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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To my loving family…….. Dedicated to Ruby…….
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!
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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 ii
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.
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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 iv
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 v
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 vi
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
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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
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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 ix
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 x
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
Figure 7.3 Simulation of electric field distribution and equipotential lines in the model at 50 Hz and 10 kVrms when the second PD
occurs ...... 116
Figure 7.4 Cross-section plots of field magnitude in the model before and
after the second PD in Figure 7.3 ...... 117
Figure 7.5 Simulation of electric field distribution and equipotential lines
in the model at 0.1 Hz and 10 kVrms when the first PD occurs ... 118
Figure 7.6 Cross-section plots of field magnitude in the model before and
after the first PD in Figure 7.5 ...... 119
Figure 7.7 Simulation of electric field distribution and equipotential lines in the model at 0.1 Hz and 10 kVrms when the second PD
occurs ...... 120
Figure 7.8 Cross-section plots of field magnitude in the model before and
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
Figure 7.13 Simulation of electric field and PD magnitude for 10 cycles at
0.1 Hz under applied voltage of 9 kV ...... 129
Figure 7.14 Simulation of electric field and PD magnitude for 10 cycles at
0.1 Hz under applied voltage of 10 kV ...... 130
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Figure 7.15 Simulation of electric field and PD magnitude for 10 cycles at
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
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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 xiii
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
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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 1 Chapter 1: Introduction
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 2 Chapter 1: Introduction
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 3 Chapter 1: Introduction
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 4 Chapter 1: Introduction
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
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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
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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.
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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.
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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.
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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.
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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 11 Chapter 2: Literature Review 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.
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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 13 Chapter 2: Literature Review 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 14 Chapter 2: Literature Review 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].
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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].
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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
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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.
Vc Fc Ca V~ Cc Va
Cb Vb
(a) characteristics circuit elements
ib Cb
ic + ib ic ib
Fc Cc Ca Va
(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 18 Chapter 2: Literature Review 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
qVCCrcbc () (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
qVCVCaaacb (2.2) From equation (2.1) and (2.2), we have
CCbb qqqarr (2.3) CCCbcc
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
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qrdS .. (2.4) S
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
qKEE()incext 0 (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 20 Chapter 2: Literature Review 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
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(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].
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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 23 Chapter 2: Literature Review 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 24 Chapter 2: Literature Review 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.
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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 26 Chapter 2: Literature Review 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 EB Epinc 1 n (2.7) ppdcr () where Ep , B and n are parameters related to the gas ionisation process, cr p is the pressure in the void and d is the cavity diameter. For air, these parameters are Ep = 24.2 VPa-1m-1, n = 0.5 and B = 8.6 Pa1/2 [28,31,36]. cr
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 27 Chapter 2: Literature Review 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.
page 28
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.
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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:
D f (3.1)
f J f 0 (3.2) t 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 J f is the free current density. Since DE and EV where is the material permittivity, E is the electric field and V is the electric potential, equation (3.1) can be rewritten as
( V) f (3.3)
As JEf , by substituting equation (3.3) into equation (3.2), it can be expressed as follows ( VV ) ( ) 0 (3.4) t where is the material electrical conductivity.
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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.
Cylindrical void Void surface High voltage electrode
Symmetric axis Dielectric Material Ground Electrode
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.
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Figure 3.2 2D model geometry with meshed elements
11 9 10 7 8 5 12 13 14 6 3 4 1 2
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
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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 r 0
11 Electric potential VUsqrtpift rms *(2)*sin(2***) 2 Ground V 0 14 Electric insulation nJ*0
4,6,8,10,12,13 Continuity n J*( J ) 012
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 33 Chapter 3: Modelling of Internal Discharge 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 34 Chapter 3: Modelling of Internal Discharge
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 eN e e e (3.5) mcee
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 qe N (3.6) e 43r3 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 35 Chapter 3: Modelling of Internal Discharge
tdt q I t d t () PD (3.7) t 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 36 Chapter 3: Modelling of Internal Discharge
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.
E0 fcE0 Ecav Eq
E0 fcE0 Ecav Eq
(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 37 Chapter 3: Modelling of Internal Discharge
NtNtNPDesev()() (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
Etcav () NtNes () (3.9) Einc
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 38 Chapter 3: Modelling of Internal Discharge
EtEt()() tt NtN()expexpcavcav PD es (3.10) EEincdecayinc
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
EtEt( )( ) tt NtNN( )expexp cavcav PD PDev (3.11) EEincdecayinc
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
PtNtt()()PD (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 39 Chapter 3: Modelling of Internal Discharge 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
Value Description Symbol 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 -3 Cavity conductivity during PD cavH 5x10 S/m 6 Electric inception field Einc 3.93x10 V/m 6 Electric extinction field Eext 1x10 V/m
Cavity surface low conductivity sL 0 S/m -11 -9 Cavity surface high conductivity sH 1x10 1x10 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 40 Chapter 3: Modelling of Internal Discharge
-3 whole cavity, the conductivity of the cavity, cav, is set equal to 5x10 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
-3 discharge. If cav is chosen higher than 5x10 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
-3 magnitude. On the other hand, if cav is set lower than 5x10 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 6 (2.7), which results in 3.93x10 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 6 was found that Eext is equal to 1x10 V/m for all simulations.
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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
-9 frequencies. When Ecav and Eq have the same direction, sH is equal to 1x10 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 Applied voltage N decay N (Hz) (kV) (ms) ev 8 30 1000 2 0.1 9 15 800 3 10 30 800 3 8 2500 2 40 50 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 42 Chapter 3: Modelling of Internal Discharge element method model at each time step and PD occurrence determination, are shown in Figure 3.5 to Figure 3.7.
Start
Model initialised
Y Increase time step End time?
N Update boundary cav cavH and subdomain
Solve FEM model Save results Solve FEM model
N Ecav < Eext ? N Ecav > Einc ? Y End
Y cav cavL Calculate P Y Eq/Ecav > 0 s sH Y P > R ? N
N s sL
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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Input
Calculate electron generation rate, NPD(t)
Compute probability P
Generate random number R
Y N P > R
Discharge is No discharge set to occur occurs
Update subdomain and boundary settings
Output
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 45 Chapter 3: Modelling of Internal Discharge 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.
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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.
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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
page 48 Chapter 4: Test Setup and Partial Discharge Measurements 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
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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
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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.
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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 52 Chapter 4: Test Setup and Partial Discharge Measurements 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 n Iq i (4.1) T i1 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).
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n r (4.2) T n r (4.3) K 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 n P q v ii (4.4) T i1 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).
n 1 2 Dq i (4.5) T i1 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 n qqave i (4.7) n i1
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 54 Chapter 4: Test Setup and Partial Discharge Measurements 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.
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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
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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] r VV1 b (4.8) d 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).
Needle tip
d
R = 25 mm
Ground electrode
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 58 Chapter 4: Test Setup and Partial Discharge Measurements 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. l
1 mm 3 mm 1 mm 1 mm
50 mm 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
Vb VVVVacc b 1 (4.9) Vc
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
VEdccav (4.10)
VtdEb ()0 (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
E0 td VVac1 (4.12) Edcav
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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:
EEcavr 0 (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 V V a c 1 td 1 (4.14) r d 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
Vpdpdbreakdown 6.7224.36() (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.
A
Vc Ca V~ d Cc t Va
Cb Vb
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 61 Chapter 4: Test Setup and Partial Discharge Measurements 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
page 62 Chapter 4: Test Setup and Partial Discharge Measurements 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.
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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.
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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.
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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.
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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
page 68 Chapter 5: Corona Discharge Activities: Effects of Applied Voltage Waveforms and Ambient Conditions 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
page 69 Chapter 5: Corona Discharge Activities: Effects of Applied Voltage Waveforms and Ambient Conditions 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
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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
page 72 Chapter 5: Corona Discharge Activities: Effects of Applied Voltage Waveforms and Ambient Conditions 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) 3.8 48.4 35.5 45 0.4 0.1 4 75.7 61.3 69.7 2.2
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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) 3.8 45 35 39.5 0.4 0.1 4 58 45 53 0.8
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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.
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(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
page 76 Chapter 5: Corona Discharge Activities: Effects of Applied Voltage Waveforms and Ambient Conditions 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
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(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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(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 Temperature PD magnitude (pC) Repetition rate (Hz) (oC) max min ave (pps) 20 59 50 53 0.2 30 60 30 50 0.055 0.1 35 88 30 57 19.1 40 115 20 60 0.11 20 88 63 75 3.5 30 88 40 50 2.0 50 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
page 79 Chapter 5: Corona Discharge Activities: Effects of Applied Voltage Waveforms and Ambient Conditions 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.
120 20C 120 20C 30C 30C 100 35C 100 35C 40C 40C 80 80
60 60
40 40
PDMagnitude (pC) PD magnitude (pC) magnitude PD 20 20
0 0 180 210 240 270 300 330 360 180 225 270 315 360 Phase angle (degree) Phase angle (degree)
(a) Maximum PD magnitude (b) Average PD magnitude Figure 5.12 Discharge distribution at PDIV and 0.1 Hz
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120 20C 120 20C 30C 30C 100 35C 100 35 C 40C 40C
80 80
60 60
40 40
PD magnitude (pC) PD magnitude (pC) 20 20
0 0 180 210 240 270 300 330 360 180 225 270 315 360 Phase angle (degree) Phase angle (degree)
(a) Maximum PD magnitude (b) Average PD magnitude 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 Temperature PD magnitude (pC) Repetition rate (Hz) (oC) max min ave (pps) 20 98 32 55 1108 30 116 23 66 465 0.1 35 100 35 63 1155 40 200 30 98 45 20 77 30 54 1215 30 120 25 57 6 50 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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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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220 20C 160 20C 200 30C 140 30C 180 35C 35C 120 160 40C 40C
140 100 120 80 100
80 60
60
40
PD magnitude (pC) PD magnitude (pC) 40 20 20
0 0 180 210 240 270 300 330 360 180 210 240 270 300 330 360 Phase angle (degree) Phase angle (degree)
(a) Maximum PD magnitude (b) Average PD magnitude 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
page 84 Chapter 5: Corona Discharge Activities: Effects of Applied Voltage Waveforms and Ambient Conditions 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
page 86 Chapter 5: Corona Discharge Activities: Effects of Applied Voltage Waveforms and Ambient Conditions frequency by performing partial discharge measurements in a cavity as a function of cavity size and applied voltage waveforms.
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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
page 88 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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.
3500
3000
2500
2000 0.1 Hz Q_average 1500 0.1 Hz Q_max
1000 50 Hz Q_average PD magnitude (pC) magnitude PD 50 Hz Q_max 500
0 0 1 2 3 4 Time (h)
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
page 89 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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
page 90 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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.
100 90 80 70 60 50 0.1 Hz 40 30 50 Hz
Phase Angle (degree) Angle Phase 20 10 0 0 1 2 3 4 Time (h)
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
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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
page 92 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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.
250
200
150
0.1 Hz 100 50 Hz
PD repetition rate (pps) rate repetition PD 50
0 0 1 2 3 4 Time (h)
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 page 93 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms
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
page 94 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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.
6000
5000
4000
3000 0.1 Hz
2000 50 Hz PD Magnitude (pC) Magnitude PD 1000
0 0 30 60 90 120 150 Time (minutes)
Figure 6.7 Average PD magnitude over the testing period at 0.1 Hz and 50 Hz under square voltage application of 10 kV
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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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+V
0
-V
+++++++ ------
E0 Ep E0 Er Ep
------+++++++ (a) (b) (c)
+ : Free Charges E0: External applied electric field
: Bounded Charges Ep: Internal electric field due to polarized charges
: 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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4500 4000 3500 3000 2500 2000 0.1 Hz 1500 50 Hz 1000 Discharge magnitude (pC) magnitude Discharge 500 0 2 4 6 8 Void diameter (mm)
(a) Maximum magnitude
1400
1200
1000
800
600 0.1 Hz
400 50 Hz
Discharge magnitude (pC) magnitude Discharge 200
0 2 4 6 8 Void diameter (mm)
(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 page 100 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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 (a) Upeak (b)
t
t1 t2 t3
T/2
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
page 103 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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.
0.1 Hz 50 Hz
800
600
400
200 Maximum PD Magnitude (pC) Magnitude PD Maximum 0 8 9 10 Applied Voltage Urms (kV)
(a) Maximum PD magnitudes and repetition rate
0.1 Hz 50 Hz 0.1 Hz 50 Hz
400 20
300 15
200 10
100 5
Repetition Rate (ppc) Rate Repetition Average PD Magnitude (pC) Magnitude PD Average 0 0 8 9 10 Applied Voltage Urms (kV)
(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
page 104 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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) 9 2555 316 8.4 50 10 6467 976 8.8 11 1122 516 2.1 0.1 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: t 1 *100% (6.1) T /2
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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
page 106 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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) 9 167 81 2.6 50 10 2074 1719 8.1 10% 11 1493 665 4.52 0.1 12 1713 675 5.57 13 1766 706 8.47 9 84 61 0.25 50 10 1699 885 6.5 20% 11 1014 469 2.47 0.1 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) 1 1388 218 9.07 0.1 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
page 108 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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
page 109 Chapter 6: Void Discharge Behaviours as a Function of Cavity Size and Applied Waveforms 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.
E0
Emax
Einc Eq Ecav
Eext t
-Eext
-Einc
-Emax
(a) Charge decay ignored
E0
Emax
Einc Eq
Ecav Eext t
-Eext
-Einc
-Emax
(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.
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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
page 113 Chapter 7: Void Discharge Behaviours: Comparison between Measurements and Simulations 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
page 114 Chapter 7: Void Discharge Behaviours: Comparison between Measurements and Simulations 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
page 115 Chapter 7: Void Discharge Behaviours: Comparison between Measurements and Simulations 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 Figure 7.3 Simulation of electric field distribution and equipotential lines in the 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
page 116 Chapter 7: Void Discharge Behaviours: Comparison between Measurements and Simulations 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).
(a) Along the z-axis (b) Along the r-axis Figure 7.4 Cross-section plots of field magnitude in the model before and after the 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
page 117 Chapter 7: Void Discharge Behaviours: Comparison between Measurements and Simulations 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 Figure 7.5 Simulation of electric field distribution and equipotential lines in the model at 0.1 Hz and 10 kVrms when the first PD occurs
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(a) Along the z-axis (b) Along the r-axis Figure 7.6 Cross-section plots of field magnitude in the model before and after the 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. page 119 Chapter 7: Void Discharge Behaviours: Comparison between Measurements and Simulations
(a) Before the second PD occurrence
(b) After the second PD occurrence Figure 7.7 Simulation of electric field distribution and equipotential lines in the model at 0.1 Hz and 10 kVrms when the second PD occurs
(a) Along the z-axis (b) Along the r-axis Figure 7.8 Cross-section plots of field magnitude in the model before and after the 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 Applied voltage (kV) 8 9 10 Maximum PD magnitude (pC) 528 629 696 Average PD magnitude (pC) 267 276 304 Minimum PD magnitude (pC) 144 145 144 Repetition rate (ppc) 1.13 2.20 2.40
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
page 122 Chapter 7: Void Discharge Behaviours: Comparison between Measurements and Simulations 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 page 125 Chapter 7: Void Discharge Behaviours: Comparison between Measurements and Simulations 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 Applied voltage (kV) 8 9 10 Maximum PD magnitude (pC) 411 439 480 Average PD magnitude (pC) 183 222 245 Minimum PD magnitude (pC) 146 144 144 Repetition rate (ppc) 1.1 2.2 2.4
Table 7.4 Simulation results at 0.1 Hz under different applied voltages Applied voltage (kV) 8 9 10 Maximum PD magnitude (pC) 415 440 481 Average PD magnitude (pC) 197 201 207 Minimum PD magnitude (pC) 146 144 144 Repetition rate (ppc) 2.7 3.3 3.8
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 -3 Cavity conductivity during PD, cavH 5x10 S/m 6 Electric inception field, Einc 3.93x10 V/m 6 Electric extinction field, Eext 1x10 V/m
Cavity surface low conductivity, sL 0 S/m -11 -9 Cavity surface high conductivity, sH 1x10 1x10 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
page 127 Chapter 7: Void Discharge Behaviours: Comparison between Measurements and Simulations 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 Applied Voltage N decay N (Hz) (kV) (ms) ev 8 30 1000 2 0.1 9 15 800 3 10 30 800 3 8 2500 2 40 50 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
(a) Electric field simulation
(b) Discharge magnitudes Figure 7.13 Simulation of electric field and PD magnitude for 10 cycles at 0.1 Hz under applied voltage of 9 kV
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(a) Electric field simulation
(b) Discharge magnitudes Figure 7.14 Simulation of electric field and PD magnitude for 10 cycles at 0.1 Hz under applied voltage of 10 kV
(a) Electric field simulation
(b) Discharge magnitudes Figure 7.15 Simulation of electric field and PD magnitude for 10 cycles at 50 Hz under applied voltage of 10 kV
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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.
tn tn tn
stat stat stat
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
Average statistical time lag stat (ms) Applied voltage U (kV) 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
page 132 Chapter 7: Void Discharge Behaviours: Comparison between Measurements and Simulations 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.
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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
page 134 Chapter 8: Conclusion and Future Work 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.
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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.
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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 137 Chapter 8: Conclusion and Future Work 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 138 Chapter 8: Conclusion and Future Work 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 139 Chapter 8: Conclusion and Future Work 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.
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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: <100 kHz: 0.10 dB (relative to 1 kHz) 100 kHz to 5 MHz: 0.15 dB 5 MHz to 20 MHz: 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%
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– 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
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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: Greater than 800 V/ s (10% to 90%, typical) – Large signal bandwidth: DC to greater than 5.2 kHz – Small signal bandwidth: DC to greater than 20 kHz
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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
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measuring frequency settings are 250 kHz of centre frequency and 300 kHz of bandwidth.
3 1 6
4
2
5
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.
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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.
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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.
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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.
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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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References
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