Frequency response analysis for transformer winding condition monitoring ( TQL)

Frequency Response Analysis for Transformer Winding Condition Monitoring
Mohd Fairouz Bin Mohd Yousof
B. Eng. (Electrical) M. Eng. (Electrical - Power)

A thesis submitted for the degree of Doctor of Philosophy at
The University of Queensland in 2015
School of Information Technology and Electrical Engineering


Abstract
The large power transformer is one of the most expensive assets in a power system network.
Special attention needs to be taken to monitor this expensive asset. Among the most critical aspect
of a transformer that needs to be monitored is the mechanical condition of the windings and core.
One of the best approaches to achieve this is by performing the Frequency Response Analysis
(FRA) test on the transformer. The test measures the transfer function response of the transformer
winding. If any physical changes occur, it will affect the original response, which can be used to
detect any abnormality. However, the critical challenge in this technique is to correctly interpret the
measured response in determining the transformer status. Although various investigations have
focussed on this issue, the interpretation aspect of FRA is still not fully established.
In order to contribute to the improvement of a FRA interpretation scheme, this thesis
investigates the sensitivity of FRA measurement on several common winding deformations and
explores a new potential diagnostic scheme of FRA. A wide range of power transformers have been
used throughout this study ranging from a small sized prototype laboratory transformer to a 30
MVA power transformer installed at a substation.
Initially, a mathematical model is established to simulate the frequency response of a power
transformer. This is achieved by comparing three models, which are available in the literature.
These models are compared in terms of their accuracies to simulate the response and their
applicability to studying winding deformation. The comparison shows that the multi-conductor
transmission line model is the best approach due to its ability to model each turn of a winding.
With the developed model, the sensitivity of the winding response is investigated. This study
shows that a minor change to the winding geometrical parameters could cause a considerable

change on the response. On a different issue, it is found that a similar winding failure mode may
cause a different response variation depending on the winding type. A study based on measurement
is also conducted to investigate the influence of windings from other phases to the tested winding. It
reveals that the end to end open circuit response is susceptible to the condition of an adjacent
winding. Additionally, investigation on the winding response sensitivity due to the tap changer
setting is also carried out.
This thesis studies several winding deformations, which includes tilting and bending of
conductors and inter-disc fault. These three faults are examined in terms of their severity of damage
and location of the fault. Statistical analysis is applied to determine the overall condition of the
winding. On the other hand, transfer function based analysis is proposed to extract further
ii


information if the winding is found to be faulty. This includes using the pole plot and Nyquist plot,
in which the latter proved to be useful for all winding failure modes. The transfer function is
achieved by applying vector fitting algorithm.
Several case studies are presented in this thesis based on the measured responses in the
university substation and also provided by various power utilities. The proposed analysis uses
statistical indicators and the Nyquist plot. Additionally, analysis from the proposed method is also
compared with two other interpretation schemes available in the literature. These two interpretation
schemes are known as relative factor analysis and α analysis for determining transformer overall
condition and winding failure modes respectively. The former is found to agree with most of the
results of the proposed methodology while the latter is found to be inapplicable to most of the cases.
Finally, the influence of the non-mechanical aspect of a transformer on the frequency response
is investigated. Based on laboratory experiments conducted on accelerated ageing of transformer
insulation, both FRA and Frequency Domain Spectroscopy (FDS) tests are conducted. Two
analyses are proposed from the FRA measurement for observing the increase in moisture content in
the insulation and for computing the inter-winding capacitance. Comparison with the results from
the FDS test proved the applicability of the proposed methodologies.
Overall, the findings from this thesis could be very useful in improving the understanding of

various factors which may influence FRA measurement and subsequently in examining the
frequency responses using the proposed approaches.

iii


Declaration by author
This thesis is composed of my original work, and contains no material previously published or
written by another person except where due reference has been made in the text. I have clearly
stated the contribution by others to jointly-authored works that I have included in my thesis.
I have clearly stated the contribution of others to my thesis as a whole, including statistical
assistance, survey design, data analysis, significant technical procedures, professional editorial
advice, and any other original research work used or reported in my thesis. The content of my thesis
is the result of work I have carried out since the commencement of my research higher degree
candidature and does not include a substantial part of work that has been submitted to qualify for
the award of any other degree or diploma in any university or other tertiary institution. I have
clearly stated which parts of my thesis, if any, have been submitted to qualify for another award.
I acknowledge that an electronic copy of my thesis must be lodged with the University Library
and, subject to the policy and procedures of The University of Queensland, the thesis be made
available for research and study in accordance with the Copyright Act 1968 unless a period of
embargo has been approved by the Dean of the Graduate School.
I acknowledge that copyright of all material contained in my thesis resides with the copyright
holder(s) of that material. Where appropriate I have obtained copyright permission from the
copyright holder to reproduce material in this thesis.

iv


Publications during candidature
(1)

M. F. M. Yousof, Chandima Ekanayake, Tapan K. Saha, and Hui Ma, “A Study on
Suitability of Different Transformer Winding Models for Frequency Response Analysis”,
Proceedings of IEEE PES General Meeting, San Diego, USA, July 26-29, 2012, pp. 1-8

(2)

M. F. M. Yousof, C. Ekanayake, and T. K. Saha, “Study of Transformer Winding
Deformation by Frequency Response Analysis”, Proceedings of IEEE PES General
Meeting, Vancouver, Canada, July 21-25, 2013, pp. 1-5

(3)

M. F. M. Yousof, C. Ekanayake, and T. K. Saha, “Locating Inter-disc Faults in Transformer
Winding using Frequency Response Analysis”, Proceedings of 22nd Australasian
Universities Power Engineering Conference, AUPEC 2013, Hobart, Australia, Sept. 29 Oct. 3, 2013, pp. 1-6

(4)

M. F. M. Yousof, T. K. Saha, and C. Ekanayake, “Investigating the Sensitivity of Frequency
Response Analysis on Transformer Winding Structure”, Proceedings of IEEE PES General
Meeting, Washington D.C., USA, July 27-31, 2014, pp. 1-5

(5)

M. Fairouz M. Yousof, C. Ekanayake and T. K. Saha, “Examining the Ageing of
Transformer Insulation Using FRA and FDS Techniques”, IEEE Transactions of Dielectrics
and Electrical Insulation, Volume 22, Number 2, pp. 1258-1265, April 2015.

(6)

M. Fairouz M. Yousof, C. Ekanayake and T. K. Saha, “Frequency Response Analysis to
Investigate Deformation of Transformer Winding”, Paper accepted for publication in the
IEEE Transactions of Dielectrics and Electrical Insulation, 29 January 2015 (in press).

v


Publications included in this thesis
(1)

M. F. M. Yousof, Chandima Ekanayake, Tapan K. Saha, and Hui Ma, “A Study on
Suitability of Different Transformer Winding Models for Frequency Response Analysis”,
Proceedings of IEEE PES General Meeting, San Diego, USA, July 26-29, 2012, pp. 1-8
– incorporated as Chapter 3.

Contributor

Statement of contribution

M. F. M. Yousof (Candidate)

Programming, simulation and modelling (100%)
Analysis and discussion (80%)
Wrote the paper (80%)

Chandima Ekanayake

Discussion on the results (10%)
Reviewed and edited the paper (10%)

Tapan K. Saha

Discussion on the results (10%)
Reviewed and edited the paper (8%)

Hui Ma

(2)

Reviewed and edited the paper (2%)

M. F. M. Yousof, C. Ekanayake, and T. K. Saha, “Study of Transformer Winding
Deformation by Frequency Response Analysis”, Proceedings of IEEE PES General
Meeting, Vancouver, Canada, July 21-25, 2013, pp. 1-5
– incorporated as Chapter 5.

Contributor

Statement of contribution

M. F. M. Yousof (Candidate)

Programming, simulation and modelling (100%)
Analysis and discussion (80%)
Wrote the paper (80%)

C. Ekanayake

Discussion on the results (10%)

Reviewed and edited the paper (15%)

T. K. Saha

Discussion on the results (10%)
Reviewed and edited the paper (5%)

vi


(3)

M. F. M. Yousof, C. Ekanayake, and T. K. Saha, “Locating Inter-disc Faults in Transformer
Winding using Frequency Response Analysis”, Proceedings of 22nd Australasian
Universities Power Engineering Conference, AUPEC 2013, Hobart, Australia, Sept. 29 Oct. 3, 2013, pp. 1-6
– incorporated as Chapter 5.

Contributor

Statement of contribution

M. F. M. Yousof (Candidate)

Experiment and measurement (100%)
Analysis and discussion (80%)
Wrote the paper (80%)

C. Ekanayake

Discussion on results (10%)

Reviewed and edited the paper (12%)

T. K. Saha

Discussion on results (10%)
Reviewed and edited the paper (8%)

(4)

M. F. M. Yousof, T. K. Saha, and C. Ekanayake, “Investigating the Sensitivity of Frequency
Response Analysis on Transformer Winding Structure”, Proceedings of IEEE PES General
Meeting, Washington D.C., USA, July 27-31, 2014, pp. 1-5
– incorporated as Chapter 4.

Contributor

Statement of contribution

M. F. M. Yousof (Candidate)

Programming, simulation and modelling (100%)
Analysis and discussion (80%)
Wrote the paper (80%)

T. K. Saha

Discussion on results (10%)
Reviewed and edited the paper (12%)

C. Ekanayake

Discussion on results (10%)
Reviewed and edited the paper (8%)

vii


(5)

M. Fairouz M. Yousof, C. Ekanayake and T. K. Saha, “Examining the Ageing of
Transformer Insulation Using FRA and FDS Techniques”, IEEE Transactions of Dielectrics
and Electrical Insulation, Volume 22, Number 2, pp. 1258-1265, April 2015.
– incorporated as Chapter 7.

Contributor

Statement of contribution

M. Fairouz M. Yousof (Candidate)

Experiment and measurement (90%)
Analysis and discussion (80%)
Wrote the paper (80%)

C. Ekanayake

Experimental setup (10%)
Discussion on results (10%)
Reviewed and edited the paper (12%)

T. K. Saha

Discussion on results (10%)
Reviewed and edited the paper (8%)

(6)

M. Fairouz M. Yousof, C. Ekanayake and T. K. Saha, “Frequency Response Analysis to
Investigate Deformation of Transformer Winding”, Paper accepted for publication in the
IEEE Transactions of Dielectrics and Electrical Insulation, 29 January 2015 (in press).
– incorporated as Chapter 5 and 6.

Contributor

Statement of contribution

M. Fairouz M. Yousof (Candidate)

Programming, simulation and modelling (100%)
Analysis and discussion (80%)
Wrote the paper (80%)

C. Ekanayake

Discussion on results (10%)
Reviewed and edited the paper (12%)

T. K. Saha

Discussion on results (10%)

Reviewed and edited the paper (8%)

viii


Contributions by others to the thesis
The transformer used in the ageing experiment was designed by Prof. Tapan K. Saha and Dr.
Chandima Ekanayake. FDS measurement was conducted by Dr. Hui Ma and Yi Cui.

Statement of parts of the thesis submitted to qualify for
the award of another degree
None

ix


Acknowledgements
All praise is due to Allah, the Most Gracious and the Most Merciful. I am truly grateful to
many people for their support towards my study and finally completing this thesis.
First and foremost, I would like to express my sincere gratitude to my principal advisor
Professor Tapan Kumar Saha and my associate advisor Dr. Chandima Ekanayake for their countless
guidance, advice and support during my PhD candidature. I have learned a lot from them especially
the entire research culture, being professional and ethical at work. Their professionalism always
inspires me. Their expertise always impresses me. Their enthusiasm always motivates me.
I appreciate Mrs Maureen Shields for the assistance she has given me in administrative matters.
My appreciation also goes to all my colleagues in the Power and Energy Systems group. Those who
have left the group and those who are still pursuing their Ph.D.’s, thank you for your help and being
wonderful friends. I would also like to extend my gratitude to Dr Hui Ma for his guidance in the
early period of my study and Mr. Steven Wright for his assistance in the laboratory and
proofreading many of the papers and the thesis.

Not to forget the financial support I received from various sources during my Ph.D.
candidature. Ministry of Education Malaysia for the primary scholarship, Universiti Tun Hussein
Onn Malaysia for the funding to attend conferences, University of Queensland for the research
assist fund and Professor Saha for the funding of my final conference in 2014.
Finally, I would like to express my deepest gratitude to all my family members for their endless
support, love and prayers especially my mother for her encouragement, my wife Huda for her great
patience and support throughout my study and my daughter Maryam for giving us joy every day.

x


Keywords
power transformer, winding deformation, frequency response analysis, condition monitoring

Australian and New Zealand Standard Research
Classifications (ANZSRC)
ANZSRC code: 090607, Power and Energy Systems Engineering (excl. Renewable Power), 100%

Fields of Research (FoR) Classification
FoR code: 0906, Electrical and Electronic Engineering, 100%

xi


Table of Contents
Abstract .......................................................................................................................................... ii
Declaration by author ..................................................................................................................... iv
Publications during candidature ...................................................................................................... v
Publications included in this thesis ................................................................................................. vi
Contributions by others to the thesis ............................................................................................... ix

Statement of parts of the thesis submitted to qualify for the award of another degree ...................... ix
Acknowledgements ......................................................................................................................... x
Keywords....................................................................................................................................... xi
Australian and New Zealand Standard Research Classifications (ANZSRC) .................................. xi
Fields of Research (FoR) Classification.......................................................................................... xi
Table of Contents .......................................................................................................................... xii
List of Figures .............................................................................................................................. xvi
List of Tables ............................................................................................................................... xxi
List of Abbreviations ................................................................................................................. xxiv
1

Introduction ......................................................................................................................... 1

1.1 Background and Motivation ................................................................................................. 1
1.2 Thesis objectives .................................................................................................................. 5
1.3 Outline of the Thesis ............................................................................................................ 5
2 Frequency Response Analysis on the Mechanical Deformation of Power Transformer
Winding ...................................................................................................................................... 7
2.1 Introduction .......................................................................................................................... 7
2.2 Winding Deformations ......................................................................................................... 8
2.2.1

Deformations Instigated by Axial Forces ................................................................... 9

2.2.2

Deformations Instigated by Radial Forces ................................................................ 11

2.2.3

Other Failure Modes ................................................................................................ 11

2.3 Frequency Response Analysis ............................................................................................ 12
2.3.1

FRA Test Configuration ........................................................................................... 14

2.3.1.1

End to end open circuit test ............................................................................... 15

2.3.1.2

End to end short circuit test ............................................................................... 16

2.3.1.3

Capacitive inter-winding test............................................................................. 16

2.3.1.4

Inductive inter-winding test .............................................................................. 17

2.4 Analysing and Interpreting FRA Measurement ................................................................... 18
2.4.1

Available Standard on FRA ..................................................................................... 18
xii

2.4.1.1

The Chinese Standard DL 911/2004 .................................................................. 18

2.4.1.2

CIGRE WG A2.26 Brochure............................................................................. 19

2.4.1.3

IEC 60076-18 ................................................................................................... 20

2.4.1.4

IEEE C57.149................................................................................................... 20

2.4.2

Statistical Analysis for Comparing Responses .......................................................... 21

2.4.2.1

Frequency Region or Sub-Band ........................................................................ 22

2.4.2.2

The Size of Data Set ......................................................................................... 24

2.5 FRA on Winding Deformation ........................................................................................... 25
2.5.1

Axial Winding Displacement ................................................................................... 25

2.5.2

Axial Bending .......................................................................................................... 26

2.5.3

Winding Buckling .................................................................................................... 27

2.5.4

Inter-turn Fault ......................................................................................................... 27

2.5.5

Conductor Tilting..................................................................................................... 27

2.6 Summary ............................................................................................................................ 28
3

Modelling the Transformer Winding Frequency Response ............................................... 30

3.1 Introduction ........................................................................................................................ 30
3.2 Modelling the Transformer Winding Frequency Response .................................................. 31
3.2.1

Ladder Network Model ............................................................................................ 31

3.2.2

Multi-Conductor Transmission Line (MTL) ............................................................. 32

3.2.3

Hybrid MTL ............................................................................................................ 37

3.2.4

Computing the Winding Capacitance ....................................................................... 39

3.3 Parameter calculation on the experimental transformer ....................................................... 42
3.4 Comparison between simulation and experimental ............................................................. 45
3.4.1

Measurements on the Prototype Transformer ........................................................... 45

3.4.2

Ladder Network Model ............................................................................................ 46

3.4.3

MTL Model ............................................................................................................. 46

3.4.4

Hybrid MTL Model ................................................................................................. 47

3.5 Summary ............................................................................................................................ 49
4

The Sensitivity of Transformer Frequency Response ........................................................ 51

4.1 Introduction ........................................................................................................................ 51
4.2 FRA Sensitivity on the Winding Geometry......................................................................... 52
4.3 Different Winding Construction on a Similar Winding Damage ......................................... 54
4.3.1

The Tilting of Conductors ........................................................................................ 54

4.3.2

The Axial Bending of Conductors ............................................................................ 56
xiii


4.4 The Influence of Windings from Other Phases .................................................................... 58
4.4.1

Influence of Other Windings on Winding in Phase A ............................................... 60

4.4.2

The Influence between Phase B and C Windings ...................................................... 62

4.5 The Influence of Tap Changer on the Frequency Response ................................................. 64
4.5.1

End to end Open and Short Circuit Tests on HV Winding ........................................ 65

4.5.2

End to end Open Circuit Tests on LV Winding ........................................................ 66

4.5.3

Inductive Inter-winding Test .................................................................................... 67

4.6 Summary ............................................................................................................................ 69
5

Developing Interpretation Method for Analysing Faulty Winding Response .................... 71

5.1 Introduction ........................................................................................................................ 71
5.1.1

Statistical Analysis ................................................................................................... 72

5.1.1.1
5.1.2

Benchmark Limits ............................................................................................ 73

Other Proposed Methods for Analysing Winding Response ..................................... 73

5.1.2.1

Vector Fitting ................................................................................................... 74

5.1.2.2

Pole-Zero Mapping and Nyquist Plot Analysis .................................................. 76

5.2 Inter-disc Fault on the HV Winding .................................................................................... 76
5.2.1

Statistical Analysis on the Measured Response ........................................................ 79

5.2.2

Pole Plot Analysis .................................................................................................... 80

5.2.3

Nyquist Plot Analysis .............................................................................................. 81

5.3 Analysis on the Simulated Response ................................................................................... 83
5.3.1

Tilting of Conductors on an Interleaved Winding ..................................................... 84

5.3.1.1

Winding Electrical Parameters due to Deformation ........................................... 84

5.3.1.2

Simulated Response and Statistical Analysis ..................................................... 87

5.3.1.3

The Nyquist Plot Analysis ................................................................................ 88

5.3.2

Tilting of Conductors on a Continuous Winding ...................................................... 89

5.3.2.1

Simulated Response and Statistical Analysis ..................................................... 89

5.3.2.2

The Nyquist Plot Analysis ................................................................................ 91

5.3.3

Axial Bending on a Continuous Winding ................................................................. 92

5.3.3.1

Winding Parameters due to Deformation........................................................... 92

5.3.3.2

Simulated Responses and Statistical Analysis ................................................... 93

5.3.3.3

The Nyquist Plot Analysis ................................................................................ 94

5.4 Summary ............................................................................................................................ 95
6

Winding Fault Analysis on Field Transformers ................................................................ 97

6.1 Introduction ........................................................................................................................ 97
xiv


6.2 Analysis on FRA from the Field Measurement ................................................................... 98
6.2.1

Comparison with other Interpretation Schemes ........................................................ 99

6.3 Power Transformers with Good Working Condition ......................................................... 100
6.3.1

Indonesian Distribution Utility ............................................................................... 100

6.3.2

University Substation ............................................................................................. 102

6.3.3

Distribution Company 1 ......................................................................................... 103

6.3.4

Power Station......................................................................................................... 104

6.4 Power Transformers with Suspected Winding Damage ..................................................... 106
6.4.1

Steel Mill 1 ............................................................................................................ 106

6.4.2

Distribution Company 2 ......................................................................................... 108

6.4.3

Steel Mill 2 ............................................................................................................ 111

6.5 Summary .......................................................................................................................... 113
7

The Investigation of Insulation Ageing using FRA ......................................................... 115

7.1 Introduction ...................................................................................................................... 115
7.2 Investigating the Ageing of Insulation via FRA ................................................................ 115
7.3 The Test Configuration of FDS ........................................................................................ 117
7.4 The Proposed Methodology .............................................................................................. 118
7.4.1

Electrical Parameters on the Ageing of Insulation .................................................. 118

7.4.2

Capacitance Ratio of the End to End Test .............................................................. 118

7.4.3

Capacitance of the Capacitive Inter-Winding Test .................................................. 120

7.5 Case Study ....................................................................................................................... 122
7.6 FDS Measurement ............................................................................................................ 123
7.7 HV End to End Short Circuit Test .................................................................................... 126
7.8 LV End to End Short Circuit Test ..................................................................................... 128
7.9 Capacitive Inter-Winding Test .......................................................................................... 130
7.9.1

Computing the Inter-Winding Capacitance............................................................. 130

7.9.2

Repeatability Test on the Measurement .................................................................. 131

7.10 Summary .......................................................................................................................... 133
8

Conclusions and Future Works ....................................................................................... 135

8.1 Conclusions ...................................................................................................................... 135
8.2 Future Works.................................................................................................................... 140
List of References ....................................................................................................................... 141
Appendices….……………...…………………………..………………………………………….147

Publications during candidature…………………………………………………………………...155
xv


List of Figures
Figure 1.1 KEMA survey on 102 transformers for IEC withstand test [1]. ...................................... 2

Figure 2.1 Flux lines and forces directions on HV and LV windings. ............................................. 8
Figure 2.2 Axial displacement of HV winding. ............................................................................... 9
Figure 2.3 Axial bending of conductors. ....................................................................................... 10
Figure 2.4 (a) Conductors in tilted position. (b) From an actual case reported in [7]. .................... 10
Figure 2.5 Buckling of winding [24]. (a) Forced buckling. (b) Free buckling. (c) Actual case of
forced buckling on common winding of 400 MVA autotransformer. ............................................. 11
Figure 2.6 Inter-turn fault within winding. (a) Complete breakdown between turns. (b) Picture
from an actual case [24]. ............................................................................................................... 12
Figure 2.7 FRA measurement on the power transformer. .............................................................. 13
Figure 2.8 FRA test configurations for three phase transformer. (a) End to end open circuit test. (b)
End to end short circuit test. (c) Capacitive inter-winding test. (d) Inductive inter-winding test. .... 14
Figure 2.9 An example of measured frequency response from end to end open circuit test. (a)
Magnitude plot. (b) Phase plot....................................................................................................... 15
Figure 2.10 An example of measured frequency response from end to end short circuit test. (a)
Magnitude plot. (b) Phase plot....................................................................................................... 16
Figure 2.11 An example of measured frequency response from capacitive inter-winding test. (a)
Magnitude plot. (b) Phase plot....................................................................................................... 16
Figure 2.12 An example of measured frequency response from inductive inter-winding test. (a)
Magnitude plot. (b) Phase plot....................................................................................................... 17
Figure 2.13 The performance of statistical indicators on the given example. (a) Example case of
two responses. (b) CC with various data size. (c) ASLE with various data size. (d) CSD with
various data size. ........................................................................................................................... 24

Figure 3.1 Ladder network model with four network units. .......................................................... 32
Figure 3.2 Cross-section of an interleaved disc winding containing 36 turns in 6 discs. ................ 33
Figure 3.3 Multi-conductor transmission line model of a transformer winding.............................. 34
Figure 3.4 End to end short circuit test of single phase transformer winding. ................................ 36
Figure 3.5 Cross section of an interleaved winding with two discs and five turns on each disc. .... 40
xvi


Figure 3.6 (a) A laboratory transformer consisting of three different windings. (b) Measuring the
dimensions of the conductor of HV winding phase A. ................................................................... 42
Figure 3.7 Cross section of the conductor of HV winding phase A. .............................................. 43
Figure 3.8 Total inductance (self and mutual) for each disc in the winding. .................................. 44
Figure 3.9 Measured frequency response of the HV winding of phase A from 20 kHz to 1 MHz.
(a) Linear plot. (b) Logarithmic plot. ............................................................................................. 45
Figure 3.10 Simulated frequency response using ladder network model. ...................................... 46
Figure 3.11 Simulated frequency response using MTL model....................................................... 47
Figure 3.12 Simulated frequency response using hybrid MTL model. .......................................... 48
Figure 3.13 Frequency response of the input impedance of the transformer winding taken from [75]
(a) Simulated frequency response using hybrid MTL model. (b) Measured frequency response. (c)
Simulated frequency response using MTL model. ......................................................................... 49

Figure 4.1 Frequency responses of winding B with the variation of its geometrical parameters [76].
..................................................................................................................................................... 53
Figure 4.2 Two different forms of winding damage. (a) The tilting of conductors. (b) The axial
bending of conductors. .................................................................................................................. 54
Figure 4.3 Frequency response of normal and damaged winding due to the tilting of conductors.
(a) Winding A. (b) Winding B. (c) Winding C............................................................................... 55
Figure 4.4 Frequency response of normal and damaged winding due to the bending of conductors.
(a) Winding A. (b) Winding B. (c) Winding C............................................................................... 57
Figure 4.5 (a) Three phase transformer with changeable winding configuration used in this study.

(b) Diagram of all three HV windings. .......................................................................................... 59
Figure 4.6 Measured frequency responses of HV windings of phase A, B and C using end to end
open and short circuit tests. ........................................................................................................... 60
Figure 4.7 Comparison between responses of open and short circuit tests on the influence of
windings B and C on winding A. ................................................................................................... 60
Figure 4.8 Influence of HV winding arrangement of phases B and C on winding phase A. ........... 61
Figure 4.9 Comparison between responses of end to end open and short circuit tests on the
influence of phase C winding on phase B winding response. ......................................................... 63
Figure 4.10 Comparison between responses of end to end open and short circuit tests on the
influence of phase B winding on phase C winding response. ......................................................... 63
Figure 4.11 100 kVA three phase power transformer with tap changer. ........................................ 64
xvii


Figure 4.12 (a) Winding configuration of the transformer. (b) Tap contact or switch position. ...... 65
Figure 4.13 Measured responses of HV winding using end to end open circuit test with five
different tap switch positions. ........................................................................................................ 66
Figure 4.14 Measured responses of HV winding using end to end short circuit test with five
different tap positions. ................................................................................................................... 66
Figure 4.15 Measured responses of LV winding using end to end open circuit test with five
different tap positions. ................................................................................................................... 67
Figure 4.16 Measured responses using inductive inter-winding test with five different tap positions.
..................................................................................................................................................... 68

Figure 5.1 Flowchart for the modified vector fitting algorithm. .................................................... 75
Figure 5.2 Comparison of FRA measurements of normal and faulted conditions. (a) For faults in
top half. (b) For faults in bottom half [82]. .................................................................................... 78
Figure 5.3 Pole plot of normal and faulted conditions. (a) For fault in top half. (b) For fault in
bottom half [82]. ........................................................................................................................... 80
Figure 5.4 Nyquist plots of normal and faulted conditions. (a) For fault in top half. (b) For fault in

bottom half [82]. ........................................................................................................................... 81
Figure 5.5 Linear relationship between the absolute difference and the fault location index. ......... 83
Figure 5.6 FEM to compute the inter-turn capacitance, Ct. (a) Conductors in normal condition. (b)
Conductors tilted. .......................................................................................................................... 84
Figure 5.7 FEM on the current distribution on the disc. (a) Disc in normal condition. (b) Disc in
tilted condition. ............................................................................................................................. 86
Figure 5.8 Conductor resistance due to skin and proximity effects for normal and tilted conditions.
..................................................................................................................................................... 86
Figure 5.9 Simulated response of the winding for normal and deformed (conductors tilted)
conditions. .................................................................................................................................... 87
Figure 5.10 Nyquist plot of the transfer function for all six conditions. ......................................... 88
Figure 5.11 The absolute difference versus the percentage of deformed winding. ......................... 88
Figure 5.12 Simulated responses of the continuous winding for normal and deformed (conductors
tilted) conditions. .......................................................................................................................... 90
Figure 5.13 Nyquist plot of the transfer function for all six conditions. ......................................... 91
Figure 5.14 The absolute difference versus the percentage of deformed winding. ......................... 91
Figure 5.15 Axial bending of the winding. ................................................................................... 92
xviii


Figure 5.16 Simulated responses of the continuous winding for normal and deformed (axial
bending) conditions. ...................................................................................................................... 93
Figure 5.17 Nyquist plot of the transfer function for all six conditions. ......................................... 94
Figure 5.18 The absolute difference versus the percentage of deformed winding. ......................... 95

Figure 6.1 Flow chart of the proposed method to analyse the transformer frequency response. ..... 98
Figure 6.2 Flow chart of the method which was proposed in [44] for determining winding failure
mode. .......................................................................................................................................... 100
Figure 6.3 End to end open circuit responses of the HV windings with disturbance at low frequency
region. ......................................................................................................................................... 101

Figure 6.4 End to end short circuit test response on the HV windings. ......................................... 102
Figure 6.5 End to end short circuit test responses on HV winding of phase C. ............................ 103
Figure 6.6 Short circuit test responses on HV winding. .............................................................. 105
Figure 6.7 End to end open circuit responses of the HV winding with noises at low dB. ............. 106
Figure 6.8 Nyquist plot representation of the responses. ............................................................. 108
Figure 6.9 End to end short circuit responses of the HV winding. ............................................... 109
Figure 6.10 Nyquist plot representation of the responses. ........................................................... 110
Figure 6.11 End to end open circuit responses of the HV winding. ............................................. 111
Figure 6.12 Nyquist plot representation of the responses. ........................................................... 113

Figure 7.1 FDS CHL test configuration on one phase. ................................................................ 117
Figure 7.2 Frequency responses of a RLC circuit based on three different values of complex
capacitance. ................................................................................................................................ 119
Figure 7.3 Circuit representing the inter-winding capacitance from the measurement. ................ 120
Figure 7.4 Frequency responses of the inter-winding capacitance with three different complex
capacitance values. ...................................................................................................................... 121
Figure 7.5 (a) Diagram showing the location of heating element. (b) Internal view of the
transformer during the assembly process. (c) 5 kVA transformers used in this study. .................. 122
Figure 7.6 Results from FDS measurements. (a) Real part of the complex capacitance. (b)
Imaginary part of the complex capacitance. ................................................................................. 124

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Figure 7.7 The percentage of change of capacitance against the increment of moisture content for
FRA and FDS tests...................................................................................................................... 125
Figure 7.8 Frequency responses from the HV end to end short circuit test. ................................. 126
Figure 7.9 Peaks on certain responses have suppressed will cause an inaccuracy when computing
the ratio. ...................................................................................................................................... 128
Figure 7.10 Frequency responses from the LV end to end short circuit test. ................................ 128

Figure 7.11 Frequency responses from the capacitive inter-winding test. .................................... 130
Figure 7.12 Repeatability test no. 1. (a) Compared responses. (b) Absolute difference between
responses. ................................................................................................................................... 132
Figure 7.13 Repeatability test no. 2. (a) Compared responses. (b) Absolute difference between
responses. ................................................................................................................................... 132
Figure 7.14 Repeatability test no. 3. (a) Compared responses. (b) Absolute difference between
responses. ................................................................................................................................... 132

xx


List of Tables
Table 1.1 Summary of four cases of shipping the transformers [3].................................................. 3

Table 2.1 Comparison of testing techniques for transformer mechanical condition [7]. ................. 12
Table 2.2 Relative factor and the degree of deformation. .............................................................. 18
Table 2.3 Frequency regions and the corresponding influencing factors [31]. ............................... 20
Table 2.4 Types of transformer and the amount of recommended test. .......................................... 21
Table 2.5 Transformer frequency response sensitivity for various conditions. .............................. 23

Table 3.1 Parameter of the experimental transformer winding. ..................................................... 43
Table 3.2 Capacitance for the HV winding of phase A. ................................................................ 43
Table 3.3 Inductance for the HV winding of phase A using (3.28). ............................................... 44

Table 4.1 Parameters of three different windings [76]. ................................................................. 53
Table 4.2 Statistical indicators between responses for conductor tilting. ....................................... 56
Table 4.3 Statistical indicators to compare between normal and deformed winding responses for
axial bending. ................................................................................................................................ 58
Table 4.4 Factors influencing the open and short circuit test responses. ........................................ 63
Table 4.5 Tap changer position and voltage rating. ....................................................................... 65

Table 4.6 The similarity between the changes of low frequency response and the changes of
winding turn ratio. ......................................................................................................................... 68
Table 4.7 Factors influencing the open circuit, short circuit and inductive inter-winding test
responses from the tap changer position. ....................................................................................... 69

Table 5.1 Frequency response sensitivity according to sub-band [42]. ........................................... 72
Table 5.2 CC benchmark limits [42]. ............................................................................................. 73
Table 5.3 Inter-disc fault location on the winding. ......................................................................... 77
Table 5.4 CC and ASLE according to frequency sub-band. ........................................................... 79
Table 5.5 Minimum imaginary value and absolute imaginary difference for top and bottom
winding [82]. ................................................................................................................................ 82
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Table 5.6 Winding capacitance of the winding in normal and deformed conditions. ..................... 85
Table 5.7 Statistical indicators according to percentage of winding damage on selected frequency
region (100 kHz to 1 MHz). .......................................................................................................... 87
Table 5.8 Winding capacitance in normal and deformed conditions. ............................................. 89
Table 5.9 Statistical indicators according to percentage of winding damage on selected frequency
region (100 kHz to 1 MHz). .......................................................................................................... 90
Table 5.10 Winding capacitance and self-inductance of each disc in normal and deformed
conditions. .................................................................................................................................... 93
Table 5.11 Statistical indicators according to percentage of winding damage on selected frequency
region (100 kHz to 1 MHz). .......................................................................................................... 94

Table 6.1 Available information of the power transformers presented in this chapter. ................... 97
Table 6.2 Benchmark limits of CC and the proposed limits of ASLE for different comparison
scheme. ......................................................................................................................................... 99
Table 6.3 Statistical indicators to compare two responses. .......................................................... 101
Table 6.4 Statistical indicators on all phases for the selected frequency region. .......................... 103

Table 6.5 Statistical indicators from comparison between responses for the third case. ............... 104
Table 6.6 Statistical indicators from comparison between responses for the fourth case. ............. 105
Table 6.7 Statistical analysis according to four different indicators. ............................................ 107
Table 6.8 The estimated percentage of winding damage. ............................................................ 108
Table 6.9 CC and ASLE according to selected frequency region. ............................................... 109
Table 6.10 The expected percentage of winding damage. ........................................................... 110
Table 6.11 CC and ASLE on the selected frequency region. ....................................................... 112
Table 6.12 The expected percentage of winding damage. ........................................................... 113

Table 7.1 Accelerated ageing process applied on the transformer. .............................................. 123
Table 7.2 Moisture condition of the insulation in the transformer. .............................................. 124
Table 7.3 Percentage of change of capacitance from FDS CHL test. ........................................... 125
Table 7.4 Percentage of change of capacitance for selected frequencies from HV end to end short
circuit test. .................................................................................................................................. 127

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Table 7.5 Percentage of change of capacitance for selected frequencies from LV end to end short
circuit test. .................................................................................................................................. 129
Table 7.6 Real part of complex capacitance from FDS and FRA. ............................................... 131
Table 7.7 Mean and maximum absolute difference within yellow region. ................................... 133

xxiii


List of Abbreviations
AD

Axial displacement

AEI

Associated Electrical Industries

ASLE

Absolute Sum of Logarithmic Error

CC

Correlation Coefficient

CHL

Capacitance between HV and LV windings

CIGRE

Conseil International des Grands Réseaux Électriques
(International Council on Large Electric Systems)

CSD

Comparative Standard Deviation

DGA

Dissolved Gas Analysis

DP

Degree of Polymerization

DSV

Disc space variation

EAF

Electric arc furnace

EMF

Electromagnetic forces

FDS

Frequency Domain Spectroscopy

FEM

Finite element method

FI

Fault Index

FLI

Fault Location Index

FRA

Frequency Response Analysis

GEC

General Electric Company

IEC

International Electrotechnical Commission

IEEE

Institute of Electrical and Electronics Engineers

LPT

Large power transformer

MTL

Multi-conductor Transmission Line

NLTC

No-Load Tap Changer

PD

Partial Discharge

PDC

Polarization and depolarization current

RD

Radial displacement/deformation

RLC

Resistance, inductance and capacitance

RMSE

Root mean square error

RVM

Return Voltage Measurement

SD

Standard Deviation

SVM

Support Vector Machine
xxiv


SW

Switch position

TTR

Transformer Turns Ratio Test

WD

Percentage of winding damage

xxv