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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
Return loss and VSWR ....................................................................... 64
Input impedance ................................................................................ 65
Radiation Pattern .............................................................................. 65
3.5.4. Planar spiral antennas ........................................................................ 66
3.5.5. Log-spiral .......................................................................................... 67
Return loss and VSWR ....................................................................... 68
Input impedance ................................................................................ 69
Radiation Pattern .............................................................................. 69
3.5.6. Archimedean spiral ............................................................................ 70
Return loss and VSWR ....................................................................... 71
Input impedance ................................................................................ 72
Radiation Pattern .............................................................................. 73
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
5.5.1. Experimental set-up ........................................................................... 140
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
5.6.1. Experimental set-up ........................................................................... 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 6.16: PD localization error plots for PD location 2 ................................... 194
Figure 6.17: PD localization error plots for PD location 3 ................................... 194
Figure 6.18: PD localization error plots for PD location 4 ................................... 195
Figure 6.19: PD localization error plots for PD location 5 ................................... 195
Figure 6.20: PD localization error plots for PD location 6 ................................... 196
Figure 6.21: PD localization error plots for PD location 7 ................................... 196
Figure 6.22: PD localization error plots for PD location 8 ................................... 197
Figure 6.23: PD localization error plots for PD location 9 ................................... 197
Figure 6.24: PD localization error plots for PD location 10 ................................. 198
xxi
Figure 6.25: PD localization error plots for PD location 11 ................................. 198
Figure 6.26: PD localization error plots for PD location 12 ................................. 199
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
Chapter 1 Introduction
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
Chapter 1 Introduction
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.
Chapter 1 Introduction
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
Chapter 1 Introduction
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.
Chapter 1 Introduction
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
Chapter 2 Literature Review
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].
Chapter 2 Literature Review
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:
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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:
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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:
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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)
Chapter 2 Literature Review
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:
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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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
Chapter 2 Literature Review
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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
Chapter 2 Literature Review
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:
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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.
Chapter 3 Sensor to detect PD in transformer
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:
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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:
Chapter 3 Sensor to detect PD in transformer
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:
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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]
Chapter 3 Sensor to detect PD in transformer
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.
Chapter 3 Sensor to detect PD in transformer
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].
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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:
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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]
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in 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.
Chapter 3 Sensor to detect PD in transformer
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].
Chapter 3 Sensor to detect PD in transformer
61
Figure 3.9: S11 parameter of varying length of monopole antenna.
Figure 3.10: Varying length Monopole antenna VSWR parameter.
Chapter 3 Sensor to detect PD in transformer
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.
Chapter 3 Sensor to detect PD in transformer
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.
Chapter 3 Sensor to detect PD in transformer
64
Return loss and VSWR
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.
S-P
aram
eter
(d
B)
Chapter 3 Sensor to detect PD in transformer
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)
Chapter 3 Sensor to detect PD in transformer
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’).
Chapter 3 Sensor to detect PD in transformer
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)
Chapter 3 Sensor to detect PD in transformer
68
Return loss and VSWR
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
S-P
aram
eter
(d
B)
Chapter 3 Sensor to detect PD in transformer
69
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.
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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].
Return loss and VSWR
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
S-P
aram
eter
(d
B)
Chapter 3 Sensor to detect PD in transformer
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)
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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
S-P
aram
eter
(d
B)
Chapter 3 Sensor to detect PD in transformer
77
Figure 3.30: VSWR of selected sensors
Figure 3.31: Input Impedance of selected sensors
Imp
edan
ce (
oh
m)
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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.
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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
Chapter 3 Sensor to detect PD in transformer
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)
Chapter 3 Sensor to detect PD in transformer
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.
Chapter 3 Sensor to detect PD in transformer
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
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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:
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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).
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
106
(a) (b)
(c) (d)
Figure 4.14: Total energy of full-span spectra with varying barrier positions, void PD
source.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 4 Step pulse, frequency response and sensor sensitivity to detect PD
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
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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.
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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:
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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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].
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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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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:
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
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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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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 :
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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]
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
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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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
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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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
5.5.1. Experimental set-up
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
pressboardKraft paper
High Voltage
Electrodemetal
pressboardKraft paper
High Voltage
Electrodevoid
pressboardKraft paper
metal
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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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
5.6.1. Experimental set-up
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
pressboardKraft paper
High Voltage
Electrodevoid
pressboardKraft paper
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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.
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 5 UHF PD recognition using PD waveform and PRPD pattern
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
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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.
Chapter 6 UHF PD localization in transformer
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(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
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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.
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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.
Chapter 6 UHF PD localization in transformer
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.
Chapter 6 UHF PD localization in transformer
178
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
Chapter 6 UHF PD localization in transformer
179
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.
Chapter 6 UHF PD localization in transformer
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,
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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.
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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.
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
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
Coordinates x, y , z (cm) Error (cm)
Original Denoised Original Denoised
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
Chapter 6 UHF PD localization in transformer
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
Coordinates x, y , z (cm) Error (cm)
Original Denoised Original Denoised
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
Chapter 6 UHF PD localization in transformer
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.
Chapter 6 UHF PD localization in transformer
191
Table 6.6: PD location and error calculated by using TDOA of the cumulative energy curve
PD
Location
Coordinates x, y , z (cm) Error (cm)
Original Denoised Original Denoised
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.
Chapter 6 UHF PD localization in transformer
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-
Chapter 6 UHF PD localization in transformer
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
Chapter 6 UHF PD localization in transformer
194
Error plot
Transformer tank
Location 2
118 cm
71
.5 c
m
Figure 6.16: PD localization error plots for PD location 2
Transformer tank
118 cm
71
.5 c
m
Location 3
Figure 6.17: PD localization error plots for PD location 3
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
Chapter 6 UHF PD localization in transformer
195
Error plot
Transformer tank
Location 4
118 cm
71
.5 c
m
Figure 6.18: PD localization error plots for PD location 4
Transformer tank
Error plotLocation 5
118 cm
71
.5 c
m
Figure 6.19: PD localization error plots for PD location 5
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
Chapter 6 UHF PD localization in transformer
196
Error plot Transformer tank
Location 6
118 cm
71
.5 c
m
Figure 6.20: PD localization error plots for PD location 6
Error plot
Transformer tankLocation 7
71
.5 c
m
118 cm
Figure 6.21: PD localization error plots for PD location 7
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
Chapter 6 UHF PD localization in transformer
197
Error plot
Transformer tankLocation 8
71
.5 c
m
118 cm
Figure 6.22: PD localization error plots for PD location 8
Error plot
Transformer tank
Location 9
71
.5 c
m
118 cm
Figure 6.23: PD localization error plots for PD location 9
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
Chapter 6 UHF PD localization in transformer
198
Error plot
Transformer tank
Location 10
71
.5 c
m
118 cm
Figure 6.24: PD localization error plots for PD location 10
Error plot
Transformer tank
Location 11
71
.5 c
m
118 cm
Figure 6.25: PD localization error plots for PD location 11
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
Chapter 6 UHF PD localization in transformer
199
Transformer tank
Error plot
118 cm
71
.5 c
m
Location 12
Figure 6.26: PD localization error plots for PD 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
First peak – original Cross-correlation – original Cumulative energy – original First peak – denoised Cross-correlation – denoised Cumulative energy – denoised
Chapter 6 UHF PD localization in transformer
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
202
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.
Chapter 7 Conclusion and suggestion for future research
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.
Chapter 7 Conclusion and suggestion for future research
204
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
Chapter 7 Conclusion and suggestion for future research
205
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.
Chapter 7 Conclusion and suggestion for future research
206
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
Chapter 7 Conclusion and suggestion for future research
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
Chapter 7 Conclusion and suggestion for future research
208
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.
209
References
[1] G.P. Cleary and M.D. Judd; “UHF and current pulse measurements of partial discharge activity in mineral oil”, IEE Proceeding of Science Measurement Technology, Vol.: 153, No.: 2, pp. 47 – 54, 2006.
[2] M. D. Judd, L. Yang, and I. B. B. Hunter, “Partial discharge monitoring for power transformers using UHF sensors Part 2: Field Experience”, IEEE Electrical Insulation Magazine, Vol. 21, No. 3, pp. 5-13, 2005.
[3] Martin D. Judd, Li Yang, and Ian B. B. Hunter, “Partial Discharge Monitoring for Power Transformers Using UHF Sensors Part 1: Sensors and Signal Interpretation”, IEEE Electrical Insulation Magazine, Vol. 21, No. 2, pp. 5- 14, 2005.
[4] B.G. Stewart, A.J. Reid, M.D. Judd, and R.A. Fouracre, “UHF and IEC60270 correlation analysis of radiated frequency band measurements on resin insulation void samples”, Electrical Insulation Conference and Electrical Manufacturing Expo, Nashville, USA, pp.138 – 141, Oct. 2007.
[5] K. Raja and T. Floribert, “Comparative investigations on UHF and acoustic PD detection sensitivity in transformers” , Conference Record of the 2002 IEEE International Symposium on Electrical Insulation, Boston, USA, pp,150 – 153, April 2002.
[6] S.M. Markalous, T. Strehl, and E. Lemke, “Advances in PD measuring system techniques: Parallel synchronous detection, time domain and frequency domain processing for improved sensitivity”, Conference on Condition Monitoring and Diagnosis, Beijing, China, pp. 37 – 41, 2008.
[7] J. Lopez-Roldan, T. Tang, and M. Gaskin, “Optimization of a Sensor for Onsite Detection of Partial Discharges in Power Transformers by the UHF Method”, IEEE Transaction on Dielectrics and Electrical Insulation, Vol. 15, No. 6; pp.1634- 1639; 2008.
[8] T. J. Gallagher and A. J. Pearmain, High Voltage: Measurement, Testing and Design, Eds. John Wiley & Sons, New York, 1983.
[9] IEC 60270: 'IEC International Standard 60270. High Voltage Test Techniques - Partial Discharge Measurements, International Electrotechnical Commission (lEC), Geneva, Switzerland, 3rd edition, 2000.
[10] F. H. Kreuger, Partial Discharge Detection in High-Voltage Equipment; London: Butterworths, 1989.
210
[11] R. Bartnikas, Partial Discharges, Their Mechanism, Detection and Measurement, IEEE Transaction on Dielectric and Electrical Insulation, Vol. 9, pp. 763-808, 2002.
[12] F. H. Kreuger, Industrial High Voltage, Delft University Press, 1991.
[13] E. Kuffel , W. S. Zaengl and J. Kuffel, High Voltage Engineering Fundamentals; Newnes, 2000.
[14] Dustin H. Froula, Siegfried H. Glenzer, Neville C. Luhmann, and Jr., John Sheffield, Plasma Scattering of Electromagnetic Radiation, 2nd ed., Elsevier, 2001.
[15] K. Lonngren and S. Savov, Fundamentals of Electromagnetics with MATLAB, 1st ed., SciTech Publishing, 2005.
[16] Panteleimon D. Agoris, “Sensitivity verification of radio frequency partial discharge detection in high voltage equipment”, PhD Thesis, University Press, Delft University of Technology, The Netherlands, 2009.
[17] M.D. Judd and O. Farish, “High Bandwith Measurement of Partial Discharge Current Pulses”, The International Symposium on Electrical Insulation (ISEI), Toyohashi, Japan, Vol.2, pp. 436-439, June 1998.
[18] Judd, M.D, Cleary, G.P, Bennoch, C.J, Pearson, and J.S, Breckenridge, “Power transformer monitoring using UHF sensors: site trials; Electrical Insulation”, Conference Record of the IEEE International Symposium on Electrical Insulation, Boston, USA, pp, 145 – 149, 2002.
[19] A. J. Reid, M. D. Judd, B. G. Stewart, and R. A. Fouracre, "Partial discharge current pulses in SF6 and the effect of superposition of their radiometric measurement". Journal Of Physics D, Applied Physics, Institute of Physics Publishing, Vol. 39, pp, 4167 – 177, September 2006.
[20] Murray R. Spiegel, Seymour Lipschutz, and John Liu, Mathematical Handbook of Formulas and Tables, New York , McGraw-Hill, 3rd ed. , 2009.
[21] Wanninger G; Discharge currents of free moving particles in GIS; Intl. Symp. on High Voltage Engineering Dielectrics and Insulation, Montreal, QC, Canada, vol 2; pp 219–22, 2008.
[22] Ari, N. and Blumer, W.; Transient Electromagnetic Fields Due to Switching Operations in Electric Power Systems; IEEE Trans. on Electromagnetic Compatibility, Vol.: EMC-29 , No.: 3, Page(s): 233 – 237, 1987.
[23] M. Muhr, T. Strehl, E. Gulski, K. Feser, E. Gockenbach, and W. Hauschild, Sensors And Sensing Used For Non-Conventional PD Detection, Ref No: Dl-102, Cigré, 2006.
211
[24] IEC 60505: Evaluation and qualification of electrical insulation systems, third edition, 2004.
[25] A.K. Lokhanin, G.Y. Shneider, V.V. Sokolov, V.M. Chomogotsky, and T.I. Morozova; Internal Insulation Failure Mechanisms Of HV Equipment Under Service Conditions, CIGRÉ Session 2002, Paris, France, No. 15-201, 2002.
[26] B.F. Hampton and R. J. Meats, “Diagnostic measurements at UHF in gas insulated substations”, IEE Proceedings Generation, Transmission and Distribution, Vol. 135, No. 2, pp. 137 – 145, 1988.
[27] D. Warne and A. Haddad, Advance in High voltage Engineering, London, Institution of Electrical Engineers, 2004.
[28] K. X. Lai, “Application of data mining techniques for characterization and recognition of partial discharge”, PhD Thesis, Department of Electric Power Engineering, University of New South Wales, Sydney, 2010.
[29] Hio Nam Johnson O, “Propagation of high frequency partial discharge signal in power cables”, PhD Thesis, Department of Electric Power Engineering, University of New South Wales, Sydney, 2009.
[30] G. C. Stone, “Partial Discharge Diagnostics and Electrical Equipment Insulation Condition Assessment”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 12, No. 5, pp. 891-903, 2005.
[31] M.D. Judd and O. Farish, “High Bandwith Measurement of Partial Discharge Current Pulses”, International Symposium on Electrical Insulation, Arlington, Virginia, USA, pp. 436-439, 1998.
[32] M.D. Judd, O. Farish and B. F. Hampton, “The excitation of UHF signals by partial discharges in GIS”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 3, No. 2, pp. 213 - 228, 1996.
[33] J. Lopez-Roldan, T. Tang, and M. Gaskin, “Optimisation of a Sensor for Onsite Detection of Partial Discharges in Power Transformers by the UHF Method”, IEEE Transaction on Dielectrics and Electrical Insulation Vol. 15, No. 6, December 2008, pp. 1634- 1639.
[34] Pinpart, T. and Judd, M.D.; Experimental comparison of UHF sensor types for PD location applications; Electrical Insulation Conference (EIC 2009), Montréal, Québec, Canada, pp. 26- 30, 2009.
[35] P. Agoris, S. Meijer, and J. J. Smit, “Sensitivity Check of an Internal VHF/UHF Sensor for Transformer Partial Discharge Measurements”, The Powertech '07 Conference, Lausanne, France, pp. 2065 – 2069, 2007.
[36] Atsuya Ando, Kenichi Kagoshima, Akira Kondo, and Shuji Kubota; Novel Microstrip Antenna With Rotatable Patch Fed by Coaxial Line for Personal
212
Handy-Phone System Units; IEEE Trans. On Antennas and Propagation, Vol. 56, No. 8, pp. 2747-2751, August 2008.
[37] Gaetano Marrocco; The Art of UHF RFID Antenna Design: Impedance-Matching and Size-Reduction Techniques; IEEE Antennas and Propagation Magazine, Vol. 50, No. 1, February 2008.
[38] Aycan Erentok and Richard W. Ziolkowski; Metamaterial-Inspired Efficient Electrically Small Antennas; IEEE Trans. On Antennas and Propagation, Vol. 56, No. 3, pp. 691-707, March 2008.
[39] Tang Ju; Xu Zhongrong; Zhang Xiaoxing and Sun Caixin; GIS partial discharge quantitative measurements using UHF microstrip antenna sensors; Conf. on Electrical Insulation and Dielectric Phenomena (CEIDP 2007), Vancouver, Canada, pp. 116- 119, 2007.
[40] Atanu Roy, Saswati Ghosh and Ajay Chakrabarty; Wideband Performance of Dielectric Loaded Monopole Trans-receive Antenna System; Intl. Conf. on Industrial and Information Systems (ICIIS 2007), 8 – 11 August 2007, Sri Lanka,pp. 181-185, 2007.
[41] J. Thaysen, K. B. Jakobsen, and J. Appel-Hansen, “A Wideband Balun — How Does it Work?”, Applied Microwave and Wireless, Vol. 12, No. 10, pp. 40-50, October 2000.
[42] J. W. Duncan and V. P. Minerva, “100:1 Bandwidth Balun Transformer”, Proceding of the Institute of Radio Engineers (IRE), Vol. 48, No. 2, pp. 156-164, Feb. 1960.
[43] H. H. Sinaga, B. T. Phung, and T. R. Blackburn, “Design of ultra high frequency sensors for detection of partial discharges”, International Symposium on High Voltage Engineering, Cape Town, South Africa, 2009.
[44] M. D. Judd, O. Farich, and B. F. Hampton, “Broadband coupler for UHF detection of partial discharge in gas insulated substations”, IEE Proceedings on Science, Measurement and Technology, Vol. 142, No. 3, pp. 237 - 243, May 1995.
[45] Jae-Gu Choi, Sang-Hwa Yi, and Kwang-Hwa Kim, “Development of a novel tapered balun for the UWB UHF coupler”, Conference of the 26th International Power Modulator Symposium, San Francisco, USA, pp. 493 – 496, 2004.
[46] D. Denissov, W. Köhler, S. Tenbohlen, R. Grund, and T. Klein, “Wide and narrow band PD detection in plug-in cable connectors in the UHF range”, Proceedings of 2008 International Conference on Condition Monitoring and Diagnosis, Beijing, China, pp. 1056-1059, 2008.
[47] Y. Sun, H. Yin, Q. Zhang, F. Yu, H. Wang, and Yuchang Qiu, “Partial Discharge Detection for GIS Using Narrow Band Ultra-High-Frequency (UHF)
213
Method”, International Symposium on Electrical Insulating Materials, Japan, pp. 748-751, 2005.
[48] S. Coenen, S. Tenbohlen, S. M. Markalous, and T. Strehl, “Sensitivity of UHF PD measurements in power transformers”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 15, No. 6, pp. 1153-1158, 2008.
[49] CIGRE TF 15/33.03.05, “PD Detection System for GIS: Sensitivity Verification for the UHF Method and the Acoustic Method”, Electra No.183, 1999.
[50] Coenen, S., Tenbohlen, S., Markalous, and S.M., Strehl, “Sensitivity limits of UHF PD measurements on power transformers”, International Symposium on High Voltage Engineering, Cape Town, South Africa, 2009.
[51] A. Troeger, U. Riechert, S. Burow, and S. Tenbohlen, “Sensitivity Evaluation of Different Types of PD Sensors for UHF-PD-Measurements”, International Conference on Condition Monitoring and Diagnostics, Tokyo, Japan, pp. 839-842, 2010.
[52] Z. Feng, L. Jian, L. Ruijin, and S. Grzybowski, “Aged Oil-paper Classification Using Statistical Parameters and Clustering Analysis”, Conference on Electrical Insulation and Dielectric Phenomena (CEIDP 2007), Vancouver, Canada, pp. 99-102, 2007.
[53] C. Wen-Yeau and Y. Hong-Tzer, “Application of Fuzzy C-Means Clustering Approach to Partial Discharge Pattern Recognition of Cast-Resin Current Transformers”, 8th International Conference on Properties and applications of Dielectric Materials, Denpasar, Indonesia, pp. 372-375, 2006.
[54] V. Chatpattananan and N. Pattanadech, “A Classification of Partial Discharge on High Voltage Equipment with Multinomial Logistic Regression”, IEEE Conference on Electrical Insulation and Dielectric Phenomena, Kansas City, USA, pp. 573-576, 2006.
[55] P. Seong-Hee, K. Seok-Jae, L. Kee-Joe, and K. Seong-Hwa, “Comparison of Recognition Rates Between BP and ANFIS with FCM Clustering Method on Off-line PD Diagnosis of Defect Models of Traction Motor Stator Coil”, Electrical Proceedings of 2005 International Symposium on insulating Materials (ISEIM 2005), Kitakyushu, Japan, Vol. 3, pp. 849-852, 2005.
[56] B. Karthikeyan, S. Gopal, P. S. Srinivasan, and S. Venkatesh, “Efficacy of Back Propagation Neural Network Based on Various Statistical Measures for PD Pattern Classification Task”, 8th International Conference on Properties and applications of Dielectric Materials, Denpasar, Indonesia, pp. 40-43, 2006.
[57] V. Chatpattananan, N. Pattanadech, and P. Yutthagowith, “Partial Discharge Classification on High Voltage Equipment with K-Means”, 8th International
214
Conference on Properties and applications of Dielectric Materials, Denpasar, Indonesia, pp. 191-194, 2006.
[58] C. Chang and Q. Su, “Partial Discharge Distribution Pattern Analysis Using Combined Statistical Parameters”, IEEE Power Engineering Society Winter Meeting, pp. 691-696, Vol.1, 2000.
[59] F. Massingue, S. Meijer, P. D. Agoris, J. J. Smit, and J. Lopez-Roldan, “Partial Discharge Pattern Analysis of Modeled Insulation Defects in Transformer Insulation”, IEEE International Symposium on Electrical Insulation, Toronto, Canada, pp. 542-545, 2006.
[60] M. Mansor, A. B. A. Ghani, and P. S. Ghosh, “Partial Discharge Pattern Analysis Using Statistical Technique in XLPE Cable Under Various Soil Conditions”, Conference on Electrical Insulation and Dielectric Phenomena, Cancun, Mexico, pp. 707-711, 2002.
[61] H. Tan Kay and D. Ahmad Bin, “Pattern recognition of partial discharge signal in gas insulated switchgear apparatus using visual and cluster analysis”, Proceedings of International Conference on Power System Technology (PowerCon 2002), Kunming, China, pp. 1842-1846 Vol.3, 2002.
[62] A. A. Maqrashi, “Pattern Recognition of Partial Discharges Using MATLAB Tools”, 39th International Universities Power Engineering Conference (UPEC 2004), Bristol, England, Vol. 1, pp. 197-201, 2004.
[63] L. Yang and M. D. Judd, “Recognising multiple partial discharge sources in power transformers by wavelet analysis of UHF signals”, IEE Proc. Science, Measurement and Technology, Vol. 150 , No. 3, pp. 119 – 127, 2003.
[64] T. Pinpart, J. E. Fletcher and M. D. Judd, “Methods for distinguishing between partial discharges based on the UHF detection technique”, Conference on Condition Monitoring and Diagnosis, Beijing, China, pp. 1060 – 1064, 2008.
[65] C.S. Chang, J. Jin, C. Chang, T. Hoshino, M. Hanai, and N. Kobayashi, “Separation of corona using wavelet packet transform and neural network for detection of partial discharge in gas-insulated substations”, IEEE Trans. on Power Delivery, Vol. 20 , No. 2, Part 2, pp. 1363 – 1369, 2005.
[66] T. Lin, R. K. Aggarwal, and C. H. Kim, “Identification of the Defective Equipments in GIS Using the Self Organizing Map”, IEE Proceedings - Generation, Transmission and Distribution, Vol. 151, pp. 644-650, 2004.
[67] Z. Guobin, D. M. Hepburn, Z. Chengke, S. Xiaodi, and M. Michel, “Identification and Extraction of PD Current Pulse Shapes In a Cable Monitoring System”, Universities Power Engineering Conference (UPEC 2007), Brighton, UK, pp. 499-503, 2007.
[68] C. Chang, C. S. Chang, J. Jin, T. Hoshino, M. Hanai, and N. Kobayashi, “Source Classification of Partial Discharge for Gas Insulated Substation Using
215
Waveshape Pattern Recognition”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 12, pp. 374-386, 2005.
[69] A. Cavallini, A. Contin, G. C. Montanari, and F. Puletti, “Advanced PD Inference in On-field Measurements. I. Noise Rejection”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 10, pp. 216-224, 2003.
[70] K. Jeong-Tae, K. Nam-Joon, C. Yong-Moo, J. H. Kim, and Ja-Yoon Koo, “Separation of Partial Discharge Data by Analyzing Pulse Wave Shapes”, 8th International Conference on Properties and applications of Dielectric Materials, Denpasar, Indonesia, pp. 365-367, 2006.
[71] W. Ziomek, M. Reformat, and E. Kuffel, “Application of genetic algorithms to pattern recognition of defects in GIS , IEEE Trans. Dielectrics and Electrical Insulation, Vol. 7 , No. 2, pp. 161 – 168, 2000.
[72] R. M. Sharkawy, R. S. Mangoubi, T. K. Abdel-Galil, M. M. A. Salama, and R. Bartnikas, “SVM classification of contaminating particles in liquid dielectrics using higher order statistics of electrical and acoustic PD measurements”, IEEE Transaction Dielectrics and Electrical Insulation, Vol.14, No.3, pp. 669-678, June 2007.
[73] B. Karthikeyan, S. Gopal, and S. Venkatesh, “Partial discharge pattern classification using composite versions of probabilistic neural network inference engine”, Expert Systems with Applications, Vol. 34, pp. 1938- 1947, 2008.
[74] C. Guo, L. Zhang, Y. Qian, C. Huang, H. Wang, L. Yao, and X. Jiang, “Application of adaptive neuro fuzzy inference system to the partial discharge pattern recognition”, Intelligent Computing and Intelligent Systems (ICIS 2009), Shanghai, China pp. 729 – 732, 2009.
[75] P. Kakeeto, M. D Judd, J. Pearson, and D. Templeton, “Experimental investigation of positional accuracy for UHF partial discharge location”, Conference on Condition Monitoring and Diagnosis, Beijing, China, pp.1070-1073, 2008.
[76] X. Song, C. Zhou, and D. M. Hepburn, “An Algorithm for Indentifying the Arrival Time of PD Pulses for PD Source Location”, Conference on Electrical Insulation Dielectric Phenomena, Québec City, Canada, pp. 379 - 382, 2008.
[77] H. H. Sinaga, B. T. Phung, P. L. Ao, and T. R. Blackburn, “Partial Discharge Localization in Transformers Using UHF Sensors”, Electrical Insulation Conference (EIC), Anneapolis, USA, 2011.
[78] Z. Tang, C. Li, X. Cheng, W. Wang, J. Li, and Jun Li, “Partial discharge location in power transformers using wideband RF detection”, IEEE Transaction on Dielectrics and Electrical Insulation, Vol. 13, No. 6, 2006.
216
[79] Y. Jing-gang, L. Da-jian, L. Junhao, Y. Peng, and Li Yan-ming, “Study of time delay of UHF signal arrival in location partial discharge”, Conference on Condition Monitoring and Diagnosis, Beijing, China, pp. 1088 – 1092, 2008.
[80] Z. G. Tang, C. R. Li, X. Huang, Z. Li, and S. Fu, “The feasibility of locating PD source in transformer using the UHF technology”, IEEE Conference on Electric Insulation and Dielectric Phenomena, Colorado, USA, pp. 477-480, 2004.
[81] S. Meijer, R. A. Jongen, E. Gulski, and J. J. Smit, “Location of Insulation Defects in Power Transformer Based on Energy Attenuation Analysis”, Proceedings of 2005 International Symposium on Electrical Insulating, Mateflak, June 2005, Kitakyushu, Japan, pp. 698-701.
[82] H. H. Sinaga, B. T. Phung, A. P. Ao, and T. R. Blackburn, “UHF Sensors sensitivity in detecting partial discharge sources in a transformer”, International Symposium on High Voltage Engineering, Hannover, Germany, 2011.
[83] S. Meijer, A. Bovis, E. Gulski, J. J. Smit, and A. Girodet, “Analysis of the sensitivity of the UHF PD measuring technique”, Intl. Symp. On Electrical Insulation, Anaheim, CA, USA, pp. 395 – 399, 2000.
[84] El Mountassir, O., Stewart, B.G., McMeekin, S.G. and Ahmadinia, A.; Intl. Conf. on Evaluation of an iterative method used for partial discharge RF location techniques Environment and Electrical Engineering (EEEIC), Rome, Italy, pp. 1- 4, 2011.
[85] El Mountassir, O.; Stewart, B. G., McMeekin, S. G. and Ahmadinia, A.; Intl. Conf. on Effect of sampling rate on the location accuracy of measurements from radiated RF partial discharges signals; Environment and Electrical Engineering (EEEIC), Venice, Italy, pp. 891- 896), 2012.
[86] Xiaoxing Zhang, Ju Tang and Yanbin Xie; Taylor-genetic Algorithm on PD Location; Intl. Conf. on High Voltage Engineering and Application, Chongqing, China, November 9-13, pp.685-688, 2008.
[87] Shuangzan Ren, Xu Yang Ruihua Zhu, Baofeng Xi,Xu Man and Xiaolong Cao; Ultrasonic localization of Partial Discharge in Power Transformer Based on Improved Genetic Algorithm; Proc. of Intl. Symp. on Electrical Insulating Materials, 2008, Yokkaichi ,Mie, Japan, pp.:323-325, 2008.
[88] B. X. Du, Y. H. Lu, G. Z. Weil, and Y. Tian, “PD Localization Based on Fuzzy Theory using AE Detection Techniques”, Annual Report Conference on Electrical Insulation and Dielectric Phenomena, Tennessee, USA, pp. 449-453, 2005.
[89] Luo Ri-cheng , Bai Kai and Liu Shao-yu; Study on Partial Discharge Localization by Ultrasonic Measuring in Power Transformer Based on Particle
217
Swarm Optimization; Intl. Conf. on Sensing Technology, Taiwan, pp. 426-430, 2008.
[90] Luo Ri-cheng, Bai Kai, Deng Chun,Liu Shao-yu and Xu Guo-zheng; Study on Partial Discharge Localization by Ultrasonic Measuring in Power Transformer Based on Particle Swarm Optimization; Intl. Conf. on High Voltage Engineering and Application, Chongqing, China, pp.:600-603, 2008.
[91] H. C. Schau and A. Z. Robinson, “Passive source localization employing intersecting spherical surfaces from time-of-arrival differences”, IEEE Transaction on Acoustic, Speech and Signal Processing, Vol. ASSP-35, No. 8, pp. 1223-1225, Aug. 1987.
[92] Y. T. Chan and K. C. Ho, “Simple and Efficient Estimator for Hyperbolic Location”, IEEE Transactions on Signal Processing, Vol. 42, No. 8, pp. 1905-1915, August 1994.
[93] CST Microwave Studio Suite, Python Software Foundation, 2009.
[94] AS/NZS 60076.3:2008, Power transformers Part 3: Insulation levels, dielectric tests and external clearances in air, Australia/New Zealand Standard, 2008.
[95] J. Lopez-Roldan, T. Tang, and M. Gaskin, “Design and Testing of UHF Sensors for Partial Discharge Detection in Transformers”; International Conference on Condition Monitoring and Diagnosis, Beijing, China, April 21-24, 2008.
[96] G. C. Stone, H. G. Sedding, N. Fugimoto and J. M. Braun, "Practical implementation of ultrawide band PD detectors", IEEE Transactions on Electrical Insulation, Vol. 27, pp. 70-77, 1992.
[97] S. A. Boggs and G. C. Stone, “Fundamental Limitations in the Measurement of Corona and Partial Discharge”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 17, pp. 143-150, 1982.
[98] Constantine A. Balanis, Antenna Theory Analysis and Design, John Wiley and Son, Second Edition, USA, 1997.
[99] David M. Pozar, Microwave Engineering, John Wiley & Son, New York, USA, Second Edition, 1998.
[100] http://www.ittc.ku.edu/~jstiles/723/handouts/section_5_7_Chebyshev_ Multisection_Matching_Transformer_package.pdf
[101] microwaves101.com, http://www.microwaves101.com/encyclopedia/coplanar waveguide .cfm
[102] Rainee N. Simons, Coplanar Waveguide Circuits, Components, and Systems, John Wiley & Sons, 2001.
218
[103] S. Gevorgian, L. J. P. Linner, and E. L. Kollberg, “CAD Models for Shielded Multilayered CPW”, IEEE Transaction on Microwave Theory Technology, Vol. 43, No. 4, pp. 772—779, April 1995.
[104] E. Chen and S. Y. Chou, “Characteristics of Coplanar Transmission Lines on Multilayer Substrates: Modeling and Experiments”, IEEE Transaction on Microwave Theory Tech., Vol. 45, No. 6, pp. 939—945, June 1997.
[105] J. Thaysen, K. B. Jakobsen, and J. A. Hansen, “A Logarithmic Spiral Antenna for 0.4 to 3.8 GHz”, Applied Microwave and Wireless, Vol: 13, No. 2, pp. 32-45, 2001.
[106] P. J. G. Orr, A. J. Reid, and M. D. Judd, “Sensor response characteristics for UHF location of PD sources”, Conference on Condition Monitoring and Diagnosis, Beijing, China, pp. 1119 – 1122, 2008.
[107] V. H. Rumsey, “Frequency Independent Antennas”, IRE National Convention Record, pt. 1, pp. 114–118, 1957.
[108] J.D. Dyson, “The Equiangular Spiral Antenna,” IRE Transactions on Antennas and Propagation, pp. 181–187, 1959.
[109] J. A. Kaiser, “The Archimedean Two-Wire Spiral Antenna”, IRE Transactions on Antennas and Propagation, Vol. AP-8, pp. 312-323, 1960.
[110] V. Trifunovic and B. Jokanovic, “Four decade Bandwidth Uniplanar Balun,” Electronics Letters, Vol. 28, pp. 534–535, 1992.
[111] A. Cavallini, G. C. Montanari, and M. Tozzi, “PD apparent charge estimation and calibration: A critical review”, IEEE Transactions on Dielectrics and Electrical Insulation, pp. 198 – 205, 2010.
[112] Martin D. Judd and Owen Farish, “A Pulsed GTEM System for UHF Sensor Calibration”, IEEE Transactions on Instrumentation and Measurement, Vol. 47, No. 4, pp. 875-880, 1998.
[113] M. D. Judd, “Transient calibration of electric field sensors”, IEE Proc-Sci. and Meas. Technol. Vol.146, No.3, pp. 113-116, 1999.
[114] N. W. Kang, J. S. Kang, D. C. Kim, and J. H. Kim, “Fabrication of Small Reference Probe and Its Application”, IEEE Transactions on Instrumentation and Measurement, Vol.56, No.2, pp.435-438, 2007.
[115] Shinobu Ishigami and Masayuki Hirata, “A New Calibration Method for an Electric-field Probe using TEM Waveguides”, Proceedings 20th Int. Zurich Symposium on EMC, Zurich, Swiss, pp. 425-428, 2009.
[116] M. D. Judd, O. Farish, and J. S. Pearson, “UHF couplers for gas-insulated substations: a calibration technique”, IEE Proceedings - Science, Measurement and Technology, Vol.: 144 , No. 3, pp. 117 - 122, 1997.
219
[117] S. Meijer, E. Gulski, J. J. Smit, and H. F. Reiinders; “Sensitivity check for UHF PD detection on power transformers”, Conference Record of the 2004 IEEE International Symposium on Electrical Insulation, Indianapolis, USA, pp., 58-61; 2004.
[118] P. Agoris, S. Meijer, and J. J. Smit, “Sensitivity Check of an Internal VHF/UHF Sensor for Transformer Partial Discharge Measurements”, The Powertech '07 Conference, Lausanne, France, pp. 2065 – 2069, 2007.
[119] Lecture 10: TEM, TE and TM Modes for Waveguides. Rectangular Waveguide, http://whites.sdsmt.edu/classes/ee481/notes/481Lecture10.pdf
[120] P. D. Agoris, “Sensitivity Verification of Radio Frequency Partial Discharge Detection in High Voltage Equipment”, PhD Thesis, Delft University of Technology, Netherlands, 2009.
[121] S. W. Wentworth, Applied Electromagnetics - Early Transmission Lines Approach; John Wiley & Sons, ISBN-10: 0-470-04257-5, 2007.
[122] ANSYS® Academic Research, Release 13.0, Maxell electromagnetic field, ANSYS, Inc., 2010.
[123] T. Kato, F. Endo, and S. Hironaka; “ Sensitivity Calibration of UHF Partial Discharge Monitoring System in GIS” ; IEEJ Transactions on Power and Energy, Vol. 122-B, No. 11; 2002.
[124] S. Meijer, E. Gulski, J. H. Johan, Frank J. Wester, T. Grun, and M. Turner; “Interpretation Of PD In GIS Using Spectral Analysis” ; International Symposium on High Voltage Engineering, London, England, pp. 124 – 127, 1999.
[125] S. Rengarajan, R. N. Parmar, A. Bhoomaiah, and J. S. Kuntia, “Development of an UHF detection system for partial discharge measurement in transformer insulation”; International Symposium on Electrical Insulation, Toronto, Canada, pp.100 – 103, 9-12 June 2008.
[126] S. S. Haykin, Neural Networks and Learning Machines, 3rd ed., New York: Prentice Hall, 2009.
[127] J. S. R. Jang, C. T. Sun, and E. Muzutani , Neuro-Fuzzy and Soft Computing-A computational approach to learning and machine intelligence, Pearson Education Inc., 1997.
[128] Laurenene Fausett, Fundamentals of Neural networks architecture, algorithms and application, Prentice Hall, 1993.
[129] Simon Haykin, Neural networks: a comprehensive foundation, 2nd ed., Prentice Hall, 1999.
[130] The Number of Hidden Layers, http://www.heatonresearch.com/node/707
220
[131] D. E. Rumelhart, G. E.Hinton, and R. J. Williams, “Learning representations by back propagating errors”, Nature, Vol. 323, pp. 533-536, 1986.
[132] B. Krose and P. van der Smagt, An introduction to neural networks, Eighth edition, The University of Amsterdam, 1996.
[133] J. S. R. Jang, "ANFIS: adaptive-network-based fuzzy inference system", IEEE Transaction on Systems, Man and Cybernetics, Vol. 23, pp. 665-685, 1993.
[134] L. A. Zadeh, “Fuzzy sets”, Information and Control, Vol. 8, pp. 338-353, 1965.
[135] Hongxing Li, C. L. Philip Chen, and H. P. Huang, Fuzzy Neural: Mathematical Foundation and the Applications in Engineering, CRC Press, 2001.
[136] J. Yen and R. Langari, Fuzzy Logic: Intelligence, Control, and Information, Upper Saddle River, NJ: Prentice Hall, 1999.
[137] E. H. Mamdani and S. Assillian, “An experiment in linguistic synthesis with a fuzzy logic controller”, International Journal of Man-Machine Studies, Vol. 7 No.1, pp. 1- 13, 1975.
[138] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control”, IEEE Transactions on Systems, Man, and Cybernetics, Vol.15, No.1, pp. 116-132, 1985.
[139] Y. Tsukamoto, An Approach to Fuzzy Reasoning Method, in Advances in Fuzzy Set Theory and Applications,(eds M. Gupta, R. Ragade, and R.Yager), Elsevier, Amsterdam, pp. 137–149, 1979.
[140] J. S. R. Jang and Chuen-Tsai Sun, “Neuro fuzzy modeling and control”, Proceedings of the IEEE, Vol. 83, No. 3, pp. 378-406, 1995.
[141] M. Aminghafari, N. Cheze, and J. M. Poggi, “Multivariate de-noising using wavelets and principal component analysis”, Computational Statistics & Data Analysis, No.50, pp. 2381-2398, 2006.
[142] L. Yang, M.D. Judd, and C. J. Bennoch, “Denoising UHF signal for PD detection in transformers based on wavelet technique”, Annual Report Conference on Electrical Insulation and Dielectric Phenomena, Colorado, USA, pp.166-169, 2004.
[143] M. Florkowski and B. Florkowska, “Wavelet-based partial discharge image denoising”, IET Generation, Transmission & Distribution, Vol. 1 , No. 2, pp. 340 - 347, 2007.
[144] Chengke Zhou, Donald M. Hepburn, Xiaodi Song and Matthieu Michel, “Application of Denoising Techniques to PD measurement Utilising UHF, HFCT, Acoustic Sensors and IEC60270”, International Conference and Exhibition on Electricity Distribution - Part 1, Prague, Czech, pp. 1 – 4, 2009.
221
[145] 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”, Australasian Universities Power Engineering Conference, Adelaide, Australia, 2009.
[146] W. H. Foy, “Position-location solutions by Taylor-series estimation”, IEEE Transaction on Aerospace Electronic System, Vol. AES-12, pp. 187-194, March 1976.
[147] D. J. Tonieri, “Statistical theory of passive location systems”, IEEE Transaction on Aerospace Electronic System, Vol. AES-20, pp. 183-198, March 1984.
[148] R. N. Bracewell, The Fourier Transform and Its Application, McGraw-hill, 2000.
[149] S. J. Orfanidis, Optimum Signal Processing. An Introduction, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 2007.
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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
PD signalsDenoised and undenoised
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
TDOA of sensor 1,2 and 3 to reference sensor 4
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
TDOA of sensor 1,2 and 3 to reference sensor 4
PD signalsDenoised and undenoised
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
% x2 = original signal of channel 2
% x3 = original signal of channel 3
% x4 = original signal of channel 4
% x1_d = denoised signal of channel 1
% x1_d = denoised signal of channel 2
% x3_d = denoised signal of channel 3
% x4_d = denoised signal of channel 4
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;
[x_den, npc, nestco] = wmulden(x2, level, wname, npc_app,npc_fin,
tptr, sorh);
x2_d=x_den;
[x_den, npc, nestco] = wmulden(x3, level, wname, npc_app,npc_fin,
tptr, sorh);
x3_d=x_den;
239
[x_den, npc, nestco] = wmulden(x4, level, wname, npc_app,npc_fin,
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
xx2(:,i)=((abs(x2(:,i))/max(abs(x2(:,i)))));
end
x=rot90(xx2);
for i=1:ns
[maxtab, mintab] = peakdet(x(i,:), thr);
arrival_time2(:,i)=maxtab(1,1);
end
%===================================================
% sensor 3
for i=1:ns
xx3(:,i)=((abs(x3(:,i))/max(abs(x3(:,i)))));
end
x=rot90(xx3);
for i=1:ns
[maxtab, mintab] = peakdet(x(i,:), thr);
arrival_time3(:,i)=maxtab(1,1);
end
%===================================================
% sensor 4
for i=1:ns
241
xx4(:,i)=((abs(x4(:,i))/max(abs(x4(:,i)))));
end
x=rot90(xx4);
for i=1:ns
[maxtab, mintab] = peakdet(x(i,:), thr);
arrival_time4(:,i)=maxtab(1,1);
end
%===================================================
% Calculate time of arrival difference
%===================================================
TD12=arrival_time1-arrival_time2;
TD32=arrival_time3-arrival_time2;
TD42=arrival_time4-arrival_time2;
TDOA12=mean(TD12)*25; % data resolution = 25 ps
TDOA32=mean(TD32)*25; % data resolution = 25 ps
TDOA42=mean(TD42)*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
[maxtab, mintab] = peakdet(x(i,:), thr);
arrival_time_d1(:,i)=maxtab(1,1);
end
%===================================================
% sensor 2
for i=1:ns
xx2_d(:,i)=(abs(x2_d(:,i)/max(abs(x2_d(:,i)))));
end
x=rot90(xx2_d);
for i=1:ns
[maxtab, mintab] = peakdet(x(i,:), thr);
arrival_time_d2(:,i)=maxtab(1,1);
end
%===================================================
% sensor 3
for i=1:ns
xx3_d(:,i)=(abs(x3_d(:,i)/max(abs(x3_d(:,i)))));
end
x=rot90(xx3_d);
for i=1:ns
[maxtab, mintab] = peakdet(x(i,:), thr);
arrival_time_d3(:,i)=maxtab(1,1);
end
%===================================================
% sensor 4
for i=1:ns
242
xx4_d(:,i)=(abs(x4_d(:,i)/max(abs(x4_d(:,i)))));
end
x=rot90(xx4_d);
for i=1:ns
[maxtab, mintab] = peakdet(x(i,:), thr);
arrival_time_d4(:,i)=maxtab(1,1);
end
%===================================================
% Calculate time of arrival difference
TD12_d=arrival_time_d1-arrival_time_d2;
TD32_d=arrival_time_d3-arrival_time_d1;
TD42_d=arrival_time_d4-arrival_time_d1;
TDOA12_d=mean(TD12_d)*25; % data resolution = 25 ps
TDOA32_d=mean(TD32_d)*25; % data resolution = 25 ps
TDOA42_d=mean(TD42_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)));
[CRa32(:,i) CRb32(:,i)] = max(abs(CR32(:,i)));
[CRa42(:,i) CRb42(:,i)] = max(abs(CR42(:,i)));
end
CR_12=2.5*(4212-CRb12); % data resolution = 25 ps
CR_32=2.5*(4212-CRb32); % data resolution = 25 ps
CR_42=2.5*(4212-CRb42); % data resolution = 25 ps
% Mean of data
Mean_S12=mean(CR_12);
Mean_S32=mean(CR_32);
Mean_S42=mean(CR_42);
% ==================================================================
% 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)));
[CRao32(:,i) CRbo32(:,i)] = max(abs(CRo32(:,i)));
[CRao42(:,i) CRbo42(:,i)] = max(abs(CRo42(:,i)));
end
CRo_12=25*(4212-CRbo12); % data resolution = 25 ps
CRo_32=25*(4212-CRbo32); % data resolution = 25 ps
CRo_42=25*(4212-CRbo42); % data resolution = 25 ps
Mean_So12=mean(CRo_12);
Mean_So32=mean(CRo_32);
Mean_So42=mean(CRo_42);
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;
x2_ED(i,ii)=x2_ED(i-1,ii)+x2_ED(i,ii);
end
end
for i=1:ns;
x2_NED(:,i)=x2_ED(:,i)/max(x2_ED(:,i));
end;
x2_ANED=sum(rot90(x2_NED));
%-----------------------------------------------
%Channel 3
%-----------------------------------------------
[a,b]=size(x3_d);
x3_ED=((x3_d).^2);
for ii=1:ns;
for i=2:a;
246
x3_ED(i,ii)=x3_ED(i-1,ii)+x3_ED(i,ii);
end
end
for i=1:ns;
x3_NED(:,i)=x3_ED(:,i)/max(x3_ED(:,i));
end;
x3_ANED=sum(rot90(x3_NED));
%-----------------------------------------------
% Channel 4
%-----------------------------------------------
[a,b]=size(x4_d);
x4_ED=((x4_d).^2);
for ii=1:ns;
for i=2:a;
x4_ED(i,ii)=x4_ED(i-1,ii)+x4_ED(i,ii);
end
end
for i=1:ns;
x4_NED(:,i)=x4_ED(:,i)/max(x4_ED(:,i));
end;
x4_ANED=sum(rot90(x4_NED));
% **********************************************
% 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;
x2_EDn(i,ii)=x2_EDn(i-1,ii)+x2_EDn(i,ii);
end
end
for i=1:ns;
x2_NEDn(:,i)=x2_EDn(:,i)/max(x2_EDn(:,i));
end;
x2_ANEDn=sum(rot90(x2_NEDn));
%-----------------------------------------------
247
%Channel 3
%-----------------------------------------------
[a,b]=size(x3_dn);
x3_EDn=((x3_d).^2);
for ii=1:ns;
for i=2:a;
x3_EDn(i,ii)=x3_EDn(i-1,ii)+x3_EDn(i,ii);
end
end
for i=1:ns;
x3_NEDn(:,i)=x3_EDn(:,i)/max(x3_EDn(:,i));
end;
x3_ANEDn=sum(rot90(x3_NEDn));
%-----------------------------------------------
% Channel 4
%-----------------------------------------------
[a,b]=size(x4_dn);
x4_EDn=((x4_d).^2);
for ii=1:ns;
for i=2:a;
x4_EDn(i,ii)=x4_EDn(i-1,ii)+x4_EDn(i,ii);
end
end
for i=1:ns;
x4_NEDn(:,i)=x4_EDn(:,i)/max(x4_EDn(:,i));
end;
x4_ANEDn=sum(rot90(x4_NEDn));
%===============================================
% 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;
x2_UD(i,ii)=x2_UD(i-1,ii)+x2_UD(i,ii);
end
end
for i=1:ns;
x2_UDn(:,i)=x2_ED(:,i)/max(x2_ED(:,i));
end;
248
x2_UDnA=sum(rot90(x2_UDn));
%-----------------------------------------------
%Channel 3
%-----------------------------------------------
[a,b]=size(x3);
x3_UD=((x3).^2);
for ii=1:ns;
for i=2:a;
x3_UD(i,ii)=x3_UD(i-1,ii)+x3_UD(i,ii);
end
end
for i=1:ns;
x3_UDn(:,i)=x3_UD(:,i)/max(x3_UD(:,i));
end;
x3_UDnA=sum(rot90(x3_UDn));
%-----------------------------------------------
% Channel 4
%-----------------------------------------------
[a,b]=size(x4);
x4_UD=((x4).^2);
for ii=1:ns;
for i=2:a;
x4_UD(i,ii)=x4_UD(i-1,ii)+x4_UD(i,ii);
end
end
for i=1:ns;
x4_UDn(:,i)=x4_UD(:,i)/max(x4_UD(:,i));
end;
x4_UDnA=sum(rot90(x4_UDn));
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))));
S14(i,j)=sum(abs((x1_NED(1:(T-i),j))-(x4_NED(i+1:T,j))));
S34(i,j)=sum(abs((x3_NED(1:(T-i),j))-(x4_NED(i+1:T,j))));
S31(i,j)=sum(abs((x3_NED(1:(T-i),j))-(x1_NED(i+1:T,j))));
S41(i,j)=sum(abs((x4_NED(1:(T-i),j))-(x1_NED(i+1:T,j))));
S43(i,j)=sum(abs((x4_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))));
SS14(i,j)=sum(abs((x1_UDn(1:(T-i),j))-(x4_UDn(i+1:T,j))));
SS34(i,j)=sum(abs((x3_UDn(1:(T-i),j))-(x4_UDn(i+1:T,j))));
SS31(i,j)=sum(abs((x3_UDn(1:(T-i),j))-(x1_UDn(i+1:T,j))));
SS41(i,j)=sum(abs((x4_UDn(1:(T-i),j))-(x1_UDn(i+1:T,j))));
SS43(i,j)=sum(abs((x4_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))
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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;
K2= sensor2(1)^2 + sensor2(2)^2 + sensor2(3)^2;
K3= sensor3(1)^2 + sensor3(2)^2 + sensor3(3)^2;
K4= sensor4(1)^2 + sensor4(2)^2 + sensor4(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)