detection, identification and localization of partial discharges in power transformers using uhf

DETECTION, IDENTIFICATION AND

LOCALIZATION OF PARTIAL DISCHARGES IN

POWER TRANSFORMERS USING UHF

TECHNIQUES

A THESIS SUBMITTED FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

HERMAN HALOMOAN SINAGA

Supervisor: Dr. Toan Phung

School of Electrical Engineering and Telecommunications,

The University of New South Wales, Australia

March 2012

THIS SHEET IS TO BE GLUED TO THE INSIDE FRONT COVER OF THE THESIS

PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES

Thesis/Dissertation Sheet

Surname or Family name: SINAGA

First name: HERMAN Other name/s: HALOMOAN

Abbreviation for degree as given in the University calendar:

School: Electrical Engineering and Telecommunications Faculty: Engineering

Title: Detection, Identification and Localization of Partial Discharges in Power Transformers Using UHF Techniques

Abstract 350 words maximum: (PLEASE TYPE)

Partial discharge (PD) detection using the ultra high frequency (UHF) method has proven viable in monitoring the insulation condition of GIS. Recently, it is being extended and applied to transformer diagnostics. The UHF PD detection method shows advantages over traditional electrical PD detection such as the standardized IEC 60270 method. The main advantage of the UHF method is its impunity over environmental noise.

The UHF detection method applies sensors (antennas) to detect the electromagnetic signals emitted by the PD source. These signals, once picked up by the sensor, can then be captured with appropriate recording equipment. The sensor is thus one of the most important parts of UHF PD detection. The sensors must be able to pick up the electromagnetic signals which lie in the UHF range.

In this thesis, the sensors were designed using special purpose electromagnetic software. Four types of antenna were designed with various dimensional constraints: monopole, conical-skirt monopole, spiral and log-spiral. All sensors were then tested to find the most suitable sensor for PD detection and localization. The log-spiral sensor was found to be a better sensor for PD detection and recognition whilst the monopole sensor was more suited to PD localization.

PD detection and recognition were carried out by recording the PD signals in time and frequency domain. The recorded signals were then used as input to recognize the different PD defect types. Recognition was achieved by applying neuro-fuzzy and artificial neural network methods. The results show that both methods can be used to recognize and classify the PD sources with high accuracy.

An array of 4 sensors was used for PD localization. The PD location can be determined from the time difference of arrival (TDOA) of the signals arriving at sensors and at different positions. Three methods were used to determine the TDOA, i.e. first peaks, cross-correlation and cumulative energy curve. The first-peaks method showed the lowest error compared to the other two methods, followed thereafter by the cross-correlation and the cumulative energy curve method.

Declaration relating to disposition of project thesis/dissertation I hereby grant to the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all property rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstracts International (this is applicable to doctoral theses only). ………………………………………………………… ……………………………………..……………… ……….……………………...…….… Signature Witness Date The University recognises that there may be exceptional circumstances requiring restrictions on copying or conditions on use. Requests for restriction for a period of up to 2 years must be made in writing. Requests for a longer period of restriction may be considered in exceptional circumstances and require the approval of the Dean of Graduate Research.

FOR OFFICE USE ONLY Date of completion of requirements for Award:

COPYRIGHT STATEMENT ‘I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstract International (this is applicable to doctoral theses only). I have either used no substantial portions of copyright material in my thesis or I have obtained permission to use copyright material; where permission has not been granted I have applied/will apply for a partial restriction of the digital copy of my thesis or dissertation.' Signed ……………………………………………........................... Date ……………………………………………........................... AUTHENTICITY STATEMENT ‘I certify that the Library deposit digital copy is a direct equivalent of the final officially approved version of my thesis. No emendation of content has occurred and if there are any minor variations in formatting, they are the result of the conversion to digital format.’ Signed ……………………………………………........................... Date ……………………………………………...........................

ORIGINALITY STATEMENT

‘I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.’

Signed ……………………………………………....

Date ................................................................

TO MY PARENTS, BROTHER, SISTERS AND FAMILY MEMBERS FOR THEIR LOVE AND SUPPORT

i

ACKNOWLEDGEMENT

The completion of this thesis report was made possible by the co-operation of numerous

individuals. I would like to take this opportunity to express my greatest appreciation for

their valuable contributions.

First and foremost I like to express my deep appreciation to my supervisor Dr. Toan

Phung, for his support, advice, guidance and helpful comments throughout the

completion of this report.

I would also like to thank my co-supervisor Associate Professor Trevor Blackburn.

Thank you for your valuable advice. Special thanks are due to Mr. Zhenyu Liu, whom I

would like to thank for his support during the experimental work.

Also, I wish to express my deepest gratitude and appreciation to my dearest parents,

brothers and sisters, for your endless love, continual support and encouragement.

Herman Halomoan Sinaga

Sydney,

April 2012

ii

ABSTRACT

Partial discharge (PD) detection using the ultra high frequency (UHF) method has

proven viable in monitoring the insulation condition of GIS. Recently, it is being

extended and applied to transformer diagnostics. The UHF PD detection method shows

advantages over the traditional electrical PD detection such as the standardized IEC

60270 method. The main advantage of the UHF method is its impunity over

environmental noise. In terms of frequency components, the noise at the power plant is

typically from a few kHz to some tens of MHz, thus well below the UHF range.

Although noise also appears in the UHF range, it is mainly a narrow band noise whose

frequency is well known, such as mobile phone and digital TV signals.

The UHF detection method applies sensors to detect electromagnetic waves emitted by

the PD source. These signals once captured by the sensor can then be recorded with

appropriate measuring instruments. The sensor is thus one of the most important parts

of UHF PD detection. The sensors must be properly designed, e.g. high sensitivity, so to

be able to pick up electromagnetic signals which lie in the UHF range.

In this thesis, the sensors were designed using special purpose electromagnetic software

called CST Microwave Studio. The sensors were treated as an antenna in the design

process. The aim of the design was to get the best possible sensors with favourable

antenna parameters. Four types of antennae were designed with their various

dimensional constraints: monopole, conical-skirt monopole, spiral and log-spiral. The

first two are quarter wavelength monopole antennas, and the last two are dual-arm

planar sensors which are etched on a PCB board.

Following the design and simulation, the sensors were fabricated and put through

several series of tests. The first test detected small PD signals with varying distances up

to 2 m. All sensors showed capability to detect 5 pC discharges emitted by a corona

source at a distance of 1.5 m. The magnitude of the recorded PD was easily recognized

as the corona pattern. As the distance increased, the magnitude of the PD pattern was

reduced. At a distance of 2 m, the pattern captured by the monopole sensor was almost

iii

unrecognizable as a corona pattern. The log-spiral was found to have the highest

capability to detect small PDs within a distance of 2 m.

The second test was the step pulse response. The monopole showed the fastest response

with the least oscillation. A similar response was shown by the conical with just slight

oscillation. The spiral had the most oscillatory response with the signal peaks distorted.

The log-spiral showed a higher magnitude with oscillation up to 30 ns which was

caused by the length and structure of the spiral being much longer than other sensors.

The third test was the frequency response. The sensors were tested using a TEM cell.

The log-spiral sensor had the flattest response for the frequency range of 100 MHz to

2000 MHz. The monopole and conical had quite similar responses where both sensors

had almost flat responses up to 1000 MHz. The spiral sensor showed a lot of oscillation

in its response, caused by the spiral conductor structure.

The final test was to determine the sensor’s sensitivity to detect different PD sources in

the transformer. In this experiment, the sensors were tested to detect PD signals emitted

by two different PD defects. The effect of the transformer structure was simulated by

placing a solid barrier between the sensors and the PD source. All sensors showed a

capability to detect PDs as small as 20 pC, with or without the presence of the barrier.

In terms of the amount of pC, the log-spiral sensor had higher sensitivity than other

sensors. From the antenna design using CST software and the four tests, the log-spiral

showed better results in PD detection and was therefore chosen to detect PD in the

experiment. For the monopole sensor, although it had a lower sensitivity than others, it

had the fastest response to a fast step pulse with the least oscillation. This result shows

that the monopole is the better sensor for PD localization, where the least oscillation of

the PD waveform is necessary.

UHF PD detection can record PD signals in two domains, i.e. time domain and

frequency domain. Both methods have their own advantages. The advantage of

frequency domain measurement over time domain measurement is its frequency range

flexibility. The PD measuring frequency ranges used were broadband, narrow band or at

a single frequency (zero span). The disadvantage of frequency domain measurement is

that, due to its measurement principle, a relatively long integration time is needed to

iv

build up the spectrum display. Nevertheless, both methods can be applied to determine

the presence of PD events in transformers.

Using two recording methods, the presence of PD in transformers was detected using a

log-spiral sensor. The recorded signals could then be used as input to recognize the

different PD sources. Two artificial intelligence (AI) networks were used to classify the

defect types from their PD signals. The results showed that both methods can be used to

recognize and classify the PD sources with high accuracy.

UHF PD detection can also be applied to determine the PD location in a transformer.

The challenge of using UHF PD detection in localization of PD sources is the fact that

electromagnetic signals emitted by the PD source travel almost as fast as the speed of

light, i.e. 2 x108 m/s in mineral oil. At this speed, an error of 1 ns means that the PD

location could be missed by as much as 20 cm.

For PD localization, the monopole sensor was used in the test because of its best

response to a step pulse. The PD location is determined from the time difference of

arrival (TDOA) of the signals at different sensors at different positions. Three methods

were used to determine the PD location, i.e. first peaks, cross-correlation and

cumulative energy curve methods. The first peaks method shows the lowest error

compared to the other two methods, followed by cross-correlation and cumulative

energy curve respectively. The smallest error using the first peak method was ~14 cm

(c.f. typical transmission transformer tank size of several meters in each dimension).

The error might have been able to be reduced if the sensor was shortened. However, the

sensitivity of the sensor will decrease as the length is shortened. Perhaps, there is a

compromise between the sensitivity and the length of the sensor which could reduce the

error in PD localization.

v

LIST OF PUBLICATIONS

Journal Paper

1. H.H. Sinaga, B.T. Phung, and T.R. Blackburn, "Partial Discharge Localization

in Transformers Using UHF Detection Method", IEEE Transaction on

Dielectrics and Electrical Insulation, Paper number 3436, submitted 16 January

2012, revised 20 March 2012.

Conference Papers

1. H.H. Sinaga, B.T. Phung, and T.R. Blackburn, “Design of Ultra High

Frequency Sensors for Detection of Partial Discharges”, 16th International

Symposium on High Voltage Engineering (ISH 2009), 24th-28th August 2009,

Cape Town, South Africa, Paper D-10.

2. H.H. Sinaga, B.T. Phung, and T.R. Blackburn, “Partial Discharge Measurement

for Transformer Insulation Using Wide and Narrow Band Methods in Ultra High

Frequency Range”, 19th Australasian Universities Power Engineering

Conference (AUPEC’09), 27-30 September 2009, Adelaide, Australia, paper

PP027.

3. H.H. Sinaga, B.T. Phung, and T.R. Blackburn, "Neuro Fuzzy Recognition of

Ultra-High Frequency Partial Discharges in Transformers", 9th Int. Conf. on

Power and Energy (IPEC2010), Oct.27-29, 2010, Singapore, pp.346-351.

4. H.H. Sinaga, B.T. Phung, and T.R. Blackburn, "Recognition of Single and

Multiple Partial Discharge Sources in Transformer Insulation", Int. Conf. on

Condition Monitoring and Diagnosis (CMD2010), Sept.6-11, 2010, Tokyo,

Japan, paper A4-4.

vi

5. H.H. Sinaga, B.T. Phung, P.L. Ao, and T.R. Blackburn, "Partial Discharge

Localization in Transformers Using UHF Sensors", 30th Electrical Insulation

Conference (EIC), Annapolis, Maryland, USA June 5-8, 2011, pp. 64-68.

6. H.H. Sinaga, B.T. Phung, A.P. Ao, and T.R. Blackburn, "UHF Sensors

Sensitivity in Detecting PD Sources in a Transformer", XVII International

Symposium on High Voltage Engineering, Hannover, Germany, August 22-26,

2011, Paper D-069.

7. H.H. Sinaga, B.T. Phung, and T.R. Blackburn, “UHF Sensor Array for Partial

Discharge Location in Transformers”, submitted to Int. Conf. on Condition

Monitoring and Diagnosis (CMD2012), Bali, Indonesia, September 23-27, 2012.

8. H.H. Sinaga, B.T. Phung, and T.R. Blackburn, “Partial Discharge Localization

in Transformers Using Monopole and Log-Spiral UHF Sensors”, submitted to

IEEE 10th International Conference on Properties and Applications of Dielectric

Materials (ICPADM), Bangalore, India, July 24-28, 2012.

vii

TABLE OF CONTENTS

Acknowledgement ................................................................................................... i

Abstract .................................................................................................................... ii

List of Publications .................................................................................................. v

Acronyms ................................................................................................................. xiii

List of Figures .......................................................................................................... xv

List of Tables ........................................................................................................... xxii

Chapter 1 Introduction

1.1. Background ........................................................................................ 1

1.2. Objectives .......................................................................................... 3

1.3. Synopsis of this thesis ....................................................................... 4

1.4. Summary of original contributions .................................................... 5

Chapter 2 Literature Review

2.1. Introduction ....................................................................................... 7

2.2. PD mechanism and terminology ....................................................... 7

2.3. Electromagnetic radiation generated in the event of PD ................... 9

2.3.1. PD pulse ............................................................................................. 14

2.4. UHF PD pulse and spectra ................................................................ 15

2.5. PD detection ...................................................................................... 18

2.5.1. Direct coupling method to detect the PD event ................................. 19

2.5.2. UHF PD detection method ................................................................ 23

2.6. Classifications of partial discharge .................................................... 24

2.6.1. Corona ............................................................................................... 24

2.6.2. Surface discharge ............................................................................... 25

2.6.3. Internal discharge .............................................................................. 26

2.7. UHF PD detection in high voltage equipment .................................. 27

2.7.1. UHF PD detection in GIS ................................................................. 28

2.7.2. UHF PD detection in transformer ...................................................... 29

viii

2.7.3. Sensors to detect PD in transformer .................................................. 30

2.7.4. PD waveform and pattern measurement ............................................ 32

2.7.5. Sensor sensitivity ............................................................................... 33

2.8. UHF PD source recognition ............................................................. 33

2.9. UHF PD source localization ............................................................. 35

Chapter 3 Sensor to Detect PD in Transformer

3.1. Introduction ....................................................................................... 38

3.2. Sensor to detect PD ........................................................................... 38

3.3. Sensor fundamental ........................................................................... 40

3.3.1. Bandwidth .......................................................................................... 40

3.3.2. Radiation pattern ............................................................................... 41

3.3.3. Input impedance ................................................................................ 42

3.3.4. Voltage standing wave ratio (VSWR) ............................................... 43

3.3.5. Return loss ......................................................................................... 44

3.3.6. Directivity .......................................................................................... 44

3.3.7. Gain ................................................................................................... 45

3.4. Balun .................................................................................................. 46

3.4.1. Tapered balun .................................................................................... 47

3.4.2. Microstrip balun ................................................................................ 48

3.4.3. Quarter wave matching transformer .................................................. 49

3.4.4. Chebyshev multi-section matching transformer ................................ 51

3.4.5. Planar transmission lines ................................................................... 53

Coplanar waveguide (CPW) lines ..................................................... 54

Coplanar strip line (CPS) .................................................................. 56

3.5. Sensor design ..................................................................................... 58

3.5.1. Types of the sensors ......................................................................... 58

3.5.2. Monopole ........................................................................................... 59

Return loss and VSWR ....................................................................... 60

Input impedance ................................................................................ 62

Radiation Pattern .............................................................................. 62

3.5.3. Conical ............................................................................................... 63

ix


Input impedance ................................................................................ 65


3.5.4. Planar spiral antennas ........................................................................ 66

3.5.5. Log-spiral .......................................................................................... 67


Input impedance ................................................................................ 69


3.5.6. Archimedean spiral ............................................................................ 70


Input impedance ................................................................................ 72


3.5.7. Balun .................................................................................................. 73

Log-spiral balun ................................................................................ 74

Archimedean spiral balun ................................................................. 75

3.6. Sensor comparison ............................................................................. 75

3.7. Sensor testing to detect PD signals .................................................... 78

3.7.1. Result and discussion ........................................................................ 79

3.8. Conclusion ......................................................................................... 84

Chapter 4 Step Response, Frequency Response and Sensor Sensitivity

to Detect PD

4.1. Introduction ....................................................................................... 85

4.2. UHF Electromagnetic Signal ............................................................. 86

4.2.1. Electromagnetic propagation modes ................................................. 87

4.2.2. Electromagnetic propagation in transformer ..................................... 88

4.3. Sensors Step Pulse and Frequency Response ................................... 89

4.3.1. TEM cell ............................................................................................ 89

4.3.2. Step pulse response ............................................................................ 91

4.3.3. Frequency response ........................................................................... 92

4.4. Sensor Sensitivity to Detect PD ........................................................ 94

4.4.1. Experimental set-up ........................................................................... 94

x

4.4.2. Full span and zero span measurement ............................................... 95

4.4.3. PD spectrum ...................................................................................... 99

4.4.4. Quantifying PD measurement ........................................................... 101

4.4.5. Sensitivity to detect different PD sources ......................................... 102

4.4.6. Barrier effect ...................................................................................... 103

Void .................................................................................................... 104

Floating metal ................................................................................... 111

4.5. Conclusion ......................................................................................... 115

Chapter 5 UHF PD Recognition Using PD Waveform and PRPD Pattern

5.1 Introduction ....................................................................................... 116

5.2 UHF PD detection ............................................................................. 117

5.2.1 Recognition of PD source ................................................................. 117

5.3. Artificial neural network ................................................................... 118

5.3.1. Biological neural networks ................................................................ 118

5.3.2. Artificial neuron model .................................................................... 120

5.3.3. Neural networks ................................................................................. 121

Architecture ....................................................................................... 121

Learning process ............................................................................... 123

Activation function ............................................................................. 124

5.3.4. Back-propagation neural network ..................................................... 127

5.4. Neuro-fuzzy ....................................................................................... 129

5.4.1. Fuzzy set ........................................................................................... 130

5.4.2. Membership function ......................................................................... 131

5.4.3. Fuzzy if-then rules ............................................................................. 133

5.4.4. Fuzzy inference system ..................................................................... 134

5.4.5. ANFIS ................................................................................................ 136

5.5. Recognition of different sources of PD from the PD waveform ........ 139


5.5.2. UHF PD signals ................................................................................. 142

5.5.3. Multivariate denoising ....................................................................... 143

5.5.4. Signal decomposition and features extraction ................................... 146

xi

5.5.5. Feature measure and selection ........................................................... 148

5.5.6. Recognition results ........................................................................... 151

Denoised PD signals .......................................................................... 152

Original (noisy) PD signals ................................................................ 152

5.6. Recognition single and multiple PD sources from the phase

resolved PD pattern ........................................................................... 154


5.6.2. PD pattern and signatures .................................................................. 156

PRPD pattern of zero span measuring .............................................. 156

UHF PD signatures ........................................................................... 157

5.6.3. Results and discussion ....................................................................... 157

PD pattern ......................................................................................... 157

PD features ........................................................................................ 160

The ANFIS rules, training and testing ............................................... 161

5.7. Conclusion ......................................................................................... 163

Chapter 6 UHF PD Localization in Transformer

6.1. Introduction ....................................................................................... 165

6.2. Signals propagation and waveform timing ........................................ 166

6.3. PD source positioning ....................................................................... 167

6.4. Time difference of the arrival signals ................................................ 169

6.4.1. First peaks .......................................................................................... 169

6.4.2. Cross-correlation ............................................................................... 172

6.4.3. Cumulative energy ............................................................................. 174

6.5. Sensor consideration .......................................................................... 177

6.6. Experimental set-up ........................................................................... 178

6.7. Results and discussion ....................................................................... 180

6.7.1. Denoising the PD waveforms ............................................................ 182

6.7.2. First peaks .......................................................................................... 185

6.7.3. Cross correlation ................................................................................ 187

6.7.4. Cumulative energy ............................................................................. 189

6.7.5. Comparison between the three methods ............................................ 192

xii

6.8. Conclusion ......................................................................................... 200

Chapter 7 Conclusion and Suggestion for Future Research

7.1. General .............................................................................................. 201

7.2 Sensor Design .................................................................................... 202

7.3. Sensor pulse response and sensitivity test in oil ................................ 203

7.4. PD detection and recognition using UHF method ............................. 204

7.5. PD localization using UHF method ................................................... 205

7.6. Future Work ....................................................................................... 207

Reference ............................................................................................................ 209

Appendix A Sensor Design Using CST Microwave Studio ................................. 222

Appendix B TEM Cell ............................................................................................ 226

Appendix C Experiment Set-Up ............................................................................ 229

Appendix D PD localization ................................................................................... 232

Appendix E Matlab Script of the PD Localization .............................................. 235

E.1. Data loading and denoising function ............................................................ 238

E.2. Calculation of the TDOA .............................................................................. 240

E.2.1. First Peak ........................................................................................... 240

E.2.2. Cross-correlation ............................................................................... 244

E.2.3. Cumulative energy ............................................................................. 245

E.3. Calculation the PD source coordinates ......................................................... 251

xiii

ACRONYMS

ABW absolute band width

AI artificial intelligence

ANFIS adaptive neural network fuzzy inference system

ANN artificial neural network

BNC connector Bayonet Neill–Concelman

BPN back-propagation neural network

Balun balance unbalance

CPS coplanar strip line

CPW coplanar waveguide

CST computer simulation technology

CT current transformer

dBm power ration in decibels (dB) of measured power referenced to 1 mW

FBW fractional bandwidth

FFT fast fourier transform

FM floating metal of PD sample

GA genetic algorithm

GIS gas insulated switchgear

MCD minimum covariance determinant

MIC microwave integrated circuit

PCA principal component analysis

PCB printed circuit board

PD partial discharge

PRPD phase-resolved partial discharge

S11 return loss

SA spectrum analyzer

SD surface discharge

STFT short-time fourier transform

RF radio frequency

RL return loss

xiv

TOA time of arrival

TDOA time difference of arrival

UHF ultra high frequency

UWB ultra wide band

VSWR voltage standing wave ratio

xv

LIST OF FIGURES

Figure 2.1: Electric and magnetic fields of a moving charge particle Q ........... 10

Figure 2.2: The production of radiation during the acceleration of

charge process ................................................................................. 11

Figure 2.3: Pulse shape of the radiation field at point M-N and L-J

modelled as a Gaussian pulse .......................................................... 11

Figure 2.4: The electric field at angle θ caused by charge q accelerated

from point A to B then moving with constant speed until

reaching point C .............................................................................. 12

Figure 2.5: PD pulse waveforms using Gaussian pulses of similar

current magnitude value but different pulse rise times .................... 16

Figure 2.6: Normalized spectra of Gaussian pulses of different

pulse rise times ................................................................................ 17

Figure 2.7: Methods of PD detection ................................................................. 19

Figure 2.8: Direct coupling PD measurement diagram ..................................... 20

Figure 2.9: (a) An internal discharge defect and (b) the electrical circuit

equivalent diagram, known as the abc model ................................. 20

Figure 2.10: Typical UHF PD detection diagram ................................................ 24

Figure 2.11: Surface discharge ............................................................................ 25

Figure 2.12: (a) Cross section of insulation with cavity presence within,

and (b) the analogue capacitance circuit diagram ........................... 26

Figure 3.1: Reference terminal and losses on an antenna .................................. 46

Figure 3.2: Cross-section of a coaxial cable, unbalanced at high frequency ...... 47

Figure 3.3: Tapered balun transformer .............................................................. 47

Figure 3.4: Four-stage microstrip balun ............................................................ 49

Figure 3.5: Partial reflection and transmission coefficients on a single

section of matching transformer ...................................................... 49

Figure 3.6: CPW schematic on a dielectric substrate ........................................ 54

Figure 3.7: CPS schematic on a dielectric substrate of finite thickness ........... 56

Figure 3.8: Design of monopole antenna with 4 cm FR4 substrate

xvi

as antenna base ................................................................................ 60

Figure 3.9: S11 parameter of varying length of monopole antenna .................. 61

Figure 3.10: Varying length Monopole antenna VSWR parameter .................... 61

Figure 3.11: Input impedance of monopole antennas .......................................... 62

Figure 3.12: Radiation pattern of monopole antenna at varying frequencies ...... 62

Figure 3.13: Conical antenna design with 4 cm FR4 substrate as antenna base . 63

Figure 3.14: S11 parameter of varying length of conical antenna ....................... 64

Figure 3.15: VSWR parameter of varying length of conical antenna ................. 64

Figure 3.16: Impedance of varying length of conical antenna ............................ 65

Figure 3.17: Radiation pattern of conical antenna at varying frequencies ........... 65

Figure 3.18: Log-spiral design, (a) tapered end (design1),

and (b) truncated end (design2) ....................................................... 67

Figure 3.19: S11 result of Log-spiral antenna ...................................................... 68

Figure 3.20: VSWR result of Log-spiral antenna ................................................ 68

Figure 3.21: VSWR result of Log-spiral antenna ................................................ 69

Figure 3.22: Radiation pattern of Log-spiral antenna at varying frequencies ..... 70

Figure 3.23: Five turn-Archimedean spiral ......................................................... 70

Figure 3.24: S11 of 5 turn-Archimedean spiral ................................................... 71

Figure 3.25: VSWR of 5 turn-Archimedean spiral .............................................. 72

Figure 3.26: Impedance of 5-turn Archimedean spiral ........................................ 72

Figure 3.27: Radiation pattern of spiral antenna at varying frequencies ............. 73

Figure 3.28: Surface current of the 6-section balun terminated with

impedance of 160 ohms, at frequency 3 GHz and

phase current 180 degrees ............................................................... 74

Figure 3.29: S11 parameter of selected sensors ................................................... 76

Figure 3.30: VSWR of selected sensors .............................................................. 77

Figure 3.31: Input Impedance of selected sensors ............................................... 77

Figure 3.32: Realized gain of selected sensors .................................................... 78

Figure 3.33: Experiment diagram for testing sensor ability to detect PD ............ 78

Figure 3.34: Corona pattern recorded using Mtronix PD detector, corona

on negative half-cycle shows values at around 5-10 pC ................. 80

Figure 3.35: Corona patterns recorded using zero span mode captured by

xvii

various sensors, the sensor distance to the PD source is 100 cm .... 81

Figure 3.36: Corona patterns recorded using zero span mode at different

frequencies at PD level of 60 pC in positive half-cycle and

5 to 10 pC in negative half-cycle: (a) Conical, (b) Log-Spiral,

(c) Spiral, and (d) Monopole ........................................................... 83

Figure 4.1: A rectangular wave guide ................................................................ 87

Figure 4.2: Cross section of strip line geometry ................................................ 89

Figure 4.3: Field plot of designed strip line ....................................................... 90

Figure 4.4: Test diagram for frequency response measurement and

pulse response ................................................................................. 91

Figure 4.5: Step pulse response of the four sensors ........................................... 92

Figure 4.6: Sensors frequency response ............................................................ 93

Figure 4.7: Experimental diagram to test the sensor sensitivity

to detect different PD sources and effect of internal

physical barriers .............................................................................. 95

Figure 4.8: PD patterns recorded by Mtronix PD detector,

(a) Floating metal and (b) Void ....................................................... 96

Figure 4.9: PD patterns recorded by the UHF method, (a) Floating metal

and (b) Void, associated with Figure 4.8 ......................................... 97

Figure 4.10: Full span spectra recorded by using 4 different sensors,

(a) Floating metal at 70 pC and (b) Void at 60 pC ......................... 98

Figure 4.11: The background noise spectrum recorded by 4 different sensors .... 99

Figure 4.12: Full span PD spectra recorded by the UHF method,

(a) Floating metal at 30 pC and (b) Void at 20 pC ......................... 100

Figure 4.13: The total energy of zero span of different PD sources,

(a) Void and (b) Floating metal ....................................................... 103

Figure 4.14: Total energy of full-span spectra with varying barrier positions,

void PD source ................................................................................ 106

Figure 4.15: Total energy of zero-span spectra with varying barrier positions,

void PD source; (a) Conical sensor, (b) Log-spiral, (c) Spiral

and (d) Monopole ............................................................................ 107

Figure 4.16: Total energy of zero-span spectra measured by different sensors;

xviii

(a) no-barrier, (b) barrier distance 5 cm, (c) barrier distance 10 cm,

(d) barrier distance 15 cm, and (e) barrier distance 20 cm

from the sensor. ................................................................................ 108

Figure 4.17: Maximum value of zero-span spectra with varying

barrier positions, void PD source; (a) Conical sensor,

(b) Log-spiral, (c) Monopole and (d) Spiral .................................... 109

Figure 4.18: Magnitude of the zero-span spectra of void PD; (a) no-barrier,

(b) barrier distance 5 cm, (c) barrier distance 10 cm,

(d) barrier distance 15 cm, and (e) barrier distance 20 cm .............. 110

Figure 4.19: Total energy of full-span spectra with varying barrier positions,

floating metal PD source: (a) Log-Spiral, (b) Conical,

(c) Monopole, and (d) Spiral ........................................................... 112

Figure 4.20: Total energy of the zero-span spectra of Floating metal PD;

(a) no barrier, (b) barrier distance 5 cm, (c) barrier distance 10 cm,

(d) barrier distance 15 cm, and (e) barrier distance 20 cm .............. 113

Figure 4.21: Total energy of the zero-span spectra of the Floating metal

PD source for varying barrier distances: (a) Log-Spiral,

(b) Conical, (c) Monopole, and (d) Spiral ....................................... 114

Figure 5.1: Biological neuron ............................................................................ 119

Figure 5.2: Mathematical model of a neuron ..................................................... 120

Figure 5.3: Single layer neural net ..................................................................... 121

Figure 5.4: Architectural graph of multilayer net with two hidden layers ........ 123

Figure 5.5: Plot of threshold function ................................................................ 125

Figure 5.6: Plot of piecewise-linear function .................................................... 125

Figure 5.7: Plot of uni-polar sigmoid function .................................................. 126

Figure 5.8: Plot of bi-polar sigmoid function .................................................... 127

Figure 5.9: Plot of hyperbolic tangent function ................................................. 127

Figure 5.10.a: Membership grades of a fuzzy set of a Triangle shape ................... 132

Figure 5.10.b: Membership grades of a fuzzy set of a Gaussian shape .................. 132

Figure 5.10.c: Membership grades of a fuzzy set of a Bell shape .......................... 133

Figure 5.11: Block diagram of a fuzzy inference system ................................... 134

Figure 5.12: (a) A two-input first-order Sugeno fuzzy model with two rules;

xix

(b) The ANFIS architecture ............................................................ 137

Figure 5.13: Flowchart of the recognition method .............................................. 139

Figure 5.14: Experiment diagram of PD signal detection and recording ............ 140

Figure 5.15: PD defect models (a) electrodes and sample arrangement

(b) void, (c) floating metal and (d) mixture of void and

floating metal .................................................................................. 141

Figure 5.16: A typical waveform from void discharges ...................................... 142

Figure 5.17: A denoising example (a) original signal, (b) denoising

using multivariate thresholding, and (c) result after

retaining PCA component ............................................................... 144

Figure 5.18: Denoised PD signals using db2 wavelets (a) Floating metal,

(b) Void, and (c) mix of Floating Metal and Void .......................... 145

Figure 5.19: A five-level wavelet-packet decomposition tree ............................. 146

Figure 5.20: The mother wavelets (a) db2 and (b) sym2 ..................................... 147

Figure 5.21: Signal decomposition (a) original Floating metal (FM) signal,

(b) denoising FM PD signal, (c) node (2,1), (d) node (5, 0) and

(e) node (5, 26) ................................................................................ 148

Figure 5.22: Features plot of the best nodes using different wavelets,

decomposed using (a) db2, (b) sym2 .............................................. 150

Figure 5.23: A three-layer neural network .......................................................... 151

Figure 5.24: Features plot of the best nodes of the original signals,

decomposed using different wavelets (a) db2, (b) sym2 ................ 153

Figure 5.25: PD defect models (a) void, (b) floating metal and

(c) surface discharge ....................................................................... 155

Figure 5.26: Typical PD pattern captured by the log-spiral sensor

at different distances ....................................................................... 156

Figure 5.27: PRPD of different PD sources at different frequencies .................. 158

Figure 5.28: Fuzzy inference system (FIS) generated by genfis1 ........................ 161

Figure 5.29: Membership function (a) before training (generated by Genfis1)

and (b) after training using ANFIS .................................................. 162

Figure 6.1: Coordinate system of the PD source P (x, y, z)

and sensor S (x1, y1, z1) .................................................................... 168

xx

Figure 6.2: (a) PD waveforms captured by different sensors,

and (b) the unipolar and normalized PD waveform ........................ 171

Figure 6.3: Peak detection of unipolar PD waveform ....................................... 171

Figure 6.4: Cross correlation of the waveforms between sensor i (i = 1,2,3)

and reference sensor 4. The peaks are marked with * ..................... 173

Figure 6.5: Normalized cumulative energy curves of

sensor voltage waveforms ............................................................... 175

Figure 6.6: Step pulse responses of different sensors: (a) waveforms,

and (b) normalized cumulative energy curves ................................ 177

Figure 6.7: Experimental setup: (a) layout and circuit for PD generation

and detection, (b) coordinate system for location ........................... 180

Figure 6.8: Typical waveforms captured by sensors in different locations ....... 181

Figure 6.9: Low magnitude of waveform captured by sensors

in different locations ........................................................................ 182

Figure 6.10: Noise background and PD spectrum captured by monopole

sensor installed inside transformer tank .......................................... 183

Figure 6.11: (a) The PD waveform captured by the sensor, and

(b) the denoised waveform .............................................................. 184

Figure 6.12: Peaks of normalized unipolar denoised PD waveforms ................... 185

Figure 6.13: The zoom of the cross-correlation waveforms to show

the time difference of different signals ........................................... 187

Figure 6.14: Time difference curve calculated using similarity function ............ 190

Figure 6.15: PD localization error plots for PD location 1 ................................... 193









Figure 6.24: PD localization error plots for PD location 10 ................................. 198

xxi



xxii

LIST OF TABLES

Table 3.1: Log-spiral balun impedance and dimension ......................................... 74

Table 3.2: Archimedean spiral balun impedance and dimension ......................... 75

Table 4.1: Background noise captured by different sensors ................................. 101

Table 4.2: Total energy of the PD detected by UHF sensor at inception

voltage of void and floating metal PD sources .................................... 102

Table 5.1: The largest J values of the three features ............................................. 149

Table 5.2: Percentage of correct classification using

feed-forward neural network ............................................................... 152

Table 5.3: Data checking arrangement ................................................................. 160

Table 5.4: Test results using trained FIS ............................................................... 163

Table 6.1: UHF Sensors position ......................................................................... 178

Table 6.2: PD source coordinates .......................................................................... 179

Table 6.3: The PD location and error calculated by using TDOA of

the first peak method ............................................................................ 186

Table 6.4: The PD location and error calculated by using TDOA of

the cross-correlation method ................................................................ 188

Table 6.5: PD location and error calculated by using TDOA of

the cross-correlation method (5 ns of waveform) ................................ 189

Table 6.6: PD location and error calculated by using TDOA of

the cumulative energy curve ................................................................ 191

Table 6.7: Average errors of the PD localization: (a) original, (b) denoised ......... 192

CHAPTER 1

INTRODUCTION

1.1. Background Transformers play a very important role in power transmission and distribution systems.

The majority of power transformers are oil-filled type. Their rating can vary from

several hundred kVA to a few hundred MVA. Failure of a power transformer whilst in

service will not only incur the cost of a replacement unit but also may cause

environmental damage from any oil spilled, endanger people in the vicinity, disrupt the

supply and lead to loss of revenue. Thus it is important to maintain transformer

condition at peak reliability.

On the other hand, power utilities always aim to maximize the utilization of their

equipment. For this reason, it is desirable to operate the transformer at its optimal power

rating and continuously. With time, the operating stress on the transformer insulation

can lead to its degradation. Weak spots thus created can be the starting point for

catastrophic failure of the insulation.

To avoid equipment breakdown, on-line monitoring plays an important role in detection

and determination of the condition of the insulation. From the monitored data, the

insulation condition can be ascertained and appropriate action can be determined. In

cases of severe deterioration of the insulation, further actions such as regular inspection

and repair can be taken to prevent catastrophic insulation failure.

Condition monitoring of a transformer is intended to detect and monitor the presence of

any faults or defects in the transformer insulation. The presence of defects such as a


2

cavity or a metal particle trapped in the insulation is undesirable. These defects will

enhance the local electric stress and if the field exceeds the dielectric strength, local

breakdown or partial discharge (PD) will occur and electromagnetic pulses will be

emitted as a result. These pulses have a very short duration, which can be less than 1 ns

in rise time and a few ns of pulse width [1]. Their spectra span over a wide frequency

range, typically from a few tens of kHz to a few GHz. This includes a particular

frequency range known as Ultra High Frequency (UHF), i.e. 300 MHz to 3 GHz.

Partial discharge detection by capturing the UHF signals emitted by the source, known

as UHF PD detection, has been proven effective in detecting discharges in gas insulated

switchgear (GIS). More recently, this method is being applied to detect PD in power

transformers [2]. PD detection using the UHF method has some advantages compared to

other approaches such as the conventional IEC60270 method. The advantages of the

UHF method mainly arise from the impunity of UHF sensors from noise and

interference [3 - 5].

UHF PD detection can be carried out in both time domain and frequency domain mode

[6]. Each detection mode can be used to detect, recognize and locate the PD source. The

PD signals can be analysed by applying time-frequency analyses such as Short-time

Fourier transform (STFT), Wavelet and Wigner transform. In this thesis, wavelet

decomposition is used for analyses and recognizes the PD source type as the wavelet

transform produces a balance in the time and frequency resolution and is able to

decompose the signals into component wavelets [6].

To be able to detect PDs using the UHF method, sensors which can work in the UHF

range are needed. The sensor can be installed as a probe which is inserted via an oil

drain valve or fitted via a dielectric window, crafted on the transformer tank [3]. The

first method can be completed without any modification to the transformer tank, while

the latter needs specially fitted dielectric windows which can be installed during a

maintenance period for already operating transformers or designed for installation

before initial usage of new transformers [7].

Unequivocal correlation between long-term partial discharge activity and insulation

failure has not yet been proven. However it is believed that transformer failure is most


3

commonly due to failure in the insulation, usually started by the occurrence of partial

discharges [8]. Based on the presence or absence of PD activity in transformer

insulation, an evaluation of transformer condition can be undertaken.

The presence of a specific PD defect type can be determined from the pattern recorded

in either the frequency domain or the time domain. It is also possible to determine the

location of the PD source by analyzing the PD waveform. This thesis examines UHF

PD detection, starting by designing the sensor then using it to recognize and locate the

PD source in transformers.

1.2. Objectives

The main objective of this research is to detect, recognize and locate the presence of

PDs in an oil-filled power transformer using UHF sensors (antennas). To this end, two

types of sensors were designed and tested to detect and locate the PD sources: a sensor

type that can be inserted to a transformer via its oil drain valve and another that can be

attached to a dielectric window.

The sensors were applied to detect and capture electromagnetic waves emitted by the

PD sources. The PD signals were recorded in both frequency and time domain to obtain

the integrated phase-resolved PD patterns and individual signal waveforms. These are

utilized to recognize and distinguish differences in the PD signals that are emitted by

each specific PD defect source. PD defect sources are created to mimic real PD sources

that might occur in transformer insulation.

The specific primary objectives of this thesis are:

1. To design UHF sensors that can be used to detect PD signals in power

transformers.

2. To analyze the sensitivity of the sensors to detect different PD sources.

3. To demonstrate the technique of the application of the UHF sensor to

recognize different PD sources in transformer insulation.


4

4. To demonstrate the technique of the application of UHF sensors to

distinguish single and multiple PD sources.

5. To demonstrate the use of an array of UHF sensors to locate the PD source

in transformers by geometric triangulation.

1.3. Synopsis of this thesis

Chapter 1 - Introduction. This chapter provides the background of the study, research

objectives and summary of this thesis.

Chapter 2 – Literature Review. This chapter describes the PD mechanism and

detection method, followed by the electromagnetic radiation caused by PD sources in

transformers and subsequently the waveforms and spectra of the PD signals. The

chapter ends with a review of the application of UHF PD detection and monitoring in

power transformers, including PD recognition and PD localization.

Chapter 3 - Sensor to detect PD in transformer. This chapter presents the sensor

design methodology that is applicable for detection of PD in transformers. The sensors

are designed based on a combination of various antenna parameters such as VSWR,

S11, input impedance and directivity. Electromagnetic software by the name of CST

Microwave Studio is utilised in the design process. Physical constraints on the sensor

dimension are taken into account in determining the sensor with the best parameters.

Discussion then continues on to testing of sensors to evaluate their ability to detect PD

signals generated by a corona source. The benchmark for comparison is ability to detect

PDs of 5 pC within a distance of 2 meters.

Chapter 4 – Step Response, Frequency Response and Sensor Sensitivity to Detect

PD. This chapter discusses the sensitivity of the designed sensors. The discussion

commences with the electromagnetic propagation mode which forms the basis for the

step pulse and frequency response testing of the sensor. Following this is a discussion


5

on sensitivity of sensors to detect different PD defect types. The effect of transformer

parts inside the tank in the form of a barrier is also discussed.

Chapter 5 - UHF PD Recognition Using PD Waveform and PRPD Pattern. This

chapter discusses the application of the UHF detection method in transformers to

recognize the PD source. The discussion starts with the different measurement modes,

i.e. in time domain and frequency domain. The method of data extraction from the UHF

signals is then discussed and the experimental data is applied to recognize the PD source

using artificial intelligence. The data extraction starts with denoising the PD waveform

then decomposing the PD waveform using two types of mother wavelets. Neuro-fuzzy

and artificial neural network methods are implemented to recognize the different PD

sources, either single or multiple.

Chapter 6 - UHF PD localization in transformer. This chapter discusses PD

localization in transformers using the UHF detection method. An array of four

monopole sensors is used to capture the electromagnetic signals emitted by the PD

source. The reasons for choosing monopole sensors are discussed in this chapter. To

determine the PD location, the time difference of arrival (TDOA) is calculated using

three methods: first peak, waveforms cross-correlation and cumulative energy. The

TDOA is calculated for three sensors using the fourth sensor as reference. The PD

location is then calculated using geometric triangulation.

Chapter 7 – Conclusion and future study. This chapter concludes the study and

suggests future research related to the measurement of PDs in power transformers using

UHF detection.

1.4. Summary of original contributions

The original contributions by the author from this research are:

1. Development of various UHF sensors using CST software for PD detection

application.


6

2. Development of a methodology for a sensitivity test to calibrate the sensor output

to the amount of pC using the phase resolved partial discharge (PRPD) pattern

recorded by a spectrum analyser in zero span mode.

3. Development of methods to determine suitable sensors for PD detection and

localization.

4. Demonstration of neuro-fuzzy recognition of different PD defect types from the

UHF PD signals recorded in time and frequency domain.

5. Development of a new method to determine the time difference of signal arrival

time (TDOA) using the peak detection method.

6. Demonstration of PD localization by comparing three methods of determining the

TDOA, i.e. first peak, cross-correlation and cumulative energy.

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

This chapter presents a review of partial discharge (PD) in transformers. It starts with

the definition of PD and continues on to the basic theory of electromagnetic pulses

emitted by PD events. These electromagnetic pulses have a very fast rise time so their

spectra extend into the GHz frequency range. The discussion continues on to different

approaches to PD detection and the position of the ultra high frequency (UHF) detection

technique among the various PD detection methods. The discussion then moves on to

the classification of the PD source.

UHF PD detection in high voltage equipment is discussed in the following section,

which looks at UHF PD detection in GIS and transformers. The sensors needed to detect

PD signals are also discussed, continuing on to signal waveform and pattern

measurement, and the sensor sensitivity. This chapter ends with discussion of the

application of the UHF PD detection method to recognize different types PD defect and

to locate the source.

2.2. PD mechanism and terminology

Partial discharge (PD) as defined by IEC 60270 [9] is a localized electrical discharge

that only partially bridges the insulation between conductors and which can or cannot

occur adjacent to a conductor. As per the definition, the PD can occur in the middle of


8

insulation between two electrodes or near the electrode, as long as the discharge occurs

only locally. When the discharge increases in size and crosses the insulation between

electrodes/conductors or, in other words, the charges bridge the two electrodes, then full

breakdown occurs. Although there is no direct correlation between PD and breakdown,

for instance, where the breakdown is not always started with the presence of a PD event,

it is believed that PD events in the insulation will weaken the insulation strength and

can lead to breakdown if the discharges are allowed to develop over time.

The PD mechanism in gas/liquid starts when an atom collides with a free electron which

is accelerated by the surrounding field. The collision can produce more free electrons

and further collisions. This repeated collision process can increase the number of

electrons exponentially causing “electron avalanche”.

The mechanisms of partial discharge can be categorized into two most common types

[10, 11], i.e. Townsend discharge and streamer discharge. In Townsend discharge, the

gap current grows as a result of ionization by electron impact and electron emission at

the cathode by positive ion impact [10]. The electron and ion have a small space charge

compared to the external field and can be neglected, thus the ionization process is

mainly a direct ionization [11]. The Townsend discharge occurs within a short-gap and

has the following forms: rapid and slow rise time spark-type pulses, true pulseless

glows or pseudo-glow discharges [11] which are all cathode emission sustained

discharges. The rise time of these pulses can be as long as several tens of nanoseconds

and its duration can last several hundreds of nanoseconds [12].

Unlike the Townsend discharge, the streamer discharges are independent of cathode

emission, but dependent upon the photoionization process in the gas volume [11]. The

streamer discharge occurs in longer gaps and involves ionization wave propagation in a

very high field region where ionization and influx of electrons at the discharge head is

produced by a space charge field due to the separation of positive and negative charges

[11]. The space charge fields have an important role in the corona and spark discharge

in non-uniform field gaps [13]. Streamer discharges are commonly of shorter duration

than Townsend discharges; the streamer discharge pulse length can vary from 1 ns to 10

ns [11].


9

Each pulse generated by both of the above types is represented by the presence of a

partial discharge pulse. The partial discharge pulse (PD pulse) is defined as a current or

voltage pulse that results from a partial discharge occurring within the object under

test. The pulse is measured using suitable detector circuits, which have been introduced

into the test circuit for the purpose of the test [9].

2.3. Electromagnetic radiation generated in the event of PD

In the event of a discharge in transformer insulation, free electron charges which were

initially at rest are accelerated and decelerated by an external force. The acceleration

and deceleration processes produce a time varying electromagnetic field which radiates

outward from the PD location. The cause of radiation and the subsequent process are

discussed below, drawing on Froula et al, 2001 as well as Longren and Savov, 2005.

[14, 15].

A stationary charge has only electric field which is radiated radially. As the charge is in

motion, electric field and magnetic field are produced. The electric field at any point

near the moving charge with a speed v in the ux direction as shown in Figure 2.1, can be

calculated as:

2 20

14 r

QE ur x

2.1

or:

20

14 r

QE uR

2.2

where R2 = r2 + x2, x is displacement distance and r is the distance of the charge to the

observer after moving a distance x.

The magnetic field caused by this moving particle can be calculated by using the Biot-

Savart law, producing:


10

02 2( )

4rQ v xuB

r x

2.3

Figure 2.1: Electric and magnetic fields of a moving charge particle Q [14]

Assume the charge Q at point A is initially at rest then accelerated in x direction as

shown by Figure 2.2 to reach point B after which it moves with velocity v until it

reaches point C (v << speed of light). The time needed during the acceleration process is

∆t seconds. The electric field lines at any point in the x direction in the path of the

moving charge are entirely radial and must be continuous since they are produced by the

same charge.

During the acceleration of the charge, the electric field lines are always updating its

position. However, due to the time needed by the electric field lines to adjust, the lines

will have disrupted the direction or become misaligned. This line disruption is known as

a ‘kink’ [15]. The kinks, as shown in Figure 2.2, have both a static Coulomb field and

an electric field which are perpendicular to each other. The transverse electric field

produced by this process then causes radiation. The maximum radiation occurs along

the line perpendicular to the direction of the acceleration. The radiation at point m

where maximum radiation occurs is drawn in Figure 2.3 as a pulse shape. In the same

direction with the acceleration there is no transverse electric field component produced,

only a static Coulomb field thus no radiation occurs.

B

E

Q

Qr

x

R

Q'

v

Er

Ex

E

B


11

A B CX

J

L

M

N kink

Coulomb’s fieldRadiation field

no kink

no radiation field

Electric field line

Figure 2.2: The production of radiation during the acceleration of charge process [15]

M N

L J

Et

x

E

Figure 2.3: Pulse shape of the radiation field at point M-N and L-J modelled as a

Gaussian pulse


12

A B C

θ

EoEt

L

J

K

Electric field line

vt sin θ

x

≈ vt

ρ = ct

c ∆t

Figure 2.4: The electric field at angle θ caused by charge q accelerated from point A to

B then moving with constant speed until reaching point C.

The electric field lines in the kink region have both transverse electric field and

Coulomb component, as aforementioned. Assume the kink occurs at point L as shown in

Figure 2.4. The charge accelerates from stationary at point A until reaching point B,

with the velocity at any moment during acceleration defined as v = a ∆t, where a is

acceleration. Then the charge is moving constantly from B to C for t seconds. By

assuming the ∆t << t, so distance d=AB+BC ≈ BC = vt.

The radial field Eo can then be calculated by using Equation 2.2 and can be written as:


13

0 2 20 0

1 14 4 ( )

Q QER ct

2.4

From Figure 2.4, the transverse electric field component (Et) can be calculated as:

0 t

E JK c tE KL vt sin

2.5

Solving for Et:

0 t

vt sinE Ec t

2.6

Inserting Equation 2.4 into Equation 2.6, it becomes:

20

1 4 ( ) t

Q vt sinEct c t

or

20

1 4 t

Q v sinEc t c t

2.7

By substituting 21o oc and also using ct (from Figure 2.4), Equation 2.7 can

be written as:

0 4 t

Q sin vEt

2.8

The factor v/∆t is called retarded acceleration, which is a time delay of the electric field

to reach point L due to the time needed by the accelerating charge to propagate from

point C to L. Or in other words, at point L the electric field of the moving charge Q is

sensed at the previous time t’. Simplifying Equation 2.8 by introducing the retarded

acceleration [a] factor [15], the transverse electric field can then be written as:

0 [ ] 4 t

Q a sinE

2.9


14

where 'a a t t c and for N number of charges:

0 [ ] 4 t

N Q a sinE

2.10

In case of the transverse electric field caused by PD events, the electromagnetic signals

can then be captured and recorded using appropriate sensors and measuring systems.

From Equation 2.10, the characteristics of the electromagnetic PD signal that is

produced during discharge events depend on:

Number of charges produced during the discharge process

The acceleration of the charges which are affected by the magnitude of the

surrounding field forces.

Permeability of the medium where the PD took place.

The position of the observer angle and distance from the accelerating charge.

2.3.1. PD pulse

As mentioned in a previous section, the discharge characteristic depends on 4 variables.

The first three are the effect of the type of PD source and the surrounding medium and

the last is the position of the sensor that is used to detect the PD. These four variables

will affect the PD pulse characteristic, for example, the greater the number of charges

the higher the magnitude of the pulse and the faster the charges are accelerated and

move the steeper the pulse rise time [16].

In GIS, the rise time of PD pulses caused by protrusions can be as low as 50 ps thus

producing electromagnetic signals with frequencies of up to 20 GHz [17]. In

transformer oil, however, due to its higher permittivity, the rise time is much longer.

Typical pulse rise time of protrusion PD source in oil is 0.9 ns during the positive half-

cycle and 2.0 ns during the negative half-cycle [1].

Besides the medium in which electromagnetic waves propagate, the PD source type also

affects the pulse rise time. The rise time measured for free metallic particle PD source is


15

2.5 ns during the positive half-cycle, and 2.7 ns during the negative half-cycle. Bad

contact defects produce pulses with slower rise time, up to 10 ns and 17 ns during

positive and negative half-cycles respectively [1].

2.4. UHF PD pulse and spectra

The electromagnetic signals emitted by the PD sources in transformer insulation are

propagated inside the transformer tank, reflected and refracted by the component parts

of the transformer. By inserting an appropriate sensor inside the transformer, these

electromagnetic signals can be captured and recorded by a measuring unit connected to

the sensor. The PD signals can be recorded in two modes, i.e. time domain and

frequency domain.

The time domain mode is usually carried out with the use of an oscilloscope to record

the signals. In this mode, the signal waveforms i.e. magnitude and time for specific time

range are recorded. In frequency domain mode, the magnitudes of the constituent

frequency components over a specific frequency range are recorded, usually with a

spectrum analyser (SA). The measurement in frequency domain mode can be completed

in two modes i.e. full-span (including narrow span) and zero span mode. In full span

mode the signal’s spectrum is recorded over the maximum range of frequency of the

SA. Measurement can also be completed in narrow band to reveal the PD occurrences in

a specific frequency band. The second mode is zero span, which records PD signals at a

single frequency over a specific time range to build up a phase resolved partial

discharge (PRPD) pattern. Both methods have advantages and disadvantages, and can

be used to detect the presence of PD sources in transformer insulation.

Different PD sources have different PD pulse shapes. The pulse generated by the PD

source is captured by the sensor and recorded in one of the modes discussed above.

Depending on the pulse shape, the waveform signals can be oscillating up to 100 ns

[11]. These oscillating pulses have frequencies in a wide band [16-18].

The PD pulse can be approached as a Gaussian pulse [19]. The Gaussian pulse is

defined as the following equation:


16

2 2/2t

maxi t I e 2.11

where: Imax = magnitude of the peak current

σ = pulse width which is chosen to fit the pulse shape with measured

pulses and measured at half of the maximum value.

The spectrum of the Gaussian pulse of Equation 2.11 can be obtained by using the

Fourier transform [20]:

2 2/2 t j t

maxF I I e e dtt

2.12

and produces:

2 2

22 maxI I e

2.13

The pulse rise time (T) of the Gaussian pulse is defined as the time required for signal

magnitude to change from 10% to 90% and calculated as:

14 erf (0.8)T

2.14

The graph of different Gaussian pulses is shown in Figure 2.5, and their spectra are

shown in Figure 2.6 using Equations 2.11 and 2.13 respectively.

Figure 2.5: PD pulse waveforms using Gaussian pulses of similar current magnitude

value but different pulse rise times


17

Figure 2.6: Normalized spectra of Gaussian pulses of different pulse rise times

Beside the Gaussian pulse, the PD pulse also can be approached as other equivalent

pulses; such as Wanninger [21] and double exponential [22]. The Wanninger equations

for both time and frequency domain are written as:

11 /1

1

( ) t TIi t teT

2.15

2

1

( )1

qIj T

2.16

where I1 is the peak amplitude, T1 controls the rise time, and q is the total charge in the

current pulse.

The double exponential equation is expressed as:

( ) [(1 ) (1 )t tmi t I t e t e 2.17

1 1 1 1( ) mI Ij j j j

2.18


18

where Im is the current amplitude and, α and β are a pair of constants which control the

pulse shape.

2.5. PD detection

The reliability of high voltage equipment such as power transformers mainly depends

on the condition of their insulation. Therefore any symptom that may lead to

catastrophic failure must be detected at an early stage. Even though there is no direct

correlation between the occurrence of PD in HV equipment and transformer failure, it is

widely accepted that the presence of PD may start and lead to the failure of the

insulation system. If the PD pulse is allowed to grow overtime, it can cause the

insulation material to deteriorate which may then lead to a complete breakdown of the

transformer insulation. In addition, PD produces localized heat and also can initiate a

complex chemical reaction which can accelerate the ageing of the insulation.

PD occurs in the transformer insulation due to the presence of defects. Defects can

cause high electric stress to occur and may lead to the presence of PD events. A PD

event resulting from an insulation defect can cause macroscopic-physical effects, such

as dielectric losses, electromagnetic transient signals, pressure wave, sound, light, heat

and chemical reaction [23]. All these effects can locally reduce the dielectric strength of

the insulation [24-26]. By applying specific sensors and measurement methods to

measure those effects, the presence of PD can be detected and monitored. The data

results will give information about the insulation defects and can thus be used to assess

the insulation condition.

Various non-conventional techniques have been developed for detection of PD in HV

equipment over the years. Two of the most common methods in use are electromagnetic

and acoustic PD detection [23]. These techniques do not conform to IEC 60270

standards because they detect different PD quantities as compared to the apparent

charges set out in IEC 60270. Several non-conventional PD detection methods which

are used for PD detection and localization are shown in Figure 2.7.


19

In this thesis two measurement methods are employed: the conventional method (IEC

60270) and the detection of the electromagnetic transient particularly in UHF range

(300 MHz to 3000 MHz). The direct coupling method is applied to measure the amount

of PD charge in pC unit. This method complies with the IEC 60270 standard.

Measurement of PD using the non-conventional method is done by detecting and

recording the electromagnetic transient signals using sensors which act as antennas to

capture the propagated electromagnetic waves emitted by the PD source. The sensors

were designed to work in the UHF frequency range using CST software. This non-

conventional method is known as the UHF method [2, 3, 27].

Figure 2.7: Methods of PD detection [23]

2.5.1. Direct coupling method to detect the PD event

Figure 2.8 shows the direct coupling measurement diagram, which fulfils the IEC 60270

standard. The measuring components consist of the capacitor arrangement and the test

object which are energised by a high voltage source. A series resistor is usually

connected to the voltage source to protect the source from high current in case the test

object breaks down.

Non-conventional methods Detection of electromagnetic transients

- HF/VHF (3 MHz to 300 MHz) - UHF (300 MHz to 3000 MHz)

Detection of acoustical emission (10 kHz to 300 kHz)

Detection of optical occurrences Detection of chemical compounds

Conventional methods (IEC 60270) Detection and measurement of the

apparent charge Measurement of the amount of pC

PD Detection


20

The test object is represented by capacitor CX connecting in parallel to a high voltage

blocking capacitor CB, the latter is connected in series with the measuring impedance Z.

CB

RL

TR

ZPD

Aqcuisition Unit

CX

Figure 2.8: Direct coupling PD measurement diagram [28]

If a discharge happens in the test object, the pulse current will be re-distributed between

the sample capacitor CX and the blocking capacitor CB. The distribution current is

explained below.

(a) (b)

Figure 2.9: (a) An internal discharge defect and (b) the electrical circuit equivalent

diagram, known as the abc model [13]

The PD source in the test object and its equivalent electrical circuit are shown in Figure

2.9. It is represented as an insulation layer between two electrodes at the top (high

A

B

SVS Ca

Cc

Cb

Rc

Vb

Vcib (t)


21

voltage) and bottom (ground). The PD is due to the presence of a void in the middle of

the insulation. The cavity in Fig. 2.9(a) is represented as Cc in Fig. 2.9(b), and the two

parts of the insulation above and below the cavity, in the area I, are represented by Cb’

and Cb” respectively. The remaining insulation in area II is modeled by capacitances

Ca’ and Ca”. The switch S in Fig. 2.9(b) represents the presence of discharge events.

The total capacitance of the solid insulation in series with the cavity can be calculated

as:

' '' ' '' / b b b b bC C C C C 2.19

and the capacitance of area II:

' ''a a aC C C 2.20

Note that [13]:

a c bC C C 2.21

The switch S in Fig 2.9(b) is a voltage dependent switch type which is controlled by the

voltage Vc. When the Vc value is high enough to ignite the PD in the void, the switch S

will close and a charge q≈i(t) is released. The current will flow for a short time through

the resistor Rc which represents the occurrence of the PD itself. This current has a Dirac

shape [13] and can be modeled using a Gaussian pulse as in Figure 2.5 [3]. In reality,

this charge (current) cannot be measured directly [13].

The approach to analyse and calculate the apparent (measurable) charge can be

described as follows. Assume the capacitor circuit in Figure 2.9(b) has been charged so

the voltage between terminal A and B is Va. Then the PD occurs in a void (Cc) which

causes the voltage at Cc to drop to δVc (this will also cause the Cc to be short circuited).

The capacitor Ca will try to balance the voltage equilibrium in the circuit by releasing

the charge toward Cb. This will cause the voltage Va to drop. The amount of the voltage

drop can be written as:


22

ba c

a b

CV VC C

2.22

This equation shows the relation of the charge released during the discharge event and

the drop voltage at terminals A-B. The drop voltage depends on the value of both Cb and

Ca, which are impossible to measure in reality. Thus direct measurement of the drop

voltage Va is not feasible.

To measure the drop voltage δVa, the insulation sample is then connected to the

measurement circuit as shown in Figure 2.9(a). The overall capacitance of the insulation

sample during the discharge event is Cx = Ca + Cb. When the discharge occurs, the

capacitor CB will release charge to the circuit to balance the voltage in the circuit due to

the drop voltage δVa. The charge current released by CB can be written as:

( )x a a b aq i t C V C C V 2.23

Substitute equation 2.22 into equation 2.23:

b cq C V 2.24

The charge which is measured by Equation 2.24 is called ‘apparent charge of a PD

pulse’ because it not really equal to the true amount of charge release locally in void Cc.

The IEC [9] noted the apparent charge as ‘That charge which, if injected within a very

short time between the terminals of the test object in a specified test circuit, would give

the same reading on the measuring instrument as the PD current pulse itself.’

The measuring impedance Z will pick-up the apparent charge and feed it to the PD

acquisition unit. The amount of PD can then be recorded. The computer which forms

part of the PD measurement system can carry out further analysis on the recorded data

to generate other useful PD parameters, e.g. discharge current, power, quadratic rate,

etc.

It should be noted that the choice for the blocking capacitor CB is important [28]:

1. The capacitor must be discharge free.


23

2. To compensate the drop voltage δVa, due to the discharge current in the void, the

capacitor CB must be considerably larger than capacitor CX ( )B XC C .

In this thesis, this measurement method is used to obtain the PD apparent charge and the

PD phase-resolved patterns for reference, i.e. to enable evaluation of the UHF detection

method.

2.5.2. UHF PD detection method

PD events emit electromagnetic signals in the manner described in the previous section.

Electromagnetic signals have different frequency spectra depending on the type of the

PD source and medium of the surrounding defects [3, 17]. Protrusion defects can

generate PD pulses with a very fast rise time, up to ~0.9 ns in oil [17]. The fastest rise

time for bad contact defects measured by [17] was ~17 ns. These PD pulses have

spectra in the frequency range of 300 – 3000 MHz. This frequency range is known as

the Ultra High Frequency (UHF) range. Thus, the method of detection of PD signals in

this frequency range is known as the UHF PD method [2, 3, 27].

The basic diagram of the UHF PD detection method is shown in Figure 2.10. The main

component to detect the PD signals is an antenna which acts as a sensor that picks up

electromagnetic signals emitted by the PD sources. The sensor is connected to a

measurement unit to show and record the PD signals. In cases when the PD signal is too

small, an amplifier can be installed between the sensor and the measurement unit. Using

an amplifier which has a specific operational frequency, the PD signals can be

magnified whilst blocking the noise signals. In the UHF range, the noise mainly comes

from known communication sources such as digital TV or mobile phone signals. Thus

using a specific amplifier which excludes known noise frequencies, a clear PD signal

can be shown and recorded by the measurement unit. The PD signals can be recorded in

two different modes of measurement, i.e. time domain and frequency domain. Both

modes have their own advantages and purposes.

The UHF PD detection method is the main method used and discussed in this thesis.

Further review of UHF is discussed in the next section.


24

Figure 2.10: Typical UHF PD detection diagram [18]

2.6. Classifications of partial discharge

Partial discharge may occur in voids in solid insulation, gas bubbles in liquid insulation

or around the edge of sharp electrodes in gas [10]. Generally, based on the location and

mechanism PDs can be classified into three categories: corona discharge, surface

discharge and internal discharge [10, 12].

2.6.1. Corona

The presence of sharp points or edges, rough surfaces or small radii on the electrode can

enhance the electric field at those places. The stress could be as much as 10 times higher

relative to the average stress [8]. This high stress can initiate an ionization process thus

producing discharge which is called corona discharge. The discharge takes place in the

vicinity of the point (without bridging the gap) between it and the nearest other

electrode. Coronas occur when the field stress gradient exceeds a certain value. The

critical field strength at which the ionization starts for dry air can be calculated by using

Peek’s equation:

0.330 1cE mr

kV/cm 2.25

where: σ = relative air density = 0.92b/T

b = atmospheric pressure in cm Hg


25

T = absolute temperature in degrees Kelvin

r = conductor radius in cm

m = stranding factor (0<m<1), typically 0.9 for weathered stranded

conductors.

In the case of the electrode in air, which depends on the voltage polarity, the inception

voltage is around 36 kV/cm for positive polarity and 38 kV/cm for negative polarity

[10].

2.6.2. Surface discharge

Surface discharge occurs due to inadequate stress equalization or can be produced by

leakage current flowing through a conducting layer on the surface of electrical

insulation [8]. Figure 2.11 illustrates surface discharge between two electrodes. High

stress at the edge of the electrode can initiate discharge along the surface of the

insulation with the ambient medium having lower dielectric strength (e.g. air and oil).

Surface discharge seldom occurs on polymer or ceramic type insulation where their

surfaces are almost smooth, but for paper insulation surface discharge can be easily

ignited [13].

High Voltage

Ground

Solid Insulation

Electrode

Figure 2.11: Surface discharge


26

2.6.3. Internal discharge

Internal discharge in insulation occurs due to the presence of cavities or inclusion within

the insulation or on the boundaries between solid insulation. These cavities commonly

are filled with lower dielectric strength materials such as gas or liquid which can occur

during fabrication due to the impurities of materials, an imperfect dielectric mixture or a

fault in the vacuum impregnation process [29].

The filler materials also commonly have lower permittivity than the solid insulation so

the electric field which surrounds the cavities is higher than that of the solid insulation.

Due to the higher electric field, under normal voltage of the insulation system, the

cavities can start local discharge activities.

Figure 2.12 illustrates the presence of a cavity within solid insulation and the electric

circuit analogue. The insulation thickness is d and the cavity shown in the figure has

dimension thickness t and area A. In the analogue capacitance circuit, the void is

represented as Cc and the column of solid insulation in series with it as Cb. The rest of

the insulation is represented as Ca.

Figure 2.12: (a) Cross section of insulation with cavity presence within, and (b) the

analogue capacitance circuit diagram [13]

Assuming the breakdown strength of the cavity is Ecb, we can then write the PD

inception voltage in terms of the breakdown strength of the cavity as follows.

The capacitance of Cb and Cc can be expressed as:


27

o rb

ACd t

2.26

and

oc

ACt

2.27

where εr is the relative permittivity of the solid dielectric.

Then the voltage across the cavity can be calculated using the equation below:

bc a

b c

CV VC C

2.28

Substitute Equations 2.26 and 2.27 into Equation 2.28 to get:

11 1

ac

r

VVdt

2.29

Thus the voltage across the insulation which starts PD in the cavity can be written as:

11 1ai cbr

dV E tt

2.30

where:

Vai = voltage across insulation which causes the cavity to start to discharge

Ecb = breakdown strength of the cavity material

2.7. UHF PD detection in high voltage equipment

The UHF PD detection method is known to have advantages over conventional PD

detection methods. This is mainly due to the higher immunity of the UHF method to

noise. As described before, the UHF method works in a frequency range of 300 MHz to


28

3000 MHz while the noise in a substation is primarily below a few MHz [24]. Thus the

UHF range is relatively noise-free, except for interferences from well-known

communication sources such as digital TV/Radio and mobile phone.

The UHF detection method has been widely used to detect the occurrence of PD sources

in high voltage equipment, especially in Gas Insulated Switchgear (GIS). More recently,

the UHF detection method has also been applied to detect PDs in power transformers [3,

18].

2.7.1. UHF PD detection in GIS

UHF condition monitoring is widely used in GIS and has been shown to be the most

practical and effective technique [19]. In GIS, the PD signals propagate with little

attenuation and can be detected using relatively simple sensors. The attenuation at 1

GHz in GIS can be as low as 3-5 dB/km [19]. This low attenuation is due to the absence

of barriers and discontinuities inside the GIS. In cases where the PD occurs close to

discontinuities, the reflection can cause resonance and reduce the signal strength by up

to 2 dB/m [27].

The sensors to detect PDs in GIS involve a compromise between the requirements of

minimizing of the field enhancement and maximizing of the sensors’ sensitivity. The

sensor must not add any risk of electric breakdown due to a non-uniform field caused by

the sensor shape. To minimize the breakdown possibilities, a sensor is commonly

installed in a weak HV field, an inspection hatch for example. Also, in GIS the planar

shape sensors such as spiral or plate are more desirable than a monopole type sensor due

to their lower field stress [27, 30].

In GIS, the sensors (also called couplers) can be classified into two categories according

to the installation method [27]:

1. Internal couplers are couplers fitted to the GIS during construction or retrofitted

during planned outage, because degassing of the GIS chamber is a must.

Commonly the sensor has a planar shape which is insulated by a dielectric sheet.


29

The measurement connection is made through a hermetically sealed connector,

commonly connected to the center of the sensor.

2. External couplers are usually fitted to an aperture in the metal cladding such as

an inspection window or exposed barrier edge. This type of sensor is commonly

applied for periodic testing. Due to the placement method, external sensors are

sometimes less sensitive than internal sensors, and are also more prone to

external noise.

2.7.2. UHF PD detection in transformer

The transformer is one of the most important equipment items in electrical power

system networks. Any failures that lead to transformer outage must be avoided. A

correlation between the long term partial discharge activity and the insulation failure has

not been proven yet. However, it is believed that transformer failure is mostly due to

failure in the insulation and this is usually started by the occurrence of partial discharges

[8, 30]. Thus it is important to assess the transformer insulation to establish the

condition of the transformer.

The presence of defects such as a cavity or a metal particle trapped in the insulation is

undesirable. These defects will enhance the local electric stress and if it is excessive,

local breakdown will occur which is known as partial discharge. During the discharge,

the electric field will rapidly accelerate and decelerate electrons which are initially at

rest. As a result of the time-varying electric and magnetic fields, electromagnetic waves

are produced and radiated outward from the PD source.

UHF PD measurement has been shown to be effective in detecting PDs in GIS and is

now increasingly being applied to monitoring the condition of transformer insulation [2,

27]. One may wonder if the UHF measurement in GIS can be adopted and applied to

power transformers. In GIS, PD pulse rise times can be as short as 50 ps [31]; but in

power transformers, the fastest rise time is around 0.9 ns due to permittivity of oil

higher than SF6 gas [1]. Nevertheless, pulses in the UHF range (300 -3000 MHz) will be


30

excited for such a rise time [32]. Thus UHF measurement can be adopted to PD

measuring in transformers.

2.7.3. Sensors to detect PD in transformer

The purpose of transformer monitoring extends from PD detection and recognition to

PD localization. To be able to undertake UHF PD transformer monitoring, a sensor with

capabilities to detect signals in the UHF frequency range is needed. For power

transformer monitoring, the UHF sensor is inserted into the transformer tank to capture

the electromagnetic waves emitted by the PD source. There are two ways of installing

the sensor: via the oil drain valve [33] or the dielectric window [27]. The size of the oil

drain valve imposes a constraint on the sensor dimension, while the dielectric window

can be created with an appropriate size to accommodate the sensor. However, the

placement of a dielectric window sensor needs an additional hole to be fabricated on the

transformer tank. As for the oil valve sensor, this is not required because the sensor can

be easily retrofitted into the transformer via the existing built-in oil drain valve [33].

Typically, the sensor is a monopole type. It can be inserted via the oil drain valve. The

size of the sensor is usually limited by the diameter and length of the oil drain. A typical

oil drain valve sensor size is 5 cm in diameter, and 10 cm in length [33]. The shape of

the sensor can be a short monopole [33,34], plate, zigzag or conical [33,35] or any

shape as long as it is able to be fitted to the drain valve. The sensitivity of this kind of

sensor is affected by the depth of the sensor insertion [33]. The deeper the sensor is

inserted, the higher the magnitude of the PD signals acquired. However, the sensor must

not initiate breakdown due to the high electric stress at the tip of the sensor [27]. To

reduce electric stress, the sensor can be encapsulated in some dielectric material [27].

For a dielectric window, the sensors usually have a planar shape [27]. The sensor can be

a micro-strip sensor [36, 37, 38, 39], log-spiral, spiral [27, 40] or fractal [41]. This kind

of sensor is usually etched on the surface of a dielectric material, using the same process

as in making electronic printed circuit boards (PCB). The sensor is etched on the PCB

with dimensions proportional to the working frequency of the sensor. In 37, the

miniaturization of the microstrip UHF antenna was discussed by applying an impedance


31

matching technique. This technique can reduce the antenna dimensions to 5x5 cm for

example. However, even though the antenna works in UHF range, the bandwidth is very

limited. To increase the bandwidth, [38] designed a microstrip antenna using sandwich

substrate. As a result, the frequency range of the antenna has a very wide range from 30

MHz to 3000 MHz. However, to manufacture this microstrip antenna is not practical.

Most of the measuring arrangements are unbalanced systems, i.e. the input to the

measuring system is a coaxial cable which consists of a live input and ground. While

planar sensors are usually crafted as a balanced system, an unbalanced system is also

possible, such as a circular or single arm log-spiral or spiral. Thus to connect the sensor

to the measuring system, a converter from balanced to unbalanced is needed. This

connector forms part of the sensor and is called a balun.

The antennae and measurement system usually have different impedances. The typical

value for measuring equipment is 50 ohms and sometimes also 75 ohms while the

sensor impedance varies from a hundred to a few hundred ohms [41]. The balun,

besides acting as a converter from balanced to unbalanced, is also used to provide

impedance transformation between different impedance values. The balun design is

based on the working frequency and the impedance difference [41, 42]. Duncan [42]

created a balun with a high frequency bandwidth which increased up to 100:1 using the

tapered method. The balun is created by using a tapered coaxial with a specific

diameter. The impedance transition is achieved by cutting open the outer wall of the

coax so that a cross-section view shows a sector of the outer conductor removed [42].

This balun has a simple design and can use the regular coaxial cable. Also, the

impedance transition is very smooth as a result of the tapered opening. However the

length of this balun is too long for practical application. Using a standard coaxial cable,

for transition of 120 ohms to 50 ohms over UHF frequency range (300 – 3000 MHz),

the balun can be more than 50 cm in length [43, 44] which is impractical to apply in

power transformers.

To decrease the balun length, a material with higher permittivity [44, 45] can be used.

Using special high permittivity material, the balun length can be reduced to less than 10


32

cm [45] which is feasible in enabling connection to the sensor. However, it is more

difficult to fabricate a balun using such a material.

To date, advances in printed circuit board (PCB) and microwave integrated circuit

(MIC) substrate have meant that the micro-strip balun design has become more popular.

The balun can be created by etching the PCB surface to form a specific pattern. In [41]

the micro-strip balun design is set with a frequency range of 0.1 GHz to 3.85 GHz. The

overall length of the balun is only 46 mm by using a standard single layer PCB. As the

impedance transitions use several stages, the transition is not as smooth as the tapered

balun. However this balun is much easier to fabricate, uses cheaper material [41] and is

sufficient to interface with the antenna and the measuring equipment.

In this thesis two methods of sensor insertion into the transformer to detect PD are

discussed. For the balanced planar sensors, a micro-strip balun was chosen for

interfacing between the sensor and the measuring equipment.

2.7.4. PD waveform and pattern measurement

Electromagnetic signals emitted from the PD source will propagate in all directions

inside the transformer tank. As stated above, these signals can be recorded in two ways,

i.e. in time domain and frequency domain. The time domain will reveal the signals’

waveforms and is usually recorded using a digitizer such as an oscilloscope (CRO). A

spectrum analyzer is used for recording in the frequency domain.

Both measuring methods have advantages. The advantage of the spectrum analyzer

(SA) over the oscilloscope is its frequency range flexibility [46]. The measuring

frequency ranges can be broad-band, narrow-band or at a single frequency using the

zero-span method. The broad band frequency range is typically set between 100 MHz

and 1500 MHz. The narrow band performs measurement over a narrower frequency

range while the zero-span measurement at a specific frequency is applied to capture the

phase resolved partial discharge (PRPD) patterns with respect to the power frequency

(50Hz) cycle [47]. The disadvantage of using SA is that, due to its measurement


33

principle, a relatively long integration time is needed to build up the spectrum display

[30]. In this thesis, both measuring methods are investigated.

2.7.5. Sensor sensitivity

The placement of the UHF sensors to detect PD events in transformers is usually at

fixed locations. The locations of sensor installation depend on the type of sensor and

transformer construction, as described in a previous section. As the PD can occur in any

location in the transformer, the electromagnetic signal path from the PD source to the

sensor can be affected by the structure inside the transformer. The signal path is also

affected by the density of the insulation oil in the transformer tank which can also be

subjected to variations in temperature (caused by loading changes). In addition, the live

active parts of the transformer can obstruct electromagnetic signals and cause signal

attenuation whereby the signal becomes not linear to the distance. This will cause

conversion of the signal magnitude detected by the UHF sensor to an equivalent pC

level to become difficult [48].

CIGRÉ WC 15.03 [49] recommended sensitivity verification for UHF method as a

substitution for calibration. Sensitivity verification can be used on-site to determine the

minimum sensitivity of the measuring system. Although this recommendation is only

for GIS, with some adjustment this method can also be applied to power transformers

which use oil insulation. The sensitivity of the UHF measuring method is very

dependent on the type of sensor, on the type of the PD defect, and on the location of the

PD source [50, 51].

2.8. UHF PD source recognition

Apart from PD detection, the ability to recognize PD patterns is an important aspect of

transformer insulation diagnosis. Knowing the PD defect type will provide engineers

with more clues to determine the possible PD location and severity of the deterioration.

This in turn will help to plan corrective actions that have to be taken.


34

In order to classify the PD sources, two essential components are required: the

classifier, and the inputs to the classifier. The latter are signal features (or finger-prints),

usually derived from the phase resolved partial discharge (PRPD) patterns and PD

signals waveform. The classifier can be an artificial intelligence method which uses the

provided finger-print data to classify and thus recognize the PD sources.

Using the UHF detection method, the phase resolved PD pattern is recorded by applying

the zero-span function in a spectrum analyser [46]. This signal capturing mode available

from a standard spectrum analyser can be used to selectively detect a PD signal

component at a specific frequency over a certain recording time interval. This method

will capture the electromagnetic signals emitted by PD sources and show the two

dimensions (v, φ) of the phase resolved partial discharge patterns (PRPD), i.e. the

discharge patterns in relation to the applied AC voltage cycle (20ms for 50Hz supply

systems). Thus the PRPD patterns can be readily obtained for both positive and negative

voltage half-cycles.

From the PRPD patterns, statistical values are usually extracted, for example the mean

µ, standard deviation σ, skewness Sk, kurtosis Ku, and cross-correlation factor cc [52-

62]. These statistical operators are then used in an artificial intelligence system to

determine the source of the PD.

Beside PRPD analysis, PD sources can also be determined by analyzing the PD signals

waveform. Various techniques based on the UHF PD signals waveform have been

investigated to recognize the PD sources. A wavelet analysis method was proposed by

Yang and Judd (2003) [63] to recognize PD sources in power transformers. However,

this method requires intensive computational effort which slows down the recognition

process. To reduce the computational complexity, [64] proposed the use of envelope

analysis to distinguish between partial discharges. It was asserted that the envelope of

PD signals can be used as a PD signature and thus a similarity function can be applied

to distinguish PD sources. In another investigation [65], a method was proposed to

classify the PD events in GIS by extracting PD features from the UHF signals. Here, the

signals were decomposed by using wavelet transforms and then PD features were

extracted from the decomposed signal. This method gives a fast and accurate


35

classification of GIS PD events, and is also able to separate air corona interference from

the PD signals.

The features can also be obtained by transforming time domain waveforms into the

frequency domain using Fast Fourier Transforms (FFT). In [66], the power spectral

density is used as input to the AI system to recognize the PD sources.

PDs can arise from single or multiple defects within the insulation structure. To

recognize multiple PDs, [63] proposed wavelet analysis to extract the features and

distinguish multiple PD sources. Pulse wave shape analysis is used in [67-70] to

separate multiple PD signals with the aim of recognizing multiple PD sources.

Although there are many UHF PD recognition methods, as discussed above, most of

them have been specifically developed for GIS. Thus for applications in transformers

with oil insulation, recognition of PD detected by the UHF method still needs further

exploration and development. In this thesis, PD detection was carried out using a UHF

sensor. The PD detection discussion in the thesis includes the sensitivity of the UHF

sensor to detect the PD signal, to recognize the PD source from the PD waveforms and

to recognize single and multiple PD sources.

AI classifiers used in the recognition of PD sources have been investigated by various

researchers [71-74]. A number of PD pattern recognition methods can be used as

classifiers, such as genetic algorithm [71], support vector machine [72], neural network

[73] and fuzzy logic [74]. Among all these methods, fuzzy logic and neural network

show the highest success rate.

2.9. UHF PD source localization

Besides detection and recognition of PD sources, localization is another important issue

for transformer condition monitoring and diagnostics. Knowing the exact location of PD

events in the transformer not only provides information about the presence of the PD

but can also help engineers in determining the severity of defects and speeding up the

repair process.


36

To locate PDs, a minimum of three sensors must be applied to record PD signals and

enable triangulation. By comparing the arrival time at each sensor, the PD location can

then be determined. The time of arrival (TOA) of the PD signals at each sensor can be

used to calculate the time difference of arrival (TDOA) between each sensor pair.

The arrival time of the PD signals at specific sensors can be acquired by selecting the

first peak of the oscillating PD signals [75-77]. This method requires simple procedures

and less calculation. However to determine the first peaks itself is not always an easy

process, especially if the PD waveform has a lot of oscillations at its front. In addition,

the presence of noise can obscure the waveform thus producing error.

Another method is to examine the cumulative energy of the PD signal [77-78]. From the

energy curve, the time difference between signals is determined by finding the knee

point where the change is sudden [75, 77, 79]. The drawback is that human judgment is

required to decide on the knee point [75]. To avoid ambiguity due to potential human

error, the TDOA can be acquired from the similarity between the cumulative energy

curves [75, 77, 78]. Due to the fact that PD signals may undergo multiple reflections

during their propagation, another research group [78] used only part of the PD

waveforms to extract the energy curves. This resulted in a higher level of accuracy.

However, the method still relies on human judgment and thus possible human error, as

stated previously.

PD localization using the UHF method is carried out by applying sensors to capture the

electromagnetic waves emitted by the PD sources. In the transformer oil medium, these

signals travel slower than the speed of light but still very fast (~2x108 ms-1). This makes

measurement difficult especially within the space limitation of a transformer tank. The

transformer tank is usually limited to a few meters; hence the travel time of the

electromagnetic signal lies within a range of nanoseconds only.

To increase the time difference between sensors and thus facilitate accurate time

difference determination, sensors can be installed at positions far apart, such as on

opposing sides of the transformer tank. However due to the nature of the

electromagnetic waves which are always subjected to reflection and refraction, the PD

signals received by different sensors can be very dissimilar. This method can lead to


37

higher error. To minimize the dissimilarity of the signals waveform, the sensors can be

installed in close proximity to each other [78]. By installing them in this manner, the PD

signals can then be very similar. However, the disadvantage of this method is that it

requires very fast measuring equipment in order to resolve the very small time

difference between signals [77, 78, 80].

Besides using time domain measuring systems, the PD location can also be revealed by

analysing the energy attenuation which is recorded in frequency domain [81]. However,

the energy spectrum does not always have linear correlation to the distance of the sensor

from the PD source [82]. The presence of barriers and active parts of the transformer

has a great effect on the total energy recorded by the sensor [51, 83] and thus may cause

a high degree of error.

The PD source coordinates can be determined by applying many methods. In [84, 85] a

least square algorithm was applied to calculate the PD coordinates. However, this

algorithm can easily cause results to fall into local minima and thus actual PD

coordinates cannot be located. In [40, 86, 87, 88] a genetic algorithm is applied to

determine the PD coordinates. This algorithm has a good ability to determine the PD

coordinates but it needs a substantial computational effort. In [40, 88] the position of the

source signal is determined by using the fuzzy method. The input of the fuzzy system

was extracted from the decomposed PD signals. The fuzzy algorithm not only produces

accurate PD coordinates but is also able to be applied to locate multiple PD sources

[40]. To reduce computational efforts, particle swarm optimization was used to locate

the PD sources in [89, 90]. The optimization was based on a non-linear function.

Another method, which applied a simple computation, was introduced in [91, 92] where

the location of the signal source is determined purely from the time difference of the

arrival signals by using matrix manipulation.

CHAPTER 3

SENSOR TO DETECT PD IN TRANSFORMER

3.1. Introduction

Electromagnetic waves are emitted from PD sources due to very short current pulses

generated during the discharge process. These electromagnetic signals contain wide

frequency spectra including a range from a few hundred MHz to a few thousand MHz,

otherwise known as ultra-high frequency (UHF).

These electromagnetic signals propagate inside the transformer tank, are then refracted

and reflected by complex interior obstacles such as windings, the core structure and the

transformer tank itself. Using appropriate sensors, i.e. UHF sensors (antennas), the

electromagnetic signals can be detected and recorded by a measuring device connected

to the sensor.

This chapter discusses the design of sensors for the purpose of PD detection. The sensor

fundamentals are similar to those of antennas for communication purposes. A software

package by the name of CST Microwave Studio [93] was used to design the sensor.

3.2. Sensor to detect PD

The dimension of the sensor to detect the UHF PD signals in a transformer is limited by

size constraint. There are two possible places to install sensors in a transformer [7, 95],

via the oil drain valve or by creating dielectric windows on the top of the transformer.

Chapter 3 Sensor to detect PD in transformer

39

The typical size of the oil drain valve is 5 cm in diameter and 10 cm in length [7]. For

dielectric windows, not usually provided by the manufacturer, the typical diameter of

the sensor is 15 cm [3].

Taking into account the dimension constraint above, sensors for this research are

designed using CST Microwave Studio software. Four different sensor designs are

considered, two for each application type. Short monopole and conical are developed

for the oil drain valves; spiral and log-spiral are developed for dielectric windows. The

best design for the four sensors will be built and tested to detect PD signals.

In GIS application, CIGRÉ TF 15/33.03.05 [49] has provided a technical guidance

which states that UHF sensors must be able to pick up PD signals as low as 5 pC. As the

UHF PD detection is being applied for transformer condition monitoring, this same

guidance is used to design the sensor for this dissertation. This level however is much

lower than the acceptance criterion of the PD test for power transformers, i.e 500 pC,

according to the AS/NZS 60076.3:2008 standard [94]. Thus by adopting the CIGRÉ TF

15/33.03.05 guidance, the aim of the sensor design is to be able to pick up PD signals as

low as 5 pC at a distance of 2 meters in the air. The lower PD level will assure that the

sensor will have more than adequate capabilities to detect PD in transformers for the PD

test.

As the PD signals are emitted in a wide frequency range 300 ~ 3000 MHz, an ultra-

wideband antenna is needed to detect them. An Ultra Wide Band (UWB) antenna

requires consistent operation in its frequency range. Antenna characteristics such as the

voltage standing wave ratio (VSWR), S11 parameter, gain, and impedance should be

stable across the frequency range. Due to the PD detection function of an antenna,

VSWR and gain do not have to have very high values but rather need to be as flat as

possible over the working frequency range [45].

In addition, the size limitation makes the design of an antenna with excellent parameter

values difficult to achieve. There must therefore be some compromise between the

antenna performance and the size limitation.


40

Measurement of PD signals in wideband mode has advantages over using narrow

bandwidth [96]. The PD signal to noise ratio shows improvement as the measurement

bandwidth increases [97]. The wide bandwidth measurement resulted in a more precise

PD pulse shape rather than just an integral of the PD pulse when using a lower

bandwidth measuring device. Also the wideband measuring system reduces the external

noise interference [96] by permitting the measurement of the direction of pulse

propagation and/or pulse travel time. As an example, with PD measurement using two

wide bandwidth couplers, one coupler located closer to the PD source than the other

one, the closer coupler will detect the PD signals first followed by the one further away.

In this measurement, it clear that the coupler must be able to detect the ns PD signals to

be able to distinguish the time difference of the signal arrival. Therefore wide

bandwidth PD detection can lead to certain noise elimination on a pulse-by-pulse basis,

rather than by depending on a statistical elimination of noise based on macroscopic

pulse pattern properties [96].

3.3. Sensor fundamental

The sensor for PD detection is a metallic structure designed and built to receive

electromagnetic waves. The sensor acts as a transitional structure between the

transmission line (in the case of PD measurement this is a coaxial cable) and the

surrounding medium (transformer oil in this dissertation). The working of the sensor is

similar to an antenna. The antenna (sensor) fundamentals are discussed below. Most of

the coverage in this section derives from Balanis, 1997 [97].

3.3.1. Bandwidth

Bandwidth (BW) is the range of frequencies where the antenna performances with

respect to antenna parameters fulfill a specified standard. The frequency bandwidth can

be expressed as absolute bandwidth (ABW) or fractional bandwidth (FBW). The ABW

is defined as the difference between the highest and the lowest frequency, and the FWB

is the percentage difference between the highest and lowest frequency over the centre

frequency. Both terms can be expressed as:


41

H LAWB f f 3.1

100 H L

c

f fFBW xf

3.2

where:

fH = the highest frequency (Hz)

fL = the lowest frequency (Hz)

fC = the centre frequency (Hz)

In terms of wideband antenna, BW is defined as the ratio of the highest to lowest

frequencies of acceptable operation and expressed as:

H

L

fBWf

3.3

For example, the UHF frequency range is 300 MHz ~ 3000 MHz, thus the antenna

covering the whole of this frequency range will need a bandwidth of 10.

3.3.2. Radiation pattern

Radiation Pattern is defined either as a mathematical function or a graphical

representation of the radiation properties of the antenna as a function of space

coordinates. Radiation properties include power flux density, radiation intensity, field

strength, directivity phase or polarization. The plots of the radiation patterns can be

drawn in three or two dimensions. For two dimensions, as in this dissertation, the plot is

made on a spherical surface of a constant radius r away from the antenna centered at the

origin. The electric (or magnetic) field trace plotted shows the amplitude field pattern

which is usually normalized with respect to the maximum values.

There are three radiation patterns that are commonly used to describe the antenna’s

properties:

a. Directional is defined as the ability of an antenna to transmit or receive the

signal in some direction more effective than others. The antenna is defined as


42

directional if that antenna has maximum directivity significantly greater than

that of a half-wave dipole.

b. Isotropic is a theoretically lossless antenna which also has equal radiation in

every direction. Antennas with this type of pattern represent ideal cases and are

not physically realizable. They are usually used as a reference to describe the

directivity of an actual antenna.

c. Omni-directional is a special case of directional antenna, where the antenna has

directional capability in any orthogonal plane but has a non-directional pattern in

the given plane.

3.3.3. Input impedance

Balanis [98] defined input impedance as “the impedance presented by an antenna at its

terminals or the ratio of the voltage to current at a pair of terminals or the ratio of the

appropriate components of the electric to magnetic fields at a point”. The antenna input

impedance, ZA, refers to the impedance seen looking into the terminals of the antenna

and defined as:

Za = Ra + jXa 3.4

where Ra is the input resistance which consists of two components i.e. RL, the loss

resistance of the antenna and RR, the radiation resistance of the antenna. Xa is the

antenna reactance.

Besides referring to the antenna terminals, the input impedance can also refer to the

lossless feed of length L and is defined as:

tanhtanh

a oin o

o a

Z Z LZ ZZ Z L

3.5

where:

Zo = characteristic impedance of the transmission line (feed)

Za = antenna input impedance


43

γ = α+jβ

2

1 12

and 2

1 12

where: γ = complex propagation constant

α = attenuation constant

β = propagation constant

ω = angular frequency

µ = permeability

ε = dielectric constant

σ = conductivity

From Equation 3.5, if the characteristic impedance of the transmission line (Zo) and

antenna input impedance (Za) are equal, then the input impedance refers to the feed (Zin)

is equal to Zo. This case is called perfect matching condition of the antenna to the line.

In this condition, the power is thus all absorbed by the antenna and there is no

reflection. In this dissertation, the transmission line or coaxial cable in use has a

characteristic impedance of 50 ohms.

3.3.4. Voltage standing wave ratio (VSWR)

If an antenna is connected to the input transmission line and the antenna impedance

does not match with the impedance of the transmission line, some of the signal will be

lost as reflected at the junction point. The loss due to miss-match impedance is known

as the voltage standing wave ratio (VSWR).

The VSWR is expressed as:

1 Γ 11 Γ

VSWR

3.6


44

Γ r in s

i in s

V Z ZV Z Z

3.7

where:

Γ = the reflection coefficient

Vr = amplitude of the reflected wave

Vi = amplitude of the incident wave

Zin = antenna impedance

Zs = transmission line impedance

3.3.5. Return loss

Return loss (RL) or the reflection coefficient is the parameter that describes the portion

of signal which will pass through the port and the portion of signal that is rejected (loss)

when the antenna port is terminated by a matched load. This parameter is similar to

VSWR in that it indicates the degree of matching achieved between the line and

antenna. The return loss is expressed as:

1020 ΓRL log (dB) 3.8

The return loss is also known as the S11 parameter.

3.3.6. Directivity

The directivity is the ratio of the radiation intensity in a given direction from the

antenna to the radiation intensity averaged over all directions. The average radiation

intensity is equal to the total power radiated by the antenna divided by 4π. If the

direction is not stated, the maximum radiation is implied. The directivity can be written

as:


45

0

4

rad

U UDU P

3.9

If the direction is not specified, the maximum radiation intensity is implied, and the

equation will be:

00

4max maxmax

rad

U UD DU P

3.10

where:

D = Directivity (dimensionless)

D0 = Maximum directivity (dimensionless)

U = Radiation intensity (W/unit solid angle)

Umax = Maximum radiation intensity (W/unit solid angle)

Uo = Radiation intensity on isotropic angle (W/unit solid angle)

Prad = Total radiated power (W)

The directivity as shown in Equations 3.9 and 3.10 has no dimension.

3.3.7. Gain

The gain is defined as the ratio of the intensity in a given direction to the radiation

intensity that would be obtained if the power accepted by the antenna were radiated

isotropically. In mathematical form, it can be written as:

, 4

in

Uradiationintensitygaintotal input accepted power P

3.11

Referring to Figure 3.1, the total radiated power (Prad) related to the power input (Pin) is:

Prad = ecd Pin 3.12

where ecd is the radiation efficiency of the antenna, thus the gain (Equation 3.11) in

terms of θ and ϕ can be written as:


46

, ( , )cdG e D 3.13

The gain in Equation 3.13 is dimensionless.

Figure 3.1: Reference terminal and losses on an antenna [98]

3.4. Balun

Most measuring equipment can be categorized as an unbalanced system. Coaxial cable

is an example of an unbalanced system (Figure 3.2). The ground plane below the

coaxial cable becomes the third conductor of the three-wire system. The outer conductor

of the coaxial cable has a capacitance to ground while the inner conductor has no

capacitance to ground. Thus, current that flows on the ground can unbalance the current

on the coaxial.

To connect an unbalanced system to a balanced antenna (such as dipole, dual arms

spiral, or dual arms log-spiral) a balun is needed. Besides functioning to form a bridge

between the balanced antenna and an unbalanced measuring system, the balun also

works as an impedance transition due to different impedances operating within the

system. There are various balun types such as folded, sleeve, spit coaxial, transformer,

Input terminal(gain reference)

Output terminal(directivity reference)

Antenna

reflection dielectric lossconduction


47

tapered or microstrip baluns. Tapered [41, 42, 45] and microstrip baluns [41, 45] have a

high bandwidth capability and are thus suitable to use with a UHF antenna.

Figure 3.2: Cross-section of a coaxial cable, unbalanced at high frequency

3.4.1. Tapered balun

Figure 3.3 shows the structure of a tapered balun. The balun forms a transition which

matches the impedance from a coaxial line to a balanced antenna at the open end. The

transition is accomplished by cutting the coaxial across the particular length L.

Figure 3.3: Tapered balun transformer [42]


48

The balun impedance can thus be written as:

0azZ z Z e for 0<z<L 3.14

where:

Z(z) = the balun impedance (ohms)

Z0 = the impedance of non-tapered coaxial (ohms)

a = the angle of open sector (radians)

The tapered balun has a wideband capability up to 100 [42] and is suitable to connect

with a log-spiral sensor [41, 45]. However, this balun has a minor disadvantage in that

the total length of the balun can be up to 48 cm [41, 45] for a frequency range of 300 ~

3000 MHz. To overcome the length problem, it is suggested that material with a higher

dielectric constant (εr) be used to design the tapered balun [45]. As a result, the length of

the tapered balun can be reduced to just 9.5 cm, achieved by using alumina which has a

dielectric constant of 9.5 [45].

3.4.2. Microstrip balun

The microstrip balun has some advantages compared to the tapered balun. The size of

the microstrip balun is relatively small compared to the tapered balun. It also has lower

insertion loss [41]. An example of a microstrip balun is shown in Figure 3.4. This balun

is a coplanar-waveguide to coplanar-stripline (CPW-to-CPS) balun and has 4 transition

sections. It is designed to transform an unbalanced CPW feed line to a balanced CPS

feed line. The number of sections depends on the impedance of the antenna and the

coaxial and also on the reflection coefficient chosen.


49

Figure 3.4: Four-stage microstrip balun [41]

3.4.3. Quarter wave matching transformer

The transmission line reflection which underlies the basic theory of multi-section

microstrip baluns is discussed below, drawing on the work of Pozar (1998) [99]. For the

narrow bandwidth balun, one section can be sufficient but for wide bandwidth

application, a multi-section is needed.

Figure 3.5: Partial reflection and transmission coefficients on a single section of

matching transformer [99].


50

Figure 3.5 shows a single-section transformer connected to an antenna which is

represented as ZL. The partial reflection coefficient is calculated as:

2 11

2 1

Γ Z ZZ Z

3.15

2 1Γ Γ 3.16

23

2

Γ L

L

Z ZZ Z

3.17

The partial transmission coefficient is formulated as:

221 1

2 1

2T 1 Γ ZZ Z

3.18

112 2

2 1

2T 1 Γ ZZ Z

3.19

Assume the load (antenna) does not perfectly match Z2, and thus produces a small

reflection. The total reflection coefficient can be approximated as:

21 3Γ Γ Γ je 3.20

For the multi-sectional transformer, the fractional coefficient reflection can be

calculated as:

1 00

1 0

Γ Z ZZ Z

1

1

Γ n nn

n n

Z ZZ Z

Γ L NN

L N

Z ZZ Z


51

Thus for multi-section transformers the reflection coefficient can be formulated

approximately as:

2 4 6 20 1 2 3Γ Γ Γ Γ Γ Γj j j Nj

Ne e e e

or:

0 12 Γ cos Γ cos 2

Γ 2Γ 2 ( )

j

N

N Ne

cos N G

3.21

where:

/ 2

( 1) / 2

1 Γ for even2

Γ for odd

N

N

NG

cos N

3.4.4. Chebyshev multi-section matching transformer [99]

To determine the impedance transition, the Chebyshev multi-section transformer can be

used to calculate the impedance of the transition.

The nth order of the Chebyshev polynomial is defined as:

1 22 ( )n n nT x xT x T x 3.22

The first four Chebyshev polynomials are:

1T x x

22 2 1T x x

33 4 3T x x x

4 24 8 8 1T x x x


52

By inserting the substitution cos sec mx to the Chebyshev polynomial above and

substituting to Equation 3.21, it yields:

Γ jNN

m

cosAe Tcos

Γ (cos sec )jNN mAe T 3.24

To find the constant A, assume θ=0 which corresponds to zero frequency, thus:

0

0

Γ 0 (sec )LN m

L

Z Z ATZ Z

Solved to get the constant A:

0

0

1 (sec )

L

L N m

Z ZAZ Z T

3.25

When the balun is designed, the maximum coefficient reflection (Γm) parameter is

usually determined first. Then, from Equation 3.24, Γm A , since the maximum value

of (cos sec )jNN me T is unity. Substitute to Equation 3.25 and solve for θm:

0

0

1secΓ

LN m

m L

Z ZTZ Z

0

1sec2Γ

LN m

m

ZT lnZ

3.26

From Equation 3.26 the values of θm and Γm show an inverse relation. When the balun is

designed to get a higher bandwidth then the coefficient reflection will worsen as it will

be higher and if the balun is designed to get a lower coefficient reflection then the

bandwidth will be lower.

After θm is known, the fractional bandwidth can then be calculated as:


53

0

42 mff

3.27

and the impedance can be approximated, using:

11Γ2

nn

n

ZlnZ

3.27

To summarize, the impedance calculation using the Chebyshev polynomial can be

completed using the following steps [99, 100]:

1. Determine the number of sections (N) which are required to meet the appropriate

bandwidth and ripple Γm requirements.

2. Expand the Chebyshev function to N section

3. Determine all Γn by equating terms to the symmetric multi-section transformer

equation:

20 1Γ 2 Γ cos Γ cos 2 Γ 2 ( ) j

Ne N N cos N G

4. Calculate the impedance of each section Zn using the approximation:

11Γ2

nn

n

ZlnZ

5. Determine section length 0 / 4l or equivalent to 02n 41 /

3.4.5. Planar transmission lines [100]

In this dissertation, a microstrip balun is chosen for bridging the planar sensor to the

coaxial cable. The reason is that the microstrip balun provides higher working

frequency, which can be up to 100 GHz [101] with dimension small enough to be used

for antenna application [45].

The multi-section microstrip balun is designed to transform the balanced antenna to the

unbalanced coaxial cable, and also to provide a smooth impedance transition. Thus the

balun has two different waveguides at each end, i.e. coplanar waveguide (CPW) and


54

coplanar stripline (CPS). On the one end which is connected to the antenna part, a

coplanar waveguide is used. On the other end which is connected to the coaxial cable, a

coplanar strip line is used.

Coplanar waveguide (CPW) lines

The coplanar waveguide can be constructed using a dielectric substrate such as a printed

circuit board (PCB). A typical cross-sectional view of a coplanar waveguide (CPW) in

air is shown in Figure 3.6. The center strip conductor has width S and is equal to 2a.

The two semi-infinite grounds are separated at distance 2b. Thus slot width W is equal

to b-a. The thickness of the CPW conductor is t. The dielectric thickness is h1 and

relative permittivity εr1.

Figure 3.6: CPW schematic on a dielectric substrate [102]

The capacitances of the dielectric and air are C1 and Cair, thus making the total

capacitance CPW:

CCPW = C1 + Cair 3.28


55

Capacitance C1 is given by [87]:

11 0 1 '

1

( )2 1( )r

K kCK k

3.29

where 1( )K k and '1( )K k are moduli of complete elliptic integrals and defined as :

1

11

sinh( / 4 )sinh ( 2 ) / 4

S hkS W h

' 21 11k k

The capacitance of the surrounding air is given by [103]:

00 '

0

( )4( )air

K kCK k

3.30

where 0k is:

0 2Sk

S W

' 20 01k k

Approximation for εeff is defined as [103]:

CPWeff

air

CC

'1 1 0

'1 0

1 ( ) ( )12 ( ) ( )

reff

K k K kK k K k

3.31

The phase velocity (vph) and characteristic impedance (Z0) are defined as [103]:

pheff

cv

3.32


56

01

CPW ph

ZC v

3.33

where c is light velocity in free space. By combining Equations 3.28, 3.31 and 3.32, and

solving to get the characteristic impedance of the CPW:

'0

00

1 30 ( ) ( ) air eff eff

K kZK kcC

3.34

Equation 3.34 is used to calculate the coplanar waveguide line in the sensor design.

Coplanar strip line (CPS)

The coplanar strip line consists of two parallel strip conductors separated by a narrow

gap. Similar to the CPW, the CPS is also built above or between dielectric layers. The

CPS is a balanced transmission line which is made suitable to connect to printed

balanced antennas such as spiral, bowtie and log-spiral ones.

Figure 3.7: CPS schematic on a dielectric substrate of finite thickness [102]


57

The strip line construction can be in a combination of similar size (symmetrical) or

different (asymmetrical) as shown in Figure 3.7. In this design, the symmetry of the

CPS will be discussed.

The capacitance of the coplanar waveguide is expressed as [104]:

CCPS = C0 + C5 3.35

The capacitance C0 is defined as [104]:

0 0 '( )( )

K kCK k

3.36

where K is the complete elliptical integral of the first kind. The arguments k and k’ are

given by [104]:

1 akb

3.37

and

' 212

a Sk kb S W

3.38

Equations 3.37 and 3.38 show that both k and k’ are dependent on the geometry of the

CPS.

The effective permittivity of the CPS can expressed as [104]:

'1

51

1 ( ) ( )1 ( 1)2 ( ') ( )

CPSeff r

K k K kK k K k

3.39

where:

2

11

2

1

( )21

( )2

asinhhk bsinhh


58

and

' 21 1 ik k

The phase velocity vph and characteristic impedance Z0 are given by:

'CPSph CPS

eff

cv

3.40

0120 ( ').

( )CPS

CPSeff

K kZK k

3.41

where c’ is the velocity of light.

3.5. Sensor design

In antenna design, several factors must be taken into consideration including bandwidth,

impedance, radiation, compatibility, directivity, radiation pattern, losses and physical

profile. The values above must meet minimum requirements. However, when designing

the antenna to be applied to detecting PD, the value setting might be not applicable.

Rather than set a specific value, it is more important to achieve a flatter and smoother

antenna factor. In addition, some parameters such as gain, radiation and compatibility

might be almost meaningless in judging sensor performance. In this sensor design,

several antenna shapes are designed, simulated, fabricated and tested. Among the

sensors are short monopole, monopole-conical shape, spiral and log-spiral. The last two

sensors are designed as a planar-microstrip type. Electromagnetic software called CST

Microwave Studio 2009 [93] was used for the design process.

3.5.1. Types of sensors

In transformers, two possible locations can be used to install the sensor to detect PD, i.e.

via the oil valve which is usually provided to drain the oil from the power transformer


59

or by creating a dielectric window on the transformer tank. Both of the installation

methods thus limit the type and size of the possible sensor dimension.

Sensor dimension for insertion into oil valves is 10 cm in length and 4 cm in diameter.

With this limitation a monopole antenna is chosen for this kind of sensor. Two

monopole types are chosen, a short linear monopole and a conical skirt monopole. For

convenience, the short linear monopole will be referred to as ‘monopole’ and the

conical-skirt monopole as ‘conical’. Meanwhile for a dielectric window sensor type, a

planar sensor is chosen. The dimension of the sensor is limited to a radius of 15 cm.

Two antenna types were designed, i.e. log-spiral and spiral. Both are balanced antennas

so a balun will be needed to transform them to an unbalanced measurement system.

To determine the best size of sensor for each type, 4 antenna parameters will be

discussed, i.e. return loss (S11), voltage standing wave ratio (VSWR), impedance and

directivity. For the first three parameters, emphasis is on keeping the value as flat as

possible which means the antenna has a wider frequency band. The last parameter, the

directivity, is to evaluate the ability of the antenna to selectively capture the signals

from the point where the discharge is predicted to occur.

3.5.2. Monopole

The monopole sensor is a short conductor mounted on top of the ground plane as shown

in Figure 3.8. The length of the conductor is usually correlated to the λ/4 of the working

frequency. The monopole sensor is omnidirectional, capable of receiving signals from

all directions. Stronger signals are received if the signals are in a horizontal direction to

the sensor.

The monopole antenna has physical dimensions as follows: a diameter of 1.8 mm and a

maximum length of 10 cm. In the simulation, all metal parts were defined as ideal

conductors. A PCB base with a diameter of 4 cm is put between the antenna and the

BNC connector. The CST diagram of the monopole antenna is shown in Figure 3.8.


60

Figure 3.8: Design of monopole antenna with 4 cm FR4 substrate as antenna base.

Return loss and VSWR

Figure 3.9 shows the return loss (S11) graph of monopole antennas. A longer antenna

has a relatively higher S11 value thus providing a better performance. As a λ/4 antenna,

the result shows two peak values in the range 300 MHz to 3000 MHz which are

associated with the resonant frequency of the antenna. For a 10 cm antenna the resonant

frequency is 750 MHz and 1500MHz with lower magnitude. The return loss and VSWR

graphs show that this antenna is a narrow bandwidth antenna.

The VSWR fluctuates at around 10 for the complete length of the antenna which is

correlated to around 1.7 dB of the S11 parameter. If considering the antenna as a

“receiver and transmitter” this value is too low. Usually a VSWR value of 2 is needed

which is correlated to 10 dB of the S11 parameter. However, for PD measurement a

monopole antenna is preferable as it has a fast response, suitable for capturing fast

changing signals [77, 106].


61

Figure 3.9: S11 parameter of varying length of monopole antenna.

Figure 3.10: Varying length Monopole antenna VSWR parameter.


62

Input impedance

The average input impedance of an antenna shows a direct relationship with its length.

A longer antenna has higher input impedance than a shorter one, although not so

significant. Also a longer antenna has a higher fluctuation.

Figure 3.11: Input impedance of monopole antennas.

Radiation pattern

The radiation pattern graph shows that the antenna will receive signals from almost all

directions. A higher signal is received if it comes from a position horizontal to the

sensor. Lower signal strength will be received by the antenna if the signal source

approaches the top of the antenna.

Figure 3.12: Radiation pattern of monopole antenna at varying frequencies.


63

3.5.3. Conical

To obtain the broadband characteristics of the monopole type antenna, the geometric

configuration of the antenna can be varied. One of the most common shapes is conical,

hence the naming of this kind of antenna as conical skirt monopole. For convenience,

this antenna will be referred to as ‘conical’.

As the conical is also a monopole antenna type, the overall pattern is essentially the

same as the short linear monopole discussed before. The benefits of using the conical

shape are wider bandwidth, higher gain and higher VSWR [98]. As a monopole

antenna, the conical is also nearly omnidirectional.

The conical antenna is designed to fit a dimensional limitation, i.e. 5 cm of maximum

diameter and 10 cm length. The conical shape is built on top of a 4 cm FR4 substrate,

similar to the linear short monopole.

Figure 3.13: Conical antenna design with 4 cm FR4 substrate as antenna base.


64


Figure 3.14 shows the return loss (S11) graph of conical skirt monopole antennas. As

expected from the monopole characteristics, the length of the antenna is always

correlated with its resonant frequency. This characteristic can be seen in similar results

with the linear short monopole. The difference is that the bandwidth is wider and the

S11 parameter value higher.

The VSWR fluctuates at around 4 but well below 5. If the VSWR value target is 5, the

conical monopole antenna has a bandwidth starting from around 600 MHz to 3 GHz for

the longer antenna, i.e. 10 cm.

Figure 3.14: S11 parameter of varying length of conical antenna

Figure 3.15: VSWR parameter of varying length of conical antenna.

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65

Input impedance

The average input impedance of different length antennas shows an inverse relation to

the antenna length. A longer antenna has a higher input impedance than a shorter one

although not so significant. The longer antenna also has a higher fluctuation.

Figure 3.16: Impedance of varying length of conical antenna.

Radiation pattern

Similar to the monopole antenna, the conical antenna also has an omnidirectional

capability. The benefit of the conical structure is that the signal from the top of the

antenna is still able to be picked up by the antenna.

Figure 3.17: Radiation pattern of conical antenna at varying frequencies.

Imp

edan

ce (

oh

m)


66

3.5.4. Planar spiral antennas

Antenna characteristics such as radiation pattern, impedance, and so forth are based on

the antenna dimensions expressed in wavelength. With the wavelength inversely

proportional to the frequency, antennas such as the monopole antenna discussed above

are of the frequency dependent type, where the antenna dimensions have a very strong

effect on the antenna characteristics. With decreasing the sensor dimension, important

characteristics such as bandwidth then becomes narrow, thus affecting overall

performance.

To achieve wider bandwidth, frequency independent antennas can be used. In the

frequency independent antenna, the characteristics are invariant to a change of the

physical size if a similar change is also made in the operating frequency. [107]

discussed the design of frequency independent antennas by using a conical-spiral design

structure. The function of the wavelength is expressed as:

1( )[ ln( )/ ] aa a aA e Ae Ae

3.42

where

oaoA e

3.43a

11 ln( )a

3.43b

From Equation 3.42, it can be seen that changing the wavelength is equivalent to

varying which results in nothing more than just a rotation of the infinite structure

pattern.

The following discussion will focus on two frequency independent antennas which are

derived from a spiral shape, i.e. log-spiral and archimedean spiral (simplified as

‘spiral’).


67

3.5.5. Log-spiral

The log-spiral antenna arm is calculated using the pair equations which are derived from

Equation 3.42:

1 0ar r e 3.44a

0( )2 0

ar r e 3.44b

where: r1 = outer radius of the spiral

r2 = inner radius of the spiral

r0 = initial outer radius of spiral

a = rate of spiral growth

= angular position

The number of arms is usually set to an even value such as 2 or 4. In this thesis, a 2

armed log-spiral is used. The number of turns is 1.5 which produces an adequate

radiation pattern [104, 108]. The end of the spiral arms is designed in two different

shapes. The first design has a truncated end which produces a smaller physical antenna

and the second is tapered, resulting in a more constant impedance [105, 109]. The size

of the antenna is limited to a diameter of 15 cm and it is constructed using commercially

available FR4 substrate.

Figure 3.18: Log-spiral design, (a) tapered end (design1), and (b) truncated end

(design2)


68


For similar sized antennas, the S11 parameter value of design 1 (tapered end) is of a

higher value than that of design 2 (truncated end). The bandwidth performance is quite

similar for both designs. The antenna with larger dimensions shows a higher S11

parameter. In view of the superior results of the S11 and VSWR, the tapered log-spiral

with diameter 15 cm was chosen and built for PD detection.

Figure 3.19: S11 result of Log-spiral antenna

Figure 3.20: VSWR result of Log-spiral antenna

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Input impedance

The antenna with the tapered end design produced slightly flatter impedance as

predicted. Larger antennas tend to have a lower cut-off frequency, and thus are

preferable to smaller ones. The input impedance of the log spiral antenna at the centre

frequency of 1.85 GHz is 155 ohms. Consequently, a balun is required to match the

impedance to a 50 ohm coaxial cable.

Figure 3.21: VSWR result of Log-spiral antenna

Radiation Pattern

The log-spiral will receive stronger signals via the top (face) of the antenna. However

since this kind of sensor is usually installed at the top of the transformer, the directivity

problem can be avoided.


70

Figure 3.22: Radiation pattern of Log-spiral antenna at varying frequencies.

3.5.6. Archimedean spiral

Similar to the log-spiral shape, the Archimedean spiral is derived from the equi-angular

spiral equation 3.42. The Archimedean spiral uses the first terms of Taylor’s expansion

of the equi-angular spiral for a small value of ‘a’. The antenna arm is calculated as:

0(1 )r r a 3.45

Figure 3.23: Five-turn Archimedean spiral


71

The Archimedean spiral has a wider bandwidth with a similar diameter to the log-spiral.

However for higher frequency, the feed region of the Archimedean spiral is tighter thus

making it more difficult to create. Also as there are a large number of turns, the ohmic

RF loss-resistance is large thus reducing the antenna gain [109].


The S11 and VSWR of a 5 turn-Archimedean spiral are shown in Figures 3.24 and 3.25.

The antenna has a smooth S11 and a VSWR value above 600 MHz. The S11 parameter

of the smaller antenna shows slightly lower values but the bandwidth remains similar.

For the VSWR parameter, at lower frequency there is substantial oscillation then it is

flat above 750 MHz which implies that the antenna has good performance at higher

frequency but poor performance at lower frequency.

Figure 3.24: S11 of 5-turn Archimedean spiral

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72

Figure 3.25: VSWR of 5-turn Archimedean spiral

Input impedance

Input impedances are higher for larger antenna diameters but the patterns of both 130

mm and 150 mm show similarities. The input impedance of the 150 mm antenna is 180

Ω at the centre of the bandwidth frequency range. So, similarly to log-spiral antenna, a

balun is needed to provide impedance matching and a balanced to unbalanced

transformation to a 50 ohm coaxial cable.

Figure 3.26: Impedance of 5-turn Archimedean spiral

Imp

edan

ce (

oh

m)


73

Radiation pattern

As planar sensors are similar to the log-spiral, the spiral sensor can also be directional.

The electromagnetic signals will be received by the sensor better if the signal is

orthogonal to the sensor. However, similar to the log-spiral type, since the installation

location for this sensor is by means of a dielectric window on the top of the transformer,

the direction problem may not be so obvious.

Figure 3.27: Radiation pattern of spiral antenna at varying frequencies.

3.5.7. Balun

The wideband transition from CPW to CPS which is provided by a microstrip balun is

accomplished through a radial slot. The slot represents a very wideband open circuit,

which forces the electric field to be located mainly between the two conductors of the

CPS [41]. The optimum angle of the slot is 450 with a depth of around 6 mm [41, 110].

The balun scheme and the surface current are shown in Figure 3.28.

The length of the balun section should conform to λ/4 of the operational frequency of

the balun. For an upper frequency of 3000 MHz and lower frequency of 300 MHz, the

center frequency is 1650 MHz. Thus the length of the section should be 45 mm, making

the overall length of the balun impractical (where the overall length of the balun is 405


74

mm). The length of the section is then reduced by a factor (2n+1). By taking n = 7 the

length of the balun section is 3 mm. Hence, the overall length of the balun now becomes

48 mm.

Figure 3.28: Surface current of the 6-section balun terminated with impedance of 160

ohms, at frequency 3 GHz and phase current 180 degrees.

Log-spiral balun

The balun was designed using the Chebyshev multi-section transformer method which

is defined in section 3.4.4. The size of the CPW and CPS strip are then calculated with

Equations 3.54 and 3.63 respectively. The balun is designed to provide a VSWR of not

more than 0.2. Calculation results for the 6 sections are shown in Table 3.1.

Table.3.1: Log-spiral balun impedance and dimension

Section

Design Impedance

(ohms)

S (mm) W (mm)

S+W (mm)

Calculated Impedance

(ohms) coaxial 50 4.8 0.7 6.2 49 CPW 1 65.06 3.7 1.25 6.2 65

2 73.24 3.1 1.55 6.2 73.7 3 83.54 2.5 1.85 6.2 83 4 95.75 1.8 2.2 6.2 95.5 5 109.23 1.2 2.5 6.2 109.6 6 122.9 0.8 2.7 6.2 122.5 160 0.5 2.2 6.2 159.3

CPS 160 3 2.7 8.4 160.6


75

Archimedean spiral balun

The balun was designed using the same method as the log-spiral’s. The number of

sections and length are determined by a trade-off between a high bandwidth and a low

reflection coefficient. In the balun design for the Archimedean spiral, the length is

targeted to be similar to the log-spiral’s. However, this will make the reflection

coefficient limited to 0.2 which cannot be maintained. To keep the length of the balun

as short as possible, in this case 48 mm, a compromise was made by allowing the

VSWR to go above the target. By using 6 sections the VSWR is slightly above the

target, i.e. 2.3. Using a 6-section balun and a similar length to the log-spiral, dimensions

of the CPW and CPS of the Archimedean spiral are shown in Table 3.2.

Table.3.2: Archimedean spiral balun impedance and dimension

Section

Design Impedance

(ohms)

S (mm) W (mm)

S+W (mm)

Calculated Impedance

(ohms) coaxial 50 4.8 0.7 6.2 49 CPW 1 66.95 8 1.75 11.5 67

2 76.2 7 2.25 11.5 75.4 3 88.05 5.5 3 11.5 88.6 4 102.2 4 3.75 11.5 103.75 5 118.07 2.9 4.3 11.5 117.6 6 134.42 1.9 4.8 11.5 134.5 180 0.5 5.5 11.5 183.4

CPS 180 3.5 4 11.5 179.4

3.6. Sensor comparison

The simulation results of all sensors designed are shown in Figures 3.29 to 3.32.

Comparing the S11 characteristics (Figure 3.29), the spiral sensor has the most

consistent response: mostly flat although uneven at frequencies below 700 MHz. Thus

this sensor would be suitable for use in wideband measurement. Meanwhile, the conical

and monopole sensors have a very high S11 parameter for some short frequency


76

intervals. The log spiral also has a very flat response with a high S11 value. Thus

overall, this sensor appears to have the best S11 parameter characteristic.

The monopole has two significant dips in S11 value at around 900 MHz and 2.1 GHz.

On this basis, the monopole sensor is not a wideband antenna. A similar dip was

observed with the conical sensor at around 700 – 900 MHz. For the bowtie and spiral,

there are also fluctuations in the range 500 – 700 MHz.

Figures 3.30 and 3.31 show the VSWR and impedance of the selected sensors. The

conical, spiral and log-spiral have similar patterns, where all sensors have good

performance above frequency 750 MHz. The monopole has a significant oscillation at

around 1500 MHz and 3000 MHz. Similar oscillation is also shown by the impedance

plot, at around 1100 MHz and 2200 MHz. This oscillation shows that the monopole is

not a wide bandwidth sensor.

Figure 3.32 shows the sensor realized gain responses. The conical has higher gain at

lower frequency but decreasing rapidly after about 1900 MHz. The monopole also has a

similar response, decreasing sharply after around 2 GHz. Thus, these two sensors are

not suitable for wideband measurement or for detection at the higher end of the UHF

band. The spiral and log spiral sensors yield similar gain, but the log spiral has a

smoother gain.

Figure 3.29: S11 parameter of selected sensors

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Figure 3.30: VSWR of selected sensors

Figure 3.31: Input Impedance of selected sensors

Imp

edan

ce (

oh

m)


78

Z Spectrum Analyser

Acquisition Unit

Input Unit

Blocking Capacitor

Resistor

Transformer Sensor

PD source

Figure 3.32: Realized gain of selected sensors

3.7. Sensor testing to detect PD signals

Four sensors designed using CST software are tested to check their capability to detect

PD signals. The experiment diagram is shown in Figure 3.33. The PD source is a

needle-plate electrode arrangement. With this arrangement, corona discharges are

generated from the needle electrode connected to the HV source. By making use of the

stable PD signals (magnitude and phase), it is thus possible to check the ability of the

sensor to detect PD signals at specific values.

Figure 3.33: Experiment diagram for testing sensor ability to detect PD


79

The amount of PD is measured using an acquisition unit which can be calibrated to the

IEC 60270 standard. The acquisition unit used in the experiment is the Mtronix

Advanced Partial Discharge Analysis System MPD600. The sensor was installed at a

distance of 2 meters from the PD sources and a spectrum analyser was used to record

the signals captured by the sensor.

3.7.1. Result and discussion

Corona produced by a needle to ground plane electrode arrangement is chosen as the PD

source. The resultant discharges are very stable. Sensors will therefore detect a similar

amount of pC values.

The applied voltage was 7 kV which is well above the inception. Corona discharges

occurred around the voltage peaks in both half-cycles. The phase-resolved PD pattern

was recorded using the Mtronix system and shown in Figure 3.34. Note that the PD

magnitude (apparent charge) on the positive half-cycle is ~60 pC, much larger than that

in the negative half-cycle (~5 to 10 pC). These measurements were taken as the

reference for evaluating the UHF detection scheme that was carried out next.

Initially the PD signals were recorded in the time domain mode, i.e. using a CRO to

record the PD waveform. However, it was difficult to know if the triggering level was

appropriate. Consequently, it was not possible to distinguish if the signals recorded

came from the 60 pC or 5 pC discharges or even from the background noise. In

addition, comparison to the Mtronix measurement was not possible. Thus the

measurement was then carried out in the frequency domain. A spectrum analyser was

used to record the PD pattern captured by the sensors. Zero-span mode was chosen for

recording which would give similar patterns to the phase-resolved patterns recorded by

the Mtronix system. Thus the measurement results can be compared to the standardized

measurement method.


80

The corona produced in the experiment only appeared at a frequency below 200 MHz.

This is actually below the UHF range. However, the sensors were still able to pick up

the corona signals and all sensors showed this ability.

Figure 3.34: Corona pattern recorded using Mtronix PD detector, corona on negative

half-cycle shows values at around 5-10 pC.

Different sensors have different antenna characteristics, thus their working frequencies

are different and a direct comparison of the sensors’ capabilities to detect corona

discharges cannot be made. As an example, Figure 3.35 shows the PD pattern captured

at the same frequency of 80 MHz by different sensors at a distance of 100 cm. At this

particular frequency, PD activities of 5 pC magnitude (around the peak of the negative

half-cycle) can be recognized from the PD pattern captured by the log-spiral and spiral

sensors. However, the conical and monopole PD results show almost unrecognizable

pattern of the 5 pC discharges.

Target 5 pC


81

Figure 3.35: Corona patterns recorded using zero span mode captured by various

sensors, the sensor distance to the PD source is 100 cm.

The next set of examples is shown in Figure 3.36, each corresponds to a particular

sensor and measured at a frequency that yields the highest magnitude response (most

sensitive). When comparing the magnitude of each sensor, the conical has the highest

magnitude, followed by log-spiral and spiral. The monopole sensor shows the lowest

ability to detect PD signals. Nevertheless, all sensors show a capability to detect a small

amount of PD as low as 5 pC at a distance up to 1.5 m. This also applies when the

distance is 2 m, except for the monopole sensor.

The PD patterns captured by all sensors have very similar patterns to measurement

results gathered using the Mtronix equipment. The PD patterns in Figure 3.36 were

recorded for approximately 3 minutes for each measurement. During the measuring

process, the corona source sometimes generates large PD pulses in both positive and

negative half-cycles. The PD patterns which had these large intermittent spikes were

discarded in the analysis.

Overall, experimental results show that the sensors are able to be used to detect PD in

transformers for testing purposes. Discharges as low as 5 pC can be measured. This

value is clearly well within the acceptance criterion of the PD test for power

transformers, i.e. 500 pC according to AS/NZS 60076.3 standard [94]. However, it


82

should be noted that the noise level in the laboratory environment is very low, i.e. ~3 pC

as shown in Figure 3.34. Further discussion on the sensitivity of sensors to detect

different PD sources and conditions can be found in Chapter 4.

(a)

(b)


83

(c)

(d)

Figure 3.36: Corona patterns recorded using zero span mode at different frequencies at

PD level of 60 pC in positive half-cycle and 5 to 10 pC in negative half-cycle: (a)

Conical, (b) Log-Spiral, (c) Spiral, and (d) Monopole.


84

3.8. Conclusion

Four different UHF sensors suitable for mounting via transformer oil drain valve holes

and dielectric windows were investigated. CST software was used to perform simulation

and obtain the sensor responses over a frequency range of 300 MHz to 3 GHz. Results

show that the conical sensor has higher gain compared to the monopole, but the latter

has a simpler construction. Among the disk sensors, the log spiral has higher and

smoother gain than the spiral. Its impedance characteristic is also relatively more stable.

All the sensors tested can detect UHF signals. Log-spiral, conical and spiral sensors

show similar ability to capture corona discharge signals. For PD levels at around 5 pC,

these three sensors are still able to pick up the signals up to a distance of 2 meters.

However for monopole sensors, the corona signals of 5 pC are almost unrecognized

when the distance is more than 1.5 meters.

CHAPTER 4

STEP RESPONSE, FREQUENCY RESPONSE AND

SENSOR SENSITIVITY TO DETECT PD

4.1. Introduction

In every measurement system, calibration which compares the output of a piece of

measuring equipment to a standard value is required. The calibration establishes with

certainty the amount being measured. However, this is not the case for the UHF

detection method. The output of the UHF sensors cannot be calibrated as per IEC 60270

as they do not directly quantify the amount of charge of the PD pulses [111].

The reason is that a PD can occur at almost any location inside the transformer tank.

The path of the electromagnetic signals from the PD source to the sensor is affected by

the structure inside the transformer. The PD signal propagation can be obstructed by

some solid material parts inside the transformer. The active parts of the transformer also

affect the attenuation of the electromagnetic signals which caused the attenuation not

linear to the distance. Thus without knowing the exact location of the PD, it is difficult

to convert the amount of PD detected by the UHF sensor to an equivalent pC level [48].

To provide information about the sensor capabilities, it is important to set up tests which

are repeatable and can be used to test various sensors. In [112, 113] sensor calibration is

introduced and information is provided about the sensor frequency response. A µ-TEM

cell was used in [114] to test antenna response. In [113, 115], a TEM cell was built to

test the sensor frequency response in an attempt to calibrate the sensor for PD detection.

Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD

86

The TEM cell can also be used to test the sensor response for specific pulses such as the

step pulse [51, 116] in order to find the most suitable sensor for application of PD

diagnostic and monitoring. Using a step pulse to determine the frequency response of

the sensors has an advantage over the sweep frequency generator [116]. This is because

the step pulse contains all necessary frequency components so only one measurement is

needed. Also, the cost of the test can be reduced as the frequency generator can be

eliminated. However, the sweep frequency generator will provide real frequency

response where input and output can be compared directly, unlike the step pulse where

the pulse signals must be converted to frequency response.

As the UHF sensors cannot be calibrated based on a pC value, CIGRE WG 15.03 [49]

has recommended a method for its sensitivity verification which can be used to

determine on-site the minimum sensitivity of this measuring method in GIS. The

sensitivity test will show the amount of PD which can be measured by the UHF method.

The sensitivity of the UHF method is very dependent on the type of sensor, types of PD

source and the surrounding structure [48, 83, 117, 118].

In this chapter, sensor frequency and step pulse response tests are discussed. A TEM

cell was used to simulate the transverse mode of the PD electromagnetic waves in the

transformer tank. The sensor sensitivity was also tested to detect real PD signals emitted

by two types of PD sources in oil. The effect of change in structure is also discussed.

4.2. UHF Electromagnetic Signal

The electromagnetic pulses generated by the PD source as expressed by Equation 2.10

can carry a wide band frequency signal depending on their rise time. In air, the

propagation velocity of the electromagnetic signals is approximately as fast as the speed

of light (c). In other media, the speed of the electromagnetic signal (v) depends on the

permittivity and permeability of the material. This factor is called the refractive index of

the material and is expressed as:

r ro o

cv

4.1


87

where r o is the permittivity of the material, and r o is the permeability of

the material (expressed as a product of its relative value and the absolute value of free

space). In a vacuum, the propagation velocity of electromagnetic signals is the speed of

light, i.e. 3 x 108 m/s.

4.2.1. Electromagnetic propagation modes

When electromagnetic signals travel, they carry both electric and magnetic components

which are perpendicular to each other. Depending on the structure in which the

electromagnetic signals propagate, there are three modes into which the propagated

signals may be divided. The three modes are discussed below using the rectangular

waveguide as an example.

Figure 4.1: A rectangular wave guide [119].

Assume the waveguide with rectangular shapes in Figure 4.1 is filled with a non-

dissipative medium. If the waveguide lies along the z direction, then the electric and

magnetic fields along the waveguide are expressed as:

2z z

xc

j E HHk y x

4.2a


88

2z z

yc

j E HHk x y

4.2b

2z z

xc

j E HEk x y

4.2c

2z z

yc

j E HEk y x

4.2d

where 2 2 2ck k , 2 2k and β is the phase constant.

The field patterns which accompany the wave propagation can then be distinguished

within the three modes [119]:

1. Transverse electric (TE) Mode, in which the electric field component is

transverse to the direction of propagation. For TE mode, the condition is Ez = 0

and Hz ≠ 0.

2. Transverse magnetic (TM) mode, in which the magnetic field component is

transverse to the direction of propagation. For TM mode, we have the condition:

Hz = 0 and Ez ≠ 0.

3. Transverse electric and magnetic (TEM) mode is a mode where both electric and

magnetic components are transverse to the direction of propagation. In this

condition Ez, Hz = 0 everywhere.

4.2.2. Electromagnetic propagation in transformer

The electromagnetic signal aroused by the PD source in a power transformer is defined

as a transverse electromagnetic wave (TEM) [120]. The phase velocity of the TEM

waves at high frequencies for insulators with conductivity o r is similar for

each frequency [121]. The signals travel at the same speed without dispersion regardless

of their frequencies. For oil the speed at which the signals travel can be approximated

using equation 4.3.


89

1gv

4.3

With a relative permittivity of εr =2.2 and µr = 1, the propagation velocity of the

electromagnetic signals is around 2 x 108 m/s.

4.3. Sensors step pulse and frequency response

The sensor step pulse and frequency responses were evaluated using a TEM cell. The

TEM cell is designed to match the sensor impedance, i.e. 50 ohms and simulate the

propagation mode of PD in the transformer.

4.3.1. TEM cell

A parallel plate is one of conductor arrangements which transverses both electric and

magnetic signals. The cell structure is shown in Figure 4.2 and consists of two

aluminum plates with different widths. The bottom plate is connected to ground and the

top plate is of a specific width positioned at a specific distance from the bottom one so

that the cell meets the required impedance. The cell was designed to meet the

impedance of the antenna, i.e. 50 ohms.

w

dεr

Figure 4.2: Cross section of strip line geometry.


90

The impedance of the strip line for w/d ≥ 1 is defined by [99]:

120/ 1.393 0.667ln( / 1.444o

r

Zw d w d

4.4

or if the characteristic impedance Zo is known, the w/d ratio can be calculated as:

28 / 2

22 1 0.611 ln(2 1) ln( 1) 0.39 / 2

2

A

A

r

r r

e for w dew

d B B B for w d

4.5

where : 1 1 0.110.2360 2 1

o r r

r r

ZA

2

s

o r

ZBZ

with

Zs = impedance of free space (for air ≈ 377 ohms),

εr = dielectric constant of substrate (air),

w = width of metal strip,

d = thickness of substrate (air),

Figure 4.3: Field plot of designed strip line.


91

The largest sensor diameter is 15 cm which is used as a constraint in the design process

of the TEM cell. The electromagnetic field between the two plates must be uniform and

has a height which is at least the size of the sensor. Using Maxwell electromagnetic

field software [122], the dimension of the cell can be determined, and where the top

electrode width is 50 cm the electric field is fairly uniform with a coverage width of 25

cm. The overall dimensions and diagram of the cell can be found in Appendix B.

The cell was designed to have an impedance of 50 ohms, and the tapered sections at

both ends were terminated with 50 ohm connectors. One end is then connected with a

50 ohm terminator. The signal input was fed from the other end which was connected

using BNC with the same impedance as the cell.

Z

CRO

Matched Termination 50 Ohm

Signal Generator

Sensor

TEM Line

Er

Figure 4.4: Test diagram for frequency response measurement and pulse response.

4.3.2. Step pulse response

The rise time of the step pulse input was around 0.5 ns and the length was maintained

for quite a long time so the sensor response was only due to the changed input voltage.

Figure 4.5 shows the step pulse response of all sensors. The monopole had a faster

response with the least oscillation. A similar response was given by the conical with just

slight oscillation. The spiral had the most oscillation in its response with the peaks of

the signals distorted. The log-spiral showed a higher magnitude with oscillation up to 30

ns, which was caused by the length and structure of the spiral being much longer than

other sensors. Thus, signals received at the end point needed more time to arrive at the

feed point.


92

Figure 4.5: Step pulse response of the four sensors.

The aim of the step pulse response is to establish the response of the sensors to fast

change of rise time signals such as PD signals. Knowing the step response means that

the most suitable sensor for PD location application can be selected. For the purpose of

PD localization, the sensor with the lowest oscillation response and therefore the fastest

to reach maximum energy is likely to be used [77, 106]. The lowest level of oscillation

means that the first peaks of the signals are easier to pick up. Thus error due to false

determination of the peaks can be minimised.

4.3.3. Frequency response

Using the TEM cell the frequency response of each sensor is also tested. The procedure

is similar to the pulse step response by means of changing the input from step pulse to

sinusoidal function. To record the input and sensor magnitude, a spectrum analyser is

used instead of a CRO. The frequency response (He) is calculated as:


93

( )( )( )

se

i

VHV

4.6

where Vs is the sensor amplitude and Vi is the input amplitude.

Figure 4.6: Sensors frequency response.

The log-spiral sensor has the flattest response for the frequency range of 100 MHz to

2000 MHz. The monopole and conical have quite similar responses where both sensors

have almost flat responses up to 1000 MHz. The spiral sensor shows responses with a

lot of oscillation which is caused by the spiral conductor structure.

The input Vi(ω) is a sinusoidal function generated by a function generator. The function

generator has a frequency range of 9 kHz to 2 GHz. The amplitude of the sinusoidal

function is set to 1 volt, for all frequency ranges. Although the function generator output

is set to 1 volt, the real output of the function generator shows slight variations in the

frequency range, and must thus be recorded in all frequency ranges. The sensor output

Vs(ω) is the output voltage of the tested sensor. Both Vi(ω) and Vs(ω) were recorded by

using a spectrum analyzer to record the amplitudes.


94

4.4. Sensor sensitivity to detect PD

The sensitivity test is an attempt to find the minimum PD value in pC that is still able to

be detected by the UHF detection method, and where possible, to find the relation of the

power recorded by the UHF to the amount of pC. For sensitivity tests, the requirement

is that the amount of power be recorded in full span mode [83, 123, 124]. The full span

mode provides information on the energy of the PD signals in specific time over the

whole frequency range. The full span mode does not have any requirement to scan the

single frequency to determine the occurrence of the PD. However, the full span mode

result cannot show the PD pattern as the pattern is normally shown by a conventional

measuring unit, such as Mtronix. The phase resolved PD pattern however, can be

recorded in zero span mode. Thus comparison based on the pattern can be made. Thus

comparison based on the pattern can be made. In this thesis, zero span mode is also

included as a comparator to determine the sensor sensitivity.

4.4.1. Experimental set-up

The experimental diagram is shown in Figure 4.7. The experiment was done using a

tank which is 120 cm long, 72 cm wide and 90 cm high. The tank is filled with oil up to

a height of 60 cm. Void and floating metal defect models were fabricated to generate

two different PD patterns. The defect models were crafted using three layers of solid

insulation sandwiched between two flat copper electrodes: 2 layers of pressboard and a

layer of Kraft paper on top. For both void and floating metal, the middle layer of the

pressboard was punctured to create a hole with a diameter of 0.5 mm. For the floating

metal sample, a metal plate was fitted into the hole. The samples were immersed in oil

inside a fully covered distribution transformer tank in the laboratory. The PD sources

were positioned 70 cm from the sensor. Between the sensor and the PD source, a barrier

of solid insulating material was placed at varying distances from the sensor to

investigate the effect of different structures on signal propagation.


95

(a) (b) (c) (d) Figure 4.7: (a) Experimental diagram to test the sensor sensitivity to detect different PD

sources and effect of internal physical barriers (b) top view of the transformer tank, (c)

void PD source and (d) floating metal PD source

The background noise was recorded without the presence of a PD signal. The presence

of the PD was acknowledged from results from the Mtronix acquisition unit. The PD

recorded started at the inception voltage. As the voltage was increased higher PD values

were generated. The amount of PD generated by PD defect at every level was recorded

using the Mtronix acquisition unit. All measurements were recorded for a 3 minute

duration, for both the Mtronix and UHF methods for each sensor.

4.4.2. Full span and zero span measurement

Typical PD patterns of both void and floating metal defects are shown in Figure 4.8.

The patterns were recorded using an Mtronix PD acquisition unit. At the same time as

High Voltage

metalElectrode

pressboardKraft paper

High Voltage

voidKraft paperpressboard

Electrode

PD Source

Sensor

CB

RL

TR

Spectrum Analyzer

Barrier

ZInput unit

Mtronix Aqcuisition

Unit

PD Source Sensor

Barrier

Distance


96

the PD was being recorded by Mtronix, a sensor was applied to capture the

electromagnetic signals emitted by the PD source which was then fed into a spectrum

analyser to be recorded.

(a)

(b)

Figure 4.8: PD patterns recorded by Mtronix PD detector, (a) Floating metal and (b)

Void.


97

Using a spectrum analyser to record the PD, the PD pattern can be shown in two modes,

i.e. wide span and zero span. Figure 4.9 shows the PD recorded by the spectrum

analyser using different sensors for zero span mode. All sensors have a similar pattern

with differences in magnitude only. The zero span result shows a similar pattern to the

PD pattern recorded by Mtronix. The full span spectra associated with the same amount

of PD is shown in Figure 4.10.

(a)

(b)

Figure 4.9: Figure 4.9: PD patterns recorded by the UHF method, (a) Floating metal

recorded at frequency 312 MHz and (b) Void recorded at frequency 416 MHz,

associated with Figure 4.8.


98

The magnitude of PD during the experiment was measured using the Mtronix

acquisition unit. The magnitude of PD was recorded at the same time by the spectrum

analyser. The typical PD patterns of the two PD defect models are shown in Figures

4.8(a) and 4.8(b). Corresponding patterns recorded by the UHF method are shown in

Figures 4.9(a) and 4.9(b), for floating metal and void respectively. As the spectrum

analyser is only able to record the maximum value of the input, the patterns recorded

using the UHF method only show the envelope of the PD pattern.

(a)

(b)

Figure 4.10: Full span spectra recorded by using 4 different sensors,

(a) Floating metal at 70 pC and (b) Void at 60 pC.


99

4.4.3. PD spectrum

By comparing the full span spectrum measuring of events with and without PD signals,

the occurrence of PD can be recognized. Figure 4.11 shows the typical noise

background recorded by using a spectrum analyser for all 4 sensors. Two groups of

external interference at a frequency below 300 MHz and at around 900 MHz can be

noticed. This interference comes from known sources such as digital radio/television

and mobile telecommunication respectively.

The full span measuring result recorded by the UHF method is shown in Figure 4.9 for

PD at 60 pC. By comparing Figure 4.10 with Figure 4.11, the presence of PD can be

recognized. The recorded PD signals have spectra at frequencies of around 200 MHz to

600 MHz. However for much lower PD levels, as in Figure 4.12 where the PD is 30 pC

and 20 pC for Floating metal and Void respectively, the presence of the PD cannot be

distinguished from the noise background spectra. Thus it is necessary to extract some

parameters to distinguish between them.

Figure 4.11: The background noise spectrum recorded by 4 different sensors.


100

(a) Floating metal

(b) Void

Figure 4.12: Full span PD spectra recorded by the UHF method, (a) Floating metal at

30 pC and (b) Void at 20 pC.


101

4.4.4. Quantifying PD measurement

The sensor sensitivities (in capturing PD signals) can be compared from the frequency

spectra of both full span and zero span. However, direct comparison of the spectra such

as shown in Figure 4.11 and 4.12 is difficult. The spectra patterns look very similar so

subtle differences cannot be easily distinguished. Therefore, some parameter must be

extracted from the spectra [51, 76, 108, 109] to be used as a comparator. For example,

the total energy can be extracted from both full and zero span measuring results. The

total energy of the spectrum is calculated as:

( /10)

110log 10 k

nx

kTE

4.7

where: TE = total energy

xk = kth data point

n = total points of data

For the full-span measurement result, the total energy of the spectrum with PD is

subtracted from background noise energy. The background noise energy is extracted

from the spectrum without PD. Table 4.1 shows the total energy of background noise

for each sensor.

Table 4.1: Background noise captured by different sensors

Spiral

(dBm)

Monopole

(dBm)

Log Spiral

(dBm)

Conical

(dBm)

Background Noise -48.13 -48.58 -48.91 -47.89

The second parameter is the magnitude of the PD spectra. This parameter is useful for

zero span spectra where the magnitude of the PD recorded by Mtronix can be

approached from the magnitude of the zero span spectra. However, for the full span

magnitude of the spectra it is almost impossible to compare the amount of PD because


102

the result shows that the magnitude of background noise is very high. Thus the

magnitude of the full span spectra cannot be used since it will cause error.

4.4.5. Sensitivity to detect different PD sources

Different PD sources have different PD levels at their inception voltage. The PD level at

inception voltage is ~20pC for the void PD source, whilst for floating metal it is at

~30pC. All sensors show a capability to detect PD as low as 20 pC but yield different

total energy. Table 4.2 shows the total energy of the PD at inception voltage. The total

energy of all sensors is just slightly above the background noise. This is understandable

since the full span spectra of all sensors also show little difference when compared to

the spectra of background noise of each sensor.

Table 4.2: Total energy of the PD detected by UHF sensor at inception voltage of void

and floating metal PD sources.

Spiral

(dBm)

Monopole

(dBm)

Log Spiral

(dBm)

Conical

(dBm)

Void (20 pC) -47.89 -48.12 -48.26 -47.36

FM (30 pC) -47.66 -48.10 -48.13 -47.04

ΔVoid* -60.61 -58.10 -56.82 -56.81

ΔFM* -57.56 -57.88 -55.98 -54.55 * ∆Void and ∆FM = energy difference between PD inception and background noise energies,

for both void and floating metal PD sources.

Figure 4.13 shows graphs of the sensors detecting different PD sources. The total

energy of all sensors has a linear relation with the amount of pC measured. Similar

results are shown by different sensors. Both PD sources also show a linear tendency as

far as the total energy and the amount of PD are concerned. From these results, the total

energy of the sensors shows possibilities of conversion to the PD magnitude (in pC).


103

However this might be true only if the structure of the transformer is known. Or in other

words, if the structure of the inside of the transformer is changed, the relation between

the total energy and PD levels might also change.

(a) (b)

Figure 4.13: The total energy of zero span of different PD sources, (a) Void and (b)

Floating metal.

The presence of the PDs, when they are lower than 30 pC, cannot be detected in full-

span mode, but are detectable in zero-span mode. As the measurement is a UHF method

which uses an antenna as a sensor, the measurement sensitivity perhaps can be increased

by using a more sensitive sensor. This could be achieved by designing a different

antenna, which is more sensitive to low-level input.

4.4.6. Barrier effect

A PD can occur at almost any location inside the transformer tank. The path of the

electromagnetic signals from the PD source to the sensor is affected by the structure

inside the transformer. PD signal propagation can be obstructed by some solid material

parts inside the transformer. In the experiment, for simplification, the presence of an


104

inner structure was simulated by placing a barrier between the sensor and the PD

source. The barrier (bakelite plate) was positioned in varying locations i.e. 5 cm, 10 cm,

15 cm and 20m from the sensor.

With the presence of a barrier between the sensor and the PD source, the zero span

results still show similar patterns to the Mtronix. There is no significant change of

pattern due to the presence of the barrier. The barrier did not totally block the PD

signals, i.e the electromagnetic signals still travel around the barrier and get to sensor.

The full span spectra also show similar patterns to those where no barrier is present, i.e.

the PD can be recognized in the frequency range of 200 MHz to 600 MHz.

Void

Figure 4.14 shows the total energy graphs of full span for all sensors with a varying

barrier distance between the barrier and the sensor and where the background noise has

been subtracted. The presence of the barrier almost had no effect on the sensor

capability to detect the PD. All sensors were still able to capture PDs as low as 20 pC.

Additionally, as the PD level increased, the total energy captured by sensors also

increased.

The presence of the barrier has a random effect on the total energy and shows little

correlation to its position. It is not possible to tell the relation between the amount of

energy and the position of the barrier. The amount of total energy is too random to

establish such a relationship. All sensors show a similar effect.

A similar random effect is also shown in the zero span measuring results. The amount of

total energy and magnitude value indicate a random value in relation to the presence of

the barrier. Thus the amount of PD charge cannot be related to the amount of energy

recorded by the zero span. However, in the same conditions, i.e. the barrier at a fixed

position, for all sensors the amount of energy and magnitude value have linear

relationship to the amount of pC measured by the Mtronix. This applies for all the

positions of the barrier setup. Thus zero-span mode can probably be used to calibrate


105

the amount of pC for a known structure of a transformer, or at least to check the

sensitivity of the UHF measuring system.

A similar random effect is also shown in the zero span measuring results. The amount of

total energy and magnitude value indicate a random value in relation to the presence of

the barrier. Thus the amount of PD charge cannot be related to the amount of energy

recorded by the zero span. However, under the same conditions, i.e. the barrier at a

fixed position, for all sensors, the amount of energy and the magnitude value have a

linear relationship to the amount of pC measured by the Mtronix. This applies for all the

positions of the barrier setup. The exception is only for the conical sensor when the

barrier is set 10 cm from the sensor. The variation of the total energy for this particular

sensor and distance might be caused by the direction of the sensor being incorrect or

changed from the previous setting. Thus the zero-span mode can probably be used to

calibrate the amount of pC for a known structure of a transformer, or at least to check

the sensitivity of the UHF measuring system.


106

(a) (b)

(c) (d)

Figure 4.14: Total energy of full-span spectra with varying barrier positions, void PD

source.


107

(a) (b)

(c) (d)

Figure 4.15: Total energy of zero-span spectra with varying barrier positions, void PD

source; (a) Conical sensor, (b) Log-spiral, (c) Spiral and (d) Monopole.


108

(a) (b)

(c) (d)

(e)

Figure 4.16: Total energy of zero-span spectra measured by different sensors; (a) no-

barrier, (b) barrier distance 5 cm, (c) barrier distance 10 cm, (d) barrier distance 15 cm,

and (e) barrier distance 20 cm from the sensor.


109

(a) (b)

(c) (d)

Figure 4.17: Maximum value of zero-span spectra with varying barrier positions, void

PD source; (a) Conical sensor, (b) Log-spiral, (c) Monopole and (d) Spiral.


110

(a) (b)

(c) (d)

(e)

Figure 4.18: Magnitude of the zero-span spectra of void PD; (a) no-barrier, (b) barrier

distance 5 cm, (c) barrier distance 10 cm, (d) barrier distance 15 cm, and € barrier

distance 20 cm.


111

Floating metal

The full-span spectrum of the floating metal is similar to that of the void. As mentioned

previously, the frequency range of both void and floating metal is mainly in the range

200 MHz to 500 MHz.

The presence of a solid insulating barrier at different locations has no significant

correlation to the total energy of the full-span and zero span mode results. For similar

PD levels, the total energy of the full-span spectra shows random values, Figure 4.19.

This result suggests that knowing the location alone is not enough to enable converting

the total energy to an equivalent pC value. One needs to know the detailed structure of

the transformer as parts of the transformer may block the travelling path of the PD

signals to the sensors.

The total energies of the full-span and zero span spectra of PDs from the void and

floating metal show a similar trend. All sensors can detect both PD sources with a PD

inception of 20 pC. For similar conditions, i.e. barrier at the same position, the total

energy and magnitude of zero-span spectra show linear correlation to the PD level.

Similar results are observed for all sensors, as shown in Figure 4.20 and 4.21.


112

(a) (b)

(c) (d)

Figure 4.19: Total energy of full-span spectra with varying barrier positions, floating

metal PD source: (a) Log-Spiral, (b) Conical, (c) Monopole, and (d) Spiral.


113

(a) (b)

(c) (d)

(e)

Figure 4.20: Total energy of the zero-span spectra of Floating metal PD; (a) no barrier,

(b) barrier distance 5 cm, (c) barrier distance 10 cm, (d) barrier distance 15 cm, and (e)

barrier distance 20 cm.


114

(a) (b)

(c) (d)

Figure 4.21: Total energy of the zero-span spectra of the Floating metal PD source for

varying barrier distances: (a) Log-Spiral, (b) Conical, (c) Monopole, and (d) Spiral.


115

4.5. Conclusion

Four types of sensors were designed and constructed, their frequency response then

tested, and their response to a step pulse examined. Also their sensitivity to detect PD in

transformers was evaluated.

The Log spiral shows a flatter frequency response than other types of sensors. Thus it is

likely to be chosen for PD detection application. Meanwhile, the short-monopole and

the conical show quite a similar frequency response. This is expected since both of them

are ‘monopole’ antenna types. The short-monopole has a faster pulse step response,

although it shows lower magnitude. This will make the monopole sensor the better

sensor for PD-localization application. The spiral sensor has a very fluctuated frequency

response which means the sensor has good working capability for specific frequency

ranges but not for others.

The sensitivity test shows the sensors capability to pick-up PD signals as low as 20 pC

in oil at a distance of 70 cm. All sensors show a similar ability. The barrier did not

affect the sensors capability to detect the PD signals. All sensors were still able to pick

up PD signals as low as 20 pC with the barrier placed between the sensor and the PD

source. The amount of PD cannot be converted to the amount of power received by the

sensor without knowing the exact location and structure of the transformer. The total

energy and magnitude of the zero-span spectra show a linear correlation to the amount

of PD for the barrier in the same position. All sensors show similar results.

CHAPTER 5

UHF PD RECOGNITION USING PD WAVEFORM

AND PRPD PATTERN

5.1 Introduction

UHF PD signals can be recorded in two modes, i.e. time domain and frequency domain.

This chapter discusses the application of UHF PD detection to recognize the PD source

types from the PD signals which are recorded in the two aforementioned modes. This

chapter started with UHF detection then followed on with the description and

background of artificial neural networks and neuro-fuzzy systems. It then continued on

to the application of these to recognize PD sources.

As the UHF detection method can be carried out to detect PD in two modes, PD

recognition will be applied using both detection modes. The recognition is done by

applying a back propagation neural network to recognize single and multiple PD

sources which were recorded in time domain, and neuro fuzzy to recognize the different

PD sources. Back propagation neural network is the most popular method for use in

pattern recognition [126], whilst neuro fuzzy has the advantage of flexibility to tolerate

imprecise data and for its ease of use [127].

Chapter 5 UHF PD recognition using PD waveform and PRPD pattern

117

5.2 UHF PD detection

The electromagnetic signals emitted by PD sources in the transformer can be picked up

by appropriate sensors. Using a measuring unit which is connected to the sensor, the PD

signals can be recorded in two modes, i.e. frequency and time domain. Using frequency

domain measuring, the presence of PD signals can be discovered by comparing the full

span measuring result to the noise background and if needed, the phase resolved partial

discharge pattern can be acquired by setting the span to a specific frequency value and

recording for a specific time such as 3 minutes. A spectrum analyzer is usually used for

this work.

The PD waveform can be recorded using a CRO or digitizer. The waveform will show

the sensor response to the fast pulse of the PD signals. The oscillation graph of sensor

output is dependent on the sensor type.

5.2.1 Recognition of PD source

Apart from PD detection, the ability to recognize the PD patterns is an important aspect

of transformer insulation diagnosis. Knowing the PD defect type will enable the engineer

to determine the possible location and the severity of the PD deterioration. This in turn

will help to determine corrective actions that have to be taken.

Both of the PRPD and the waveform of different PD sources tend to have their own

pattern and this pattern is unique to each type of PD source. Thus the type of the PD

source can be revealed from both the PRPD and PD waveform.

In order to classify the PD sources, two essential components are required: the

classifier, and the signal features (or finger prints) as the classifier inputs. A number of

PD pattern recognition methods can be used as a classifier such as genetic algorithm

[71], support vector machine [72], neural network [73] and fuzzy logic [74]. The

classifier input can be a group of features extracted from the PD pattern [71-73] or the

PD signal itself [74]. However, the latter suffers from the complexity of the analysis due

to the large amount of data inputs.


118

In this chapter the use of back-propagation neural network and neuro-fuzzy to recognize

PD sources will be discussed. The signal features are extracted from PRPD recorded in

frequency domain, and PD waveforms in time domain.

5.3. Artificial neural network

Artificial neural network (ANN) is a “computational model” with particular abilities

such as the ability to learn, to generalize, or to cluster or organize data. To explain the

artificial neural network systems, biological systems are often described as parallel

illustrations. However, so little is known to date about the workings of the biological

neuron, with the result that the artificial neural network model might be an

oversimplification of the biological neuron.

5.3.1. Biological neural networks [126,129]

A close analogy can be made between the processing element (or artificial neuron) and

the structure of the biological neuron (such as a brain or nerve cell). Thus learning about

the biological neuron may help to clarify the characteristics of artificial neural networks.

The biological neuron as shown in Figure 5.1 has three components that are of interest

in understanding an artificial neuron: dendrites, soma and axon. The dendrites receive

signals from neighboring neurons by picking up the electrical impulse that is transmitted

across a synaptic gap by means of a chemical process. The synapses modify the

incoming signals, typically by scaling the input signal frequency similar to the weights

process in an artificial neural network.


119

Figure 5.1: Biological neuron [127]

All the signals picked up by the dendrites are connected to the soma and summed up. If

the information collected by the soma is sufficient, the cell fires i.e. it transmits a signal

to other cells via its axon. Whether the cell either fires or not can be viewed in binary

terms and can also be viewed as a signal summation producing either greater or lesser

magnitude with respect to a certain threshold level.

Key features of the artificial neural network are drawn from the properties of the

biological neuron, that is [128]:

1. The processing element receives many signals

2. The signals can be modified by a weight process

3. The weighted inputs are summed by the processing element

4. When the input is sufficient, the neuron transmits an output

5. The output of a particular neuron may go to many other neurons

Another important aspect in which the artificial neural network is similar to the

biological neural system is in fault tolerance. The fault tolerance of the biological neural

system allows incomplete or somewhat different input signals to be recognized, such as

when a human recognizes a person in a picture even though they have never met face to

face. Also, biological neural systems tolerate damage to the neural system itself. When

the human brain suffers from minor damage some of the neurons die, yet we still

continue to learn. Other neurons can be trained to take over the damaged cell function.


120

Similar to the biological neural system, the artificial neural network can be retrained if

minor damage happens to the network such as a loss of data or connection.

5.3.2. Artificial neuron model [129]

The biological neuron in Figure 5.1 can be approached as an artificial neuron model as

shown in Figure 5.2.

wk1

wk2

wkm

∑ f (·)uk Output yk

Summing junction

x1

x2

xm

Input signals

Biasbk

Synaptic weights

Activation function

Figure 5.2: Mathematical model of a neuron

The neuron output is calculated as:

( )k k ky f u b 5.1

where the summation function uk is defined as:

1

m

k kj jj

u w x

5.2

The bias is similar to a weight, only its value is a constant input of 1. The bias can be

omitted in a particular neuron if not desired.


121

The neuron output of the eq. 5.1. is dependent on the type of activation f(·). This will be

discussed in the next section.

5.3.3. Neural networks

A neural network is characterized by (i) its pattern of connections between the neurons

(called its architecture), (ii) its method of determining the weights on the connections

(called its training, or learning algorithm), and (iii) its activation function [128]. The

three characteristics are discussed below.

Architecture

In neural networks, the neurons are usually arranged in layers. Neural network

architecture can be classified as a single layer or multilayer.

x1

xi

xn

Y1

Yi

Yn

w11

wnn

wi1

wn1

w1i

wii

win

win

wni

Input units

One layer of weights

Output units

Figure 5.3: Single layer neural net

1. Single layer

The network consists of input units which receive signals from outside and output units

which show the response of the network (Figure 5.3). A single layer net has only one


122

layer of connection weights. The weights for one output unit do not affect the weights

for other output units.

2. Multilayer

A multilayer net (Figure 5.4) has one or more layers of nodes, and is commonly called

the hidden layer, between the input units and output units. The hidden neurons in each

layer of the net can receive their inputs from the preceding layer (or from input units

from the first layer) and their outputs provide input to the subsequent layer (or for the

output units for the last layer). There is no connection between the neurons within the

same layer. Multilayer networks can be applied to solve more complicated problems

than single-layer networks can. However the training may involve excessive training

effort and thus more time consuming.

The neurons in the hidden layer act as feature detectors which extract special features

from the input unit for classification. However, determining both the number of hidden

layers and the number of neurons in each of these hidden layers is a matter of trial and

error. Using too many hidden units may result in overtraining. The network actually fits

the learning samples, but with a large hidden layer the network will fit all the learning

samples instead of making a smooth approximation. For example, where the data

contains a large amount of noise, the network will fit the noise of all learning samples.

This will lead to a reduction in the learning error. However, adding the hidden layer will

first lead to a reduction in test error but then as the hidden layer number increases the

test error tends to increase as well. This effect is called the peaking effect. Besides the

peaking effect, increasing the layer number will also increase the time required for

training the network.

As a rule of thumb for trial and error, the number of layers and neurons can be

determined by following rules [130]:

1. The number of hidden neurons should be between the size of the input layer and

the size of the output layer.


123

2. The number of hidden neurons should be 2/3 the size of the input layer, plus the

size of the output layer.

3. The number of hidden neurons should be less than twice the size of the input

layer.

First hidden Layer

Input layer

Output layer

Second hidden Layer

Output signal

(response)

Input signal

(stimulus)

Figure 5.4: Architectural graph of multilayer net with two hidden layers

Learning process

Artificial neural network training can be classified in two ways which form a supervised

and an unsupervised learning process. Supervised learning or associative learning is the

training method whereby the network trains by providing input and matching the output

pattern. The goal is to teach the network to recognise precise output of an input set

while keeping error as low as possible or meeting the error criterion. The input-output

pairs can be provided by an external teacher, or by the system which is contained in the

network (self-supervised). Back-propagation learning is one of the examples of the

supervised learning process. Thus, it can be used to train the network to recognize the

input pattern to a specific goal output such as recognizing the PD pattern.

Unsupervised learning is a learning process without supervision. There is no a priori set

given, thus the network must update the weights only on the basis of the input patterns.


124

The learning process involves the adjustment of the winning units and the weights in the

neighbourhood around the winning unit based on a similarity or dissimilarity

measurement. For similarity measurement, the winning unit is the one with the highest

or largest activation level. If dissimilarity is used the winning unit is considered to be

the one with the smallest activation level.

When the learning process is starting all the inputs are presumed to be winners. Then as

the learning proceeds the size of the winning neighbourhood is reduced until it includes

only the winning unit itself.

Because the learning system target is mainly to group the input with the closest group,

unsupervised learning is commonly employed for data clustering, similarity detection

and feature extraction.

Activation function

An activation function is used to limit the amplitude of a neuron in a limited range of

the activation function. This function is called the squashing function because it

squashes the amplitude range of the output signals to some finite value. There are three

most common activation functions [129].

1. Threshold function

This activation function is defined by:

1 0 ( )

0 0if u

f uif u

5.3

This threshold function is commonly referred as Heaviside function. Similarly, the

threshold function for the output of neuron k is expressed as:

1 0 0 0

kk

k

if uy

if u

5.4

where uk is the induced local field of the neuron, and defined as:


125

1

m

k kj j kj

u w x b

5.5

Figure 5.5: Plot of threshold function

2. Piecewise-Linear Function.

The piecewise-linear function shown in Figure 5.6 can be expressed as:

12

1 1 12 2 2

12

1,,

0,

for uf u u for u

for u

5.6

This activation function may be viewed as an approximation to a non-linear

amplifier. The operating of the piecewise-linear function has two conditions:

a linear combiner arises if operating in the linear region

the function reduces to threshold function if the amplification factor is

infinitely large.

Figure 5.6: Plot of piecewise-linear function


126

3. Sigmoid function

This function is the one most commonly used in the construction of neural

networks. The sigmoid function has some variations such as unipolar sigmoid,

bipolar sigmoid and tanh.

a. Uni-polar sigmoid function

1

1 kk uf ue

5.7

This function has advantages in training the neural network by back-propagation

algorithms because it can minimize the computation [126].

Figure 5.7: Plot of uni-polar sigmoid function

b. Bi-polar sigmoid function

11

k

k

u

k uef ue

5.8

This type of activation function suits applications that produce output values in

the range of [-1, 1].


127

Figure 5.8: Plot of bi-polar sigmoid function

c. Hyperbolic Tangent Function

This function is defined as the ratio between the hyperbolic sine and cosine

functions or the ratio of the half-difference and half-sum of two exponential

functions.

sinh( )tanhcosh( )

k k

k k

u uk

k k u uk

u e ef u uu e e

5.9

Figure 5.9: Plot of hyperbolic tangent function

5.3.4. Back-propagation neural network

Back propagation or back error propagation is a neural network with the supervised

learning type using multilayer perceptron architecture, first developed by Rumelhart

et.al [151] in 1986. Their idea was to find a solution to the problem of adjusting the

weights from input to hidden units of a two layer feed forward network. To address this

problem, the errors of the unit of the hidden layers are determined by back-propagating


128

the error of the output layer unit. For this reason, this method is called the back-

propagating learning method. The process involves two phases, a forward propagating

and a backward propagating step.

In forward phases, the training input set is fed into the input layer. The input signals

propagate through the network until they reach the output layer. The output determined

by the network is displayed as the output pattern. The network output is then compared

to the desired output values and the result shows as the error (eo). If eo = 0, then the

training is finished. However, this is not so for almost all networks where an error value

of eo ≠0 is usually produced and higher than the minimum error criterion.

In the backward phase, the output error produced by the network is propagated back to

the network in a backward direction which is used to adjust the weight of each unit.

For each neuron in the output layer, the error is calculated as:

'( ) ( )o o o od y F s 5.10

where do is the desired output pattern, yo is the output of the network, and '( )oF s is the

derivative of the sigmoid function. Using a bi-polar sigmoid activation function in

Equation 5.8, the error is equal to:

( ) (1 )o o o o od y y y 5.11

Regarding the choice of activation function, the sigmoid function is chosen since it is

differentiable.

As for the hidden layer, we do not have a value for δ. For the hidden layer, the errors in

the output layer neurons are actually a result of their own incorrect synaptic weights and

the hidden layer neurons that produce the wrong outputs [28]. To solve this, the chain

rule is used, proceeding as follows: distribute the error of an output unit o to all the

hidden units that it is connected to, weighted by its connections [132]. Thus the error for

the hidden unit can be acquired using:


129

'

1

( )oN

h h h hoo

F s w

5.12

and again, using a bi-polar sigmoid activation function, the error for the hidden layer

can be written as:

1

(1 )oN

h h h h hoo

y y w

5.13

Next, the weight of the connection from layer j to layer k is adjusted using the

generalized delta rule [131]:

jk k jw y 5.14

The constant γ is known as the learning rate of the network. In practical terms, the

learning rate is chosen to be as high as possible without causing oscillation. To avoid

oscillation at large γ, the weight change is made dependent on past weight change by

adding a momentum term:

( 1) ( )jk k j jkw t y w t 5.15

The constant α determines the effect of the previous weight change.

5.4. Neuro-Fuzzy

A neuro-fuzzy is a combination of neural network and fuzzy system whereby the neural

network is used to approximate the fuzzy rule based system. In neuro-fuzzy, the neural

networks are viewed as a black box model which have learning ability to train the

examples while the fuzzy inference systems deduce the knowledge from the set of given

fuzzy rules.

The neural network was discussed in the previous chapter. In this section, fuzzy logic

will be discussed first then followed by a discussion of the Adaptive Neural Network

Fuzzy Inference System (ANFIS) [127, 133] as one of the neuro-fuzzy types.


130

5.4.1. Fuzzy set [125, 129]

The fuzzy concept comes from a common everyday life reality. As an example, the

concept of rain, which is a common phenomenon, is difficult to describe precisely since

the rain can vary from a sprinkle of water to a heavy downpour of water. The rain might

be able to be classified as light rain, moderate rain or heavy rain. But again, each of

these classifiers is also ambiguous. Thus the concept of rain classification can be said to

be a fuzzy concept.

A concept has both intension and extension. The intension of the concept means the

attributes of the concept, such as “rain” and the extension of the concept means all

objects defined by the concept such as “light rain”, “moderate rain” and “heavy rain”.

Thus the “set” of extension is used to express the concepts.

A classical set can be denoted by the notation:

A={a│p(a)} 5.16

where A is the set and “a” an object or element of A. The expression p(a) means a

satisfies p and the symbol {} means all elements that satisfy p are included to form the

set A. In logic expression, this can be written as:

( )a a A p a 5.17

The logic above is true (in logic normally denoted as 1) only if all elements of p that

forms the set A are precise, i.e. objects in property p are satisfied, or else the logic is

false (in logic normally denoted as 0). This set is called a crisp set. However, human

logic hardly has crisp extensions. With the example of rain above it is difficult to form a

set based on the classical set. One person may see the rain as “light”, another may say

“rather light” and etc.

To describe the fuzzy phenomenon in mathematical terms, Zadeh [134] introduced the

concept of the fuzzy set theory. In a fuzzy set, for any s S of a set A on the given


131

universe S, there is a corresponding real number ( ) 0,1A s to s, where ( )A s is the

membership grade of s belonging to A [135].

The membership function of set A can be mapped as:

: 0,1 , ( )A AS s s 5.18

The notation [0, 1] means the values of the membership function µA are in the range of 0

to 1.

5.4.2. Membership function

The membership of the elements s of the universe set S in the fuzzy set A can be

described by the membership function µA. The shapes of the membership function (MF)

vary, the most popular perhaps being triangular, trapezoidal, Gaussian and bell shapes.

For reasons of simplicity and computational efficiency, triangular and trapezoidal

membership functions are commonly used [136], whereas the Gaussian and bell shape

membership functions have the advantage of having smooth functions. Additionally,

when a derivative of the membership function is needed due to fine tuning of input and

output of the fuzzy inference system, Gaussian and bell and other continuous

membership functions can be used.

Below are shown the equations of three MFs, i.e. triangular, Gaussian and bell shapes.

1. Triangular MF is defined as:

0( ) / ( )

( )( ) / ( )

0

for x ax a b a for a x b

f xc x c b for b x c

for x c

5.19


132

Figure 5.10.a: Membership grades of a fuzzy set of a Triangle shape

2. Gaussian MF is defined as:

2

20.5( )( ) exp x cf x

5.20

where c is the mean and σ is the variance.

Figure 5.10.b: Membership grades of a fuzzy set of a Gaussian shape

3. Bell MF is defined as:

21( )

1bf x

x ca

5.21

where a, b and c are constants. Furthermore, c is the centre of the MF.


133

Figure 5.10.c: Membership grades of a fuzzy set of a Bell shape

5.4.3. Fuzzy IF-THEN rules [127]

Fuzzy rules or fuzzy “If-Then” rules are a logic operation which specifies the

relationship between the input and output of the fuzzy sets. The singleton fuzzy rule

takes the form: “if x is A, then y is B” where x U and y V , and has membership

function defined as ( , )A B x y where ( , ) [0,1]A B x y .

The if part of the rule, “x is A”, is called the antecedent or premise and the then part of

rule, “y is B”, is called the consequence or conclusion.

The consequents of fuzzy rules can be categorized into three types:

1. Crisp consequent :

IF … THEN y=a

where a is a numeric or symbolic value

2. Fuzzy consequent

IF … THEN y is A

where A is a fuzzy set

3. Functional consequent :


134

IF x1 is A1, x2 is A2,… and xn is An THEN 1

*n

o i ii

y a a x

where ao, a1,…, an are constants

5.4.4. Fuzzy inference system [127]

The fuzzy inference system (FIS) applies fuzzy rules to map the input data vector into a

scalar output. A block diagram of the fuzzy inference system (FIS) is shown in Figure

5.11 which consists of four components: the fuzzifier, inference engine, rule base and

defuzzifier. The fuzzifier plots input number into corresponding memberships. The

membership function type which is used by the fuzzifier determines the degree of each

input value in the fuzzy sets. The inference engine maps the input fuzzy sets into output

fuzzy sets. Using the given rule base, the inference engine determines the degree to

which the antecedent satisfies the rule. The inference engine is only applied to obtain

one number that represents the result of the antecedent even if the antecedent of a given

rule has more than one clause. When more than one rule fire at the same time, the

outputs of all rules are then aggregated to get a single value. In FIS, the outputs are not

affected by the order of the rule firing sequences. The fuzzy output of the inference then

maps to a crisp number by the defuzzier. The most popular defuzzification method is

the centroid, which aggregates the fuzzy set and returns its center of gravity. Other

methods that are commonly used in the defuzzification process are maximum, mean of

maxima, height and modified height.

fuzzifierInference

enginedefuzzifier

rule base

input

Xoutput

Y

Figure 5.11: Block diagram of a fuzzy inference system [127]


135

Based on the use of the defuzzification and fuzzy if-then rules, most fuzzy inference

systems can be classified into three types:

a. Mamdani fuzzy model

The Mamdani fuzzy model [137] used two fuzzy inference systems to control

the output and max-min combination as the defuzzification method. The fuzzy

rule in this model takes the form:

IF x1 is Ai1 … and xn is Ain THEN y is Ci

where xj (j=1,2,…,n) is the input variable, Aij and Ci are fuzzy sets for xj and y

respectively, y is the output variable.

b. Sugeno fuzzy model

The Sugeno fuzzy model was proposed by [138] in an attempt to generate fuzzy

rules from a given input-output data set. The fuzzy rule for two input systems for

this model has the form:

IF x is A and y is B then z = f(x,y),

where A and B are fuzzy sets in the antecedent and z = f(x,y) is a crisp function in

the consequent. The function z = f(x,y) can be any function as long as it can

represent the output of the model within the fuzzy region specified by the

antecedent of the rule. Normally, the function is polynomial and the fuzzy

inference system is commonly named after the order of the polynomial function.

Thus the first-order Sugeno fuzzy model refers to a first order polynomial of the

z = f(x,y) function. The computation time for the Sugeno model is far less than

that of the Mamdani model. This is achieved by simplifying the defuzzification

process where the overall output of the FIS is obtained via a weighted average.

Thus this model is by far the most popular and is widely in use.


136

c. Tsukamoto fuzzy model

The Tsukamoto fuzzy model [139] uses a fuzzy set with a monotonical MF to

represent the consequent of each fuzzy if-then rule. A typical fuzzy if-then rule

of the Tsukamoto model has the form:

IF x is Ai THEN y is Ci,

where x is input variable, y is output variable, Ai is a fuzzy set with a

monotonical MF and Ci is a crisp output value.

Similarly to the Sugeno model, this model also uses a weighted average method

in the defuzzification process and thus is a less time consuming process than

Mamdani. However this model is not as transparent as either the Mamdani or the

Sugeno fuzzy model. Consequently, it is not often used.

5.4.5. ANFIS [127, 133, 140]

ANFIS which stands for Adaptive Neural Network Fuzzy Inference System combines

the neural network and fuzzy system to determine the best fuzzy parameters. ANFIS

constructs a set of fuzzy if-then rules with appropriate membership functions that can be

used to generate the stipulated input-output pairs.

Figure 5.12 shows the ANFIS architecture using two inputs x and y and one output z. The

rules are defined by the first-order Sugeno fuzzy model. The rule set with two fuzzy if-

then sets for a first order Sugeno model is written as follows:

Rule 1: If x is A1 and y is B1, then f1 = plx + q1y + rl,

Rule 2: If x is A2 and y is B2, then f2 = p2x + q2y + r2.

where A1, A2, B1, B2 are the fuzzy sets; a1, a2, b1, b2, r1 and r2 are the coefficients of the

first-order of a polynomial function.


137

f1 = plx + q1y + rl,

1 1 2 2

1 2

1 1 2 2

w f w ffw w

w f w f

f2 = p2x + q2y + r2.

(a)

(b)

Figure 5.12: (a) A two-input first-order Sugeno fuzzy model with two rules; (b) The

ANFIS architecture [127].

The operation of each layer is described below:

Layer 1: In this first layer, all nodes (A1, A2, B1, and B2) are adaptive nodes. The

outputs of layer 1 are the fuzzy membership grade of the inputs (x and y)

1, ( ) ( ),ii AO x x 5.22

A1

A2

B1

B2

X

Xx

Y

Yy

W1

W2


138

where x is the input to node i and Ai is the linguistic label (small, medium,

large, etc) associated with the function µA. The member function µA is

usually a continuous type such as bell or Gaussian MFs.

Layer 2: In this layer, all nodes are fixed and perform as a simple multiple of the

incoming signal and produce the outputs that are the so-called firing

strengths of the rules.

2, ( ) ( ), 1,2.i ii i A BO w x y i 5.23

Layer 3: This layer normalizes the triggering strengths from the previous layer. All

nodes on this layer are fixed nodes. The i-th node calculates the ratio of the

i-th firing strength:

3,2

, 1,2.ii i

i

wO w iw w

5.24

The outputs of this layer are called normalized firing strengths.

Layer 4: All the nodes in this layer are adaptive with a node function:

4, ( ),i i i i i i iO w f w p x q y r 5.25

The outputs of this layer are the product of the normalized firing strength

and a first order polynomial (for the first order Sugeno model).

Layer 5: There is only one single fixed node in this layer that performs the

summation of all incoming signals.

Overall output = 5,1i ii

i ii ii

w fO w f

w

5.26


139

5.5. Recognition of different sources of PD from the PD

waveform

The PD signal can be captured in time mode which records the PD waveforms. In this

section, the back-propagation neural network is applied to recognize the PD sources

from the signal waveforms generated by three different PD defect models. A log-spiral

sensor was used to capture electromagnetic waves generated by the PD sources and a

CRO was used to record the PD waveform signals.

Figure 5.13 shows the flowchart diagram of the signal processing and recognition of PD

sources. The process is divided into five stages: signal denoising, signal decomposition,

feature extraction, features measuring and selection to choose the most separable

features, and classification.

Input Signals

Signals Decomposition

Signals Denoising

PD source Recognition

Features Extraction

Features Measure and Selection

Classification

Figure 5.13: Flowchart of the recognition method


140

The PD waveforms recorded by CRO are firstly denoised by applying the multivariate

denoising method. Then waveforms in time domain are decomposed into a wavelet-

packet-domain (WPD) tree. The features are then extracted from each node of the WPD

tree for all PD waveforms. The features are then weighed to select the best nodes which

are used as input for the back-propagation neural network to recognize the PD source.


In this thesis, three different PD defect models were constructed to simulate discharges

due to a void, floating metal and a combination of both. The PD defect models were

built using three layers of insulation sandwiched between two flat electrodes: 2 layers of

pressboard and a layer of Kraft paper on top. The middle layer of pressboard was

punctured to create a hole with diameter of 0.5 mm. For the floating metal sample, a

metal plate was fitted into the hole. Figures 5.14 and 5.15 show the experiment diagram

and the PD defect models. All samples were immersed in oil inside a fully covered

small distribution transformer tank in the laboratory.

PD Source

Sensor

CB

RL

TR

X

Z

YOscilloscope

ZInput unit

Mtronix Aqcuisition

Unit

SA

Figure 5.14: Experiment diagram of PD signal detection and recording


141

(a) (b)

(c) (d)

Figure 5.15: PD defect models (a) electrodes and sample arrangement (b) void, (c)

floating metal and (d) mixture of void and floating metal

A log spiral sensor (antenna) was fitted through a small opening at the top of the

transformer tank to capture the electromagnetic signal emitted by the PD defect. The

sensor output was connected to an oscilloscope to digitize the signal and the captured

data were transferred to a computer for processing and analysis. The sensor output was

also connected in parallel to a spectrum analyzer to record the frequency spectra of the

electromagnetic signals. To record the fast and wide frequency range of the partial

discharge, an oscilloscope with a bandwidth of 4 GHz and a sampling rate of up to 40

GS/s was used. A spectrum analyzer with frequency range from 9 kHz up to 3 GHz was

also used to detect the PD signals in frequency domain.

High Voltage

Electrodevoid


High Voltage

Electrodemetal


High Voltage

Electrodevoid


metal


142

The applied test voltages were set to 6.5 kV for the void, 7 kV for the floating metal and

8 kV for the combination of both. A higher voltage was set for the mixed model to

ensure that PD would occur in both defects. To confirm no discharges occurred from

other sources such as surface discharges from the test sample itself, a 'plain' sample

without void or floating metal was used for checking. It was confirmed that the

inception for surface discharges was >10 kV.

5.5.2. UHF PD signals

The UHF PD technique detects and measures the electromagnetic pulses emitted by the

PD sources. These electromagnetic pulses have a very short duration, typically less than

1 ns of rise time and a few ns of pulse width [1]. Thus it is a broad band signal which

contains frequency components well into the GHz range, i.e. covering the UHF

frequency band (300 MHz – 3 GHz). The sensor captures those frequency components of

the signal that fall within its working frequency range. In addition, the sensor will pick

up other unwanted noise/interference present in the same frequency band. This will

affect the analysis result. Therefore, it is important to remove the noise before applying

further analysis.

Figure 5.16: A typical waveform from void discharges


143

5.5.3. Multivariate denoising [141]

The UHF detection method has a very high sensitivity and is able to capture the fast

electromagnetic transient signals emitted by PD events. However, the PD pulse signals

are not always clear even for a well-designed UHF sensor. The magnitude of the PD

signals is dependent on various parameters as shown in Equation 2.10. The high

permittivity of the oil insulation not only reduces the speed but also attenuates the

electromagnetic signals. This situation is further exacerbated by the interference from

unwanted signals or noise. The noise interferences in the UHF range consist of digital

radio, television and telecommunication signals, thermal noise in the detection system

and periodic pulses from switching operations [142-144].

PD signals which are free from unwanted noise can be recovered by denoising the PD

signals captured by the sensor. In this thesis, a multivariate wavelet denoising tool is

utilized as it is proven effective to denoise the multichannel signal readings. This

technique deals with regression models of the form:

X(t)= f(t) + ε(t), t = 1,….,n. 5.27

where:

(X(t))1≤t≤n = observed signals

ε(t) 1≤t≤n = centered Gaussian white noise of unknown variance σ2

f = unknown function to be recovered

The multivariate denoising procedure can be carried out in four steps as follows:

1. Perform wavelet transform at level J for all columns of X. This step produces

matrices D1,…, DJ which contain detail of coefficient at level 1 to J of the p signals

and approximation coefficients Aj of the p signals.

2. Remove noise by a simple multivariate thresholding after a change of basis. The

noise covariance estimator is calculated using minimum covariance determinant

(MCD) of the matrices DJ and defined as 1

ˆ ( )MCD D

and is used to compute matrix

V such that ˆ TV V where ( ,1 )idiag i p . Apply to each detail after change


144

of basis, the p univariate thresholding using threshold 2 log( )i it nl= for each

ith column. Figure 5.17(b) shows a typical result of this step. The denoised signal

using a simple multivariate thresholding shows a satisfactory result. However, it can

still be further improved.

3. Improve the obtained result by applying principal component analysis (PCA) and

retaining fewer principal components. Perform PCA of the matrix AJ and select the

appropriate number pJ+1 of useful principal components.

4. Reconstruct the denoised matrix X from the simplified detail by inverting the

wavelet transform. Figure 5.17(c) shows a typical result of this step.

(a)

(b)

(c)

Figure 5.17: A denoising example (a) original signal, (b) denoising using multivariate

thresholding, and (c) result after retaining PCA component


145

The multivariate denoising method is a useful tool to denoise a multiple signal as it

makes use of the relationships between the signals to provide additional denoising effect

[141]. This additional denoising effect is able to remove not only more noise but also

incite buried elements of the original signals.

(a)

(b)

(c)

Figure 5.18: Denoised PD signals using db2 wavelets (a) Floating metal, (b) Void, and

(c) mix of Floating Metal and Void


146

Denoising the PD waveform

The measured signals were denoised by applying the multivariate denoising method

through the use of Matlab ‘wmulden’ command. The “wmulden” script is a built-in

Matlab script which is run in the multivariate denoising step discussed earlier. Typical

denoised waveforms for different PD defects are shown in Figure 5.18. It is evident that

the multivariate wavelet denoising method can remove the irregular spikes. Noise spikes

that occur before the PD signals appear can be removed almost completely although the

PD magnitude is slightly reduced.

5.5.4. Signal decomposition and features extraction

The total number of signals acquired from the experiment was 600, i.e. 200 data records

for each PD defect model. The signals are recorded by using CRO in the time domain.

To extract the information, the signals are decomposed into the wavelet packet domain

producing a wavelet-packet decomposition (WPD) tree. The decomposition level is set

to 5, thus producing a total of 63 nodes (Figure 5.19). The mother wavelets db2 and

sym2 are used to decompose the PD waveform. Figure 5.20 shows the db2 and sym2

mother wavelets.

Figure 5.19: A five-level wavelet-packet decomposition tree.


147

Figure 5.20: The mother wavelets (a) db2 and (b) sym2

Figure 5.21 shows the typical decomposition of a floating metal denoised signal and its

data for nodes (2,1), (5,0) and (5,26) together with the denoised signal. For both

processes of denoising and decomposing the signals, two different mother wavelets

were used, i.e. db and sym. The mother wavelet of order 2 was chosen as it is sufficient

to remove irregular spikes (noise) [141]. Choosing a higher order will consume

significantly more computing time.

Features extraction is used to reduce the number of inputs for the neural network

training and thus providing a possible solution to the problem of large dimensionality.

Three features were extracted from each node: the skewness, kurtosis and energy.

Skewness is a parameter expressing the asymmetry of the data around the sample mean.

Kurtosis shows how sharp the distribution of the data is. Energy indicates the

percentage of the signal energy of each node.


148

(a)

(b)

(c)

(d)

(e)

Figure 5.21: Signal decomposition (a) original Floating metal (FM) signal, (b)

denoising FM PD signal, (c) node (2,1), (d) node (5, 0) and (e) node (5, 26)

5.5.5. Feature measure and selection

The total number of signals acquired from the experiment was 600, i.e. 200 data records

for each PD defect type. For each PD defect type, 150 data were used as the training

input and 50 for testing of the neural network scheme. Altogether, 450 data were used

for training and 150 data were used for testing. From each node, 3 features were


149

extracted and thus produced a total of 3 x 63 x 150 = 85050 data. This is a fairly large

amount of data for use as neural network training input. Besides, the inclusion of

undesirable data features can make the classification process more difficult. Therefore,

the number of data must be reduced by using only the features that preserve maximum

separability.

In order to get the node with the feature that has the most separable value, a criterion

known as the J criterion is used. The J criterion compares the extent of scattering of

feature values for between-class and within-class. The best node with the largest J value

is selected as the input for the neural network. This criterion is defined as:

2

1

2

1

( ( , )) ( , ))( , )( , )( , ) ( , )

Lc

cb c

Lcw

cc

N m j n m j nS j n NJ j n

NS j n j nN

5.28

where: Sb = between-class scatter value

Sw = within-class scatter value

Nc = number of samples belong to a class c, where c is the type of PD

defect (Nc = 200)

N = total number of samples (N = 600)

mc(j,n) = mean values of feature at node (j,n) for class c

m(j,n) = mean values of feature at node (j,n) for all samples

σc (j,n) = variance of the features at node (j,n)

Table 5.1: The largest J values of the three features

Feature Node

(db2)

Node

(sym2)

J max

(db2)

J max

(sym2)

Kurtosis (5,0) (5,0) 2.7611 2.7611

Skewness (2,1) (2,1) 3.0516 3.0516

Energy (5,26) (5,26) 6.1229e+6 6.1229e+6


150

The denoised signals are then decomposed to 5 levels and produced 63 nodes. From each

node three features were extracted, i.e. kurtosis, skewness and energy. The J criterion is

used to determine the node that will be used as the neural network input. The same

mother wavelet was used to denoise and decompose the signals. Both db and sym

wavelets resulted in the same total J values and nodes. These are summarized in Table

5.1.

(a)

(b)

Figure 5.22: Features plot of the best nodes using different wavelets,

decomposed using (a) db2, (b) sym2


151

Figure 5.22 shows the features plot of the best nodes using db2 and sym2 wavelets.

Both wavelets resulted in the same best nodes, determined by applying the J criterion

formula. It also can be seen that by using the J criterion, the features can be clustered

together for each PD source. For floating metal and void, all the feature values are

totally separated. As for the combination of both defects, some feature values are very

close to those associated with the single defects.

5.5.6. Recognition result

After the best node was selected, the features from its node were input into a feed-

forward neural network to train the back-propagation learning rule for PD recognition.

Figure 5.23 shows the structure of the multi-level perceptron neural network.

Kurtosis

Skewness

Energy

1 2 3

Void

FM Mix

InputLayer

HiddenLayer

OutputLayer

Figure 5.23: A three-layer neural network

The feed-forward neural network has 3 inputs, 2 hidden layers and one output layer with

a three-class problem. Each hidden layer has 20 neurons of sigmoid type. The output as

shown in the figure has 1 layer, a linear type which is associated with void as 1, floating

metal as 2, and mix of void and FM as 3.


152

Denoised PD signals

A feed-forward neural network with back propagation was used to classify the source

of the PDs. The network had 10 hidden layers and the training error was set to 0.01. The

data set (600 in total) was divided into two groups: 450 data for use as training input to

train the neural network, and 150 data as testing input using the trained network to

classify the PD sources. Classification was done for both features that were obtained

using db2 and sym2 wavelets as shown in Figure 5.21. The results, summarized in

Table 5.2, show that the single and multiple PD sources can be classified and thus

recognized with high success rate.

Table 5.2: Percentage of correct classification using feed-forward neural network

PD type Number of

sample

Number of correct classification

Denoised Original

db2 sym2

Void 50 50 50 50

Floating Metal (FM) 50 45 45 22

Mix of Void & FM 50 48 48 41

Correctness (%) 95.3 95.3 75.33

Original (noisy) PD signals

The denoising process is one of the most time consuming steps in this recognition

process. In addition, denoising might remove some useful parts of the PD signals and

cause incorrect recognition results. Thus it is important to verify that the denoising

process was of benefit to the recognition results.

By using a similar recognition process as shown in the flowchart in Figure 5.13, except

that the denoising process was excluded, the results now show different nodes as the

best ones. The best nodes are (5, 0), (2,1) and (5,16) for kurtosis, skewness and energy

nodes respectively. The same best nodes were produced by both mother wavelet types.

The features plot of the best nodes after decomposition is shown in Figure 5.24. The


153

plot result has poorer separation compared to the ‘original one’ which is shown by the

overlapping value of each feature of the mixed and the floating metal. This poor

separation causes the recognition result of the un-denoised case to be lower than the

denoised one. With the latter, the result of the neural network classification as shown in

Table 5.2 shows significant increase of the correct recognition for both types of mother

wavelet. The mix of void and FM type shows the most significant improvement, from

22 correct (undenoised) to 45 correct (denoised). The overall percentage correctness

without the denoising process is 75.33 % and after denoising, using the multivariate

denoising tool, it increases to 95.3%.

(a)

(b)

Figure 5.24: Features plot of the best nodes of the original signals, decomposed using

different wavelets (a) db2, (b) sym2.


154

The correctness rate can be increased by adjusting the neural network training value, for

example, by minimizing the error level of the neural network. However the effort to

minimize the error thus increases the correctness level and presents a compromise to

other factors. In the case of lower error level, the time consumed might be increased

significantly or even cause an inability to achieve a solution. In addition, sometimes the

correctness level cannot be increased to a very high level as the samples have

distributed feature values.

5.6. Recognition single and multiple PD sources from the

phase resolved PD pattern

As aforementioned, the PD signals can be recorded in two modes i.e. time domain and

frequency domain. Section 5.5 discussed the use of PD waveforms which are recorded

in the time domain to recognize the PD source. In this section, the phase resolved PD

pattern will be used to recognize the PD sources.

The PRPD patterns are recorded using a spectrum analyzer set to zero span mode. The

zero span capturing mode available from a standard spectrum analyzer can be used to

selectively detect a PD signal component at a specific frequency over a certain

recording time interval. This method will capture the electromagnetic signals emitted by

PD sources and show the two dimensions ( v , φ ; where v is magnitude of signal and φ

is phase angle position) of the phase resolved partial discharge (PRPD) patterns, i.e. the

discharge patterns in relation to the applied AC voltage cycle (20ms for 50Hz supply

systems). Thus the PRPD patterns can be readily obtained for both positive and negative

voltage half-cycles.


The experimental diagram is similar to the previous experiment. The adjustment was the

use of a spectrum analyzer instead of a CRO and the PD defect construction was

changed as shown in Figure 5.25. Three defects were set up to generate PDs in the

experiment: void, floating metal and surface discharge. All were constructed by using


155

High Voltage

Electrodemetal

pressboard

Kraft paper

three layers of insulation, the two bottom layers being pressboard and the top layer

Kraft paper. The sample dimension and the electrode arrangement are shown in Figure

5.24. Both void and floating metal have the same diameter size of 5 mm which is carved

into the center of the PD defect samples. The diameter of the PD defect model is 6.5 cm.

(a) (b)

(c)

Figure 5.25: PD defect models (a) void, (b) floating metal and (c) surface discharge

All PD defect models were immersed in a small distribution transformer tank filled with

oil. The UHF sensor was positioned 75 cm from the PD source and its output connected

to a spectrum analyzer via a 50 Ω coaxial cable. In addition, a direct coupling detection

circuit (blocking capacitor in series with a quadripole) was also used to measure the PD

level, based on the conventional PD detection method, i.e. IEC60270 Standard. The

High Voltage

Electrode


High Voltage

Electrodevoid



156

circuit setup is shown in Figure 5.14. The input voltage was increased until PD

inception occurred and the PD magnitude QIEC can be read from the Mtronix digital PD

detector. The voltage was 6 kV, 7 kV and 10.5 kV and produced PDs of 140 pC, 100 pC

and 150 pC for void, floating metal and surface discharge respectively.

5.6.2. PD pattern and signatures

PRPD pattern of zero span measuring

One of the advantages of the spectrum analyzer over the oscilloscope is its ability to

capture signal in a single frequency and display results over a desired time span period

[46, 145]. By applying this so-called zero span method, the PD pattern in relation to the

supply voltage cycle can be captured and recorded. Here, the time span is determined by

the frequency of the power supply system, e.g. 20 ms for a 50 Hz AC supply system.

Figure 5.26 shows a typical PD pattern captured by operating the spectrum analyzer in

the zero span mode. The PD source is a corona which generated PD at constant values.

The magnitudes of the PD are dependent on the distance of the PD source to the sensor,

but the shape of the pattern remains similar. Thus capturing the PRPD pattern can be

achieved by installing a sensor at any location inside the transformer tank without

distorting the shapes of the PD pattern.

Figure 5.26: Typical PD pattern captured by the log-spiral sensor at different distances


157

UHF PD signatures

From the experimental results, a total of 107 PD patterns were recorded and analyzed.

They comprise 26 void data, 40 floating metal data and 41 surface discharge data. From

each PD pattern, 3 statistical operators were used to extract statistical values from the

two voltage half-cycles (positive and negative). Thus, there are 6 parameters that can be

used as inputs for the fuzzy analysis:

Mean (+), Mean (-): the first statistical moment (mean value) of the PD pattern for the

positive and negative halves of the voltage cycle, respectively.

Sk (+), Sk (-): the third statistical moment (skewness coefficient) of the PD

pattern for the positive and negative halves of the voltage cycle,

respectively.

Ku (+), Ku (-): the fourth moment (kurtosis) of the PD pattern for the positive and

negative halves of the voltage cycle, respectively.

For analysis purposes, the 107 data were divided into three groups. The first group

consisted of 73 data: 18 from void discharges, 32 from floating metal discharges and 33

from surface discharges. These data were used to train the fuzzy scheme by applying

ANFIS. The second group consisted of 3 data from each type of PD and were used for

checking the trained fuzzy scheme. The last group consisted of 5 data from each PD type

to test the trained fuzzy scheme ability to recognize the PD source. The first and second

group of data were arranged into a seven column matrix with the last column containing

single vector output data. This vector output data assigns the PD type to a specific

number: 1 for void, 2 for floating metal and 3 for surface discharge.

5.6.3. Result and discussion

PD pattern

Different PD sources emit signals in different ranges of frequency. Thus, the PD

patterns for each PD defect were recorded at a number of different frequencies. Also the


158

data was recorded only once for each zero span measurement, or in other words one

data for one single frequency. For this reason, the number of data produced in this

experiment is not as many as in the previous experiment discussed in section 5.5.

The data recorded in the experiment started from a frequency of 300MHz and increased

to 1500 MHz. The magnitude of the PRPD depends on the type of the PD source and

the selected frequency. The magnitude of the PRPD pattern shows a tendency to

decrease as the frequency increases as described in chapter 2.4.

Figure 5.27: PRPD of different PD sources at different frequencies

Three different defect models were used to generate the discharges. In total, 107 PD

patterns were recorded which comprise 26 patterns from void discharges, 40 from


159

floating metal discharges, and 41 from surface discharges. The number of data for each

PD defect model depends on the PD signal level in the UHF range (300 – 3000 MHz).

Experiment results showed that PD signals associated with void occur less than the

other two PD defect models. The void PDs mainly occur in the lower frequency range

of 300 – 600 MHz, while floating metal and surface discharge were produced in the

higher frequency range up to more than 1000 MHz. Figure 5.27 shows typical PD

patterns for all PD defect models at various frequencies.

In this thesis, a comparison is made of the shape of the PRPD patterns to recognize the

PD source. As the PD sources are different, it is evident that the shape patterns are

different and they also have different frequencies. However, the shapes of same PD

sources show similar patterns regardless of different frequencies. Thus comparison

should be able to be carried out regardless of different frequencies.

Note that Figure 5.26 shows the corona patterns as shown also in chapter 3. These

corona patterns were generated by a needle to plate electrode configuration. The applied

voltage was increased well above the inception to get steady corona discharges which

appeared on both half-cycles. From experimental results obtained, it was found that the

corona spectrum is evident only in the low frequency range, mainly below 100 MHz.

This is not within the UHF range. For this reason, the corona was not included as a test

sample and thus excluded from the analysis.

The values represent the characteristics of the PRPD pattern shapes. For example, the

kurtosis value of the surface discharge kurtosis (+) has a value of 10.0550 which means

that the positive cycle has much more peaked shape than the negative cycle where the

kurtosis (-) has a much smaller value of 1.9882.


160

Table 5.3: Data checking arrangement

PD

sources

Mean

(+)

Mean

(-)

Skewness

(+)

Skewness

(-)

Kurtosis

(+)

Kurtosis

(-)

Void 0.0710 0.0308 3.9680 4.8835 19.0655 28.3938

Void 0.0532 0.0218 2.6332 3.8853 9.4247 18.2825

Void 0.0828 0.0435 2.2471 3.7006 6.7417 15.5048

Void 0.0655 0.0390 2.7235 4.2616 8.7747 20.5322

Void 0.0516 0.0443 2.6060 2.8877 8.4147 9.8055

FM* 0.3406 0.3227 0.3347 0.3806 1.4311 1.4325

FM 0.2740 0.3532 0.2824 0.3485 1.3487 1.5117

FM 0.1792 0.2110 1.0561 0.8507 2.4923 2.0518

FM 0.1782 0.2208 1.4825 1.2809 3.7568 3.1687

FM 0.3456 0.3207 0.5158 0.5951 1.6416 1.7277

SD** 0.2121 0.1883 0.6981 1.0043 1.9465 2.5452

SD 0.1893 0.1752 0.9200 1.0887 2.3846 2.6280

SD 0.2542 0.2476 0.5645 0.4689 2.4588 1.9036

SD 0.1667 0.1359 1.9981 0.3266 10.0550 1.9882

SD 0.1901 0.1578 1.6862 1.6790 4.7255 4.9129

*FM = floating metal, **SD = surface discharge

PD features

From the PD pattern data, 3 statistical parameters were extracted which are: mean,

skewness and kurtosis for positive and negative voltage half-cycles (total 6 features).

These data features were then divided into three groups and used (i) as input to build

and train the fuzzy inference system, (ii) to check the fuzzy training, and (iii) as testing

data. The three groups have similar compositions of 6 data columns for the 6 features.

In addition, the first two groups have an extra column for marking the code of the PD

defect type. Table 5.3 shows the arrangement for data checking.


161

Figure 5.28: Fuzzy inference system (FIS) generated by genfis1.

The ANFIS rules, training and testing

Figure 5.29(a) shows the un-trained membership functions generated by the ‘genfis1’

command. They correspond to 6 input parameters. Each function is divided into three

regions, namely: low, medium, and high and built with the same ‘gbellmf’ type shape.

Total data used to generate the FIS are 73 and 729 rules were produced (an example

shown in Figure 5.28). Such a large number of rules made it impractical for direct

implementation, thus the need for optimizing the membership functions.

The optimized membership functions of the FIS are shown in Figure 5.29(b). ANFIS

was used to train the FIS. These functions are arranged in order (from top to bottom) of

the mean, skewness and kurtosis for positive and negative voltage half-cycles. It can be

seen that the most significant changes to the membership-function occur to the mean

input for both voltage half-cycles. Changes can also be easily recognized from the

kurtosis of the positive half-cycle.

The ANFIS used 73 data patterns for training the membership function and 9 additional

data patterns for checking the training result. After 50 training periods, the error value is

reduced to 1.1549x10-3.


162

(a) (b)

Figure 5.29: Membership function (a) before training (generated by Genfis1) and (b)

after training using ANFIS

After the training process was carried out and completed, 15 data records were used to

evaluate the ability of the ANFIS classifier to recognize the PD sources. The test results,

summarized in Table 5.4, show excellent success rate. Out of 15 test data patterns, only

1 surface discharge source was misclassified as a floating metal discharge.


163

Table 5.4: Test results using trained FIS

PD

sources

Evaluation

result

Rounding PD

type

Void 0.885 1 1

Void 1.113 1 1

Void 0.781 1 1

Void 0.935 1 1

Void 0.674 1 1

*FM 1.967 2 2

FM 2.102 2 2

FM 2.099 2 2

FM 1.900 2 2

FM 1.821 2 2

**SD 3.251 3 3

SD 1.721 2 3

SD 3.080 3 3

SD 3.400 3 3

SD 2.736 3 3

*FM = floating metal, **SD = surface discharge

5.7. Conclusion

The PD signals can be detected and recorded in two modes, i.e. time domain and

frequency domain. Both recording modes can provide information about the type of the

PD source. In this chapter, PD detection using both modes is discussed along with its use

in recognizing the PD sources.

The PD waveform signals can be recorded using the time domain mode. These PD

waveforms were used to recognize different PD sources, both single and multiple. Three

features were extracted from the PD signals and used as inputs into a neural network to

recognize the PD sources. The features were extracted from the decomposed signal


164

components. The J criterion was applied to determine the best nodes, i.e. those that give

the most separability of the features. For both the de-noising and decomposing steps,

similar wavelets were applied (db2 and sym2) and resulted in similar J values and

nodes.

The presence of noise/interference will affect the analysis result. Thus it is important to

denoise the recorded signals before further analysis can be carried out. In this work, this

was achieved by applying the multivariate denoising method.

Using a feed-forward neural network, it was demonstrated that single and multiple PD

events can be classified and thus recognized by the proposed method. The pre-

decomposing of denoising signals shows a significant recognition improvement, from

75.33% to 95.3%.

Another mode of PD recording is frequency domain, also discussed in this chapter.

Three different PD models were used to simulate some defects in transformer windings.

These were developed and tested. The PD signals were captured using the UHF zero

span measuring method. Corona discharge was not included in this investigation because

its signal spectrum is below the minimum frequency of the UHF range.

Three statistical operators were extracted from the phase-resolved PD distributions for

both positive and negative voltage half-cycles and used as features for training a fuzzy

inference system (FIS). The membership function of the FIS was obtained with the aid of

the Matlab function ANFIS. The training results show some significant changes of the

membership functions for the mean and kurtosis.

The trained FIS was then applied to evaluate its accuracy to recognize the PD sources.

Test results show high success rate. Thus, it is possible to recognize the source of PD

based on its PD pattern captured by the UHF zero span method.

CHAPTER 6

UHF PD LOCALIZATION IN TRANSFORMER

6.1. Introduction

Localization of the PD source in the transformer will not only help engineers to

determine the location of the PD itself, but also provide information about the condition

of the transformer and thus help the maintenance process.

To determine the PD location, a minimum of three sensors must be used to record PD

signals and enable triangulation. When sensors are installed in varying positions, PD

signals will arrive at different times. The time of arrival (TOA) can then be used to

calculate the time difference of the arrival (TDOA) between sensors. From this

information together with knowledge of the signal propagation velocity, the position of

the PD source then can be determined by using geometric triangulation.

PD localization using the UHF PD detection method will be discussed in this chapter.

The PD signals are captured by 4 monopole sensors which are connected to a 4 channel

CRO to record the PD waveforms. These are then processed to determine the TDOA

between the signals. Three methods of TDOA are used and discussed, i.e. cross-

correlation, first peak and cumulative energy signals.

The aim is to calculate TDOA values solely based on mathematical formulas. A specific

threshold value enables an algorithm to determine the first peak. The TDOA can also be

derived from where the cross-correlation between two signals reaches its maximum

Chapter 6 UHF PD localization in transformer

166

value. Alternatively, a similarity function between two cumulative energy curves is

evaluated to search for the minimum.

6.2. Signals propagation and waveform timing

The propagation velocity of the electromagnetic signal in any medium is:

1v 6.1

where µ is the permeability and ε is the permittivity of the medium. In a vacuum, the

propagation velocity of the electromagnetic signal is similar to the speed of light (i.e.

3x108 m/s). In oil, the propagation speed is much lower due to its higher relative

permittivity ( 2.2r ). This was verified by experiment in this research. The

propagation velocity of the electromagnetic signals was measured by capturing the

signal using two sensors which are placed at a specific distance from one another and in

line with the source. The propagation velocity of the signal is the distance between the

sensors divided by the time difference of arrival (TDOA). It was found that the

propagation velocity of the electromagnetic signal was 2x108 m/s [77], or in more

convenient notation for the purpose of localization the propagation velocity can be

written as 20 cm/ns.

Consider an arbitrary array of PD sensors installed at different locations in a transformer

tank. Electromagnetic waves emitted by a PD source propagate in the transformer tank

and arrive at these sensors at different time instants. Denote t1 the time of arrival (TOA)

at sensor 1, t2 the TOA at sensor 2, etc. The time difference of signal arrival (TDOA)

between sensor 1 and 2 is then defined as:

12 1 2t t t 6.2

The time of arrival (TOA) of PD signals is affected by several factors such as:

- The presence of noise which alters the PD waveform. When the PD is emitted

and the sensor is applied to capture the electromagnetic signals, eventually the

sensor not only captures the PD signals but also any background noise


167

surrounding the sensor. The PD signals are often very weak with very low

amplitude even for well-designed sensors [77].

- Sensors response time. Different sensors have different response times [106] and

result in different waveforms [77].

- Sensor placement. Sensors in a similar location (or close position) may have

more similar patterns than sensors in a different location (or far away). This may

lead to a false TOA determination [77].

- PD current rise time. Different PD sources will generate different PD pulses, and

sometimes the PD pulses can have a very long time-front. For instance, a 1 ns

PD pulse already occupies a radial distance as much as 1 ns x 20 cm.ns-1 = 20

cm in terms of radiated electromagnetic signals. The error for this case should be

reasonable and in the range of ~20 cm. However, the pulse width of PD signals

can be more than 17 ns, which is the fastest rise time case for bad contact in oil

[1], the error of the PD localization can be much higher.

6.3. PD source Positioning

When the PD signals are emitted from their original location, they will propagate in all

directions at the same speed, assuming that the surrounding environment is uniform.

Then, sensors at different ranges from the source should receive signals at different

times. Closer sensors obtain the signals before ones further away. Thus there is a finite

time delay in receiving the signal between the sensors. This time delay is correlated to

the distance of the PD source to the sensors.

The distance of the PD source to any sensor i such as the composition shown in Figure

6.1 can be calculated using the Pythagorean Theorem:

2 2 2 2( ) ( ) ( )i i i ir x x y y z z 6.3

where (x, y, z) are the coordinates of the PD source and (xi, yi, zi) are the coordinates of

sensor i. To determine the PD source, it is necessary to operate at least three sensors to

record PD signals at simultaneous times. When the signals arrive at each sensor, there


168

will be an arrival time difference between the sensors. As the sensors’ positions are

known the PD location can be calculated.

S1 (x1,y1,z1)

P (x,y,z)

X

Z

Y

S2 (x2,y2,z2)

S3 (x3,y3,z3) S4 (x4,y4,z4)

Figure 6.1: Coordinate system of the PD source P (x, y, z) and sensor S (x1, y1, z1).

To determine the source of signals from the non-linear Equation 6.3, many methods can

be applied. A common method is the Newton-Raphson method, which applies Taylor

series expansion to linearize the equation set [146, 147]. The number of equations in the

set is defined by the number of sensors in use. As the Newton-Raphson method is an

iterative method the initial value must be given. Sometimes, the computation time is

very substantial. In [88] the position of the source signal is determined by solving

Equation 6.3 using the fuzzy method. The input of the fuzzy system was extracted from

the decomposed PD signals. However, this method will also need substantial

computational effort. A simple computation was introduced in [91, 92] where the

location of the signal source is determined purely from the time difference of the arrival


169

signals by using matrix manipulation. This method was selected for use in this thesis

and the procedure is as follows.

When four sensors are applied to capture PD signals and the sensors are positioned

randomly, the coordinate of the PD source can be written in terms of the distance

between the PD source and a reference sensor [92]. Without loss of generality, choose

(r4) as the reference sensor, it can be shown that:

1 214 14 14 14 14 1 4

224 24 24 24 4 24 2 4

234 34 34 34 34 3 4

12

x x y z r r K Ky x y z r r r K Kz x y z r r K K

6.4

where (x,y,z) are the coordinates of the PD source, (xi4, yi4, zi4) denote differences in

coordinates between sensor 'i' and the reference sensor (sensor 4), ri4 is the TDOA

between sensor i and sensor 4 times the speed of the PD signal in oil, r4 is the distance

of sensor 4 to the PD source and Ki is calculated as 2 2 2

i i i iK x y z . Note that all the

parameters on the right-hand side of Equation 6.4 are known except r4. Utilizing this

equation, one can substitute x,y,z in term of r4 into Equation 6.3 and solve that quadratic

equation. The positive root value of r4 acquired from Equation 6.3 is then input back

into Equation 6.4 to determine the PD source coordinates.

6.4. Time difference of the arrival signals

To determine the time delay of similar signals, the calculation can be made in several

ways. Three methods are discussed in this chapter, i.e. first peaks of the signals, cross-

correlation of the PD waveform, and similarity of the energy curve of the PD waveform.

6.4.1. First peaks

When the signals in the transformer tank propagate in the same manner in all directions,

the sensors will capture the same PD pulse then produce similar waveforms. The time

difference between signals can then be determined from the first peaks of the


170

waveforms recorded by different sensors. To avoid error due to the presence of noise,

the waveform can be denoised [77] and/or a threshold value used as the minimum limit

of the first peak [75, 77]. The work by both [75, 77] determined the first peak point

based on visual examination. This is neither convenient nor practical in that it is

susceptible to human error and requires a huge effort to observe large set of data. Thus

in this research, a clearly-defined criterion is proposed to enable the first peak to be

calculated using Matlab. The program scans through the data array consecutively and

compares each point in the waveforms to a value before. If the value decreases, the last

higher value is taken as a peak. The first peak is defined as the first occurrence of a peak

whose value exceeds a specific threshold.

The procedure to determine the time difference between the first peaks of two PD

signals is as follows:

1. Denoise the original signal by applying multivariate denoising tool. The

denoising process is done to the PD signals captured at the same time by the

sensors.

2. Process both the original (original) and denoised signals to make the

waveforms unipolar, achieved by taking absolute value of each point of the

waveform.

3. Normalize the signals so all the waveforms have similar magnitude, as shown

in Figure 6.2.

4. Choose the same threshold setting, for example 25% of the signals

magnitude.

5. Pick the first peak point above the threshold value by applying the peak point

detector, Figure 6.3. This point is then used to determine the arrival time.

6. Calculate the time difference between the two first peaks of the PD signals.


171

(a)

(b)

Figure 6.2: (a) PD waveforms captured by different sensors, and (b) the unipolar and

normalized PD waveform

Figure 6.3: Peak detection of unipolar PD waveform


172

6.4.2. Cross-correlation [148]

Cross-correlation can be used to measure the similarity of two waveforms as a function

of a time lag applied to one of them. One waveform is considered in stationary position

and the other is shifted toward the stationary one. Then, the similarity of the waveforms

is calculated. The cross-correlation value is the largest when waveforms are most

similar to each other. When both waveforms show high similarity then the product of

the two functions is more positive. If the products have both positive and negative

characteristics, integration yields a smaller cross-correlation value. For perfectly

uncorrelated, such as a random function, the cross-correlation value is zero.

The cross correlation f(x) of two functions g(x) and h(x) is defined as:

( ) ( ) ( ) ( ) ( )f t g t h t g t h t * 6.5

where * denotes convolution and ( )g t is the complex conjugate of g(t). From the

convolution of functions g(x) and h(x):

( ) ( ) ( ) ( )g t h t g h t d

6.6

Substituting Equation 6.6 into Equation 6.5 yields:

( ) ( ) ( ) ( ) ( )f t g t h t g h t d

* 6.7

Assign , ,, d d , insert to Equation 6.7:

, , ,( ) ( ) ( ) ( ) ( ) ( )

( ) ( )

f t g t h t g h t d

g h t d

*

6.8

If g or h is even, then

( ) ( )g t h t* = ( ) ( )g t h t 6.9


173

Furthermore, if these functions are discrete time series of finite duration then [149]:

1

0

1 N n

mf n g m h n m

N

6.10

where N is the number of data points.

Figure 6.4: Cross correlation of the waveforms between sensor i (i = 1,2,3)

and reference sensor 4. The peaks are marked with *.

The cross-correlation shifts incrementally the reference waveform over the others to

look for a matching signal. If a matching pattern is found the correlation value increases

to a maximum value. On the other hand, it decreases towards a minimum value if the

pattern is inverted. The time delay between waveforms is determined from the

maximum value of its cross-correlation.


174

Figure 6.4 shows an example of the cross-correlation between the signal captured by the

reference sensor 4 and that from the other three sensors. Also shown is the auto-

correlation of the reference signal. The number of data points of each waveform is

20000, thus the cross correlation will result in twice the data points, i.e. 40000 data

points. Note that in the Figure, the maximum value for each cross-correlation is very

close to each other and thus difficult to recognize. The TDOA is determined from the

offset (in terms of data point number) between the peaks. The reference is the peak of

the auto-correlation. Each data point offset corresponds to 25 ps. In this particular

example, the offsets are 47, 146, -24 data points for sensors 1, 2, 3 respectively which

translate to TDOAs of 1.175 ns, 3.650 ns and -0.600 ns. It should be noted that in

practice, the presence of the core and winding assembly in the tank will exacerbate the

difference between the transmission paths to the sensors and thus the cross-correlation

would be much more diminished

6.4.3. Cumulative energy

Time difference determination by applying the cross-correlation method is made on the

assumption that the PD waveforms have similar pattern. In cases where the patterns are

too dissimilar, the cross-correlation method might be not applicable. An alternative

solution is to apply a similar concept to calculate the TDOA from the cumulative energy

curves of the PD waveforms

When the sensors are installed ‘quite far’ from each other, the PD waveforms received

tend to have different patterns [77]. However, the energy of the PD signals can be

assumed to be dependent on the distance from the PD source [81]. By converting the PD

amplitude to the cumulative energy [75, 77], a similar trend is expected for the increase

in the cumulative energy with time. Therefore, the time difference can be determined

from these cumulative energy curves

The PD waveforms are usually captured using a high-bandwidth oscilloscope or

digitizer and the results are recorded in terms of voltage magnitude versus time. Given a

fixed measuring impedance R and since 2Energy V R dt , the cumulative energy


175

can be determined from the square of the voltage curve. Thus the cumulative energy up

to time kt can be approximated by:

2

1

( )k

k ii

U t V t

6.11

where iV t is the sampled input signal at time it . If N is the total number of data

samples in each voltage curve (20000) then ( )NU t corresponds to the total energy of the

signal.

The time differences between signals are acquired from the cumulative energy curves

by exploiting a unique point in the curves. The most significant point that can be used to

determine the arrival time of the signal and thus to determine the time differences

between sensors is the knee point. The knee point is defined as the point where a sudden

increase in the energy occurs [71, 79, 81]. However determination of the knee point is

not easy and involves human judgment. The interpretation of the knee point by different

observers may result in different arrival times of the signals. This can result in

ambiguous PD locations. Since there is no restriction on or clear definition of the knee

point, such as one that can be written mathematically, the knee point method to

determine the time of arrival is not considered in this thesis.

Figure 6.5: Normalized cumulative energy curves of sensor voltage waveforms


176

Another method is to apply a similarity function between signals. The time difference is

calculated from the cumulative curve energy using the similarity method. One curve is

shifted towards the other and then the difference between signals is calculated. The time

difference is reached if the similarity reaches the minimum value. The similarity value

is calculated as:

1 21

( ) ( )N k

k i i ki

S t U t U t

6.12

where U1 and U2 are the two cumulative energy curves. k denotes the amount of

shifting, each increment corresponds to a time step of 25 ps. U1 and U2 are also

interchanged to produce shifting in the opposite direction. The process is iterative and

the solution is found when the similarity value reaches the minimum.

The electromagnetic signal emitted by the PD source in the transformer tank will radiate

in all directions. During its travel path, this signal can be attenuated and reflected by the

transformer tank and the live parts inside the tank. Thus, the sensor captures not only

the original PD signal but also the reflections. The PD signals which are captured by

sensors in different positions show similar waveform patterns but mostly at the

beginning of the signals. If all the waveform data are used to determine the time

difference the result might give a higher error [77, 78]. In order to reduce the error, [78]

suggested using only part of the PD waveform, i.e. the front part of it, to evaluate the

cumulative energy. This was done by setting a time window with specific length.

However, manually determining the length of the windows is very subjective. Such a

task is imprecise and strongly influenced by how the observer interprets the waveforms.

In order to avoid this ambiguity, one can assign a fixed percentage of the data for use in

the cumulative energy calculation [77].

In this thesis, the TDOA is acquired from the cumulative energy by applying the whole

length of data. This will eliminate the ambiguity of the TDOA determination process.

All Matlab scripts to calculate the TDOA and PD coordinates are shown in Appendix E.


177

6.5. Sensor consideration

The cumulative energy curves which derive from the PD waveform are very affected by

the sensor choice. As different sensors give different responses to PD pulses, the

waveform produced by different sensors also yields different patterns. From discussion

in Section 4.3.2, it was shown that a monopole sensor has a faster response in that it is

fastest to reach the maximum value and has less oscillation. Thus it is easier to

determine the first peak of its PD waveform. Less oscillation will also mean less

ambiguity in the cross-correlation results, since the integration as shown in Equation 6.8

will also produce less oscillation near the peak value of the cross-correlation.

(a)

(b)

Figure 6.6: Step pulse responses of different sensors: (a) waveforms, and (b)

normalized cumulative energy curves.


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Figure 6.6(a) shows the response of 4 sensors to step pulse input, with the

corresponding cumulative energy curve shown in Figure 6.6(b). From the pulse

response in Figure 6.6(a) the monopole sensor shows the sharpest peaks thus making it

easier to determine the magnitude value of the first peaks. Since the monopole has faster

sensor response in terms of less oscillation, the cumulative energy curve yields a faster

response to reach the maximum value. For this reason, the monopole is a better choice

to use for PD localization.

6.6. Experimental set-up

Figure 6.7 shows the schematic diagram of the experiment. Four UHF sensors were used

to capture the PD signals. The sensors were immersed in oil in an attempt to simplify the

calculation of the path of the PD signals. If any sensors were installed above the oil level,

the effect of the medium density difference would need to be included. The sensor

outputs were connected to a 4-channel digital oscilloscope via coaxial cables of identical

10 meter length. The sensors and the PD sources were immersed in oil and their

coordinates are shown in Table 6.1. The sensors used in the experiment were of the

monopole type. The reasons for this choice were discussed in Section 4.3.2.

Table 6.1: UHF Sensors position

x (cm) y (cm) z (cm)

Sensor 1 -50 -25 48

Sensor 2 45 -20 46

Sensor 3 45 20 49

Sensor 4 -50 20 45

The PD source is needle-plate electrodes between which a piece of ‘bakelite’ insulator

is inserted to avoid breakdown during the experiment. With this electrode arrangement,

the PD signals generated by the PD source were not only from the corona but mostly

from surface discharges. This is shown by the PD pattern recorded by the Mtronix. To

generate PDs, the voltage was raised to 19 kV. To record the PD signals, an


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oscilloscope was used with 40 Gs/s resolution for each channel and a built-in computer

system to record the data. With a sampling rate of 40 Gs/s, the time resolution is 25 ps.

Table 6.2: PD source coordinates

Position No. x (cm) y (cm) z (cm)

1 -11 14 37

2 -11 5 37

3 -11 -4 37

4 -3 14 37

5 -3 5 37

6 -3 -4 37

7 6 15 37

8 6 5 37

9 6 -5 37

10 12 15 37

11 12 5 37

12 12 -5 37

The PD source was positioned at 12 different locations. The coordinates of the PD

source are shown in Table 6.2. For each PD location, some 50 sets of PD waveforms

were recorded for the purpose of analysis. The time difference was averaged from the

50 signals.


180

Oscilloscope

PD

S1S2

S3

CB

RL

TR

S4

(a)

PD

S1 S2

S3S4

X

Z

Y(0,0,0)

(b)

Figure 6.7: Experimental setup: (a) layout and circuit for PD generation and detection,

(b) coordinate system for location.

6.7. Result and discussion

In the experiment set-up, the PD source was installed in the middle of the tank with

coordinates as shown in Table 6.1. The tank was filled with oil and contained no

barriers or objects that could be considered to obstruct the PD signals’ path. However,


181

even with that arrangement, the signal patterns captured by the sensors in different

positions tended to be different, as shown in Figure 6.8. This was probably caused by

several effects, such as the non-homogeneous density of the oil, reflection by the

transformer tank and most importantly, the positions of the sensor in relation to the PD

source. As described in Section 2.3 the pulse shape of the electromagnetic signals is

affected by the position of the observer. Thus it is difficult to get similar patterns if the

sensors are installed at varying distances.

Figure 6.8: Typical waveforms captured by sensors in different locations

Although the experiment was done in the laboratory, where the noise environment is

very low, the PD waveform was still affected by the presence of the background noise.

Figure 6.8 shows the typical PD waveform recorded by sensors in different positions.

The noise level is very low compared to the PD signals. Thus noise might not have to be


182

considered in this case. However, the PD signals captured by the sensors do not always

show clear waveforms due to the lower PD magnitude. The PD waveforms can have a

very low magnitude as shown in Figure 6.9, so the PD signals can become very

distorted by noise. Such signals will make the determination of the time difference very

difficult, especially for the first peak method. Thus denoising the PD waveforms might

give a clearer image and help to determine the first peak of the signal.

Figure 6.9: Low magnitude of waveform captured by sensors in different locations

6.7.1. Denoising the PD waveforms

In practical substation environment, noise or interference mainly consists of continuous

sinusoidal-carrier signals (radio frequency) from telecommunication systems, transients

caused by thyristor operation or network switching, and thermal noise associated with

the detection system [142-144]. By virtue of its construction, the transformer tank acts


183

as an RF shield against the radiated noise to a certain extent but conductive noise can

still propagate into the tank and affect the measurement. Note that here the experiments

were conducted in the laboratory where the noise level encountered is much less

compared to the substation environment. Figure 6.10 shows the background noise level

recorded by spectrum analyser (without presence of PD activity inside the transformer).

Evidence of interference from communication signals can be seen at around 200 to 500

MHz for digital radio and TV, and at around 850 MHz and 900 MHz for mobile

communication systems [145].

Figure 6.10. Noise background and PD spectrum captured by monopole sensor installed inside transformer tank.


184

In this chapter, the same denoising method used in Chapter 5 was applied. Multivariate

denoising [141] was applied for each waveform recorded by the sensors at the same

time. Figure 6.11 shows the denoising results for all waveforms recorded by the sensors.

The magnitudes of the denoised waveforms are slightly reduced with the irregular spike

removed. Both original and denoised signals were used as input for the calculation of

the time arrival difference between sensors.

(a)

(b)

Figure 6.11: (a) The PD waveform captured by the sensor, and (b) the denoised

waveform


185

6.7.2. First peaks

Processing of the time arrival of the PD signals is determined by picking the first peak

above the threshold value of 25% as shown in Figure 6.12. The threshold value chosen

is somewhat arbitrary. There is no strict rule. Here, 25% of the normalized PD signal

was chosen as the threshold value in order to adequately remove the noise. Slight

oscillation in front of the waveform can also be avoided.

Figure 6.12: Peaks of normalized unipolar denoised PD waveforms

As an example from Figure 6.12, after applying a signal threshold of 25%, the TOA for

sensor 1 is 84.950 ns and that for sensor 4 is 84.425 ns. Thus the TDOA between these

two particular waveforms is 0.525 ns. This set of waveforms is a denoised one, thus the

threshold of 25% is well above the remnant noise. Also note that the small-magnitude


186

initial oscillations of the waveforms are discarded in the calculation of the arrival time

of the signals.

The calculated coordinates using the first peak method are shown in Table 6.3. All

locations show the PD sources inside the transformer tank. The coordinates acquired by

both original and denoised signals show quite similar values.

Table 6.3: The PD location and error calculated by using TDOA of the first peak

method

PD

Location

Coordinates x, y , z (cm) Error (cm)

Original Denoised Original Denoised

1 -1.84, 0.04, 37.99 -2.00, 0.52, 44.28 16.73 17.76 2 -2.21, 0.58, 44.21 -2.18, 0.81, 43.87 12.20 11.94 3 -2.26, -0.24, 46.74 -1.92, 0.56, 37.24 13.61 10.17 4 -2.45, -1.12, 57.52 -2.22, -0.82, 50.64 25.50 20.15 5 -1.51, 0.98, 33.36 -1.66, 1.09, 37.79 5.62 4.21 6 -1.85, 0.55, 45.29 -1.32, 1.71, 30.74 9.53 8.64 7 -1.88, -0.5, 46.05 -1.49, -0.25, 37.95 19.60 17.01 8 -1.59, 0.59, 40.97 -1.32, 0.69, 37.52 9.63 8.51 9 -2.21, 1.03, 51.96 -1.96, 0.71, 36.57 18.10 9.80 10 -0.87, -0.34, 41.9 -0.75, -0.96, 52.54 20.62 25.67 11 -1.79, 1.56, 61.11 -3.89, -4.79, 45.3 27.99 20.42 12 -1.41, 1.29, 47.87 -1.24, 0.99, 42.07 18.37 15.39

The errors of the first peak method are also shown in the table for both original

(original) and denoised signals. The denoising processes improve the localization

results. Almost all PD locations show accuracy improvement after the waveforms are

denoised. Out of 12 PD locations, 10 locations resulted in improvement in the PD

location accuracy with only 2 showing the opposite result. The highest error when using

the original waveforms is 27.99 cm and this error is reduced to 20.42 cm after the

waveforms were denoised.


187

6.7.3. Cross correlation

Figure 6.13 shows the zoomed cross-correlation example for 4 waveforms recorded by

sensors as well as the auto-correlation of sensor 4, taken from the data set of PD

location 12. The maximum value is used to determine time shifting which shows the

time difference between sensors. From this sample, the cross-correlation of waveforms

from sensor 1 and sensor 4 produces a time difference of 0.750 ns. It is 3.150 ns

between sensors 2 and 4, and -1.050 ns between sensors 3 and 4. Note that the

maximum value of the auto-correlation of sensor 4 corresponds to 0 ns.

Figure 6.13: The zoom of the cross-correlation waveforms to show the time difference

of different signals

Table 6.4 shows the coordinates of PD localization using the cross-correlation method.

Many data show coordinates outside the transformer tank, which correspond to a high


188

error in localization. The cross-correlation is carried out by using the full waveform

data, i.e. data recorded over a duration of 500 ns. Regarding electromagnetic signals

travelling in the oil, this time corresponds to 500 x 20 cm = 10000 cm of length,

whereas the transformer tank used in the experiment had a width of just 100 cm. Thus

the PD signal captured by the sensors in the time duration of 500 ns is a combination of

the original PD signal and possible subsequent reflections or new PD signals. This can

cause error on the TDOA results and yield false PD localization.

Table 6.4: The PD location and error calculated by using TDOA of the cross-correlation

method

PD

Location



1 -0.65, -4.56, 14.42 -0.51, -4.65, 15.38 31.01 30.42 2 0.58, -6.42, -13.44 2.21, -8.73, -48.32 53 87.42 3 4.69, -10.62, -76.43 3.39, -9.24, -55.51 114.7 93.77 4 -1.49, -4.00, 22.83 -0.63, -4.97, 7.75 22.96 34.94 5 0.20, -5.85, -5.57 0.43, -6.17, -10.59 44.04 49 6 0.12, -5.72, -3.56 0.12, -5.73, -3.72 40.72 40.88 7 -0.09, -5.46, 0.55 -0.16, -5.55, 2.06 42.24 41 8 0.06, -5.54, -2.08 -0.10, -5.46, 1.47 40.9 37.54 9 -0.09, -5.40, 1.47 -0.01, -5.50, -0.11 36.05 37.6 10 -0.79, -3.09, 36.87 -1.04, -2.99, 38.42 22.15 22.26 11 -0.12, -5.37, 2.08 -0.16, -5.27, 3.58 38.39 37.02 12 -0.08, -5.33, 2.25 -0.08, -5.33, 2.18 36.79 36.85

To improve the accuracy of PD localization only the data from recording lengths

corresponding to the transformer dimensions can be used. With the assumption that the

PD signals travel inside the transformer tank in a straight line, the maximum distance

the PD signals travel without reflection is around 100 cm which corresponds to 5 ns in

time. The data from just 5 ns after triggering can be assumed to be waveforms arriving


189

at the sensors without any reflections. The PD coordinates which result by applying this

assumption are shown in Table 6.5. It can be seen that the accuracy is greatly improved.

Table 6.5: PD location and error calculated by using TDOA of the cross-correlation

method (5 ns of waveform)

PD

Location



1 -3.76, 0.41, 44.63 -1.05, -1.03, 51.02 17.19 22.84 2 -3.58, 6.74, 68.85 -0.28, -4.44, 1.89 32.75 37.9 3 -4.80, -0.33, -6.79 -5.60, -2.92, 47.46 44.38 11.82 4 -3.78, 8.05, 62.82 -1.24, -3.28, 25.93 26.5 20.6 5 -3.56, 4.58, 64.46 -1.08, -3.10, 28.6 27.47 11.82 6 -3.35, 2.32, 68.54 -2.14, -2.56, 37.01 32.16 1.67 7 -4.93, 4.87, 0.13 -7.06, -1.18, 68.86 40.01 38.04 8 -4.35, -2.60, 8.66 -4.61, -3.50, 24.4 31.12 18.54 9 -4.52, -3.08, 0.52 -4.39, -2.30, 2.11 39.01 40.55 10 -5.01, 6.12, 0.48 0.53, -2.29, 42.09 42.10 21.37 11 -4.64, 5.93, 16.63 0.43, -2.13, 44.27 26.31 15.41 12 -3.88, -3.15, 29.96 -4.40, -4.82, 18.5 17.46 24.72

Similar to the first peak results, for the cross-correlation method, the results show

improvement after the waveforms are denoised. The highest error produced by using

original (noisy) waveforms is 44.38 cm. After the waveform is denoised, the error is

reduced to 11.82 cm which occurred at PD location 3. The denoising process resulted in

an improvement in accuracy, with 8 locations having better accuracy after the signals

were denoised.

6.7.4. Cumulative energy

The time difference of the signals is calculated using the similarity function (Equation

6.12). From this equation, it can be seen that the value of the similarity will cross the


190

zero value at a point where the two energy curves have the same total energy. The

similarity value should be higher at the start of the process where the signal has not yet

been shifted. Then, as one curve shifts towards the other, the similarity should decrease

until it reaches zero (or minimum value). If the shifting process is continued the

similarity will increase again. Figure 6.14 shows the similarity curve during the shifting

process. The TDOAs are calculated using sensor 4 as a reference. In this particular

sample, the time differences are 0.950 ns, 0.075 ns, and 0.675 ns for d14, d24 and d34

respectively.

Figure 6.14: Time difference curve calculated using similarity function

The calculated coordinates using the cumulative energy method are shown in Table 6.6.

The denoising process produced almost random results, with the results showing better

accuracy for some but worse for others. Out of 12 PD locations, only 5 cases produced

better accuracy when the signals were denoised with others showing the opposite result.


191

Table 6.6: PD location and error calculated by using TDOA of the cumulative energy curve

PD

Location



1 -0.91, -2.91, 43.4 -2.25, -3.69, 44.06 20.71 20.96 2 -1.18, -2.98, 51.43 6.27, -22.48, 0.38 19.19 48.93 3 -1.61, -2.47, 58.19 6.15, -12.84, 36.86 23.23 19.29 4 -3.27, -1.49, 62.15 -3.3, -2.3, 45.82 29.54 18.54 5 -3.19, 0.31, 62.48 -2.85, -0.76, 46.37 25.91 11.00 6 -2.1, 1.18, 55.57 -14.85, -1.33, -9.25 19.3 47.82 7 -3.59, -2.49, 47.89 -4.59, 32.71, 59.45 22.73 30.49 8 -2.57, -2.29, 48.83 -3.05, 2.61, 42.96 16.32 11.1 9 -3.31, -1.5, 59.74 -10.7, 14.46, 69.29 24.82 41.23 10 -4.26, -2.47, 48.5 -3.52, -2.49, 47.11 26.49 25.48 11 -2.54, -0.15, 47.62 -2.92, 22.88, 56.27 18.72 30.23 12 -3.3, 0.94, 53.3 -11.93, 7.83, 67.82 23.13 41.07

This result suggests that the denoising process does not always improve the accuracy of

PD localization using the cumulative energy method while the denoising process itself

increases the computational burden. With or without the denoising process, this method

also consumed a fairly significant computational time compared to the first two

methods. Improvement may be achieved as suggested by [79] by “windowing” the

waveform so that the data point included in the calculation is just a small part of the PD

waveform, i.e. the front portion. This will significantly reduce the computational effort

as a result of Equations 6.11 and 6.12 where the computational effort is dependent on

the number of points of data used. This method however would then have the

disadvantage of involving human judgment to determine how many points of data

should be used.


192

6.7.5 Comparison between the three methods

The comparison of the localization accuracy using the three methods is summarized in

Table 6.7. The error values are taken from Table 6.3 to 6.6. The first peak method has

the highest accuracy. Overall average errors for original and denoised waveforms are

16.65 cm and 14.33 cm respectively.

Table 6.7: Average errors of the PD localization: (a) original, (b) denoised.

PD Loc. First Peak (cm)

Cross-correlation (cm)

Cumulative energy (cm)

a b a b a b 1 16.73 17.76 17.19 22.84 20.71 20.96

2 12.20 11.94 32.75 37.9 19.19 48.93

3 13.61 10.17 44.38 11.82 23.23 19.29

4 25.50 20.15 26.5 20.6 29.54 18.54

5 5.62 4.21 27.47 11.82 25.91 11.00

6 9.53 8.64 32.16 1.67 19.3 47.82

7 19.60 17.01 40.01 38.04 22.73 30.49

8 9.63 8.51 31.12 18.54 16.32 11.1

9 18.10 9.80 39.01 40.55 24.82 41.23

10 20.62 25.67 42.10 21.37 26.49 25.48

11 27.99 20.42 26.31 15.41 18.72 30.23

12 18.37 15.39 17.46 24.72 23.13 41.07

Average 16.65 14.33 31.37 22.11 22.51 28.84

For the cross-correlation method, the overall average error is 31.37 cm for original

signals and reduces to 22.11 cm after the signals were denoised. Compared to the first

peak method, the cross-correlation method yields less accurate results. This indicates

that sensors at different positions will not receive exactly identical waveforms even after

further processing has been applied to remove possible corruption at the tail end of the

signals.

For the cumulative energy method, the average errors by the denoised cumulative

energy curve method are mostly higher than the corresponding results from the cross-


193

correlation method. The overall average errors are 22.51 cm and 28.84 cm for the

original and denoised PD signals respectively.

A graphical approach to present the results is by plotting circles (on x-y plane) around

the true PD locations. Their radii correspond to location errors obtained from various

methods (Table 6.7). Results for all 12 different PD locations are shown in Figure 6.15

to 6.26.

Error plot

Transformer tank

Location 1

118 cm

71

.5 c

m

Figure 6.15: PD localization error plots for PD location 1

First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised


194

Error plot

Transformer tank

Location 2

118 cm

71

.5 c

m


Transformer tank

118 cm

71

.5 c

m

Location 3





195

Error plot

Transformer tank

Location 4

118 cm

71

.5 c

m


Transformer tank

Error plotLocation 5

118 cm

71

.5 c

m





196

Error plot Transformer tank

Location 6

118 cm

71

.5 c

m


Error plot

Transformer tankLocation 7

71

.5 c

m

118 cm





197

Error plot

Transformer tankLocation 8

71

.5 c

m

118 cm


Error plot

Transformer tank

Location 9

71

.5 c

m

118 cm





198

Error plot

Transformer tank

Location 10

71

.5 c

m

118 cm


Error plot

Transformer tank

Location 11

71

.5 c

m

118 cm





199

Transformer tank

Error plot

118 cm

71

.5 c

m

Location 12


The electromagnetic signal emitted by the PD sources has a very fast rise time and thus

produces sharper transition which is advantageous for accurate measurement of signal

arrival time. On the other hand, the very fast propagation velocity of UHF signals

combined with the dimensional effect of the small experimental tank used here presents

a challenge. By and large, location error results from Table 6.7 appear to indicate ~20

cm as representative. As the propagation velocity of EM waves in oil is 20 cm/ns, an

error of 20 cm in distance corresponds to 1 ns in signal propagation time. Considering

the sampling rate is quite adequate (25 ps in between samples), it is likely that there are

other factors contributing to the uncertainty in the timing of signals and thus required

further investigations.

The sensor dimension might contribute to the error of the PD localization. The sensors

used in the experiment were monopole sensors of 10 cm length. Depending on where on

the sensor that the excitation from the electromagnetic waves starts, the uncertainty can

be up to 0.5 ns. As the TDOA measurement relies on 2 sensors, the uncertainty would



200

be doubled, i.e. 1 ns in the worst case. It is likely that the error can be reduced by using

a shorter monopole sensor. However, other problems will then arise. As the monopole

sensor shortens, the sensitivity or sensor capability to capturing electromagnetic signals

will decrease. Perhaps there is a balanced solution regarding the sensor dimension and

any possible reduction in error, or perhaps another type of sensor might be considered.

6.8. Conclusion

Three methods to determine the time difference of arrival (TDOA) between sensors are

discussed in this chapter, i.e. cross-correlation, first peak and cumulative energy. The

TDOA from all three methods can be acquired by defining the time of arrival (TOA)

mathematically. The process to acquire the TOA value can be done automatically

without relying on visual examination of waveforms.

The TDOAs obtained from the three methods were then used to determine the PD

location. The method based on finding the signal first peak was found to give the best

accuracy, followed by the cross-correlation, and lastly the cumulative energy. Typical

(overall average) errors are 14.33, 22.11, and 34.35 cm respectively. The results indicate

the viability of the UHF method to be applied to determine the PD location in

transformers. These results were achieved with additional denoising. Although

denoising produces consistent accuracy improvement when applied to the first peak

method, its effect is reduced or even adverse for the other two methods. Among all the

different test configurations, the best result was achieved with the first peak method

combined with denoising, resulting in a location error of 4.21 cm.

CHAPTER 7

CONCLUSION AND SUGGESTIONS FOR FUTURE

RESEARCH

7.1. General

The aim of this thesis is to develop an ultra-high frequency (UHF) partial discharge

(PD) detection method which is able to detect and capture electromagnetic waves

emitted by PD sources in an oil-filled power transformer. The development starts with

the sensor design then continues on to PD detection, recognition and localization.

The UHF PD detection method has a number of advantages compared to conventional

PD detection methods. This is achieved mostly due to its immunity against background

noise or other unwanted signals that can affect the measurement. In the UHF range (300

MHz – 3000 MHz), the interference is mostly generated by known communication

sources, such as radio, digital television and mobile phone signals. Their carrier

frequencies are fixed as well as their associated side-bands. Thus, these interferences

can be avoided by using special filters to block known frequencies from the PD

waveform or by setting the measurement in specific frequency ranges. Furthermore, by

virtue of the internal sensors used for UHF detection, the transformer metal tank

provides good shielding against external radiative interference.

Chapter 7 Conclusion and suggestion for future research

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7.2 Sensor design

The key component in UHF PD detection is the sensor which works to capture

electromagnetic waves emitted by the PD source. In transformers, for the purposes of

installation, the sensor can be designed to be inserted via a drain valve or attached via

dielectric windows. The first option is normally available in a power transformer but not

the second one. The dielectric windows, however, can be crafted on the transformer

tank during a retrofit or created when the transformer is still in the process of being

manufactured. The sensor inserted via a drain hole has a very limited size due to the

drain valve constraints. The size limitation reduces the shape and construction options

for sensor design. With the size limitation, the most suitable type of sensor is a

monopole. The monopole sensor design for this thesis uses two shapes, i.e. straight

monopole and conical skirt monopole (for convenience, they are referred to as

monopole and conical respectively).

As for the sensors used in dielectric windows, these normally have a planar shape as

adapted from the dielectric sensor used in gas insulated switchgear (GIS). In this thesis,

three planar sensors were designed with the maximum diameter constraint of 150 mm.

They are the dual arm spiral, the log spiral with tapered end, and the log spiral with

truncated end.

The sensors were designed using CST Microwave Studio, an electromagnetic software

package which is capable of simulating sensors with varying shapes and dimensions.

The monopole type sensors were designed in varying lengths from 5 cm to 10 cm. The

longer sensors have better parameters than the shorter ones. The aim of the design is to

create sensors with the appropriate constraints that lead to better performance in the

UHF range.

The planar sensors were designed with two diameter sizes, 13 cm and 15 cm. Similar to

monopole sensors, the bigger sensors have better parameter performances. Out of the

five sensors designed, the conical and the log-spiral with tapered end have better

performances for both types of sensor. The sensors were also tested to capture PD

which was produced by a corona (needle to plate electrodes) source. The aim was to test

the sensor capability to capture PDs as low as 5 pC in the air at a distance of 2 meters.


203

Four sensors passed the test, except the monopole where the sensor failed to detect this

PD level at distance more than 1.5 meters, making it the least sensitive in detecting PD

signals. The design and test results indicate that the log-spiral with tapered end had the

best performance and hence was chosen to be used for PD detection in this thesis.

7.3. Sensor pulse response and sensitivity test in oil

Although the monopole has lower sensitivity, it does however have a faster pulse

response. The pulse response is important especially for PD localization. Here, the

sensor is required to have a fast response and less oscillation, important factors in the

determination of time difference of arrival (TDOA) between signals recorded by

different sensors as a part of the process of determining PD location. These two

prerequisites are achieved by the monopole sensor. For this reason, although the

monopole is less sensitive in the capture of PD signals, it was chosen for use in the PD

localization experiment.

The sensitivity of the sensors to detect and capture PD signals is discussed in this thesis.

Two different defects were used to generate different PD patterns: void and floating

metal. The void has a PD inception value of 20 pC whilst that for floating metal is 30

pC. To mimic the presence of solid structure inside transformer, a barrier was placed in

varying positions between the sensors and the PD source. Experimental results show

that the presence of a barrier had a random effect on both the magnitude and total

energy captured by sensors, i.e the energy captured by sensors did not correlate to the

barrier distance. The sensors showed ability to detect and pick up PD signals as low as

20 pC, produced by the void defect, with or without the presence of the barrier. With the

barrier at the same position, the total energy of the PD signals which were recorded in

zero span mode showed a linear correlation with the amount of pC recorded by a

standardized Mtronix PD detector. In terms of dB/pC, in attempts to convert the energy

of recorded signals to an amount of pC, the log-spiral showed a higher value and can

thus be said to be more sensitive. However, the signal captured by sensors cannot be

readily converted to an amount of pC without knowing the exact structure (barrier)

inside the transformer. This makes calibration of UHF PD detection difficult.


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7.4. PD detection and recognition using UHF method

PD detection using the UHF method can be recorded in two domains, i.e. time domain

and frequency domain. The time domain recording is usually carried out by applying a

digitizer or CRO. The PD signals recorded in time domain show the waveforms with

magnitudes varying in specific time ranges. The frequency domain is recorded using a

spectrum analyzer. The advantage of frequency domain recording over time domain

recording is its frequency range flexibility. The frequency ranges used in the

measurement of PD were broad band, narrow band or single frequency (zero span). The

broad band frequency range is typically set between 300 MHz and 3000 MHz (the UHF

frequency range). The narrow band performs measurement over a narrower frequency

range. The zero span is applied to capture the signal constituent at a specific frequency

and recording can be synchronized to the power frequency (50Hz) cycle to produce the

phase resolved partial discharge (PRPD) patterns. The disadvantage of using frequency

domain measurement is that, due to its measurement principle, a relatively long

integration time is needed to build up the spectrum display.

In this thesis, two domain recordings were used in the detection of the presence of PDs.

Both recording results can be used to recognize the type of the PD source which

generated the signals. Apart from PD detection, the ability to recognize the PD patterns

is an important aspect of transformer insulation diagnosis. Knowing the PD defect type

will enable engineers to gauge the severity of the deterioration caused by PDs. This in

turn will help to determine corrective actions that have to be taken.

To recognize the PD source, artificial intelligence (AI) is applied to classify the PD

signals and thus recognize the appropriate PD source. A back propagation neural

network (BPN) is applied to recognize the PD source from the PD waveform which is

recorded in time domain; neuro-fuzzy is applied to recognize different PD sources from

the PRPDs recorded in frequency domain.

The inputs to the BPN were extracted from the decomposition of the PD waveform. The

waveform was recorded from the PD signals emitted by three PD defect models, single

and multiple PD sources i.e. void, floating metal and a combination of void and floating

metal. The time domain PD waveforms were firstly decomposed into 5 frequency


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domain levels thus producing 63 nodes. Then, three features were extracted from each

node and in each level. The features of each level were then weighted. The node with

the most separated features was chosen as the input of the AI system. The result shows

that single and multiple PD sources can be classified with high precision. It was also

established that denoising of the PD waveform before decomposition increased the

accuracy of the recognition.

While the BPN is used to recognize single and multiple PD sources from their signal

waveforms, the neuro-fuzzy system is used to recognize different PD sources from the

PRPDs recorded in the frequency domain. The PRPD pattern was recorded using a

spectrum analyzer in zero-span mode. The shapes of the PRPDs recorded in zero-span

mode show similarity to the PRPD envelopes of the standardized IEC 60270 measuring

system.

For the neuro-fuzzy inputs, three statistical operators were extracted from both positive

and negative half-cycles of the PRPD, giving 6 input features. The data input was

divided into three groups: data training, testing and checking. The first group of data

was used to train a fuzzy inference system (FIS) whose results are then checked to

confirm the validation of the FIS. Both of the two first data groups contain information

which indicates the PD source. The last set of data is for the purpose of testing the FIS

using data without information about the source of the PD. The results show a high level

of accuracy of the neuro-fuzzy system to recognize the different PD sources.

From both detection and recognition methods, it can be concluded that UHF

measurement using appropriate sensors is a viable method that can be applied to detect

and recognize PDs in transformers.

7.5. PD localization using UHF method

Besides the purpose of PD detection, localization of the PD source in transformers is an

essential diagnostic tool for monitoring the state and condition of the insulation of the

transformer. Knowing the exact location of the PD source helps to determine the area of

the transformer that needs repair during a maintenance period.


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To locate the PD in a transformer, a minimum of three sensors is needed to enable

geometric triangulation. In this thesis, PD localization using an array of four UHF

sensors was investigated. The sensors are connected to a 4 channel CRO to record the

PD waveforms. The challenge of localizing PD sources using the UHF method is the

fact that electromagnetic signals emitted by the PD source travel very fast, at a speed

comparable to the speed of light. As the dimensions of a power transformer lie within a

range of a few meters, the time thus needed by a PD signal to propagate in a transformer

falls to less than a hundred nanoseconds. So to be able to locate the PD source using the

UHF method two important aspects must be fulfilled, i.e. a fast signal digitizer and a

fast response sensor are essential. For the former, a digitizer with accuracy in the pico-

second range is needed. Regarding the latter, in the sensor test to the step pulse response

the monopole sensor was shown to have the fastest response and produce less

oscillation. Thus, although the monopole has less sensitivity than other sensors, it is

most suited for choice as the sensor for PD location application.

The location of the PD source is determined using the time difference of arrival

(TDOA) between signals received by different sensors. In the experiment 4 sensors

were used, where one sensor was used as a reference, thus giving 3 TDOA readings.

The TDOA is calculated by using three methods, i.e. first peak, cross-correlation and

cumulative energy of the PD waveform.

The first peak method is defined as the first peak to arrive at the sensor with a threshold

value above 25%. The first peak is taken as the time of arrival (TOA) at a specific

sensor. Then the TDOA is calculated as the difference of the TOA at a specific sensor

compared to another reference sensor.

The cross-correlation method calculates the correlation strength between different

waveforms. The highest cross-correlation value shows the TDOA of a specific sensor

compared to the reference sensor.

The last method is the cumulative energy method. This method is based on the

observation that waveforms received by sensors far apart are likely to be dissimilar, thus

leading to failure of the cross-correlation to determine the correct TOA. The TDOA is

calculated by shifting one energy curve towards the other and calculating the similarity


207

value between them. The TDOA is defined as the point where the similarity value

between the two curves is at a minimum.

From the three methods used for determining the TDOA, the first peaks method shows

the highest degree of accuracy with error less than 20 cm. It is followed by the cross-

correlation method and lastly the cumulative energy method.

Although the UHF method has high noise immunity, the noise background still affected

the waveforms in the experiment. In an attempt to increase the accuracy of PD

localization, multivariate denoising was applied to eliminate the background noise. The

result shows that the denoising process increases accuracy for the cross-correlation and

first peak methods, while for the cumulative energy method the denoising process led to

a higher error.

7.6. Future work

The sensors designed in this thesis are expected to work in the ultra-high frequency

(UHF) range i.e. 300 MHz to 3000 MHz. The design follows procedures for antenna,

thus antenna parameters such as voltage standing wave ratio (VSWR) must be fulfilled

within a specific value. However, the sensors in this thesis barely fulfill the S11

parameters over the full UHF range with a value of -10 dB. Perhaps different shaped

sensors could fulfill the antenna parameters needed.

The most inferior aspect concerns the capability of the UHF method as compared to

conventional PD detection (IEC 60270) in quantifying the charge measurement. The

UHF method is difficult, if not impossible, to calibrate. The energy of electromagnetic

waves captured by sensors depends on the sensor type, PD source and most importantly

on the distance of the sensor from the PD source. Due to these factors, calibration of the

energy captured by the sensors to the amount of pC (apparent charge) is difficult. As a

substitution to calibration, the sensitivities of the sensor could be tested. The sensitivity

test of the UHF sensor in this thesis was carried out in a simple structure and only

examines the relationship between the sensor and the PD source with the presence of a


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simple barrier. In reality, the transformer structure is far more complicated. This makes

it important to conduct further investigation of the sensitivity of different sensors with

varying PD sources in real transformer structures.

The calibration should also clarify the effects of the working field types. As the UHF

sensor was applied to detect PD in a limited space, i.e the transformer size was limited

to a few metres only, the sensor seems to be working in a near field region only. It is

important to establish the implications of this field mode to the sensors’ sensitivity and

performance.

The back propagation neural network (BPN) recognition of PDs in this thesis used the

waveforms generated by single and multiple PD sources. The input features were

directly extracted from PD waveforms. The features extraction could be done anew by

separating PD waveforms generated by multiple PD sources into original waveforms of

the constituents. Also, comparison between different types of ANN to recognize the PD

sources needs to be carried out.

The number of PD defects used in the experiments was limited to three types for each

recognition method. Perhaps, this represents an oversimplification of real PD sources in

transformers. Many other PD sources might be needed to be investigated. This would

not only be for the purpose of enriching the analysis data but also to check the capability

of the UHF sensors to capture different PD sources.

For PD localization, sensors of different types and dimensions are needed to be

investigated. In this thesis, the monopole sensor used in the experiment had a 10 cm

length. For this size and as the propagation velocity of electromagnetic waves in oil is

~20 cm/ns, the monopole sensor itself can produce a time resolution error up to 500 ps

(on the assumption that electromagnetic signals reach a different end of the sensor).

Thus it is desirable to reduce the sensor dimensions for PD localization, although this

will tend to reduce the sensitivity of the sensor to detect electromagnetic signals. It is

worth exploring a balanced solution between these two conflicting requirements.

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222

APPENDIX A Sensor Design Using CST Microwave Studio

The CST Microwave Studio is a graphical interface software. The opening window of

the CST Microwave Studio is shown in Figure A.1. The components of the sensors such

as wire, plate, conical, and torus are provided and available on the interface front panel.

However for some special shapes such as the spiral and log spiral, the sensor must be

designed with support from other software. In this Appendix the log-spiral sensor

design 2, described in Chapter 3, will be discussed and its design method outlined.

Figure A.1: Opening view of the CST Microwave Studio software

223

From Section 3.5.5, the equation of the log-spiral sensor is a combination of two

equations:

1 0ar r e A.1

0( )2 0

ar r e A.2

where: r1 = outer radius of the spiral

r2 = inner radius of the spiral

r0 = initial outer radius of the spiral

a = rate of spiral growth

= angular position

The CST Microwave Studio does not provide an input method to draw the lines by

using equations. CST does, however, provide an input method by inserting the pair

coordinates (x, y) of the sensor. The coordinates for the dual arm of the log-spiral can be

calculated, and in this thesis we used Matlab (Figure A.2) to compute Equations A.1

and A.2 to get the pair x and y. Then the coordinates’ results are saved into a file in

ASCII format. The saved coordinates are then loaded into the CST Microwave Studio as

curves (Figure A.3). The four curves are then arranged as dual arm log-spiral design 2

(Figure A.4). The port which is connected to the balun is the pair of points in the inner

arms of the log-spiral. The simulation can then be run to get the sensor characteristics

such as impedance, VSWR, S11, radiation pattern and any other important parameters.

224

Figure A.2: The Log-spiral design 2 drawn using Matlab

Figure A.3: Drawing polygon curve with the coordinates produced by Matlab, (a)

loading coordinate points, and (b) curve drawing

225

Figure A.4: Dual arms Log-spiral sensor design 2, with connected port between arms

and built on the surface of PCB with diameter 150 mm

226

APPENDIX B

TEM Cell

Most of the TEM cells are designed to have 50 ohms of characteristic impedance. The

open TEM cell used in this thesis is also designed to work at 50 ohms. This is done so

that the cell has same impedance as the sensors. Using Equations 4.4 and 4.5, the TEM

cell dimensions can be determined.

The largest sensor diameter is 15 cm and attached to a balun with a length of 4.8 cm.

This is the size limitation for the TEM cell dimensions. By using Equations 4.4 and 4.5

we get the width and height of the cell as 50 cm and 11.5 cm respectively. The

impedance with this cell structure is 51.1347 ohms. For the exact Zo = 50 ohms, the

height of the cell is 11.2 cm. However, a precise construction is difficult to build and

also a sag factor might also have to be included for the middle section of the cell. The

diagram and photo of the TEM cell are shown in Figures B.1 and B.2 respectively.

Figure B.3 shows typical screen shot of the input steep pulse and log-spiral sensor

response, testing using TEM cell.

Both ends of the cell are tapered and bend, as shown in Figures B.1(b) and B.1(c). The

end of the top electrode is then decreased to 1 cm width and bent so that the distance

between the top electrode and the bottom plate is 2.5 mm.

227

800 mm

250 mm 250 mm

600 mm

10 mm

1200 mm (a)

10 mm

500 mm

100.5 mm 1000 mm 100.5

mm

(b)

1000 mm

105 mm

2.5 mm

100 mm 100 mm

PVC (c)

800 mm500 mm

(d)

Figure B.1: Diagram of the TEM cell (a) bottom plate, (b) top plate, (c) side view, and

(d) top view

228

Figure B.2: Set-up for frequency response measurement of the sensor, left-side end is connected with 50-ohm termination.

Figure B.3: The screen shot of the steep pulse and log-spiral sensor response

TEM Cell Function Generator

CRO

sensor

229

APPENDIX C

Experimental Set-Up

This Appendix shows photos of the set-up for all experiments which took place using

the transformer tank from Chapters 4 to 6. For simplification, only the schematic

diagrams are given in those chapters. Figure C.1 is an example from Section 4.4.1.

PD Source

SensorCB

RL

TR

X

Z

YSpectrum Analyzer

Barrier

ZInput unit

Mtronix Aqcuisition

Unit

(a) (b)

Figure C.1: (a) The experiment diagram [from Figure 4.7], and (b) the PD source.

The sensor in this diagram is connected to a spectrum analyser, but in another diagram

(experiment) it can be connected to a CRO. The transformer tank which is filled with oil

is shown in Figure C.2 with the top of the tank covered by a removable aluminium

sheet. The capacitance CB and input unit are shown in Figure C.3. The voltage regulator

and computerized Mtronix acquisition system are shown in Figure C.4. The Mtronix is

used to record the amount of PD in pC value (apparent charge) and the PRPD patterns.

This unit is an IEC 60270 compliant PD measuring system. The spectrum analyser and

the CRO are shown in Figure C.5.

230

Figure C.2: Transformer tank

Figure C.3: Blocking capacitor CB and input unit Z.

CB

Input Unit Z

Coaxial cables connected to sensors inside tank. The numbers of cables depend on the experiment needed.

HV input to PD source

Transformer HV output, connected to CB via RL

231

Figure C.4: Voltage regulator and Mtronix acquisition unit.

Figure C.5: Measurement units, CRO and spectrum analyser.

Computerized Mtronix acquisition unit,

acquire input from input unit Z

Voltage regulator

Computerized 4 GHz CRO

3 GHz Spectrum analyzer

1.5 GHz Spectrum analyzer

1.5 GHz CRO

Coaxial cable from sensors

Computer connected to 1.5 GHz CRO

232

APPENDIX D

PD Localization

The coordinates of the PD sources location are determined using the equation below:

1 214 14 14 14 14 1 4

224 24 24 24 4 24 2 4

234 34 34 34 34 3 4

12

x x y z r r K Ky x y z r r r K Kz x y z r r K K

D.1

where:

xi4, yi4 and yi4 = coordinates distance of sensor i to reference sensor 4 (i=1,2,3).

ri4 = TDOA between sensor i and 4 multiplied with the propagation speed.

r4 = the distance of sensor 4 to the PD source

Ki is calculated as 2 2 2

i i i iK x y z .

In Equation D.1, all variables on the right hand side are known except r4, where r4 is the

distance of the reference sensor 4 to the PD source.

Equation D.1 can be simplified as:

xyz

=-B-1 {C r4 + D} or xyz

= -B-1 C r4 + (-B-1) D D.2

where:

B= 14 14 14

24 24 24

34 34 34

x y zx y zx y z

, C=14

24

34

rrr

and D =

214 1 4

224 2 4

234 3 4

12

r K Kr K Kr K K

Furthermore Equation D.2 can be simplified by arranging it as:

233

4

xy P r Qz

D.3

where P = -B-1 C

Q = (-B-1) D

Then, the coordinates (x,y,z) of the PD source are :

1 4 1

2 4 2

3 4 3

x P r Qy P r Qz P r Q

D.4

The equation above is the coordinate of the PD source in terms of r4.

The distance of the PD source to the reference sensor (r4) can be calculated using the

Pythagorean theorem:

2 2 2 2

4 4 4 4( ) ( ) ( )r x x y y z z D.5

where (x, y, z) are the coordinates of the PD source and (x4, y4, z4) are the coordinates of

reference sensor 4.

Substituting Equation D.4 to D.5 to calculate the distance of the reference sensor (r4) to

the PD source:

2 2 2 2

4 4 4 41 4 1 2 4 2 3 4 3(( ) (( ) (( )) ) )r x y zP r Q P r Q P r Q

2

4 1 4 1 4

42 4 2 4

43 4 3 4

2 2 2 21 4 1 1 4 1 4

2 2 2 22 4 2 2 4 2

2 2 2 23 4 3 3 4 3

2 2( )

2 2( )

2 2( )

r x x

y y

z z

P r Q P r Q P r Q

P r Q P r Q P r Q

P r Q P r Q P r Q

By arranging the above to form a quadratic equation in terms of the reference sensor

(r4):

234

2

4 1 2 3 4

4

4 41 2 3 4 4 4

2 2 2 2

1 1 2 2 3 3 4 1 4 2 4 3 42 2 2 2 2 2

1 4 2 3

( )

2( ) 2( )

( ) ( ) 2( )

r

x z

x y z x y z

P P P r

P Q P Q P Q r P P y P rQ Q Q Q Q Q

or

1 2 3 4

4

4 44 4 4 1 2 3

2 2 2 2

1 1 2 2 3 3 4 1 4 2 4 3 42 2 2 2 2 2

1 4 2 3

0 (( ) 1)

2( ) 2( )

( ) ( ) 2( )

x z

x y z x y z

P P P r

P Q P Q P Q r P P y P rQ Q Q Q Q Q

D.6

Equation D.6 is a quadratic equation and can be written as:

2

4 4 0r rL M N D.7

where:

L= sum(P2)-1

M= 2(sum(PQ)) - 2(sum(P(sensor4))

N=sum((sensor4)2 + sum(Q2) - 2(sum(Q(sensor4)))

The roots of Equation D.7 are the distance of the reference sensor (r4) to the PD source.

Those roots are put back into Equation D.1 to find the coordinates of the PD source.

There are two values yielded by Equation D.7, thus producing two possible PD source

positions. Those values usually have very large variances. Typically, one solution is

illogical (i.e. resultant coordinates outside the tank). Thus the choice of the solution for

the PD source coordinates can be easily determined.

235

APPENDIX E

Matlab Script of the PD Localization

The PD localization is determined by solely using Matlab script. The flowchart diagram

of the PD localization is shown in Figure E.1

Input Signals

Signals Denoising

Calculate the TDOA

PD localization

PD source coordinates

Figure E.1: PD localization flowchart

The input signals are a set of 50 PD waveforms recorded by using a CRO with a

sampling rate of 40 GS/s. The signals are then denoised using a multivariate denoising

tool, a tool with script provided by Matlab. Then the TDOA of the denoised and

undenoised (original) signals are calculated by each of the following methods: first

peak, cross-correlation and cumulative energy. The flowcharts of each method are

shown in Figures E.2 to E.4. The calculated TDOAs are then used to determine the PD

coordinates.

236

PD signalsDenoised and undenoised

Convert signals to unipolar

Normalize the signals

Set threshold value

Pick the first point above the threshold value as TOA

value

Determine the TDOA

TDOA of sensor 1,2 and 3 to reference sensor 4

Figure E.2: TDOA calculation using First-Peak method

237


Calculate cross-correlation of signals sensor 1,2 and 3

with signal sensor 4

Get the maximum value of the cross-correlation as the

TDOA


Figure E.3: TDOA calculation using Cross-Correlation method

Calculate the cumulative energy of the signals

Normalize the cumulative energy

Calculate the similarity value of the cumulative

energy of signals 1,2 and 3 with signals 4

Get the minimum value of the similarity value as the

TDOA



Figure E.4: TDOA calculation using Cumulative Energy method

238

E.1. Data loading and denoising function

function [x1,x2,x3,x4,x1_d,x2_d,x3_d,x4_d,time_t]=Dataload_P(ns);

% ns = number of sample

% x1 = original signal of channel 1




% x1_d = denoised signal of channel 1




level = 5;

mother_wavelet_parameter = 'sym2';

wname = mother_wavelet_parameter;

tptr = 'heursure';

sorh = 's';

npc_app = 'kais';

npc_fin = 'kais';

% ===============================================

% Signal Loading and Denoising

% ===============================================

cd C:\\MATLAB\50ns % adjust to appropriate directory

i = 1;

while (i < 10)

a = load(strcat('100',(48 + i),'.csv'));

x1(:,i) = a(1:20000,2);

x2(:,i) = a(1:20000,3);

x3(:,i) = a(1:20000,4);

x4(:,i) = a(1:20000,5);

time_t=a(1:20000,1);

i = i+1;

end

while (i <= ns)

a = load(strcat('10',(floor(i/10)+48),(mod(i,10)+48),'.csv'));

x1(:,i) = a(1:20000,2);

x2(:,i) = a(1:20000,3);

x3(:,i) = a(1:20000,4);

x4(:,i) = a(1:20000,5);

i = i+1;

end

[x_den, npc, nestco] = wmulden(x1, level, wname, npc_app,npc_fin,

tptr, sorh);

x1_d=x_den;


tptr, sorh);

x2_d=x_den;


tptr, sorh);

x3_d=x_den;

239


tptr, sorh);

x4_d=x_den;

cd C:\\MATLAB\ % return to origin directory

240

E.2. Calculation of the TDOA

E.2.1. First Peak

% number of signals

ns=50

% threshold value

thr=0.25

% Data loading

[x1,x2,x3,x4,x1_d,x2_d,x3_d,x4_d]=Dataload(ns);

% ++++++++++++++++++++++++++++++++++++++++++++++++++

% TDOA calculation of original signal (undenoised)

% ++++++++++++++++++++++++++++++++++++++++++++++++++

%===================================================

% sensor 1

for i=1:ns

xx1(:,i)=((abs(x1(:,i))/max(abs(x1(:,i)))));

end

x=rot90(xx1);

for i=1:ns

[maxtab, mintab] = peakdet(x(i,:), thr);

arrival_time1(:,i)=maxtab(1,1);

end

%===================================================

% sensor 2

for i=1:ns


end

x=rot90(xx2);

for i=1:ns



end

%===================================================

% sensor 3

for i=1:ns


end

x=rot90(xx3);

for i=1:ns



end

%===================================================

% sensor 4

for i=1:ns

241


end

x=rot90(xx4);

for i=1:ns



end

%===================================================

% Calculate time of arrival difference

%===================================================

TD12=arrival_time1-arrival_time2;



TDOA12=mean(TD12)*25; % data resolution = 25 ps



TDOA_Undenoised=[TDOA12 TDOA32 TDOA42];

% ++++++++++++++++++++++++++++++++++++++++++++++++++

% TDOA calculation of denoised signal

% ++++++++++++++++++++++++++++++++++++++++++++++++++

%===================================================

% sensor 1

for i=1:ns

xx1_d(:,i)=(abs(x1_d(:,i)/max(abs(x1_d(:,i)))));

end

x=rot90(xx1_d);

for i=1:ns


arrival_time_d1(:,i)=maxtab(1,1);

end

%===================================================

% sensor 2

for i=1:ns


end

x=rot90(xx2_d);

for i=1:ns



end

%===================================================

% sensor 3

for i=1:ns


end

x=rot90(xx3_d);

for i=1:ns



end

%===================================================

% sensor 4

for i=1:ns

242


end

x=rot90(xx4_d);

for i=1:ns



end

%===================================================

% Calculate time of arrival difference

TD12_d=arrival_time_d1-arrival_time_d2;



TDOA12_d=mean(TD12_d)*25; % data resolution = 25 ps



TDOA_Denoised=[TDOA12_d TDOA32_d TDOA42_d];

243

Peak detection function

function [maxtab]=peakdet(v, delta, x)

maxtab = [];

v = v(:);

mn = Inf; mx = -Inf;

mnpos = NaN; mxpos = NaN;

lookformax = 1;

for i=1:length(v)

this = v(i);

if this > mx, mx = this; mxpos = x(i); end

if this < mn, mn = this; mnpos = x(i); end

if lookformax

if this < mx-delta

maxtab = [maxtab ; mxpos mx];

mn = this; mnpos = x(i);

lookformax = 0;

end

end

end

244

E.2.2. Cross-correlation

% number of signals

ns=50

[x1,x2,x3,x4,x1_d,x2_d,x3_d,x4_d]=Dataload(ns);

% ==================================================================

% cross correlation for denoised signals

% ==================================================================

for i=1:ns

CR12(:,i)=xcorr(x1_d(:,i),x2_d(:,i));

CR32(:,i)=xcorr(x3_d(:,i),x2_d(:,i));

CR42(:,i)=xcorr(x4_d(:,i),x2_d(:,i));

end

for i=1:ns;

[CRa12(:,i) CRb12(:,i)] = max(abs(CR12(:,i)));



end

CR_12=2.5*(4212-CRb12); % data resolution = 25 ps



% Mean of data

Mean_S12=mean(CR_12);



% ==================================================================

% cross correlation for denoised signals

% ==================================================================

for i=1:ns

CRo12(:,i)=xcorr(x1(:,i),x2(:,i));

CRo32(:,i)=xcorr(x3(:,i),x2(:,i));

CRo42(:,i)=xcorr(x4(:,i),x2(:,i));

end

for i=1:ns;

[CRao12(:,i) CRbo12(:,i)] = max(abs(CRo32(:,i)));



end

CRo_12=25*(4212-CRbo12); % data resolution = 25 ps



Mean_So12=mean(CRo_12);



undenoised=[Mean_So12 Mean_So32 Mean_So42]

denoised=[Mean_S12 Mean_S32 Mean_S42]

245

E.2.3. Cumulative energy

Function to calculate the cumulative energy, for both denoised and undenoised

signals. This function also normalize the energy curve

function

[x1_UDn,x2_UDn,x3_UDn,x4_UDn,x1_UD,x2_UD,x3_UD,x4_UD,x1_ED,x2_ED,x3_ED,x4_ED,x1_NED,x2_N

ED,x3_NED,x4_NED,x1_NEDn,x2_NEDn,x3_NEDn,x4_NEDn,x1_ANED,x2_ANED,x3_ANED,x4_ANED]=Energy

(x1,x2,x3,x4,x1_d,x2_d,x3_d,x4_d,x1_dn,x2_dn,x3_dn,x4_dn,ns);

% ED = Energy of denoised signals

% NED = Normalized Energy of denoised signals

% ANED = Averaged Normalized Energy of denoised signals

%===============================================

% Energy-cumulative of the denoised signals

%===============================================

%-----------------------------------------------

% Channel 1

%-----------------------------------------------

[a,b]=size(x1_d);

x1_ED=((x1_d).^2);

for ii=1:ns;

for i=2:a;

x1_ED(i,ii)=x1_ED(i-1,ii)+x1_ED(i,ii);

end

end

for i=1:ns;

x1_NED(:,i)=x1_ED(:,i)/max(x1_ED(:,i));

end;

x1_ANED=sum(rot90(x1_NED));

%-----------------------------------------------

% Channel 2

%-----------------------------------------------

[a,b]=size(x2_d);

x2_ED=((x2_d).^2);

for ii=1:ns;

for i=2:a;


end

end

for i=1:ns;


end;


%-----------------------------------------------

%Channel 3

%-----------------------------------------------

[a,b]=size(x3_d);

x3_ED=((x3_d).^2);

for ii=1:ns;

for i=2:a;

246


end

end

for i=1:ns;


end;


%-----------------------------------------------

% Channel 4

%-----------------------------------------------

[a,b]=size(x4_d);

x4_ED=((x4_d).^2);

for ii=1:ns;

for i=2:a;


end

end

for i=1:ns;


end;


% **********************************************

% Normalized energy

% **********************************************

%-----------------------------------------------

% Channel 1

%-----------------------------------------------

[a,b]=size(x1_dn);

x1_EDn=((x1_d).^2);

for ii=1:ns;

for i=2:a;

x1_EDn(i,ii)=x1_EDn(i-1,ii)+x1_EDn(i,ii);

end

end

for i=1:ns;

x1_NEDn(:,i)=x1_EDn(:,i)/max(x1_EDn(:,i));

end;

x1_ANEDn=sum(rot90(x1_NEDn));

%-----------------------------------------------

% Channel 2

%-----------------------------------------------

[a,b]=size(x2_dn);

x2_EDn=((x2_d).^2);

for ii=1:ns;

for i=2:a;


end

end

for i=1:ns;


end;


%-----------------------------------------------

247

%Channel 3

%-----------------------------------------------

[a,b]=size(x3_dn);

x3_EDn=((x3_d).^2);

for ii=1:ns;

for i=2:a;


end

end

for i=1:ns;


end;


%-----------------------------------------------

% Channel 4

%-----------------------------------------------

[a,b]=size(x4_dn);

x4_EDn=((x4_d).^2);

for ii=1:ns;

for i=2:a;


end

end

for i=1:ns;


end;


%===============================================

% Energy-cumulative of the denoised signals

%===============================================

%-----------------------------------------------

% Channel 1

%-----------------------------------------------

[a,b]=size(x1);

x1_UD=((x1).^2);

for ii=1:ns;

for i=2:a;

x1_UD(i,ii)=x1_UD(i-1,ii)+x1_UD(i,ii);

end

end

for i=1:ns;

x1_UDn(:,i)=x1_ED(:,i)/max(x1_ED(:,i));

end;

x1_UDnA=sum(rot90(x1_UDn));

%-----------------------------------------------

% Channel 2

%-----------------------------------------------

[a,b]=size(x2);

x2_UD=((x2).^2);

for ii=1:ns;

for i=2:a;


end

end

for i=1:ns;

x2_UDn(:,i)=x2_ED(:,i)/max(x2_ED(:,i));

end;

248


%-----------------------------------------------

%Channel 3

%-----------------------------------------------

[a,b]=size(x3);

x3_UD=((x3).^2);

for ii=1:ns;

for i=2:a;


end

end

for i=1:ns;

x3_UDn(:,i)=x3_UD(:,i)/max(x3_UD(:,i));

end;


%-----------------------------------------------

% Channel 4

%-----------------------------------------------

[a,b]=size(x4);

x4_UD=((x4).^2);

for ii=1:ns;

for i=2:a;


end

end

for i=1:ns;

x4_UDn(:,i)=x4_UD(:,i)/max(x4_UD(:,i));

end;


249

Function to calculate time shifting; the inputs are gotten from the energy

function

function

[timeshift_Denoised,timeshift_unDenoised]=T_shift(x1_UDn,x2_UDn,x3_UDn

,x4_UDn,x1_NED,x2_NED,x3_NED,x4_NED,T,ns);

%========================================================

% Denoised Signals

% =======================================================

T=20000;

k=5000

for j=1:ns

for i=1:k

S13(i,j)=sum(abs((x1_NED(1:(T-i),j))-(x3_NED(i+1:T,j))));






end

end

% Find the minimum value

i=1:ns;

[a13(i) b13(i)] = min(S13(:,i));

[a14(i) b14(i)] = min(S14(:,i));

[a34(i) b34(i)] = min(S34(:,i));

[a31(i) b31(i)] = min(S31(:,i));

[a41(i) b41(i)] = min(S41(:,i));

[a43(i) b43(i)] = min(S43(:,i));

% Calculate minimum value in ns

% Averaging time shifting

bv13=0.025*(mean(b13))

bv14=0.025*(mean(b14))

bv34=0.025*(mean(b34))

bv31=0.025*(mean(b31))

bv41=0.025*(mean(b41))

bv43=0.025*(mean(b43))

%=========================================================

% UN-Denoised Signals

% ========================================================

for j=1:ns

for i=1:k

SS13(i,j)=sum(abs((x1_UDn(1:(T-i),j))-(x3_UDn(i+1:T,j))));






end

end

% Finding the minimum value

i=1:ns;

[ao13(i) bo13(i)] = min(SS13(:,i));

250

[ao14(i) bo14(i)] = min(SS14(:,i));

[ao34(i) bo34(i)] = min(SS34(:,i));

[ao31(i) bo31(i)] = min(SS31(:,i));

[ao41(i) bo41(i)] = min(SS41(:,i));

[ao43(i) bo43(i)] = min(SS43(:,i));

% Calculate minimum value in ns

% Averaging time shifting

bvo13=0.025*(mean(bo13))

bvo14=0.025*(mean(bo14))

bvo34=0.025*(mean(bo34))

bvo31=0.025*(mean(bo31))

bvo41=0.025*(mean(bo41))

bvo43=0.025*(mean(bo43))

251

E.3. Calculation the PD source coordinates

function [Location1,Location2]=location(TDOA)

% Speed of signal in the medium in cm/ns

signal_speed = 20;

% sensor coordinates

sensor1 = [-50 -25 -47];

sensor2 = [45 -20 -49];

sensor3 = [45 20 -46];

sensor4 = [-50 20 -50];

% Input distance difference calculated as : TDOA times speed of the

% signal

C=transpose(TDOA*signal_speed);

%co-ordinate differences delta_x=[sensor1(1)-sensor4(1) sensor2(1)-sensor4(1) sensor3(1)-sensor4(1)];

delta_y=[sensor1(2)-sensor4(2) sensor2(2)-sensor4(2) sensor3(2)-sensor4(2)];

delta_z=[sensor1(3)-sensor4(3) sensor2(3)-sensor4(3) sensor3(3)-sensor4(3)];

delta=[delta_x;delta_y;delta_z];

B=delta';

%Compute K values

K1= sensor1(1)^2 + sensor1(2)^2 + sensor1(3)^2;




K=[K1 K2 K3 K4];

% variables of equation D.1

% with C is the TDOA times speed of signal in oil

L=-(inv(B)*C);

for m=1:3;

M(m,1)=0.5*((C(m,1)^2)-K(m)+K(4));

end

N=-(inv(B)*M);

% inserted to equation D.5

P=sum(L.^2)-1;

Q=2*sum(L.*N)-2*sum(sensor4(1,:)'.*L);

R=sum(sensor4(1,:).^2)+sum(N.^2)-2*sum(sensor4(1,:)'.*N);

%solve the roots of equation D.5

r1=real(roots([P Q R]));

% insert back to equation D.1 to solve the co-ordinates difference to

% reference sensor S4

Location1=-(inv(B))*(C*r1(1)+M)

Location2=-(inv(B))*(C*r1(2)+M)

detection, identification and localization of partial discharges in power transformers using uhf

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