Partial Discharge Diagnostic Testing of Electrical Insulation ...

Partial Discharge Diagnostic Testing of Electrical

Insulation Based on Very Low Frequency

High Voltage Excitation

Hong Viet Phuong Nguyen

Supervisor: Associate Professor Toan Phung

A thesis in fulfilment of the requirements for the degree of

Doctor of Philosophy

School of Electrical Engineering and Telecommunications

Faculty of Engineering

University of New South Wales

March 2018

THE UNIVERSITY OF NEW SOUTH WALES

Thesis/Dissertation Sheet

Surname or Family name: NGUYEN

First name: HONG VIET PHUONG

Other name/s:

Abbreviation for degree as given in the University calendar: Ph.D.

School: Electrical Engineering and Telecommunications

Faculty: Engineering

Title: Partial Discharge Diagnostic Testing of Electrical Insulation based on Very Low Frequency High Voltage Excitation

Abstract 350 words maximum: (PLEASE TYPE)

High voltage diagnostic testing such as partial discharge measurement plays a vital role in determining the condition of

equipment insulation. Performing the testing with applied voltage at very low frequency significantly reduces the power required from the supply. However, partial discharge behaviour varies with frequency and thus existing knowledge on interpretations of partial discharge at power frequency cannot be directly applied to test results measured at very low frequency for insulation diagnosis. The motivation of this research is to study partial discharge behaviours at very low frequency and search for physical explanations of such differences.

Laboratory experiments were performed to gather data on corona discharge and internal discharge using a commercial

measurement system. In the tests, individual discharge events were recorded including magnitude and phase position to enable phase-resolved pattern analysis.

A comprehensive study of corona discharges at different applied voltage waveforms, such as sinusoidal wave and square

wave, was carried out under the excitation at very low frequency. Experimental results showed that the inception voltage is dependent on applied voltage waveforms. Furthermore, the increase of ambient temperature results in larger discharge magnitude and causes corona discharges to occur earlier in the phase of the voltage cycle.

Characteristics of internal discharges in a cavity are strongly dependent on applied frequency. A dynamic model for numerical

computation was developed to study this dependence. This model has a minimum set of adjustable parameters to simulate discharges in the cavity. Simulation results revealed that charge decay has a significant contribution to discharge characteristics at very low frequency. Charge decay causes reduction of the initial electron generation rate which results in lower discharge magnitude and repetition rate. Also, the statistical time lag of discharge activities is calculated and it exhibits strong dependence on applied frequency.

The contributions of this research include the development of a discharge model to characterise physical processes of

discharge in a cavity, discussions on differences in partial discharge characteristics at very low frequency and power frequency as a function of cavity size, voltage waveforms and ambient temperatures. These findings provide better understanding of discharge behaviours at very low frequency excitation.

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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. I have either used no substantial portions of copyright material in

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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

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To my loving family……..

Dedicated to Ruby…….

page i

Acknowledgement

The journey of my PhD research has not been easy and smooth. Without

support from many people along the way, it would not have been possible to

complete this thesis.

First and foremost, I would like to sincerely thank my supervisor, Associate

Professor Toan Phung, for guiding me through every single step of this research.

I truly appreciate your valuable comments, advice, corrections and endless

support over the past four years regardless of the day or night, weekday or

weekend, working time or holiday.

I also express my appreciation to all the technical staff of the School of

Electrical Engineering and Telecommunications, especially Mr Zhenyu Liu for

accompanying me in the UNSW High Voltage laboratory during the

experiments. I appreciate the time we spent together working on the experimental

equipment.

It would not have been possible to come to UNSW Australia without

financial support from the Australia Awards Scholarship. I would like to

acknowledge all the support from the scholarship liaison officers during my PhD

candidature.

I also thank all my friends who shared memorable times. To Thinh, Minh,

Hau, Dai and other Vietnamese students, thank you for broadening my cultural

perception. To Hana, Tariq, Majid, Morsalin and other international friends, I

really appreciate your friendship.

Last but not least, no words can express my deepest gratitude to my parents

and parents-in-law. Thank you, Dad, for making me tougher through your hard

words. Thanks Mom for your understanding and always being on my side. To my

wife and son, you are the best. Apologies are not enough for all your sufferings

during the time without me. Thank you so much for being with me during the ups

and downs in life. I love you all!

page ii

Abstract

Electrical insulation plays an important role in the proper functioning of

high voltage power system equipment/components. Examining the condition of

insulation is crucial to keep the equipment safe and functioning efficiently. High

voltage diagnostic tests, in particular partial discharge measurements, are very

effective in detecting early signs of insulation damage. This type of diagnostic

test is generally conducted at the power frequency to emulate normal operating

condition. However, it is difficult to perform the test on-site due to the large

reactive power required when testing high-capacitance objects such as cables.

An alternative approach is to conduct the test at very low frequency

excitation, commonly at 0.1 Hz, because the required power is proportional to the

applied frequency and thus is significantly reduced. However, partial discharge

behaviour varies with frequency and thus existing knowledge on interpretations

of partial discharge at power frequency cannot be directly applied to test results

measured at very low frequency for insulation diagnosis. The motivation of this

research is to study partial discharge behaviours at very low frequency and

search for physical explanations of such differences.

Therefore, this thesis explains those differences in two types of partial

discharge, corona discharge and internal discharge, based on extensive

experimental measurements and computer simulation. Partial discharge patterns

were obtained and analysed using the phase-resolved partial discharge technique.

A comprehensive study of corona discharges at different applied voltage

waveforms, such as sinusoidal wave and square wave, was carried out under the

excitation of very low frequency. Experimental results showed that the inception

voltage of corona discharges at very low frequency is dependent on applied

voltage waveforms. Furthermore, effects of ambient air on corona discharges

were investigated thoroughly at temperatures between 20C and 40C at very low

frequency excitation and power frequency for comparison purposes. Measured

corona discharge characteristics showed that the increase of ambient temperature

page iii

results in larger discharge magnitude and causes corona discharges to occur

earlier in the phase of the voltage cycle.

This research also investigated internal discharge behaviour in a cavity at

very low frequency using measurement and simulation. Measurement results

showed that partial discharge characteristics are strongly dependent on applied

frequency. A dynamic model for numerical computation was developed to study

this dependence. The advantage of this model is that it has minimum adjustable

parameters to simulate discharges in the cavity. These values were determined

using a trial and error approach to fit the simulation results with measured data.

Simulation results showed that charge decay has a significant contribution to

discharge characteristics at very low frequency. Charge decay causes a reduction

of the initial electron generation rate which results in lower discharge magnitude

and repetition rate. Also, the statistical time lag of discharge activities was

calculated and found exhibiting a great dependence on applied frequency.

All in all, the major contribution of this thesis is the development of a

dynamic model to characterise physical processes of partial discharge in a cavity.

It enables determination of key parameters influencing partial discharge

behaviour such as the statistical time lag and the charge decay time constant at

different applied frequencies. Moreover, differences in partial discharge

characteristics at very low frequency and power frequency as a function of cavity

size, voltage waveforms and ambient temperatures are discussed and explained in

detail. The findings from this research provide better understanding of discharge

behaviours at very low frequency excitation.

page iv

Table of Contents

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

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

Table of Contents ................................................................................................ iv

List of Figures .................................................................................................... viii

List of Tables ..................................................................................................... xiii

Chapter 1: Introduction ....................................................................................... 1

1.1 Background of study and problem statement ............................................. 1

1.2 Thesis objectives ......................................................................................... 4

1.3 Research methodology ............................................................................... 5

1.4 Original contributions ................................................................................. 7

1.5 Thesis structure ........................................................................................... 8

1.6 Publications ................................................................................................. 9

Chapter 2: Literature Review ............................................................................ 11

2.1 Introduction ............................................................................................... 11

2.2 Gas breakdown mechanisms .................................................................... 11

2.2.1 Ionisation ......................................................................................... 11

2.2.2 Townsend mechanism ..................................................................... 12

2.2.3 Streamer mechanism ....................................................................... 13

2.3 Partial discharge definition and classification .......................................... 13

2.3.1 Corona discharge ............................................................................. 14

2.3.2 Surface discharge ............................................................................. 16

2.3.3 Internal discharge ............................................................................ 16

2.4 Internal discharge model .......................................................................... 17

2.4.1 Three capacitance model ................................................................. 17

2.4.2 Pedersen’s model ............................................................................. 19

2.4.3 Niemeyer’s model ........................................................................... 20

page v

2.4.4 Finite element analysis model ......................................................... 21

2.5 Initial electron generation rate .................................................................. 22

2.5.1 Surface emission .............................................................................. 23

2.5.2 Volume ionisation ........................................................................... 23

2.6 Parameters affecting partial discharge activity ......................................... 24

2.6.1 Time constants ................................................................................. 24

2.6.2 Statistical time lag ........................................................................... 26

2.6.3 Inception field .................................................................................. 27

2.7 Conclusion ................................................................................................ 27

Chapter 3: Modelling of Internal Discharge .................................................... 29

3.1 Introduction ............................................................................................... 29

3.2 Finite Element Method model .................................................................. 30

3.2.1 Field model equation ....................................................................... 30

3.2.2 Model geometry and meshing ......................................................... 31

3.2.3 Boundary and domain settings ........................................................ 31

3.3 Cavity discharge model and charge magnitude calculation ..................... 33

3.3.1 Cavity conductivity ......................................................................... 34

3.3.2 Discharge magnitude ....................................................................... 35

3.3.3 Charge decay simulation ................................................................. 36

3.4 Modelling of initial electron generation rate ............................................ 37

3.5 Simulation flowchart in MATLAB .......................................................... 39

3.5.1 Parameters for simulation ................................................................ 39

3.5.2 Program flowchart ........................................................................... 42

3.6 Conclusion ................................................................................................ 46

Chapter 4: Test Setup and Partial Discharge Measurements ........................ 48

4.1 Introduction ............................................................................................... 48

4.2 Partial discharge measurement setup ........................................................ 48

4.3 Partial discharge analysis .......................................................................... 52

4.3.1 Basic discharge quantities ............................................................... 53

4.3.2 Pulse sequence analysis ................................................................... 54

4.3.3 Phase-resolved partial discharge analysis ....................................... 55

page vi

4.4 Test object preparation ............................................................................. 57

4.4.1 Test object to produce corona discharge ......................................... 57

4.4.2 Test object to produce internal discharge ........................................ 58

4.5 Measurement methods .............................................................................. 61

4.5.1 Pre-measurement ............................................................................. 61

4.5.2 Corona discharge measurements at different temperatures ............. 62

4.5.3 Discharge measurements at various applied frequencies ................ 64

4.6 Conclusion ................................................................................................ 66

Chapter 5: Corona Discharge Activities: Effects of Applied Voltage

Waveforms and Ambient Conditions ............................................ 67

5.1 Introduction ............................................................................................... 67

5.2 Effects of applied waveform on corona discharge ................................... 68

5.2.1 Corona discharge at different applied frequencies under

excitation of sinusoidal waveform ................................................... 68

5.2.2 Corona discharge at very low frequency under excitation of

square waveform .............................................................................. 72

5.2.3 Corona discharge at very low frequency under sine wave with

DC offset .......................................................................................... 74

5.3 Effects of temperature on corona discharges ............................................ 76

5.3.1 Corona discharge under sine wave excitation ................................. 76

5.3.2 Corona discharge under sine wave with DC offset ......................... 84

5.4 Conclusion ................................................................................................ 86

Chapter 6: Void Discharge Behaviours as a Function of Cavity Size

and Applied Waveforms ................................................................. 88

6.1 Introduction ............................................................................................... 88

6.2 Discharge behaviours under long exposure to partial discharge .............. 88

6.2.1 Partial discharge characteristics under excitation of sine wave ...... 88

6.2.2 PD characteristics under excitation of square wave ........................ 93

6.3 Effects of cavity size on partial discharge behaviours under sine

wave voltage ............................................................................................ 99

6.4 Effects of voltage waveforms on partial discharge behaviours .............. 102

page vii

6.4.1 Partial discharge behaviours under sinusoidal waveform ............. 103

6.4.2 Partial discharge patterns under symmetric triangle waveform .... 103

6.4.3 Partial discharge patterns under trapezoidal-based voltage

waveform ....................................................................................... 105

6.4.4 Partial discharge patterns under square waveform ........................ 108

6.4.5 Effects of surface charge decay ..................................................... 109

6.5 Conclusion .............................................................................................. 112

Chapter 7: Void Discharge Behaviours: Comparison between

Measurements and Simulations ................................................... 113

7.1 Introduction ............................................................................................. 113

7.2 Results from simulation model ............................................................... 113

7.2.1 Electric field distribution in the model .......................................... 113

7.2.2 Simulation of electric field against time ........................................ 119

7.3 Comparison of measurements and simulations ...................................... 122

7.3.1 Partial discharge activities at 50 Hz .............................................. 122

7.3.2 Partial discharge activities at 0.1 Hz ............................................. 124

7.3.3 Values of simulation parameters ................................................... 125

7.3.4 Simulation for 10 applied voltage cycles ...................................... 127

7.4 Calculation of statistical time lag of partial discharge events ................ 131

7.5 Conclusion .............................................................................................. 132

Chapter 8: Conclusion and Future Work ...................................................... 134

8.1 Conclusion .............................................................................................. 134

8.2 Future research directions ....................................................................... 139

Appendix A: Variable Power Source Specifications ..................................... 141

Appendix B: Usage of Mtronix MPD600 Software ...................................... 144

References ......................................................................................................... 150

page viii

List of Figures

Figure 2.1 Diagram representation of external field distortion due to

space charge field [36] .................................................................... 13

Figure 2.2 Partial discharge categories [39] ..................................................... 15

Figure 2.3 Three capacitance model of partial discharge in a cavity ............... 18

Figure 3.1 The axial-symmetric 2D model ...................................................... 31

Figure 3.2 2D model geometry with meshed elements .................................... 32

Figure 3.3 Boundary line numbers in the model .............................................. 32

Figure 3.4 Behaviours of space charges left after a PD as a function of

field directions ................................................................................ 37

Figure 3.5 Main flowchart in MATLAB .......................................................... 43

Figure 3.6 Flowchart of “Solve FEM model” at each time step ...................... 43

Figure 3.7 Flowchart of PD occurrence determination .................................... 44

Figure 4.1 Circuit setup for partial discharge measurement [76] ..................... 49

Figure 4.2 Partial discharge measurement setup in the laboratory .................. 50

Figure 4.3 Control bench of partial discharge measurement system ............... 50

Figure 4.4 Mtronix MPD600 graphic user interface ........................................ 52

Figure 4.5 Partial discharge characteristics mapping process [35] .................. 56

Figure 4.6 Example of a 2D phase-resolved PD pattern .................................. 56

Figure 4.7 Test setup for generating corona discharges ................................... 57

Figure 4.8 Air breakdown around the needle tip over a distance d .................. 58

Figure 4.9 Test object dimensions .................................................................... 59

Figure 4.10 An example of a test object to generate internal discharge ............ 59

Figure 4.11 Test cell to generate internal discharge ........................................... 60

Figure 4.12 Electrical discharge in the cavity and its equivalent circuit ........... 61

Figure 4.13 Corona discharge setup for variable air temperature

measurements .................................................................................. 63

Figure 4.14 Thermostat control system and temperature sensor ........................ 65

page ix

Figure 5.1 Phase-resolved patterns at PDIV with various applied

frequencies ...................................................................................... 69

Figure 5.2 Phase-resolved patterns at PDIV under very low frequencies ........ 70

Figure 5.3 Phase-resolved patterns at 1.1 PDIV with different applied

frequencies ...................................................................................... 71

Figure 5.4 Phase-resolved patterns at 1.1 PDIV with different applied

frequencies ...................................................................................... 72

Figure 5.5 Reverse testing at 0.1 Hz at different voltage levels ...................... 72

Figure 5.6 Phase-resolved PD patterns under excitation of square

waveform at frequency of 0.1 Hz .................................................. 73

Figure 5.7 Reverse phase-resolved PD patterns under excitation of

square waveform at frequency of 0.1 Hz ........................................ 74

Figure 5.8 Phase-resolved PD patterns at PDIV with DC offset of -0.7

kV at different applied frequencies ................................................. 75

Figure 5.9 Phase-resolved PD patterns at DC offset of -0.8 kV at

different applied frequencies .......................................................... 76

Figure 5.10 Phase-resolved patterns at PDIV and 0.1 Hz excitation ................. 78

Figure 5.11 Phase-resolved patterns at PDIV and 50 Hz excitation .................. 79

Figure 5.12 Discharge distribution at PDIV and 0.1 Hz .................................... 80

Figure 5.13 Discharge distribution at PDIV and 50 Hz ..................................... 81

Figure 5.14 Phase-resolved patterns at 1.1 PDIV and 0.1 Hz for four

temperatures .................................................................................... 82

Figure 5.15 Phase-resolved patterns at 1.1 PDIV and 50 Hz for four

temperatures .................................................................................... 83

Figure 5.16 PD phase-resolved distribution at 1.1 PDIV and 0.1 Hz for

four temperatures ............................................................................ 84

Figure 5.17 Phase-resolved pattern at PDIV, frequency of 0.1 Hz with DC

offset of –0.7 kV at two temperatures ............................................. 85

Figure 5.18 Phase-resolved pattern at PDIV, frequency of 0.05Hz with DC

offset of –0.7 kV at two different temperatures .............................. 86

Figure 6.1 Maximum and average PD magnitude at 0.1 Hz and 50 Hz .......... 89

page x

Figure 6.2 Phase-resolved PD patterns at 0.1 Hz (a, b) and 50 Hz (c, d) at

1 and 4 hours after applying voltages ............................................. 90

Figure 6.3 Average phase distribution at 0.1 Hz and 50 Hz ............................ 91

Figure 6.4 Number of PDs per second at 0.1 Hz and 50 Hz ............................ 93

Figure 6.5 Changes of PD pattern at 0.1 Hz under the application of 10

kV square voltage at different times over the test duration ............ 96

Figure 6.6 Changes of PD pattern at 50 Hz under the application of 10

kV square voltage at different times over the test duration ............ 97

Figure 6.7 Average PD magnitude over the testing period at 0.1 Hz and

50 Hz under square voltage application of 10 kV .......................... 97

Figure 6.8 Surface charges accumulation in the void under square wave

voltage ............................................................................................. 99

Figure 6.9 PD magnitudes as a function of cavity size at 0.1 Hz and 50

Hz 100

Figure 6.10 Electric field distribution in test samples ...................................... 102

Figure 6.11 Trapezoid-based testing voltage waveform .................................. 103

Figure 6.12 Discharge behaviours as a function of applied voltage under

0.1 Hz and 50 Hz .......................................................................... 104

Figure 6.13 PD phase-resolved patterns under triangular voltage

waveform ...................................................................................... 105

Figure 6.14 PD phase-resolved patterns under trapezoidal voltage with

time factor of 10% ..................................................................... 106

Figure 6.15 PD phase-resolved patterns under trapezoidal voltage with

time factor of 20% ..................................................................... 107

Figure 6.16 PD phase-resolved patterns under 0.1 Hz trapezoidal

waveform at 10 kV applied voltage with different rise time ........ 108

Figure 6.17 PD phase-resolved patterns under approximately square

voltage waveform .......................................................................... 109

Figure 6.18 Electric field behaviour due to discharges under applied

trapezoid-based waveform ............................................................ 111

page xi

Figure 7.1 Simulation of electric field distribution and equipotential lines

in the model at 50 Hz and 10 kVrms when the first PD occurs .... 114

Figure 7.2 Cross-section plots of field magnitude in the model before and

after the first PD in Figure 7.1 ...................................................... 115


in the model at 50 Hz and 10 kVrms when the second PD

occurs ............................................................................................ 116


after the second PD in Figure 7.3 ................................................. 117


in the model at 0.1 Hz and 10 kVrms when the first PD occurs ... 118


after the first PD in Figure 7.5 ...................................................... 119


in the model at 0.1 Hz and 10 kVrms when the second PD

occurs ............................................................................................ 120


after the second PD in Figure 7.7 ................................................. 120

Figure 7.9 Electric field and PD magnitude in the first two cycles at 0.1

Hz (a, c) and 50 Hz (b, d).............................................................. 121

Figure 7.10 Phase-resolved PD patterns of measurement and simulation

results at different applied voltage under 50 Hz excitation .......... 123

Figure 7.11 Phase-resolved PD patterns of measurement and simulation

results at different applied voltage under 0.1 Hz excitation ......... 125

Figure 7.12 Simulation of electric field and PD magnitude for 10 cycles at

0.1 Hz under applied voltage of 8 kV ........................................... 129


0.1 Hz under applied voltage of 9 kV ........................................... 129


0.1 Hz under applied voltage of 10 kV ......................................... 130

page xii


50 Hz under applied voltage of 10 kV .......................................... 130

Figure 7.16 Calculation of statistical time lag of PD events ............................ 131

Figure 7.17 Distribution of statistical time lag under different applied

voltages at different applied frequencies ...................................... 132

Figure A.1 Front control panel of the waveform generator ............................ 141

Figure A.2 Front control panel of high voltage amplifier ............................... 142

Figure B.1. Mtronix MPD600 Graphic User Interface .................................... 145

Figure B.2. Charge calibration prior to measurements .................................... 146

Figure B.3. Voltage calibration in Mtronix MPD600 ...................................... 147

Figure B.4. An example of time histogram of discharges ............................... 148

Figure B.5. Replay procedures to export data into Matlab compatible files ... 149

page xiii

List of Tables

Table 3.1 Defined constants for finite element method model ....................... 32

Table 3.2 Electrical characteristics of subdomain settings ............................. 33

Table 3.3 Boundary line settings..................................................................... 33

Table 3.4 Values of all constants used for all simulations .............................. 40

Table 3.5 Values of adjustable parameters for simulation .............................. 42

Table 4.1 Test sample properties .................................................................... 59

Table 5.1 PD characteristics at 0.1 Hz and different applied voltages ........... 73

Table 5.2 PD characteristics at reverse testing at 0.1 Hz and different

applied voltages .............................................................................. 74

Table 5.3 PD characteristics at PDIV with DC offset of -0.7 kV ................... 76

Table 5.4 PD characteristics at PDIV with DC offset of -0.8 kV ................... 76

Table 5.5 PD characteristics at PDIV under excitation of 0.1 Hz and 50

Hz .................................................................................................. 79

Table 5.6 PD characteristics at 1.1 PDIV under excitation of 0.1 Hz and

50 Hz ............................................................................................... 81

Table 6.1 PD characteristics under triangular voltage waveform with

different applied frequencies ........................................................ 105

Table 6.2 PD characteristics under trapezoidal voltage waveform at 50

Hz and 0.1 Hz with different rise time factor ............................... 107

Table 6.3 PD characteristics under 0.1 Hz trapezoid-based waveform

with customised rise time.............................................................. 108

Table 7.1 Measurement results at 50 Hz under different applied voltages ... 122

Table 7.2 Simulation results at 50 Hz under different applied voltages ....... 122

Table 7.3 Measurement results at 0.1 Hz under different applied

voltages ......................................................................................... 126

Table 7.4 Simulation results at 0.1 Hz under different applied voltages ...... 126

Table 7.5 Simulation parameters .................................................................. 127

page xiv

Table 7.6 Values of adjustable parameters ................................................... 128

Table 7.7 Average statistical time lag under different applied voltages at

0.1 Hz and 50 Hz .......................................................................... 132

Chapter 1: Introduction

1.1 Background of study and problem statement

High voltage cables are increasingly being used and operated at higher

voltage levels than ever before in modern power systems. The cable insulation is

under significant stress, especially when they have been in continuous operation

for a long time. Thus, monitoring the insulation is essential to ensure the cables

are in good condition and able to function reliably. Testing of cable insulation is

important to determine the health of the insulation. The testing must be carried

out at a high voltage level that simulates normal operating electrical stress on the

insulation. An off-line high voltage excitation with separate supply is required

for this kind of test.

In the majority of cases, power system networks are AC and the normal

operating frequency is 50/60 Hz. On-site off-line high voltage testing of cables at

the power frequency has always been difficult due to the large reactive power

required for the test [1-2]. The amount of reactive power is proportional to the

frequency, test object capacitance and the square of applied voltage amplitude.

Therefore, the power required from the test supply is substantial when

performing on equipment with large capacitance such as cables. One solution is

using an AC resonant test system with a variable reactor which, together with the

test object capacitance, can be tuned to achieve resonance and reduced the

required power. Nevertheless, such a system is still physically large and heavy,

making it difficult to transport to site for field testing.

An alternative method is to perform testing at very low frequency,

commonly at 0.1 Hz, which considerably reduces the amount of power required

[3-5]. Although the very low frequency test has been used for many years as a

withstand test, diagnostic very low frequency tests have only been developed in

recent years with the development of power electronic techniques [6]. Very low


page 2

frequency diagnostic testing was introduced to examine the health of power

cable’s insulation in the late 1990s [7-8]. As it gradually becomes an emerging

trend, a guide of on-site diagnostic tests at very low frequency has been

introduced [9].

Electrical insulation plays an important role in the proper functioning of

high voltage equipment/components and partial discharge measurement is

arguably the most effective diagnostic test for insulation assessment. Partial

discharge is localised electrical breakdown in the insulation [10]. It normally

happens in areas with high concentration of electric fields, such as sharp points

of metal electrodes or cavities, cracks and joints in high voltage insulation

system. Although partial discharge occurrence does not cause instant complete

breakdown, it is an indication of defect existence in the insulation and affects its

performance considerably. Long-term continuous partial discharge exposure

during operation causes degradation of insulation system and energy loss [11].

Insulation degradation could eventually lead to the whole system breakdown

depending on the defect type and location [12].

Partial discharge diagnosis under the normal 50/60 Hz power frequency

voltage stress has been well explored and documented. The use of very low

frequency excitation rather than power frequency brings into question the

validity of using existing interpretations of partial discharge results. In other

words, the partial discharge data from very low frequency diagnostics may not be

comparable with those at the power frequency and thus new methods of data

analysis, in terms of insulation condition assessment are required for very low

frequency testing. This is the main motivation of this research.

To date, a number of investigations have been carried out to study partial

discharge at different applied frequencies. Comparative analysis of corona

discharge at very low frequency and power frequency was conducted in [13]

under different applied waveforms such as sinusoidal and cos-rectangular wave.

Obtained results indicated that there was not much difference between partial

discharge activities at both frequencies under the excitation of sine wave.

However, it was complicated to compare the phase-resolved patterns of corona


page 3

discharge under the cos-rectangular waveform at very low frequency and power

frequency. Another experimental investigation of corona discharge under

excitation of sinusoidal waveform [14] showed that the phase-resolved partial

discharge patterns were dependent on supply voltage frequency. Positive corona

discharges were observed at very low frequency whilst they were not detected

under power frequency or higher at the same applied voltage level. Investigation

of corona discharge at very low frequency range was also carried out in [15].

Measurement results from this work showed that the inception and extinction

voltage of corona discharge are almost constant for a wide range of applied

frequencies, from 0.01 Hz to 50 Hz. This work also reported the possibility of

measured errors at very low frequency due to the measurement system.

Extensive investigations of partial discharge in cavities have been

conducted and showed controversial results at various applied frequencies. An

early work of these researches was performed by Miller et al [16]. It was shown

that partial discharge characteristics were generally independent on applied

frequency range from 0.1 Hz to 50 Hz. However, later studies revealed that

discharge behaviours are strongly depedent on applied voltage waveforms and

frequencies [17-21]. In [17-18], the partial discharge characteristics at frequency

below 50 Hz showed inconsistent results, either similar or different to discharge

behaviours at 50 Hz. The phase-resolved patterns of partial discharge seemed to

be independent on applied frequencies. On the contrary, the discharge patterns

changed at different applied frequencies in [21]. The maxium discharge

magnitude was smaller at lower applied frequency. A similar observation of

discharge behaviours at various applied frequencies was presented in [22].

Discharge magnitudes increased at higher applied frequencies under the same

voltage level while the recorded discharge repetition rate reduced at lower

frequency.

In attempting to explain differences of measured discharge behaviours,

modelling of partial discharge in cavities has been considered in a number of

research. An advantage of partial discharge modelling is that key parameters

affecting partial discharge under different stress conditions can be identified.


page 4

Well-known partial discharge models are the three capacitance model [23-26]

and the Perdersen’s model [27-30]. Another stochastic discharge model proposed

in [31-32] enable the simulation of partial discharge in cavities. However, these

models had been used to investigate partial discharge at power frequency only. In

order to investigate partial discharge at different applied frequencies, a dynamic

model using Finite Element Analysis method was developed in [33]. This work

successfully simulate partial discharge actitivities in the frequency range of 0.01

Hz – 100 Hz. The improvement of this model has been done in [34-35] by taking

into account the charge decay time constant and effectively simulate discharge

behaviours from 1 Hz to 50 Hz. However, it is assumed that the time decay

constant is independent on applied frequencies. A detailed review of all these

partial discharge models is described in Chapter 2.

As partial discharge is stochastic, considerable discharge data are needed

for trending in order to explain the controversy of discharge behaviours at

different applied frequencies. Therefore, this thesis aims to comprehensively

investigate corona discharge and internal discharge characteristics at very low

frequency and power frequency under various stress conditions. A discharge

model is developed to investigate effects of these stress conditions on partial

discharge activities in a cavity. Comparison of discharge behaviours at very low

frequency and power frequency is made to propose possible correlation in order

to have a reasonable explanation of discharge phenomenon at very low

frequency.

1.2 Thesis objectives

The aim of this thesis is to investigate characteristics of partial discharge

occurring in insulation medium at very low frequency excitation and explain the

results obtained in terms of physical phenomenon. To fulfil this goal, extensive

experimental work on partial discharge at very low frequency and power

frequency is performed to gain sufficient discharge data for the analysis. Also, a

numerical simulation approach of partial discharge at very low frequency is


page 5

developed and used to identify what kind of physical parameters discharge

characteristics are strongly dependent on.

To achieve the goal of this study, the main objectives are to:

1. Develop a simulation model describing partial discharge in a cavity

embedded in a solid dielectric material using the finite element analysis

method.

2. Gain a better understanding of partial discharge in a cavity under

different electric stress conditions such as voltage amplitude and applied

frequency via the partial discharge model.

3. Determine from the model the key parameters influencing discharge

characteristics by comparison between computer simulated data and real

measured data from laboratory experiments on fabricated test

specimens.

4. Investigate dependence of partial discharge characteristics in a cavity at

different conditions such as applied voltage amplitude, voltage

waveform and cavity size at both very low frequency and power

frequency via experimental work.

5. Study the effects of ambient temperature and voltage waveform on

corona discharge activities under the excitation of very low frequency

and power frequency.

1.3 Research methodology

The work involves experimental testing and computer modelling. To this

end, various fabricated samples are tested to gain enough measurement data in

different testing conditions to verify the partial discharge simulation model

developed during the research.

This thesis mainly focuses on two types of partial discharge: corona

discharge and internal discharge occurring in a dielectric material. As discharge

activities are stochastic phenomena, a large volume of experimental data is

acquired during the research to support the proposed hypothesis made. With the

help of an arbitrary waveform generator, several voltage waveforms are used to


page 6

apply to test objects to investigate their influences on partial discharge activities.

The sinusoidal waveform had been used in most of the previous research but

Cavallini’s work [20-21] highlights the considerable effects of square waveform

on partial discharge at very low frequency. Therefore, in this research, various

voltage waveforms including triangle, square and offset sinusoidal waveform are

studied to explore effects of the voltage waveshape on partial discharge

phenomena at very low frequency excitation. To facilitate comparison of

discharge characteristics across various applied voltage waveforms, the well-

known phase-resolved partial discharge analysis technique is used to investigate

discharge activities at both very low frequency and power frequency. The

discharge magnitudes, rate of occurrence and phase position are evaluated in the

forms of integrated parameters and phase-resolved distribution patterns.

The measurement and simulation of partial discharge in a cylindrical cavity

within an insulation material is carried out at various amplitudes and frequencies

of the applied voltage. The simulation approach is based on previous work but it

is improved further in this research by introducing a set of numerical parameters

to account for the physical effects in the cavity on partial discharge phenomena at

very low frequency. Cavity geometry is restricted to a basic cylindrical shape to

reduce the computation time of simulation. A discharge model with only three

adjustable parameters is developed to describe the discharge phenomenon

occurred in a single void within a solid dielectric at very low frequency range

under various voltage amplitudes. The simulated data are then matched with

experimental measurements to optimise the values of adjustable parameters. The

simulation results reveal key parameters affecting discharge behaviours which

include the electron generation rate, surface charge decay time constant and

statistical time lag. These parameters are strongly dependent on applied voltage

amplitudes and frequencies.

For corona discharge, extensive experimental work is performed at very

low frequency and power frequency to determine the inception voltage of corona

discharge. Characteristics of corona discharges are analysed at inception level

and higher levels under different ambient temperatures and applied voltage


page 7

waveforms. By comparing discharge data obtained at very low frequency and

power frequency, the dependence of discharge activities on these stress

conditions is assessed and explained in terms of physical behaviour.

1.4 Original contributions

The original contributions of this thesis are summarised as follows:

1. Development of an improved partial discharge model for numerical

simulations. This model incorporates a minimal set of adjustable

parameters and the charge decay time constant which has adaptable

values to account for different applied frequencies. These features make

the investigation of partial discharge at very low frequency possible in a

reasonable simulation time; such a computer simulation study at very

low frequency had not been explored before.

2. Assessment of the effects of charge decay on the cavity surface upon the

partial discharge characteristics at various applied frequencies through

simulation. The detailed distribution of surface charge before and after a

discharge and its effects on the following partial discharge event can be

evaluated with finite element method based software.

3. Assessment of physical parameters influencing partial discharge

behaviour which cannot be directly measured such as the discharge

statistical time lag. By simulating partial discharge dynamically, the

statistical time lag of every single discharge event can be calculated

numerically under different conditions of applied voltage amplitudes

and frequencies.

4. Investigation of the trend of partial discharge characteristics in a cavity

as a function of cavity size and applied voltage waveform under very

low frequency and power frequency excitation. Differences in partial

discharge characteristics at different applied frequencies under similar

stress conditions are discussed and explained in terms of physical

processes.


page 8

5. Investigation of corona discharge characteristics as a function of applied

voltage waveform and ambient temperature under very low frequency

and power frequency excitation. Measurements show that the

dependence of corona discharge on different applied frequencies under

similar stress conditions is different and the physical explanations to

justify are reasonable.

1.5 Thesis structure

This thesis is structured in eight chapters. Chapter 1 introduces the

background and motivation of this research, the goal of this thesis and related

objectives and the contributions of this research.

Chapter 2 provides an in-depth literature review of the concept of partial

discharge including discharge mechanisms in gas and discharge in a cavity

bounded by solid insulation material in particular. This includes the definition of

partial discharge, the generation of free electrons, the developed models of

internal discharge in a cavity and physical parameters affecting partial discharge

activities.

Chapter 3 describes in detail the proposed model developed to dynamically

simulate partial discharge in a cavity by using a finite element method based

software of COMSOL Multiphysics interfaced with MATLAB. The key

advantage of this proposed model is that it utilises only three adjustable

parameters to characterise the partial discharge mechanisms and it includes a

flexible charge decay time constant dependent on applied frequency. This chapter

also includes equations for the initial electron generation rate, the process of

discharge model, the mechanism of charge decay on cavity surface and the

flowcharts of the MATLAB codes.

Chapter 4 presents the preparation of test objects to produce corona

discharge and cavity discharge. The discharge measurement system and how the

measurements were performed are also explained in this chapter.


page 9

Chapter 5 presents the experimental results of corona discharge at very low

frequency and power frequency under various stress conditions. These conditions

are different ambient temperatures and applied voltage waveforms.

Chapter 6 presents measurement results of cavity discharge at both very low

frequency and power frequency as a function of cavity size and applied voltage

waveform. The differences of discharge characteristics under excitation of

various frequencies are discussed and explained in this chapter.

Chapter 7 compares the measurement and simulation results to investigate

the effects of sinusoidal voltage amplitudes and frequencies on partial discharge

events. This comparison identifies the critical parameters affecting cavity

discharge characteristics under different applied frequencies, namely the initial

electron generation rate, charge decay time constant and statistical time lag of

discharge activities.

Finally, Chapter 8 presents the conclusion of this research and identifies

possible directions for future work to extend this thesis.

1.6 Publications

Journal papers

1. H. V. P. Nguyen and B. T. Phung, “Void Discharge Behaviors as a Function

of Cavity Size and Voltage Waveform under Very Low Frequency

Excitation,” IET High Voltage, paper HVE-2017-0174, provisionally

accepted 11 Dec. 2017, revised paper re-submitted 11 Jan. 2018.

2. H. V. P. Nguyen and B. T. Phung, “Measurement and Simulation of Partial

Discharge in Cavities under Very Low Frequency Excitation,” submitted to

IEEE Transaction on Dielectrics and Electrical Insulation.

Conference papers

1. H. V. P. Nguyen and B. T. Phung, “Cavity discharge behaviors under

trapezoid-based voltage at very low frequency,” in 3rd International

Conference on Condition Assessment Techniques in Electrical Systems

(CATCON 2017), Rupnagar, India, 2017, pp. 160–165.


page 10

2. H. V. P. Nguyen, B. T. Phung, and S. Morsalin, “Modelling partial

discharges in an insulation material at very low frequency,” in 2017

International Conference on High Voltage Engineering and Power Systems

(ICHVEPS), Bali, Indonesia, 2017, pp. 451–454.

3. H. V. P. Nguyen, B. T. Phung, and T. Blackburn, “Partial discharge

behaviors in cavities under square voltage excitation at very low frequency,”

in 2016 International Conference on Condition Monitoring and Diagnosis,

Xi’an, China, 2016, pp. 866–869.

4. H. V. P. Nguyen, B. T. Phung, and T. Blackburn, “Effects of aging on

partial discharge patterns in voids under very low frequency excitation,” in

2016 IEEE International Conference on Dielectrics (ICD), Montpellier,

France, 2016, pp. 524–527.

5. H. V. P. Nguyen, B. T. Phung, and T. Blackburn, “Influence of voltage

waveforms on very low frequency (VLF) partial discharge behaviours,” in

19th International Symposium on High Voltage Engineering (ISH2015),

Pilsen, Czech Republic, 2015.

6. H. V. P. Nguyen, B. T. Phung, and T. Blackburn, “Effect of temperatures on

very low frequency partial discharge diagnostics,” in 2015 IEEE 11th

International Conference on the Properties and Applications of Dielectric

Materials (ICPADM), Sydney, 2015, pp. 272–275.

7. H. V. P. Nguyen, B. T. Phung, and T. Blackburn, “Effects of ambient

conditions on partial discharges at very low frequency (VLF) sinusoidal

voltage excitation,” in 2015 IEEE Electrical Insulation Conference (EIC),

Seattle, USA, 2015, pp. 266–269.

8. D. Thinh, B. T. Phung, T. Blackburn, and H. V. P. Nguyen, “A comparative

study of partial discharges under power and very low frequency voltage

excitation,” in 2014 IEEE Conference on Electrical Insulation and Dielectric

Phenomena (CEIDP), Des Moines, USA, 2014, pp. 164–167.

Chapter 2: Literature Review

2.1 Introduction

This chapter provides an in-depth literature review of the concept of partial

discharge (PD) including discharge mechanisms in gases and discharge in a

cavity bounded by solid insulation material in particular. The general breakdown

mechanisms in gases are presented in Section 2.2. Section 2.3 describes the

physical phenomena of the three most common discharge categories: corona

discharge, surface discharge and internal discharge. Several internal discharge

models previously developed for discharge simulation are introduced in Section

2.4. These models are widely used to study physical behaviours of discharge in

cavities. Critical parameters affecting discharge characteristics which can be

determined from simulation results, such as the initial electron generation rate,

time constants, statistical time lag and inception field, are presented in Section

2.5 and Section 2.6.

2.2 Gas breakdown mechanisms

2.2.1 Ionisation

A free electron gains kinetic energy when it is exposed to an electric field.

The amount of kinetic energy gained is strongly dependent on the field intensity

and it becomes larger when approaching the anode electrode. During the

movement of the free electron, it may collide with neutral molecules which are in

its path. If the electron has sufficient kinetic energy, the collision could cause the

neutral molecules to separate into a positively-charged ion and one or more free

electrons. This mechanism is called ionisation due to collision. The generated

free electrons are then accelerated to the anode due to the application of the

electric field. The collision between free electrons and neutral molecules could

happen again during the electrons’ movements. Eventually, a large number of


page 12

electrons are released and create an electron avalanche towards the anode

electrode [36-37]. This process continues for each initial electron released from

the cathode until it reaches the anode or combines with another positive ion to

form a neutral molecule. The efficiency of electron impact ionisation is strongly

dependent on the amount of kinetic energy the electron gains during the

acceleration in the electric field.

Another ionisation mechanism is the generation of free electrons due to

photoionisation. Accelerated electrons with lower energy than the required

ionisation level may excite the gas atom to higher states of energy after the

collision [36]. After a certain period of time, this excited atom returns to a lower

state and releases a quantum energy of photon. This emitted energy may ionise a

nearby neutral molecule whose potential energy is close to the ionisation level.

This process is called ionisation due to photoionisation.

2.2.2 Townsend mechanism

Townsend found that electron avalanches can be sustained when the

potential difference between the two electrodes is large enough [38]. The self-

sustaining process is caused by the impact of the positive ions which are released

from ionisation on the cathode. If positive ions have sufficient kinetic energy,

two free electrons can be released from the cathode upon the impact of each ion.

One electron neutralises the positive ion while the other is about to ignite an

electron avalanche due to electric field acceleration. The latter electron is called

the secondary electron and it ignites new avalanches.

Free electrons can be emitted from the cathode under the tunnel effect.

Under this effect, the potential barrier to prevent electrons from escaping the

metal material is changed and allows certain electrons to pass through the barrier

when the electric field close to the cathode is large enough [36].

Another mechanism to generate free electrons from the cathode is

photoelectric impact. The cathode surface absorbs the radiated photon energy and

releases free electrons if this energy is larger than the surface work function.


page 13

2.2.3 Streamer mechanism

The accumulation of space charges generated from ionisation, i.e. positive

ions and free electrons, is considered in the streamer mechanism. The electric

field between two space charge heads is plotted in Figure 2.1. As can be seen

from Figure 2.1, the field is enhanced in all regions between the electrodes

except the area between the two space charge heads. They generate a local field

which opposes the external electric field E0. During the movement of space

charge heads towards their corresponding electrodes, they gain in size and thus

the electric field is enhanced further in certain regions. When the number of

charge carriers in the avalanche reaches a critical value at which the space charge

field is equal to the external applied field, a streamer is initiated.

Figure 2.1 Diagram representation of external field distortion due to space charge

field [36]

2.3 Partial discharge definition and classification

Partial discharge is defined in IEC 60270 standard [10] as “a localized

electrical discharge that only partially bridges the insulation between conductors

and which may or may not occur adjacent to a conductor”. In other words, it is an

electrical breakdown that does not occur through a complete insulation channel


page 14

between the electrodes but in a part of it. Partial discharges usually happen in a

very short time (order of nanoseconds) with different levels of magnitude. When

a partial discharge occurs, it is often accompanied by other physical phenomena

such as light, sound, heat emission and chemical reactions [10]. In high voltage

power equipment, the characteristics of partial discharge activity occurring can

be utilised to diagnose the insulation condition of the equipment such as the type

of faults/defects, and stage of aging. Therefore, it is essential to measure partial

discharge activity level.

Partial discharges occur when two conditions are met: a starting electron is

available and the applied voltage exceeds the critical threshold called the

inception voltage. To determine this inception value, the applied voltage is

slowly increased from a low voltage level at which no partial discharges occur

until reaching the voltage level when the first partial discharges are observed

repetitively. On the other hand, the extinction voltage is defined as the voltage

amplitude at which the discharges cease. To determine this value, the applied

voltage is slowly reduced from a higher amplitude at which partial discharges are

occurring to a lower value at which partial discharges disappear completely. The

extinction voltage is generally lower than the inception voltage.

Partial discharges are generally classified into three fundamental categories:

corona discharge, surface discharge and internal discharge [37,39]. These three

partial discharge sub-classes are illustrated in Figure 2.2 [39]. Discharges

occurring in the electrical tree in Figure 2.2c can also be considered as internal

discharge.

2.3.1 Corona discharge

Sharp metal points and edges commonly exist in high voltage conductors of

power equipment due to imperfect manufacturing and finishing. When high

voltage is applied, a significant non-uniform, locally concentrated electric field

appears around these sharp points which could lead to partial breakdown of the

surrounding air. These discharges are defined as corona discharge [36]. Corona

discharges usually happen at high voltage potential. Sharp edges on the ground


page 15

side, such as metallic particles or loose thin wire, could also be a source of

corona discharge production [37,39]. Corona discharge occurrence is only

observed in gases and liquids but not solids as the discharge mechanisms in

solids are completely different. To avoid corona discharge, high voltage

connectors must be made rounded and smooth. On the ground side, sharp points

and protrusions must also be eliminated.

(a) Corona discharge (b) Surface discharge

(c) Internal discharge

Figure 2.2 Partial discharge categories [39]

Negative corona discharge occurs when negative voltage polarity is applied

to the sharp point. Due to the electric field concentration around the tip region,

free electrons are emitted and repelled away from the cathode. These electrons

move towards the anode due to exposure to the electric field and trigger

avalanches in the mobility paths. The electron avalanches eventually reach the

anode if the field is large enough. Negative corona discharge was studied in

detail by Trichel and hence is also called Trichel pulse [40].


page 16

Positive corona discharge occurs when the voltage polarity applied to the

sharp protrusion is positive. It is triggered at a higher voltage amplitude than that

of negative corona discharge since there is no cathode appearance in this case.

Streamers are likely to appear around the tip vicinity when the field is strong

enough. The positive space charges generated from streamers are attracted to the

anode and act like a shield which surrounds the tip region. This shield reduces

the local field around the tip and hence the discharge is stopped. Then the

positive space charges drift away from the sharp point and the corona discharge

reignites due to the reduction of the electric shield. At a higher voltage level,

long streamers develop and cannot be extinguished by positive space charges.

2.3.2 Surface discharge

Surface discharge is a discharge propagating along the interface between

two different insulation materials when a large stress component exists parallel to

the dielectric surface. Figure 2.2b shows that the surface discharge occurs at the

edge of the high voltage electrode and propagates along the solid insulation

surface. Surface discharges are generally observed in high voltage bushings,

cable terminations or the overhang of generator windings [41].

2.3.3 Internal discharge

Solid and liquid dielectrics are usually not completely uniform

(homogeneous) as there are cavities or inclusions within the insulation due to

flaws in the manufacturing processes or in-service conditions. These cavities are

normally gas-filled and have lower electric breakdown strength. Since the

permittivity of the gas in cavities (relative permittivity of ~1) is lower than the

permittivity of surrounding dielectric material, the electric field in cavities is

enhanced and higher than that in the surrounding dielectric. Thus, electrical

breakdown easily occurs in cavities when high voltage is applied. When the

electric stress in the cavity is sufficiently high and exceeds the breakdown

strength of the gas, an internal discharge can be initiated [36,42]. During a partial

discharge, gas contents in the cavity change from a non-conducting to conducting

state, resulting in a decrease of electric stress in a very short time [43].


page 17

Discharges due to electrical treeing can be also categorised as internal

discharges. Electrical trees can be found in solid insulations such as polymers,

epoxy resins and rubbers.

Consequences of partial discharge activities in a cavity within high voltage

insulation can be very severe as partial discharge could eventually lead to

complete failure of the insulation system. Continuing internal discharge is one of

the main causes of dielectric deterioration and accelerates the electrical treeing

process. Repetition of partial discharges gradually lengthens the electrical trees

due to the progressive decomposition of organic elements. Ultimately, electrical

trees stop growing when tree channels provide a completely conducting path

between the electrodes, with complete breakdown of insulation [44-46].

2.4 Internal discharge model

2.4.1 Three capacitance model

A well-known model to describe a partial discharge encapsulated in an

insulation material is the three capacitance model or ‘abc’ model [36]. A

discharge is simulated by an instantaneous change of charging stage of an

imaginary capacitance represented by the cavity in the dielectric. This model is

widely used to describe the transient behaviours of a discharge activity such as

discharge current, apparent charge magnitude as a function of time due to the

voltage change across the cavity during the discharge. However, this model is not

practical to describe charge movement properties during a discharge as there is

charge accumulation on the cavity surface which makes it not an equipotential

surface [47]. An improvement of this model was made to consider the

accumulated charges on the cavity surface [48]. This model was simulated by

using a variable resistance dependent on time and applied voltage, which

characterises the partial discharge as a cavity changing from a non-conducting

state to a conducting state.

Figure 2.3 illustrates a typical capacitive equivalent circuit of a cavity

surrounded by an insulation material. Here, Ca is essentally the bulk insulation

capacitance of the test object, and Cb represents the capacitance of the healthy


page 18

dielectric in series with the cavity. The cavity is represented by a capacitance Cc

which is in parallel with a spark gap Fc. Va is the applied voltage on the test

object and Vc is the voltage across the cavity.

V~

Vc

Vb

Va

Ca

Cb

Cc

Fc

(a) characteristics circuit elements

VaCa

Cb

CcFc

ib

ibicic + ib

(b) transient currents flowing through PD equivalent circuit

Figure 2.3 Three capacitance model of partial discharge in a cavity

A partial discharge is assumed to ignite when the voltage dropped across

the cavity, Vc, is larger than the inception voltage, Vinc, and discharge stops when

Vc is lower than the extinction voltage, Vext. In the event of discharge, a combined

transient current between the discharging current in the cavity and the current

through the capacitance Cb flows through the spark gap. The current flowing

through Cb also passes through the object capacitance Ca. These currents are

generated by a sudden drop of voltage across the cavity during the discharge. In

the measurement of partial discharge, it is important to distinguish the internal

charge from the external charge. The internal charge, also called the physical

(true) charge, is calculated by the time integral of the current flowing through the

cavity, which includes ib and ic. The external charge, also known as apparent


page 19

charge, as measured by the partial discharge detection circuit is computed by the

time integral of the transient current flowing through the test object, ib.

Generally, the condition of Cb << Cc << Ca is valid in most insulation material,

and the physical charge, qr can be calculated by

( )r c b cq V C C (2.1)

The apparent charge, qa, is determined by integrating the transient current ib

flowing through both series-connected capacitors Ca and Cb over time. Since the

voltage dropped on Ca, Va is proportional to the capacitive divider ratio of

Cb/(Ca + Cb) Cb/Ca, the apparent charge can be obtained by

a a a c bq V C V C (2.2)

From equation (2.1) and (2.2), we have

b b

a r r

b c c

C Cq q q

C C C

(2.3)

As it is assumed Cb << Cc, the apparent charges detected from the test

objects are much smaller than the physical charges occurring in the cavity.

2.4.2 Pedersen’s model

The three capacitance model was considered inappropriate by Pedersen [29]

on the basis that the cavity cannot be represented by a virtual capacitance.

Pedersen introduced a theoretical approach to describe a partial discharge

transient by using the dipole concept [29,49]. The induced charges by dipoles are

expressed by the charge difference on the electrodes before and after the partial

discharge occurred in the cavity. Charges accumulated on the cavity surface

during the partial discharge occurrence increase the surface charge density,

decreasing the local electric field in the cavity, and the discharge vanishes when

the local field is below a certain value. The induced charges on cavity surfaces

create a dipole orientation due to the field generated by these charges. Charges

will also be induced on the electrode. The charge induced on the electrode is

calculated by


page 20

. .

S

q r dS

(2.4)

where is the dipole moment due to deposited charges on the cavity

surface S, r is the radius vector along the surface S, is the surface charge

density and is a dimensionless scalar function which depends on the space

charge location relative to the electrodes.

If the cavity is either ellipsoidal or spherical, the induced charge q or the

apparent charge from equation (2.4) can be calculated as

0( )inc extq K E E (2.5)

where K is the constant depending on cavity dimensions and geometry, is

the volume of the cavity, is dielectric permittivity, 0 is the Laplace’s equation

solution at the cavity location for material without any cavity [28], Einc is the

inception field and Eext is the extinction field. The boundary conditions used to

solve Laplace’s equation are 0 = 1 at the measured electrode and 0 = 0 at the

other electrode.

The induced charge transient has been investigated by analysing charges

and potential on electrodes just before and after a discharge [28]. It is assumed

that V and Q are the voltage and charge on the electrode before a partial

discharge. After a discharge is finished, the electrode potential drops by a value

of V while the amount of charge on the electrode gains Q, which is the

supplied charge from the external source. As a result, the induced charge q can

be expressed by

q C V Q C V (2.6)

where C is the system capacitance. If the circuit impedance is high relative

to the discharge current, the term Q can be ignored in equation (2.6).

2.4.3 Niemeyer’s model

A partial discharge model based on the streamer type process has been

developed by Niemeyer [31]. This model consists of a mathematical model of

initial electron generation rate, a model of streamer mechanism and the


page 21

evaluation of partial discharge magnitude. By solving Poisson’s equation, the

electric field in the cavity can be found and the field enhancement in the cavity is

leveraged to gain the field enhancement factor. This factor is used to calculate

the field enhancement due to the external applied field and the field of

accumulated charge on the cavity surface.

This model was used to simulate partial discharge pulses in a spherical

cavity and then compared with measurement results. The initial electron

generation sources were subdivided into surface emission and volume ionisation,

which are associated with detailed equations related to various physical

parameters of the dielectrics.

The real charge magnitude of the partial discharge is determined by

C*UPD, where UPD is the voltage reduction across the cavity during the

discharge event and C is the capacitance of the cavity which is dependent on

cavity geometry [31]. The apparent charge magnitude is calculated as the

induced charge on the measured electrode, which is reliant on cavity location in

the test object, cavity shape and cavity orientation of the applied electric field

[27,28,50].

This model has been simulated and quantitatively compared with

measurement data and it presented a good agreement between simulation and

measurement. A similar discharge model using a comparable method of field

enhancement estimation was used to investigate discharge behaviours in a

spherical cavity embedded in epoxy resin [51]. A stochastic approach has been

used to simulate cavity discharges with a streamer mechanism to analyse effects

of aging on discharge activities [32]. These models have successfully simulated

cavity discharges within material of epoxy resin and produced simulation results

with good agreement to measured data. However, this research was only

conducted at a single value of applied frequency of 50 Hz.

2.4.4 Finite element analysis model

A dynamic electric field-based model has been developed by Forssen to

investigate partial discharge characteristics [52] using finite element analysis


page 22

(FEA) method. Partial discharge behaviours in a cylindrical cavity surrounded by

a solid dielectric under various applied frequencies have been simulated by this

model. This model was run dynamically and interfaced with a MATLAB code to

calculate partial discharge characteristics. The model includes an insulation

material with a cylindrical cavity inside and two spherical electrodes. A partial

discharge is simulated by an instantaneous change of cavity conductivity during

the discharge from the insulating to conducting state, i.e. increase of cavity

conductivity and the electric field of the whole model is obtained numerically by

using the finite element analysis method. The apparent charge is computed by

integrating the current through the ground electrode over the discharge duration.

The charge decay in the cavity is modelled by the change of cavity surface

conductivity. The simulation results of partial discharge characteristics at

frequency range of 0.01 Hz to 100 Hz were then verified with experimental data

to discuss effects of physical parameters on partial discharge behaviours.

However, this model did not take into account decay mechanisms of space

charges generated after a partial discharge. Illias improved this model to study

partial discharge behaviours in a spherical cavity within a dielectric under

various applied frequencies [35]. The expansion of the partial discharge model in

[35] included the introduction of a charge decay rate via a charge decay time

constant to simulate discharge activities in a spherical void. However, this

research did not investigate partial discharge behaviours at very low frequency of

0.1 Hz, and the charge decay constant was assumed to be independent of applied

voltage amplitudes and frequencies.

2.5 Initial electron generation rate

One of the conditions of partial discharge inception is that an initial starting

electron must be available to initiate the electron avalanche [36]. Free electrons

generated within a cavity are generally from two main sources: surface emission

and volume ionisation [18,31].


page 23

2.5.1 Surface emission

Surface emission is an electron generation mechanism in which free

electrons are generated from the cavity surface under the effects of electric stress

and temperature. Free electrons are mainly from an electron detrapping process

of shallow traps near or on the cavity surface, injected electrons from electrodes,

electrons accumulated on the cavity surface after a discharge and electrons

emitted from ionised impact processes. Under ongoing partial discharge pulses,

electrons emitted from the cavity surface are the main sources of free electrons

[16,22]. The surface-emitted electron rate is further enhanced by increasing the

electric stress or the temperature in the cavity [54]. The initial electron generation

rate is strongly dependent on the applied voltage level, insulation material

characteristics and the geometry and location of the cavity within the dielectric.

Electron avalanches can be developed along the void surface which is

parallel to the local electric field. When a free electron is released from the cavity

surface due to photoionisation, the ionised process of electrons can be triggered

along the cavity wall. Thus, the electron avalanche developed from this process

may cause free electrons to be deposited with high density on a small area of the

cavity surface. This results in a similar amount of positive charges trapped at the

material region where accumulated electrons exist. This phenomenon usually

occurs in a relatively narrow cavity which is parallel to the applied field.

2.5.2 Volume ionisation

Volume ionisation is a process under which free electrons are emitted by

radiative gas ionisation between energetic photons and gas molecules [55]. As a

result, free electrons are generated from the detachment of electrons and positive

ions. This ionisation rate is dependent on gas pressure, gas volume exposed to the

volume ionisation and gas contents. Volume ionisation is the main source of

initial free electrons in a virgin cavity which has never been exposed to partial

discharge occurrence as the electron detrapping energy required from the unaged

cavity surface is generally higher than that in an aged cavity [31]. Moreover, a


page 24

free electron can be generated by the photoionisation mechanism, where gas

molecules absorb photons with sufficient energy to release electrons.

2.6 Parameters affecting partial discharge activity

Partial discharge characteristics in a cavity within a solid dielectric are

generally affected by the applied electric stresses and cavity conditions. The

electric stress characteristics influencing partial discharge activities include the

magnitude, waveform and frequency of applied voltage [17,18,33,56,57]. Cavity

conditions that affect partial discharge characteristics are the size and shape of

cavity, cavity location within the insulation and gas parameters in the cavity such

as humidity and pressure [58-61]. Physical parameters with effects on partial

discharge activities are time constants related to charge transport and decay rate,

the statistical time lag and the inception field.

2.6.1 Time constants

Free charges generated from a partial discharge are accumulated on the

cavity surface and will decay with time [14,19-20]. These charges can decay via

charge recombination in the cavity, charge conduction along the cavity surface,

charge diffusion into deeper traps on the cavity surface or charge neutralisation

by gas ions in the cavity. The charge decay rate is controlled by several physical

time constants such as cavity surface time constant, s, the effective charge decay

time constant, decay, and the material time constant, mat [18,31,33]. These time

constants have a significant effect on partial discharge characteristics such as

partial discharge magnitude level and phase distribution.

Free charges generated after a partial discharge event are deposited on the

cavity surface and are able to move freely along the cavity surface via charge

conduction. During this movement, these charges have a possibility of

recombination when they meet with opposite sign charges, resulting in a decrease

in the amount of free charges. This decay rate is regulated by the cavity surface

time constant, s, which is strongly dependent on the cavity surface conductivity,

s [19,28-30,32]. The higher the value of s is, the faster the charge movement is,


page 25

resulting in higher chances of charge recombination. Therefore, the initial

electron generation rate is reduced between two consecutive discharges [18].

Cavity surface conductivity is increased after long exposure to repetitive

discharges due to chemical deterioration and aging conditions [63,65]. If the

cavity surface time constant s is smaller than the period of applied voltage, the

charge decay via cavity surface conduction is substantial.

A certain amount of charges accumulated on the cavity surface will be

trapped in shallow traps on the surface. These charges may diffuse into deeper

traps in the cavity surface, or may diffuse further into the bulk insulation material

after a certain time. The rate of this movement can be assigned a charge decay

time constant, decay [31-32,51]. A shorter time constant reflects a faster rate of

charge transport process from shallow traps into deeper traps. If this time

constant decay is smaller than the time period of applied voltage, it means there is

a considerable surface charge transport into deeper traps. Consequently, the

surface emission of electrons is reduced but the local electric field in the cavity is

hardly changed as these charges still have a contribution to the surface charge

field. However, electrons in deeper traps are less likely to contribute to igniting a

partial discharge than those trapped in shallow traps.

Surface charges left on the cavity wall after a partial discharge event may

also diffuse into the bulk insulation via volume conduction because, realistically,

the material always has a finite value of conductivity. Hence, the amount of free

charges accumulated on the cavity surface may decrease with time. The rate of

surface charge diffusion via this charge transport process is determined by the

material time constant, mat [22], which is obviously dependent on the material

conductivity. A relatively long time constant mat indicates a slow charge decay

rate, which hardly changes the local electric field and the number of free

electrons and vice versa. In fact, the time constant mat is considerable compared

with the period of applied voltage in this thesis due to the very low conductivity

of the material used in partial discharge experiments, and thus this charge decay

process is fairly slow and can be ignored in its contribution to partial discharge

activities.


page 26

2.6.2 Statistical time lag

Two conditions must be fulfilled to incept a partial discharge: the electric

field in the cavity must exceed the inception value and a free electron must be

available to ignite an electron avalanche. When the local electric field in the

cavity is higher than the inception value, Einc, there may not be a starting electron

to initiate a discharge. Such a case would have a time delay for partial discharge

occurrence when the inception threshold is exceeded. The average time delay

between the instant the inception field is exceeded and the moment a partial

discharge occurs is called the statistical time lag, stat [31,33]. Because of stat,

partial discharges usually occur at electric stress larger than the inception value.

As the electron generation rate varies with stress conditions, the statistical

time lag is strongly dependent on the frequency and amplitude of the applied

voltage. At high frequency, time intervals between consecutive discharges are

relatively small, thus fewer free charges vanish after a partial discharge event. As

a result, there are more charges available for the following discharge. Therefore,

the electron generation rate is higher and the next partial discharge may be

incepted immediately when the electric field exceeds the critical value, thus

decreasing the statistical time lag. On the other hand, fewer free charges are

available after a discharge at low frequency as more free charges are likely to

decay due to relatively long time intervals between consecutive partial

discharges. Therefore, the electron generation rate is smaller when the following

partial discharge is expected to happen. It is a reason for longer statistical time

lag as partial discharges may not occur immediately after the inception value is

exceeded [66]. Regarding amplitude dependence, stat is likely to decrease with

the increase of applied voltage level as free electron emission is enhanced at a

higher applied voltage.

The statistical time lag can differ between successive partial discharges.

The waiting time for the first partial discharge could be longer than that of

following discharges within the same applied voltage cycle. A cavity which has

not yet been exposed to partial discharge occurrence lacks free electrons as

sources of available electrons are limited. However, there are abundant free


page 27

charges generated after the first partial discharge is incepted which act as the

main source of free electrons for the following partial discharges. Therefore, the

waiting time of free electrons for subsequent partial discharges is reduced and

shorter than the first partial discharge. As the accumulated charges on the cavity

surface decay in time, the number of charges ready for the next partial discharge

decreases. Thus, the time delay between consecutive partial discharges is

dependent on the charge decay rate and free electron availability [32].

2.6.3 Inception field

The inception value of the electric field is the minimum field in the cavity

required for a discharge to ignite. This value for partial discharges with the

streamer process in a cavity is dependent on many parameters such as cavity

geometry, pressure, material permittivity, ionisation mechanisms and the gap

between two electrodes [31,32,51,66]. The value of the inception field for

streamer type partial discharge could be calculated by

1

( )inc n

cr

E BE p

p pd

(2.7)

where cr

E p , B and n are parameters related to the gas ionisation process,

p is the pressure in the void and d is the cavity diameter. For air, these parameters

are cr

E p = 24.2 VPa-1m-1, n = 0.5 and B = 8.6 Pa1/2 [28,31,36].

2.7 Conclusion

This chapter reviewed literature related to partial discharge, especially

corona discharge and internal discharge in cavities. Physical mechanisms leading

to partial discharge were discussed in detail. To date, several well-known models

have been developed to simulate discharges in cavities: the th ree capacitance

model, Pedersen’s model and finite element analysis based model. The

advantages and drawbacks of these simulation models were discussed. These

models provide a practical approach for studying cavity discharges within a solid

insulation material to identify critical physical parameters affecting discharge

behaviours. The parameters of significance include the statistical time lag, charge


page 28

decay time constant and inception field. The availability of initial electrons also

influences discharge characteristics. The following chapter presents the

development of an improved approach built on the finite element analysis based

model. This new approach involves a minimal set of adjustable parameters and

adaptable charge decay time constant depending on applied frequency.

Chapter 3: Modelling of Internal

Discharge

3.1 Introduction

The partial discharge model proposed in this thesis is an improvement of

the finite element analysis (FEA) model developed by previous researchers

[35,52]. The proposed model involves a minimal set of adjustable parameters: the

number of free electrons generated at inception field, number of free electrons

due to volume ionisation and surface charge decay constant which is adopted to

applied frequency. This model is built in a finite element method based software,

i.e. COMSOL Multiphysics, and interconnected with MATLAB program

language to simulate discharges in a cylindrical cavity embedded in a solid

dielectric material. The modelling of partial discharge is described in detail

together with governing equations. Sections in this chapter cover model creation

and settings in COMSOL, cavity discharge process simulation, model of initial

electron generation rate and flow charge of partial discharge simulation. In order

to reduce the simulation time, several assumptions proposed in the model to

simplify the work are explained thoroughly. The advantage of this improved

model over the previous work is also discussed.

The developed model has been tested under various conditions of applied

stress in terms of voltage amplitudes and frequencies. The obtained simulated

data are then compared with measurement results to identify critical parameters

affecting the discharge process in the cavity at different stress conditions. The

determined critical parameters are the field inception and extinction, charge

decay constant and conductivity of the cavity surface. Physical phenomena

considered to directly influence discharge activities are the charge conduction

along cavity surfaces and the initial electron generation rate.

Chapter 3: Modelling of Internal Discharge

page 30

3.2 Finite Element Method model

The model was developed in symmetric two-dimensional (2D) axis of finite

element method (FEM) based software, i.e. COMSOL Multiphysics, and was

interfaced with MATLAB program language. The electric field and electric

potential in the model are solved by using partial differential equations. Two-

dimensional symmetric geometry of the model was chosen to reduce the

simulation time as fewer meshing elements required to solve the finite element

method in the software were employed during the calculation. In the COMSOL

environment, the physics of “electric currents” are used to solve the electric field

and potential distribution in the model.

3.2.1 Field model equation

The distribution of electric potential in the model is governed by several

mathematical equations. The fundamental equations of the field model are:

fD (3.1)

0

ffJ

t

(3.2)

where equation (3.1) is the field equation from Gauss’ law, and equation

(3.2) is the current continuity equation [67]. In these equations, D is the electric

displacement (flux density), f is the free charge density and fJ is the free

current density. Since D E and E V where is the material

permittivity, E is the electric field and V is the electric potential, equation (3.1)

can be rewritten as

)( fV (3.3)

As fJ E , by substituting equation (3.3) into equation (3.2), it can be

expressed as follows

( ) ( ) 0V V

t

(3.4)

where is the material electrical conductivity.


page 31

Equation (3.4) is solved by using the finite element method in order to

determine the electric potential distribution in the field model.

3.2.2 Model geometry and meshing

Details of the test sample model geometry developed in the simulation

software are shown in Figure 3.1. The model is a homogeneous solid dielectric

material with a thickness of 3.0 mm and radius of 25 mm. A cylindrical void with

1 mm radius and 1 mm height is introduced at the centre of symmetrical axes

(horizontal r-axis and vertical z-axis) to represent a cavity embedded completely

inside a solid insulation material. The cavity surface of 0.1 mm is also created to

simulate the charge mobility on the cavity wall. The upper electrode is applied

with sinusoidal voltage at various frequencies whilst the lower electrode is

always grounded. A meshing method with 2D unstructured triangular elements is

used. The resolutions of cavity and cavity surface meshes are set at “fine” in the

software as higher accuracy of field calculation is needed within these areas. The

model meshing is shown in Figure 3.2.

High voltage electrode

Dielectric Material

Void surface

Ground Electrode

Cylindrical void

Symmetric axis

Figure 3.1 The axial-symmetric 2D model

3.2.3 Boundary and domain settings

Assigned constants, sub-domain settings and boundary settings of the

model used for simulation are summarised in Table 3.1 to Table 3.3. Boundary

line settings in the model are shown in Figure 3.3. In Table 3.3, n is the normal

vector to a boundary and J is the total current density.


page 32

Figure 3.2 2D model geometry with meshed elements

1

2

34

56

12

11

107

8

9

13 14

Figure 3.3 Boundary line numbers in the model

Table 3.1 Defined constants for finite element method model

Description Symbol Unit

Applied voltage amplitude Urms kV

Number of simulation cycles n

Time step during no PD t s

Time step during PD dt s

Relative permittivity of insulation r

Cavity surface relative permittivity r

Cavity relative permittivity cav

Cavity conductivity during no PD cavL S/m

Cavity conductivity during PD cavH S/m

Electric inception field Einc V/m

Electric extinction field Eext V/m

Cavity surface low conductivity sL S/m

Cavity surface high conductivity sH S/m

Conductivity of dielectric material mat S/m


page 33

Table 3.2 Electrical characteristics of subdomain settings

Subdomain Relative permittivity Electrical conductivity

Dielectric material r mat

Cavity surface r s

Cavity cav cav

Table 3.3 Boundary line settings

Boundary line Boundary condition Expression

1,3,5,7,9 Symmetrical axis 0r

11 Electric potential * (2)*sin(2* * * )rmsV U sqrt pi f t

2 Ground 0V

14 Electric insulation * 0n J

4,6,8,10,12,13 Continuity 1 2*( ) 0n J J

After the model is developed and set with appropriate settings, it is meshed

and ready to be solved with the physics of “Electric Currents” analysis. As the

simulation is required to run in a timely manner, the “Time Dependent” solver is

selected in the tab “Study”. When there is no PD, the time step, t, is defined at

the value of 1/500f where f is the applied frequency, i.e. 4x10-5 s and 0.02 s at 50

Hz and 0.1 Hz, respectively; otherwise, PD time step, dt, is set at 1x10-9 s at both

frequencies during the PD occurrence. Then, the model is solved by clicking the

“Compute” button in the Study tab. The electric field and potentials can be found

under the Results tab. Postprocessing of the model solution to obtain parameters

of interest such as field distribution and electric potentials is done using “2D

Plot” and “Derived Values” functions within this tab. The solved model is then

saved as a .m file so that it can be interfaced and edited in MATLAB program.

3.3 Cavity discharge model and charge magnitude calculation

There is an electric field applied to the test object and also that from surface

charges on the cavity surfaces. Cavity discharges are driven by the local

enhancement of the electric field due to the mismatch of relative permittivity of

the cavity and solid dielectric material. In this model, PD is simulated

dynamically and the electric field in the cavity is calculated numerically at each


page 34

time step by solving the partial differential equation via the finite element

method. From the simulation results, the electric field distribution is symmetrical

along the r and z-axes. Hence, the assumption that there is symmetry of electric

field and charge distribution in the cavity along both axes can be made before

and after a PD occurrence. As a result, this can be done in the finite element

method model by assuming that discharges occur in the whole cavity.

In order to reduce the simulation time, there are several assumptions to

simplify the finite element method model developed. Firstly, details of PD

mechanisms, such as the mobility of free electrons and ions during the

propagation of electron avalanches in the cavity, are not included in detail. This

electron avalanche phenomenon has a considerable impact on cavity surface

characteristics after each PD event but it is difficult to determine the physical

parameters related to the cavity surface itself. Instead, a discharge is assumed to

occur in the whole cavity. In the model, this assumption can be made by

changing the conductivity of the whole cavity during PD occurrence.

Secondly, it is assumed that cavity discharges have the characteristics of

streamer discharges. Streamer propagation in air by charge carriers under the

influence of drift and diffusion has been modelled in previous research [68].

Partial discharge development has also been simulated by using particle

modelling, which studies the particle dynamics during the discharge process [69].

However, details of streamer mechanisms are not simulated in this work as the

parameters of interest for PD are charge magnitude and phase only. Hence, a PD

event is assumed to influence the whole cavity when it occurs along the void

symmetrical axis. As a result, an instantaneous electric field is extracted at the

centre of the cavity in the model and it is only dependent on time.

3.3.1 Cavity conductivity

When discharges are simulated dynamically, a discharge occurrence can be

illustrated by changing the physical state of the cavity from a non-conducting to

conducting condition as PD is assumed to affect the whole cavity. This can be

done by increasing the cavity conductivity from its initial value when there is no


page 35

PD occurrence, to a higher conductivity value during the PD activity. When the

cavity conductivity is increased, it causes the electric field in the cavity to drop

continuously within discharge duration. When the field is below the extinction

value, the discharge event stops and cavity conductivity recovers to its initial

state, or non-conducting condition. The value of cavity conductivity during the

conducting state, i.e. during a PD process, can be estimated via electron

conductivity in plasma as conductivity due to ions is assumed to be insignificant.

In [70], the electron conductivity in plasma, e, can be computed by using

2

e e ee

e e

N

m c

(3.5)

where e is the coefficient related to electron energy distribution and mean

free path, me is the mass of the electron, e is the electron mean free path, ce is

the electron thermal velocity and Ne is the electron density, which can be

calculated as

34 3

e

q eN

r (3.6)

where q/e is the number of electrons in the streamer channel, q is total

charge in the streamer channel, e is the electric charge of the electron and r is the

cavity radius. During the PD process, the current flow through the cavity, Icav(t)

increases from zero to a certain maximum value while the electric field begins to

decrease. Then, the current Icav(t) starts to drop while the cavity field Ecav(t) keeps

decreasing. A PD ceases when the cavity field drops below the extinction field,

Eext. After the PD event stops, the cavity conductivity, cav, is reset to its initial

value and the cavity current disappears.

3.3.2 Discharge magnitude

An advantage of this model is that PD charge magnitudes can be calculated

numerically as discharges are modelled dynamically. From the solved model in

COMSOL, it is possible to calculate the real and apparent charge for each PD

event by integrating the current flowing through the cavity and through the

ground electrode, over the discharge time duration, that is


page 36

( )

t dt

PD

t

q I t dt

(3.7)

The current flowing through the cavity and ground electrode is computed

by integration of the current density over the cavity cross-section area and

ground electrode surface area, respectively. The current density is obtained from

the solved model and dependent on the electric field distribution. As the field

distribution in the test sample is not uniform due to the cavity presence, the finite

element method is very helpful in solving electric field distribution and facilitates

dynamic calculation of both real and apparent charges during PD occurrence.

3.3.3 Charge decay simulation

Free charges generated after PD activities are eventually accumulated on

the cavity surface due to the applied electric field. These accumulated charges

decay in time via several mechanisms. Firstly, opposite charges have chances to

neutralise others via the recombination process during the movement path under

the applied field. Secondly, during the discharge process, when the first charge

group arrives on the cavity surface, it repels the next charges coming and thus

delays their arriving time. Consequently, it is assumed that there are charges

remaining on the cavity surface for a certain period of time. Some charges will be

trapped in shallow traps on the cavity surface and may diffuse into deeper traps.

Others could be moved along the cavity walls and dispersed into the bulk

insulation.

The accumulated surface charges will generate a residual electric field, Eq,

which has a contribution to the local field in the cavity. Figure 3.4 shows the

behaviour of space charges left after a PD as a function of cavity field direction.

The cavity field is a summation of the electric field due to the external applied

voltage, fcE0, and the residual field, Eq, where E0 is the external electric field in

the test sample and fc is the modification factor due to the permittivity mismatch

between the cavity and the dielectric material. As can be seen in Figure 3.4a, the

majority of accumulated charges still remain on the cavity surface when Ecav and

Eq have opposite directions. When Ecav has the same direction as Eq as in Figure


page 37

3.4b, a number of surface charges will vanish due to the mobility of space

charges under the effects of the local electric field. As Ecav increases, the charge

movement along the cavity wall is faster, resulting in an increase of cavity

surface conductivity.

EqEcavE0 fcE0

EqEcavE0 fcE0

(a) Opposite direction (b) Same direction

Figure 3.4 Behaviours of space charges left after a PD as a function of field

directions

To simulate this charge dynamic due to local field alternation, it is assumed

that the cavity surface conductivity, s, will increase from its initial value, sL, to

a higher value, sH, to model the charge mobility when Ecav and Eq have the same

direction. On the other hand, the conductivity of the cavity surface will resume

its initial value, sL, when Ecav and Eq have opposite directions.

3.4 Modelling of initial electron generation rate

A PD is incepted if there is an initial free electron to ignite electron

avalanches when the inception field is exceeded. The sources of initial electrons

are from surface emission and volume ionisation. The quantity of free electrons

will influence the discharge characteristics in terms of PD magnitude, phase

position and repetition rate.

The amount of available electrons to ignite a PD defined in this research is

the total electron generation rate (EGR), NPD(t). As there are two main sources of

initial electrons, it is assumed that the total electron generation rate is a

summation of electron generation rate due to surface emission, Nes(t), and

electrons released by volume ionisation, Nev, that is


page 38

( ) ( )PD es evN t N t N (3.8)

As discharges are assumed to occur along the symmetrical axis, the electron

generation rate due to surface emission Nes(t) is dependent on time only.

It is assumed that free electrons due to surface emission are mainly from

detrapping charges from the shallow traps on the cavity surface. Hence, the

amount of these charges is strongly dependent on the local electric field in the

cavity. To simplify the model, a simple equation is introduced to calculate the

number of free electrons due to surface emission as follows

( )( ) cav

es

inc

E tN t N

E (3.9)

where N is the number of free electrons generated at the inception field Einc,

and Ecav(t) is the local electric field in the cavity at a time t. A similar equation

has been introduced in [33] to represent the dependence of electron generation on

the applied voltage. Equation (3.9) is motivated by the Richardson-Schottky law

[31] because many of the material parameters in the Richardson-Schottky law are

difficult to quantify. Thus, this equation aims to simulate an acceptable field

dependence of electron generation rate instead of describing a detailed physical

model with a number of unknown parameters.

After a PD occurrence, free electrons generated during the discharge

process decay in time via the previously mentioned mechanisms such as charge

recombination and diffusion into deeper traps. Hence, these decayed charges are

assumed to no longer contribute to the initial electron generation rate to trigger

the following discharge when it is likely to occur. This decay rate is determined

by a charge decay time constant, decay. It is assumed that charges decay

exponentially with time. The term of charge decay time constant, decay, has been

introduced successfully in previous research [19,71-72], to model the

disappearance rate of free charges accumulated on the cavity surface. Moreover,

the electron generation rate due to surface emission has been stated as a function

of increasing electric field after a discharge [27,48-49]. It is assumed that this is

exponentially dependent on the ratio of the cavity electric field and inception

field. As a result, equation (3.9) can be rewritten as


page 39

( ) ( )( ) exp expcav cavPD

es

inc decay inc

E t E tt tN t N

E E

(3.10)

where tPD is the moment the previous discharge occurred and (t-tPD) is the

time elapsed from the previous discharge. Hence, equation (3.8) can be expressed

in full to illustrate the total initial electron generation rate as

( ) ( )( ) exp expcav cavPD

PD ev

inc decay inc

E t E tt tN t N N

E E

(3.11)

In this equation, the three constants, i.e. N, decay and Nev, are freely

adjustable to fit the simulation data with measurement results.

A PD is incepted when two conditions are met: the local electric field

exceeds the inception value and a starting electron is available. The free electron

condition is dependent on the electron generation rate. Due to the stochastic

nature of PD activities, a probability approach is used to determine the likelihood

of PD occurrence. The possibility of PD occurrence, P(t), is calculated when the

cavity field Ecav(t) is larger than inception value Einc. P(t) can be determined by

( ) ( )PDP t N t t (3.12)

where t is the time interval of calculation. P(t) is then compared with a

random number R between 0 and 1. A PD will only occur when P(t) is larger

than R. A discharge will always be incepted if P(t) is larger than 1.

3.5 Simulation flowchart in MATLAB

3.5.1 Parameters for simulation

Table 3.4 shows the parameters used for all simulations in this work. The

number of simulated voltage cycles is 500. This allows sufficient PD

characteristics to be obtained from the simulation for analysis at both very low

frequency and power frequency. As can be seen in this table, the time step of

simulation is chosen as 1/500f when there is no PD occurrence, where f is the

frequency of applied voltage. This value guarantees the simulation time is an

acceptable time span while keeping good precision results of the electric field at

each time step. If the chosen t is too short, the total simulation time would be


page 40

lengthened significantly with little benefits in the simulated results. Otherwise, if

it is too large, the electric field varies too much in one time step, resulting in less

accuracy of the PD phase occurrence if there is any.

Table 3.4 Values of all constants used for all simulations

Description Symbol Value

Unit 0.1 Hz 50 Hz

Applied voltage amplitude Urms 8, 9, 10 kV

Number of simulation cycles n 500

Time step during no PD t 1/500f s

Time step during PD dt 1x10-9 s

Relative permittivity of insulation r 3.1

Cavity surface relative permittivity r 3.1

Cavity relative permittivity cav 1

Cavity conductivity during no PD cavL 0 S/m

Cavity conductivity during PD cavH 5x10-3 S/m

Electric inception field Einc 3.93x106 V/m

Electric extinction field Eext 1x106 V/m

Cavity surface low conductivity sL 0 S/m

Cavity surface high conductivity sH 1x10-11 1x10-9 S/m

When a PD event is set to occur, the time step during PD occurrence, dt, is

adjusted to 1 ns. Again, this value is chosen to balance the simulation time and

the precision of charge magnitude obtained. If it is set longer than 1 ns, the

simulation time will be shorter but the discharge magnitude will also be less

accurate as the rate of electric field change in the cavity would increase

considerably during PD occurrence. On the other hand, simulation time will be

increased greatly for unnoticeable benefits of discharge magnitude value when

the time step during PD, dt, is shorter than 1 ns. Moreover, the value of 1 ns is

reasonable as a discharge process normally happens within a fraction of of a

nanosecond.

It is assumed that the cavity is filled with air. When there is no PD

occurrence, the cavity conductivity is set to 0 S/m as no current flows through the

cavity during these moments. During PD occurrence, the physical state of the

cavity is changed from non-conducting to conducting, which allows discharge

currents flowing through the cavity. As it is assumed that a discharge affects the


page 41

whole cavity, the conductivity of the cavity, cav, is set equal to 5x10-3 S/m

during the PD process. This value is reasonable to keep the simulation time short

enough while ensuring the cavity field does not decrease too fast during a

discharge. If cav is chosen higher than 5x10-3 S/m, the cavity field will drop

significantly in a short time and the discharge will be stopped at a field level

much lower than the extinction value, resulting in a much larger PD charge

magnitude. On the other hand, if cav is set lower than 5x10-3 S/m, it is found that

simulation time increases greatly while there are unnoticeable changes of

simulation results.

The thickness of the cavity surface layer is set equal to 0.1 mm. Several

values around this choice were trialled, which showed that the difference of

electric field distribution in the model with various cavity surface thicknesses is

quite small. The simulation time also increased considerably if this thickness was

set too small, i.e. lower than 0.1 mm, as many more meshing elements were

required to solve the model.

The relative permittivity of the insulation material, r, is determined from

the measurement of test samples in the laboratory using dielectric frequency

response analysis in the range from 0.1 Hz to 50 Hz. This value of 3.1 is

acceptable because the relative permittivity of Acrylonitrile-Butadiene-Styrene, a

type of thermoplastic resin, is within the range of 2.8 to 3.2 found in the literature

[75]. The cavity surface permittivity is set equal to r as it is considered a part of

the solid insulation material. The cavity relative permittivity, cav, is set to 1 as it

is assumed the cavity is filled with air.

The simulation value of the inception field, Einc, is calculated from equation

(2.7), which results in 3.93x106 V/m. The value of the extinction field, Eext,

should be lower than the inception field and is chosen based on the minimum

measured discharge. If this value is set too high, it will cause the discharge to

occur within a shorter time, which results in less discharge magnitude. On the

other hand, discharge will happen for a long time which increases the discharge

magnitude if Eext is set too low. After experimenting with numerous values, it

was found that Eext is equal to 1x106 V/m for all simulations.


page 42

It is assumed that surface charges do not decay when the cavity field Ecav

and residual field Eq have opposite directions. Thus, the initial value of cavity

surface conductivity, sL, is set equal to 0 S/m in both cases of applied

frequencies. When Ecav and Eq have the same direction, sH is equal to 1x10-9

S/m at frequency of 50 Hz and 1x10-11 S/m at very low frequency. These values

were determined after numerous trials to fit the simulated PD repetition rate with

the measurement results.

In equation (3.11), the values of N, decay and Nev are freely adjustable to fit

the simulation results with measured data. As these parameters are dependent on

applied frequency and voltage amplitude, their values would be different in

various scenarios. By applying trial and error procedures to minimise differences

with the expected values, the values of N, decay and Nev have been determined as

shown in Table 3.5 and are described in detail in Chapter 7 for comparison

between simulation and measurement results.

Table 3.5 Values of adjustable parameters for simulation

Frequency

(Hz)

Applied voltage

(kV) N

decay

(ms) Nev

0.1

8 30 1000 2

9 15 800 3

10 30 800 3

50

8 2500 2 40

9 2500 2 50

10 3500 2 50

3.5.2 Program flowchart

A loop program was developed in MATLAB programming language to

determine all simulation parameters and interface with the finite element method

model to solve the electric field distribution. The program includes iterations

over time, probability determination of a discharge event, calculation of

discharge characteristics such as charge magnitude, phase occurrence and

discharge duration, calculation of initial electron generation rate and post-

processing of simulation results. Flowcharts of the main code, solving the finite


page 43

element method model at each time step and PD occurrence determination, are

shown in Figure 3.5 to Figure 3.7.

Start

Model initialised

Increase time step End time?

Update boundary

and subdomain

Ecav > Einc ?

Calculate P

P > R ?

cav cavH

Solve FEM model

Ecav < Eext ?

Eq/Ecav > 0

s sL

s sH

cav cavL

Save results

EndY

Y

Y

Y

N

N

N

N

Solve FEM model

N

Y

Figure 3.5 Main flowchart in MATLAB

Input

Mapping current solutions

to extended mesh

Update subdomain and

boundary settings

Solve FEM model

Output

Figure 3.6 Flowchart of “Solve FEM model” at each time step


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P > R

Input

Calculate electron

generation rate, NPD(t)

Compute probability P

Generate random

number R

Output

Discharge is

set to occur

No discharge

occurs

Update subdomain and

boundary settings

Y N

Figure 3.7 Flowchart of PD occurrence determination

Initially, the MATLAB workspace was cleared to ensure there are no

foreign variables affecting the simulation process. Then, all constants, variables

and parameters required for simulation were initialised to predefined values as

well as the dimensions of the test object and the cavity. The applied frequency,

voltage amplitude and number of simulated cycles were also determined in this

step.

Next, the finite element method model was created with input parameters

defined in the previous steps. The model geometry was then meshed and

boundary settings were chosen with values that have been assigned. After all

settings and the sub-domain were set, the model was solved with initial

conditions to give the necessary data, such as electric field and potential

distribution, required to commence the main loop.


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After that, the main loop was launched. The MATLAB code interacts with

the finite element method model to update the boundary and sub-domain settings

at each time step. The electric field and potential distribution were extracted from

the solved model at each time step to update the settings for the next time step

and determine the likelihood of PD occurrence. The electric field in the cavity,

Ecav was regularly compared with the inception value Einc. If Ecav was larger than

Einc, the probability calculation of PD occurrence was triggered. The total initial

electron generation rate was computed and then the likelihood of a PD event was

calculated using equation (3.12). Then, P(t) was compared with a random

number R in the range from 0 to 1. If P(t) was larger than R, a discharge was

assumed to happen. If not, the no-discharge condition still remained and the loop

moved on to the next time step.

When a discharge occurrence is determined, the distribution of the electric

field and equipotential lines in the model just before and after the first two PDs is

saved. In general, solved models at any time step can be saved providing that

they are predefined before running the main program. In this work, the solved

models of the first two discharges were chosen due to interest in the surface

charge effect on the local electric field distribution just before and after the

discharge. For the first PD, it is assumed that no surface charges existed in the

cavity before discharge occurrence.

After the first PD, surface charges accumulated on the cavity surface have a

considerable influence on the field distribution before the second PD occurrence.

During the discharging state, the conductivity of the cavity was increased to the

predefined value as mentioned above. Boundary and sub-domain settings were

updated to solve the model with discharge occurrence conditions. The time step

was changed to 1 ns and the electric field and flown current in the cavity were

extracted continuously from the model at each time step to calculate the

discharge magnitude during the PD. Discharge was set to stop when Ecav was

lower than the extinction value, Eext. When the discharge ceased, the cavity

conductivity returned to its initial value and the main loop moved on to the next


page 46

time step. The discharge magnitude and phase of occurrence for the

corresponding discharge were saved in the MATLAB workspace.

The main loop of program continued to run until the predefined number of

voltage cycles was reached. The discharge phase and magnitude of all PDs

occurring during the simulation were saved and then analysed. From these

parameters, the phase-resolved PD patterns at simulated applied voltage and

frequency can be plotted and compared with measurement results from

experiments. Details of PD patterns are described further in Chapter 4.

3.6 Conclusion

This chapter described the development of a model of partial discharge

occurring in a cavity surrounded by solid dielectric material, using a combined

software platform of COMSOL interfaced with MATLAB. The physical

behaviours of partial discharge were explained in detail with mathematical

equations and how the finite element method model represents each physical

phenomenon accordingly. The advantages of this model are:

1. With the help of the finite element method, the electric field and potential

distribution in any void geometry within a solid insulation material can be

obtained at any time related to the discharge moment, i.e. before, during and after

the discharge.

2. Discharge events can be simulated dynamically. Moreover, real and

apparent discharge magnitudes can be calculated numerically from currents

flowing through the cavity and through the ground electrode, correspondingly

during the discharge activity under excitation of very low frequency and power

frequency.

3. The distribution of electric field and potential in the material can be

plotted graphically which gives an insight into pre-discharge processes.

4. The conduction of accumulated surface charges along the cavity can be

simulated by varying the conductivity of the cavity surface under various

frequency excitations.


page 47

The next chapter describes the preparation of the real test samples modelled

in this chapter. The experimental setup including the partial discharge

measurement system and how measurements were performed are also explained.

Chapter 4: Test Setup and Partial

Discharge Measurements

4.1 Introduction

In this chapter, partial discharge measurement setups in the laboratory are

presented in detail to explain how to detect different types of discharges, i.e.

corona discharges and internal discharges in cavities, using an IEC 60270 [10]

compliant testing circuit. The instruments and components required for the

measurement circuit are introduced in Section 4.2. The raw discharge data

recorded from measurements are extracted for further analysis via phase-resolved

partial discharge (PRPD) analysis. A set of parameters for characterising

discharge behaviour are presented in Section 4.3. The design and fabrication of

test objects to produce discharges is described in Section 4.4. Section 4.5

explains the discharge measurement procedures at various stress conditions to

ensure that obtained experimental data are consistent and accurate.

4.2 Partial discharge measurement setup

The partial discharge experiments of this research were conducted in the

UNSW High Voltage laboratory. A partial discharge measurement circuit fully

compliant with specifications in IEC 60270 Standard was used as shown in

Figure 4.1. The main components of the measuring circuit comprise a variable

high voltage power source, blocking capacitor Ck, test object Cx and a measuring

impedance Z which is part of the quadripole unit (CPL542). The detailed PD

measurement setups in the laboratory are shown in Figure 4.2 and Figure 4.3. For

variable frequency high voltage power source, an arbitrary function generator

(Agilent Keysight HB35000B) was connected to a high voltage amplifier (Trek

20/20C-HS). This function generator is able to generate various waveforms at

Chapter 4: Test Setup and Partial Discharge Measurements

page 49

low voltage, including preset and user customised defined signals. The high

voltage amplifier is capable of amplifying the input signal with a gain of 2000

and able to produce maximum voltage amplitude of 20 kV. Specifications of the

function generator and high voltage amplifier are provided in Appendix A. The

blocking capacitor has a value of 1.1 nF and discharge-free up to 50 kV.

The PD measurement device is an Mtronix Advanced Partial Discharge

Analysis System MPD600. The measuring impedance Z is placed in the coupling

unit CPL542 which is connected in series with the blocking capacitor. The

captured PD and applied voltage signals are sent from the coupling unit to the

acquisition unit MPD600. Here, the measured data are converted to optical

signals and then transmitted via optical fibres to the controller MCU502. Finally,

the raw data are converted back to digital electrical signals and transferred to the

computer via a USB interface.

Figure 4.1 Circuit setup for partial discharge measurement [76]

The fundamental purpose of the PD measurement circuit is to measure the

transient current pulse flowing through the test object when a discharge occurs.

During a PD occurrence, the voltage across the test object is momentarily


page 50

reduced and there is some charge movement from the blocking capacitor Ck to

the test object to compensate the voltage drop. As a result, a corresponding

voltage pulse, V0(t), develops across the measuring impedance Z due to a short

duration of current pulse, i(t), in the nanosecond range flowing in the circuit. The

amount of transferred charge in this process is defined as the apparent charge.

Figure 4.2 Partial discharge measurement setup in the laboratory

Figure 4.3 Control bench of partial discharge measurement system


page 51

The acquisition unit MPD600 [76] is the key component of this

measurement circuit. It is powered by a 12V DC battery to minimise interference

from external power supply to PD detection. This unit is capable of bipolar PD

detection in a wide range of frequencies. For consistency, throughout all the

experiments carried out in this work, the centre frequency was set at 250 kHz and

the bandwidth was set at 300 kHz. This setting complies with wide-band PD

measurements in the IEC 60270 Standard. Specifications of wide-band PD

measurements regulated by this standard are as follows:

1. 30 kHz ≤ f1 ≤ 100 kHz

2. f2 ≤ 1 MHz

3. 100 kHz ≤ f ≤ 900 kHz

where f1, f2 are the lower and upper cut-off frequencies and f is the

measurement bandwidth.

With the help of Mtronix MPD600 software, PD data can be recorded and

analysed further using a range of playback options. An example of phase-

resolved PD patterns recorded in Mtronix software Graphic User Interface (GUI)

is shown in Figure 4.4. Detailed instructions for using this software are described

in Appendix B. The raw PD data recorded can also be exported in various

formats so they can be processed in other software enviroments such as

MATLAB, Excel.

Prior to any discharge measurements, off-line calibration of the measured

circuit has to be performed by injecting a known amount of charges into the

circuit. This task is done by using the Omicron CAL542 calibrator which is able

to generate various charge magnitudes of 5 pC, 10 pC, 20 pC, 50 pC or 100 pC.

Referring to Figure 4.4, the target value of charge in the “Calibration Settings”

box is set equal to the injected specific amount of charge from the calibrator. The

calibration process is finished by pressing the “Compute” button in the Mtronix

GUI to calibrate the Mtronix software readings with the measurement circuit.

The calibrator must be disconnected from the circuit before conducting the live

PD experiments.


page 52

Figure 4.4 Mtronix MPD600 graphic user interface

The Mtronix GUI is also able to calibrate the applied voltage magnitude.

This can be done by applying a known voltage (its amplitude measured using a

separate voltage divider) to the test setup and the procedures of voltage

calibration are similar to charge calibration but under the “V” tab of the Mtronix

GUI as can be seen in Figure 4.4. The applied voltage characteristics such as

amplitude, frequency and waveform can be obtained visually from the GUI.

Users can interact with this GUI to view the phase-resolved PD pattern and PD

signal statistics instantly during the measurement.

4.3 Partial discharge analysis

The advantage of the Mtronix MPD600 software is that it allows export of

the recorded raw PD data to MATLAB compatible files for further analysis. This

function can be accessed in the “Replay” tab while playing back the

measurement recorded files to obtain the phase-resolved PD patterns. As a result,

the user can analyse and process PD data in detail to meet research interests,

including evaluation of PD sequences during the experiment or acquiring PD

magnitude and phase distributions. Although the exported files are compatible

for processing in MATLAB, codes for importing these data must be written as


page 53

these files use binary format for storing the numerical values. Thus, MATLAB

scripts have been written to import and post-process PD data to investigate PD

characteristics obtained from the measurement results. The common discharge

characteristics to be investigated are the PD repetition rate (the number of PDs

per cycle or per second), maximum and average discharge magnitudes and PD

phase distribution.

4.3.1 Basic discharge quantities

The basic parameters related to each single record discharge ith are as

follows:

– apparent discharge magnitude: qi, in pico-coulombs (pC)

– discharge polarity: pi, positive or negative

– phase position (in relation to the AC voltage cycle): i, in degrees

– moment of occurrence (relative to the start of test): ti, in seconds

Since PD phenomena are complicated and exhibit stochastic behaviour,

these basic quantities show strong statistical inconsistency. Hence, it is not

realistic to interpret PD characteristics based merely on any single discharge for

diagnosis of dielectric conditions. This has led to the introduction of integrated

discharge parameters to analyse PD activities. These integrated parameters are

derived from basic quantities. They provide the general trend of discharge

behaviour over a predefined number of AC voltage cycles [39]. These integrated

values are specified in [10] in detail and summarised as follows:

1. Average discharge current I – the summation of all absolute magnitudes

of apparent charge in a given period of time T divided by that period,

specified in amperes (A) or coulombs per second (C/s).

1

1 n

i

i

I qT

(4.1)

2. Discharge repetition rate r – the average number of PD events over a

given period of time T or a given number of AC cycles K, expressed in

pulses per second (pps) or pulses per cycle (ppc).


page 54

nr

T (4.2)

nr

K (4.3)

3. Discharge power P – the average power injected into test object

terminals due to apparent discharge over a given period of time T,

specified in watts (W).

1

1 n

i i

i

P q vT

(4.4)

4. Quadratic rate D – the summation of the square of each apparent

discharge magnitude qi over a given period of time T divided by that

period, specified in coulombs square per second (C2/s).

2

1

1 n

i

i

D qT

(4.5)

where n is the total number of discharge pulses in the given period of time

T, vi is the instantaneous value of applied voltage at the occurrence moment of

discharge qi.

Other integrated parameters associated with the apparent discharge

magnitude qi are:

1. Maximum discharge magnitude qmax – the largest magnitude of all

apparent charges recorded in a given duration of time T, expressed in

coulombs (C).

qmax = max[q1, q2, ….., qn] (4.6)

2. Average discharge magnitude qave – the average magnitude of all

apparent charges recorded in a given duration of time T, expressed in

coulombs (C).

1

1 n

ave i

i

q qn

(4.7)

4.3.2 Pulse sequence analysis

Pulse sequence analysis is a method to examine partial discharge

phenomena by evaluating the sequence of individual PDs in terms of the


page 55

relationship between two consecutive PD events [77]. The voltage difference and

the time interval between these sequential PD events are used to investigate the

‘memory’ effects of a preceding PD event on the following PD activity. These

effects are attributed to space charges accumulated after the first discharge,

especially in a case of solid dielectric material. The resultant voltage difference

patterns provide another way to characterising PD behaviour. The drawback is

that it does not exploit the phase information and more importantly, the main

concern is that it does not directly account for the effect of the discharge

magnitude. For insulation diagnostics, the discharge magnitude is always the

most important parameter. Therefore, this research is focused only on the more-

commonly used phase-resolved pattern analysis.

4.3.3 Phase-resolved partial discharge analysis

One of the most common techniques used to analyse PD data is phase-

resolved partial discharge analysis (PRPDA), which has been applied by many

researchers [35,52,78-88]. It is often used to investigate PD patterns related to

AC voltage at 50 Hz frequency. This technique was developed further to measure

PD activities at various applied frequencies [56]. In general, PRPDA equipment

detects the apparent discharge magnitude and occurrence phase of each single

partial discharge and the phase-resolved pattern is obtained by arranging and

counting single discharge magnitude, qi, happening at the phase i regarding the

AC voltage cycle in a two-dimensional (2D) data array. Then, the phase-resolved

PD pattern is acquired by mapping all discharge parameters, including discharge

magnitude and occurrence phase, over a number of recorded voltage cycles into a

representative single cycle. The occurrence phase of discharges is characterised

in X channels which are in the range of 0 to 360. The discharge magnitudes are

characterised in Y channels, with half of them for positive discharges and the

other half for negative discharges [35]. The mapping process of discharge

characteristics into XY channels is shown in Figure 4.5. The value of C(n, qm) is

the counted number of discharges occurring at phase n with discharge

magnitude qm.


page 56

Figure 4.5 Partial discharge characteristics mapping process [35]

In a 2D phase-resolved PD pattern plot, the x-axis represents the phase

channels while the y-axis illustrates the discharge magnitude channels. All

discharges are mapped onto this graph with corresponding discharge magnitude

and occurrence phase. The number of discharges with the same magnitude and

occurrence phase, i.e. C(n, qm), is displayed in this graph with different colour,

where the larger number of discharge events is represented by higher colour

intensity. Figure 4.6 shows an example of a phase-resolved PD pattern obtained

from the experiment. The advantage of this pattern is that discharge magnitude

and occurrence phase of each PD can be seen visually in the graph. Thus, partial

discharge analysis based on 2D phase-resolved PD patterns is used in this thesis

to discuss discharge behaviours under various applied frequencies. The analysis

aims to obtain integrated quantities for each single phase window and plot them

against the phase coordinate .

Figure 4.6 Example of a 2D phase-resolved PD pattern


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4.4 Test object preparation

4.4.1 Test object to produce corona discharge

To generate corona discharges under high voltage application, a needle and

bowl configuration was used as shown in Figure 4.7. The brass bowl has a

hemispherical geometry with a radius of 25 mm whereas the needle has a tip

radius of 61.88 m. The whole setup is housed inside an airtight chamber made

from perspex material. The insulation medium between the needle and the bowl

is air. Corona discharge is ignited when the electric field around the needle tip

exceeds the breakdown strength of air. The common configuration of corona

discharge testing is to apply high voltage to the needle while the bowl is

grounded. The reverse testing is to connect high voltage to the hemispherical cup

while the needle is connected to earth.

25 mm radius

Hemispherical brass

electrode

(a) Configuration layout (b) Test object in the laboratory

Figure 4.7 Test setup for generating corona discharges

To calculate the inception voltage of this configuration, the electrodes can

be considered as two concentric spheres with radius r for the needle tip and

radius R for the hemisphere. The air in the vicinity of the needle tip experiences

breakdown over a distance d as in Figure 4.8 when the voltage across this


page 58

distance d is larger than the breakdown voltage Vb derived from Paschen’s curve

[36]. In the typical case of R >> r, the relationship between the applied voltage V

of the test object and the breakdown voltage Vb of the air around the needle tip

can be expressed by the equation [37]

1 b

rV V

d

(4.8)

When the gap between the electrodes increases, the average electric field

decreases. However, this does not significantly influence the local field

concentration near the vicinity of the needle tip and thus the hemisphere radius R

hardly affects the inception voltage. Hence, this parameter is not present in

equation (4.8).

d

Needle tip

Ground electrode

R = 25 mm

Figure 4.8 Air breakdown around the needle tip over a distance d

4.4.2 Test object to produce internal discharge

To produce partial discharge in cavities within a solid dielectric material,

test samples with a cylindrical void were fabricated to investigate internal

discharges. These samples were produced by a 3D printer which uses

Acrylonitrile-Butadiene-Styrene (ABS), a type of thermoplastic resin, as its

printing material. An advantage of using a 3D printer is that the test object can be

created with high accuracy; if desired, complicated cavity shapes with precise


page 59

dimensions inside the solid test sample can be designed and manufactured. In this

study, the test sample geometry was disc-shaped with a diameter of 50 mm and

thickness of 3 mm. The cylindrical cavity was designed to be at the centre with

diameter of l mm, height of 1 mm and distance of 1 mm from the top and bottom

surfaces of the sample. The cavity was filled with air as it was printed under

normal ambient conditions. The schematic diagram is shown in Figure 4.9. In

this thesis, test samples with four values of cavity diameter l were fabricated and

tabulated in Table 4.1.

3 mm1 mm1 mm1 mm

50 mm

l

Figure 4.9 Test object dimensions

Table 4.1 Test sample properties

Sample 1 2 3 4

l (mm) 2 4 6 8

Figure 4.10 shows an example of a test sample used in this research. The

test sample was sandwiched between two brass electrodes with curvature on their

edges to reduce field concentration when high voltage is applied. This

configuration was held tightly by a mechanical arrangement and fully submerged

in mineral oil (standard transformer oil) in a test cell to prevent unwanted surface

discharges as shown in Figure 4.11.

Figure 4.10 An example of a test object to generate internal discharge


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Figure 4.11 Test cell to generate internal discharge

The partial discharge inception voltage for this test object can be estimated

by using the three capacitance model [36] described in Section 2.3.1. Referring to

Figure 4.12, the voltage across the test object, Va is

1 b

a c cb

c

VV V V V

V

(4.9)

where Vc is the voltage across the cavity and Vb is the voltage across the

healthy part of the solid dielectric in series with the cavity. It is assumed that the

electric field between the electrodes is uniform, thus

c cavV E d (4.10)

0( )bV t d E (4.11)

where E0 and Ecav are the electric field in the solid insulation and the cavity,

respectively; t is the thickness of the test sample and d is the depth of the cavity.

From equation (4.9) to equation (4.11), the voltage Va becomes

01a c

cav

E t dV V

E d

(4.12)


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It is assumed that the cavity is filled with air since the test object was

fabricated in normal conditions. Since the electric displacement is the same in the

cavity and the solid dielectric, the electric field in the cavity can be expressed as:

0cav rE E (4.13)

where r is the relative permittivity of the dielectric. By substituting

equation (4.13) into equation (4.12), the voltage across the cavity is

11

ac

r

VV

t d

d

(4.14)

For convenience, an empirical formula for Paschen’s curve of air at 20C is

used to determine the breakdown voltage Vbreakdown [36] in the cavity

6.72 24.36( )breakdownV pd pd (4.15)

At room temperature of 20C and normal pressure in the cavity which is not

too small (pd > 0.1 bar.mm), equation (4.15) is used to calculate the breakdown

voltage in the cavity [39]. From equation (4.14) and (4.15), the inception voltage

for the test samples can be estimated.

V~

Vc

Vb

Va

Ca

Cb

Cc

td

A

Figure 4.12 Electrical discharge in the cavity and its equivalent circuit

4.5 Measurement methods

4.5.1 Pre-measurement

It is essential to ensure that there are no air bubbles in the mineral oil

(trapped under the flat electrode) since discharges occurring in these bubbles

cause interference to measurement results when applying high voltage. Sharp

edges were also eliminated in metallic mechanical supporting elements to avoid


page 62

unwanted corona discharges. Before conducting the experiments, the setup was

tested without the corona discharge test cell and also with the internal discharge

test cell using a dummy test sample of same dimension but with no internal

cavity. This is to ensure the whole system was partial discharge free at the

desired working voltage. It was found to be free of partial discharge up to 19

kVpeak. Any higher voltage level was not tested since the maximum output of

the high voltage amplifier is limited at 20 kVpeak and the actual voltage level

used to stress the test specimens was below 15 kV.

In the measurement of corona and internal discharges, the voltage at which

the first discharge appears may not be the actual inception value when a new test

object is used. With the first high voltage application, there may be a time delay

for discharge to occur in test objects. This is due to the lack of free electrons to

trigger electron avalanches around the needle tip area or in the cavity, especially

for a virgin cavity which has never been exposed to partial discharge before.

Consequently, test objects were pre-excited with a high voltage level below the

estimated inception value for 30 minutes at 50 Hz frequency, that is 2 kV for

corona discharges and 6 kV for internal discharges, before conducting the

discharge measurements.

After the pre-excitation process, the high voltage amplitude applied to the

test object was increased in steps of 100 V after every two minutes until the

discharges were detected repetitively by the measurement device at a certain

voltage level and that level of voltage was recorded as the inception voltage

value (note that applying too fast a rate of voltage rise is likely to cause over-run

and thus inaccurate inception voltage). The applied voltage was then increased to

the desired value for recording partial discharge data.

4.5.2 Corona discharge measurements at different temperatures

For corona discharge measurements at different temperatures, the test

object was placed in an oven in which the ambient temperature was monitored by

a thermocouple as can be seen in Figure 4.13. This forms part of the thermostat

control system which operates the switching of the heating element to regulate


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the temperature. The oven temperature was very stable during the data

acquisition period. Experiments were conducted at four different temperature

settings: 20C, 30C, 35C and 40C.

An optical fibre temperature sensor (ASEA 1010) was inserted into the test

chamber. Note that with this fibre sensor (instead of conventional thermocouple

wire), it was possible to position the sensor close to the electrode tip of the test

object to record the ambient air temperature during the test. The thermostat

control system and optical fibre temperature monitor equipment are shown in

Figure 4.14. High voltage from the supply outside was connected to the test cell

via a bushing through the oven wall (top side). The test chamber was airtight and

the oven door was also completely closed during the whole test experiment

series. Thus, the humidity level in the test chamber was expected to remain

constant at all times and assumed to be approximately equal to normal room

conditions.

Figure 4.13 Corona discharge setup for variable air temperature measurements


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4.5.3 Discharge measurements at various applied frequencies

The test object was stressed at high voltage amplitude continuously at

various applied frequencies to measure corona discharges and cavity internal

discharges. For corona discharge testing, the determination of inception voltage

was carried out by slowly increasing the applied voltage amplitude until the first

discharge appeared after the pre-excitation period at 50 Hz frequency. The

voltage level was kept constant for a period of 5 minutes for recording discharge

data at inception value. Then the applied voltage was increased to a higher level

which was then left for another 5 minutes before starting discharge measurement.

This process helped achieve a steady, regular discharge activity. Once the

measurements under 50 Hz frequency were finished, the applied voltage was

reduced slowly to the initial value which was at the pre-excited stage. The

applied frequency was then decreased slowly to the very low frequency range

which was 0.1 Hz, 0.08 Hz and 0.05 Hz while high voltage was still applied to

test object. Under the excitation of each very low frequency level, the applied

voltage was kept unchanged for another 30 minutes before increasing the voltage

level to determine the inception value. This period of time was to ensure the

charge mobility had become steady under the new frequency application and to

minimise the memory effects of applied frequency on discharge behaviours.

Another 30 minutes was given at each measured voltage level before recording

the stable corona discharge data. The total test time to record all discharge data at

all applied frequencies was around 8 hours. For each type of measurement

presented in Chapter 5, the test procedures were repeated three times for

consistency of results.


page 65

Figure 4.14 Thermostat control system and temperature sensor

The measuring process for the void discharge measurements presented in

Chapter 6 and Chapter 7 was also begun at 50 Hz frequency after a pre-excitation

period under the same voltage waveform for each investigation of the effects of

different applied waveforms. At each particular applied waveform, the voltage

amplitude was slowly increased to a desired value and then left for 5 minutes

before recording partial discharge data. The measurements were taken in

ascending order of voltage amplitude. Once it was finished at 50 Hz frequency

excitation, the voltage level was decreased to its initial value at pre-excitation

period and the applied frequency was then reduced to a frequency of 0.1 Hz. The

test object was stressed at a high voltage level continuously during the change of

applied frequency in order to provide a consistent stress condition. At 0.1 Hz

frequency excitation, the sample was left for 30 minutes to eliminate any

memory affects of applied frequency before any measurement at very low

frequency was taken. The voltage was then slowly increased to the desired value

described in Chapter 6 and Chapter 7. An additional 30 minutes was given at

each voltage level before recording partial discharge data. This was to ensure that

quasi-stable conditions were obtained in the test object at each voltage amplitude.

The total test time was around 7 hours for each measurement at a particular

voltage waveform. The test procedures were also repeated three times for each

type of measurement.


page 66

4.6 Conclusion

This chapter described preparation of the test objects used to produce

corona discharges and cavity discharges in this thesis. A needle and bowl

configuration was used to generate corona discharge under variable applied

frequencies and at different ambient temperatures controlled by appropriate

hardware setup. For void discharges, test samples with a cylindrical cavity of

accurate dimension within the solid dielectric were fabricated for partial

discharge measurements under various stress conditions, such as voltage

waveforms, voltage amplitudes and applied frequencies. An Omicron MPD 600

commercial system fully compliant with the IEC 60270 standard was used to

record measurements. Individual partial discharge events were captured for

analysis. Discharge characteristics are quantified in terms of the phase-resolved

patterns, the discharge repetition rate, maximum and average discharge

magnitudes. The measurement results of corona discharges and cavity discharges

under different applied frequency excitation are presented and analysed in

Chapter 5 and Chapter 6, correspondingly. A comparison between measurement

and simulation results of void discharges at different applied voltage amplitudes

under very low frequency and power frequency excitation is described in Chapter

7. This allows key parameters influencing partial discharge characteristics at

different applied frequencies to be determined.

Chapter 5: Corona Discharge

Activities: Effects of Applied Voltage

Waveforms and Ambient Conditions

5.1 Introduction

In this chapter, corona discharge behaviours at two applied frequencies of

0.1 Hz and 50 Hz are presented and analysed. Two different applied voltage

waveforms, traditional sine wave and square wave, were used to stress the test

object at various voltage amplitude levels. A hybrid AC-DC voltage waveform

was also used to further investigate the effects of voltage waveforms on corona

discharge characteristics at different applied frequencies. Corona discharge

measurements were performed at various ambient temperatures to observe how

ambient conditions influence discharge behaviours at very low frequency and

power frequency.

To generate corona discharges, a test object of a point and bowl electrode

configuration in air was used. This test object was described in detail in Chapter

4 and summarised here. It is a brass cup of hemispherical geometry with a radius

of 25 mm, and the needle has a tip radius of 61.88 m. The insulating medium

between the needle and the bowl is ambient air. The effects of applied voltage

waveforms such as sine wave, square wave and hybrid AC-DC wave on corona

discharge at different frequencies are reported in Section 5.2. Section 5.3

presents the effects of ambient temperatures on corona discharge characteristics.

Chapter 5: Corona Discharge Activities: Effects of Applied Voltage Waveforms and

Ambient Conditions

page 68

5.2 Effects of applied waveform on corona discharge

5.2.1 Corona discharge at different applied frequencies under excitation

of sinusoidal waveform

In this section, a traditional sine wave was applied to the test object. The

high voltage source was connected to the needle and the bowl was grounded. The

partial discharge inception voltage (PDIV) was determined by gradually

increasing the applied voltage level in steps of 100 V until corona discharges

were detected steadily in the partial discharge measurement system described in

Chapter 4. At inception voltage, corona discharges only occur around the peak of

the negative half-cycle (270o phase angle) as shown in Figure 5.1 and Figure 5.2.

The phase-resolved partial discharge patterns were recorded for the same

duration of 3 minutes in order to compare the repetition rate. Such a pattern is

well known and can be explained. Electrons are injected from the negative

electrode. Under the applied electric field, these negatively-charged electrons

move to the positive electrode. On the way, they collide with other gas

molecules, cause ionisation and release more free electrons which results in an

exponential increase in the number of electrons (i.e. electron avalanches) and

hence electrical discharge.

In the negative voltage half-cycle, the needle tip is at negative potential and

the very high stress at the tip accelerates the injected electrons to produce an

avalanche. In contrast, in the positive half-cycle, the bowl is at negative potential.

Because the electric field near the round surface is more uniform and less

enhanced than the field near a sharp point (i.e. needle) [36], free electrons can

hardly be injected into the air and thus the absence of PDs in the positive half-

cycle. However, if the applied voltage is increased much further, the resultant

electric field increase will also cause PDs in the positive half-cycle.

An interesting observation when comparing Figure 5.1 and Figure 5.2 is

that, under very low frequency, the PDs tend to lag and occur slightly away from

the peak of the negative voltage half-cycle. Also, their magnitudes are not as


Ambient Conditions

page 69

uniform as those cases of higher frequencies which have a distinct cone shape

instead of a flat distribution.

Under the applied frequency in the 10 to 50 Hz range, the PDIV was found

to be different. At 50 Hz and 40 Hz, the PDIV was 2.6 kV while at 30 Hz, 20 Hz

and 10 Hz, it was progressively higher at 2.8 kV, 3.0 kV and 3.5 kV,

respectively. As expected, with higher applied voltage, the number of PDs

increased as shown in Figure 5.1c and Figure 5.1d. For PD occurrence in the AC

cycle, it can also be observed that the PDs spread out with increasing applied

voltage.

(a) 50 Hz (b) 40 Hz

(c) 30 Hz (d) 20 Hz

Figure 5.1 Phase-resolved patterns at PDIV with various applied frequencies

Average PD magnitudes were recorded above the threshold of 10 pC to

eliminate background noise of the test facility. Over the very low frequency

range, the PDIV was the same as that at 50 Hz, i.e. 2.6 kV. However, the averave

PD magnitude under very low frequency excitation (i.e. 65 pC) was higher than


Ambient Conditions

page 70

that under power frequency (i.e. 56 pC) during the recorded duration of 3

minutes.

Similar to the finding in [7], the results confirmed that the number of PDs

which occurred under power frequency is much higher than those which occurred

under very low frequency. The average pulse repetition rate is ~180 pulses per

second (pps) at 50 Hz compared to ~1.6 pps at 0.1 Hz, which is equivalent to 3.6

PDs per cycle under 50 Hz applied voltage and 16 PDs per cycle under 0.1 Hz

applied voltage.

(a) 0.1 Hz (b) 0.08 Hz

Figure 5.2 Phase-resolved patterns at PDIV under very low frequencies

With different applied frequencies, the applied voltage was increased up to

1.1 PDIV to investigate discharge characteristics further. The patterns were

captured and shown in Figure 5.3 and Figure 5.4. The figures show that, as

expected, the number of PDs as well as PD magnitude increased. In general, with

increased applied voltage, it can be seen that the PDs spread out over a wider

phase position window. In terms of the number of PDs which occurred over the

recording period of 3 minutes, with a 10% increase in applied voltage, the

number of PDs grew by 333% at power frequency but at a lower level of 156%

for very low frequency.

In terms of PD magnitude, at 1.1 PDIV level applied, the PD magnitude

under very low frequency excitation (i.e. 83 pC) was lower than the PD

magnitude under power frequency (i.e. 92 pC).


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The corona source setup was also subjected to the test in reverse with high

voltage connected to the bowl and the needle connected to ground. Other

conditions of the experiment were unchanged. The inception voltage in this case

was found slightly higher at 2.7 kV. The results at PDIV and 1.1 PDIV level are

presented in Figure 5.5. As anticipated, PDs only occurred in the positive half-

cycle. When the needle was at a negative potential relative to the other electrode,

it injected free electrons into the surrounding high field near the needle tip,

causing ionisation and then subsequent partial discharges.

(a) 50 Hz (b) 40 Hz

(c) 30 Hz (d) 20 Hz

Figure 5.3 Phase-resolved patterns at 1.1 PDIV with different applied frequencies


Ambient Conditions

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(a) 0.1 Hz (b) 0.08 Hz

Figure 5.4 Phase-resolved patterns at 1.1 PDIV with different applied frequencies

(a) PDIV (b) 1.1 PDIV

Figure 5.5 Reverse testing at 0.1 Hz at different voltage levels

5.2.2 Corona discharge at very low frequency under excitation of square

waveform

In this section, the needle and bowl test object was subjected to square

voltage at the excited frequency of 0.1 Hz. The voltage level was increased

gradually in steps of 100 V to determine the inception value of corona discharge.

The PDIV was found at 3.8 kV. Phase-resolved PD patterns at PDIV and 1.05

PDIV level are shown in Figure 5.6 and PD characteristics are summarised in

Table 5.1. Figure 5.6 shows that PD activities only occurred in the negative half-

cycle at both voltage levels. Unlike the distribution of PD events in the case of

sine wave, corona discharges spread out almost over the whole half-cycle under

square voltage. This dissimilarity could be caused by the duration of voltage peak

magnitude on electrodes. In the square waveform case, the voltage at the needle


Ambient Conditions

page 73

is maintained at peak level for almost the whole half-cycle which provides more

time to inject free electrons and induce PD events. Thus, discharges appear

across the “flat” part of the voltage waveform. In contrast, PD activities only

occur around the negative peak of sinusoidal voltage as the electric stress is

highest at this instant to pull out electrons from the needle.

The corona testing setup was also subjected to a reverse polarity experiment

with high voltage connected to the bowl and the needle grounded. Other

conditions and procedures of the experiment were unchanged. The inception

voltage was also found at 3.8 kV. The phase-resolved patterns at PDIV and 1.05

PDIV are presented in Figure 5.7 and PD parameters are summarised in Table

5.2. As expected, corona discharges only occur in the positive half-cycle. The

needle is at negative potential during this half-cycle so it easily injects electrons

to the area surrounding the tip to initiate partial discharges.

(a) at PDIV (b) at 1.05 PDIV

Figure 5.6 Phase-resolved PD patterns under excitation of square waveform at

frequency of 0.1 Hz

Table 5.1 PD characteristics at 0.1 Hz and different applied voltages

f (Hz) U (kV) Qmax (pC) Qmin (pC) Qave (pC) Repetition rate (pps)

0.1 3.8 48.4 35.5 45 0.4

4 75.7 61.3 69.7 2.2


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page 74

5.2.3 Corona discharge at very low frequency under sine wave with DC

offset

PD behaviour under the superimposed effect of AC and DC stress was

investigated in this section. This kind of stress can occur in many practical

situations, such as outdoor insulators in hybrid AC/DC overhead transmission

lines, winding insulation on the valve side of converter transformers, and AC

ripple voltage on HVDC transmission cables. An AC voltage of 3.0 kV was

firstly applied to the test object then a negative DC offset was gradually

introduced in steps of 100 V to determine the PDIV. At a DC offset of -0.7 kV,

corona discharges appear steadily which gives the PDIV of 3.7 kV negative peak

in total under both applied frequencies of 0.05 Hz and 0.1 Hz. This PDIV level is

slightly lower than PDIV values under sinusoidal and square waveform

excitations which implies that the PDIV might be dependent on the voltage

waveforms at very low frequency.

(a) at PDIV (b) at 1.05 PDIV

Figure 5.7 Reverse phase-resolved PD patterns under excitation of square

waveform at frequency of 0.1 Hz

Table 5.2 PD characteristics at reverse testing at 0.1 Hz and different applied voltages

f (Hz) U (kV) Qmax (pC) Qmin (pC) Qave (pC) Repetition rate (pps)

0.1 3.8 45 35 39.5 0.4

4 58 45 53 0.8


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page 75

In terms of PD characteristics, phase-resolved PD patterns are shown in

Figure 5.8 and PD parameters are summarised in Table 5.3. Average PD position

is around the negative peak at 270 as expected for corona discharges. However,

the repetition rate of PD events of 26.9 pps at 0.1 Hz is larger than that of 3.45

pps at 0.05 Hz. PD magnitude at 0.1 Hz is also scattered over a slightly wider

range of 21 pC to 227 pC than the range under 0.05 Hz of 28 pC to 205 pC.

These differences might be due to the voltage rise rate at the negative half-cycle

as in the case of the square voltage wave presented above. The higher rate of rise

might result in higher PD magnitudes and repetition rate.

(a) at 0.05 Hz (b) at 0.1 Hz

Figure 5.8 Phase-resolved PD patterns at PDIV with DC offset of -0.7 kV at

different applied frequencies

The DC offset was then extended to -0.8 kV to investigate its effect on the

PD behaviours. Phase-resolved PD patterns and characteristics are shown in

Figure 5.9 and Table 5.4. At the negative applied voltage peak of -3.8 kV, it can

be observed that PD positions have changed considerably. The discharges occur

earlier than the previous case under applied frequency of 0.1 Hz. Average phase

angle of the distribution shifts from 270 to 254 when the DC offset value is

reduced. On the other hand, this value only changes slightly from 269 to 265

under the applied frequency of 0.05 Hz which suggests that at higher AC-DC

applied voltage, PD activities tend to occur earlier in the voltage cycle.


Ambient Conditions

page 76

(a) at 0.05 Hz (b) at 0.1 Hz

Figure 5.9 Phase-resolved PD patterns at DC offset of -0.8 kV at different applied

frequencies

Table 5.3 PD characteristics at PDIV with DC offset of -0.7 kV

f (Hz) Qmax (pC) Qmin (pC) Qave (pC) Repetition rate (pps)

0.05 205 28 78 3.45

0.1 227 21 94 26.9

Table 5.4 PD characteristics at PDIV with DC offset of -0.8 kV

f (Hz) Qmax (pC) Qmin (pC) Qave (pC) Repetition rate (pps)

0.05 265 20 78 13.3

0.1 297 19 82 104.2

5.3 Effects of temperature on corona discharges

5.3.1 Corona discharge under sine wave excitation

In this section, the needle and bowl electrode configuration was used to

produce corona discharge in air at different frequencies and temperatures. To

control the ambient temperature, the test object was placed in a controlled

temperature oven. The oven had a thermocouple suspended inside to monitor the

oven air temperature. This forms part of the thermostat control system which

operates the switching of the heating element to regulate the temperature. The

oven temperature was very stable during the data acquisition period. Experiments


Ambient Conditions

page 77

were conducted at four different temperatures as read from the optical-fibre

thermometer: 20C, 30C, 35C and 40C. Because of the temperature constraint

due to the perspex material used to make the housing of the test object, it was not

possible to conduct the experiment at temperatures exceeding 45C.

By using the function generator, the applied frequency was varied from

power frequency (50 Hz) to very low frequency (0.1 Hz). Phase-resolved partial

discharge activities are recorded under each applied frequency at room

temperature (20C) and above (30C, 35C and 40C). The partial discharge

inception voltage (PDIV) was determined by gradually increasing in steps of 100

V until steady PDs were observed. PD magnitudes were recorded for those pulses

above the threshold of 10 pC to eliminate background noise in the test facility.

Due to PD stochastic characteristics, the recorded time must be set long enough

to achieve a stable PD trend at each applied frequency. In this work, this is equal

to 90 full voltage cycles for the very low frequency range (0.1 Hz and 0.05 Hz).

Figure 5.10 shows the phase-resolved PD patterns of corona discharges at

0.1 Hz at four different temperatures (20C, 30C, 35C and 40C) at PDIV.

Results are consistent at each temperature level when the experiments were

repeated five times. The PDIV of 3.9 kV peak is found for all four cases. As can

be observed from Figure 5.10, PD activities occur in the negative half-cycle. The

highest stress applied is only 1.1 PDIV so no PDs in the positive half-cycle are

anticipated from the test object. The presence of a few disturbances observed in

some of the results is believed to be from external interference.

(a) 20C (b) 30C


Ambient Conditions

page 78

(c) 35C (d) 40C

Figure 5.10 Phase-resolved patterns at PDIV and 0.1 Hz excitation

For comparison with PD activities at power frequency, the corona PD

patterns at PDIV under applied frequency of 50 Hz are captured and shown in

Figure 5.11 at different temperature levels. The acquisition time at this frequency

is 3 minutes for steady record. The voltage of 3.9 kV peak is also the PDIV in

these cases. The phases of PD events are positioned precisely at the negative

peak of the voltage cycle.

(a) 20C (b) 30C


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page 79

(c) 35C (d) 40C

Figure 5.11 Phase-resolved patterns at PDIV and 50 Hz excitation

Table 5.5 shows comparison of PD characteristics at each temperature at

0.1 Hz and 50 Hz. For 0.1 Hz, the phase positions of PD activities are slightly

shifted from 270 to 285 as found in [89]. This is a very steady observation at

all temperatures. At 30C, the average PD magnitude of 50 pC and repetition rate

of 0.055 pulses per second (pps) are the lowest among the four temperatures

tested. PD magnitude steadily increases when the temperature is increased from

30C to 40C. The maximum and average discharges increase from 60 pC and 50

pC at 30C to 115 pC and 60 pC at 40C. The difference between maximum and

minimum magnitude also increases at higher temperatures. This value increases

from 30 pC at 30C to 95 pC at 40C. It is also noted that the maximum

discharge at 40C is the highest value of 115 pC whereas the highest repetition

rate is 19.1 pps at 35C. At 20C, the average PD magnitude is the highest value

of 70 pC. In addition, the minimum PD magnitude consistently occur at lower

value when the temperature is increased. The minimum discharge of 50 pC at

20C decreases to 20 pC at 40C.

Table 5.5 PD characteristics at PDIV under excitation of 0.1 Hz and 50 Hz

Frequency

(Hz)

Temperature

(oC)

PD magnitude (pC) Repetition rate

(pps) max min ave

0.1

20 59 50 53 0.2

30 60 30 50 0.055

35 88 30 57 19.1

40 115 20 60 0.11

50

20 88 63 75 3.5

30 88 40 50 2.0

35 78 50 60 0.4

40 120 30 70 19

For 50 Hz, from Table 5.5, the average discharge gradually increases from

50 pC to 70 pC with the increase of temperature from 30C to 40C. PD

magnitude has the highest maximum and lowest minimum discharges of 120 pC

and 30 pC respectively. These circumstances are similar to scenarios under the


Ambient Conditions

page 80

applied frequency of 0.1 Hz. However, the increase of maximum PD magnitude

only happens from 35C to 40C, from 78 pC to 120 pC, at 50 Hz but not from

30C to 40C as in the case of 0.1 Hz. The increase of differences between

maximum and minimum discharges is also observed at 35C, not at 30C at 0.1

Hz. Moreover, the discharge repetition rate fluctuates in both cases of 0.1 Hz and

50 Hz. It progressively decreases from 3.5 pps at 20C to 0.4 pps at 35C and

suddenly increases to 19 pps at 40C under 50 Hz excitation while it differs in

the case of 0.1 Hz. In the reverse order, the minimum discharge steadily reduces

from 50 pC at 20C to 20 pC at 40C under 0.1 Hz whereas it varies in the case

of 50 Hz.

Figure 5.12 only shows the discharge distribution of negative voltage half-

cycle under 0.1 Hz excitation for the sake of clarity. It shows the discharge

magnitude gradually increases when the temperature increases from 30C to

40C. There are no significant differences of maximum PD magnitude at 20C

and 30C. It is interesting to note that PD events happen earlier in the voltage

cycle when the temperature increases from 30C to 40C. For comparison, the

discharge distribution of negative voltage half-cycle at 50 Hz is shown in Figure

5.13. PD events also occur earlier when the temperature increases from 30C to

40C. On the other hand, the maximum PD magnitude fluctuates more when the

ambient temperature increases.

180 210 240 270 300 330 360

0

20

40

60

80

100

120 20C

30C

35C

40C

PD

ma

gn

itu

de

(pC

)

Phase angle (degree)

180 225 270 315 360

0

20

40

60

80

100

120 20C

30C

35C

40C

PD

Ma

gn

itu

de

(pC

)


(a) Maximum PD magnitude (b) Average PD magnitude

Figure 5.12 Discharge distribution at PDIV and 0.1 Hz


Ambient Conditions

page 81

180 210 240 270 300 330 360

0

20

40

60

80

100

120 20C

30C

35C

40CP

D m

ag

nit

ud

e (p

C)


180 225 270 315 360

0

20

40

60

80

100

120 20C

30C

35C

40C

PD

ma

gn

itu

de

(pC

)



Figure 5.13 Discharge distribution at PDIV and 50 Hz

To investigate PD activities at higher voltage stress, the voltage level of 1.1

PDIV is applied under both 0.1 Hz and 50 Hz excitation at different

temperatures. Figure 5.14 and Figure 5.15 show the patterns of corona discharges

at different temperatures under 0.1 Hz and 50 Hz excitation, respectively, when

1.1 PDIV is applied to investigate PD activities at above PDIV. The PD

characteristics are summarised in Table 5.6. It can be seen from Table 5.6 that

previous findings at PDIV are also observed at this voltage level. The average

discharges gradually increase when the ambient temperature increases, from 66

pC at 30C to 98 pC at 40C in the case of 0.1 Hz and from 54 pC at 20C to 68

pC at 40C at power frequency. At 40C, the maximum PD magnitude which is

approximately 200 pC at both applied frequencies of 0.1 Hz and 50 Hz is the

highest value. The minimum discharge at this temperature is also the lowest at

both frequencies.

Table 5.6 PD characteristics at 1.1 PDIV under excitation of 0.1 Hz and 50 Hz

Frequency

(Hz)

Temperature

(oC)

PD magnitude (pC) Repetition rate

(pps) max min ave

0.1

20 98 32 55 1108

30 116 23 66 465

35 100 35 63 1155

40 200 30 98 45

50

20 77 30 54 1215

30 120 25 57 6

35 85 34 60 1195

40 197 20 68 79

However, similar trends of PD phase distribution to PDIV patterns are only

obtained under power frequency excitation while the PD characteristics for 0.1


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Hz are quite different. PD phase distributions of maximum and average PD

magnitude under 0.1 Hz excitation are shown in Figure 5.16. The distribution

shows that maximum PD magnitude slightly increases when temperature

increases as also observed at PDIV. However, the average discharges fluctuate at

higher ambient temperature. In terms of phase distribution, electrical discharges

start relatively earlier in the phase when the temperature increases from 20C to

40C, not from 30C to 40C in the case of PDIV voltage level. This might be

due to the combination of the temperature effect and voltage stress. At a higher

voltage level, free electrons tend to be injected earlier from the needle tip as the

electric field is high enough before the peak negative value is reached. Also,

higher temperatures might make free electrons available earlier as explained

above. These effects superimpose on free electron availability to make them

available faster and hence discharges occur at an earlier phase position.

(a) 20C (b) 30C

(c) 35C (d) 40C

Figure 5.14 Phase-resolved patterns at 1.1 PDIV and 0.1 Hz for four temperatures


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page 83

The difference of PD activities at various temperatures may be explained in

the following way. Negative corona discharges are generally initiated by impact

ionisation of gas molecules. The first free electrons are injected to air from the

cathode and accelerated to the positive electrode. On their movements, they

ionise gas molecules and create more free electrons. These electrons then

produce more electron avalanches and hence electrical discharges. Therefore, the

instant of the availability of the first free electrons determines the moment corona

discharges start. As shown in Figure 5.12 and Figure 5.13, the available free

electrons pulled out from the negative electrode exist earlier when the ambient

temperature increases from 30C to 40C at both 0.1 Hz and 50 Hz excitation.

Therefore, it may support a hypothesis that ambient temperature increase would

generate available free electrons earlier at a certain voltage level from a critical

temperature under very low frequency excitation.

(a) 20C (b) 30C

(c) 35C (d) 40C

Figure 5.15 Phase-resolved patterns at 1.1 PDIV and 50 Hz for four temperatures


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page 84

180 210 240 270 300 330 360

0

20

40

60

80

100

120

140

160

180

200

220 20C

30C

35C

40C

PD

ma

gn

itu

de

(pC

)


180 210 240 270 300 330 360

0

20

40

60

80

100

120

140

160 20C

30C

35C

40C

PD

ma

gn

itu

de

(pC

)



Figure 5.16 PD phase-resolved distribution at 1.1 PDIV and 0.1 Hz for four

temperatures

It is also worth observing that PD activities occur later at 0.1 Hz excitation

than under power frequency excitation at a certain ambient temperature,

especially at 20C and 30C. PDs start at 274 at 20C and at 283 at 30C,

under 0.1 Hz excitation while they are at 261 and 268 at the frequency of 50

Hz. This difference may be explained by taking account of the mobility of the

space charges left after electron avalanches around the needle vicinity. As stated

above, the needle injects electrons into its surrounding area and hence results in

fast moving electrons and slowly travelling positive ions. If the voltage polarity

changes from negative to positive in a relatively short time, positive space

charges shield the sharp point to make discharges stop, then diffuse and new

discharges are initiated. Therefore, the neutralising probability of the positive

ions is relatively low. The availability of free electrons to initiate electrical

discharges is reasonably high. However, this situation is completely different at

very low frequency. If the negative voltage is maintained for a sufficiently long

time, all positive ions will be neutralised when touching the negative electrode.

This may delay the availability of free electrons emitted from the needle tip and

hence electrical discharges are initiated at a later moment.

5.3.2 Corona discharge under sine wave with DC offset

As hybrid AC-DC transmission is an emerging trend, the experimental

work was extended to investigate PD behaviour under this hybrid stress. A


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page 85

sinusoidal voltage waveform with a DC offset value of -0.7 kV was applied to

the test object at 20C and 40C. Applied frequencies were 0.05 Hz and 0.1 Hz.

Again, the voltage magnitude was increased in steps of 100 V to determine the

PDIV which is 3.7 kV negative peak at both temperatures. It is lower than the

inception value when using the waveform without DC offset value. The phase-

resolved PD patterns are captured and shown in Figure 5.17 and Figure 5.18.

It can be seen that the small phase shift of PD events from the negative peak is

still observed at 0.1 Hz and 0.05 Hz at room temperature of 20C. However at

40C, this phase shift is only observed at 0.05 Hz but not at 0.1 Hz. In terms of

PD repetition rate, this value at 20C is lower than that at 40C for both cases,

3.24 pps versus 104.2 pps at 0.1 Hz and 6.94 pps versus 13.3 pps at 0.05 Hz. On

the other hand, the PD magnitude distribution is comparable to trends found from

the cases of sinusoidal waveform without DC offset. At 40C, the maximum and

minimum discharge is higher and lower than those values at 20C for both 0.05

Hz and 0.1 Hz excitation, 200 pC and 24 pC respectively. Also, the average PD

magnitude increases when the temperature increases, from 78 pC at 20C to 89

pC at 40C under 0.1 Hz excitation and from 78 pC to 82 pC at 0.05 Hz.

(a) 20C (b) 40C

Figure 5.17 Phase-resolved pattern at PDIV, frequency of 0.1 Hz with DC offset of

–0.7 kV at two temperatures


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(a) 20C (b) 40C

Figure 5.18 Phase-resolved pattern at PDIV, frequency of 0.05Hz with DC offset of

–0.7 kV at two different temperatures

5.4 Conclusion

This chapter reported a comprehensive study of corona discharges at

different applied voltage waveforms (sinusoidal wave and square wave) under

the excitation of very low frequency, i.e. 0.1 Hz. Experimental results show that

the inception voltage of corona discharges at very low frequency is dependent on

applied voltage waveforms. Under the application of a square wave and sine

wave with DC offset, corona discharges are initiated at lower voltage amplitude

than under a pure sinusoidal waveform. This could be mainly due to the longer

duration of the high level of negative voltage amplitude to trigger negative

corona discharges. There is also evidence to suggest that the rate of voltage rise

affects discharge characteristics. A faster rate of voltage rise causes more

discharges and larger magnitudes.

The effects of ambient air on corona discharges were investigated

thoroughly at four temperature points between 20C and 40C at very low

frequency excitation and power frequency for the sake of comparison. Measured

corona discharge characteristics show that the increase of ambient temperature

results in larger discharge magnitude and causes corona discharges to occur

earlier in the phase of the voltage cycle. This might be due to more availability of

free electrons emitted from the negative electrode at higher temperatures. The

following chapter extends the partial discharge investigation at very low


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frequency by performing partial discharge measurements in a cavity as a function

of cavity size and applied voltage waveforms.

Chapter 6: Void Discharge

Behaviours as a Function of Cavity

Size and Applied Waveforms

6.1 Introduction

This chapter reports measured PD characteristics in a cylindrical void

embedded in the insulation material under the excitation of very low frequency

and power frequency. The test samples were described in Chapter 4. In this

investigation, various voltage waveforms such as sinusoidal wave, trapezoidal

wave and user-customised wave were applied to stress the test objects under

different conditions to investigate PD behaviours. PD characteristics obtained at

very low frequency and power frequency are discussed thoroughly to study

effects of cavity size and applied waveforms at both frequencies.

Section 6.2 presents the trend of partial discharge activities occurring

continuously over a long period of time at 0.1 Hz and 50 Hz. Section 6.3 reports

the partial discharge characteristics in different cavity sizes under very low

frequency and power frequency excitation. The effects of voltage waveforms on

internal discharge are presented in Section 6.4.

6.2 Discharge behaviours under long exposure to partial discharge

6.2.1 Partial discharge characteristics under excitation of sine wave

This section describes how PD characteristics change over the test duration

at two different frequencies, 0.1 Hz and 50 Hz, under excitation of sine wave

voltage. PD activities in the insulated void are measured at applied voltage

amplitude of 10 kV. Experiments were performed for a duration of 4 hours, using

a new test object at each frequency. PD measurements were recorded periodically

Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied

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every hour from the beginning of the voltage application at each applied

frequency. PD characteristics were measured for a duration of 15 minutes at the

0.1 Hz frequency (i.e. 90 full voltage AC cycles), and for 5 minutes at the 50 Hz

frequency. As expected, PD patterns are mostly symmetrical in positive and

negative half-cycles at both 0.1 Hz and 50 Hz. Hence, PD data are only shown

here in the positive half-cycle for comparison.

Figure 6.1 shows the maximum and average PD magnitude at different

points in time during the testing period at 0.1 Hz and 50 Hz. At the beginning of

the testing period, large discharges occur as shown in Figure 6.1. After 1 hour of

applied voltage, PD characteristics at both frequencies change significantly. For

the case of 50 Hz, the maximum PD magnitude reduces greatly to 1628 pC as

compared to 2548 pC at the start. A similar decrease is also observed at 0.1 Hz,

from 3192 pC to 2510 pC. In terms of average magnitude, the decrease of PD

magnitude is only seen at 50 Hz, from 1771 pC to 862 pC, whereas this value

does not change much at 0.1 Hz.

Figure 6.1 Maximum and average PD magnitude at 0.1 Hz and 50 Hz

From 1 hour after the test start, there are clearly different trends of PD

magnitudes at 0.1 Hz and 50 Hz. Under applied frequency of 50 Hz, both

maximum and average PD magnitude gradually increase to 2282 pC and 1501

pC respectively until 3 hours after the start and then suddenly decrease to 2100

0

500

1000

1500

2000

2500

3000

3500

0 1 2 3 4

PD

mag

nit

ud

e (p

C)

Time (h)

0.1 Hz Q_average

0.1 Hz Q_max

50 Hz Q_average

50 Hz Q_max


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pC and 943 pC. On the other hand, for 0.1 Hz, maximum PD magnitude

continues decreasing over time while average PD value slightly fluctuates. Figure

6.2 shows only the phase-resolved PD patterns for 0.1 Hz and 50 Hz at 1 hour

and 4 hours after applying voltages as they reveal great difference in PD

activities.

(a) 0.1 Hz at 1 hour (b) 0.1 Hz at 4 hours

(c) 50 Hz at 1 hour (d) 50 Hz at 4 hours

Figure 6.2 Phase-resolved PD patterns at 0.1 Hz (a, b) and 50 Hz (c, d) at 1 and 4

hours after applying voltages

Regarding the phase position of PD activity, discharges are generally

observed later in the phase at frequency of 0.1 Hz when compared with higher

applied frequency, similar to [90] and [91], as shown in Figure 6.3. It is

interesting to note that PD activity happens at higher instantaneous voltage value

at the beginning for both frequencies, and then it occurs earlier in the voltage

cycle after applying voltage for a while. At 50 Hz excitation, PD activities occur

steadily from 1 hour after applying voltage, with average phase distribution of

45. However, this is not the case at 0.1 Hz. The average phase distribution of


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discharges gradually decreases from the start till 3 hours later, from 93.7 to

73.6, and then increases to 84.1 when the testing period ends. It means that PD

activity steadily occurs earlier when the voltage is applied longer to a certain

point of time, then it happens slightly later in the phase.

In general, PD activities over long duration of applied sine voltage could be

characterised in two stages at both frequencies. In the first stage, large electric

discharges occur at the beginning and the discharge magnitude rapidly decreases.

This could be due to a statistical time lag. At the beginning of testing, lack of

initial free electrons for igniting discharges inside the cavity may cause

discharges to occur at higher voltage across the cavity; therefore magnitudes of

PD activities are large. The second stage begins with smaller discharges when

more free electrons are generated from the cavity surface and previous

discharges. However, durations of these two degradation stages are different at

0.1 Hz and 50 Hz. It takes less than 1 hour to finish the first stage at 50 Hz but

more than 3 hours at 0.1 Hz. This time discrepancy is likely to be explained by

changes of physical parameters such as surface conductivity of the cavity and

charge decay mechanisms.

Figure 6.3 Average phase distribution at 0.1 Hz and 50 Hz

When PDs occur inside the cavity, byproducts produced during discharges

are deposited on the cavity surface; hence, surface conductivity of the cavity is

changed [46]. Surface conductivity of the cavity and bulk conductivity of the

insulation material surrounding the cavity are also at their lowest value when

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4

Ph

ase

An

gle

(deg

ree)

Time (h)

0.1 Hz

50 Hz


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PDs happen. Charges and byproducts generated from discharges cover the

surface of the cavity and they act as a shield to slightly decrease the electric field

across the cavity. As a result, maximum PD magnitude decreases. This process

takes longer at 0.1 Hz than at 50 Hz so it takes more time to finish the first stage

at 0.1 Hz than at 50 Hz.

Charge decay mechanisms may also contribute to this time difference.

Charges spread over the area where PD activity happens. These charges can

decay via three possible mechanisms: surface conduction, bulk conduction and

neutralisation by recombination. As noted above, when PDs continue to occur

repeatedly, surface and bulk conductivity increases which accelerates the rate of

charge decay. Also, the rate of charge recombination is different under different

rates of voltage rise. The rate of charge decay is relatively less at higher

frequency. These reasons are likely to explain why PDs are observed later in the

voltage phase position and at higher voltage value at 0.1 Hz than at 50 Hz.

In terms of PD repetition rate, a trend found in [92] is also observed here at

50 Hz as shown in Figure 6.4. The number of PD events per second increases

during the first stage and then slowly decreases in the second stage. This increase

of PD repetition rate could be related to changes of gas composition and pressure

inside the cavity. According to [93], the amount of oxygen drops to very low

values due to PD activities. Hence, the lower the amount of oxygen, the higher

the probability of discharge occurrence as oxygen is an electro-negative gas. It is

also shown in [94] that the gas pressure inside the cavity may decrease when

discharges start to ignite. As the pressure in this study is at normal conditions, i.e

1 atm of atmospheric pressure, and cavity dimensions are small, a drop in

pressure would reduce the breakdown strength according to Paschen’s law which

could explain the increase in PD repetition rate. At the second stage, the

reduction of electric field in the cavity due to the accumulation of PD byproducts

and charges might decrease the number of PDs.

On the other hand, it is worth noting that the PD repetition rate under 0.1

Hz excitation gradually decreases in the first aging stage and slightly increases in

the second aging stage. At the first stage, the charge decay rate is relatively high


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and the electron emission rate from the cavity surface is low. Therefore, the PD

repetition rate steadily reduces during the 3 hours of the first stage. After 3 hours

of PD exposure, gas contents in the cavity gradually recover, and electro-

negative gases such as CO2 and H2O are generated due to PD aging. Conductivity

distribution along the cavity surface is not uniform due to PD deterioration, and

charge migration may cause field enhancement locally at some points on the

surface. As a result, these factors may enhance the PD repetition rate in the

second stage.

Figure 6.4 Number of PDs per second at 0.1 Hz and 50 Hz

6.2.2 PD characteristics under excitation of square wave

This section describes discharge patterns under two different applied

frequencies, 0.1 Hz and 50 Hz, under excitation of square wave voltage. PD

activities occurring in the cavity were recorded at applied voltage amplitude of

10 kV. Each test was carried out over 150 minutes, using a new test sample each

time. PD data were recorded regularly every 30 minutes; the duration of each

recording was 1 minute for the case of 50 Hz frequency and 5 minutes at 0.1 Hz

frequency (i.e. 30 AC cycles).

Figure 6.5 shows the discharge patterns at 0.1 Hz excitation, captured at

different times over the test period. As expected, most discharge activities

occurred within two narrow phase windows where the transition between two

opposite voltage levels took place. However, there were a few discharges with

small magnitudes occasionally observed outside these windows (as in Figure

0

50

100

150

200

250

0 1 2 3 4

PD

re

pet

itio

n r

ate

(pp

s)

Time (h)

0.1 Hz

50 Hz


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6.5a, 6.5c and 6.5f). The average discharge magnitude steadily increased during

the first 60 minutes of the voltage application and hardly changed from 90

minutes onward.

For comparison, the PD characteristics at 50 Hz frequency are shown in

Figure 6.6, similar to the PD patterns observed in another study [63]. Figure 6.7

shows the average PD magnitude at both 0.1 Hz and 50 Hz excitation. At the

beginning, discharges occurred with high magnitude (2000 pC) but decreased to

1076 pC after 30 minutes of voltage application. Then, the PD magnitude

increased gradually to 3129 pC at 60 minutes after applying voltage and to 5023

pC after 90 minutes. Fluctuation of discharge magnitude was observed after 2

hours of voltage application.

It is interesting to observe that discharge magnitudes are much larger at 50

Hz than at 0.1 Hz. This may be due to dependence of the PD magnitude on the

rate of rise of the applied voltage. Measurements showed that the high voltage

square waveform has a rise time of 112 s at 50 Hz and 12 ms at 0.1 Hz. The rise

time difference was due to limitations of the signal generator and high voltage

amplifier. In [95], surface charge accumulation was reported to be dependent on

the rise of voltage during the amplitude transition.

The charge polarisation process under square wave is illustrated in Figure

6.8. In this condition, a sudden polarity reversal replaces free charges of opposite

sign, and polarised charges represent the effect of dipoles. The dielectric is

polarised by the DC component of the square wave when the voltage is positive

(as in Figure 6.8a). Dipoles and free charges both exist at this period. When the

polarity reversal is happening, only dipoles which have higher relaxation

frequency could follow changes of the external electric field without any delay.

The remaining dipoles with lower relaxation frequency cannot respond quickly

during this time. Therefore, some charges would be bounded by these residual

dipoles when the voltage amplitude reaches zero value (Figure 6.8b). When the

voltage rapidly becomes negative (Figure 6.8c), opposite free charges promptly

accumulate on the surface and neutralise these bounded charges. However,

polarised charges due to lower relaxation frequency dipoles still remain and form


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a residual electric field with the same direction as the external electric field. As a

result, the local electric field in the cavity could be enhanced. A PD can be

incepted under both conditions: the local electric field is sufficiently high and

free electrons are available to ignite a discharge avalanche. Because of the

stochastic nature of igniting electrons, the discharge process could begin with

some delay after the instant the local electric field is larger than the inception

value. Hence, the shorter the rise time is (i.e. the faster the rate of rise of applied

voltage), the greater overvoltage could be at which PDs occur.

(a) 0 minutes (b) after 30 minutes

(c) after 60 minutes (d) after 90 minutes


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(e) after 120 minutes (f) after 150 minutes

Figure 6.5 Changes of PD pattern at 0.1 Hz under the application of 10 kV square

voltage at different times over the test duration

(a) 0 minutes (b) after 30 minutes

(c) after 60 minutes (d) after 90 minutes


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(e) after 120 minutes (f) after 150 minutes

Figure 6.6 Changes of PD pattern at 50 Hz under the application of 10 kV square

voltage at different times over the test duration

The substantial difference of time duration of aging stages due to PDs could

be explained by variation of the local electric field inside the void because of

chemical and physical changes. At 50 Hz, the byproducts generated from

discharges are gradually deposited on the void surface; hence void surface

conductivity is changed progressively during the discharge period. Accumulated

charges and byproducts perform as a shield to slightly reduce the local electric

field in the void. Therefore, the PD magnitude tends to reduce over time in the

first stage.

Figure 6.7 Average PD magnitude over the testing period at 0.1 Hz and 50 Hz

under square voltage application of 10 kV

0

1000

2000

3000

4000

5000

6000

0 30 60 90 120 150

PD

Mag

nit

ud

e (p

C)

Time (minutes)

0.1 Hz

50 Hz


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On the other hand, the discharge magnitude gradually increases in the first

stage in the case of 0.1 Hz excitation. This could be due to the lack of free

electrons to start the discharge avalanche. At the beginning, free electrons are

very limited so that discharges are incepted at a higher local electric field. Free

electrons generated from the void surface and previous discharges are neutralised

via the following mechanisms. When PDs are incepted, cavity surface

conductivity is at its lowest value and then increases over the PD inception time.

As a result, it accelerates the charge decay rate which reduces the amount of free

electrons. Another factor contributing to reduction of free electrons is the charge

recombination process. At the frequency of 0.1 Hz, charges and free electrons

have many more chances to recombine along the charge moving paths due to

electric forces than those at 50 Hz. Therefore, the discharge avalanche needs time

to develop to a full process across the cavity. Hence, it takes more time to finish

the first stage at 0.1 Hz than at 50 Hz.

As can be seen in Figure 6.7, the first PD aging stage is around 30 minutes

from the beginning of the experiment under 50 Hz excitation whilst it takes

approximately 90 minutes at 0.1 Hz. After the first stage, the average discharge

magnitudes fluctuate greatly at 50 Hz during the rest of the experiment. During

this second stage, discharge magnitudes could be solely dependent on the rate

rise of square voltage as free charges and byproducts are accumulated steadily on

the cavity surface. On the contrary, average discharge magnitudes in the second

stage at 0.1 Hz are hardly changed and lower than those at the first stage. This

could be explained by the decay of free charges in the cavity during such a long

duration of constant voltage at 0.1 Hz excitation.


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----------

0

-V

+V

ErEpE0

+++++++

EpE0

----------

+++++++

+ : Free Charges

: Bounded Charges

: Polarized Charges

(c)(b)(a)

E0: External applied electric field

Ep: Internal electric field due to polarized charges

Er: Residual electric field due to polarized charges

Figure 6.8 Surface charges accumulation in the void under square wave voltage

6.3 Effects of cavity size on partial discharge behaviours under

sine wave voltage

This section presents effects of cavity size on PD characteristics at very low

frequency and power frequency under excitation of sinusoidal waveform. PD

behaviours in an insulated disc-shaped cavity with four test diameters of 2, 4, 6

and 8 mm were recorded at the applied voltage level of 10 kV and frequency of

0.1 Hz and 50 Hz. Maximum and average discharge magnitudes are shown in

Figure 6.9.


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(a) Maximum magnitude

(b) Average magnitude

Figure 6.9 PD magnitudes as a function of cavity size at 0.1 Hz and 50 Hz

As can be seen in Figure 6.9, the maximum discharge gradually increases

when the cavity size is larger at both frequencies. This may be due to the

availability of free charges generated in the void. With increased void diameter,

the cavity surface which is perpendicular to the electric field is larger, thus it can

emit more free charges under the effect of applied voltage. Therefore, PD

inception level is decreased when the void size is increased. Consequently, under

the same applied voltage, PDs in larger voids are ignited at a higher overvoltage

ratio compared to inception voltage, which results in larger discharge

magnitudes. Note that the cavity depth is unchanged, therefore the relative field

distribution in the void and in the solid insulation above and below it is not

affected and so the inception voltage is not affected by the cavity size. The

0

500

1000

1500

2000

2500

3000

3500

4000

4500

2 4 6 8

Dis

char

ge m

agn

itu

de

(pC

)

Void diameter (mm)

0.1 Hz

50 Hz

0

200

400

600

800

1000

1200

1400

2 4 6 8

Dis

char

ge m

agn

itu

de

(pC

)

Void diameter (mm)

0.1 Hz

50 Hz


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simulation of electric field distribution in test samples at the positive voltage

peak, at time of 5 ms, is shown in Figure 6.10. Simulation results show that the

field distribution in test samples with various void size is almost identical.

Hence, Figure 6.10a shows only the electric field and potential distribution in the

sample with diameter of 2 mm. Field values along the axis of symmetry parallel

to the electric field, i.e. the z-axis, are plotted in Figure 6.10b for all test samples.

It is interesting to observe that average discharge magnitude at very low

frequency increases with the void size whilst it is slightly reduced when the void

diameter is larger than 4 mm at frequency of 50 Hz as in Figure 6.9b. This could

be explained by effects of surface charges on PD activities. At very low

frequency, more space charges generated after a PD are likely to decay as the

time span between two consecutive discharges is considerably large, i.e. in the

order of hundreds of milliseconds. Hence, it reduces the electron generation rate

igniting the following discharge. As a result, the next PD has a higher possibility

of being incepted at a voltage level higher than the inception value which gives

larger discharge magnitudes. On the other hand, the statistical time lag at 50 Hz

is much shorter than at very low frequency so free charges generated after a

discharge are less likely to decay. Therefore, when the local electric field

recovers and exceeds the critical inception value, the large electron generation

rate available presents a favourable condition for discharges to be incepted.

According to measurements, many discharges with low magnitudes were

recorded, which implies discharges are incepted very soon as the critical

inception value is exceeded as available electrons are abundant in this moment.

As the void size is increased, the discharge area is enlarged and thus the

accumulated charge distribution may not be uniform over the whole surface area.

Thus, there could be multiple charge concentration points on the cavity surface

which enables multiple discharges to be ignited simultaneously. This also

explained the increase of PD repetition rate when the cavity diameter is larger.


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(a) Field and potential distribution in sample 1 with diameter of 2 mm

(b) Field values along the z-axis

Figure 6.10 Electric field distribution in test samples

6.4 Effects of voltage waveforms on partial discharge behaviours

In this section, test sample 1 with a void diameter of 2 mm was used to

investigate PD behaviours under different applied voltage waveforms including

traditional sine wave and trapezoid-based wave. Parameters for the trapezoid-

based waveform are shown in Figure 6.11: a symmetric trapezoidal wave with

equal linear rising and falling edge period is shown in trace (b), i.e. t1 = t3, and a

symmetric triangle wave is shown in trace (a), i.e. t2 = 0.


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U

Upeak

t1

T/2

t2 t3

(a)(b)

t

Figure 6.11 Trapezoid-based testing voltage waveform

6.4.1 Partial discharge behaviours under sinusoidal waveform

The test sample was subjected to a traditional sinusoidal waveform at

frequencies of 0.1 Hz and 50 Hz and applied voltage over the range from 8 kV to

10 kV. Discharge characteristics as a function of applied voltage at both

frequencies are shown in Figure 6.12. For both very low frequency and power

frequency, discharge behaviours are clearly dependent on applied voltage levels.

As voltage level is increased, maximum discharges increase from 393 pC to 480

pC for 0.1 Hz and 488 pC to 742 pC for 50 Hz. Also for both frequencies, the PD

occurrence rate is progressively intensified at higher voltage levels. On the

contrary, average discharges at power frequency and very low frequency show

opposite tendency when the voltage level is increased. At 50 Hz, the average PD

magnitude gradually decreases from 303 pC to 155 pC, whilst it steadily

increases from 75 pC to 121 pC at frequency of 0.1 Hz. The former is caused by

an intensified number of low magnitude discharge activities at a higher voltage

level at power frequency.

6.4.2 Partial discharge patterns under symmetric triangle waveform

In this section, the symmetric triangular voltage waveform was used to

stress the test object at frequencies of 0.1 Hz and 50 Hz. As expected, PD

activities happened evenly in both voltage half-cycles. Therefore, for the sake of

analysis and discussion, only the PD characteristics in the positive half-cycle are

considered and they are summarised in Table 6.1. It can be seen from this table

that discharge behaviours are strongly dependent on the applied voltage under


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both very low frequency and power frequency. Discharge magnitudes and

repetition rate at both frequencies are larger at higher applied voltage. PD

characteristics at 0.1 Hz at 12 kV and 50 Hz at 10 kV are fairly similar. PD

phase-resolved patterns under these conditions are also quite similar as shown in

Figure 6.13.

(a) Maximum PD magnitudes and repetition rate

(b) Average PD magnitudes and repetition rate

Figure 6.12 Discharge behaviours as a function of applied voltage under 0.1 Hz and

50 Hz

However, the rate of rise of voltage is greatly different between these

frequencies, hence causing significant dissimilarity of PD magnitudes at the same

voltage level. Under excitation of power frequency, discharge repetition rates

0

200

400

600

800

8 9 10

Max

imu

m P

D M

agn

itu

de

(pC

)

Applied Voltage Urms (kV)

0.1 Hz 50 Hz

0

5

10

15

20

0

100

200

300

400

8 9 10

Re

pet

itio

n R

ate

(pp

c)

Ave

rage

PD

Mag

nit

ud

e (p

C)

Applied Voltage Urms (kV)

0.1 Hz 50 Hz 0.1 Hz 50 Hz


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gradually increase from 8.4 pulses per cycle (ppc) to 8.8 ppc when the applied

voltage is increased from 9 kV to 10 kV. In contrast, discharges were hardly

observed at the voltage level below 11 kV under very low frequency excitation.

Under such a low frequency excitation, discharge magnitudes and occurrence

rate increase considerably when the voltage is increased from 11 kV to 12 kV.

Table 6.1 PD characteristics under triangular voltage waveform with different

applied frequencies

f (Hz) U (kV) Qmax (pC) Qave (pC) Repetition rate (ppc)

50 9 2555 316 8.4

10 6467 976 8.8

0.1 11 1122 516 2.1

12 5379 1045 7.3

(a) 50 Hz at 10 kV (b) 0.1 Hz at 12 kV

Figure 6.13 PD phase-resolved patterns under triangular voltage waveform

6.4.3 Partial discharge patterns under trapezoidal-based voltage

waveform

In this section, symmetric trapezoid-based waveforms with different linear

ramping rates of voltage rise were used at very low frequency and power

frequency. For comparison purposes, it is useful to quantify the fraction of

voltage varying duration (i.e t1 or t3) with respect to one half voltage period. This

parameter can be expressed as:

1 *100%/ 2

t

T (6.1)


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Two values of (10% and 20%) were selected to investigate effects of the

rising rate of trapezoidal voltage on PD characteristics. As expected, the PD

patterns were fairly symmetrical in both half-cycles of voltage waveform as

shown in Figure 6.14 and Figure 6.15. Hence, only the positive half-cycle PD

parameters are tabulated in Table 6.2. This table provides comparison between

0.1 Hz and 50 Hz and at different voltage levels. Interestingly, most of PD

activities occur during the voltage changing period. From Table 6.2, it can be

seen that PD parameters are strongly dependent on . At both excitation

frequencies, discharge magnitudes are larger at smaller value of , that is a

shorter voltage changing period t1. At 50 Hz, few discharges with low

magnitudes were observed at 9 kV at both of 10% and 20%, 167 pC and 84 pC

respectively. When the applied voltage was raised further to 10 kV, a significant

increase of PD magnitudes was recorded at 2074 pC and 1699 pC for of 10%

and 20%, respectively. At very low frequency, PDs were barely detected at

voltage level below 11 kV in both cases of . A similar dependent tendency of

PD magnitudes on was also experienced at applied voltage above 11 kV.

(a) 50 Hz at 10kV (b) 0.1Hz at 13 kV

Figure 6.14 PD phase-resolved patterns under trapezoidal voltage with time factor

of 10%

Measurement data indicate that PD behaviours are strongly dependent on

the ramping rate of voltage dU/dt rather than the applied voltage level. In fact,

for the same value, the rise time of voltage at very low frequency is much

longer than that at power frequency. For instance, with = 10%, the rise time t1

is 1 ms at 50 Hz but increases dramatically by a factor of 500 at 0.1 Hz. As a


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consequence, an applied voltage of 10 kV at power frequency could induce larger

discharges and higher occurrence rate than under a higher applied voltage of 13

kV at very low frequency.

Table 6.2 PD characteristics under trapezoidal voltage waveform at 50 Hz and 0.1

Hz with different rise time factor

f (Hz) U (kV) Qmax (pC) Qave (pC) Repetition rate (ppc)

10%

50 9 167 81 2.6

10 2074 1719 8.1

0.1

11 1493 665 4.52

12 1713 675 5.57

13 1766 706 8.47

20%

50 9 84 61 0.25

10 1699 885 6.5

0.1

11 1014 469 2.47

12 1101 587 4.01

13 1504 636 6.9

(a) 50 Hz at 10 kV (b) 0.1 Hz at 13 kV

Figure 6.15 PD phase-resolved patterns under trapezoidal voltage with time factor

of 20%

To investigate further the influence of voltage rise time on PD activities, a

customised 0.1 Hz trapezoid-based waveform with comparable rise time to 50 Hz

was used. The rise time t1 of these voltage waveforms is 1 ms and 2 ms while the

peak voltage period t2 is 4998 ms and 4996 ms, respectively. The PD phase-

resolved patterns under these customised waveforms at 10 kV are shown in


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Figure 6.16. The discharge characteristics for positive voltage polarity are

summarised in Table 6.3. From Table 6.2 and Table 6.3 at frequency of 0.1 Hz, it

can be seen that voltage waveforms with a shorter rise time can trigger more

discharges per cycle and larger discharge magnitudes even at a lower applied

voltage.

Table 6.3 PD characteristics under 0.1 Hz trapezoid-based waveform with

customised rise time

f (Hz) t1 (ms) Qmax (pC) Qave (pC) Repetition rate (ppc)

0.1 1 1388 218 9.07

2 1323 81 7.6

(a) t1 = 1 ms (b) t1 = 2 ms

Figure 6.16 PD phase-resolved patterns under 0.1 Hz trapezoidal waveform at 10

kV applied voltage with different rise time

6.4.4 Partial discharge patterns under square waveform

An approximately square voltage waveform was obtained by increasing the

constant voltage time to t2 = T/2 at frequency of 0.1 Hz and 50 Hz. As expected,

discharges mostly occur at the voltage polarity transition at both frequencies as

shown in Figure 6.17. The discharge magnitudes, however, are greatly different

between the two frequencies. At power frequency, discharge magnitudes are

significantly larger, about five times, as compared to the very low frequency. As

can be seen from PD patterns, discharge activities tend to intensify at large

magnitudes at 50 Hz whereas at 0.1 Hz a majority of discharge activity is

incepted with low magnitudes. This significant difference is likely to be


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attributed to the constant voltage duration in the waveform at each frequency.

The longer period of constant peak applied voltage in the 0.1 Hz case results in a

decrease in discharge magnitudes.

Measurement results generally indicate that discharge magnitudes at power

frequency are larger than those at very low frequency. Furthermore, the applied

frequency also affects the PD occurrence rate in such a way that there are more

discharges per cycle at higher applied frequency. It is assumed that the discharge

mechanism is based on “streamer discharge” type. As noted in Chapter 2, two

conditions must be met to ignite a discharge: a sufficiently high local electric

field and a starting electron. The local cavity electric field, in general, is

enhanced by two factors. The first one is the enhancement of the external field in

the cavity due to the mismatch of permittivity between the cavity and solid

insulation material. The second factor is associated with space charges generated

by previous discharges. These space charges accumulate on the cavity surface

and hence generate a surface-charge electric field contributing to the total field in

the cavity. These two factors determine the amount of charges when a discharge

is incepted. Consequently, the discharge magnitude is proportional to the total

electric field in the cavity at the inception moment.

(a) 0.1 Hz (b) 50 Hz

Figure 6.17 PD phase-resolved patterns under approximately square voltage

waveform

6.4.5 Effects of surface charge decay

A starting electron igniting the streamer process could be generated from

two sources: volume ionisation and surface emission. Volume generation is due


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to gas ionisation by photon impact and field detachment of electrons from

negative charges. The second process is electron emission from the cavity

surface, which includes electrons detrapped from shallow traps at the surface,

electron generation by ion collision and the surface photo effect. The source of

starting electrons is greatly enhanced by free charges generated after a discharge.

As the cavity surface has a finite value of conductivity, surface deposited charges

decay with time by drifting into deeper traps, by a recombination process or by

moving along the cavity wall under the effects of the local electric field. This

decay rate is commonly represented by the average charge decay time constant

decay.

Differences in PD characteristics observed in the measurement results may

be attributed to the charge decay rate. If decay is smaller than the duration of the

applied voltage period, i.e. decay << 1/f , it is assumed that most of the free

charges have already decayed and thus surface deposited charges are not

contributing much in the PD process. On the other hand, if the decay time is

longer than the voltage period, i.e decay >> 1/f , charges are not decayed and will

make a significant contribution to the total field in the cavity. In this case,

discharge magnitudes are strongly dependent on the applied frequency as seen in

Section 6.4.1. At frequency of 50 Hz, free charges are not decayed between two

consecutive discharges and hence PDs would be incepted at the instant when the

local field exceeds the critical value. Consequently, more discharges with low

magnitudes are produced at higher applied voltage.

The effect of charge decay under a trapezoid-based applied waveform is

illustrated in Figure 6.18. Here, it is assumed that a residual electric field does

not exist initially; the cavity field, i.e. Ecav (blue straight line), is equivalent to the

external field associated with the applied voltage, E0 (black dashed line). A

discharge will be incepted when Ecav is larger than the inception value, Einc, and a

starting electron is available. During the discharge process, the cavity field is

dropping rapidly and stops at the residual value Eres lower than the extinction

value, Eext, which determines the PD ceased condition. Free charges released

after a PD process deposit on the cavity surface and then produce an electric


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field, Eq, which has the opposite direction to the external field E0. If the constant

voltage period is shorter than the decay time constant (e.g. in the case of 50 Hz),

Eq is fairly stable as charges are not decayed. When E0 reverses its polarity, E0

and Eq have the same direction and thus the total cavity field is enhanced

significantly as seen in Figure 6.18a. Therefore, the following PD would be

incepted at a higher electric field and thus result in a larger discharge magnitude.

On the contrary, free charges do not contribute much in the enhancement of the

cavity electric field at 0.1 Hz as charges are decayed due to the relatively long

period as in Figure 6.18b. Consequently, the next PD pulse would be ignited at a

lower electric field and smaller discharge magnitude.

t

t

E0

Ecav

Eq

Einc

-Einc

Eext

-Eext

Emax

-Emax

E0

Ecav

Eq

Einc

-Einc

Eext

-Eext

Emax

-Emax

(a) Charge decay ignored

(b) Charge decay considered

Figure 6.18 Electric field behaviour due to discharges under applied trapezoid-

based waveform


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6.5 Conclusion

This chapter reported a comparative study of internal discharges in a

cylindrical cavity bounded by solid insulation material as a function of cavity

size and applied voltage waveforms at very low frequency and power frequency.

Changes of PD characteristics after long discharge exposure under excitation of

sinusoidal and square waveforms were discussed in detail at both frequencies.

Various waveforms including sinusoidal and trapezoid-based type were

employed to stress the test samples. Various PD characteristics (magnitude,

repetition rate, phase-resolved patterns) were analyzed. It is concluded that PD

behaviors are strongly dependent on the applied frequency and the slew rate of

voltage. PD magnitudes at very low frequency are generally lower than those at

power frequency excitation regardless of applied voltage waveforms. A larger

cavity could also lead to more discharges with low magnitudes as the discharge

surface area is increased. The main reason for these behaviours is the

contribution of the charge decay mechanism in the enhancement of the cavity

field. Charge decay plays a significant impact on PD characteristics at 0.1 Hz. In

the following chapter, the measurement results of partial discharge in a cavity are

used to compare with computer simulation data to determine critical parameters

affecting discharge behaviours, especially the decay of accumulated charges on

the cavity surface.

Chapter 7: Void Discharge

Behaviours: Comparison between

Measurements and Simulations

7.1 Introduction

This chapter describes PD and electric field behaviours obtained from a

simulation model and compares measurement data with simulated results. The

physical progress of the electric field in the cavity is discussed together with the

PD magnitude when discharges occur. From the simulation model, critical

parameters that significantly influence PD events can be identified. Cycle to

cycle PD behaviours are investigated through simulation of the electric field and

PD events against time. The statistical time lag of PD activities can be calculated

at very low frequency and power frequency at different applied voltages to

consider dependence on applied frequency and voltage amplitudes.

Section 7.2 presents the simulation results obtained from the partial

discharge model. In Section 7.3, the model is then verified with the measured

data from experiments at very low frequency and power frequency as a function

of applied voltage amplitudes. This verification enables the calculation of key

parameters affecting partial discharge behaviours such as the statistical time lag

which is reported in Section 7.4.

7.2 Results from simulation model

7.2.1 Electric field distribution in the model

The equipotential lines and electric field distribution in the simulated model

just before and after the first PD are shown in Figure 7.1. The cavity which is

cylindrical with a radius of 1 mm and height of 1 mm is within the insulation

Chapter 7: Void Discharge Behaviours: Comparison between Measurements and

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material with thickness of 3 mm. The model is simulated at frequency of 50 Hz

and applied voltage of 10 kVrms. As can be seen in Figure 7.1a, the electric field

in the cavity before the PD event is much higher than the surrounding area of

material because the relative permittivity of the cavity is lower than that of the

insulation material. This is presented with the yellow-red colour scale in the

cavity area with more closely packed equipotential lines.

(a) Before the first PD occurrence

(b) After the first PD occurrence

Figure 7.1 Simulation of electric field distribution and equipotential lines in the

model at 50 Hz and 10 kVrms when the first PD occurs

Furthermore, the electric field is highest at the void surfaces closest to the

electrodes as the applied field is nearly perpendicular to the surfaces. This can be

observed in the cross-section plot of electric field magnitude along the z-axis of

the model in Figure 7.2a. The field distribution is not homogeneous but

symmetrical along the z-axis as the cavity size is comparably large relative to the


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sample thickness. Consequently, the field in the cavity closest to the electrodes is

enhanced with closer equipotential lines than those at the middle of the cavity.

The r-axis electric field magnitude distribution is plotted in Figure 7.2b which is

different from Figure 7.2a as the field is parallel to the electrode surfaces.

(a) Along the z-axis (b) Along the r-axis

Figure 7.2 Cross-section plots of field magnitude in the model before and after the

first PD in Figure 7.1

Just after the PD occurrence, the electric field distribution is greatly

changed due to the redistribution of electric charge movement as shown in Figure

7.1b, assuming the whole cavity is affected. As charges move dynamically

during the PD event, the field in the cavity is significantly decreased after the PD

event as represented by the dark blue colour area in Fig 7.1b. At the same time,

the electric field in the solid dielectric close to the upper and lower cavity

surfaces is considerably increased. This can be seen in the cross-section plot of

field magnitude along the z-axis as in Figure 7.2b. This phenomenon can be

explained by the charge accumulation on the cavity surfaces after the PD event.

Accumulated charges generate an opposing electric field which greatly decreases

the total electric field in the cavity, resulting in the lowest electric field at the

upper and lower cavity surfaces. On the other hand, the electric field in the

material regions close to these two surfaces is enhanced, especially at the cavity

surface layers which directly influence characteristics of the next PD event.

After the first PD event is complete, the electric field in the cavity rises

again due to the increase of applied voltage. The next PD event could happen if

the field exceeds the inception value. Figure 7.3 illustrates the electric field


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distribution and equipotential lines in the simulation model when the second PD

occurs. Figure 7.4 shows the cross-section plots of electric field magnitude along

the z-axis and r-axis.

(a) Before the second PD occurrence

(b) After the second PD occurrence


model at 50 Hz and 10 kVrms when the second PD occurs

As shown in Figure 7.3a, the electric field in the cavity is significantly large

compared with Figure 7.1a, presenting with the dark red colour scale and highly

dense equipotential lines. This could be explained by the effect of accumulated

charges on the upper and lower cavity surfaces when the voltage polarity

changes. Note that the first and second PD occur in different half-cycles (i.e. at

2.68 ms and 12.76 ms, respectively), so that the external electric field due to

applied voltage alters and has the same direction with the field due to surface

accumulated charges in the cavity. As a result, the total electric field in the cavity


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is significantly enhanced. This effect can also be observed in Figure 7.4a with the

electric field fluctuation at the cavity surface layer (the depth of 0.1 mm in the

model) between the insulation material and the cavity. After the second PD, the

electric field has similar trends to the first PD. Since free charges generated from

the first PD still deposit on the cavity surface when the second PD is incepted,

the amount of surface charges is considerably increased just after the second PD

occurs. Consequently, the electric field on the upper and lower surface of cavity

is higher as can be seen in Fig 7.4a (6.20 MV/m vs 5.46 MV/m in Fig 7.2a).



second PD in Figure 7.3

The model is also simulated at frequency of 0.1 Hz (and same applied

voltage of 10 kVrms) for comparison. Similar distributions of electric field and

equipotential lines to simulation results of 50 Hz are also observed at the first PD

occurrence as shown in Figure 7.5 and Figure 7.6. The electric field in the cavity

is enhanced due to the mismatch of the relative permittivity of air in the cavity

and solid insulation material as can be seen in the light yellow colour scale in

Figure 7.5a. Once the first PD is incepted, the electric field in the cavity reduces

significantly as in Figure 7.5b with the dark blue colour scale. The solid

dielectric areas closest to the upper and lower cavity surfaces have the highest

electric field magnitude distribution as shown in Figure 7.6a.

After the first PD occurrence, the applied voltage continues increasing,

resulting in the increase of electric field distribution in the dielectric material as


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well as the cavity. When the inception field is exceeded, the cavity is ready to be

exposed to the second PD occurrence. Figure 7.7 shows the distribution of

electric field and equipotential lines just before and after the second PD

occurrence and Figure 7.8 shows field magnitude along the z-axis and r-axis. As

shown in Figure 7.7a and Figure 7.8, the field magnitude in the cavity is lower

than that in the dielectric before the second PD occurrence. This is well expected

as both PDs occur in the first half-cycle (i.e. at 0.96 s and 2.32 s, accordingly). In

this circumstance, due to surface charges generated by the first PD, the electric

field has opposite direction to the external applied field, which reduces the total

field in the cavity.

(a) Before the first PD occurrence

(b) After the first PD occurrence


model at 0.1 Hz and 10 kVrms when the first PD occurs


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first PD in Figure 7.5

It is interesting to observe that there are no fluctuations of electric field

distribution in the upper and lower cavity surface layers as in Figure 7.8a when

compared to those under 50 Hz excitation as in Figure 7.4a. This could be due to

the charge decay mechanism of accumulated charges on cavity surfaces under

such a very low frequency excitation. At 0.1 Hz, accumulated charges generated

after the first PD have more chances to decay as the time span between two

consecutive PDs is significantly longer. Free charges could disappear via several

physical mechanisms such as charge recombination or diffusion into the solid

dielectric. As a consequence, the amount of charges existing on the cavity

surfaces is reduced considerably at the moment the second PD is incepted. Thus,

the surface charges hardly affect the distribution of the electric field on the upper

and lower cavity surfaces.

7.2.2 Simulation of electric field against time

The electric fields within the test sample and discharge magnitudes in the

first two cycles are shown in Figure 7.9. As it is assumed that there are no free

charges initially, the electric field due to these charges, Eq, exists just after the

first discharge is incepted. This field varies significantly, depending on the field

polarity at which the following discharge occurs. It would increase further if the

next discharge occurs at the same field polarity as the previous discharge.

Otherwise, it would decrease when two consecutive discharges are incepted at

the same field polarity.


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(a) Before the second PD occurrence

(b) After the second PD occurrence


model at 0.1 Hz and 10 kVrms when the second PD occurs



second PD in Figure 7.7


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Comparing the Eq behaviour due to local electric field polarity reversal at

0.1 Hz and 50 Hz, it is relatively easier to observe a slight decrease of Eq at very

low frequency excitation than at power frequency. This could be explained by the

effect of surface charge decay. When Ecav reverses polarity, mobility of charges

on the cavity wall is enhanced and exhibits an increase of cavity surface

conductivity. Thus, these charges decay with time and Eq is slightly reduced. As

a period duration at very low frequency is much longer than at power frequency,

the decrease of Eq is much greater at 0.1 Hz. Charge decay also affects the

moment the first PD is incepted after field polarity reversal. The availability of

starting electrons after the cavity field zero-crossing points is reduced due to

charge decay mechanisms and thus makes the first PD after polarity reversal

occur at a higher field which results in larger magnitudes.

(a) 0.1 Hz (b) 50 Hz

(c) 0.1 Hz (d) 50 Hz

Figure 7.9 Electric field and PD magnitude in the first two cycles at 0.1 Hz (a, c)

and 50 Hz (b, d)


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7.3 Comparison of measurements and simulations

7.3.1 Partial discharge activities at 50 Hz

In this section, PD activities in a cylindrical cavity with a radius of 1 mm

and height of 1 mm are presented under excitation of power frequency. Figure

7.10 shows the phase-resolved PD patterns of measurement and simulation

results as a function of the applied voltage under 50 Hz excitation for a duration

of 500 cycles. PD characteristics under various applied voltage are summarised

in Table 7.1 and Table 7.2.

Table 7.1 Measurement results at 50 Hz under different applied voltages

Applied voltage (kV) 8 9 10

Maximum PD magnitude (pC) 488.2 610 742

Average PD magnitude (pC) 263 306 303

Minimum PD magnitude (pC) 144 144 144

Repetition rate (ppc) 1.15 2.28 2.46

Table 7.2 Simulation results at 50 Hz under different applied voltages


Maximum PD magnitude (pC) 528 629 696




Comparing measurement and simulation results, it can be seen that the

simulations are in agreement with measurements for different applied voltages.

PD parameters such as the maximum discharge, average discharge and repetition

rate of simulation results closely match the measured data. From the phase-

resolved PD patterns, the simulated model is able to generate a similar shape of

PD distribution over the voltage cycle. The “rabbit-ear” shape of PD patterns is

clearly seen in both measured and simulated results at applied voltage of 9 kV

and 10 kV. This “rabbit-ear” shape consists of PD events with higher discharge

magnitude which denotes a unique pattern of internal discharge. From the


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simulation, it is interesting to note that this pattern is generated by high

magnitude PD events occurring after the change of electric field polarity in the

cavity as described in section 7.2.2.

(a) 8 kV Measurement (b) 8 kV Simulation

(c) 9 kV Measurement (d) 9 kV Simulation

(e) 10 kV Measurement (f) 10 kV Simulation

Figure 7.10 Phase-resolved PD patterns of measurement and simulation results at

different applied voltage under 50 Hz excitation


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When the polarity of the electric field changes between two consecutive

discharges, the magnitude of the electric field is enhanced significantly due to the

residual field of surface charges. Hence, the next PD event is incepted at higher

field magnitude which results in larger discharge magnitude. On the other hand,

the next PD occurs with lower magnitude when there is no field polarity

alternation. These discharges produce the broad “straight-line” shape in the

phase-resolved PD patterns. Also, a few discharges happened before the zero-

crossing moment of applied voltage (i.e. at 180 and 360) at higher voltage as

the electron generation rate and surface charges are enhanced under the higher

applied electric field.

7.3.2 Partial discharge activities at 0.1 Hz

For comparison purposes, the model was used to simulate under 0.1 Hz

excitation at different applied voltages. The phase-resolved patterns of PD

activities from measurement and simulation data are shown in Figure 7.11.

Measured PD characteristics are summarised in Table 7.3 and simulated PD

characteristics in Table 7.4. The simulated model generates good agreement with

the measurement data, with discharge magnitude and repetition rate of simulation

results closely matched with measured values. However, there is slight difference

in PD patterns between measurements and simulations which could be due to

several possible reasons. There might be unavoidable measurement errors during

the running of the experiment caused by external noise from other testing

activities in the laboratory. That aside, it is most likely because the simulation

model relies on several assumptions to simplify the model as noted in Chapter 3,

leading to approximate estimation of freely adjustable parameters, i.e. N, decay

and Nev. Therefore, the PD model could be improved further by fine tuning of

these values or by modifying the electron generation rate equations.

However, the simulation results in general show good agreement with the

measurement data, which confirms that some of the simulation parameters of

developed model were chosen appropriately and could be used to investigate PD

characteristics at very low frequency as well as power frequency.


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(a) 8 kV Measurement (b) 8 kV Simulation

(c) 9 kV Measurement (d) 9 kV Simulation

(e) 10 kV Measurement (f) 10 kV Simulation

Figure 7.11 Phase-resolved PD patterns of measurement and simulation results at

different applied voltage under 0.1 Hz excitation

7.3.3 Values of simulation parameters

The values of simulation parameters used in Sections 7.3.1 and 7.3.2 are

tabulated in Table 7.5. It can be seen that most parameters are kept unchanged at

both frequencies of 0.1 Hz and 50 Hz except for the cavity surface conductivity


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value. It has been shown in previous research such as [74] and [96] that value of

cavity surface conductivity is dependent on applied frequency. Higher applied

frequency leads to rapid changes of electric field in the cavity, which stimulates

the surface charge mobility on cavity walls. Hence, surface charge decay via a

conduction mechanism on the cavity wall may be more significant.

Consequently, the enhancement of the electric field in the cavity is less

substantial and discharges are incepted with lower maximum magnitude. After

trial and error, void surface conductivity values of 1x10-9 S/m and 1x10-11 S/m

were chosen for 50 Hz and very low frequency simulation to keep the PD

maximum magnitude and repetition rate a close match with the measured data.

Table 7.3 Measurement results at 0.1 Hz under different applied voltages






Table 7.4 Simulation results at 0.1 Hz under different applied voltages






The electric field inception field is calculated from equation (2.7), and is

assumed independent of applied frequency and voltage. The extinction field is

determined based on the minimum discharge magnitude obtained from

measurements. It is also assumed to be constant as measured data shows that

minimum discharge magnitude is independent of applied voltage and frequency

excitation.

Once the parameters for the inception field, extinction field and cavity

surface conductivity have been determined, the three freely adjustable


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parameters, i.e. N, decay and Nev, are chosen via a trial and error method to yield

minimum errors between the simulation and measurement results at all applied

voltages and frequencies. Values of these parameters, shown in Table 7.6, were

obtained after many simulation trials. These values are not the real physical

parameters. However, their values are physically sensible to describe what

happens in the cavity. From simulation parameters, values of N and Nev are

smaller at lower frequency. They are physically sensible as the time span

between PD events is much longer at very low frequency, causing more surface

charges to disappear via several charge decay mechanisms such as charge

recombination and drifting into deeper traps in the bulk insulation. As a result,

the electron generation rate is reduced significantly and there are fewer free

charges ready for the next PD event.

Table 7.5 Simulation parameters

Parameters 0.1 Hz 50 Hz Unit

Applied voltage, Urms 8, 9, 10 kV

Number of simulation cycles, n 500

Time step during no PD, t 1/500f s

Time step during PD, dt 1x10-9 s

Relative permittivity of insulation, r 3.5

Cavity surface relative permittivity, r 3.5

Cavity relative permittivity, cav 1

Cavity conductivity during no PD, cavL 0 S/m

Cavity conductivity during PD, cavH 5x10-3 S/m

Electric inception field, Einc 3.93x106 V/m

Electric extinction field, Eext 1x106 V/m

Cavity surface low conductivity, sL 0 S/m

Cavity surface high conductivity, sH 1x10-11 1x10-9 S/m

7.3.4 Simulation for 10 applied voltage cycles

Figure 7.12 to Figure 7.14 shows the simulated electric field and PD

magnitude behaviours, cycle to cycle, under different applied voltages at 0.1 Hz

for 10 successive cycles. In general, there are more PD events and larger PD

magnitude at higher applied voltage as observed in the measurement results. The

simulation shows a PD event with larger magnitude is incepted at a higher cavity


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electric field. Another following PD event with lower magnitude occurs just after

the large magnitude PD. This could be explained in such a way that after a large

PD occurrence, the amount of free charges generated is high. Thus, it stimulates

the following PD activity with lower magnitude just after the local electric field

exceeds the inception value. It is interesting to note that when there is no field

polarity change, more PD events occur with similar magnitude. This is because

the electron generation rate is high after a PD event which makes the following

PD likely to occur, especially at high applied voltage, as in Figure 7.13 and

Figure 7.14. When the field polarity alternates, there is a reduction in the electron

generation rate and the following PD with larger magnitude will happen at a

higher electric field. Also, fewer PDs are likely to occur after a large magnitude

PD is incepted during the time the field polarity is unchanged.

Table 7.6 Values of adjustable parameters

Frequency

(Hz)

Applied Voltage

(kV) N

decay

(ms) Nev

0.1

8 30 1000 2

9 15 800 3

10 30 800 3

50

8 2500 2 40

9 2500 2 50

10 3500 2 50

For comparison, the simulated PD behaviours in 10 cycles under applied

voltage of 10 kV at 50 Hz are shown in Figure 7.15. Similar observations as

above can also be seen at power frequency. It is interesting to observe that there

are no PDs in some voltage cycles at this voltage level. This could be due to the

combination of PD occurrence probability and low electron generation rate,

which is affected by surface charge decay controlled by the time decay constant

between consecutive discharges.


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(a) Electric field simulation

(b) Discharge magnitudes

Figure 7.12 Simulation of electric field and PD magnitude for 10 cycles at 0.1 Hz

under applied voltage of 8 kV






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Figure 7.15 Simulation of electric field and PD magnitude for 10 cycles at 50 Hz



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7.4 Calculation of statistical time lag of partial discharge events

As described in Chapter 2, the statistical time lag is the average time span

between the moment the inception field is exceeded and the moment the

discharge actually occurs. With the help of simulation of the proposed partial

discharge model, this value could be determined for every single PD event.

Figure 7.16 shows the simulation of the electric field in a cavity in time and how

the statistical time lag is calculated. It is determined from the time when the local

field, Ecav, exceeds the inception value, Einc, to the time the following PD

happens. The average value of this time constant is equal to the sum of each time

lag divided by the total number of PD events.

stat stat stat

tn tn tn

Figure 7.16 Calculation of statistical time lag of PD events

Figure 7.17 shows the distribution of statistical time lag under different

applied voltage at 0.1 Hz and 50 Hz for 500 simulation cycles as described in

Section 7.3. The average time lag values are tabulated in Table 7.7. At both

frequencies, the average statistical time lag is lower with higher applied voltage.

This is expected as higher amplitude of the applied field increases the electron

generation rate, which reduces relatively the average waiting time for available

electrons to ignite a PD event when the inception field is exceeded. It is also

confirmed by the parameter value of the number of electrons generated at

inception field Einc, i.e. N, which is larger at higher simulated applied voltage at

both frequencies.


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The time lag at very low frequency is also much longer than that at power

frequency under the same applied voltage. This is due to the great difference of

time intervals among consecutive PD events at both applied frequencies. At

lower applied frequency, the time span between the previous discharge and the

next discharge likely to ignite is longer. Hence, less free charges generated from

the previous discharge are available to start the next PD event. As a result, the

statistical time lag is increased at lower applied frequency due to reduction of the

electron generation rate.

(a) 0.1 Hz (b) 50 Hz

Figure 7.17 Distribution of statistical time lag under different applied voltages at

different applied frequencies

Table 7.7 Average statistical time lag under different applied voltages at 0.1 Hz

and 50 Hz

Applied voltage U (kV) Average statistical time lag stat (ms)

0.1 Hz 50 Hz

8 127.8 10.5

9 110.1 4.8

10 95.8 4.2

7.5 Conclusion

This chapter presented electric field and discharge magnitudes obtained

from model simulations. In general, measurement and simulation data are in

good agreement. PD activities at very low frequency and power frequency are

quite different and the differences could be explained. PD magnitudes at very

low frequency are generally lower than those at 50 Hz at the same applied


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voltage. The number of discharges per cycle is higher at larger applied voltage at

both frequencies. From simulation, they could be due to the dependence of the

electron generation rate on applied voltage and frequency. It has been confirmed

that free electrons generated from surface emission and volume ionisation are

larger at higher frequency although their values are not the actual physical

parameters. The surface charge decay also contributes significantly to the

difference of partial discharge activities at both frequencies. At higher applied

frequency, cavity surface conductivity is larger which results in more

accumulated charges decay because charge movement along the cavity wall is

faster due to the shorter period of applied voltage. However, the effect of surface

charge decay is reduced at higher applied frequency as the time span between

consecutive discharges is much shorter. Hence, the statistical time lags are much

shorter at higher frequency and more discharges are incepted almost immediately

after the inception field is exceeded.

By comparing measurement and simulation results, critical parameters

influencing partial discharge activities at different applied voltage and frequency

can be determined including the inception field, extinction field, cavity surface

conductivity and effective charge decay time constant. Physical mechanisms

involved in partial discharge activities are the electron generation rate via surface

emission and volume ionisation and charge decay through charge trapping,

charge conduction along the cavity wall and charge recombination. The

following chapter summarises and concludes the research.

Chapter 8: Conclusion and Future

Work

8.1 Conclusion

This thesis developed and reported extensive empirical work to investigate

partial discharge under different stress conditions at very low frequency and

power frequency. The measurements have been done with two types of partial

discharge: corona discharge and internal discharge in a cavity. For corona

discharge, the test object was stressed under different applied waveforms such as

sine wave, square wave and sine wave with DC offset. The effects of ambient

temperatures on corona discharge were also investigated at very low frequency

and power frequency under excitation of sine wave and sine wave with DC

offset. Measurements of internal discharge in a cylindrical cavity have been

undertaken extensively at both frequencies of 0.1 Hz and 50 Hz as a function of

cavity size and applied voltage waveforms including sinusoidal and trapezoid-

based voltages. In order to determine critical parameters affecting internal

discharge behaviours, a discharge model has been developed and verified with

measurement results. The comparison between measurement and simulation

results revealed that physical parameters in the cavity are strongly dependent on

the applied frequency. A summary of experimental, analytical and simulation

studies of partial discharge characteristics in this thesis, together with main

findings drawn from the work, is presented below.

Chapter 1 presented the motivation of this research and explained the

importance of partial discharge diagnostic tests at very low frequency excitation.

Literature on partial discharge was reviewed in Chapter 2, including several

partial discharge models which have been developed using analytical and

dynamic approaches to simulate the internal discharge in a cavity. Critical

parameters affecting discharge activities identified from the simulation included

Chapter 8: Conclusion and Future Work

page 135

the initial electron generation rate, charge decay time constant, statistical time lag

and inception field. However, the analytical models were only applied for

investigation at power frequency. Of the dynamic models, one proposed model

was used to simulate partial discharge in the frequency range of 0.01 Hz to 100

Hz but it did not take into account the charge decay phenomenon. Another

proposed dynamic model did consider the charge decay phenomenon but it was

assumed that the charge decay time constant is fixed over the frequency range

studied (1 Hz to 50 Hz). This model was not verified at very low frequency.

Therefore, the discharge model developed and presented in this thesis aims

to include the charge decay phenomenon with frequency-dependent values for

the charge decay time constant. The proposed discharge model to simulate

internal discharge dynamically was described in detail in Chapter 3. The model

has a minimal set of adjustable parameters which allows it to simulate the

discharge behaviours at different frequencies in a reasonable period of time. This

advantage made it possible to investigate partial discharge under various stress

conditions such as voltage amplitudes and applied frequencies. The surface

charge distribution and its effects on subsequent partial discharges were also

obtained using this proposed model.

In order to investigate the partial discharge, an important task is to conduct

experiments and gather raw discharge data. The conventional partial discharge

measurement system fully compliant to the IEC 60270 standard was used to

record the partial discharge characteristics. The equipment setup was described in

Chapter 4. The partial discharge analysis, calculation of discharge parameters

and phase-resolved partial discharge pattern technique were also presented. Two

types of discharges, corona discharge and internal discharge, were generated in

the laboratory by preparing the appropriate test objects. A needle and bowl

electrode configuration was used to produce corona discharge. Internal discharge

was generated in a cylindrical cavity embedded in a solid dielectric test sample

which was fabricated by using a 3D printer. The experiment procedures were

described extensively to ensure the consistency of recorded partial discharge data

at different applied stress conditions.


page 136

Chapter 5 presented experimental results of corona discharge at very low

frequency and power frequency. It was found that the applied voltage waveform

affects the inception voltage of corona discharge at very low frequency.

Inception voltage, in the case of applied square wave and sine wave with DC

offset, was found to be lower than that under the pure sine wave. This is likely to

be explained by the longer duration of high negative voltage amplitude applied to

the needle under the square wave and sine wave with DC offset. The high level

of negative voltage amplitude causes the negative corona discharge to be

triggered more easily. The experiment results supported a hypothesis that a faster

rise time of voltage results in larger discharge repetition rate and discharge

magnitudes.

The effects of ambient temperatures on corona discharge were also

investigated at both frequencies of 0.1 Hz and 50 Hz. It was shown that discharge

characteristics under both frequencies had similar behaviours in such a way that

higher ambient temperature caused discharges to occur with larger magnitudes

and earlier regarding the voltage phase. This was due to the increase of free

electron availability injected from the needle at higher temperatures.

Chapter 6 described one of the main contributions of this thesis. A

comparative experimental study of cavity discharges was presented as a function

of cavity size and applied voltage waveforms at frequencies of 0.1 Hz and 50 Hz.

Changes of discharge characteristics after long discharge exposure were obtained

at various applied frequencies. This could be due to the differences of cavity

surface conductivity evolution during the exposed discharge period. Cavity

discharge characteristics were found to be strongly dependent on applied voltage

waveforms and the rate of voltage rise. Discharge magnitudes were generally

smaller at lower applied frequency regardless of applied voltage waveforms. It

was found that more discharges with low magnitudes occurred in a larger cavity

as the effective discharge area was increased. These findings could be explained

by the dependence of surface charge decay on applied frequency. The surface

charge decay was likely to be more significant at lower applied frequency.


page 137

The simulation results presented in Chapter 7 confirmed the effects of

charge decay on cavity discharge characteristics. The simulated value of cavity

surface conductivity, which was verified by measurement results, increased at

higher applied frequency and thus there was more surface charge decay in time

despite it not being the actual physical value. However, the charge decay rate was

reduced at frequency of 50 Hz since the time span between consecutive

discharges was much shorter.

The effect of charge decay also contributed to differences in partial

discharge behaviours at different applied frequencies. Discharge magnitudes at

very low frequency were found to be lower than those at power frequency at the

same voltage amplitude. The discharge repetition rate was also lower at lower

applied frequency. These differences were attributed to the dependence of the

adjustable parameters in the simulation model on applied frequency. It was

verified that the amont of free electrons generated from surface emission and

volume ionisation was smaller at lower frequency while the charge decay time

constant was shorter at higher frequency. From simulation, the effects of charge

distribution on the cavity surface on subsequent discharges were analysed at both

very low frequency and power frequency. The statistical time lag of every single

discharge was calculated numerically to illustrate the dependence of discharge

behaviours on applied frequency.

In summary, this thesis presents extensive empirical work investigating

partial discharge at very low frequency and power frequency under different

stress conditions. The phase-resolved partial discharge patterns obtained from

simulations and measurements were analysed thoroughly to explore the discharge

differences. The explanation of these differences was discussed analytically and

confirmed via a simulation approach.

For corona discharges, it was found that maximum and average discharge

magnitudes at 50 Hz were larger than those at 0.1 Hz under the same applied

voltage amplitude. Although the repetition rate of corona discharge at 0.1 Hz was

larger than that at 50 Hz in terms of pulses per cycle, it was lower at 0.1 Hz than


page 138

at 50 Hz in terms of pulses per second. The obtained phase-resolved patterns

were fairly similar at both applied frequencies.

For internal discharge, discharge behaviours were found to be dependent on

applied voltage waveforms. Under the sinusoidal voltage excitation, maximum

and average discharge magnitudes at 50 Hz were generally larger than those at

0.1 Hz under the same voltage amplitude. The repetition rate of discharges at 50

Hz was also larger than that at 0.1 Hz in terms of both pulses per second and

pulses per cycle. The obtained phase-resolved patterns were quite different under

different applied frequencies. The discharge patterns at 50 Hz had the “rabbit-

ear” shape which was formed by large discharges occurring early in voltage

phase. On the contrary, this distinct shape was hardly observed at 0.1 Hz since

most large discharges occurred later in voltage phase.

Under square voltage excitation, maximum and average discharge

magnitudes at 0.1 Hz were much lower than those at 50 Hz under the same

applied voltage. Although the repetition rate of discharges at 0.1 Hz was smaller

than that at 50 Hz at different voltage amplitudes in terms of pulses per second, it

was higher at 0.1 Hz than at 50 Hz in terms of pulses per cycle. The obtained

phase-resolved patterns at both frequencies were clearly different. Discharge

occurrence at 0.1 Hz was concentrated in the duration of voltage polarity

reversal. Discharges were barely detected during the period of constant voltage.

On the contrary, the majority of discharges occurred at the voltage changing

period under 50 Hz excitation. There were a number of discharges with low

magnitudes observed during the “flat” peak voltage of square waveform.

Under triangular voltage excitation, maximum discharge magnitude at 50

Hz was generally larger than that at 0.1 Hz even at lower applied voltage

amplitude. Average discharge magnitude at 50 Hz was larger as compared to 0.1

Hz at the same applied voltage. The repetition rate of discharges at 50 Hz was

larger than that at 0.1 Hz even at lower applied voltage in terms of both pulses

per second and pulses per cycle. The obtained phase-resolved patterns were quite

different. Discharge distribution at 50 Hz was mainly in the front voltage rise. On


page 139

the contrary, discharge distribution at 0.1 Hz was mainly around the peak voltage

regions with large discharges occurring at later voltage phase.

Under trapezoidal voltage excitation, maximum and average discharge

magnitudes at 0.1 Hz were generally lower than those at 50 Hz even at higher

applied voltage amplitudes. The repetition rate of discharges at 0.1 Hz was

smaller than that at 50 Hz even at higher applied voltage in terms of both pulses

per second and pulses per cycle. The obtained phase-resolved patterns were quite

similar. Most of detected discharges occurred during the voltage polarity reversal

period. There were a few discharges with low magnitudes occurred during the

constant voltage period at both applied frequencies.

8.2 Future research directions

The partial discharge model with a minimal set of adjustable parameters

proposed in the thesis successfully simulates discharge activities in a cylindrical

cavity at very low frequency of 0.1 Hz and power frequency of 50 Hz. Although

the measurement and simulation results show good agreement, there are still

some differences. These discrepancies might be due to the measurements or the

simulations. For instance, the measured discharge data might not be recorded

accurately due to switching interferences from the very low frequency test supply

(high voltage amplifier) or other testing activities in the laboratory.

There might be errors in simulated partial discharge results due to several

assumptions made to simplify the model. The differences might also be caused

by estimation of the model adjustable parameters due to the time-consuming trial

and error procedures. Therefore, the discharge model can be improved with

further work. Also, it should take into account other factors such as temperature

and pressure in the cavity whilst retaining the minimal number of adjustable

parameters if possible. By adopting state-of-the-art optimisation algorithms, it

should be more efficient and the simulation time to search for the best parameter

values can be reduced.

The simulation work of this thesis only used sinusoidal voltage at frequency

of 0.1 Hz and 50 Hz although the measured discharge data under other applied


page 140

voltage waveforms are available. Thus, this study should be extended in

simulating cavity discharges under other applied waveforms such as triangular,

trapezoid-based and customised wave. This will enable a broader understanding

of discharge behaviours across multiple voltage waveforms.

With the capability of the arbitrary function generator, voltage waveforms

with a wide range of frequencies can be generated. As a result, future research on

partial discharge should be conducted at more values of applied frequencies. This

will provide extensive discharge results across a wide frequency range of applied

voltage to give an in-depth analysis of discharge characteristics. These measured

results can be used to verify the simulation under the same conditions to exploit

more valuable information on discharge behaviours over a broad range of

frequencies.

The cavity discharge study in this thesis was restricted to a cylindrical void

in Acrylonitrile-Butadiene-Styrene (ABS) material. Although ABS material is

not widely used for high voltage insulation, this research successfully

demonstrates the cavity discharge behaviours in a plastic material at very low

frequency and power frequency. A similar methodology can be used in future

partial discharge research on various cavity geometries with different types of

insulation materials. Of course, this will depend on the ability of 3D printing

technology to work with such materials.

Despite the different physical mechanisms between cavity discharge and

corona discharge, corona discharge can be simulated dynamically by using a

similar approach. A corona discharge model can be developed to investigate the

effects of various insulating media on corona discharge activities.

Another ambient condition affecting the corona discharge which was not

considered in this research is humidity. As high voltage equipment is usually

operated under varying humidity levels, it is essential to investigate the effects of

humidity on corona discharge at very low frequency.

Appendix A: Variable Power Source

Specifications

A.1 Function generator specifications

The arbitrary waveform generator used in this thesis is Keysight Agilent

33500B Series which has one output channel. The front control panel of this

equipment is shown in Figure A.1.

Figure A.1 Front control panel of the waveform generator

For the purposes of this research, the waveform characteristics extracted

from the product’s specifications in [97] are summarised as follows:

(a) Sine waveform:

– Frequency range: 1 Hz to 20 MHz, 1Hz resolution

– Amplitude flatness:

(relative to 1 kHz)

<100 kHz:

100 kHz to 5 MHz:

5 MHz to 20 MHz:

0.10 dB

0.15 dB

0.30 dB

(b) Square waveform:

– Frequency range: 1 Hz to 20 MHz, 1Hz resolution

– Rise and fall times: Square: 8.4 ns, fixed

– Overshoot: < 2%

Duty cycle: 0.01% to 99.99%

– Pulse width: 16 ns minimum

(c) Triangle and ramp waveform:

– Frequency range: 1 Hz to 20 kHz, 1Hz resolution

– Ramp symmetry: 0.0% to 100.0 %, 0.1% resolution

(0% is negative ramp, 100% is positive ramp,

50% is triangle)

– Nonlinearity: < 0.05% from 5% to 95% of the signal amplitude

(d) Arbitrary waveform:

– Waveform length: 8 Sa to 1 MSa

– Sample rate: 1 Sa/s to 250 MSa/s, 1 Sa/s resolution

– Voltage resolution: 16 bits

A.2 High voltage amplifier specifications

In this research, high voltage amplitudes at variable waveforms are

generated by using a Trek 20/20C-HS high voltage amplifier receiving the input

signal from the waveform generator. This instrument amplifies the received

signal 2000 times and generates high voltage at the output terminal. The front

control panel of this equipment with the settings used during the experiments is

shown in Figure A.2.

Figure A.2 Front control panel of high voltage amplifier

Details of amplifier specifications are summarised as below [98]:

– Output voltage range: 0 to ±20 kV DC or peak AC

– Output current range: 0 to ±20 mA DC or ±60 mA peak for 1 ms

(must not exceed 20 mA rms)

– Input voltage range: 0 to ±10 V DC or peak AC

– DC voltage gain: 2000 V/V

– DC voltage gain accuracy: Better than 0.1% of full scale

– DC offset voltage : Better than ±2 V

– Output noise: Less than 1.5 V rms

– Slew rate:

(10% to 90%, typical)

Greater than 800 V/ s

– Large signal bandwidth: DC to greater than 5.2 kHz

– Small signal bandwidth: DC to greater than 20 kHz

Appendix B: Usage of Mtronix

MPD600 Software

B.1 Graphic User Interface of Mtronix MPD600

Main sections of the general Graphic User Interface (GUI) of Mtronix

MPD600 are shown in Figure B.1. Details of these sections are as follows:

1. Acquisition unit display: Types of acquisition units detected by the

software are shown in this area.

2. Visualisation display: This area visually displays the majority of the

parameters and graphs needed by user’s interests. It occupies most of

the left half of the user interface. This section includes a large scope

view at the top left corner (4), a smaller scope view at bottom left corner

(5) and a display box of measured quantities at the centre of the

interface (6).

3. Control panel: This provides access to all functions of the software via

appropriate tabs.

4. Large scope view: This normally displays the phase-resolved pattern of

discharges during measurements.

5. Small scope view: This area can display the spectrum of input signal,

time-domain signal and trend curves of measured quantities.

6. Measured quantities display: This box displays values of measured

quantities such as apparent charges, number of recorded discharges,

recording duration and measurement bandwidth.

B.2 Calibration procedures prior to measurements

Calibration must be done prior to any measurements in this thesis. The

calibrator CAL542 is connected in parallel with the test object and injects a

known amount of charges, i.e. 50 pC, into the measurement circuit. The

measuring frequency settings are 250 kHz of centre frequency and 300 kHz of

bandwidth.

1

5

2

4

63

Figure B.1. Mtronix MPD600 Graphic User Interface

Calibration steps in Figure B.2 are as follows:

1. Under Q tab: go to Charge intergration settings, set fCenter = 250 kHz

and f = 300 kHz.

2. Under Q tab: go to Display settings, set Qmax and Qmin equal to 100 pC

and 1 pC, respectively in order to display the calibration signal of 50 pC

properly.

3. Under Q tab: go to Calibration Settings, set QIEC (target) equal to 50

pC.

4. Press Compute button to finish the calibration.

Once the calibration is done, the QIEC (measured) should display a reading

very close to 50 pC.

Figure B.2. Charge calibration prior to measurements

B.3 Procedure for measuring and recording of discharge signals

Prior to high voltage application to the test object, it is vital to physically

remove the calibrator out of the measurement circuit.

The calibration of applied voltage can be done via two steps. For instance, it

is assumed that a known voltage of 2 kVrms is currently applied to the test

object. Two steps of voltage calibration in Figure B.3 are as follows:

1. Under V tab: go to Calibration, set Vrms (target value) equal to 2 kV.

2. Press Compute button to finish the voltage calibration. An

approximately value of 2 kV should be then displayed in Vrms

(measured value).

Figure B.3. Voltage calibration in Mtronix MPD600

The discharge actitivites should be displayed visually in the large scope

view when the applied voltage is increased to the desired value of discharge

measurement. The measuring and recording procedures are as follows:

1. Under Q tab: go to Display settings, appropriately adjust Qmax and Qmin

values to observe discharge events clearly in the large scope view.

2. To view the discharge histogram for a specific time length, check the

Time histogram acquisition box under the Q tab and set the desired time

length. Then, press Go! Button as in Figure B.2.

3. To record discharge activities, firstly specify the file name and its location

in the Record file(z) under the Q tab. To start recording, press the

Record button. To finish recording, press the Record button again.

Figure B.4 shows an example of recorded time histogram plot of

discharges.

Figure B.4. An example of time histogram of discharges

B.4 Procedures of exporting recorded data to MATLAB

compatible files

Procedures of exporting recorded data in Figure B.5 for further analysis are

as follows:

1. Open the desired recorded file with filename extension .stm. A Replay

tab should be displayed in the Control Panel area.

2. Under Replay tab: go to Replay range and set desirable time length in

Start replay at and replay for boxes.

3. Under the Replay tab: go to Export to Matlab and specify the location

of exported data. Then, check the boxes of Export Matlab-compatible

files and generate phase vector file before pressing the play button.

The exported data are saved in the specified location with different filename

extension .PH, .Q and .V. The data in these files can be imported in MATLAB

via functions written in MATLAB.

Figure B.5. Replay procedures to export data into Matlab compatible files

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