DEPARTMENT OF ELECTRICAL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY MADRAS

DATA SHEET

Name : S. GopalaKrishna

Registration Number : EE05D008

Specialization : Measurements and Instrumentation

Category : Regular

Research Guide : Dr. V. Jayashankar

Joining Date : 3rd August 2005

Date of Registration : 3rd August 2005

Resident at the Institute : F-2/21

Date of First DC Meeting : 30-08-2006

Date of Second DC Meeting : 22-08-2007

Date of third DC Meeting : 20-8-2008

Comprehensive Exam : April 2006

Courses Completed

Course Name Course

No.

Category Sem-Year Grad

e

Power Converter

Analysis

EE586 Core Odd-2005 A

Instrumentation

Engineering

EE507 Core Odd-2005 S

Synthesis of Control

Systems

EE665 Elective Odd-2005 A

Introduction to DSP EE508 Elective Odd-2005 C

Research Methodology Id602 Compulsory Odd-2005 pass

Signature of Guide Signature of

Scholar

Date:

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1. Area of Research

Detection of winding deformation in power transformer

2. Objectives

1. To develop a method for online detection of winding deformation in

power transformers during short circuit test.

2. To estimate the forces during short circuit test using finite element

method and to establish a design margin for the short circuit withstand

capability at the laboratory stage.

3. Using FEM and mathematical analysis for reducing the number of short

time rating test in current transformers.

4. To develop methods to improve the sensitivity in the detection of

winding deformation.

3. Introduction

Short Circuit Test on a Power Transformer:

In power systems, transformer is one of the essential equipment and

failures of a large transformer can cause serious problems in electric utility

operation. The mechanical strength of the windings in a power transformer

can be assessed by a special test called short circuit test. The secondary of

the transformer is shorted and primary is excited with rated voltage. Short

circuit currents which are very large in magnitude interact with magnetic flux

in the conductors and results in strong electromagnetic forces. If the windings

do not have sufficient mechanical strength to withstand these forces, it

results in deformation of the windings.

These deformations can be detected by any of the following methods.

Reactance comparison method: If the reactance after the test deviates

from the reactance before the tests by more than 2%, the transformer

windings are subjected to deformation.

Frequency response analysis method (FRA): A sinusoidal voltage, swept

from few kilohertz to 1 MHz is applied as an excitation across transformer

terminals. Transfer function is computed by measuring the current response.

Plot of this transfer function versus frequency is known as the signature of

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the transformer. Failures are assessed by comparing the signatures of the

transformer before and after the test.

4. Work Done in Previous Years

Presented in the 2nd DC

1. Online methods for the detection of winding deformation using ratio

and phase error measurements, real and reactive power

measurements and impedance measurements were developed.

2. A transformer model with scaled dimensions was simulated so as to

give similar amount of forces as in large power transformer and

identify critical stress regions. The simulation was done by using a FEM

based software MAGNET.

Presented in the 3rd DC

1. Improvement in sensitivity of online method by optimization of the

high frequency signals which were superimposed on power frequency

excitation.

2. Issues related to design of a CT were analyzed by closed form

expressions. A configuration which was optimal for testing of a CT was

suggested. The mathematical analysis on filament conductors was

followed by finite element analysis of conductors of finite dimensions.

5. Present Work

The sensitivities of high frequency excitations and that of 50 Hz

sinusoidal excitation to the winding displacement are evaluated and

compared. Simulation studies are done on a benchmark winding which has

been extensively tested in the literature. Experimental work is carried out on

a single layer winding and 25 MVA, 110 kV/ 33 kV transformer.

5.1 Description of Coil and Model

In order to study the sensitivity of methods to identify deformation it

would be appropriate to consider a benchmark winding which has been

validated for other studies. We choose the coil proposed in [3] as it has a

uniform layer winding, its resonant frequencies are known and several

practical measurements are performed on it.

As is known the typical deformation that occur in windings [4] are axial

displacement, buckling and radial compression. Axial displacement generally

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occurs in the end of the winding whereas the inner winding compression and

the outer winding buckling occur near the centre of the winding. The same

winding is used to create all the effects. The benchmark winding was

modeled by lumped parameters using 10 and 20 sections in [3]. Here, the

same winding is considered for simulation and 10 sections model is chosen

for simplicity in calculations. The self and mutual inductances are

recalculated as per the dimensions given in [3], whereas the capacitances

and resistances are taken directly. The coil is grounded solidly and it consists

1794 turns of 0.0226 inch diameter copper wire with 0.00205 inch enamel

insulation, closely wound on a 23 inch diameter form, 48 inch in length. The

coil is shielded by an inner shield 22-11/16 inches in diameter and an outer

shield 25 inches in diameter. The 10 sections model shown in Fig. 1 has the

following values of the lumped parameters. Cg=8.5x10-10 F, CS=3.4x10-12 F,

Rg=2.1x1011 Ω, RS=1.65x105 Ω, rS=22.6 Ω. The values of self and mutual

inductances are calculated using the formulas and tables taken from [5] with

an accuracy of 1.2%. The calculated values of self and mutual inductances

are

L11=29.186 mH

M1-2=13.620 mH M1-3=6.228 mH M1-4=3.379 mH

M1-5=1.981 mH M1-6=1.243 mH M1-7=0.817 mH

M1-8=0.551 mH M1-9=0.405 mH M1-10=0.292 mH

Fig. 1 The 10 sections model of the single layer winding

5.2 Simulation of Winding Deformation

In order to compare the changes in the impedance to winding deformation at

power frequency and high frequencies, different cases of the deformations

are considered. To simplify the analysis, deformation is assumed to occur in

RS

Rg Cg

CS

L11 rS

RS

Rg Cg

CS

L11 rS

RS

CS

L11 rS

4

one section, without any mechanical effects on the other sections. Fig. 2(a)

shows the schematic of the coil without deformation.

Fig.2 (a) Coil without deformation (b) Axial displacement (c) Radial inward compression (d) Radial outward buckling

Case 1: Axial Displacement

The first section of the coil is deformed in axial direction, away from the other

sections of the coil as shown in Fig. 2(b). Series capacitance CS and mutual

inductances are predominantly affected by winding deformation. Capacitance

CS and mutual inductances are calculated for 11 different positions of the first

section situated at a distance of nΔL from the other sections. ΔL is the

incremental shift in the first section and n varies from 0 to 10. For ease of

understanding this distance is expressed as percentage of total length of the

coil. A one volt sinusoidal source is applied across the terminals of the coil

with frequency swept from 10 Hz to 100 kHz. The variation of the impedance

with frequency before deformation is shown in Fig. 3. The values of

resonance and anti-resonance frequencies are found to be similar to [3]. The

current variation with frequency before deformation is shown in Fig. 4. As the

first section of the coil is shifting away, the impedance varies differently at

different frequencies. The percentage variations of impedance at 50 Hz and

resonance frequencies are shown in Fig. 5 and Fig. 6, respectively. While the

percentage change of impedance at 50 Hz is nearly 1% for 4% displacement

in first

Core

Winding

First section

Fifthsection

(a) (b) (c) (d)

5

10 20 30 40 50 60 70 80 90 100-100

-80

-60

-40

-20

0

20

40

60

80

100

Frequency (kHz)

kilo

Ohm

sResistance

Reactance

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

Frequency (kHz)

mA

Fig. 3 Variation of impedance with frequency Fig. 4 Variation of input current with frequency

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

Winding displacement(%)

Z-C

hang

es (

%)

0 0.5 1 1.5 2 2.5 3 3.5 4-20

-10

0

10

20

30

40

50

60

70

80

Winding displacement(%)

Z-C

hang

es (

%)

RF-1RF-2RF-3RF-4RF-5RF-6RF-7RF-8

Fig. 5 Variation of impedance with winding displacement at 50 Hz

Fig. 6 Variation of impedance with winding axial displacement at different resonant frequencies

section, it is nearly 70% at first resonant frequency (7.37 kHz). All other

resonant frequencies also show substantial changes, which are above 10%.

This shows that the high frequency excitations are more sensitive to axial

displacement than the power frequency.

Case 2: Radial Compression

One of the sections of the coil gets compressed in radial direction as shown in

Fig. 2(c). The percentage changes in impedance at resonant frequencies

when fifth section is compressed are shown in Fig. 7. Here also the same

phenomenon can be observed that high frequencies are more sensitive than

the power frequency. The impedance at 50 Hz changed only by 0.3%, while

eight resonant frequency shows a change above 60% as shown in Fig. 7.

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0 0.5 1 1.5 2 2.5 3 3.5 4

0

10

20

30

40

50

60

Winding displacement(%)[Section-5]Z

-Cha

nges

(%

)

RF-1RF-2RF-3RF-4

RF-5RF-6RF-7RF-8

Fig. 7 Variation of impedance with winding compression at different resonant frequencies

Case 3: Outward Buckling

The one of the sections of the coil gets buckled as shown in Fig. 2(d). Here

also 50 Hz showed an impedance change less than 1%, while eighth resonant

frequency showed nearly 60% change.

5.3 Experimental Validation on Single Layer Winding

We have constructed a uniform single layer winding similar to the coil

used in [3], but without the outer shield. The constructed winding has 1250

turns; with a length of 650 mm and a radius of 55 mm. The lack of outer

shield reduces the earth capacitance thus increases the resonant

frequencies. This should make the test more difficult than the benchmark

coil.

Axial displacement: The first 250 turns are moved by a total distance of 60

mm with an incremental shift by 10 mm. A 1 kV standard impulse signal is

applied to the winding and current response at 11 different positions are

measured and compared. The first and second resonant frequencies shows a

change of 0.58 % and 3.67 % in the input current respectively, while the

impedance change at 50 Hz is 0.05 %. Fig. 8 shows the current response

without winding displacement. The first two resonant frequencies occur at

77.5 kHz and 215 kHz. Fig. 9 shows the percentage changes in the current at

these resonant frequencies.

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Radial displacement: The first 250 turns are compressed on one side which

results in an elliptical shape of the coil. The compression is done in 5 steps

which cause 10 mm decrease in the minor axis of the ellipse at each step. A 1

kV standard impulse signal is applied to the winding and current is found to

change only by 0.07 % at 50 Hz and 1.58 % at the first resonant frequency. A

virtual instrument was developed for online analysis of winding deformation

at power frequencies [6] and the work can be extended for high frequency

excitations.

5.4 Experimental Validation on 25 MVA, 110 kV/ 33 kV

Transformer

Experimental work is done on a single phase of a 25 MVA, 110 kV/ 33 kV

transformer as shown in Fig. 10. The LV winding is excited with 20 V peak to

0 50 100 150 200 250 300-1

0

1

2

3

4

5

Frequency (kHz)

Log(

I)

Fig. 8 Current response of the test winding frequencies

Hz

0 2 4 6 8 10-1

0

1

2

3

4

Winding axial displacement (%)

Cur

rent

cha

nge

(%)

RF-1

RF-2

Fig. 9 Current changes due to axial displacement of winding at first two resonant frequencies Hz

8

peak sinusoidal voltage from a Hewlett Packard 33120A, 15 MHz, arbitrary

waveform generator. The HV winding is shorted. The HV winding is a

combination of two coils connected in series. The bottom coil is rigid but the

top coil is moved with the help of the crane. The initial gap between the two

coils is 8.5 cm and the total height of the HV winding is 170 cm. With this

initial gap, frequency response is found by sweeping the frequencies from 10

Hz to 50 kHz and plotted as shown in Fig. 11. The readings of the current at

different frequencies are measured using Yokogawa DL750 Scopecorder.

Resonant frequencies occur at 16.1 kHz (RF-1), 19 kHz (RF-2) and 23 kHz (RF-

3). To show that currents are more sensitive to winding deformation at

resonant frequencies, readings are taken at three resonant peaks, i.e., RF-1,

RF-2 and RF-3. The top coil is now moved to 5 % of the total height in steps

on 1% on either direction, i.e., 8.5 cm above and 8.5 cm below equivalent to

expansion and compression of the winding. Readings of current are taken at

every 1% movement. Percentage changes in the current with increase in the

gap between the upper and lower coil is shown in Fig. 12 and with decrease

in gap is shown in Fig. 13. A comparison of the sensitivities shows that high

frequencies have a better sensitivity than power frequency.

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0 10 20 30 40 5010

-3

10-2

10-1

100

Frequency(kHz)

Cur

rent

(A)

Fig. 10 Tested phase of 25 MVA, 110 kV/ 33 kV transformer

Fig. 11 SFRA of 25 MVA, 110 kV/ 33 kV transformer

0 1 2 3 4 5-60

-50

-40

-30

-20

-10

0

10

20

distance(%)

% C

hang

e in

Cur

rent

50 Hz

RF-1RF-2

RF-3

Fig. 12 Percentage changes in the current when the gap is increased

0 1 2 3 4 5-30

-20

-10

0

10

20

30

40

distance(%)

% C

hang

e in

Cur

rent

50 Hz

RF-1RF-2

RF-3

Fig.13 Percentage changes in the current when the gap is decreased

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6. Research Publications

Journals:1. A.Palani, S.Santhi, S. Gopalakrishna and V. Jayashankar, “Real time

techniques to measure winding displacement in transformers during short-circuit tests”, IEEE Trans. on Power Delivery, vol. 23, no. 2, pp. 726-732, April 2008.

2. S. Gopalakrishna, M.K. Ilampoornan, and V.Jayashankar, “On the mechanical short time current rating of a current transformer”, IEEE Trans. on Power Del., vol. 24, no. 1, pp. 480-481, Jan. 2009.

Conferences:1. S. Gopalakrishna, Kishore Kumar, Boby George and V. Jayashankar, “Design

margin for short circuit withstand capability in large power transformer”, IPEC-2007, 3rd-6th December 2007, Singapore.

2. S.Gopalakrishna, M.K. Illampoornan and V. Jayashankar, “Sensitive method for detection of winding deformation during short circuit test”, communicated to ISEIM, Sep. 7th-11th 2008, Japan.

3. S. Gopalakrishna, Jayaraj Joseph, and V.Jayashankar, “On the use of concurrent high frequency excitation during a short circuit test in a power transformer”, (to be published in IMTC-2009).

7. References

[1] S. Santhi, S. Jayalalitha, V. Jayashankar, and V. Jagadeesh Kumar, “Detection of winding deformations during short time current tests”, Proc. IEEE-IMTC-2005, Ottawa, ON, Canada, pp. 203–208, May 2005.

[2] S. Santhi, V. Jayashankar, V. Jagadeesh Kumar, “Time frequency analysis method for the detection of winding deformation in transformer”, Proc. IEEE-IMTC 2008, Canada, pp. 2126-2130, May 12-15 2008.

[3] R. C. Degeneff, “A general method for determining resonance in transformer winding”, IEEE Trans. on Power Apparatus and Systems, vol. pas-96, no. 2 pp. 423-430, March/April 1977.

[4] Kulkarni S.V., Khaparde S.A., “Transformer Engineering, Design and Practice”, Marcel Dekker Inc., Newyork, 2004.

[5] Grover. Fredrick W, “Inductance Calculations; Working Formulas and Tables”, Dover Publications Inc, New York, 1946.

[6] A.Palani, S.Santhi, S.Gopalakrishna and V.Jayashankar, "Real time techniques to measure winding displacement in transformers during short circuit tests", IEEE Trans. on Power Delivery, vol. 23, no. 2 pp. 726-735, April 2008.

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