Detecting the Position of Winding Short Circuit Faults in-ejsr_23!4!14

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European Journal of Scientific Research

ISSN 1450-216X Vol.23 No.4 (2008), pp.644-658

EuroJournals Publishing, Inc. 2008http://www.eurojournals.com/ejsr.htm

Detecting the Position of Winding Short Circuit Faults in

Transformer Using High Frequency Analysis

M.R.Barzegaran

Department of Electrical & computer Engineering, babol

University of Technology, Babol, Iran

E-mail: [email protected]

M.Mirzaie

Department of Electrical & computer Engineering, babol

University of Technology, Babol, Iran

E-mail: [email protected]

Abstract

In order to study the position of internal short-circuit in power transformers, thehigh frequency model for winding should be set up. In this paper a special methodology is

used for establishing the high frequency model of transformer winding. This model

topology is involved to reflect the internal electromagnetic behavior of such transformer.

The proposed method is used in all part of transformer winding to completely represent thebehavior of winding in different situation. The result predicts the position of short-circuit in

each side of winding on different external condition. For better explanation several kind of

curves are indicated which are drawn by MATLAB software.

Keywords: Transformer, High frequency, fault, Short circuit

1. IntroductionPower transformer is a very critical and costly equipment in power systems. Therefore maintenanceand protection of such important equipment have been absolutely indispensible.

One of the major concerns for utilities and/or manufacturers is failure of transformers due to

external or internal short-circuits. These faults are the turn to turn short-circuit and the turn to groundshort-circuit and/or out of transformer (contacting in network).Investigation shows that about 70%-

80% of transformer failures are caused by internal winding short-circuit faults. One important reason

for these faults is erosion of the winding and conductor insulation due to vibrations initiated by the

electromechanical forces at service current and over currents. This problem leads to over-current inwindings that result terrible damages such as severe hot-spots, oil heating, winding deformation,

damage to the clamping structure, core damage, and even explosion of transformer. Also it causes

many adversities in power system (voltage sag, interruption, etc). So the short-circuit consideration isone of the most important and challenging aspects of transformer design. There exist a number of ways

such as magnetic balance test, Buchholtz relay operations, ratio-meter test to detect internal faults in

transformers.The magnetic balance test [1] is carried out on three phase transformers by energizing only one

of the phases with a lower than rated voltage and keeping all the other phases open-circuit (including


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645 M.R.Barzegaran and M.Mirzaie

the other winding(s) of the energized phase). A fault in the winding can be detected by the inducedvoltage variation in it compared to the healthy case. The faulted winding will not allow flux to flow in

the magnetic path around which is wound, resulting in very low voltage being induced in defected

winding. Also magnetizing currents are sometime useful in detecting turn-to-turn faults [2].A Buchholz relays consist of two operated switches which is floated in an oil-filled chamber

and they are normally immersed in oil [3], [4]. Fault makes gases due to increasing the heat of oil. The

gases enter the chamber and push the oil level down and operate the float switches. In incipient faults

only the top float switch operates to give an alarm, and in the severe faults condition, the lower floatswitch sends the trip signal. Later the gas sample can be collected and send for analysis which can give

the useful information about internal faults.

It has also been reported that no-load losses can detect and locate turn-to-turn short circuitfaults. The no-load loss of a transformer is often measured after any high voltage dielectric tests once it

is suspected that the winding of a transformer has failed. It has been shown that no-load losses rise

with inter-turn faults [1]. However, in older transformer, core degradation and looseness in fixturesmay also contribute to increased no-load losses [2]. Hence, measurement of no-load losses does not

seem to be an absolute method for detecting turn-to turn faults. Another way of internal fault detection

in transformer is measuring turn-ratio in open-circuit state. The turn-ratio of the faulted phase isdifferent to the other phases [3].

Therefore Fault detection studies require a capable and accurate transformer model. Differenttransformer models for such purposes have been presented. In [2], A Finite Element based phasevariable model of single-phase distribution transformers with internal short circuit faults has been

presented. The flux linkages of windings are used as the phase variables this model was developed in

light of a defined equivalent magnetizing current. The developed model is capable of providing

suitable simulation of the short circuit fault conditions. In [3], current waveforms of the normal andfault conditions of the transformer obtained from simulation, applied to the proposed Neural Network

systems and they show the characteristics of the problem. Also, turn-turn fault in a transformer has

been detected using of frequency domain analysis [4]. This method has been proposed based ondetecting odd triple harmonic line current of a faulty transformer. A distributed-parameter Laplace-

domain model for frequency analysis of a two-winding single-phase transformer has been presented

[5].It includes several important transformer parameters for obtaining an accurate frequency response.The frequency characteristics of the input impedance, under both open-circuit and short-circuit

conditions, have been examined using plots of its real part, its imaginary part, and its phase versus

frequency. Also several natural frequencies have been identified from the frequency plots. More

investigation has been also doing to detect internal short-circuit in transformer [6] - [9].In this paper the most common technique is used which splits the winding into a number of

identical lumped sections and then formulate and solve the circuit governing set of voltage and current

equations subject to the common boundary condition. One of these models is S-domain model. But themodel used in this paper is a distributed parameter S-domain model of a two winding single-phase

transformer include resistance, capacitive, and inductive parameters. In order to identify the location of

short-circuit in each side of winding, primary and secondary windings are gradually shorted in turn to

turn or turn to ground forms within different transformer working states such as external short circuit,open circuit and nominal load.

2. Principle of ModelAs it mentioned before, proposed model is built in high frequency analysis. So the proposed modelincludes not only the winding resistance and self inductance but also has ground capacitance, mutual

inductive and capacitive coupling between the two winding and the inter-turn capacitances within each

winding.Before starting introducing model some assumption should be noted:


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Detecting the Position of Winding Short Circuit Faults in Transformer Using

High Frequency Analysis 646

Winding are assumed uniformly distributed and operation is assumed in the linear region ofmagnetization curve.

The only mutual inductance considered, is between primary turn to the correspondingsecondary turn.

The models idea and basic computation of the model is taken from [5] and [10] but somethingshould be changed which will be explained in the rest.Fig.1 shows two-winding transformer in infinitesimal section.

Following notation of the elements is explained in Appendix A. Characteristics of a typical

two-winding transformer is explained in Appendix B.

Like other lumped section model by starting at location x and moving an infinitesimal distance

x toward the lower end of the winding v is verified by following equation.( , ) ( ) ( ) ( , )

( , ) ( ) ( ) ( , )

p p m p

s m s s

V x s Z s x Z s x I x s

V x s Z s x Z s x I x s

=

(1)

Where ( , )pI x s and ( , )sI x s are the current following in pZ and sZ respectively. By dividing

current by x and applying the limits 0x we obtain

[ ]

( , )( , )

( , )( , )

p

P

SS

dV x sI x sdx

ZI x sdV x s

dx

=

(2)

Which [Z] is2

1 1 2 2 2

2

2 2 1 1 1

2

1 1 2 2 1 2 1 2 1 2

1

( ) 1

m m

m m

m

Z Z Y Z Z Y Z

H Z Z Z Y Z Z Y

H s Z Y Z Y Z Z Y Y Z YY

+

+

= + + +

(3)

Like above equations by writing current equation and dividing by x and applying the limits

0x we obtain:

[ ]

( , )

( , )

( , )( , )

p

P

SS

dI x s

V x sdxY

V x sdI x s

dx

=

(4)

Y=c( ) ( ) ( )

( ) ( ) ( )

gp m m

m gs m

Y s Y s Y s

Y s Y s Y s

+ +

(5)


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Figure 1: Infinitesimal section of a two-winding transformer

By combining (2) and (4)

[ ][ ][ ]2

2

( , )( ) ( ) ( , )

d V x sZ s Y s V x s

dx

=

(6)

[ ][ ][ ]2

2

( , )( ) ( ) ( , )

d I x sY s Z s I x s

dx

=

(7)

By using the theory of long line [11] the solution of above equation is achievable.

In solving the equation by this theory at first the varieties should be changed to modal one then

by diagonalizing and other process voltage versus current would be obtained.[ ][ ]mod phase V V T V =

(8)

[ ][ ]mo d phase I I T I = (9)

The element of [ ]modV , [ ]modI are the comp-onents of the mode of propagation where [ ]VT and

[ ]IT are 2 2 matrices which diagonalize [ ] [ ]Z Y and [ ] [ ]Y Z respectively. is a 2 2 diagonal matrix

which obtained by

[ ] [ ][ ]mod modZ Y = (10)

Where

[ ] [ ] [ ][ ]1 modmodmod

00

pv i

s

zZ T Z T z

= =

(11)

[ ] [ ] [ ][ ]1 mod

mod

mod

0

0

p

i v

s

yY T Y T

y

= =

(12)

After some process [5] ,sp ssV V will be yielded i.e. voltage of top terminal in primary and

secondary respectively.


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[ ]

mod

mod

sinh0

cosh

sinh0

cosh

c p p

pSp

v

Ssc s s

s

z

VT

V z

=

[ ]T Sp

v

Ss

IT

I

(13)

Where:

modmod

mod

c

zz

y=

(14)

This can be written in more compact form as:

11 12

21 22

( ) ( )( ) ( )

( ) ( )( ) ( )

Sp Sp

Ss Ss

V s I sM s M s

V s I sM s M s

=

(15)

where ( )ijM s can be gained from (13).

For achieving frequency characteristics of the transformer we set s= j in the related equationsThe input impedance can be given by

( )( )

( )

Sp

in

Sp

V jZ j

I j

=

(16)

By using (15) and (16) we obtain

11( ) ( )in Z j M j = (17)

Also by having short-circuit in secondary terminal we obtain

12 2111

22

( ) ( )( ) ( )

( )

in

M j M j Z j M j

M j

=

(18)

By using above equations we estimate most kind of internal short-circuit in the next part.

3. Simulstion and DisscussionThe main part of the paper is to investigate different aspect of short-circuit.

The first one is to consider condition of the output which can be short-circuit, open-circuit or innominal load. In each kind of these states, frequency response of input impedance is different [5].

Second state is to assume that, winding become variably shorted (form 0% up to 100%).This

state can be in primary or secondary that cause variation in input impedance. From 0% bypass betweenwinding (healthy state) to 100% (complete short-circuit) in a typical transformer will be recognized in

this part. The next state is to recognize the input impedance in a very critical frequency that showsposition or percentage of short-circuit in windings. Therefore many kind of aspect are going to use to

identify internal short circuit that is simulated by MATLAB software and the result will be representedby essential explanation. In order to perfectly analyze states, these states are categorized below.

Categorization is in basis of output consideration. Each of different states is explained below in

details. There are two type curves in all types.The first is by considering variation of short-circuit percentage of winding in (input reactance-

frequency) curve.

The second one is by considering a critical frequency in the curve of (input reactance-percentage of short circuit).


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3.1. Open Circuit Output Terminal

Type A: Assuming that external short-circuit is in secondary terminal, variation percentage of winding

short circuit cause changes in secondary elements and mutual one so input reactance changes that isshown in Fig.2. In this figure by increasing percentage of short-circuit in secondary winding the curve

shifts to right. As it is computed first resonance is between 20 and 40 KHz and the second one is

between 70 and 80 KHz. In order to recognize the percentage of short-circuit, the amount of input

impedance of first resonant is helpful although other resonant are helpful too but they are complex insome type of these six type.

Figure 2: Input reactance of transformer in primary versus frequency by increasing percentage of short-circuit

in secondary winding from left to right

Reason of increase the input reactance in this type is that by increasing percentage of short-circuit, [Y] increases and [Z] decreases but the rate of changes in [Y] is more than [Z] and the changes

in sinh p and cosh p is approximately the same so M11 (13),(15)decreases therefore input

impedance decreases by increasing the percentage of short-circuit in secondary. Justification of other

five types is in the same way.As it is mentioned before another way of investigating the position or percentage of partial

short-circuit in Type A is by considering a critical frequency like a frequency around first resonant

frequency in the curve of (input reactance-percentage of short-circuit).we decided 25KHz and thefigure is shown in Fig.3.

As it is explained before by increasing percentage of internal short-circuit in secondary

winding, input reactance decreases. To clarify the purpose we can see in Fig.3 that for example input

reactance in 20% short-circuit of secondary is 40.75 10 and in 30% is 40.5 10 .Type B: Second type of the first state investigates the internal short-circuit in primary winding whichcause changes in primary elements and mutual one. So input reactance changes that are shown in Fig.4.


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Figure 3: Input reactance of transformer in primary versus percentage of short-circuit in secondary winding

in 25 KHz.

Figure 4: Input reactance of transformer in primary versus frequency by increasing percentage of short-circuit

in primary winding from left to right.

As it is shown in this type by increasing percentage of short-circuit in primary, input reactance

increases in contrary with Type A but shifting to right is as the same by the first type. Analysis of

second resonant frequency is useless in this type because it is too complicated.The second way of recognition is also used for investigating Type B similar with Type A. The

figure is shown in Fig.5.


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Figure 5: Input reactance of transformer in primary versus percentage of short-circuit in primary winding in

25KHz.(in open-circuit output terminal)

As it seems this figure is the same as Type A but amount of input reactance is less in Type B.

3.2. Short-Circuit Output Terminal

Considering short-circuit output terminal is a verified event in power system so our investigation

should be tested in this state.

Type A: Like Type A in the first state we consider partial short-circuit in secondary winding but herein shorted output terminal. Fig.6 indicates movement of curve because of increasing percentage of

short-circuit in secondary winding. The note of this type is that shifting the curve is in contrary with

the first state and is from right to left. The increase of input reactance in this type is irregular in higher

percentage of short-circuit.Second way of identification like other type is used here and indicated in Fig.7 which is more

simple and clear than the first one in most situations.

The frequency which is chosen here is 36 KHz. It is interesting to know that in 17% the inputimpedance is enormously high which is because of resonance in this percentage. As it is shown in

Fig.6 and Fig.7 by increasing percentage of short-circuit the state of transformer incline to the output

situation.


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Figure 6: Input reactance of primary versus frequency. By increasing percentage of short-circuit in secondary

winding, curve shifts from right to left (compare with [5]).

Figure 7: Input reactance of transformer in primary versus percentage of short-circuit in secondary winding

in 36KHz. (in short-circuit output terminal)

Type B: Partial short-circuit in primary winding in shorted output terminal is investigated in this type.Fig.8 represents result of this situation.

By increasing percentage of short-circuit the input reactance decreases and the resonant wouldhappen in farther frequency.100% short-circuit is a straight line.

The second resonant frequency of two percentages (0%, 20% left to right respectively) of short-

circuit is for pattern indicated in this figure.For analyzing all percentages the second way (constant frequency) is preferable. Fig.9 shows

percentage of partial internal short-circuit in primary winding.


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Figure 8: Input reactance of primary versus frequency. Increase percentage of short-circuit in primary

winding cause the input reactance to decrease. Frequency varies from 30KHz up to 90KHz.

Figure 9: Input reactance of transformer in primary versus percentage of short-circuit in primary winding in

40KHz. (in short-circuit output terminal)

Present investigation is to some extent useless in this type that in some percentage there are thesame input reactance like in 10% and 42% which the input reactance is 2208 and 2211 respectively.

The reason is existence of second resonant frequency. The second resonant frequency of 10% is near tothe first one of 42% so they overlap each other.

Distinction between short-circuit in secondary and primary is obvious by comparison betweenFig.7 and Fig.9. Diagnosis is very easy by having these two figures.

3. 3. Nominal Load Output Terminal

This state is the normal and common state of transformer so it should be analyzed more. For betterillustration new type of curve is used although last type of curve could be useful too.

Type A: Like 3-1 and 3-2 the secondary winding is partially shorted in Type A. By increasing

percentage of short-circuit, changes of input reactance isnt regular and monotonous so it's useless.


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Figure 12: The input reactance versus input resistance.Blue curve is for 0% short-circuit in secondary winding

red is for 20% and green is for 40%. The bigest curve is for the first resonant.

As it is shown in this figure by increasing percentage of short-circuit, reactance versus

resistance decrease (XR

) so phase of impedance ( arctan( )XR

= ) decreases too.

Type B: In this type considering partial short-circuit in primary winding is proposed which is

indicated in Fig.13.Both Fig.13 and 14 show that by increasing percentage of short-circuit in primary phase of

input impedance increases which is against Type A in this state (3-3). The reason is rising input

reactance versus resistance by increasing percentage of short-circuit in primary.

Figure 13: Phase of the input impedance versus frequency. By increasing percentage of short-circuit in

primary winding degree of the phase move up.

Figure 14: Phase of input impedance of transformer in primary versus percentage of short-circuit in primary

winding in 42KHz. (in nominal output terminal).


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By considering Fig11 and 14, comparison between primary and secondary winding is easy

because the changes of phase in these two types are against each other.

4. ConclusionA distributed-parameter s-domain model for frequency analysis of a two-winding single phasetransformer has been used for studying the behavior of internal short-circuit. By dividing states of

output terminal into three states and types of internal short-circuit into six type (two type in each state)

comparison between them has been recognized indeed.Conclusion of each state expressed completely in their part. Summary of this conclusion is

expressed below.

In open circuit output terminal, internal short-circuit in secondary and primary winding could be recognized in a critical frequency, in which input reactance in primary winding internalshort-circuit is less than secondary winding internal short-circuit.

In short-circuit output terminal, similar input reactance index is used which in secondarywinding internal short-circuit, input reactance is negative in most percentages.

In nominal output terminal, index of comparison between internal short circuit in secondary andprimary is changed for better recognition. If internal short-circuit in secondary winding occurs,

phase of input reactance will decrease by increasing percentage of short-circuit but if internalshort-circuit in primary winding occurs, phase of input reactance will increase by increasing

percentage of short-circuit.

Although the investigation has been on two-winding single-phase transformer but this methodis also useful for three-phase transformer and can be extended in this type of transformer.


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References[1] S.V. Kulkarni and S.A. Kharpade, "Transformer Engineering Design and Practice", Marcel

Dekker Inc., New York, 2004.

[2] S. Nandi D. Nandy, Deputy Chief Engineer, Substations Division, CESC Ltd., Kolkata,India.[3] A.C. Franklin and D.P. Franklin, "The J&P Transformer Book," 13th edition, Butterworths,

London, 2007.

[4] A.K. Sawhney, "A Course in Electrical Machine Design," 5th edition, Dhanpat Rai and co.New Delhi, 1984.

[5] A. S. AlFuhaid, Frequency Characteristics of Single-Phase Two-Winding Transformers UsingDistributed-Parameter Modeling, IEEE Trans. Power Delivery, Vol. 16, No. 4, Oct. 2001, pp

637-642.

[6] K. G. N. B. Abeywickrama1, Alexander D. Podoltsev2, Yuriy V. Serdyuk1, Stanislaw M.Gubanski1 Computation of Parameters of Power Transformer Windings for Use in FrequencyResponse Analysis, IEEE Trans. Magnetics, Vol. 43, No. 5, May 2007.

[7] E.P. Dick, and C.C. Erven, Transformer Diagnostic Testing by Frequency ResponseAnalysis, IEEE Trans. on Power Apparatus and Systems, Vol. PAS-97, No. 6, Nov 1978 pp2144-2153.

[8] C.Gonzlez, J.Pleite, J.Vzquez, Transformer Diagnosis Approach using Frequency ResponseAnalysis Method, IEEE Industrial Electronics, IECON 2006 - 32nd Annual Conference on.Nov. 2006 pp. 2465-2470

[9] A. Elhaffar, M. Lehtonen. High Frequency Current Transformer Modeling for TravelingWaves Detection, Power Engineering Society General Meeting, Jun 2007 pp.1-6 IEEE.

[10] J. P. Bickford, N. Mullineus, and J. R. Reed, Computation of Power System Transients: PeterPeregrinus Ltd., 1976, pp. 4662.

[11] Jos Arrillaga,Bruce. C.Smith, Power system harmonic analysis, J.Wiely & Sons, 2001

Appendix AList of symbols.

( , )iV x s -The s-domain winding voltage at locationx .( , )

iI x s -The s-domain winding current at locationx .

iR -The winding (copper) resistance per unit length.

CiR -The core (iron) equivalent resistance per unit length.

iL -The leakage self inductance per unit length.

iC -The winding self capacitance per unit length.

giC -The winding capacitance to ground per unit length.

mL -The mutual inductance between the primary and secondary windings per unit length.

mC -The mutual capacitance between the primary and secondary windings per unitlength.

x l= -The top end of the winding.0x = -The lower end of the winding (ground terminal).,i p s= -Subscripts denoting the two windings.


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The parameters of Transformer are

( )i i i Z s R sL= + ( )m m Z s sL=

( ) 1 p cp pY s R sC = + ( )

m mY s sC =

( )gi si

Y s sC =

( )s s

Y s sC =

Appendix BCharacteristics of a typical distribution two-winding single-phase transformer:

Parameter Amount Parameter Amount

S 15MVA cpR 130k

spV 34.5 kV pL 7.375mH

ssV 13.8 kV sL 1.18mH

f 50Hz sR 0.0352

pR 0.22 gpC 9nF

gsC 27nF pC 0.09nF

sC 0.27nF mL 2.8mH

mC 148pF

Detecting the Position of Winding Short Circuit Faults in-ejsr_23!4!14

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