Modeling and Simulation of Transformer Winding

1st International Conference on Modelling and Simulations (ICOMOS) VIRTUAL FORUM July 12th-26th, 2010

Modeling and Simulation of Transformer Winding Fault Using MATLAB/SIMULINK M. Yazdani-Asrami1, E. Samadaei1, S. Darvishi2, M. Taghipour3 Abstract – For each transformer, windings and insulations are the most important elements economically and technically, so highly protection should be considered for them. The main fault that occurs in a transformer is internal short circuit through the winding, which may lead to serious damage in winding on transformer including winding deformation, interruption or even the explosion of the transformer because of oil's overheating. Consequently, winding need to be frequently checked to avoid major damages. In this paper, a new method for modeling and simulation of transformer’s winding fault has been presented. According to happened variation in line current and evaluation of its symmetrical component (positive, negative and zero sequences), easy and precise algorithm has been obtained that can be used for simulation of internal fault of transformer’s winding. The algorithm has been implemented for winding faults and has been simulated by MATLAB/SIMULINK software. Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved.

Keywords: MATLAB/SIMULINK Software, Modeling, Short Circuit, Simulation, Symmetrical Component, Transformer, Winding Fault

I.

Fault detection studies require a capable and accurate transformer model. Different transformer models for such purposes have been presented. A distributedparameter Laplace-domain model for frequency analysis of a two-winding single-phase transformer has been presented [1]. 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 [2-4]. J. Faiz [5] utilized the same approach and also investigated normalized flux density along the winding. He also discriminate short-circuit and inrush current using finite element analysis. In [6] analysis of transformer performance under internal short-circuit is considered. It is demonstrated the deviation of axial and redial forces during short-circuit in windings. N. Y. Abed [7] employed discrete wavelet transform through with FEA in modeling and characterizing the internal faults. This survey is investigated in time-domain. In this paper, an easy model and algorithm has been presented and simulated in MATLAB/SIMULINK that, based on this algorithm, current variation due to internal fault of winding has been evaluated. One of the different kinds of faults is light fault and it is related to electrical part. But, the other fault is severe fault that it is related to magnetic part of transformer.

Introduction

In recent decades, reliability is an inevitable part of power system studies and operation, due to significant increase in the number of industrial electrical consumers. Power transformer is one of the major and critical elements in power system in the area of reliability issue, since their outage may result in costly and timeconsuming repair and replacement. Transformers are threatening from internal and external fault and ultimately they are damaged. Among different faults, effects of extra voltages on transformers can be mentioned and those can impose extra electrical stresses on insulations. In addition, thermal stresses due to different kinds of losses and ambient temperature of setup place and also, mechanical and environmental stresses can cause aging in transformer. Increase of voltage gradient and besides, thermal stress can cause partial discharge in paper or oil of transformer. Under effect of this phenomenon and extension of it, may occur short circuits between windings to each other or turn to turn fault and even between phases to earth. Therefore, according to expressed cases, in order to avoid outage of transformer from network, protection of this equipment during its lifetime is necessary. So, utilization of proper protective system along with efficient algorithm that could detect small fault such as short circuits of winding or turn to turn fault seems essential.

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M. Yazdani-Asrami, E. Samadaei, S. Darvishi, M. Taghipour

II.

Transformer’s Current Under Different Internal Faults

e

One of the major concerns for utilities and manufacturers is failure of transformers due to external or internal short-circuits. Investigations show that about 70 percent of transformers 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. Since, one of the fault detection approaches of windings in transformer is evaluation of amplitude and/or waveform of current and voltage of the two sides of transformers. Therefore, it is necessary to make a study of effect of fault intensity on mentioned parameters. In order to this purpose, effect of light and severe fault on increase of current value in transformers is modeled and analyzed. II.1.

I 0 ,P

I b 2 ,p

I 0 ,p

0

I c1, p

In above equations,

I c 2 ,p Ib,p and

I 0 ,P

0

Ic 2 ,p

2

N F I RF

I0 ,P

N1 I a,p

Ib 2 ,p

(4)

(7)

(8)

written as: I a1, p

I a 2 ,p

I 0, p

1 NF I RF 3 N1

(9)

So, the value of increase of current in line can be easily calculated as follow: I A1,p

I A 2 ,p

(2)

(3)

(6 )

In above equation, N1 is the number of winding's turn of primary side and NF is the number of damaged winding’s turns. According to equations (7) and (8), I a1,P could be

I B,p

I c ,p are variations of

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I a 2 ,P

(1)

Ib1, p

I b 2 ,p

Now, if light fault occurs, the magnetizing force based on the value of pass current via resistance of fault (IRF) (the pass current through short circuit part or turns of winding) will be added to equivalent circuit of system. This case has been shown in Fig. 1. On the other hand, ampere-turn of short circuit turns is equal to total ampere-turn of winding as follow:

current of phase-b and phase-c in primary side of studied transformer, respectively; that according to above cases, in light fault its value is equal to zero. Index-p shows expected quantity in primary side of transformer. In above equations, indexes 0, 1 and 2 are related to zero, positive and negative sequence of currents, respectively. On the other hand: Ic1, p

2

I b1,p

I a1,P

I A,p I c ,p

1

Also, according to above equations, the components of positive, negative and zero sequence of current variations (incremental value of current) will be equal to each other. As follow:

In order to study turn to turn fault, difference of currents before and after fault should be calculated and by use of them, the rate of current increase can be determined. For simplicity, a transformer with D/Y connection has been supposed, so that, winding of phasea in primary side be faulty. This fault causes sudden increase of current and changing in symmetrical sequence components of line current and this case could be due to effect of being unbalanced in transformer's parameters. Since in this condition, fault is light kind and transformer has the large number of turn of healthy winding, as a result, these kinds of faults could not make noticeable change in coupling. In other words, variations in current of phase-a and phase-b winding will not take place. So, variations in current of winding of phase-b and phase-c are equal to zero and as a result: I b1, p

(5 )

According to variations of phase-b current in positive, negative and zero sequences due to fault in phase-a, I0,P could be written as:

Modeling of Turn to Turn Light Faults

I b,p

j2 3

I C ,p

0 NF I RF N1

NF I RF N1

(10) (11) (12)

In above equations, the A, B and C indexes are related to currents of line in primary side of studied transformer. It is mentionable that zero sequence current is not transferred to line and it is vanished in winding of D connection side of transformer.

1st International Conference on Modelling and Simulations (ICOMOS)

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M. Yazdani-Asrami, E. Samadaei, S. Darvishi, M. Taghipour

winding of transformer is created due to flux reduction in core. As a result, these equivalent variations of current in winding of secondary side are equal to: I b,s

Ic ,s

(16)

where, value of increase current can be related to value of pass current through damaged winding by using following equation: Fig. 1. Illustration of turn to turn fault in transformer winding

Therefore, value of increase of current in line is as follow: I A1,P

I A 2 ,P

3 I a1,p e

3 I a 2, p e

j 6

3 NF I RF e 6 3 N1

j 6

3 NF I RF e 3 N1

(13)

I a1,s (14)

K s Va,p

(17)

(18)

I a 2 ,p 2

I b1,p I c1, p

(19)

Ib 2 ,p

(20)

I c 2 ,p

(21)

Therefore, positive and negative sequences of referred line current in primary side are as follow:

(15)

I A1,P

3 I

a1,p e

I A2 ,P

3 I

a 2, p e

j 6

j 6

(22)

(23)

As a result, value of increase of line current for phasea in primary side of transformer is calculated as follow:

Modeling of Turn to Turn Severe Fault

The model in pervious section has a good precise at the light fault duration and in steady state, but in severe fault situation, in order to keep accuracy, this model should be changed slightly, because in light fault, noticeable change in coupling of windings is not created and voltage will be changed a little; as a result, line current in secondary side will change a little. In contrast, in severe fault, magnetic coupling is reduced. Then, voltage in winding of secondary side and load current of transformer will be changed, significantly. It is mentionable that because of reduction of coupling and value of flux, transferred power in damaged turns of winding is reduced. The gist important point is while load is not grounded, variation in current of secondary

Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved

I a 2 ,s

I a 2 ,s

I a1,p

where, KS is index of light fault and increase of its value is expressive of increase of value of fault. II.2.

I a1,s

Also, values of unbalanced current in secondary side of transformer are transferred to primary side by following equations:

In equations (13) and (14) can be obviously seen that variation of positive and negative sequence of line current in primary side of transformer is proportional to percentage of damaged turns of winding and value of pass current in resistance of fault [8]. According to above equations, the value of increase of transient current in fault state can be obtained from equation (9). Now, in order to determine intensity of light fault, coefficient KS can be defined by equation (15) that its value is ratio of terminal voltage of damaged turns of winding to current value of short circuit fault of winding (IRF). Therefore, value of IRF can be proportional to terminal voltage of winding: I RF

2

I a 2 ,s

In above equations, index s is corresponding to quantities of secondary side of studied transformer. So, using equations (17), (7) and also, according to zero sequence will not be created in star connection:

j

j 6

2

I a1,s

I A,p

3 Ia1,p

3 I´a1,s rt

(24)

where, rt is turn ratio of primary winding to secondary winding of transformer [8]. As respects above cases, secondary voltage related to damaged primary winding causes reduction of coupling in two secondary windings. As regards this issue, value of increase in negative sequence current in secondary side is in opposite direction of terminal voltage before fault. Now, as previous section, coefficient KC can be considered as coefficient of intensity of fault for severe

1st International Conference on Modelling and Simulations (ICOMOS)

70

M. Yazdani-Asrami, E. Samadaei, S. Darvishi, M. Taghipour

faults. In this equation, coefficient KC will be negative because of above mentioned reason: I a1,s

I a 2 ,s

K cVa,s

fabrication of three cores (three phases) of transformer, also short circuit in winding of transformer can cause increase of temperature around winding and as a result increase of its resistance. This issue can cause reducing zero sequence of current in severe fault. Therefore, negative sequence of current for recognizing and detecting fault of winding can be used only. According to above cases, in Fig. 2 can be observed, for resistance reduction of winding from 0.1 ohm (related to fault occurrences), effective value of fault current (IRF) has been increased extremely. In Fig. 3, variations of internal line current of studied transformer has been shown when winding of phase-a has short circuit fault. In this figure, resistance of phase-a in primary side of studied transformer has been considered about 0.03 ohm. As seen, currents of line A and C has increase and current of line B remains constant. Also, in Fig. 6, effective value of line currents has been shown. As seen in Fig. 4, variations of current in primary lines of studied transformer are coinciding with equations (10), (11) and (12). According to these figures in fault duration, current in the one of lines (line B) has not been changed but other line currents are similar to pass current through fault resistance. It should be said that these two currents are flown in opposite direction.

(25)

The line current in secondary side of transformer is increased as follow: I a,s

I a1,s

Ia 2 ,s

2 K cVa,s

I b,s

K cVa,s

(27)

I c ,s

K cVa,s

(28)

(26)

As a result, by referring above currents to primary side, following results will be obtained: I A,p I B,p I C ,p

3K c Va,s rt

(29)

0

(30)

3K c Va ,s rt

(31)

TABLE TECHNICAL SPECIFICATIONS OF SIMULATED T RANSFORMER Parameters Values

It should be mentioned that, the Coefficients KC and KS are expressed as complex number that laboratory test and simulation have shown that their imaginary part usually is negligible [9].

380 380

Rated power (kVA)

15

Connection of windings (primary/secondary)

III. Simulation and Analysis of winding fault in MATLAB/SIMULINK In this section, in order to detect short circuit fault of winding, typical three-phase transformer with technical specifications tabulated in Table has been considered. Also, connected load to this transformer is balanced and ohmic. Now, assumed to be that short circuit has been occurred in primary side of studied transformer and in phase-a. Simulation has been done in MATLAB/SIMULINK software and effective value of current (IRF) has been shown in Fig. 2. According to equation (9), it can be said that line current (IRF) in short circuit part of winding is proportional to defected line current sequences. Among of these sequences, negative sequence of faulty line current has more similarity to short circuit current. On the other hand, in addition to fault current, positive sequence of line current will be changed because change of load, i.e. positive sequence of line current are related to load. Also, zero sequence current is flown in D connection in the form of eddy current because of difference of magnetic paths in different phases. On the other hand, partial unbalance can be taken place in Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved

Primary voltage (volt) Secondary voltage (volt)

/Y

Resistance of each phase in primary side and secondary side (ohm)

0.1

Inductance of each phases in primary side and secondary side (H)

0.09

Fig. 2. Effective value of fault current (IRF) for different faults in winding of phase-a in primary side

1st International Conference on Modelling and Simulations (ICOMOS)

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M. Yazdani-Asrami, E. Samadaei, S. Darvishi, M. Taghipour

Fig. 3(a). Currents of primary lines of studied transformer (before happening fault)

Fig. 4(b). Effective value of current of primary lines of studied transformer for happening fault in phase-a for R=0.03 (after happening fault)

Fig. 5. Increase values of current, similar to each other but in different direction in line A and C TABLE THE SIMULATION RESULTS

Fig. 3(b). Currents of primary lines of studied transformer for happening fault in phase-a for R=0.03 (after happening fault)

Percentage of short circuited winding (F%)

Percentage of short circuited winding by proposed algorithm

0.1

Winding is healthy

0.11%

0.098

2%

2.08%

0.087

13%

13.33%

0.084

16%

16.29%

0.077

23%

22.89%

0.073

27%

26.44%

0.070

30%

28.99%

0.067

33%

31.43%

In this transformer, the current enters into phase-a winding of transformer through line A and makes 30Nf degree lag angle shift ( I RF ), then for exiting this N1 current from transformer into line C with 30- degree lead

Fig. 4(a). Effective value of current of primary lines of studied transformer (before happening fault)

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Resistance of phase a winding (Ra)

1st International Conference on Modelling and Simulations (ICOMOS)

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M. Yazdani-Asrami, E. Samadaei, S. Darvishi, M. Taghipour

phase shift with respect to line C enters to this line Nf I RF ). In other words, this current enters into ( N1 winding of transformer with 30-degree lag phase shift in respect of line A and inters into line C with 30-degree Nf I RF ) and lead phase shift. As a result, statements ( N1 Nf ( I RF ) have 180-degree phase shift. Ultimately, N1 final values of currents in lines A and B will be similar to each other. This subject has been shown in Fig. 5 well. Similarly, that is exist in line C and A, will be happened just when load is unit power factor. If the load does not have unit power factor, a little shift in amplitude and angle of phases A and C will be happened. Also, effective value of line A is a little more than this parameter in line C, due to inductance feature of transformer, that it shifts power factor towards lag. In Table , the rate of short circuited winding has been calculated based on proposed algorithm in the form of turn number of short circuited winding to total windings. Also, calculated value by this algorithm has been compared to reduction of resistance of damaged phase winding (a).

IV.

Conclusion

In this paper by extracting phase current of typical transformer and analyzing symmetrical sequence component of phase and line currents, it is determined that the value of fault current is proportional to negative sequence of line current. Therefore, it has been determined and simulated according to mentioned equations, presented algorithm. The results of simulation have shown that if short circuit of winding takes place, then current of negative sequence in one of lines will be extremely increased. This case can be used as a criterion for fault detection problem; and according to supposed values in rate of resistance of one of the transformer's phases, percentage of estimation fault in short circuit of windings has been calculated by using presented algorithm that is expressive of proper precision of this algorithm.

Appendix Schematic diagram of the simulation model in MATLAB/SIMULINK has been shown in Fig. 6.

Fig. 6. Schematic diagram of the used model for simulation in MATLAB/SIMULINK software package [3]

References [1]

[2]

A. S. Al Fuhaid, Frequency Characteristics of Single-Phase TwoWinding Transformers Using Distributed-Parameter Modeling, IEEE Transactions on Power Delivery, Vol. 16, No. 4, October 2001, pp.637-642. K. G. N. B. Abeywickrama1, A. D. Podoltsev, Y. V. Serdyuk and S. M. Gubanski, Computation of Parameters of Power Transformer Windings for Use in Frequency Response Analysis, IEEE Transactions on Magnetics, Vol. 43, No. 5, May 2007.

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[4]

[5]

C. Gonzalez, J. Pleite, J. Vazquez, Transformer Diagnosis Approach using Frequency Response Analysis Method, IEEE 32nd Annual Conference on Industrial Electronics (IECON 2006), November 2006, pp. 2465-2470. M. R. Barzegaran and M. Mirzaie, Detecting the Position of Winding Short Circuit Faults in Transformer Using High Frequency Analysis, European Journal of Scientific Research, Vol. 23, No. 4, 2008, pp.645-659. J. Faiz, B. M. Ebrahimi, and T. Noori, “Three- and TwoDimensional Finite-Element Computation of Inrush Current and Short-Circuit Electromagnetic Forces on Windings of a Three-

1st International Conference on Modelling and Simulations (ICOMOS)

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M. Yazdani-Asrami, E. Samadaei, S. Darvishi, M. Taghipour

[6]

[7]

[8]

[9]

Phase Core-Type Power Transformer,” IEEE Transactions on Magnetics, vol. 44, no. 5, May. 2008, pp. 590-597. G. B. Kumbhar, and S. V. Kulkarni, “Analysis of Short-Circuit Performance of Split-Winding Transformer Using Coupled FieldCircuit Approach,” IEEE Transactions on Power Delivery, vol. 22, no. 2, Apr. 2007, pp. 936-943. N. Y. Abed, and O. A. Mohammed, “Modeling and Characterization of Transformers Internal Faults Using Finite Element and Discrete Wavelet Transforms,” IEEE Transactions on Magnetics, vol. 43, no. 4, Apr. 2007, pp. 1425-1428. G. Diaz, P. Arboleya and J. Gomez-Aleixandre, Analytical Approach to Internal Fault Simulation in Power Transformers Based on Fault-Related Incremental Currents, IEEE Transactions on Power Delivery, Vol.21, Issue.1, January 2006, pp.142-149. G. Diaz, J. Gomez-Aleixandre and P. Arboleya, Electromagnetic model of turn-to-turn short circuits in transformers, The International Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), Vol. 23, No. 2, 2004, pp. 562-575.

Emad Samadaei was born in ghaemshahr, Iran, in 1985. He received a B.Sc. degree in electrical engineering from University of Mazandaran, Babol, Iran in 2008 and He is presently pursuing the M.Sc. degree at the Babol University of Technology, Babol, IRAN. His research interests include power electronic, drive and electrical machines. Email: [email protected] Sajede Darvishi was born in ghaemshahr, Iran, in 1986. He received a B.Sc. degree in electrical engineering from University of Mazandaran, Babol, Iran in 2008 and He is presently pursuing the M.Sc. degree at the University of Semnan, Semnan, IRAN. Mehran Taghipour-Gorjikolaie was born in sari, IRAN, in 1986. He received a B.Sc. degree in electrical engineering from University of Mazandaran, Babol, IRAN in 2008 and He is presently pursuing the M.Sc. degree at the Birjand University, Birjand, IRAN. His research interests include modeling and simulating of power-electronic systems, electrical machines and artificial intelligence

Authors’ information 1

Department of Electrical and Computer Engineering, Babol University of Technology, Babol, IRAN. 2 Department of Electrical and Computer Engineering, University of Semnan, Semnan, IRAN. 3 Department of Electrical Engineering, University of Birjand, Birjand, IRAN.

algorithms. Email: [email protected]

Corresponding Author Email: [email protected] and [email protected] Phone and Fax: +98111-323 9214. Mohammad Yazdani-Asrami was born in sari, IRAN, in 1986. He received a B.Sc. degree in electrical engineering from University of Mazandaran, Babol, IRAN in 2008 and He is presently pursuing the M.Sc. degree at the Babol University of Technology, Babol, IRAN. His research interests include modeling and application of power and distribution transformers, insulation materials, computer aided calculation of electromagnetic fields, finite-element modeling of transformers and high voltage engineering. Email: [email protected]

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