one-half cyclefrom the fault inception time using this technique. Accordingto this technique, one-half-cycle post-fault current samples arethe inputs for the SVM classifier. In Ref. [37], an online sweepfrequency-response analysis (SFRA) was developed to detectwinding interturn faults of power transformers in service usingthe transfer function method.

The idea of application of wavelet transform to fault diagnosis isnot new, and there are a number of research papers related to thisidea [1127]. In Ref. [12], the development and hardware imple-mentation of the wavelet transform and HMM-based classifiers todistinguish between the transients originating from faults and fromother types of transients was presented. The transient recognitionscheme uses wavelet transforms for the extraction of features, andthe HMM is used for the classification. In Ref. [13], the transientsignal analysis with discrete wavelet transform (DWT) was used

2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

DISCRIMINATING AMONG INRUSH CURRENT, EXTERNAL FAULT, AND INTERNAL FAULT IN POWER TRANSFORMERS

to identify and correctly differentiate inrush current from incip-ient internal faults. The decision algorithm is based on a ratioindex quantified in a certain window of analysis. The ratio indexis defined as the relation between the maximum coefficient fromthe first detail of the DWT decomposition and the spectral energyof the other frequency components present in the same detail.In addition, different mother wavelets were compared, and theDaubechies wavelet was found to give excellent performance andhigh efficiency in the discrimination of simulated disturbances. Animplementation of d q axis components and wavelet packet trans-form (WPT) based hybrid technique was introduced by Aktaibiet al . [2527]. This technique is based on extracting the high-frequency subband contents present in the d q axis componentsof the differential currents. It requires only one level of WPT forthe synchronously rotating reference frame (d q axis) componentsof the differential current to accurately discriminate inrush currentsfrom all types of the internal fault currents. In previous researchworks [20], the low-frequency component obtained from DWT ofdifferential current is analyzed. The proposed decision algorithmgave more satisfactory results for the separation between inter-nal fault and external fault, but the case studies were made witha power transformer that was connected with Y-Y configuration.In fact, power transformers connected with -Y are more widelyemployed than those connected with Y-Y in power systems, so thedecision algorithm should be proved to discriminate in both -Yand Y-Y connections.

Therefore, in this paper we develop a decision algorithm fordetecting and discriminating between inrush current, internal fault,and external fault for a power transformer. The decision algo-rithm is based on DWT as an alternative to or improvementupon the existing protective relaying functions. The simulationsand analyses are performed using the Alternative Transients Pro-gram/Electromagnetic Transients Program (ATP/EMTP) and MAT-LAB. ATP/EMTP is a universal program for digital simulation oftransient phenomena of electromagnetic as well as electromechan-ical nature, thus ATP/EMTP is probably the most widely usedpower system transients program in the world today. The schemeunder investigations is a part of Thailands electricity transmissionand distribution system. In addition, the transformer model withstray capacitances is used.

2. Theory

2.1. Differential protection The differential principle,as applied for protecting power transformers, can be describedwith the help of Fig. 1. The levels of currents in the primaryand secondary sides of the power transformer are reduced by thecurrent transformers (CTs). The outputs of these CTs are compared.The ratios of the primary and secondary CTs are selected suchthat the CTs produce the same secondary current for nominal linecurrent.

The operating coil of the relay is connected to the secondarywindings of the two CTs in such a way that the net current flowingthrough it is equal to the difference between the secondary currentsof CTs provided on the two sides of the power transformer. Thenet current through the operating coil of differential relay is zerofor normal operation and external faults. An internal fault in thepower transformer breaks this balance and causes a current to flowin the relays operating coil. This is shown in Fig. 1(b).

2.2. Wavelet transforms A wavelet is a small, localizedwave of a particular shape and finite duration that has an averagevalue of zero. The wavelet transform is a tool that splits up data,functions, or operators into different frequency components, andthen studies each component with a resolution adjusted to itsscale. The advantage of the transform is that the analysis band

Power transformer(a)

(b) Power transformer

Fault

Ioperating coil = 0

Ioperating coil

Fig. 1. Basic differential scheme for the power transformer.(a) Normal condition. (b) Internal fault condition

f(n)HF

HF

HF

HF = High pass filter

fs = 200 kHz

= Low pass filter

HF

2

2 2

2 2

2

2 2

2

2

HFLF

LF

LF

LF

LF

LF

50100 kHz

2550 kHz

12.525 kHz

6.2512.5 kHz

3.1256.25 kHz

03.125 kHz

5

4

3

2

1

Fig. 2. Five-level wavelet decomposition tree

can be finely adjusted so that both the high- and low-frequencycomponents are precisely detected. The results from the wavelettransform are shown in both the time domain and the frequencydomain. The wavelet transform can expand signals by using eithera shift or a translation time as well as a compression in time ora dilation of a fixed wavelet function referred to as the motherwavelet. The wavelet transform that scales the results of theanalysis by a factor of two is called a DWT as expressed in (1).

DWT(m , n) = 12m

k

f (k)

[n k2m

2m

](1)

where [

nk2m2m

]= mother wavelet (In this paper, Daubechies 4

is selected as the mother wavelet).Referring to Fig. 2, the original input signal is split up into

two parts in the first stage (scale 1) by passing the signal froma high-pass and a low-pass filter, which results in two differentversions of the same signal: the portion of the signal correspondingto low-frequency components of the signal to analyze the lowfrequencies is called approximations (low-pass portion), whilethe portion of the signal corresponding to the high-frequencycomponents of the signal to analyze the high frequencies is calleddetails (high-pass portion). The coefficients of approximations anddetails can be calculated by iterating or cascading the single-stagefilter bank to obtain a multiple-stage filter bank. The coefficientsof approximations contain most of the information content ofthe original input signal or the general trend. The coefficient of

303 IEEJ Trans 9: 302314 (2014)

A. NGAOPITAKKUL AND C. JETTANASEN

details contains its local variations or the difference between thetrue input and the value of the reconstructed input if it has tobe reconstructed from only the information given in the low-pass output. After passing these data through the filter functions,the output of the low-pass filter (coefficients of approximations)consists of the average of every two samples, and the output ofthe high-pass filter (coefficient of details) consists of the differenceof every two samples. The high-pass filter obviously contains lessinformation than the low-pass output. If the signal is reconstructedby an inverse low-pass filter of the form, then the result is aduplication of each entry from the low-pass filter output.

For other stages (scale 2, . . . , scale 5), the filters of eachstage have different cut-off frequencies and bandwidths, while theprocessed signal is still unchanged. The frequency bandwidth ofthe band decreases with growing level scale, which means thatthe frequency resolution becomes higher by increasing the levelscale. However, the higher the scale, the longer is the processingtime of the signal. The increase in processing time is a problemwhen the scale is high. In general, higher order wavelets tend toput more information into the low-pass output, and vice versa. Ifthe average amplitude of the high-pass output is low enough, thenthe high-pass half of the signal may be discarded without greatlyaffecting the quality of the reconstructed signal.

3. Power System Simulation using EMTP

3.1. Transformer winding models For a computermodel of a two-winding three-phase transformer having primaryand secondary windings in each phase, BCTRAN is a well-known subroutine on ATP/EMTP. To study internal faults of thetransformer, Bastard et al . [43] proposed a modification of theBCTRAN subroutine. Normally, the BCTRAN uses a matrix ofinductances with a size of 6 6 to represent a transformer, butwith the internal fault conditions the matrix is adjusted to be ofsize 7 7 for winding-to-ground faults and of 8 8 for interturnfaults [43]. In the research work of Bastard et al . [43], the modelwas proved to be validated and accurate as shown by a comparisonwith measurement results. However, the effects of high-frequencycomponents that may occur during the faults are not included insuch a model. Islam and Ledwich [44] described the characteristicsof high-frequency responses of a transformer due to various faults.It has been shown that the fault types and fault locations have aninfluence on the frequency responses of the transformer [44]. Asa result, in this paper the combination of the transformer modelsproposed by Bastard et al . [43], as shown in Fig. 3, with the high-frequency model including stray capacitances of the transformerrecommended by IEEE working group [45], as shown in Fig. 4, isused for simulations of internal faults in the transformer windings.

From Fig. 3, for the phase winding of the transformer withinternal faults, the winding is divided into two parts in case ofwinding-to-ground faults and three parts in case of interturn faults.

The process for simulating internal faults based on the BCTRANroutine of EMTP can be summarized as follows:

First step: Compute matrices [R] and [L] of the power trans-former from manufacturers test data [20,31,46] without consider-ing the internal faults [26].

[R] =

R1 . . . 0...

. . ....

0 R6

(2)

[L] =

L1 L12 L16L21 L2 L26...

.... . .

...

L61 L62 L6

(3)

Primary Primary SecondarySecondary

Phase A Phase A

Phase B

Phase C

Phase B

Phase C

a a

b bc2 2

3 34 4

5 56 6

Fig. 3. The modification on ATP/EMTP model [43] for a three-phase transformer with internal faults

115/23 kV50 MVA

Chg

Chl

Clg

Primary Secondary

Fig. 4. A two-winding transformer with the effects of straycapacitances

Second step: Modify (4) and (5) to obtain the new internalwinding fault matrices [R] and [L] as illustrated in (4) and(5) [43].

[R] =

Ra 0 0 0 0 0 0 00 Rb 0 0 0 0 0 00 0 Rc 0 0 0 0 00 0 0 R2 0 0 0 00 0 0 0 R3 0 0 00 0 0 0 0 R4 0 00 0 0 0 0 0 R5 00 0 0 0 0 0 0 R6

(4)

[L] =

La Mab Mac Ma2 Ma3 Ma4 Ma5 Ma6Mba Lb Mbc Mb2 Mb3 Mb4 Mb5 Mb6Mca Mcb Lc Mc2 Mc3 Mc4 Mc5 Mc6M2a M2b M2c L2 M23 M24 M25 M26M3a M3b M3c M32 L3 M34 M35 M36M4a M4b M4c M42 M43 L4 M45 M46M5a M5b M5c M52 M53 M54 L5 M56M6a M6b M6c M62 M63 M64 M65 L6

(5)

Third step: The inter-winding stray capacitances and earth capac-itances of the high-voltage (HV) and low-voltage (LV) windingscan be simulated by adding lumped capacitances connected to theterminals of the transformer, as shown in Fig. 4.

The capacitances shown in Fig. 4 are as follows:Chg = stray capacitance between the high-voltage winding and

groundClg = stray capacitance between the low-voltage winding and

groundChl = stray capacitance between the high-voltage winding and

the low-voltage winding.

304 IEEJ Trans 9: 302314 (2014)


3.2. Simulation case studies In this paper, the com-bination between the transformer models proposed by Bastardet al [43] and the high-frequency model including capacitancesof the transformer recommended by IEEE working group [45] isused for simulations of faults in the transformer windings. Thescheme under investigations is a part of Thailand electricity trans-mission and distribution system as depicted in Fig. 5. A 50-MVA,115/23-kV three-phase two-winding transformer was employed insimulations with all parameters and configuration provided by themanufacturer [20,31,46].

RE

Primary sidecurrent

MK 115/23 kV50 MVA

Load

PEAEGAT

Secondary sidecurrent

R+jX

Fig. 5. System used in simulation studies [21,32,47]

(c)

U 80 20 I v I vLineRL+/0

RL

C

RL

C

RLC

RLC

I

H L115/23

LineRL+/0

Line

20 80RL+/0

LineRL+/0

(d)

RL

C

RL

C

RLC

RLC

H L115/23U I v I v

LineRL+/0

LineRL+/0

(b)

RL

C

RL

CRLC

I

H L115/23

Line

U I I vvRL+/0 RLC

LineRL+/0

(a)

Line

U I I vLine

vRL

RL

C

RL

C

RLC

RLC

H L

I

115/23+/0 RL+/0

Fig. 6. Components of a proposed simulation model implemented in ATP/EMTP. (a) The winding-to-ground fault case. (b) The interturnfault case. (c) The external fault case. (d) The inrush case

305 IEEJ Trans 9: 302314 (2014)


Table I. Number of case studies and parameters for case ofwinding to ground fault

Parameter ofwinding-to-groundfault Detail

Numberof casestudies

Phase in whichfault occurs

Phases A, B, and C 3

Transformerwinding

High voltage and low voltage(primary and secondary)

2

Angles of faultinception

0 330 (each step is 30) andphase A voltage is reference

12

Fault position 1090% (each step is 10%)measured from the line endof the windings as shown inFig. 7(a).

9

Table II. Number of case studies and parameters for case ofinterturn fault

Parameter ofinterturn fault Detail



Phases A, B, and C 3

Transformerwinding

High voltage and low voltage(primary and secondary)

2



12

Fault position ofpoint ZAF

1080% (each step is 10%)measured from the line endof the windings as shown inFig. 7(b).

36

Fault position ofpoint ZINF

1080% (each step is 10%)measured from the line endof the windings as shown inFig. 7(b).

The ATPDraw circuit of the proposed simulation model is shownin Fig. 6; it can be seen that the transformer, which is a step-downtransformer, is connected between two subtransmission sections.The BCTRAN model based on test data can be obtained fromthe transformer manufacturers. Supporting routine of BCTRANScan be used to derive a linear representation for three-phasetransformer, using test data of both the excitation test and theshort-circuit test. The magnetizing branch is represented by ahysteretic nonlinear inductor model generated by the HYSDATsupporting routine of ATP. To implement or study the transformermodel, simulations were performed with various changes in systemparameters, as shown in Tables I IV.

The primary and secondary current waveforms can then besimulated using ATP/EMTP, and these waveforms are interfacedto MATLAB/Simulink for the construction of the fault diagnosisprocess. The fault signal in each phase is obtained from the primaryand secondary currents of the transformer, as shown in Figs 811.The data in these figures correspond to the two protection zones.The differential currents, which are the difference between theprimary current and the secondary current in all three phases, andthe zero sequence are calculated, and the resulting current signalsare extracted using the DWT.

4. Decision Algorithm and Results

From the simulated signals, the differential currents, which arethe difference between the primary current and the secondary

Table III. Number of case studies and parameters for case ofexternal fault

Parameter ofexternal fault Detail



Phase A 1

Transformer side High voltage and low voltage(primary and secondary)

2



12

Type of fault single line-to-ground, doubleline-to-ground, line-to-line,and three-phase faults (AG,ABG, AB, and ABC)

4

Fault location 20, 40, 60, and 80% measuredfrom the power transformer

4

Fault resistance 5 1

Table IV. Number of case studies and parameters for case ofinrush current

Parameter ofinrush current Detail



0 330 (each step is 30)and phase A voltage isreference

12

Magnetizing fluxes 80, 90, 100, 110, and 120% 5

current in all three phases, and the zero sequence are calculated,and the resulting current signals are employed to decomposethe high-frequency (details) and low-frequency (approximations)components from the simulated current signals using the motherwavelet daubechies4 (db4) [1820].

From our previous paper, the coefficient details of the resultingcurrent signals obtained from the DWT are squared. It is clearlyseen that when a fault occurs, the coefficients of high-frequencycomponents from each scale have a sudden change comparedwith those before the occurrence of the faults. This suddenchange is used as an index for the occurrence of faults usingcomparison of the coefficients details from each scale. However,the similarity between the waveforms of the internal faultsand the external fault signals and from coefficients of high-frequency components can be seen obviously. To overcome thisproblem, the comparison of the coefficients of the low-frequencycomponents from each phase is considered. Examples of theapproximated signal of the extracted waveform using DWT forthe differential currents from scale 1 to scale 5 are illustrated inFigs 1215.

After applying the DWT, Figs 1215 show several examplesof extraction using DWT for the differential currents and zerosequence current from scale 1 to scale 5. Figs 12 and 13 show acase of an internal fault at 20% of the winding length and a faultinception angle of 120. An example of an external fault case at20% of the length of the transmission line and fault inception angleof 120 is illustrated in Fig. 14, while an example of the inrushcurrent condition is illustrated in Fig. 15.

Generally, during normal condition the amplitude of each phasemust be nearly treated as zero, but during fault condition theamplitude of phase in which the fault occurs has a sudden change.By considering Fig. 12(a), when 20% of the length of the high-voltage winding with connection is considered as an example,

306 IEEJ Trans 9: 302314 (2014)


a

b

c

A

B

C

Fault high voltage coil 1

45

6

1

2

3

Fault

ZAF

ZCF

a

b

c

A

B

C

Fault high voltage coil 1

45

6

12

3

F

ZAF

ZCF

ZINF

(a) (b)

Fig. 7. Modification on an ATP/EMTP model for a three-phase transformer. (a) The winding-to-ground fault case. (b) The interturn faultcase

0 0.025 0.05 0.075 0.11

0.5

0

0.5

1x 104

Time (s)

(A)

Primary current

0 0.025 0.05 0.075 0.1

20001000

0

1000

2000

Time (s)

(A)

Secondary current

C BA

CA B

0 0.025 0.05 0.075 0.11000

500

0

500

1000

Time (s)

(A)

Primary current

0 0.025 0.05 0.075 0.15000

0

5000

Time (s)

(A)

Secondary current

C

C

B

B

A

A

(a) (b)

Fig. 8. Primary and secondary currents obtained from simulation for a case of winding-to-ground fault (fault at 20% of winding lengthand inception angle of 120). (a) The high- and (b) low-voltage winding fault cases

0 0.025 0.05 0.075 0.1

1

0

1

x 104

Time (s)

(A)

Primary current

0 0.025 0.05 0.075 0.1

2000

0

2000

Time (s)

(A)

(A)

(A)

Secondary current

A C

B

A B C

0 0.025 0.05 0.075 0.13000

1500

0

1500

3000

Time (s)

Primary current

0 0.025 0.05 0.075 0.13000

1500

0

1500

3000

Time (s)

Secondary current

B A

A B C

C

(a) (b)

Fig. 9. Primary and secondary currents obtained from simulation for a case of interturn fault (fault between 10 and 20% of winding lengthand inception angle of 120). (a) The high- and (b) low-voltage winding fault cases

the input differential current signal is plotted in the top trace ofthe figure. It can be observed that the amplitude of each phase isdifferent because the phases A and C (coil 1, as shown in Fig. 7(a))are the ones in which the fault occurs so that the amplitude ofphases A and C increases immediately after the fault occurrenceand has a value more than the other phase (phase B). This indicatesthat the decision algorithm can benefit from variations of thecoefficient approximations.

In addition, by considering Fig. 12(a), the input signal imple-mentation is a multisignal trace from each low-pass filter, whichcorresponds to a particular scale parameter, as shown in Fig. 12(a).The traces labeled scale 1, scale 2, . . . , scale 5 in this figurecorrespond to the filter output of Fig. 2. It can be seen that the

amplitudes of the coefficients approximations on each scale arerelated to the frequency banks according to the scale. As a result,by observing Figs 1215, it is clear that the coefficients of thelow-frequency components have a sudden change when a faultoccurs compared to those before a fault occurrence at 0.04 s.

However, by performing many case studies, the patterns in theraw data are hard to discriminate. To overcome this problem,the ratio between per-unit differential current and per-unit time iscalculated and Phmax, Phsum, and Zchk are performed as comparisonindicators in order to discriminate between the internal faultcondition and the external fault condition. Hence, the complexityof the patterns is significantly reduced. The ratio is calculated asfollows:

307 IEEJ Trans 9: 302314 (2014)


0 0.025 0.05 0.075 0.1600

300

0

300

600

Time (s)

Primary current

0 0.025 0.05 0.075 0.12000

1000

0

1000

2000

Time (s)

Secondary current

A B C

A B C

0 0.025 0.05 0.075 0.11000

500

0

500

1000

Time (s)

(A)

Primary current

0 0.025 0.05 0.075 0.15000

0

5000

Time (s)

(A)

(A)

(A)

Secondary current

C

C

B

B

A

A

(a) (b)

Fig. 10. Primary and secondary currents obtained from simulation for a case of external fault (fault at 20% of transmission line andinception angle of 120). (a) The high- and (b) low-voltage side fault cases

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.11000

500

0

500

1000

Time (s)

(A)

Primary current

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

20001000

0

1000

2000

Time (s)

(A)

Secondary current

C

C

B

B

A

A

Fig. 11. Primary and secondary currents obtained from simulationfor a case of inrush condition (inception angle of 120)

X diffchk =(X diffmaxX diffmin)

Irated(tdiff_xmax tdiff_xmin )

T

(6)

whereX diffmax = the maximum coefficient from the approximated- dif-

ferential signal of DWT

X diffmin = the minimum coefficient from the approximated differ-ential signal of DWT

tdiff_xmax = the time at which the maximum coefficient of theapproximated differential signal occurs

tdiff_xmin = the time at which the minimum coefficient of theapproximated differential signal occurs

X diffchk = comparison indicator for separation between internalfault condition and external fault condition

Irated = rated current of the power transformerT = the period of the power frequency of the systemZchk = zero sequence current of comparison indicator for

separation between internal fault condition and external faultcondition

Phmax = maximum value of comparison indicators (X diffchk ) usedin classifying the fault condition

Phsum = summation value of comparison indicators (X diffchk ) usedin classifying the fault condition

The numerator of the ratio is the difference between themaximum differential current and the minimum differential currentin terms of per unit with a base value selected at a transformersrated current. The denominator of the ratio is the differencebetween the time when tdiff_xmax occurs and the time when t

diff_xmin

occurs, with a quarter cycle of power frequency (in this case,power frequency = 50 Hz).

2000

200Phase A

200

0

200

Scal

e 1

200

0

200

Scal

e 2

200

0

200

Scal

e 3

200

0

200

Scal

e 4

0 0.05 0.1200

0

200

Scal

e 5

0.5

0

0.5Phase B

0.5

0

0.5

0.5

0

0.5

0.5

0

0.5

0.2

0

0.2

0 0.05 0.10.2

0

0.2

Time (s)

50

0

50Phase C

50

0

50

50

0

50

50

0

50

50

0

50

0 0.05 0.150

0

50

100

0

100Zero sequence

100

0

100

100

0

100

100

0

100

100

0

100

0 0.05 0.1100

0

100

100

10Phase A

100

10

Scal

e 1

100

10

Scal

e 2

100

10

Scal

e 3

100

10

Scal

e 4

0 0.05 0.110

0

10

Scal

e 5

0.50

0.5Phase B

0.50

0.5

0.50

0.5

0.50

0.5

0.20

0.2

0 0.05 0.10.2

0

0.2

Time (s)

100

10Phase C

100

10

100

10

100

10

100

10

0 0.05 0.110

0

10

0.10

0.1Zero sequence

0.10

0.1

0.10

0.1

0.10

0.1

0.10

0.1

0 0.05 0.10.02

0

0.02

(a) (b)

Fig. 12. DWT of differential currents for internal fault case (winding phase A-to-ground fault at 20% of winding length and inceptionangle of 120). Fault occurring at (a) high-voltage winding and (b) low-voltage winding

308 IEEJ Trans 9: 302314 (2014)


2000

200Phase A

2000

200

Scal

e 1

2000

200

Scal

e 2

2000

200

Scal

e 3

2000

200

Scal

e 4

0 0.05 0.1200

0200

Scal

e 5

0.20

0.2Phase B

0.20

0.2

0.20

0.2

0.20

0.2

0.20

0.2

0 0.05 0.10.2

00.2

Time (s)

2000

200Phase C

2000

200

2000

200

2000

200

2000

200

0 0.05 0.1200

0200

0.020

0.02Zero sequence

0.020

0.02

0.020

0.02

0.020

0.02

0.010

0.01

0 0.05 0.15

05

x 103

500

50Phase A

500

50

Scal

e 1

500

50

Scal

e 2

500

50

Scal

e 3

500

50

Scal

e 4

0 0.05 0.150

050

Scal

e 5

0.50

0.5Phase B

0.50

0.5

0.50

0.5

0.50

0.5

0.20

0.2

0 0.05 0.10.2

00.2

Time (s)

500

50Phase C

500

50

500

50

500

50

500

50

0 0.05 0.150

050

0.10

0.1Zero sequence

0.10

0.1

0.10

0.1

0.10

0.1

0.10

0.1

0 0.05 0.10.02

00.02

(a) (b)

Fig. 13. DWT of differential currents for internal fault case (interturn fault between 10 and 20% of winding length and inception angleof 120). Fault occurring at (a) high- and (b) low-voltage winding

100

10Phase A

100

10

Scal

e 1

50

5

Scal

e 2

20

2

Scal

e 3

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1

Scal

e 4

0 0.05 0.10.5

0

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e 5

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1Phase B

10

1

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1Phase C

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0 0.05 0.10.2

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5Zero sequence

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0 0.05 0.10.5

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0.50

0.5

Scal

e 1

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0.5

Scal

e 2

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0.5

Scal

e 3

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0.2

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e 4

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0

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e 5

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0.20

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0.5

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Time (s)

0.50

0.5Phase C

0.50

0.5

0.20

0.2

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0

0.2

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0.1Zero sequence

0.10

0.1

0.10

0.1

0.10

0.1

0.10

0.1

0 0.05 0.10.02

0

0.02

(a) (b)

Fig. 14. DWT of differential currents for external fault case (phase A-to-ground fault at 20% of transmission line and inception angle of120). Fault occurring at (a) high- and (b) low-voltage sides

100

10Phase A

100

10

Scal

e 1

100

10

Scal

e 2

100

10

Scal

e 3

100

10

Scal

e 4

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0

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Scal

e 5

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20Phase B

200

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10Phase C

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0

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10Phase A

100

10

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e 1

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e 2

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e 3

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0

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Scal

e 5

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20Phase B

200

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10Phase C

100

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100

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100

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0

10

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0.050

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0 0.05 0.10.02

0

0.02

(a) (b)

Fig. 15. DWT of differential currents for inrush current case (inception angle of 120). (a) The 100% and (b) 120% of magnetizing fluxes

The ratio is calculated for all three phases, and from a trialand error process the indices for the separation among the internalfault condition, the external fault condition, and inrush conditionare defined. The most appropriate form of the decision algorithmfrom the case studies of the system under the investigations canbe given as a flowchart illustrated in Fig. 16.

By considering Fig. 16, in the first step [19,20], the coefficientsof the signals obtained from the DWT are used to discriminate

between the normal condition and the fault condition includingthe inception of fault (time at which the fault occurs). It can beseen that if the first step can detect the fault condition, the nextstep will be carried out to discriminate between the internal faultcondition and the external fault condition, as shown in Fig. 16.

In the final step, Phmax and Phsum are performed to distinguishbetween a fault that occurs at high voltage and that at low voltage.By observing Fig. 16, if Phmax is greater than 40 and Phsum is

309 IEEJ Trans 9: 302314 (2014)


Fault detection decision algorithm andfault inception angle [19, 20]

Winding to groundfault at high

voltage winding

Interturn fault athigh voltage

winding

Interturn fault at lowvoltage winding

Inrush currentcondition

External fault athigh voltage

side

External fault atlow voltage

side

Winding to groundfault at low

voltage winding

Zchk > 5

Zchk > 1

Zchk > 0.2

Zchk < 0.5

(Phmax > 15)And

(Phsum > 35)

(Phmax > 15)And

(Phsum > 15)

(Phmax > 0.3)And

(Phsum > 0.5)

(Phmax > 40)And

(Phsum > 80)

YesNo

Yes

No

Yes

No

YesNo

No

YesNoNo

No

Yes

Yes

Protective relay must be operated astripping

Protective relay must be operated as block oruntripping

Fig. 16. Flowchart for decision algorithm

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1200

0

200Differential(a) (b)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.005

0.01

Scal

e 1

Detail

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1200

0

200

Scal

e 5

Approximation

0.0350 0.04 0.045 0.05200

0

200

Time (s)

(x= -58.64y=0.0450)

(x= 51.82 y= 0.0423)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.110

0

10Differential

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

2

4x 104

Scal

e 1

Detail

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.110

0

10

Scal

e 5

Approximation

0.035 0.04 0.045 0.05

50

5

Time (s)

(x= 4.72 y=0.0417)

(x= 0.065 y= 0.0400)

Fig. 17. Responses to the winding-to-ground fault condition. Fault occurring at (a) high- and (b) low-voltage winding

greater than 80, then internal fault can occur at the high-voltagewinding. The differential relay must activate the trip circuits ofcircuit breakers for isolating the faulted components from the restof the power system. However, the decision algorithm cannot

identify the type of fault (winding-to-ground fault or interturnfault), so Zchk is performed to classify the type of fault (winding-to-ground fault or interturn fault). This indicates a significantdifference between winding-to-ground fault and interturn fault. If

310 IEEJ Trans 9: 302314 (2014)


0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1200

0

200Differential

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.02

0.04

Scal

e 1

Detail

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1200

0

200

Scal

e 5

Approximation

0.035 0.04 0.045 0.05200

0

200

Time (s)

(x= 137.57 y= 0.042)(x= -0.85

y= 0.040)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.150

0

50Differential

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.5

1x 103

Scal

e 1

Detail

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.150

0

50

Scal

e 5

Approximation

0.035 0.04 0.045 0.0540

0

40

Time (s)

(x= 0.034 y= 0.0400)

(x= 27.27y=0.0449)

(a) (b)

Fig. 18. Responses to the interturn fault condition. (a) Fault occurring at high- and (b) low-voltage winding

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.110

0

10Differential

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.5

1

Scal

e 1

Detail

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.5

0

0.5

Scal

e 5

Approximation

0.035 0.04 0.045 0.050.5

0

0.5

Time (s)

(x= -0.169 y= 0.0400) (x= 0.2017

y= 0.0401)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.5

0

0.5Differential

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.05

0.1

Scal

e 1

Detail

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.2

0

0.2

Scal

e 5

Approximation

0.035 0.04 0.045 0.050.1

00.10.2

Time (s)

(x= 0.01 y=0.0443)

(x= 0.11 y= 0.0417)

(a) (b)

Fig. 19. Responses to the external fault condition. Fault occurring at (a) high- and (b) low-voltage sides

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.110

0

10Differential

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.02

0.04

Scal

e 1

Detail

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.110

0

10

Scal

e 5

Approximation

0.035 0.04 0.045 0.0501

0

1

Time (s)

(x= 0.054 y= 0.0405)

(x= -0.045y=0.0406)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.110

0

10Differential

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.02

0.04

Scal

e 1

Detail

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.110

0

10

Scal

e 5

Approximation

0.035 0.04 0.045 0.0501

0

1

Time (s)

(x= 0.55 y= 0.0408)

(x= -0.476y=0.0406)

(a) (b)

Fig. 20. Responses to the magnetizing inrush current condition. (a) The 100% and (b) 120% of magnetizing fluxes

Zchk is greater than 5, then it can be identified as a winding-to-ground fault at the high-voltage winding. On the other hand, aninterturn fault will be identified if Zchk is less than 5. Similarly, forthe internal fault occurring at low voltage, the decision algorithmhas a similar process.

To gain more understanding, one case of each type of faultsis considered as an example in Figs 1720. The proportion ofthe spectral differential current signal, calculated between themaximum and minimum value in a quarter cycle period ofanalyzed data and the time deviation are shown in Figs 17 20.The results illustrated in Tables VVIII are obtained from onecase of each type of faults as shown in Figs 17 20.

By observing Fig. 17(a) and the data in Table V, when the faultoccurring at 20% of the length of the high-voltage winding is

considered, it can be observed that after the fault occurrence at0.04 s, both the coefficient of detail (high-frequency components)and approximation (low-frequency components) have a suddenchange compared to those before the occurrence of a fault, sothe inception of fault can be detected. It is found, accordingthe data presented in Table V, that Phmax, Phsum, and Zchkare calculated and the all comparison indicators (Phmax, Phsum,and Zchk) have a value greater than 80. This indicates thatPhmax, Phsum, and Zchk play an important role in the decisionalgorithm.

Based on the data in Table VI, considering the interturn faultat the high-voltage winding, it can be clearly seen that Phmax andPhsum have still a value greater than 80 but Zchk has a value lowerthan 5; this is due to the effect of the interturn fault. Based on a

311 IEEJ Trans 9: 302314 (2014)


Table V. Result of identification for case of winding-to-ground fault

High-voltage winding Low-voltage winding

Coefficient of DWT A B C Zero A B C Zero

Xmax diff 51.8227 0.0592 12.8956 37.3422 4.7263 0.0611 0.0075 0.0134Xmin diff 58.6477 0.0722 14.7771 42.3332 0.0651 0.0609 4.6632 0.0076tmax diff_x 0.0412 0.0449 0.0412 0.0412 0.0417 0.0449 0.0400 0.0400tmin diff_x 0.0450 0.0400 0.0450 0.0450 0.0400 0.0417 0.0419 0.0406Xchkdiff 118.945 0.1059 29.7956 85.7877 10.5936 0.1525 9.7306 0.1312Phsum 148.8469 20.4767 Phmax 118.945 10.5936 Zchk 85.7877 0.1312Result Tripped Tripped

Table VI. Result of identification for case of interturn fault



Xmax diff 137.57 0.0633 0.8846 0.00220 27.28 0.0632 0.0441 0.00160Xmin diff 0.856 0.0524 137.60 0.000861 0.034 0.0699 27.34 0.00670tmax diff_x 42.25 44.17 40.01 40.33 44.49 44.97 40.01 40.01tmin diff_x 40.01 40.17 42.25 40.65 40.01 42.09 44.49 40.65X diffchk 247.19 0.12 247.31 0.04 24.33 0.18 24.45 0.14Phsum 494.61 48.96 Phmax 247.31 24.45 Zchk 0.04 0.14Result Tripped Tripped

Table VII. Result of identification for case of external fault



Xmax diff 0.2017 0.0645 0.012 0.0749 0.1166 0.0651 0.0255 0.0099Xmin diff 0.169 0.0609 0.1111 0.1755 0.016 0.0622 0.0842 0.0078tmax diff_x 0.0401 0.0444 0.0403 0.0403 0.0417 0.0449 0.0400 0.0400tmin diff_x 0.0400 0.0400 0.0406 0.0400 0.0443 0.0417 0.0449 0.0406X diffchk 10.5914 0.1124 1.2387 3.3386 0.1571 0.1591 0.100 0.0916Phsum 11.9426 0.4971 Phmax 10.5914 0.1591 Zchk 3.3386 0.0916Result Untripped Untripped

Table VIII. Result of identification for case of inrush current

Inrush current 100% Inrush current 120%


Xmax diff 0.5388 1.3926 0.4249 0.0006 0.555 0.928 0.4428 0.0008Xmin diff 0.456 0.0038 1.4191 0.0059 0.0476 0.0044 0.9499 0.0046tmax diff_x 0.0404 0.0450 0.0406 0.0419 0.0408 0.0450 0.0406 0.0409tmin diff_x 0.0406 0.0400 0.0450 0.0448 0.0406 0.0400 0.0450 0.0448X diffchk 24.88 1.118 1.693 0.0090 25.76 0.7467 1.279 0.0097Phsum 27.692 27.79 Phmax 24.88 25.76 Zchk 0.0090 0.0097Result Untripped Untripped

Table IX. Summary of results from all simulations

Internal fault External faults

Fault types HV winding LV winding HV side LV side Inrush current

Number of case studies 1620 1620 192 192 60Detection accuracy 100.00% 97.90% 98.96% 97.92% 96.67%

312 IEEJ Trans 9: 302314 (2014)


further analysis of Table VI, it can be concluded that the interturnfault can be detected and the differential relay must be activated.

When all conditions as stated in Section 3 are applied, the totalnumber of case studies is 3240 for internal faults condition, 384 forexternal faults condition, and 60 for inrush condition. The accuracyof the proposed decision algorithm for all case studies is shown inTable IX.

5. Conclusions

This paper proposed a technique for discriminating betweeninrush current, external fault, and internal fault. The DWT algo-rithm was employed in the protection scheme. The simula-tions, analysis, and diagnosis were performed using ATP/EMTPand MATLAB/Simulink. The current waveforms obtained fromATP/EMTP were extracted to several scales with the DWT.Daubechies4 (db4) was employed as the mother wavelet in orderto decompose the low-frequency components from fault signals.The ratio between per-unit differential current and per-unit timewas calculated and used as comparative indicator in order to dis-criminate between inrush current, external fault, and internal fault.The results obtained from the algorithm proposed in this paper candetect and indicate the fault condition with an accuracy better than95% as seen from Table IX. In addition, the proposed techniqueuses data of the differential current with a time of a quarter cyclefor the analysis, which is less than that employed in a conventionalprotection scheme.

Acknowledgments

The work presented in this paper is part of a research project sponsoredby the King Mongkuts Institute of Technology Ladkrabang Research Fund.The authors would like to thank the sponsor for financial support.

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Atthapol Ngaopitakkul (Non-member) is currently an Assis-tant Professor with the Department of ElectricalEngineering, King Mongkuts Institute of Tech-nology Laddrabang, Bangkok, Thailand. Hisresearch interests include protection relays andenergy management.

Chaiyan Jettanasen (Non-member) received the B.Eng. andM.Eng. degrees from the Institut National desSciences Appliquees (INSA) de Lyon, France,in 2005, and the Ph.D. degree from Ecole Cen-trale de Lyon, France, in 2008. He is cur-rently an Assistant Professor with the Electri-cal Engineering Department, King MongkutsInstitute of Technology Laddrabang, Bangkok,

Thailand. His research interests include EMC in power electronicsystems.

314 IEEJ Trans 9: 302314 (2014)

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