POWER TRANSFORMER MODEL FOR … · Web viewFrequency dependent transformer model may be able to represent Calculation of Skin effect of transformer winding Fig. 1 Plot for impedance

JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRICAL ENGINEERING

POWER TRANSFORMER MODEL FOR COMPUTATION OF WINDING LOSSES AT HIGH

FREQUENCIESD.S.TAKBHOURE 1, DR. N.D.GHAWGHAWE 2

1 MTech (EPS) student of Electrical Engineering at Govt. College of Engg Amravati2Associate. Prof. Electrical Engg. Dept, G.C.O.E.Amravati, Maharashtra State, India.

[email protected], [email protected]: During services the terminal of a transformer are subjected to a great variety of transient voltage wave shapes. Each of these transients affects the voltages at different locations inside the transformer. Some of them result in insulation failures. These failures are undesirable and costly events which affect the utility systems reliability. As such, they are of concern for utilities and transformer manufactures. For this reason, when building large power transformers, the design of the internal insulation structure is of considerable importance. Designing a cost effective and reliable insulation structure requires knowledge of the internal voltage distribution, the maximum voltage stresses and the times and duration of their occurrence.Engineers have extensively used detailed transformer models as an important tool in the design of the internal insulation structure of large power transformers. The behavior of large power transformer under transient conditions is of interest to both transformer designers and power engineers. The power engineer not only needs the models of transformer but also needs system in order to investigate the effects of power system transients. Key Words: Skin Effect. Proximity Effect, Inductance Calculation, Insulation Model, Transients

I. INTRODUCTION:Transient response is a result of the flow of energy between the distributed electrostatic and electromagnetic characteristics of the device. For all practical transformer winding structures, this interaction is quite complex and can only be realistically investigated by constructing a detailed lumped-parameter model of winding structure.Purpose of project: During the beginning of the 90’s the inability of existing models to represent the transformer under a wide range transient phenomena motivated researchers to look for faster, non-linear and lossy-models. Target of project is to develop transformer models satisfying utilities and manufacturers requirements and to represent the lossy nature of electromagnetic phenomena experienced by a transformer under transient conditions. The losses due to eddy currents in the core, skin and proximity effects on the winding conductors as well as dielectric losses in the transformer insulation structure has to be include in project.Methodology: the major activities used for this project Study of frequency dependent elements of transformerFrequency dependent transformer model may be able to represent1. Calculation of Skin effect of transformer winding

101

102

103

0

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Impe

danc

e du

e to

Ski

n E

ffect

in tr

ansf

omrm

er w

indi

ng, Z

skin

in O

hms

Frequemcy in Heartz

Plot Impedance due to Skin Effect w.r.t Frequency

Fig. 1 Plot for impedance due to skin with respect to increasing frequency

2. Calculation of Proximity effect of transformer winding.

The flux is calculated by computing the mutual inductance between the current carrying conductor and the filaments A, B, C and D. This results in the calculation of four mutual inductances: , , and . The flux cutting each conductor's face can be calculated by taking the difference between the mutual inductances as follows: for the inner face

ISSN: 0975 – 6736| NOV 10 TO OCT 11 | VOLUME – 01, ISSUE - 02 Page 38

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, the outer face , the top face , and the bottom face . These

differences will represent the flux lines entering or leaving each of the four faces. It was difficult to determine, by using the sign of the inductance differences, when the flux limes were entering or leaving a face. Therefore, in order to calculate the total flux cutting the open conductor the absolute value of each difference was taken. Then, based on the fact that the sum of the total number of flux lines leaving and entering a volume adds to zero, was expressed as follows.

Fig 2: Equivalent representation of two conductors.

3. calculation of Eddy current losses in core.

Where = Core length, m= Thickness of lamination=Conductivity of lamination material.= Permeability of free space

= Number of turns of the coil=Total cross sectional area of laminations.=Frequency in rad/sec

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Cor

e Im

peda

nce

of tr

ansf

omrm

er w

indi

ng, Z

core

Frequemcy in Heartz

Plot Core Impedance w.r.t Frequency

Fig .3 plot for core impedance of transformer winding with respect to increasing frequency

4. Calculation of Insulation losses5. The effect of frequency on the mutual coupling between winding section

Modeling frequency dependent elements in time domain

Developing 1. Lossy insulation model, 2.

Lossy winding model, 3. Lossy core model, 4. Inductance model

Assembling complete model

The lossy transformer model then verified using available experimental data for different transformers.

MATLAB programming is used to represent set of equations of lossy transformer.

Inductance ModelThe inductance of a group of turns can be divided in three components: and air core inductance, iron core leakage inductance and iron core magnetization inductance. The air core inductance represents the total inductance when the core is absent. The iron core leakage inductances represent the flux linkages having a path wholly or partially in air. They takes into account the change produced by the presence of the core on the flux in the air. The iron core magnetizing inductance represents the flux linking all the turns of the winding having a path totally inside the core.

Fig.4; Winding lumped parameter model

= Total number of turns in section i and j



= Relative reluctivity= Core length, m= Outer radius of coil section i and j, m= Outer radius of coil section i and j, m= Height of coil section i and j, m= Permeability of free space.= Core radius.

= Modified Bessel function of first kind.

= Modified Bessel function of second kind.

= Lanczos sigma factor.

Fig 5:Winding geometry

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1.5

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4.5x 10

-9

prox

imity

IND

UC

TAN

CE

of t

rans

fom

rmer

win

ding

, Lpr

ox

Frequemcy in Heartz

Plot for INDUCTANCE due to proximity effect w.r.t Frequency

Fig 6: Plot for inductance due to proximity effect w.r.t frequency

10-1

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prox

imity

impe

danc

e of

tran

sfom

rmer

win

ding

, Zpr

ox

Frequemcy in Heartz

Plot for Impedance due to proximity effect w.r.t Frequency

Fig 7: Plot for impedance due to proximity effect w.r.t frequency

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.221.5

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-9

prox

imity

indu

ctan

ce o

f tra

nsfo

mrm

er w

indi

ng, L

prox

DISTANCE BETWEEN CENTERS IN mm

Plot for INDUCTANCE due to proximity effect w.r.t DISTANCE BETWEEN CENTERS OF COIL SECTION

Fig 8: Plot for Inductance due to proximity effect w.r.t. Distance between centers of coil section

Winding losses:The most challenging phenomena to model in a transformer is the magnetic flux interaction involving the different winding sections and the core. Historically, this phenomenon has been modeled by dividing the flux in two main components: the common and leakage flux. Developing a transformer model capable of representing the magnetic flux behavior inside a real transformer for a wide range of different circumstances is a challenging task. In this paper the damping effect of the losses associated to leakage flux components is studied.



Fig.9 Algorithm to calculate inductance due to proximity effect.

Capacitance ModelThe inter turn capacitance and capacitance

between sections are calculated based on the type of winding used in the transformer being studied. In the existing program this can be done for the following winding types: layers, discs, helical. The capacitance is an equivalent energy storing capacitance for the section of interest and as such is completely general.

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1.48

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to T

urn

capa

cita

nce

Frequency

Frequency dependent Turn to Turn Capacitance

Fig 10: Plot for Turn to turn capacitance w.r.t. frequency

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k to

Dis

k ca

paci

tanc

e

Frequency

Frequency dependent Disk to Disk Capacitance

Fig 11: Plot for disk to disk capacitance w.r.t. frequency

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1.165

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1.195x 10

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ies

capa

cita

nce

Frequency

Frequency dependent Series Capacitance

Fig 12: Plot for Series capacitance w.r.t. frequency

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-13

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und

capa

cita

nce

Frequency

Frequency dependent Ground Capacitance

Fig 13: Plot for ground capacitance w.r.t. frequency

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5x 10

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Win

ding

to W

indi

ng c

apac

itanc

e

Frequency

Frequency dependent Inner Winding to Core Capacitance

Fig 14: Plot for Winding to winding capacitance w.r.t. frequency



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35D

iele

ctric

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ses

due

to s

erie

s an

d sh

unt c

apac

itanc

es

Frequency

Fig 15: Plot for dielectric losses due to series and shunt capacitance w.r.t. frequency

Fig 16: Complete Transformer model

Discussion Frequency dependent Lossy-transformer model to calculate the internal transformer voltage response of large power transformer has been presented in this paper. This model was developed using a starting point, a lossless lumped parameter transformer model based on the calculation of the unconnected inductance matrix. The damping effect of losses due to the skin and proximity effect on the winding’s conductors, the eddy current in the core and the dielectric losses in the transformer’s insulations structure were represented in this model. To construct the model, it was necessary to obtain the characteristics of each damping mechanism as function of frequency. For this purpose analytical formulas were used to represent the electromagnetic phenomena involving eddy currents. The frequency characteristics of the insulation losses were modeled by combining an equivalent parallel plate capacitor representation and empirical data in the form of the dielectric material properties. The frequency characteristics were approximated using rational polynomial forms in the s-plane. The bilinear transformation and the properties of the z-transformer were applied to obtain the network nodal system of equations in the time domain. The

representation of the damping effect of losses in the internal transient voltage response of large power transform was achieved by replacing the component of the winding losses lumped parameters model with frequency-dependent element. REFERENCES [1] M. Gutierrez, R.C. Degeneff, P.J. McKenny a d J.M. Schneider, "Linear, lumped parameter transformer model reduction technique," IEEE paper no. 93 SM 394-7 PWRD.[2] R.C. Degeneff, M. Gutierrez and M. Vakilian, "Lumped parameter transformer model reduction technique," IEEE paper no. 94 SM 409-9 PWRD.[3] F. de Leon and A. Semlyen, "Complete transformer model for electromagnetic trmients," IEEE Transactions on Power Delivery, vol. 9, no. 1, pp. 231-239, January 1994. [4] V.I. Kogan, J.A. Fleeman, J.H. Provanzana, D.A. Yanucci and W.N. Kennedy, "Failure analysis of EHV transformers," IEEE transactions on Power Delivery, pp. 672-683, April 1988.[5] P.I. Fergestad and T. Henriksen, “Transient oscillations in multi winding transformers," lEEE Transactions on PAS, vol. PAS93, pp. 500-507, 1974.[6] W.N. White, "An examination of core steel eddy current reaction effect on transformer transient oscillatory phenomena," General Electric Technical Information Series, TIS 77PTD012, April 1977.[7] W.N. White, “Inductance models of power transformers," General Electric Technical Information Series, TIS 78PTD003, April 1978.[8] R.C. Degeneff, "A general method for determining resonances in transformer windings," IEEE transactions on PAS, vol. 96, no. 2, pp. 423-430, March/April 1977. [9] R.C. Degeneff, W. Neugebaur, J. Panek, M.E. McCallum and C.C. Honey, "Transformer response to system switching voltages," IEEE transactions on Power Apparatus and Systems, vol. Pas-101, no. 6, pp. 1457-1465, June 1982.[10] D. J. Wilcox, M. Conlon and W.G. Hurley, "Calculation of self and mutual impedances for coils on ferromagnetic cores," IEE Proceedings, vol. 135, Pt . A, no. 7, pp. 470-476, September 1988.[11] D.J. Wilcox, W.G. Hurley and M. Conion, "Calculation of self and mutual impedances between sections of transformer windings," IEE Proceedings, vol. 136, Pt. C, no. 5, pp. 308-314, September 1989.[12] F. de Leon and A. Semlyen, "Detailed modeling of eddy current effects for transformer transients," IEEE transactions on Power Delivery, vol. 9, no. 2, pp. 1143-1160, April 1994.[13] T. Henricksen, “Including high order rational functions in EMTP: A comparison between alternative methods with emphasis on accuracy," IEEE Transactions on Power Delivery, vol. 12, no. 1, pp. 1143-1150, January 1997.



[14] R. Bartnikas, "Dielectric loss in insulating liquids," IEEE Transactions on Electrical Insulation, vol. EI-2, no. 1, pp. 33-54, 1967.[15] R. Bartnikas, "Dielectric losses in solid-liquid insulating systems," IEEE Transactions on Electrical Insulation, vol. EI-5, no. 4, pp. 113-121, 1970.[16] M.J. Jeroense and F.H. Kreuger, "Electrical conduction in HVDC mass-impregnated paper cable," IEEE Transactions on Dielectric and Electrical insulation, vol. 2, no. 5, pp. 718-723, October 1995.[17] F. De Leon and A. Semlyen, "Efficient calculation of elementary parameters of transformers," IEEE Transaction on Power Delivery, vol. 7, no. 1, pp. 376-382, January 1992.[18] S.V. Kulkarni and S.A. Khaperde “Transformer Engineering, Design and Practice,” Marcel Dekker, Inc, New York, Bsel 1972.[19] Richard L. Bean, et al “Transformer for the Electric Power Industry” McGraw Hill Book Company, Inc, New York Toronto London 1959


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POWER TRANSFORMER MODEL FOR … · Web viewFrequency dependent transformer model may be able to represent Calculation of Skin effect of transformer winding Fig. 1 Plot for impedance