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Differential Protection of Power TransformersUsing The Wavelet Transform

R. P. Medeiros, F. B. Costa, Member, IEEE, J. F. Fernandes

Abstract—Several disturbances involving power transformerscommonly occur in the Electric Power System. External faultsnear the transformer, internal faults, as well as transformerenergizing and overexcitation are the main events evaluated in theprotection of the power transformers. All of the aforementionedevents present transients, which can be properly analyzed bythe wavelet transform. The Maximal Overlap Discrete WaveletTransform (MODWT) can be used to detect transients in somepower system disturbances. This paper presents an algorithmbased on MODWT for detection and identification of externalfaults near or far the transformer, internal faults, and trans-former energization by using differential currents in the waveletdomain. A system of 230 kV was modeled using ATP/EMTPsoftware. The results reveal the advantages of using this type ofmodeling, since It provides reliability and speed in detection ofthese events.

Index Terms—Power transformers, wavelet transform, trans-former energizing, internal faults.

I. INTRODUCTION

POWER transformers are devices that require continuousmonitoring and fast protection, because they are expensive

and critical to the efficiency of the electrical power systems[1]. Similarly to other components of the power system,transformers are subject to faults. In fact, about 10% of faultstake place into power transformers, in which 70% of thesefaults are caused by short circuits in its windings [2]. Faultsin transformers cause damage, such as the cost associated withits repair and the cost of energy not supplied because of itsunavailability [3].

Differential protection is the main protection scheme ap-plied in power transforms, presenting reliable discriminationbetween internal faults and external faults or conditions ofnormal loading system. However, the differential protectionpresents significant sensitivity under certain conditions suchas magnetizing inrush current, and transformer overexcitation.

To overcome the limitations of the conventional differentialprotection, the element with harmonic restraint was introducedin the differential relays. In [4] was proposed a relay based onthe principle of harmonic restraint, being able to distinguishbetween the differential currents due to an internal fault anddue to inrush currents, and operating at high speed on thefault current and restricting the operation in the presence of

This work was supported by CAPES (Coordenacao de Aperfeicoamento dePessoal de Nıvel Superior).

F. B. Costa is with Federal University of Rio Grande do Norte - Schoolof Science and Technology, Campus Univesitario Lagoa Nova, Natal - RN,CEP:59.078-970, Brazil. E-mail: flaviocosta@ect.ufrn.br.

R. P. Medeiros and J. F. Fernandes are with Federal University of RioGrande do Norte - Department of Electrical Engineering, Campus UnivesitarioLagoa Nova, Natal - RN, CEP:59.078-970, Brazil. E-mail: digaum 34 andjessika.fonseca@hotmail.com

magnetization current. In this technique, relays are designedto restrain operation as long as the second harmonic exceedsa certain percentage of the fundamental [5]. This methodensured security for most of the inrush and overexcitationcases but still fail for cases with very low harmonic contentin the operating current [6].

In order to improve power transformer protection, newtechniques and methodologies based on intelligent tools havebeen developed to discriminate efficiently the internal faultsfrom other disturbances or switching operations. In [7] wasproposed to use a statistical method of data analysis, the prin-cipal component analysis (PCA), based on pattern recognitionfor the extraction of different characteristics of differentialcurrents. In [5], the discrete wavelet transform (DWT) wasemployed to extract transient features of transformer three-phase differential currents to detect internal fault conditions.In [8] was proposed a wavelet-based technique for monitor-ing nonstationary variations in order to distinguish betweentransformer inrush currents and transformer internal faults. In[9] was presented an extension of real-time tests of a wavelet-packet-transform-based technique for the differential protec-tion of three-phase power transformers, using a DS1102 digitalsignal processor board and tested on two different three-phasepower transformers with neutral resistance grounded. In [1]was presented an efficient method based on the combination ofClarke transform and fuzzy logic to improve the performanceof this type of protection. A differential protection schemebased on artificial neural networks using the SVM classifierwas proposed in [10].

The DWT decomposes a sampled signal in time into scalingand wavelet coefficients. The wavelet coefficients of a signal,as well as their spectral energy, have been used to detectand classify faults and some power quality (PQ) disturbances[11]–[13]. In power transformer protection, some disturbancesas external faults, internal faults and transformer energizing,which present transients, can be also properly analyzed by thistool [5], [8], [14] .

This paper proposes a differential protection scheme forthree-phase transformers by using the Maximal Overlap DWT(MODWT). The technique detects and identifies external faultsnear or far the transformer, internal faults, and transformerenergizing by using differential currents in the wavelet domain.Besides that, the method uses the wavelet coefficient energy ofthe operation and restriction currents, following the model ofthe conventional differential protection. The proposed protec-tion method was evaluated through differential current signalsobtained from the ATP/EMTP software in situations such asinternal faults, transformer energizing, and external faults, withrandom fault resistance (rf ), fault inception angle (θi), fault

978-1-4799-6415-4/14/$31.00 ©2014 IEEE

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distance to the power transformer (df ), and fault type. Theproposed protection presented an optimal performance. Theresults obtained reveal the advantages of using this type ofmodeling, since It provides reliability and speed in detectionof these events.

II. DIFFERENTIAL PROTECTION OF TRANSFORMERS

The philosophy of differential protection is applied on:power transformers protection, buses protection, large motorsand generators protection, and transmission lines protection.Its mathematical principle is based on Kirchhoff law of thecurrents, whereby the sum of the currents flowing through anode is equal to the sum of the currents leaving that samenode.

The principle of differential protection is based on thecomparison between the primary and secondary currents ofthe power transformer. Current transformers installed in pri-mary and secondary branches of the transformer provides thecurrents to the relay, which are the operating current (iD) andthe restriction current (iR). Fig. 1 depicts a typical differentialrelay connection diagram for a single-phase transformer:

PowerTransformer

DifferentialRelay

CT

i 1i 2

CT2

1:n 11:n 2

N 1 :N 2

1

Fig. 1. Differential protection for single-phase transformer.

According to [15], The operation and restriction currentsare defined as:

iD = i1 − i2, (1)

iR =i1 + i2

2. (2)

These equations are extended to the three-phase transformers.However, in three-phase transformers with two windings,

under normal operation conditions or external faults, i1 andi2 are approximately equal due to compensation made by thetransformer ratio and setting (∆ or Y ) of current transformers(CT1 and CT2). For instance, a ∆Y power transformer withN1:N2 transformer ratio requires that CT1 is connected inY configuration with a 1:n1 transformer ratio, and CT2 isconnected in ∆ configuration with a 1:n2 transformer ratio.However, when an internal fault occurs, these currents are dif-ferent. The differential protection is based on the comparison

between iD and iR. Fig. 2 depicts an example of a charac-teristic curve of a differential protection scheme, in which theregions of operation and non-operation are illustrated [15].

Op

erat

ion

cu

rren

t - i D

i0

Restriction current - iR

The relay must operatefor operation points in

this region

The relay cannot operatefor operation points in

this region

Operation points of internal faults are

located in this region

Operation points of external faults, inrush currents, and other events are located in this region

Fig. 2. Characteristic curve of the percentage differential protection.

According to Fig. 2, the relay operates only for cases inwhich the operation point (iR, iD) is above of the characteristiccurve defined by:

iD > i0 + kiR, (3)

where k and i0 are, respectively, the slope of the operationcharacteristic curve of percentage differential relay and mini-mum current of relay operation.

III. WAVELET TRANSFORM

The discrete wavelet transform is a mathematical tool foranalyzing non-stationary signals, such as those observed infault conditions or in the transformer energizing. Accordingto the algorithm of Mallat [16], both the DWT and MODWTuse low and high-pass filters (scaling and wavelet filters) todivide the frequency band of the input signal into scaling andwavelet coefficients, respectively. However, in contrast to theDWT, there is no downsampling in MODWT [13]. As a result,the MODWT provides the fastest detection of faults and otherdisturbances with transient.

Recursively, the scaling coefficients (s) and wavelet coef-ficients (w), of the MODWT, can be computed through theinner product of the sampled signal x with the filters g and h,respectively, as follows [13]:

s(k) =

L∑n=1

g(n)x(k + n− L), (4)

w(k) =

∞∑n=1

h(n)x(k + n− L), (5)

where g(n) = g(n)/√

2 and h(n) = h(n)/√

2 are the scalingand wavelet filters of the MODWT. L is the size of both filters.

The wavelet coefficient energy of the MODWT is also usedfor fault and some PQ disturbance detection [13]. The spectral

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energy E of a window of length ∆k sliding in the signal x(n),sample-by-sample, is given by:

E(k) =

k∑n=k−∆k+1

x2(n), (6)

where ∆k = fs/f is the amount of samples per cicle ofthe power frequency. According to the Parseval theorem, theenergy of a signal is given by the contributions of the scalingand wavelet coefficient energy. Recursively, the spectral energyof the signal sliding window can also be decomposed intothe scaling coefficient energy (E) and the wavelet coefficientenergy (E), at the first scale, as follows [13]:

E(k) = E(k) + E(k), (7)

where

E(k) =

k∑n=k−∆k+1

s2(n), (8)

E(k) =

k∑n=k−∆k+1

w2(n). (9)

IV. MODELING OF THE ELECTRICAL POWER SYSTEM

The 230 kV power system proposed by [17] to evaluateprotective schemes was modeled using the ATP/EMTP (Fig.3). The hatched region comprises the region of operation of thedifferential protection. The power transformer (T1), 725 MVA,132.73/22.8 kV, and Yg−∆ configuration, was connected totwo current transformers (CT1 and CT2), with transformationratios 200/5 and 1200/5, and ∆ - Y configuration, respec-tively. The power transformer is not operating at full load.Faults were simulated on line 3 (external faults) and insidethe transformer (internal faults) as well as energization of thepower transformer were simulated in order to evaluate theproposed wavelet-based differential protection.

S1line 2

line 1

line 3 S2

CB1

CB3

CB2

CB4

CB5 CB6 CB7

T1

Z1

CB8CT1 CT2

DifferentialRelay

S1

Systemequivalent

Fig. 3. Power System scheme.

V. PROPOSED PROTECTION METHOD

The first step performed by the protection algorithm is thecalculation of the three-phase differential currents, accordingto (1) and (2). These signals are conditioned (anti-aliasingfiltering and analog-digital conversion). The used samplingfrequency (fs) is equal to 15.36 kHz and the anti-aliasingfilter was designed with the 3rd order, low-pass filter withcutoff frequency fc = 0.9fs/2. Fig. 4 shows the flowchartof the proposed algorithm. The first level MODWT wavelet

coefficients and the related wavelet coefficient energy of theoperation and restriction differential currents are calculated inthe wavelet processing block.

Computationof differential

currents

Anti-aliasingA/D

Wavelet Processing

i 1(A,B,C) i 2(A,B,C)

87WProtection

E

D(A,B,C)i E

R(A,B,C)i

i

D(A,B,C) i

R(A,B,C)

E

Di

E

Ri

i

D(A,B,C) i

R(A,B,C)

Fig. 4. Proposed wavelet-based differential protection algorithm.

The 87W block performs the wavelet-based differentialprotection. Similarly to the percentage differential protection,as in (3), the relay decision algorithm is based on the analysisof two-dimensional space generated by the following axes: 1)the energy of the wavelet coefficients of the operation current(operation energy); 2) the energy of the wavelet coefficientsof the restriction current (restriction energy), as follows:

EiD(A,B,C)> kwEiR(A,B,C)

, (10)

where kw corresponds to the slope of the operation character-istic curve of the proposed wavelet-based differential relay.

A. Relay Parameterization

The characteristic curve of the wavelet-based relay(database 1) was generated with records of external faults,transformer energizing, and internal faults. In the database 1,the parameters θi, rf , and df were varied with steps ∆θi,∆rf , and ∆df , respectively. The fault type was also varied,according to Table I:

TABLE IDATABASE FOR OBTAINING THE CURVE OF THE RELAY

Fault External Internal TransformerParameters Faults Faults Energizing

0 ≤ θi ≤180 , ∆θi =10 √ √ √

5 Ω ≤ rf ≤100 Ω, ∆rf =5 Ω√ √

-14 mi ≤ df ≤248 mi,∆df =13 mi

√- -

Fault type (AG, AB, ABG, ABC)√ √

-Number of cases 150 310 38

4

Fig. 5 depicts the operation point (EiR, EiD) for eachcase analyzed in the Table I. The operation point (EiR, EiD)was calculated until five post-fault samples. The characteristiccurve was obtained for the wavelet-based relay, using db(4),where db(L) refers to the mother wavelet of the Daubechiesfamily with L coefficients. The slope of the characteristiccurve, kw = 4.05, was statistically selected to separate internalfaults from the other events in the best way as possible.

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

Transformer Energizing

External Faults

Internal Faults

kw = 4.05

.Restriction energy - E iR

.O

per

atio

n en

ergy

- E

i D

Fig. 5. Characteristic curve obtained for the wavelet-based relay with db(4).

VI. PERFORMANCE EVALUATION

The performance of the proposed wavelet-based relay wasassessed with: transformer energization, external faults andinternal faults. For this evaluation, a second database (database2) was generated with fault parameters (rf , θi, df , and faulttype) randomly selected.

A. Transformer Energizing

Different energization cases, with random closing timesof each phase of the circuit breaker CB8 (Fig. 3), in thelow voltage side, were simulated. A total of 100 simulationswas performed. Fig. 6 depicts the Operation of the proposedwavelet-based relay with db(4) in the transformer energizing.As expected, the relay did not operate in 100% of cases.

B. External Faults

Faults on line 3 (external faults) were simulated withrandom rf , θi, df , and fault type. A total of 100 simulationswas performed. Fig. 7 depicts the Operation of the proposedwavelet-based relay in the external faults. As expected, therelay did not operate in 100% of the cases.

C. Internal Faults

Internal faults in the primary and secondary sides of thepower transformer were simulated with random rf , θi, faulttype, and percentage of the amount of turns involved in thefault in primary and secondary sides of the transformer. A total

Phase APhase B

Phase C

.O

pera

tion

ene

rgy

- E

i D

.Restriction energy - E iR

0 2 4 6 8 10 12 14 16 18

0

0.5

1

1.5

2

2.5

3

3.5

4

Fig. 6. Operation of the proposed wavelet-based relay in the transformerenergizing.

2 4 6 8 10 12

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

.

Ope

rati

on e

ner

gy

- E

i D

.Restriction energy - E iR

Phase APhase B

Phase C

Fig. 7. Operation of the proposed wavelet-based relay in the external faults.

of 100 simulations was performed. Fig. 8 depicts the operationof the proposed wavelet-based relay in the internal faults. Therelay operated in 97% of cases. However, the relay did notoperate for the following types of phase-to-ground faults:

1) AG faults with fault inception angle near to 0 or 180 ;2) Proximity to the neutral of transformer primary.In the first case, AG faults with fault inception angle closed

to 0 or 180 do not present transient. Therefore, the waveletcoefficients energy are very low in this case and the transientis not detected. Nevertheless, the probability of such kind offaults is extremely low. In the second case, faults near tothe neutral of transformer primary are less abrupt, presentingdamped transients and an insignificant variations in the waveletcoefficient energy.

D. Effect of the Mother WaveletIt is well-known that wavelet-based analysis is influenced

by the choice of the mother wavelet. In this paper, the mother

5

0 2 4 6 8 10 12 14 160

10

20

30

40

50

60

Phase APhase B

Phase C

.O

pera

tion

ene

rgy

- E

i D

.Restriction energy - E iR

Fig. 8. Operation of the proposed wavelet-based relay in the internal faults.

wavelets db(4), db(12), coif(12), and db(90) were evaluated,where coif(L) refers to the mother wavelet of the coiflet fami-lies, with L coefficients. Table II summarizes the efficiency ofthe algorithm in internal faults detection. Table III summarizesthe efficiency of the algorithm in the speed of internal faultsdetection (i.e., the amount of post-fault samples which werecomputed until the detection, where kf corresponds to sampleof fault).

TABLE IIPERFORMANCE OF THE ALGORITHM FOR THE DETECTION BY USING

DIFFERENT MOTHER WAVELETS

Mother Waveletdb(4) db(12) coif(12) db(90)

Success Rate (%) 97 90 91 81

TABLE IIIPERFORMANCE OF THE ALGORITHM FOR THE RAPIDITY IN DETECTION BY

USING DIFFERENT MOTHER WAVELETS

Success Rate (%)Mother Wavelet

kf kf + 1 >kf + 2

db(4) 100 - -db(12) 47.78 31.11 21.11

coif(12) - 55 45db(90) - - 100

According to Table II and Table III, among the motherwavelets analyzed, the db(4) presented the best results, asin the correct detection of internal faults as in the speed ofdetection. In real time applications, in which features such asspeed and low computational effort should be primarily takeninto consideration, the choice of the proper mother waveletshould be performed.

VII. CONCLUSIONS

This paper presented a methodology based on waveletcoefficient energy for detection of disturbances in power

transformers, such as transformer energization, external faults,and internal faults.

The wavelet coefficients energy of the MODWT providedhigh-speed detection of the disturbances in power transform-ers. The detection was accomplished in 65 µs. With regardto the reliability, a success rate of about 97% in detection ofinternal faults was achieved.

The method was affected by the choice of the motherwavelet, presenting different success rate in the classificationof events and time delay in the fault detection for differentmother wavelets. The db(4) presented the best results.

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