KERR ELECTRO-OPTIC MEASUREMENTS IN LIQUID DIELECTRICS
by
Xuewei Zhang
B.S., Electrical Engineering
Tsinghua University, Beijing, China, 2007
M.S., Electrical Engineering
Tsinghua University, Beijing, China, 2009
Thesis Submitted to Department of Electrical Engineering and Computer Science
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
at the
Massachusetts Institute of Technology
June 2014
© 2014 Massachusetts Institute of Technology. All rights reserved.
Author……………………………………………………………………………………………………………….
Department of Electrical Engineering and Computer Science
May 21, 2014
Certified by………………………………………………………………………………………………………….
Markus Zahn
Thomas and Gerd Perkins Professor of Electrical Engineering
Thesis Supervisor
Accepted by………………………………………………………………………………………………………....
Leslie A. Kolodziejski
Chair of the Committee on Graduate Students
Department of Electrical Engineering and Computer Science
KERR ELECTRO-OPTIC MEASUREMENTS IN LIQUID DIELECTRICS
by
Xuewei Zhang
Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
Abstract
Kerr electro-optic technique has been used to measure the electric field distribution in high
voltage stressed dielectric liquids, where the difference between refractive indices for light
polarized parallel and perpendicular to the local electric field is a function of the electric field
intensity. For transformer oil, the most widely-used insulating liquids in power apparatus and
high voltage technology, Kerr effect is very weak due to its low Kerr constant. Previous Kerr
measurements have been using ac modulation technique, which is only applicable to dc steadystate electric field mapping while various instabilities develop in liquid under long-term high
voltage application. The use of the high-sensitivity CCD camera as optical detector makes it
possible to capture the weak Kerr effect in high voltage stressed transformer oil.
The first part of this thesis is to demonstrate the reliability and evaluate the sensitivity of the
measurements for various cases with identical electrodes under pulsed excitation with
insignificant flow effects. After the validation and optimization of the experimental setup,
measurements are taken to record the time evolution of electric field distributions in transformer
oil stressed by high voltage pulses, from which the dynamics of space charge development can
be obtained. Correlation between space charge distribution pattern and impulse breakdown
voltage is examined. Hypothetically, bipolar homo-charge injection with reduced electric field at
both electrodes may allow higher voltage operation without insulation failure, since electrical
breakdown usually initiates at the electrode-dielectric interfaces. It is shown that the hypothesis
is testable and correct only under specific circumstances. Besides, fractal-like kinetics for
electrode charge injection is identified from the measurement data, which enriches the
knowledge on ionic conduction in liquids by offering an experimentally-determined boundary
condition to the numerical model. Physical mechanisms based on formative steps of adsorptioni
reaction-desorption reveal possible connections between geometrical characteristics of electrode
surfaces and fractal-like kinetics of charge injection.
The second part of this thesis focuses on the fluctuations in the detected light intensity in Kerr
measurements. Up to now, within an experimentally-determined valid range of high voltage
pulse duration, the strategy to reduce fluctuation has been taking multiple measurements and
then averaging the results. For very short impulses, it is found that the light intensities near the
rough surfaces of electrodes both fluctuate in repeated measurements and vary spatially in a
single measurement. The major cause is electrostriction which brings disturbances into optical
detection. The calculated spatial variation has a strong nonlinear dependence on the applied
voltage, which generates a precursory indicator of the electrical breakdown initiation. This result
may have potential applications in non-destructive breakdown test and inclusion detection in
dielectric liquids. When the applied voltage is dc or ac, signatures of turbulent electroconvection
in transformer oil are identified from the Kerr measurement data. It is found that when the
applied dc voltage is high enough, compared with the results in the absence of high voltage, the
optical scintillation index and image entropy exhibit substantial enhancement and reduction
respectively, which are interpreted as temporal and spatial signatures of turbulence. Under lowfrequency ac high voltages, spectral and correlation analyses also indicate that there exist
interacting flow and charge processes in the gap. This also clarifies the meaning of dc steady
state and the requirement on ac modulation frequency in Kerr measurements.
Thesis Supervisor: Dr. Markus Zahn
Title: Thomas and Gerd Perkins Professor of Electrical Engineering
ii
Acknowledgements
I wish to thank my thesis supervisor Professor Markus Zahn, for guiding and helping me through
my Ph.D. studies at MIT. Working with him has been a great pleasure and valuable experience in
my life. I would also like to express my gratitude to my thesis committee members, Professors
Cardinal Warde and Joel Schindall, who made constructive suggestions for optimizing the
organization and presentation of the thesis.
I wish to thank John Kendall Nowocin who made great contributions to upgrading our
experimental setup. I also wish to thank former LEES members Hsin-Fu Huang and Shahriar
Khushrushahi for their friendship, and LEES staffs, especially Ms. Dimonika Bray, who have
helped me a lot in these years.
I wish to thank Siemens Corporation and MIT Energy Initiative for the financial support of the
research project. I also appreciate the help from the resourceful and patient people in EECS
Graduate Office and MIT Libraries. Their help definitely made things much easier for me.
I wish to thank my wife and our families for their unconditional love and true understanding.
They have always been there to encourage and support me in what I have done, and they have
made many sacrifices for me to finish the thesis. Finally, I wish to thank my little princess,
Nancy. You are actually far more inspiring than distracting.
iii
iv
Contents
Abstract……………………………………………………………………………………………i
Acknowledgements……………………………………………………………….……………...iii
List of Figures……………………………………………………………………………………ix
List of Tables……………………………………………………………………………………xvii
1 Background, motivation and scope of thesis…………………….……………………………1
Synopsis……………………………………………………………………………….…...1
1.1 Background, motivation and research plan……………………………………………2
1.2 Thesis preview………………………………………………………………….……...9
References………………………………………………………………………………..12
2 Evaluating the reliability and sensitivity of the Kerr electro-optic field mapping
measurements with high-voltage pulsed transformer oil…………………………………….13
Synopsis………………………………………………………………………………….13
2.1 Introduction…………………………………………………………………………..14
2.2 Principle of Kerr electro-optic field mapping measurement………………………...18
2.3 Experimental setup…………………………………………………………………..22
2.4 Results and discussions……………………………………………………………....27
References……………………………………………………………………………….37
3 Kerr electro-optic field mapping study of the effect of charge injection on the impulse
breakdown strength of transformer oil………………………………………………………39
Synopsis…………………………………………………………………………………39
3.1 Introduction………………………………………………………………………....40
3.2 Optimization of Kerr experimental configurations…………………………………44
v
3.3 Experimental procedure…………………………………………………….………….55
3.4 Results and discussions…………………………………………………………....…62
References………………………………………………………………………………..68
4 Transient charge injection dynamics in high-voltage pulsed transformer oil…………….71
Synopsis…………………………………………………………………………………...71
4.1 Introduction…………………………………………………………………………..72
4.2 Identification of fractal-like charge injection kinetics………………………………..77
4.3 Numerical simulations of drift-diffusion conduction model…………………………86
4.4 Discussions……………………………………………………………………………94
References………………………………………………………………………………..97
5 Electro-optic signal fluctuations as indicator of critical transitions in dielectric
liquids…………………………………………………………………………………………..101
Synopsis…………………………………………………………………………………101
5.1 Introduction…………………………………………………………………………102
5.2 Indicators of critical transitions in complex systems……………………………….106
5.3 Electro-optic precursor of breakdown initiation in transformer oil….…………...…112
5.4 Discussions………………………………………………………………………….123
References………………………………………………………………………………128
6 Electro-optic signatures of turbulent electroconvection in dielectric liquids under dc and
ac high voltages…………………………………………………………………………………131
Synopsis…………………………………………………………………………………131
6.1 Introduction…………………………………………………………………………132
6.2 Spatiotemporal statistical analysis of Kerr electro-optic signal under dc voltages…134
6.3 Spectral analysis of Kerr electro-optic signal under low-frequency ac voltages……144
6.4 Discussions………………………………………………………………………….149
References………………………………………………………………………………160
vi
7 Concluding remarks………………………………………………………………….……...163
A Physical and chemical parameters of transformer oil……………………………………171
B Approaches to improving breakdown strength in liquids………………………………..173
C Pictures of the Kerr electro-optic measurement system..…………………………………219
D List of publications from thesis research………………………………………………….225
vii
viii
List of Figures
Figure 1.1. Experimental setup for Kerr electro-optic field mapping measurements. The beam diameter of the
laser (wavelength 632.8 nm) is 0.5 mm and linearly polarized. The 20× beam expander expands the laser
beam to about 10 mm in diameter. The polarizers (P0, P, A) have an extinction ratio 500:1 and diameter of 10
cm. P0 is used to ensure the linear polarization state of the expanded laser beam and to attenuate the laser to
avoid saturating the CCD camera. The transmission angles of P and A are perpendicular to each other
(crossed polarizers). A quarter-wave plate (Q) is inserted between P and the test cell (pre-semi polariscope) to
increase measurement sensitivity. The Andor iXon camera is a megapixel back-illuminated EMCCD with
single photon detection capability. The imaging area (8×8 mm2) covers the 2 mm gap (~250 pixels across).
3
Figure 1.2. Physical processes in dielectric liquid stressed by a high voltage pulse (no electrical breakdown).
5
Figure 1.3. Two fundamental assumptions made throughout the thesis.
6
Figure 1.4. The research strategy: (1) separation of signal and noise; (2) limited by budget and time, instead
of improving accuracy by reducing noise, we study the possible relations of noise to certain physical
processes.
7
Figure 1.5. The organization of Chapters 2-6 in the thesis.
9
Figure 2.1. Coordinate system, optical instruments and definition of angles and vectors in Jones calculus.
18
Figure 2.2. Optical component arrangement for linear polariscope.
19
Figure 2.3. Experimental setup for Kerr electro-optic field mapping measurements. The diameter of the
pulsed laser beam (wavelength 532 nm) is 7.6 mm and 98% linearly polarized. The polarizers (P 0, P, A) have
an extinction ratio 500:1 and diameter of 10 cm. P0 is used to attenuate the laser to avoid saturating the CCD
camera. The transmission angles of P and A are 45°and −45°with respect to the x-axis (crossed polarizers).
The CCD camera is a megapixel back-illuminated EMCCD with single photon detection capability. The
imaging area (8×8 mm2) covers the 2 mm gap (~250 pixels across).
22
Figure 2.4. Representative waveform of the HV pulse from the Marx generator measured by the 5068:1
capacitive divider. Two triggering pulses are generated by the LabVIEW controller to first trigger the camera
and the flashlamp and then after 0.1 ms delay trigger the Q-switch to output the laser pulse.
25
Figure 2.5. The view when looking into the window of the test cell. To measure the fringing field, the laser
beam and the camera should move correspondingly. The effective exposure time of the CCD is the laser
pulse duration (several nanoseconds).
26
Figure. 2.6. Measurements of uniform field without space charge between two aluminum electrodes in
transformer oil. The position of the imaging area is shown in Figure 2.5. (a) The distribution of I1(0), where
the dark regions to left and right of the illuminated area are electrodes. The light intensity (counts of electrons
at a pixel) is represented by the colormap. (b) The distribution of I1(E) − I1(0) when the instantaneous
voltage (Uins) is 16 kV; and the camera is triggered at 0.1 ms. (c) The distribution of I1(E) − I1(0) at Uins=24
kV.
29
Figure 2.7. Ratio of I1(E) − I1(0) and I1(0) from the averaged data and power function (exponent=4) fitting.
30
Figure 2.8. Measured field distributions across the gap corresponding to Uins=24 and 16 kV.
30
Figure. 2.9. Relative errors of the measurement results: the maximum deviation of the measured field from
uniform field, and the difference between the instantaneous voltage and the integration of the measured field
over the gap.
31
ix
Figure 2.10. Measurements of space-charge free fringing field with two stainless steel electrodes in
transformer oil. The laser beam is shifted to illuminate the fringing area and the position of the CCD imaging
area is adjusted correspondingly. (a) The distribution of I1(0). The profiles of the rounded edges of the
electrodes can be seen. The light intensity (counts of electrons at a pixel) is represented by the colormap. (b)
The distribution of I1(E) − I1(0) when the instantaneous voltage (Uins) is 24 kV and the camera is triggered at
0.14 ms.
33
Figure 2.11. Measured field distributions along Oy axis indicated in Figure 2.10 corresponding to Uins=24 and
16 kV. The dot-dashed lines are numerical simulation results.
33
Figure 2.12. Dependence of the relative error of the measurement results in the range of 0< y <1.5 mm on
Uins.
34
Figure 2.13. Measurements with same-material electrode pairs under HV pulses of both polarities. The
position of the imaging area is the same as Figure 2.5. The camera is triggered at 0.7 ms with the
instantaneous voltage Uins= ±28 kV. For both polarities, the anode is located at x/d=0, while the cathode is
located at x/d=1.
35
Figure 3.1 (from [3-2]). Space charge distortion of the electric field distribution between parallel plate
electrodes with spacing d at voltage V so that the average electric field is E0=V/d. Four simplest possible
configurations are shown: (a) no space charge; (b) unipolar positive or negative charge; (c) bipolar
homocharge; (d) bipolar heterocharge.
40
Figure 3.2. Four polariscope configurations: (a) linear; (b) pre-semi; (c) post-semi; (d) circular.
44
Figure 3.3. Numerical results of the intensity ratio
when
,
and
when
,
and
vary from
to
45
.
Figure 3.4. Numerical results of the intensity ratio
48
vary from
to .
Figure 3.5. Numerical results as
Figure 3.6. Numerical results as
, and
,
Figure 3.7 Numerical results of the intensity ratio when
varies from
to
and
varies from
, ψ and
,
49
rad.
to
.
vary from
49
52
to .
,ψ
Figure 3.8 Numerical results of the intensity ratio when
rad.
Figure 3.9 Numerical results of the intensity ratio as
to
,
,
and
from
to
varies from
53
53
.
Figure 3.10. Experimental setup for Kerr electro-optic field mapping measurements.
56
Figure 3.11. Detected light fields and the distributions of
filter.
in the gap with and without the spatial
57
Figure 3.12. Electric field distributions (normalized by U(t)/d) from the measurements with a pair of brass
electrodes under 30 kV peak HV impulses of positive polarity. The anode and cathode are at
0 and
,
respectively. The scattered point plots are the measurement results at
0.3, 0.5, and 0.7 ms.
58
x
Figure 3.13. Measurement accuracy (a) and fluctuation level (b) as a function of time when the measurements
are taken with aluminum electrodes under 30 kV peak HV impulses.
59
Figure 3.14. Determination of the valid time range for the Kerr electro-optic field mapping measurements.
60
Figure 3.15. Local electric fields at anode and cathode under impulsed with 30 kV peak voltage from
to
ms for 4 combinations of electrode materials: (a) both brass; (b) both aluminum; (c) aluminum anode
and brass cathode; (d) brass anode and aluminum cathode.
65
Figure 4.1. The complexity of electric field determination. Given applied voltage and gap configuration, one
has to know the interactions between electric field and space charge to solve for electric field. However,
quantitative account of the electrode charge injection is difficult.
72
Figure 4.2. Illustration of the three-step scheme for charge injection: specific adsorption, charge transfer
reaction in EDL, desorption. While charge transport is drift-dominated in the bulk of the liquid, the EDL
processes injecting charges at the metal-liquid interface are diffusion-limited, which, as will be shown later in
this chapter, are closely related to the roughness of electrode surfaces via fractal geometry concepts and
models.
74
Figure 4.3. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (I), 10 kV.
78
Figure 4.4. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (I), 20 kV.
78
Figure 4.5. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (I), 30 kV.
79
Figure 4.6. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (II), 10 kV.
79
Figure 4.7. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (II), 20 kV.
80
Figure 4.8. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (II), 30 kV.
80
Figure 4.9. Time evolution of , total injected charge per unit electrode area, plotted in linear coordinates:
case (I).
82
Figure 4.10. Time evolution of , total injected charge per unit electrode area, plotted in linear coordinates:
case (II).
83
Figure 4.11. Time evolution of , total injected charge per unit electrode area, plotted in log-log coordinates:
case (I). The solid lines are the results of linear fitting.
83
Figure 4.12. Time evolution of , total injected charge per unit electrode area, plotted in log-log coordinates:
case (II). The solid lines are the results of linear fitting.
84
Figure 4.13. Numerical solutions of electric field distribution under 30 kV applied voltage at
0.25 ms and
0.75 ms. The number of spatial steps is 200; the number of time steps is 2000. (a) Crank-Nicolson; (b) The
Crank-Nicolson with implicit Euler for the first 10 time steps.
90
Figure 4.14. Numerical solutions of the local electric fields near anode and cathode surfaces: case (I), anode.
91
xi
Figure 4.15. Numerical solutions of the local electric fields near anode and cathode surfaces: case (I),
cathode.
91
Figure 4.16. Numerical solutions of the local electric fields near anode and cathode surfaces: case (II), anode.
92
Figure 4.17. Numerical solutions of the local electric fields near anode and cathode surfaces: case (II),
cathode.
92
Figure 4.18. Mechanisms for fractal-like charge injection kinetics. (a) If the surface reaction is adsorptionlimited, on rougher surfaces, the protrusions are dominant in adsorbing neutral molecules (D is the diffusion
constant, t is the duration of HV pulses), while on smoother surfaces, the pores also make significant
contributions. (b) If the surface reaction rate is controlled by lateral diffusion of reacting molecules,
anomalous diffusion along fractal surface may account for the origin of fractal charge injection kinetics.
95
Figure 5.1. Typical voltage (a) and corresponding current (b) waveforms when a pair of stainless steel
electrodes are stressed by 1 µs/1 ms high voltage pulses.
107
Figure 5.2. (a) Bifurcation diagram of a model desert vegetation system undergoing predictable sequence of
spatial patterns as approaching a critical transition (from [5-23], which was modified from [5-29]). (b) The
breakdown probability as a “function” of applied voltage. Catastrophic bifurcation may or may not exist. In
either case small forcing (i.e. increase in voltage) will lead to a distinct state.
109
Figure 5.3. (a) The image of the gap illuminated by an expanded laser beam. (b) The background light
intensity distribution in the gap leaked from crossed polarizers as the 1 mm gap is illuminated by a Gaussian
beam (7.6 mm in diameter). The region of interest (ROI) is recorded in a 120-by-60 (row-by-column) matrix.
113
Figure 5.4. The distributions of fluctuations (normalized by the averages) of the measured pixel light
intensities in multiple measurements. (a) with no high voltage pulse generated, at most pixels, the standard
deviations of the light intensities in the 1,000 measurements stay below 5% of the averaged light intensities;
(b) with high voltage pulses firing nearby, there is no substantial difference in the fluctuation level compared
with (a), indicating that electromagnetic compatibility is adequate for our measurement system.
114
Figure 5.5. (a) Same as Figure 5.4(a). With no applied voltage, the standard deviations of the light intensities
at most pixels in the 1,000 measurements stay around 5% of the averaged light intensities. (b) The histograms
and fitted normal distributions of the light intensities at two pixels, #1 and #2 marked in (a).
115
Figure 5.6. The average fluctuations in row i=1(cathode), 60(mid-gap), and 120(anode) at various
stantaneous voltages with rise-time of the pulses being (a) 100 µs, (b) 1 µs, and (c) 10 ns. (d) is an illustration
of matrix , which is used to store the pixel light intensity distribution in the ROI.
117
Figure 5.7. For 3 cases with about the same instantaneous voltage (+30 kV) but different rise times from 10
ns to 100 µs, the distributions of average fluctuations across the gap are shown, and the pixels with strongest
fluctuations (>10%) are marked.
119
Figure 5.8. The slice-by-slice image entropy distributions with zero and 30 kV applied voltages.
120
Figure 5.9. The coefficient of spatial variance of the cathode slice as a function of applied voltage. The error
bars are drawn based on the data from multiple measurements.
121
Figure 5.10. A phenomenon similar to critical slowing down. (a) The 1 ms square wave pulse and the ratio of
the detected light intensity and the zero field value. All light intensities have been averaged over the ROI. (b)
For 10, 20, 30 kV pulses, the time it takes for the light intensity to drop to the zero field value is
approximately 1, 3, 10 ms, respectively.
124
Figure 5.11. (From [5-32]) Localized discharges (streamers) on cathode on uniform electric field. The gap
spacing is 4 mm. The liquid is n-hexane. The image was taken about 1 µs before breakdown.
125
xii
Figure 5.12. (From [5-9], page 17) Experiment on electrostriction wave excitation in water in the system of
extended electrodes (slit scanning).
126
Figure 6.1. The view as looking into the window of the test cell. The diameter of the pulsed laser beam is 7.6
mm. The imaging area (8×8 mm2) of the CCD camera has an array of 1002×1004 pixels. The width of the
gap between two parallel-plate electrodes is d=2 mm, corresponding to about 250 pixels. The 1×1 mm2
region of interest (ROI) is chosen around the center of the gap.
135
Figure 6.2. Histogram (bar plot, 500 samples, 5 Hz sampling rate), normal fitting (solid line), and lognormal
fitting (dashed line) of the distribution of detected light intensities without high voltage (HV) application. The
inset shows the light intensity fluctuations in time.
135
Figure 6.3. The skewness of the detected light intensity distribution as a function of applied HV. The error
bars come from statistics at various pixels in ROI. The three regions partitioned by the two dashed lines
indicate that the data is very likely skewed positively (above), negatively (below), and inconclusively
(middle). The two insets of histograms of light intensities show the slightly (8 kV) and strongly (18 kV)
positively-skewed distributions.
136
Figure 6.4. The dependence of scintillation index (S) and conduction current on applied HV.
138
Figure 6.5. ROI image entropy (normalized by H0, the value in the absence of HV) versus applied HV under
3 different experimental conditions.
140
Figure 6.6. The scintillation index S evaluated with L-by-L binning (i.e., the statistics is based on the average
light intensity in a square region containing L× L pixels). The dashed line indicates the scintillation level
corresponding to about 10% detection uncertainty. The applied HV is 20 kV.
141
Figure 6.7. Results of Kerr electro-optic field mapping measurements under 2 different experimental
conditions, both of which are heterocharge configuration with enhanced electric fields near the electrodes.
The applied HV is 20 kV.
142
Figure 6.8. The scintillation index S evaluated with various exposure times. The dashed line indicates the
scintillation level corresponding to about 10% detection uncertainty. The applied HV is 20 kV.
142
Figure 6.9. Detected light intensities at two pixels labeled 1 and 2 (100 pixels or 0.8 mm apart) when the
applied HV is sinusoidal with amplitude 20 kV and frequency fac=0.1 Hz. The sampling rate is 63.53 Hz. A
sample image is presented in the inset, in which the bright band actually bounces between the two electrodes
at frequency fac.
144
Figure 6.10. Fourier spectra magnitude versus frequency at pixels 1 and 2. The dashed lines are the spectra in
the absence of HV.
145
Figure 6.11. The coefficient of correlation between the time series of light intensities at pixels 1 and 2 (2’,
which is 10 pixels away from 1) as a function of applied HV amplitude.
147
Figure 6.12. Fourier spectra magnitude versus frequency at pixel 1 with HV amplitude 20 kV and 3 different
fac values. The sampling rate is 80 Hz.
Figure 6.13. Illustration of experimental setup for Kerr electro-optic field mapping measurements with ac
modulation.
147
Figure 6.14. Errors in measured dc and ac electric fields with dc voltage
(d)
kV and various modulation voltages ( ) and frequencies ( ).
kV;
154
Figure 6.15. Reasonable ranges of ac modulation frequencies and amplitudes for
5 kV, 10 kV and 18
kV. For each
, the reasonable range is the set of the parameter pairs at the same side of the corresponding
curve as the arrow.
156
xiii
(a)
kV; (b)
kV; (c)
150
Figure 6.16. Normalized dc electric field distribution between copper electrodes in transformer oil under
various dc voltages ( ) measured with ac modulation
10 kHz and
0.5 kV.
158
Figure B.1 (from Ref. [6]). Dependence of breakdown strength Ebd (MV/cm) on time τ (μs) in saturated
hydrocarbons with gap separation of 63.5 μm: a, hexane; b. heptane; c, octane; d, nonane.
184
Figure B.2 (from Ref. [6]). Dependence of breakdown strength Ebd (MV/cm) on liquid density ρ (g/cm3)
under various experimental conditions: a, normal paraffin, τ = 1.4 μs; b, single branched-chain hydrovarbons,
τ = 1.4 μs; c, double branched-chain hydrocarbons, τ = 1.4 μs; d, normal paraffin, direct voltage; e, single
branched-chain hydrocarbon, direct voltage; f&g, straight and branched-chain benzene derivatives, τ = 1.65
μs; h, silicons, dc.
185
Figure B.3 (from Ref. [6]). Dependence of breakdown voltage Vbd (kV) on electrode separation δ (μm) for a
number of electrode materials and cathode shapes: flat cathode: a, Cr; b, Cu; c, Al (flat cathode); d, Cr, Cu,
Al (point cathode).
185
Figure B.4 (from Ref. [6]). Dependence of breakdown strength Ebd (kV/cm) on the number of breakdowns N
in transformer oil. The dashed lines indicate the limits of scatter of experimental results.
186
Figure B.5 (from Ref. [8]). Voltage-time characteristics of a transformer oil with tip-plane gap configuration
for d = 5 (1), 15 (2), and 25 cm (3).
195
Figure B.6 (from Ref. [8]). Dependence of breakdown voltage of perfluorohaxane on the frequency in the tipplane gap for an inter-electrode distance of 1.9mm.
196
Figure B.7 (from Ref. [8]). Dependence of the electric strength of the NaCl aqueous solution on the electrical
conduction in a uniform field at td = 70 ns and d = 0.02 cm (a) and in a non-uniform field at td = 90 ns and d =
0.015 cm (b) for −T +P (curve 1) and +T −P electrodes (curve 2).
198
Figure B.8 (from Ref. [8]). Dependences of the relative electric field strength (a) and standard deviation of
the water breakdown field strength (b) as function of the β-alanine concentration for austenite (curve 1),
ferrite stainless steel (curve 2) and aluminum electrodes (curve 3).
200
Figure B.9 (from Ref. [12]). Breakdown electric field as a function of distance between electrodes with (a)
different material pairs and (b) different impurity concentrations.
202
Figure B.10 (from Ref. [20]). (a) Scheme of the test cell; (b) 50% lightning impulse breakdown
voltage vs. relative position (a1/a) of the barrier for a=50 mm.
204
Figure B.11 (from Ref. [23]). Influence of testing procedures on the breakdown behavior of in- 205
service contaminated oil.
Figure B.12 (from Ref. [26]). (a) Typical dielectric strength course of insulators in insulation
systems; (b) long term degradation in ac liquid breakdown strength.
Figure B.13 (from Ref. [31]). Resistivity as a function of water content in (a) benzene and (b)
toluene.
207
Figure B.14 (from Ref. [37]). Breakdown voltage evolution of oils and mixtures with 6
measurements. [Water content (ppm) / Pollution class (NAS 1638)].
211
Figure C.1. Small Kerr cell with optical components.
219
Figure C.2. Large Kerr cell with utility grade capacitor used for substation power factor correction.
222
xiv
208
Figure C.3. Electrode holder (beginning design) and electrode module (final design).
222
Figure C.4. Filter canister (3 µm filter rating) and variable speed gear pump drive for oil filtering
and circulation.
223
xv
xvi
List of Tables
Table 3.1. Numerical results of
as
, and
Table 3.2. Numerical results as
in the range of
, and
has a deviation of
46
.
.
47
Table 3.3. Impulse breakdown test results for combinations of brass and aluminum electrodes under both
polarities.
62
Table 3.4. Impulse breakdown test results for combinations of brass and stainless steel (S-S) electrodes.
67
Table A.1. Physical and chemical parameters of the transformer oil.
171
Table B.1. Dependence of electrical breakdown strength of insulating liquids on various factors (extracted
from Ref. [7]).
190
Table B.2. Effect of polarity on breakdown initiated in various liquids for a tip-plane electrode system at T =
293 K (From Ref. [8]).
196
Table B.3. Comparing withstand voltages of non-parametric and parametric methods (from Ref. 212
[41]).
xvii
xviii
1
Background, motivation and scope of thesis
Synopsis
This thesis focuses on Kerr electro-optic measurements in transformer oil. At first glance, there
seems to be nothing attractive in this research: old physics (Kerr effect was discovered over
100 years ago and molecular theory of Kerr effect was established over 50 years ago), mature
technique (Kerr electro-optic field mapping in liquids was extensively studied in the 1960s80s), and traditional material (transformer oil is the most widely-used insulating liquid in
industry). In this introductory chapter, it will be shown that there still exist new grounds to
break. Section 1.1 presents background, motivation, and plan (including fundamental
assumptions and research strategies) of the thesis. Section 1.2 discusses the structure of the
thesis and gives a preview of each subsequent chapter.
1
1.1 Background, motivation and research plan
The dielectric liquid used in the thesis research is transformer oil (important physical
and chemical parameters are listed in Appendix A). Transformer oil is the most widely used
dielectric liquid for high voltage insulation and power apparatus cooling due to its greater
electrical breakdown strength and thermal conductivity than gaseous insulators and its ability
to self-heal and conform to complex geometries that solid insulators do not have [1-1]. The
insulating properties of transformer oil have been extensively studied in attempt to understand
the basic mechanisms of electrical breakdown [1-2] and to prevent the disastrous consequences
of insulation failure [1-3]. To improve the electrical breakdown strength (a comprehensive
literature review on this topic is provided in Appendix B), it would be necessary to know the
electric field distribution in an insulation configuration, which, however, cannot be directly
calculated from information on electrode configuration, dielectric properties and source
excitation. Space charge originating from bulk dissociation in high voltage stressed oil and
charge injection by high voltage stressed electrodes can significantly distort the electric field
distribution and play an important role in the insulation failure [1-4].
Theoretically, this formulates a highly nonlinear problem in which the generation and
motion of space charge are determined by the electric field; and meanwhile space charges have
a ‘feedback’ on the latter according to Gauss’ law. To numerically simulate the physical
processes, the main difficulty lies with the quantification of electrode charge injection as a
function of dielectric and electrode materials, impurity contents, electrode surface condition,
etc. More experimental data are needed to test the assumptions in some analytical models or
propose any new theory.
2
Figure 1.1. Experimental setup for Kerr electro-optic field mapping measurements. The beam diameter of the laser
(wavelength 632.8 nm) is 0.5 mm and linearly polarized. The 20× beam expander expands the laser beam to about
10 mm in diameter. The polarizers (P0, P, A) have an extinction ratio 500:1 and diameter of 10 cm. P0 is used to
ensure the linear polarization state of the expanded laser beam and to attenuate the laser to avoid saturating the CCD
camera. The transmission angles of P and A are perpendicular to each other (crossed polarizers). A quarter-wave
plate (Q) is inserted between P and the test cell (pre-semi polariscope) to increase measurement sensitivity. The
Andor iXon camera is a megapixel back-illuminated EMCCD with single photon detection capability. The imaging
area (8×8 mm2) covers the 2 mm gap (~250 pixels across).
High voltage stressed liquids are usually birefringent, in which case the refractive
indices for light (of free-space wavelength ) polarized parallel ( ) and perpendicular (
the local electric field are related by
, where
is the Kerr constant and
) to
is
the magnitude of the applied electric field. In parallel-plate electrode configuration, we assume
the magnitude and direction of
to be constant along the light path. Thus the phase shift
between light-field components polarized parallel and perpendicular to the applied electric
field and propagating along electrode length
is
. The modulation effect of the
electric field can be detected by comparing the intensities of incident light and transmitted light.
3
In this thesis, the Kerr electro-optic approach will be used to measure the electric field
distributions between parallel-plate electrodes in transformer oil. One of the experimental
setups for the Kerr electro-optic field mapping measurements is illustrated in Figure 1.1 (in
Appendix C, some photos of the experimental setup are provided).
Previous works [1-5, 1-6] mainly deal with high Kerr constant materials like propylene
carbonate (
(
m/V2). For small Kerr constant material like transformer oil
m/V2), to improve the detection sensitivity, ac modulation method [1-7, 1-8] has
proven to be effective in dc ‘steady state’ measurements. The steady state in quotation implies
that in reality there may not be one due to the induced flow as the dc high voltage keeps on. On
the other hand, the principles of ac modulation do not work for short high voltage pulses (
ms) with insignificant flow effects, since the lock-in amplifier used in this method needs at
least several seconds to register a signal. Kerr measurements in high voltage pulsed low Kerr
constant transformer oil without ac modulation thus presents a challenge in this research area.
We summarize the possibly new grounds to break as follows:
Firstly, many aspects of transformer oil have been intensively studied. However, there
remains a lack of detailed accounts of various physical processes of transformer oil stressed by
high electric field. Models proposed make various assumptions and approximations which
might be unrealistic.
Secondly, most of the previous Kerr measurements were taken for liquids with Kerr
constants 2-3 orders higher than that of transformer oil. For transformer oil, a technique called
ac modulation method was developed. But the drawback of ac modulation is that it assumes the
existence of steady state which would be invalid in strong electric fields. In this sense, the
measurement technique for transformer oil is not mature at all.
4
Finally, the measurable Kerr effect in transformer oil is always mixed with other
physical effects such as electrostrictive shock wave, charge injection and transport, and
electrohydrodynamic (EHD) turbulence. New physics may lie with a careful separation of
these effects.
The central question that is set out to answer in the thesis is: what information on the
underlying physical processes can be extracted from the data of Kerr measurements with
transformer oil? To be more specific, there are different aspects of this question. Under what
conditions can the electro-optic signals be used to map electric field distribution? How to
ensure the accuracy and reliability of the measurement data? What are the sources of noise and
uncertainties in the measurement system? Are they random, biased, or patterned?
Before outlining the experimental work, the fundamental assumptions made throughout
the thesis are to be introduced. Conceptually, the thesis is based on the understanding of basic
physical processes in dielectric liquid stressed by a high voltage pulse (no electrical breakdown)
shown in Figure 1.2. To take valid field mapping measurements, the experimental systems
should be able to separate the time scales shown in Figure 1.2.
Electrostrictive
Shock Wave
Ionic Conduction
Processes
(Time range:
~ rise time of the pulse)
(Electrode injection,
charge generation,
recombination, drift,
diffusion, etc.)
Charge Migration
Time
(EHD enhanced
conduction)
Electrohydrodynamic
HV Pulse
convection
Duration
Viscous Diffusion
Time
Figure 1.2. Physical processes in dielectric liquid stressed by a high voltage pulse (no electrical breakdown).
5
Depending on the high voltage duration, there are three types of physical processes:
electrostriction (caused by the sudden change of electric field which establishes pressure
gradients; the relaxation and dissipation of this shock wave behavior are very rapid); ionic
conduction which bring in space charge processes (the characteristic time for this process is
called charge migration time, i.e. the time it takes for a charge carrier to transport over a
distance, the evaluation of which can be found in Chapter 2); electroconvection (a short term
for EHD convection due to Coulomb force on charges in the liquid, the onset of which is
usually evaluated by the viscous diffusion time; see Chapter 3 for details).
Kerr Constant
Assumption 1: The Kerr constant of the dielectric liquid
for light wave of a given frequency is the same in the
1~10 kV/mm electric field range.
1
10
Electric Field (kV/mm)
(a)
~d
Assumption 2: The effective range of fringe field
is about the width of the inter-electrode gap, d;
the electro-optic modulation in the fringe area can
be neglected if the length of electrodes is much
larger than d.
Electrode
d
Light Propagation
Electric
Field
Electrode
(b)
Figure 1.3. Two fundamental assumptions made throughout the thesis.
6
On the technical side, there are two fundamental assumptions made as illustrated in
Figure 1.3. The first is that for light wave of a given frequency, the Kerr constant of the
dielectric liquid is the same in the electric field range of our measurements (1~10 kV/mm),
which means that the Kerr constant depends only on the liquid, e.g. the molecular structure,
permittivity, etc. Although no independent measurements were designed to test this assumption
(mainly because the electric field becomes distorted in an unknown way as the voltage gets
higher), the field mapping results (Chapter 2 and Chapter 3) with adequate accuracy will verify
this assumption to some extent.
The second assumption is that the fringe field effect is neglected. The light wave front
may get distorted due to the inhomogeneous anisotropic nature of this part of the media. In our
treatment, the effective range of fringe field is about the width of the inter-electrode gap, d; the
electro-optic modulation in the fringe area tends to be negligible if the length of electrodes is
much larger than d. In principle, numerical methods such as wave-propagating and ray-tracing
can be used to estimate fringe field effect. However, this is out of scope of the thesis.
Validation of Experimental Approach
Signal
Electric field and space charge
Noise
Relation to specific physical process
Improve measurement accuracy
Figure 1.4. The research strategy: (1) separation of signal and noise; (2) limited by budget and time, instead of
improving accuracy by reducing noise, we study the possible relations of noise to certain physical processes.
7
To achieve the research goal, new instruments and new insights play equally important
roles. A high-sensitivity high-resolution CCD is used to detect the Kerr effect without ac
modulation, thus making transient measurements possible. The first challenge along the way is
that the CCD can register a considerable amount of noise, even if everything has been done to
make the experimental system as precise as possible. It is natural to think of taking multiple
measurements and then averaging the results. As illustrated in Figure 1.4, after the reliability
and accuracy of this method has been evaluated and confirmed, we study signal (average) and
noise (fluctuation) separately. The former is the traditional field mapping measurements with
much higher sensitivity thanks to our CCD camera. Measurements of transient electrical
conduction dynamics in transformer oil under high voltage impulses are taken. Correlation
between charge injection pattern and impulse breakdown voltage is also an interesting topic.
The latter was supposed to focus on the identification of various noise sources and
methods to reduce the negative effects of noise. However, due to the limited budget and time,
we were not able to purchase better measurement instruments for an upgraded experimental
system. Since the noise level in the measurement results seems unlikely to improve
significantly in the current settings, we study the “message” in the noise, i.e. the fluctuations in
the detected light intensities, and explore the possible relations of noise to specific physical
processes that are the major contributors to it. As we will see in Chapter 5 and Chapter 6, this
compromise in fact led to some interesting findings.
8
1.2 Thesis preview
The schematic in Figure 1.5 shows the organization of 5 core chapters of the thesis.
Chapter 2 is the foundation of other chapters since it presents the validation of the
experimental approach. Chapter 3 and Chapter 5 discuss topics related to electrical breakdown
(this is why they are placed at the higher electric field positions). Chapter 4 and Chapter 6
discuss conduction with and without electrohydrodynamic processes; the electric field is much
HV Electric Field
lower than the breakdown strength).
Chapter 5
Chapter 3
Electrostriction-induced noise
↕
Impulse breakdown initiation
Charge injection pattern
↕
Impulse breakdown voltage
Chapter 2: Validation
Electroconvection-related noise
Transient charge injection
dynamics
Chapter 4
Chapter 6
HV Pulse Duration
Figure 1.5. The organization of Chapters 2-6 in the thesis.
An alternative perspective to view the organization of the chapters is based on the
physical processes shown in Figure 1.2. Chapter 2, Chapter 3, and Chapter 4 are all on
conduction processes (field mapping based on the averaged signal), while Chapter 5 and
Chapter 6 are on noise related to electrostriction (short impulse) and electroconvection (longer
pulse, dc or ac voltages).
The contents of subsequent chapters are described as follows:
9
In Chapter 2, with the help of a high-sensitivity charge-coupled device (CCD), the Kerr
electro-optic effect is directly measured between parallel electrodes in transformer oil stressed
by high voltage pulses. In this chapter, we demonstrate the reliability and evaluate the
sensitivity of the measurements for three cases with identical electrodes: space-charge free,
uniform electric field in the mid-region of the gap; space-charge free, non-uniform fringing
electric field; and space charge distorted electric field in the mid-region of the gap. Different
criteria are used to determine the measurement accuracy. Future directions to improve
accuracy by identifying and handling various sources of error and noise are suggested.
The smart use of charge injection to improve breakdown strength in transformer oil is
demonstrated in Chapter 3. Hypothetically, bipolar homo-charge injection with reduced
electric field at both electrodes may allow higher voltage operation without insulation failure,
since electrical breakdown usually initiates at the electrode-dielectric interfaces. To find
experimental evidence, the applicability and limitation of the hypothesis is first analyzed.
Impulse breakdown tests and Kerr electro-optic field mapping measurements are then
conducted with different combinations of parallel-plate aluminum and brass electrodes stressed
by millisecond duration impulse. It is found that the breakdown voltage of brass anode and
aluminum cathode is ~50% higher than that of aluminum anode and brass cathode. This can be
explained by charge injection patterns from Kerr measurements under a lower voltage, where
aluminum and brass electrodes inject negative and positive charges, respectively.
In Chapter 4, transient electrode charge injection in high-voltage pulsed transformer oil
is studied with Kerr electro-optic measurements. Time evolutions of total injected charges and
injection current densities from two stainless-steel electrodes with distinct surface roughness
obey a power law with different exponents. Numerical simulation results of the time-dependent
10
drift-diffusion model with the experimentally-determined injection current boundary
conditions agree with measurement data. The power-law dependence implies that the electric
double layer processes contributing to charge injection are diffusion-limited. Possible
mechanisms are proposed based on formative steps of adsorption-reaction-desorption,
revealing deep connection between geometrical characteristics of electrode surfaces and
fractal-like kinetics of charge injection.
In Chapter 5, motivated by the search for approaches to non-destructive breakdown test
and inclusion detection in dielectric liquids, we explore the possibility of early warning of
breakdown initiation in high voltage pulsed transformer oil from the data of Kerr electro-optic
measurements. It is found that the light intensities near the rough surfaces of electrodes both
fluctuate in repeated measurements and vary spatially in a single measurement. We show that
the major cause is electrostriction which brings disturbances into optical detection. The
calculated spatial variation has a strong nonlinear dependence on the applied voltage, which
generates a precursory indicator of the critical transitions.
Signatures of turbulent electroconvection in transformer oil stressed by dc and ac
voltages are identified from Kerr electro-optic measurement data in Chapter 6. It is found that
when the applied dc voltage is high enough, compared with the results in the absence of high
voltage, the optical scintillation index and image entropy exhibit substantial enhancement and
reduction respectively, which are interpreted as temporal and spatial signatures of turbulence.
Under low-frequency ac high voltages, spectral and correlation analyses also indicate that there
exist interacting flow or charge processes in the gap. This chapter also clarifies some
fundamental issues on Kerr measurements.
11
References
[1-1] R. Bartnikas (ed.), Engineering Dielectrics: Electrical Insulating Liquids, Vol. 3 (ASTM,
Philadelphia, 1994).
[1-2] I. Adamczewski, Ionization, Conductivity and Breakdown in Dielectric Liquids
(Taylor&Francis, London, 1969).
[1-3] V. Y. Ushakov, Insulation of High-Voltage Equipment (Springer-Verlag, Berlin, 2004).
[1-4] M. Zahn, “Optical, Electrical and Electromechanical Measurement Methodologies of Field,
Charge and Polarization in Dielectrics”, IEEE Trans. Dielectr. Electr. Insul. 5, 627 (1998).
[1-5] E. C. Cassidy, H. N. Cones, and S. R. Booker, “Development and Evaluation of ElectroOptic High-Voltage Pulse Measurement Techniques”, IEEE Trans. Instr. Meas. 19, 395 (1970).
[1-6] A. Helgeson and M. Zahn, “Kerr Electro-Optic Measurements of Space Charge Effects in
HV Pulsed Propylene Carbonate”, IEEE Trans. Dielectr. Electr. Insul. 9, 838 (2002).
[1-7] A. Törne and U. Gäfvert, “Measurement of the Electric Field in Transformer Oil Using Kerr
Technique with Optical and Electrical Modulation,” in Proceedings, ICPADM, Vol. 1, Xi’an
China, 24-29 June 1985, pp. 61-64.
[1-8]
T. Maeno and T. Takada, “Electric Field Measurement in Liquid Dielectrics Using a
Combination of ac Voltage Modulation and a Small Retardation Angle”, IEEE Trans. Electr. Insul.
22, 503 (1987).
12
2
Evaluating the reliability and sensitivity of the Kerr
electro-optic field mapping measurements with highvoltage pulsed transformer oil
Synopsis
Transformer oil is the most widely used dielectric liquid for high voltage (HV) insulation.
Measurements of the electric field distribution in high voltage pulsed transformer oil are of both
practical and theoretical interests. Due to its low Kerr constant, previous electro-optic
measurements with transformer oil rely on a technique called ac modulation, which is primarily
used only for dc steady-state electric field mapping. With the help of a high-sensitivity chargecoupled device (CCD), the Kerr electro-optic effect is directly measured between parallel
electrodes in transformer oil stressed by high voltage pulses. In this chapter, we demonstrate the
reliability and evaluate the sensitivity of the measurements for three cases with identical
electrodes: space-charge free, uniform electric field in the mid-region of the gap; space-charge
free, non-uniform fringing electric field; and space charge distorted electric field in the midregion of the gap. Different criteria are used to determine the measurement accuracy. Future
directions to improve accuracy by identifying and handling various sources of error and noise are
suggested.
13
2.1 Introduction
As mentioned in Chapter 1, transformer oil is the most widely-used dielectric liquid for
high voltage (HV) insulation. To improve the electrical breakdown strength, it is necessary to
know the electric field distribution in an insulation configuration. Due to the space charge
effect, generally the electric field distribution cannot be calculated from the information of
electrode configuration, dielectric properties and source excitation alone.
A comprehensive description of the mechanisms and mathematical models of space
charge generation and motion will be given in Chapter 4. Here we only briefly introduce the
basic physical picture.
In addition to dielectric liquid ionization and flow electrification, electrode charge
injection is thought to be a primary cause of space charge generation [2-1]. The electrode
injection includes two well-conceptualized charge transfer processes at the electrode-dielectric
interfaces [2-2]: emission and capture of electrons by the metal electrodes, and equilibrium or
non-equilibrium electric double layer dynamics. Contaminants (e.g. bubbles and/or particles
adhered to the surfaces and suspended in the liquid) and chemical/electrochemical reactions
between the electrode material and the liquid (e.g. specific adsorption) all contribute to charge
injection [2-3].
For practical liquid dielectrics like transformer oil, it remains challenging to disentangle
the complexity and characterize it quantitatively. Partly it is because the molecular structure
and chemical composition of the oil (containing at least tens of different compounds, with
various impurities and contaminants) are not as simple and regular as those of gases or solids,
which makes systematic investigation of its electrical behavior on microscopic scale extremely
14
difficult and sometimes inconsistent.
Theoretically, the bipolar ionic drift-diffusion model has been formulated to analyze dc
steady-state conduction [2-4] and transient behavior under a step excitation [2-5], in which
electrode charge injection is included as a boundary condition, i.e. specified charge densities at
the electrode-liquid interfaces. However, in strong dc field conduction, the thermohydrodynamic and electro-hydrodynamic effects are significant [2-6] in liquids. The former is
caused by a temperature/pressure gradient induced by electrical current/stress, while the latter
is the motion due to the Coulomb force on space charge in the fluid.
Therefore, the model seems more appropriate for describing the response under a short
HV pulse. As a prerequisite for the verification and improvement of the theoretical model,
reliable and accurate measurement data on the electric field distribution and its dynamics under
pulsed HV is needed.
The Kerr electro-optic technique [2-7] has been used to measure the electric field
distribution in HV stressed liquids, where the refractive indices for light (with free-space
wavelength ) polarized parallel,
related by
, and perpendicular,
( is the Kerr constant and
, to the local electric field are
is the electric field intensity). In a
parallel-plate electrode geometry, the -field vector is assumed to be constant along the light
path. Thus, after propagating through the electrode length , the phase shift
components polarized parallel and perpendicular to the field is
between light
, which can be
measured with two crossed or aligned polarizers. In Section 2.2, we will present a more
detailed introduction to the Kerr electro-optic effect and its measurement.
For low Kerr constant transformer oil (
traditional approach to make
~
m/V2),
is very small, and the
detectable in dc steady-state measurements is using an
15
indirect method [2-8], in which an ac modulation voltage (frequency f is so high that the ac
field has negligible effect on space charge behavior) is superposed to the dc HV. The total
electric field E has both dc and ac components. The phase shift
, proportional to E2, will
correspondingly have a dc component and two ac components with frequencies f and 2f
(although very weak, the ac components can be measured by lock-in amplifiers), from which
the dc electric field can be calculated (this method will be demonstrated in Chapter 6).
The limitations of the ac modulation method are two-fold: (a) in reality there may not be
a dc steady state due to the induced flow under higher voltages; (b) it does not work for short
HV pulses (e.g. ~10 ms in duration) with insignificant flow effects, because it takes at least
seconds for the lock-in amplifier to register stable ac components.
For this reason, taking Kerr measurements in HV pulsed transformer oil without ac
modulation has been considered as a challenge in this research area. Meanwhile, if it is realized,
our understanding of the conduction and breakdown mechanisms in transformer oil will be
greatly enriched.
In this thesis, with the help of a high-sensitivity charge-coupled device (CCD), Kerr
electro-optic field mapping measurements are conducted to determine the electric field
distribution between parallel electrodes in transformer oil stressed by HV pulses. The CCD
camera with single photon detection capability is used to measure the light intensity of a pulsed
laser beam coming through the Kerr test cell (we will also use an intensity-stabilized
continuous wave laser in Chapter 3).
High sensitivity is a double-edged sword. It makes possible the direct detection of the
small modulation effects in transformer oil. However, along with the signal of the Kerr effect,
noise originating from various uncertain and random processes in the system is also recorded.
16
For example, even without HV, the shot-to-shot variation of the light intensity at one pixel
(8×8 µm2) can be as high as 20% (averaging the data from multiple measurements can lower
this noise level to ~5%). This is because on the one hand the laser output has intrinsic
spatiotemporal fluctuations, and on the other hand the laser beam propagates in a medium with
randomness (scattering, turbulence, etc).
Due to the presence of noise, the major concerns of this chapter are the reliability and
accuracy of the Kerr electro-optic field mapping measurements, which will be evaluated from
the following three aspects: (1) measurements of space-charge-free, uniform field in the middle
section of the gap; (2) measurements of space-charge-free, non-uniform fringing field; and (3)
measurements of space charge distorted field in the middle section of the gap between samematerial electrodes. The estimation of the accuracy and sensitivity will be made by comparing
the measurement results of the space-charge-free fields with theoretical predictions.
The organization of the rest of this chapter is as follows: in Section 2.2, we will describe
the principles of field mapping measurements based on the Kerr electro-optic effect; an
introduction to the experimental setup and instrumentation for our measurements will be given
in Section 2.3; finally, after defining two criteria of the measurement accuracy, data from
measurements will be analyzed. It will be shown that Kerr measurements can produce
physically reasonable and self-consistent results in all the three cases above.
17
2.2 Principle of Kerr electro-optic field mapping
measurements
In general, all materials exhibit the Kerr effect, or electric field induced birefringence,
but it is dominant only for centrosymmetrical materials such as liquids or glasses. Dielectric
liquids, which in natural state are isotropic due to random molecular orientation, become
birefringent when stressed by electric fields. The refractive indices for light (with free-space
wavelength ) polarized parallel,
related by
, and perpendicular,
( is the Kerr constant and
, to the local electric field are
is the electric field intensity).
In a parallel-plate electrode geometry, the -field vector is assumed to be constant along
the light path. Thus, after propagating through the electrode length , the phase shift
between light components polarized parallel and perpendicular to the field is
. Next we will use the Jones matrix [2-9] representation of light
propagation through optical elements as a concise method to obtain the relation between the
initial and final light intensities in Kerr electro-optical experiments.
x
ein
x
y
z
Polarizer
(analyzer)
x
Transmission
axis
y
Laser
eout
y
z
Detector
Birefringent
components
x
Slow axis
y
Figure 2.1. Coordinate system, optical instruments and definition of angles and vectors in Jones calculus.
As shown in Figure 2.1, the light propagation is along the z-axis, and the vectors of both
the light electric field (optical polarization) and the applied HV field (dielectric polarization)
18
are in the x-y plane transverse to light propagation. Note that in Jones calculus, the light field
vector is represented by complex amplitude e, i.e. the actual light field is the real part of
, where
, is the time, and
is the (angular) frequency of the light.
For polarizer (or analyzer), supposing the transmission axis is at angle θ with respect to
the y-axis, the Jones matrix
is defined by:
 exout   cos 
 out   
 e    sin 
 y  
 sin 2 
 
 sin  cos 
sin   0 0  cos 


cos   0 1  sin 
 sin   exin 
 
cos   einy 
(2.1)
in
 ein 
sin  cos   ex 
 in   U p ( ) xin 

e 
cos 2   e y 
 y
For birefringent components like a quarter-wave plate and the Kerr cell, supposing the
slow axis is at angle ψ with respect to the y-axis and the slow wave is retarded by Δφ in phase,
we have:
 exout   cos
 out   
 e    sin
 y  
sin  1
0  cos


 i 
cos  0 e  sin
 sin  exin 
 
cos  einy 
(2.2)
 ein 
 cos 2   e  i sin 2  cos sin (e  i  1)  exin 
 in   U b ( ,  ) xin 

 
 i
e 
 1) sin 2   e  i cos 2   ey 
 cos sin (e
 y
For a quarter-wave plate,
in Equation (2.2). For a Kerr cell,
,
and the slow axis is along the direction of applied HV field.
Polarizer
Grounded electrode
E
y
e0
Laser beam
Kerr medium
x
Analyzer
y
High-voltage electrode
z
e1
x
z
Figure 2.2. Optical component arrangement for linear polariscope.
19
Figure 2.2 is a linear polariscope (without quarter-wave plates), the simplest
combination of basic Jones matrices defined in Equations (2.1)&(2.2). For the configuration
shown in Figure 2.2, supposing the complex amplitude of the electric field of the linearlypolarized light is e0 at the laser side and e1 at the detector side, we have:
 e1x 
e 
   U p ( a )U b ( m ,2BLE 2 )U p ( p ) 0 x 
e 
e 
 1y 
 0y 
(2.3)
where the subscripts a, m and p stand for analyzer, Kerr material and polarizer, respectively.
As shown in Figure 2.2, the y-axis is usually so chosen that it coincides with the direction of
applied HV field, i.e. ψm=0 in Equation (2.3). Then,
 e1x   sin 2  a
 
 e   sin  cos 
a
a
 1y  
0  sin 2  p
sin  a cos  a  1



i 2BLE 2 
cos 2  a  0 e
 sin  p cos  p
i 2BLE
 2
sin 2 a sin 2 p
 sin  sin 2   e
a
p
4
 2
i 2BLE 2
 sin  sin 2
e
cos 2  a sin 2 p
p
a


2
2

A12  e0 x 
A
 
  11
 A21 A22  e0 y 
2
sin  p cos  p  e0 x 
 
cos 2  p  e0 y 
e i 2BLE cos 2  p sin 2 a 

 e0 x 
2
2
 e0 y 
sin 2 a sin 2 p
 
i 2BLE 2
2
2
e
cos  a cos  p 
4

sin 2  a sin 2 p
Further, if the polarization angle of the laser output is
2
(2.4)
(with respect to y-axis, i.e.
), the light intensity ratio is therefore:
*
 e1x 
 A* A21
 A11 A12  e0 x 

 
(e1x , e1y )  (e0x , e0 y ) 11
*
* 
e1 y 
A12 A22  A21 A22  e0 y 
I1




e
I0
 e0 x 

  0x 
(e0 x , e0 y ) 
(e0x , e0 y ) 
 e0 y 
 e0 y 


 A 2  A21 2
A11
A12  A21
A22  sin  

e
e0 (sin  , cos  )  11
2
2
 A A  A A
 cos   0
A

A
22 21
12
22
 12 11


sin



e0
e0 (sin  , cos  )
 cos  


 A11 2  A21 2
A11
A12  A21
A22  sin  


 (sin  , cos  ) 
2
2
 A A  A A
A12  A22  cos  
22 21
 12 11
20
(2.5)
In general, Equations (2.4) and (2.5) expanded in terms of the angles and basic
parameters will be very complicated. In this chapter, we focus on a special case with crossed
polarizers, i.e.
and
. Then according to Equation (2.4),
, and Equation (2.5) is simplified:
 1  cos(2BLE 2 ) 1  cos(2BLE 2 ) 

 sin  
I1
4
4


 (sin  , cos  )
2
2
I0
 1  cos(2BLE ) 1  cos(2BLE )  cos  


4
4


2
2
1  cos(2BLE )
(sin   cos  )

(sin   cos  ) 2 
sin 2 (BLE 2 )
4
2
(2.6)
In Equation (2.6), the ratio of output and input light intensities for a linear polariscope
with crossed polarizers, which is measurable in experiments, depends on the initial polarization
angle of the incident laser, . It is straightforward to show that by setting
one can
maximize the light intensity at the detector side, which is:
I1
 sin 2 (BLE 2 )
I0
(2.7)
In this section, we only consider the simplest case. For the comparison of various
polariscopes and parameter settings, see Section 3.2.
21
2.3 Experimental setup
The experimental setup illustrated in Figure 2.3 consists of optical, electrical and control
subsystems. A test cell with transformer oil and a pair of parallel-plate electrodes (gap spacing
mm, length
m) inside is the intersection of the optical and electrical
subsystems. Vacuum and filter systems remove the bubbles and particles in the oil that may
cause premature electrical breakdown and reduce optical detection accuracy.
Figure 2.3. Experimental setup for Kerr electro-optic field mapping measurements. The diameter of the pulsed laser
beam (wavelength 532 nm) is 7.6 mm and 98% linearly polarized. The polarizers (P0, P, A) have an extinction ratio
500:1 and diameter of 10 cm. P0 is used to attenuate the laser to avoid saturating the CCD camera. The transmission
angles of P and A are 45°and −45°with respect to the x-axis (crossed polarizers). The CCD camera is a
megapixel back-illuminated EMCCD with single photon detection capability. The imaging area (8×8 mm2) covers
the 2 mm gap (~250 pixels across).
22
The Quantel Ultra Laser is a rugged Q-switched ND:YAG oscillator that is ~98%
linearly polarized with pulse energy of 30 mJ @ 532 nm, 20 Hz maximum repetition rate, and
less than a 6 mrad beam divergence. The output beam is at 1064 nm wavelength that then goes
through a manual variable attenuator. The attenuated beam goes to the frequency doubler that
provides the 2nd harmonic that is used for the test measurements. The diameter of the pulsed
laser beam (wavelength 532 nm) is 7.6 mm. Any reflections from optical or other components
back into the laser head should be prevented as it can severely damage the components. The
reflected light back into the laser can increase the laser energy internal to the head causing
stresses, high heating, and in some case melting of optical components.
A linear polariscope (no quarter wave plates) with crossed polarizers P and A is used to
measure the Kerr effect. The polarizers (P0, P, A) have an extinction ratio 500:1 and diameter
of 10 cm. P0 represents a series of polarizers used to attenuate the laser to avoid saturating the
CCD camera. To realize the optimum measurement condition required by Equation (2.7), the
last attunuation polarizer (closest to P) has its transmission axis fixed at 45°with respect to
the x-axis, while other P0 polarizers can be rotated to control the transmitted light intensity).
The transmission angles of P and A are 45°and −45°with respect to the x-axis (crossed
polarizers).
The light intensity is measured by an Andor Technology iXonEM+ electron
multiplication charge coupled device (EMCCD) camera Model DU-885K. A megapixel backilluminated EMCCD, the camera is cooled to -80°C, and sensitive enough to output 1 electron
per photon detected called a “count”. The camera can be triggered internally via the computer
or externally via a 5V trigger pulse. The exposure time can be set internally and triggered
externally if needed. The camera saturates above 16,000 photons (at a gain of 3.5) or
23
approximately 55,000 counts, and careful attention to not overexpose the camera must be taken.
If overexposure occurs the signal pixels will be capped at the saturation level. This means that
if any additional light is passed to the sensor, then no changes in pixel values will occur when
there should be pixel value changes. The imaging area of the CCD camera (8×8 mm2 having an
active pixel size array of 1004×1002 yielding an approximate pixel size of 8µm) covers the 2
mm gap (~250 pixels across). The CCD imaging area is ~1 m away from the test cell in order
not to receive the scattered light (not propagating along z direction) which makes the gap look
wider and generates extra patterns in the recorded light field (we will discuss this later in
Chapter 3 and Chapter 5).
The instruments of HV generation and measurement system include power supplies,
capacitors, capacitive dividers, oscilloscope, function generators, and related items. The
Hipotronics Marx Generator 300 kV provides the HV pulses and is configured with utility
grade capacitors to modify the rise and decay times of the pulses. The capacitive voltage
divider is a Pearson Model VD-500A. The frequency range is 15Hz to 2MHz, usable rise time
of 200 nanoseconds, and 5068:1 voltage division ratio in oil. The sensors are measured by
LabVIEW hardware and the HP Infinium Oscilloscope 500 MHz 1 GSa/s. The digital delay
generator Model 113DR (MOD) is used to provide delay and trigger timing for various pieces
of the test setup. The function generators are either Agilent Model 33220A 20MHz Single
Channel, HP Model 33120A 15MHz Single Channel, or Agilent Model 33522B 30 MHz Two
Channels with arbitrary waveform generation and delay triggering capability.
In this chapter, the HV pulse from the Marx generator has a rise time of ~250 µs, and
total duration of ~20 ms. A LabVIEW controller is designed to monitor the HV waveforms
from the capacitive divider and generate pulses to trigger the pulsed laser and the CCD camera
24
at certain instantaneous voltages. Representative waveform of the HV pulse is presented in
Figure 2.4. Two trigger signals generated by LabVIEW are: (1) for CCD exposure start and
pulse laser flashlamp trigger, the controller outputs a trigger pulse when the instantaneous
voltage (Uins) passes a preset value (in Figure 2.4, it is 20 kV); (2) for pulse laser Q-switch
trigger, the controller sends a signal after a time delay, which should be in the range of 100 to
140 µs to guarantee the output power stability of the laser.
Figure 2.4. Representative waveform of the HV pulse from the Marx generator measured by the 5068:1 capacitive
divider. Two triggering pulses are generated by the LabVIEW controller to first trigger the camera and the
flashlamp and then after 0.1 ms delay trigger the Q-switch to output the laser pulse.
Figure 2.5 below shows the view when looking into the window of the test cell. The
actual direction of the x-axis is horizontal, and the electrodes are aligned vertically in the
transformer oil filled test cell.
25
To measure the fringing field, the laser beam and the CCD imaging area shown in
Figure 2.5 should move correspondingly. Although the exposure time of the CCD is set to be
several hundred microseconds, the effective exposure time of the CCD is the laser pulse
duration (several nanoseconds).
Window of the Test Cell
Light Propagation
Laser Beam
Diameter 7.6 mm
HV Electrode
0
d=2 mm
~250 pixels
Grounded Electrode
Imaging Area
8  8 mm 2
Effective Exposure Time: < 0.1 µs
x
Figure 2.5. The view when looking into the window of the test cell. To measure the fringing field, the laser beam
and the camera should move correspondingly. The effective exposure time of the CCD is the laser pulse duration
(several nanoseconds).
26
2.4 Results and discussions
In Section 2.2, using Jones’ calculus,
, the ratio of transmitted light intensities of A
and P0 (see Figure 2.3) as a function of , has been given in Equation (2.7), which is the
theoretical result in an ideal experimental setting. In fact, if taking into consideration the light
power loss due to reflection from optical surfaces and absorption in materials, Equation (2.7)
should be re-written in a more general form:
(2.8)
where
is the fraction of light power loss (independent of HV and light polarization).
According to Equation (2.8),
should be zero corresponding to crossed polarizer
output without HV Kerr effect. However, the laser is not 100% linearly-polarized, and when no
HV is applied, a very small portion of light intensity, denoted by
, can propagate through
the crossed polarizers into the imaging area of the camera. As will be shown later, the increase
in light intensity due to the Kerr effect in transformer oil is of the same order or even less than
. Therefore, appropriate treatment and quantitative characterization of
will be an
important part of the measurements.
Preliminary measurements are conducted to determine the intensity and polarization
state of the leaked light. The main observations are stated below:
(A) When there is no applied HV, it is found that
is proportional to
(
can be
tuned by adjusting the transmission angle of P0 polarizers), i.e.
where
,
is the fraction of leaked light intensity.
(B) When inserting a polarizer P3 between A and the CCD and then adjusting its
transmission angle, there is no significant variation in
27
(however, slight
differences may be detected due to the laser beam fluctuation). Further, inserting a
quarter wave plate between A and P3 and then adjusting the angle of its optical axis,
again no variation in
is detected, indicating that the leaked light is basically
unpolarized and no Kerr effect should be expected from this part of light intensity.
According to these observations, the actual signals of the Kerr effect (the numerator and
denominator on the left side of Eq. (2.8)) should be
and
and
, instead of
. Equation (2.8) is transformed as:
(2.9)
where
has been assumed (for E~10 kV/mm,
). The degree of
polarization of the laser provided in the manufacturer test report is 98.3%, which means
or
.
Some measurement results with a space-charge free field in the mid-region of the gap
will first be presented. The characteristic time for the appearance of strong space charge effects
is the migration time τm of charge carriers across the gap (spacing d) based on mobility µ:
τm=l/(µE). Given E~107 V/m, d=2 mm, and µ~10-7 m2/Vs (called electrohydrodynamic
mobility; ion mobility is 1-2 orders lower) [2-10], then τm~2 ms. If measurements are taken at t
= 0.1 ms (t = 0 defined as the beginning of the HV pulse), the field over the majority of the gap
should be uniform due to a negligible space charge distribution.
The intensity distributions of
, and
as
,
as instantaneous voltage
are shown in Figures 2.6(a), (b), and (c),
respectively. We see that the light intensity distribution of the laser beam has a Gaussian
profile instead of a uniform one. Using the CCD area detector, we record and process the light
intensity and its variation at each pixel within the region of interest. Besides, from shot to shot,
28
the light intensity distribution has fluctuations that cannot be neglected. In view of this, under
each experimental condition, the measurement is repeated 100 times and the data is averaged
to reduce random fluctuation.
(a)
(b)
(c)
Figure. 2.6. Measurements of uniform field without space charge between two aluminum electrodes in transformer
Maximum deviation from
oil. The position of the imaging area is shown in Figure 2.5. (a) The distribution of I1(0), where
the dark regions to
uniform field
left and right of the illuminated area are electrodes. The light intensity (counts of electrons at a pixel) is represented
Difference between applied
by the colormap. (b) The distribution of I1(E) − I1(0) when the instantaneous voltage (Uins
) is 16 kV; and the
voltage and integration of
camera is triggered at 0.1 ms. (c) The distribution of I1(E) − I1(0) at Uins=24 kV.
In Figure 2.7, the ratios of
and
(as on the left side of Equation (2.9))
(e)
(d)
under various
measured field
(f)
values (0, 4, 6, 8, 10, 12, 14 kV/mm) are calculated and then fitted with a
4th power function:
. The MATLAB curve fitting tool
gives the coefficient
with 95% confidence bounds: (1.255±0.016)×10−4, and the goodness of
fit is indicated by the R-square (0.9997). Since
according to Equation
(2.9), one can evaluate the Kerr constant of transformer oil at
532 nm:
. In a previous work [2-8], we determined the Kerr constant of the used
transformer oil at
632.8 nm as
optic effect predicts that
. Classical theory of the Kerr electro-
(Havelock’s law) [2-11]. Our measurement results presented
above are in good agreement with the theory.
29
Figure 2.7. Ratio of I1(E) − I1(0) and I1(0) from the averaged data and power function (exponent=4) fitting.
Figure 2.8. Measured field distributions across the gap corresponding to Uins=24 and 16 kV.
30
In Figure 2.8, based on Equation (2.9) with the measured Kerr constant, electric field
distributions across the gap under Uins=24 and 16 kV are presented. The dashed lines in Figure
2.8 are the theoretical uniform field distribution. The measured field distribution is not
perfectly uniform; the deviation from uniformity is possibly due to the laser beam fluctuation
and other random processes in the system.
There are two measures to characterize the error of the measurement results: (i) the
maximum deviation of the measured field from theoretically-predicted uniform field (dashed
lines), which reflects the magnitude of the effect of randomness and is an indicator of
measurement sensitivity; and (ii) the difference between the instantaneous voltage and the
integration of the measured electric field over the gap, which, as a basic check of the
applicability and accuracy of experimental principles and methods, defines the measurement
reliability.
Figure. 2.9. Relative errors of the measurement results: the maximum deviation of the measured field from uniform
field, and the difference between the instantaneous voltage and the integration of the measured field over the gap.
31
The relative errors of the two types under various voltages are plotted in Figure 2.9. The
relative error of type (ii) is lower than that of type (i) because the former is essentially an
average of the latter over the gap which reduces the random fluctuations. When Uins is less than
10 kV, the maximum deviation from uniform field is ~30%, meaning that the light intensity
increase due to the Kerr effect is heavily contaminated by the random fluctuation of the laser
beam. As Uins increases, both errors become lower. While the relative error of type (ii) can be
as low as 2.5%, the random fluctuations still bring in >5% relative error of type (i), even if the
applied voltage is very close to the breakdown threshold.
Type (i) error is the primary factor that impedes the improvement of measurement
sensitivity. This can be better demonstrated by taking images of the region near the edge of the
electrodes, where the non-uniform field is called the fringing field.
In Figure 2.10, the Oy axis is defined as the midline of the gap, i.e. the two sides of the
axis are symmetric. Although the rounded edges of the two electrodes are not geometrically
identical, the fields at the points on the Oy axis are approximately along the x-direction, and the
principle of Kerr measurements for uniform gap (e.g. Equation (2.9)) also applies to field
mapping along the Oy axis.
Comparing Figure 2.10(b) with Figure 2.10(a), it is found that the increase in light
intensity is higher inside the gap than outside of the gap. From Figure 2.11, one can see that,
the measured electric field along the Oy axis generally agrees with the numerical solution in
Maxwell® 2D. The maximum deviation between measurement and the numerical results in the
range of 0< y <1.5 mm as a function of Uins is plotted in Fig. 2.12. The error bars come from
the standard deviation of 100 repeated measurements.
32
O
y
(b)
(a)
Figure 2.10. Measurements of space-charge free fringing field with two stainless steel electrodes in transformer oil.
The laser beam is shifted to illuminate the fringing area and the position of the CCD imaging area is adjusted
correspondingly. (a) The distribution of I1(0). The profiles of the rounded edges of the electrodes can be seen. The
light intensity (counts of electrons at a pixel) is represented by the colormap. (b) The distribution of I1(E) − I1(0)
when the instantaneous voltage (Uins) is 24 kV and the camera is triggered at 0.14 ms.
24 kV
16 kV
y (mm)
(c)
Figure 2.11. Measured field distributions along Oy axis indicated in Figure 2.10 corresponding to Uins=24 and 16
kV. The dot-dashed lines are numerical simulation results.
33
Figure 2.12. Dependence of the relative error of the measurement results in the range of 0< y <1.5 mm on Uins.
Under lower voltages, the errors due to randomness are more significant, while the
requirement on measurement sensitivity is higher. Therefore a tradeoff exists between
sensitivity and error. For example, if one wants to take measurements under Uins=16 kV, the
highest sensitivity, limited by the randomness-induced error, will be ~10%, which means that
the measurements do not have enough ‘contrast’ to consistently distinguish fields unless their
difference in intensity is over ~0.8 kV/mm. In order to further improve the Kerr measurement
sensitivity, it is necessary to identify and correct (if possible) various sources of randomness in
the system.
It has been demonstrated that the Kerr technique can successfully map the space-charge
free field with satisfactory accuracy when the mean field across the gap
kV/mm.
Whether or not the same method can be extended to electric field with space charge is to be
examined below. Since the mechanisms of space charge generation and transport are unclear,
34
the measured data cannot be verified by numerical models. Nevertheless, we will illustrate that
the mapped field from the Kerr measurements is physically reasonable and consistent.
With the electric field distribution measured, the space charge density
from Gauss’ law (
,
can be solved
is the dielectric constant of transformer oil). As shown
in Figure 2.13, aluminum electrodes inject negative charges (average charge density is 0.037
C/m3) into the gap, while the charge injection from titanium electrodes is much weaker.
t = 0.7 ms, Uins = ±28 kV
–
+
Figure 2.13. Measurements with same-material electrode pairs under HV pulses of both polarities. The position of
the imaging area is the same as Figure 2.5. The camera is triggered at 0.7 ms with the instantaneous voltage Uins=
±28 kV. For both polarities, the anode is located at x/d=0, while the cathode is located at x/d=1.
The results presented in Figure 2.13 indicate that since the two electrodes are made from
the same material (or approximately speaking, two identical electrodes), switching the polarity
(keeping other parameters of the applied voltage unchanged) should not affect the charge
35
injection and transport behavior. This physical consistency implies that the presence of space
charge in our experimental configurations has little effect on the physical processes involved in
the Kerr electro-optic effect and does not undermine the validity of the basic principles of the
field mapping measurement.
In this chapter, we demonstrate both quantitatively and qualitatively that Kerr electrooptic measurements with a high-sensitivity CCD camera can be used for electric field mapping.
Measurement accuracy and reliability for uniform and fringing space-charge free fields and
field with space charge have been evaluated. Generally speaking, the relative errors will be
reduced as the voltage increases. This may not be true when the voltage approaches the
breakdown threshold, since more uncertainties would be introduced due to high-field
conduction and pre-breakdown phenomena in the liquid dielectrics.
To further improve the sensitivity of the measurements, we need to identify and quantify
various sources of noise in the experimental system, including optical, electro-optical, and
electrochemical processes. Image processing techniques may also be helpful to enhance the
data quality. The most straightforward application of image processing algorithms in our
measurements is edge detection, i.e. identification of the electrode surfaces in the images taken
by the CCD camera. This would be more demanding when the oil gap is smaller, since the
same edge detection inaccuracy (e.g. 5 pixels) takes up a larger portion of the gap.
36
References
[2-1] A. Denat, “Conduction and Breakdown Initiation in Dielectric Liquids”, in Proc. ICDL,
Trondheim, Norway, Jun. 26-30, pp. 1-11 (2011).
[2-2] T. J. Lewis, “Basic Electrical Processes in Dielectric Liquids”, IEEE Trans. Dielectr. Electr.
Insul. 1, 630 (1994).
[2-3] I. Adamczewski, Ionization, Conductivity and Breakdown in Dielectric Liquids
(Taylor&Francis, London, 1969).
[2-4] U. Gäfvert, A. Jaksts, C. Törnkvist, and L. Walfridsson, “Electrical Field Distribution in
Transformer Oil”, IEEE Trans. Electr. Insul. 27, 647 (1992).
[2-5] M. Zahn, L. L. Antis, and J. Mescua, “Computation Methods for One-Dimensional Bipolar
Charge Injection”, IEEE Trans. Ind. Appl. 24, 411 (1988).
[2-6] V. Y. Ushakov (ed.), Impulse Breakdown of Liquids (Springer-Verlag, Berlin, 2007).
[2-7] M. Zahn, “Optical, Electrical and Electromechanical Measurement Methodologies of Field,
Charge and Polarization in Dielectrics”, IEEE Trans. Dielectr. Electr. Insul. 5, 627 (1998).
[2-8] X. Zhang, J. K. Nowocin, and M. Zahn, “Effects of AC Modulation Frequency and
Amplitude on Kerr Electro-Optic Field Mapping Measurements in Transformer Oil”, in Annual
Report of CEIDP, Montreal, Canada, pp. 700-704 (2012).
[2-9] E. Collett, Field Guide to Polarization (SPIE Press, Bellingham, 2005).
[2-10] M. Zahn, “Conduction and Breakdown in Dielectric Liquids”, in Wiley Encyclopedia of
Electrical and Electronic Engineering Vol. 20, pp. 89-123 (1999).
[2-11] J. W. Beams, “Electric and Magnetic Double Refraction”, Rev. Mod. Phys. 4, 133 (1932).
37
38
3
Kerr electro-optic field mapping study of the effect of
charge injection on the impulse breakdown strength of
transformer oil
Synopsis
The smart use of charge injection to improve breakdown strength in transformer oil is
demonstrated in this chapter. Hypothetically, bipolar homo-charge injection with reduced electric
field at both electrodes may allow higher voltage operation without insulation failure, since
electrical breakdown usually initiates at the electrode-dielectric interfaces. To find experimental
evidence, the applicability and limitation of the hypothesis is first analyzed. Impulse breakdown
tests and Kerr electro-optic field mapping measurements are then conducted with different
combinations of parallel-plate aluminum and brass electrodes stressed by millisecond duration
impulse. It is found that the breakdown voltage of brass anode and aluminum cathode is ~50%
higher than that of aluminum anode and brass cathode. This can be explained by charge injection
patterns from Kerr measurements under a lower voltage, where aluminum and brass electrodes
inject negative and positive charges, respectively. This work provides a feasible approach to
investigating the effect of electrode material on breakdown strength.
39
3.1 Introduction
Dielectric liquids used in power system apparatus and pulsed power technology have
their performance affected by injected space charge that distorts the electric field distribution
between electrodes. For highly purified water, Kerr electro-optic measurements and electrical
breakdown tests have shown that the magnitude and polarity of injected charge and the
electrical breakdown strength depend strongly on electrode material combinations and applied
voltage polarity [3-1].
Figure 3.1 (from [3-2]). Space charge distortion of the electric field distribution between parallel plate electrodes
with spacing d at voltage V so that the average electric field is E0=V/d. Four simplest possible configurations are
shown: (a) no space charge; (b) unipolar positive or negative charge; (c) bipolar homocharge; (d) bipolar
heterocharge.
Figure 3.1 shows four simplest configurations of space charge distorted electric field
distribution between parallel plate electrodes with spacing d at voltage V. The electric field is
40
uniform at the average field E0 when there is no space charge (Figure 3.1(a)). In Figure 3.1(b),
according to Gauss’ law, unipolar positive/negative charge distribution has the electric field
maximum at the cathode/anode, thus possibly leading to electrical breakdown at lower voltages.
For bipolar homocharge distribution shown in Figure 3.1(c), the positive charge region is near
the anode and negative charge near the cathode, so that the electric field is lowered at both
electrodes and is largest in the central region. In contrast, bipolar heterocharge distribution
(Figure 3.1(d)) has the electric field enhanced at electrodes and depressed in the central region.
It has been hypothesized that bipolar homo-charge injection (positive charge injected at
the anode and negative charge injected at the cathode) with reduced electric field at both
electrodes may allow higher voltage operation without insulation failure, since electrical
breakdown usually initiates at the electrode-dielectric interfaces [3-1,3-2]. At first glance, the
statement seems true and self-evident. Nevertheless, this problem is actually very complicated
and remains poorly understood for systems of practical interest.
Firstly, the electric field profile across the gap, the integration of which equals to the
instantaneous voltage, can actually be very complex. According to Gauss’ law, the charge
density is proportional to the divergence of electric field, which is the slope of the onedimensional electric field profile between parallel-plate electrodes [3-2]. The positive (negative)
slope at the anode (cathode) does not ensure that the local electric field is lower than the space
charge free field. The curves in Figure 3.1 are only the simplest possible cases. The electric
field distribution in the central region of the gap may exhibit more up-and-down patterns.
Secondly, reduced electric field at both electrodes may not correspond to improved
breakdown strength. For example, suppose electrode material #1 has homo-charge injection
and material #2 has no charge injection, but meanwhile the intrinsic (i.e. space charge free)
41
breakdown strength of #1 is much lower than that of #2. In this case, the hypothesis may not
hold since homocharge corresponds to lower breakdown voltage, suggesting that the intrinsic
breakdown strength should be considered as an important precondition. Besides, strong charge
injection currents, usually a destabilizing and uncontrollable factor in insulation configurations,
can cause instability at electrode surfaces [3-3].
It is also worthwhile to point out that, the hypothesis is based on the dc steady state.
However, under a strong dc electric field, turbulent flow can be induced due to
electrohydrodynamic instability [3-4]. That is, a stable dc steady state may not even exist. On
the other hand, when the applied high voltage is a short pulse (no induced flow), the validity of
the hypothesis is questionable since charge injection may be irrelevant to breakdown. The
ASTM D3300-12 standard test method for dielectric breakdown voltage in insulating oils
under 1.2/50 μs lightning impulse condition is performed using a tip opposing a grounded
sphere. The breakdown is preceded by the propagation of streamers emerging from the highvoltage tip electrode, while the space charge behavior is negligible before the streamer
inception [3-5].
Finally, for transformer oil, the most common industrial insulating liquid, experimental
evidence is on demand. Published works on the effect of electrode materials on breakdown
strength are largely empirical, and theoretical analysis based on electronic, mechanical and
thermodynamic characteristics of the metal is not in satisfactory agreement with the
experimental results [3-6]. It is partly because factors that affect the breakdown strength
significantly, such as gap geometry, applied waveform, test procedure, the state of electrode
surfaces and the quality of the transformer oil, vary in different works. Measurement method is
also a limiting factor: only monitoring voltage/current waveforms at electrical terminals cannot
42
provide detailed information on electric field distribution and space charge dynamics in
transformer oil during the conduction and pre-breakdown phases.
In this chapter, experiments are designed to examine the applicability of the hypothesis.
The measurement of the electric field distribution is made possible by the Kerr electro-optic
field mapping technique. Using a high sensitivity CCD (charge-coupled device), our recent
work [3-7] demonstrated the reliability of Kerr measurements with high voltage pulsed
transformer oil, which had been a bottleneck due to the low Kerr constant of transformer oil
and the low sensitivity of old detectors. As a continuing work, different combinations of
electrode materials will be tested in this chapter to find the connections between impulse
breakdown strength and charge injection pattern. The duration of the applied high voltage
impulses should be long enough for the space charge effect to manifest, and meanwhile, be as
short as possible to minimize induced flow in the dielectric liquids which disturbs the optical
detection.
43
3.2 Optimization of Kerr experimental configurations
In Section 2.2, the basic principle of Kerr measurement has been introduced based on a
linear polariscope with crossed polarizers. Actually, there are four different polariscope
configurations: linear, pre-semi, post-semi and circular (Figure 3.2). In each of them,
transmission axes of the polarizer and the analyzer can either be crossed or aligned.
(a) Linear polariscope
(b) Pre-semi polariscope
(c) Post-semi polariscope
(d) Circular polariscope
Figure 3.2. Four polariscope configurations: (a) linear; (b) pre-semi; (c) post-semi; (d) circular.
44
In this section, we are going to discuss which one is the optimum configuration for
practical measurements in the sense that it yields the highest accuracy and stability. There are
also many other factors that will reduce the accuracy and stability of the measurement results:
optical components not perfect or not precisely adjusted; impurities and flow of the dielectric
liquid; fluctuations of laser intensity; thermal noise within the CCD camera; environment.
Although at the current stage we only focus on the optimization of the measurement
configuration, we should not neglect the influence of these factors.
We start from a linear polariscope where the output/input light intensity ratio
can
be calculated according to Equations (2.3)−(2.5). With the help of mathematical software, we
can avoid complicated symbolic computation and easily obtain useful numerical results.
1. Aligned polarizers (
)
1.5
0.9
1
0.8
0.7
 (radians)
0.5
0.6
0.5
0
0.4
-0.5
0.3
0.2
-1
0.1
-1.5
-1.5
-1
-0.5
0
0.5
1
1.5
 (radians)
p
Figure 3.3. Numerical results of the intensity ratio
when
45
,
and
vary from
to .
The Kerr constant of transformer oil is
. If the average electric field
and the electrode length is
shift
, then it is estimated that the Kerr phase
. However, when the voltage is applied, due to space charge, the
field may not be uniform across the gap. If we want to get the non-uniform field distribution,
we must at least be able to distinguish
least be able to detect the change of
If
,
and
,
and
as small as
vary from
to
is shown in Figure 3.3. In cases with
, that is, the measurement should at
.
, the contour plot of the intensity ratio
the intensity ratio is very close to 1. When
, since the polarizer would let little light go through, the intensity ratio is
essentially zero. The two cases yield trivial results, and thus should be avoided. Somewhere in
between seems more appropriate. The appropriateness is based on two considerations: the
contrast, i.e. the capability to distinguish the light intensities for different values of
; and the
error behavior, i.e. the changes in the results as some parameter of the system has small
deviations from the theoretically specified value.
Table 3.1. Numerical results of
as
0.8535
0.7499
0.5000
0.2500
0.1464
, and
0.8534
0.7498
0.4998
0.2499
0.1464
0.8532
0.7495
0.4996
0.2498
0.1464
in the range of
0.8529
0.7491
0.4992
0.2497
0.1463
In Table 3.1, we present the numerical results of the intensity ratio
, and
in the range of
.
0.8525
0.7486
0.4988
0.2495
0.1463
as
, from which one can see that when
, the contrast is better than
(by comparing the difference between
46
and
in each case).
Numerical results of the intensity ratio
as
are given in Table 3.2. Now we assume the two polarizers are not perfectly
aligned, which means that there may be a small difference (
changes in
(
) between
and
. The
are also calculated and expressed in percentage of the values in ideal settings
). From Table 3.2 we can see that when
measurement seems more stable than
, the variation is smaller and the
.
Table 3.2. Numerical results as
, and
0.8535
0.7499
0.5000
0.8532
0.7495
0.4996
0.8525
0.7486
0.4988
.
Variation (%)
2.437
2.440
2.440
2.461
2.454
2.441
2.475
2.471
2.445
0.8327
0.7316
0.4878
0.8322
0.7311
0.4874
0.8314
0.7301
0.4866
Thus in principle, it seems that
has a deviation of
leads to the result with maximum
contrast and best error behavior.
However, to detect very small modulation effects
, the contrast of
aligned polarizers is far from adequate. The saturation level of each pixel in the CCD camera is
50000 counts (of electrons). The fluctuation level of each pixel is at least 10 to 20 counts,
which means that, in this configuration, we cannot distinguish
and
(
(
),
(
). For example, from the results shown in Table 3.1, the difference
47
)
between
and
is only
, which corresponds to only 20 counts,
approximately on the background noise level (mainly due to the fluctuations of the laser and
internal errors of the CCD). Hence we cannot obtain reliable non-uniform field distribution
across the gap in this configuration.
2. Crossed polarizers (
If
,
)
and
vary from
to , the contour of the intensity ratio
is
shown in Figure 3.4.
x 10
-5
1.5
9
1
8
7
 (radians)
0.5
6
5
0
4
-0.5
3
2
-1
1
-1.5
-1.5
-1
-0.5
0
0.5
1
1.5
0
 (radians)
p
Figure 3.4. Numerical results of the intensity ratio
when
In Figure 3.4, it is obvious that
,
and
vary from
to .
yields the maximum output light intensity.
This is useful because with crossed polarizers the transmitted light intensity is always very low
48
for low Kerr constant materials like transformer oil. The output light intensity needs to be high
enough to be detectable.
2.5
x 10
-3
2
I 1/I 0
1.5
1
0.5
0
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
 (radians)
Figure 3.5. Numerical results as
, and
varies from
to
rad.
0.03
=0.02
=0.06
=0.1
0.025
I 1/I 0
0.02
0.015
0.01
0.005
0
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
 - -/2 (radians)
p a
Figure 3.6. Numerical results as
,
and
49
varies from
to
.
In the case with
, we calculate the intensity ratio
electric field or the phase retardation
between the values of
as a function of the
. The results are plotted in Figure 3.5. The difference
when
and
is about 1/1000, which
corresponds to about 100 counts (CCD pixel information), higher than that of aligned
polarizers (20 counts).
However, with crossed polarizers,
can be set higher than the saturation level of the
CCD (50000 counts), since the detected light intensity
incident light intensity
(with aligned polarizers,
is only a very small fraction of the
). Typically we can choose
to be 3
to 5 times of the saturation level, which results in a further 3 to 5 times enhancement in the
measurement sensitivity. It can be concluded that, the contrast of crossed polarizers is much
better than that of aligned polarizers. This also explains why we used this configuration in
Chapter 2.
In practice, it may be very difficult to make sure that the polarizers are perfectly crossed.
As shown in Figure 3.6, if the two polarizers are not perfectly crossed, the deviation in light
intensity ratio can be much greater than the value in ideal settings. For example, when
and
to
(about
), the error will be over 10% of the result corresponding
. The magnitude of the error also seems to increase nonlinearly as the
imperfection in alignment is augmented.
While compared to aligned polarizers, crossed polarizers have higher contrast and
sensitivity, their poor error behavior of the crossed polarizers may be a limiting factor of the
reliability of the results when we take Kerr measurements. Next, we will try crossed polarizers
with a quarter wave plate inserted (pre-semi polariscope).
50
3. Effect of quarter wave plates (pre-semi polariscope)
Since we have known that the contrast and error behavior of the linear polariscope are
not adequate for the measurement of small signals, the next thing we tried is to insert a quarter
wave plate between the polarizer and the test cell (called pre-semi polariscope) and see if there
is any improvement.
In the discussion below, we fix the polarization angle of the laser output to
.
For quarter wave plates, the slow axis is at angle ψ with respect to the y-coordinate and
the slow wave is retarded by
 exout   cos
 out   
 e    sin
 y  
in phase:
sin  1
0

 i/2
cos  0 e
 cos

 sin
 exin 
 sin  exin 
   U q ( ) in 
e 
cos  einy 
 y
(3.1)
In the experimental setting shown in Figure 2.2, when a quarter wave plate is inserted
between the polarizer and the test cell, we have:
 e1x 
e 
   U p ( a )U b (0,  )U q ( )U p ( p ) 0 x 
e 
e 
 1y 
 0y 
(3.2)
The matrix elements in Equations (2.4) and (2.5) should now be modified
correspondingly.
, ψ and
For crossed polarizers, if
vary from
to , the contour of the
intensity ratio is shown in Figure 3.7. In Figure 3.7, the optimum case with highest output light
intensity is when ψ
function of the phase retardation
and
. In this case, we calculate the intensity ratio as a
. The results are plotted in Figure 3.8.
51
1.5
0.45
1
0.4
0.35
 (radians)
0.5
0.3
0
0.25
0.2
-0.5
0.15
0.1
-1
0.05
-1.5
-1.5
-1
-0.5
0
0.5
1
1.5
 (radians)
p
Figure 3.7 Numerical results of the intensity ratio when
,
, ψ and
vary from
to .
Comparing Figure 3.7 with Figure 3.4 (without quarter wave plate), we can find a
significant improvement on the output light intensity (from 10-3
to 10-1
). However, this
does not mean that the Kerr measurement sensitivity is also enhanced by two orders, because
the sensitivity requires a clear cut between the signals with and without Kerr electro-optic
effect. From Figure 3.8, it can be seen that the intensity ratio grows almost linearly with the
phase retardation
(or similarly
. There are detectable differences in
and
). If
between
and
(counts of electrons), this
difference (around 0.01) can be 500 counts of electrons, much greater than the noise level (20
counts). Hence the sensitivity of the pre-semi configuration is satisfactory. Next we will check
its error behavior.
52
0.555
0.55
0.545
0.54
I 1/I 0
0.535
0.53
0.525
0.52
0.515
0.51
0.505
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
 (radians)
,ψ
Figure 3.8 Numerical results of the intensity ratio when
,
,
from
to
rad.
0.555
0.55
0.545
0.54
I 1/I 0
0.535
0.53
0.525
0.52
0.515
=0.02
=0.06
=0.1
0.51
0.505
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
 - -/2 (radians)
p a
Figure 3.9 Numerical results of the intensity ratio as
and
53
varies from
to
.
In Figure 3.9, we present the numerical results of the intensity ratio
and
varies from
to
as
. As shown in Figure 3.9, if the two
polarizers are not perfectly crossed, the magnitude of the error is negligible compared with that
of the signal. For instance, when
and
lower than 1% of the result of
(about
), the error is
.
Furthermore, if the Jones’ matrix for a polarizer (see Equation (2.1)) becomes:
 Exout   cos 
 out   
 E    sin 
 y  
where
0  cos 
sin    x


cos   0 1   y  sin 
 sin   Exin 
 
cos   E yin 
(3.3)
are small quantities to characterize imperfections in the polarizer material. We
recalculate the above case. We find that, if
smaller than 1%, the imperfection of the
polarizers contributes little to the measured data.
The main conclusion for the post-semi polariscope (Figure 3.2(c)) is similar to the presemi polariscope, and the analysis of the circular polariscope (which can be used to eliminate
isoclinic lines if there are any in the measurement) yields similar results to that of the linear
polariscope. For this reason, we do not discuss here these two types of polariscope in details.
The work done in this section indicates that pre-semi polariscope with crossed polarizers
will be an optimized experimental configuration for Kerr electro-optic field mapping
measurements with low Kerr constant dielectric liquids like transformer oil. Its sensitivity
(contrast) and consistency (stability) under imperfection have been shown to be better than
those of linear polariscope.
54
3.3 Experimental procedure
We use a 0.25/20 ms high voltage pulse (the detailed reason will be discussed later). The
fitted curve for the waveform can be expressed in double-exponential form:
, where
is approximately the peak voltage,
ms and
μs are two constants.
The transformer oil is lab-aged Shell DIALA A oil without dehydration or high-standard
degassing/filtering. Although there are a vacuum pump and an oil filter in the experimental
setup, their function is to remove visible bubbles and particles in the oil that may cause
premature electrical breakdown and reduce optical detection accuracy. The electrodes have
been rinsed with reagent alcohol and conditioned in the oil by slowly increasing dc voltages
(no breakdown) for hours.
The impulse breakdown voltages of the transformer oil filled gap (width
2 mm)
between parallel-plate electrodes (4 different combinations of brass 360 and aluminum 2024,
both with approximately the same surface roughness
µm) are tested using the rising-
voltage method [3-8]. During the breakdown test, we apply the impulse waveform starting
from
~25 kV. At each voltage level, apply 3 impulse waves and allow at least 30 s between
each test.
is increased in steps of 1~2 kV until breakdown occurs. After each breakdown,
we clean the electrode surfaces and run the filter and then the vacuum to reset the test cell.
The experimental setup for Kerr measurements is illustrated in Figure 3.10. The
diameter of the laser beam (wavelength 632.8 nm, linearly polarized) is 0.5 mm. The 20× beam
expander expands the laser beam to about 10 mm in diameter. The polarizers (P0, P, A) have
an extinction ratio 500:1 and diameter of 10 cm. Plano-convex lenses L1 and L2 are 25.4 mm in
55
diameter and the effective focal length is
50.2 mm . The Andor iXon camera is a
megapixel back-illuminated EMCCD with single photon detection capability. The imaging
area (8×8 mm2) covers the
2 mm gap (~250 pixels across).
The CCD camera measures the light intensity of the laser beam coming through the presemi polariscope with crossed polarizers (P and A). Polarizer P0 is used to ensure the linear
polarization state of the expanded laser beam and to attenuate the laser to avoid saturating the
CCD camera. A quarter-wave plate (Q) is inserted between P and the test cell (pre-semi
polariscope) to increase measurement sensitivity. The angle of polarization of the laser output
is 45° (with respect to the x-axis); the transmission angles of P and A are 45° and −45°,
respectively; for the quarter-wave plate (Q) and the transformer oil-filled gap, the slow wave is
polarized along the x-axis, with phase retardation
and
is the Kerr constant of transformer oil [3-9],
along the light path, and
where
m is the electrode length
is the electric field.
Figure 3.10. Experimental setup for Kerr electro-optic field mapping measurements.
The ratio of light intensities detected by the CCD camera with and without high voltage
56
is given by
[3-2,3-9], from which the electric field intensity
at each pixel can then be calculated.
The spatial filter has been used to eliminate the effect of scattering and diffraction of the
laser beam propagating through the gap. The two images shown in Figure 3.11 are taken when
no high voltage is applied, and the fluctuation patterns in the image without the spatial filter
are due to scattering or diffraction of light when propagating through the gap. The distributions
of
are calculated from the data taken at
0.1 ms (instantaneous voltage Uins~13
kV), which should be uniform across the gap since no significant space charge distortion is
present. Obviously, the use of a spatial filter improves the measurement accuracy. Without the
spatial filter, the detected gap is wider than reality and the light intensity distribution across the
gap has some extra patterns even when there is no high voltage applied.
1500
I1(E)/I1(0)
Without Spatial Filter
y
With Spatial Filter
300
500
100
x
x (mm)
Figure 3.11. Detected light fields and the distributions of
57
in the gap with and without the spatial filter.
The exposure time of the CCD camera (starting from
to 2 ms, in steps of
10 μs (
μs) or 50 μs (
) is adjustable from 50 μs
μs). To reduce the random
fluctuations in the system (e.g. the variations of laser output intensity), for each
the
measurement is repeated 50 times and the average of these images is calculated. By
differentiating the light intensity under exposure time and
between
and
.
Ed/U(t)
of the distribution of
, we obtain the time average
Figure 3.12. Electric field distributions (normalized by U(t)/d) from the measurements with a pair of brass
electrodes under 30 kV peak HV impulses of positive polarity. The anode and cathode are at
respectively. The scattered point plots are the measurement results at
0 and
,
0.3, 0.5, and 0.7 ms.
In Figure 3.12, normalized electric field distributions between a pair of brass electrodes
under +30 kV peak HV impulses are presented. The measurements are taken at times 0.3, 0.5,
and 0.7 ms. The solid lines are polynomial fitting curves, from which one can clearly see the
advancement of the space charge fronts as marked by the arrows. The sequence displays the
58
movement of charge carriers across the gap (the mobility of charge carriers is estimated to be
~0.8×10-7 m2/Vs, which is actually the electrohydrodynamic mobility since the turbulent
motion of liquid enhances the charge transport by 1~2 orders [3-11]). Therefore the
measurement results in the presence of space charge are plausible.
The charge injection includes complex electrochemical reactions (e.g. preferential
adsorption of ions) controlled by the electrical double layer potential [3-12,3-13,3-14,3-15]. In
this case, the anode injects positive charges which drift toward the cathode under the action of
the electric field. Near the cathode, the positive ‘charge injection’ is more likely the
accumulation of positive charge carriers, since the advancing speed of the charge fronts here is
about the same as that at the anode (in transformer oil, the mobility of negative charges is
about half that of positive ones [3-3]). In Chapter 4, we will discuss the mechanism of charge
injection in more detail.
(a)
(b)
Figure 3.13. Measurement accuracy (a) and fluctuation level (b) as a function of time when the measurements are
taken with aluminum electrodes under 30 kV peak HV impulses.
59
To proceed, it remains necessary to experimentally determine a valid time range for Kerr
measurements to ensure the accuracy and consistency of the results. In our previous work [3-7],
we concluded that when the instantaneous voltage Uins < 10 kV, Kerr measurement results will
be heavily contaminated by the random fluctuation of the laser beam (the relative error exceeds
No space charge
10%).
With space charge
Limits given by
minimum voltage
Upper limit
given by the
onset of flow
Figure 3.14. Determination of the valid time range for the Kerr electro-optic field mapping measurements.
On the other hand, as shown in Figure 3.13, the relative error and fluctuation level
increase as time increases, implying that there exists an upper time limit (see Figure 3.14). In
Figure 3.13, the relative error is defined as the relative difference between the integration of
the measued electric field across the gap and the instantaneous applied voltage. The dashed
line in Figure 3.13(a) is the tolerated error, 10%. The fluctuation level represents the
consistency of the results from the 50 repeated measurements. It is the Euclidean distance
between the electric field distribution obtained from each single optical measurement and that
60
from averaged data of 50 optical measurements. The maximum and minimum fluctuation
levels at
1, 2, 4, 6, 8, 10, 12, 14, 16, 18 ms are shown in Figure 3.13(b).
In Figure 3.13(a), somewhere between 6 ms and 8 ms, the relative error crosses the
dashed line. The elevated level of the errors afterwards suggests that a certain physical process
has been involved, which is the electrohydrodynamic instability: Coulomb force on space
charge in the fluid gives rise to fluid motions. The viscous diffusion time τv=
whether fluid inertia with mass density
or fluid viscosity
determines
dominates fluid motions over a
characteristic length [3-1,3-4]. If higher spatial resolution is required (smaller ), the onset of
significant flow effects will arise earlier. We choose
, and τv is on the order of 10 ms.
The estimation supports the measurement results that for t < 6 ms there is no strong turbulence,
since the relative error is close to the space charge free case (~5%).
The main conclusions of this section are summarized in Figure 3.14, which gives the
valid time range for the Kerr measurements that can be experimentally determined. There are
three basic considerations: (1) magnitude of the electric field to be measured (if it is too low,
the Kerr effect signal will be contaminated by the noise); (2) flow effect (flows can bring in
strong local fluctuations initially and significantly lower the measurement accuracy eventually);
(3) space charge movement (in this work we did not find any limits imposed by space charge,
however, keep in mind that the theory of Kerr effect is based on a perfect dielectric material
assumption, and it is necessary to examine to what extent can conduction cause deviations
from theory).
61
3.4 Results and discussions
The procedure of impulse breakdown voltage tests outlined in Section 3.3 are repeated 5
times for each combination of electrodes, and the statistics of the 5 breakdown peak voltages
(
) are presented in Table I. Due to the long pulse duration which reduces pre-breakdown
randomness, the standard deviation of breakdown voltages in each test is < 10%.
Table 3.3. Impulse breakdown test results for combinations of brass and aluminum electrodes under both polarities.
Test #
Polarity
HV
GND
Std. (kV)
Range (ms)
1
2
+/−
+/−
Brass
Aluminum
Brass
Aluminum
46.7/47.8
32.6/33.1
2.3/2.1
1.8/2.0
1.21−1.78
0.96−1.37
51.4±3.9
49.1±3.2
3
−
Brass
4
+
Aluminum
Aluminum
33.2
2.1
Brass
33.8
2.8
0.95−1.64
49.6±4.1
5
+
Brass
Aluminum
52.0
3.3
6
−
Aluminum
Brass
50.3
2.6
0.20−0.42
50.2±4.5
While the polarity effect on
Avg. (kV)
(kV)
for dissimilar-material electrodes can be clearly seen in
Table 3.3 (there is ~50% difference in
same-material electrodes (the difference in
under opposite polarities), it is not obvious for
under two opposite polarities is within the error
bounds given by the standard deviation), indicating that the two same-material electrodes are
basically identical. Otherwise, if one of them has more micro-protrusions or adsorbed
impurities and therefore a much higher probability of breakdown inception, the streamers will
tend to develop from this electrode instead of the other. Then the breakdown voltages under the
two polarities cannot be so close, since the streamer polarity is reversed under reversed
impulse polarity and the inception voltage of positive streamers is significantly lower than that
of negative streamers [3-3,3-6].
62
From the breakdown waveforms recorded by the oscilloscope, the time
breakdown occurs (the beginning of the applied waveform is
range of
when
) can be measured. The
for each case is also presented in Table 3.3. In most cases (except in Tests #5&6)
the breakdown occurs on the falling slope of the impulse, with
ms. Since the time for
streamers to transverse the 2 mm gap (in order of nanoseconds [3-5]) is negligible compared
with
, the streamer is essentially initiated at
.
The experimental fact that breakdown is initiated after the peak passes implies that the
electric field near the electrodes at
may be higher than that at the peak, which implies the
existence of space charge distortion of the electric field. If it is interpreted as impurity-induced
breakdown, there will be difficulties in explaining why almost all breakdown events are later
than the impulse peak.
To evaluate the intrinsic breakdown strength of the electrodes, we run the breakdown
test in a different way. By applying an impulse with peak voltage two times higher than the
breakdown voltage
obtained using the rising-voltage method, the breakdown will occur on
the rising slope of the impulse (
50 μs) with uniform electric field distribution since no
significant space charge effect exists [3-7]. The instantaneous voltage at the breakdown point
(
) is measured, and the statistical results are presented in the rightmost column of Table 3.3.
No polarity effect on
is observed for all combinations of electrode materials.
In the field of dielectric breakdown and electrical insulation research, the term ‘polarity
effect’ is most commonly associated with conduction, pre-breakdown and breakdown
phenomena in non-homogeneous electric fields (e.g. tip-sphere). As in the ASTM D3300-12
standard, the polarity effect on electrical breakdown under 2.5/50 μs impulse is essentially
resulted from different inception field thresholds at the tip and propagation dynamics of
63
positive and negative streamers in the pre-breakdown stage [3-6]. On the other hand, in a space
charge free uniform electric field between parallel-plate electrodes, the initiation of streamers
can be from either the anode, the cathode, or both. As shown above, if the two electrodes are
‘symmetric’, i.e. made of the same material and with the same surface conditions, or if the
effective impulse duration is so short that the electric field is not significantly distorted by the
injected charge before streamer inception, no polarity effect on breakdown voltage is expected.
Therefore, it is generally thought that the polarity of the applied voltage has little or no effect
on the impulse breakdown strength of an insulating medium in homogeneous electric fields [310].
However, in parallel-plate electrode geometry, under longer impulses, the polarity effect
on the breakdown voltage for dissimilar-material electrodes has been observed, which may be
closely related to charge injection. To reveal this, Kerr electro-optic field mapping
measurements will be taken to determine the electric field distribution and its dynamics
between parallel-plate electrodes in high voltage pulsed transformer oil.
In Figure 3.15, we present the local electric fields at anode and cathode under impulses
with 30 kV peak voltage from
to
ms for 4 combinations of electrode materials: (a)
both brass (unipolar positive charge injection); (b) both aluminum (unipolar negative charge
injection); (c) aluminum anode and brass cathode (bipolar hetero-charge injection); (d) brass
anode and aluminum cathode (bipolar homo-charge injection, with the highest impulse
breakdown voltage
, see Table. 3.3). In order to reduce the randomness caused by small-
scale turbulent flow, the electric fields presented here are the averages of the data at the 25
pixels (0.1d) nearest to the electrode surfaces. The electric fields as a function of time are not
very smooth due to measurement error. The dashed lines are the space-charge-free uniform
64
field (Uins/d). The grey shadowed areas mark the ranges of time when breakdown occurs.
The charge injection patterns are determined not only by the resulting electric fields at
anode and cathode (for example, in unipolar positive charge injection, anode/cathode field is
lower/higher than the space charge free field), but also by the evolution of electric field profiles
such as those in Figure 3.12.
(a)
(b)
(c)
(d)
Figure 3.15. Local electric fields at anode and cathode under impulsed with 30 kV peak voltage from
to
ms for 4 combinations of electrode materials: (a) both brass; (b) both aluminum; (c) aluminum anode and
brass cathode; (d) brass anode and aluminum cathode.
65
The peak voltage of impulses used in the Kerr measurements is 30 kV, below the lowest
which is ~33 kV for cases (b) and (c). The reason for this is to avoid electrical breakdown
when the camera is acquiring data; otherwise, the detected images will be corrupted by bubbles
or bright sparks [3-16]. The consistency between the impulse breakdown tests and the Kerr
measurements under a lower voltage can be seen from three aspects:
(1) In each case, the range of
(the grey shadowed area in Figure 3.15) approximately
covers the time interval during which the field at one of the electrodes approaches and then
passes the ‘crest’, which makes sense because the electrical breakdown is more probable under
higher fields. It is understandable that there may be minor discrepancies. On the one hand,
and
,
are measured with higher voltages than that used in Kerr electro-optic
measurements. On the other hand, the Kerr measurement results have a ~5% error bounds due
to randomness in the system.
(2) The intrinsic breakdown voltages (
) for all electrode combinations are basically at
the same level, which serves as a precondition for improved
in case (d) from other cases. If
of aluminum electrodes is significantly lower than that of brass electrodes, case (a) would
have the highest
, and
in case (d) will most likely be
of the aluminum electrode
since the breakdown occurs at the peak of the high voltage impulse as shown in Figure 3.15(d).
(3) In all cases,
cannot exceed
(see Table. 3.3), which agrees with physics
intuition that space charge is ‘deleterious’ in electrical insulation. Correspondingly, in Figure
3.15, the highest field at one of the electrodes never falls below the peak of the space charge
free field (dashed line). In Figure 3.15(d), it is not bipolar homo-charge injection that allows
higher
, because the breakdown occurs when space charge effects are insignificant. In this
sense, the hypothesis should be restated as:
66
in the presence of bipolar homo-charge
injection, compared with other charge injections, may be closer to
.
Similar results are found with stainless steel and brass electrodes. As shown in Table 3.4,
with stainless steel electrodes (also injecting negative charges) replacing aluminum electrodes,
the difference in the impulse breakdown voltages of various electrode combinations can also be
explained by charge injection.
Table 3.4. Impulse breakdown test results for combinations of brass and stainless steel (S-S) electrodes.
Test #
Polarity
HV
GND
1
2
+/−
+/−
Brass
S-S
Brass
S-S
3
−
Brass
4
+
S-S
5
+
6
−
Avg. (kV)
Std. (kV)
Range (ms)
(kV)
46.7/47.8
35.4/35.5
2.3/2.1
1.5/1.7
1.21−1.78
1.03−1.55
51.4±3.9
48.8±2.5
S-S
31.6
1.9
Brass
32.1
1.4
0.93−1.47
49.3±3.2
Brass
S-S
45.7
2.4
S-S
Brass
46.9
2.7
0.25−0.37
49.8±2.9
Although further efforts should be made to test more electrode materials, the present
work clarifies some issues regarding the hypothesis at the beginning of the chapter. To test the
hypothesis, many experimental details need to be carefully considered, such as appropriate
impulse waveform, similar intrinsic breakdown voltage of different electrode materials, and
dynamic Kerr measurement before the onset of flow. Only under specific circumstances, the
hypothesis is testable and correct. On the other hand, however, this chapter demonstrates the
smart use of electrode charge injection to improve the breakdown strength in transformer oil
and more importantly, a feasible approach to investigating the effect of electrode material on the
breakdown strength, which may be difficult and inconclusive to be directly related to the
electronic, mechanical and thermodynamic characteristics of the metal. The complexity has
been reduced to charge injection patterns and intrinsic breakdown strength in this work.
67
References
[3-1] M. Zahn, Y. Ohki, D. B. Fenneman, R. J. Gripshover, and V. H. Gehman, “Dielectric
Properties of Water and Water/Ethylene Glycol Mixtures for Use in Pulsed Power System
Design”, Proc. IEEE 74, 1182 (1986).
[3-2] M. Zahn, “Optical, Electrical and Electromechanical Measurement Methodologies of Field,
Charge and Polarization in Dielectrics”, IEEE Trans. Dielectr. Electr. Insul. 5, 627 (1998).
[3-3] I. Adamczewski, Ionization, Conductivity and Breakdown in Dielectric Liquids
(Taylor&Francis, London, 1969).
[3-4] M. Zahn, “Conduction and Breakdown in Dielectric Liquids”, in Wiley Encyclopedia of
Electrical and Electronic Engineering Vol. 20, pp. 89-123 (1999).
[3-5] J. G. Hwang, M. Zahn, F. O’Sullivan, L. A. A. Pettersson, O. Hjortstam, and R. Liu,
“Effects of Nanoparticle Charging on Streamer Development in Transformer Oil-Based
Nanofluids”, J. Appl. Phys. 107, 014310 (2010).
[3-6] V. Y. Ushakov, Insulation of High-Voltage Equipment (Springer-Verlag, Berlin, 2004).
[3-7] X. Zhang, J. K. Nowocin, and M. Zahn, “Evaluating the Reliability and Sensitivity of the
Kerr Electro-Optic Field Mapping Measurements with High-Voltage Pulsed Transformer Oil”,
Appl. Phys. Lett. 103, 082903 (2013).
[3-8] Q. Liu, Z. D. Wang, and F. Perrot, “Impulse Breakdown Voltages of Ester-Based
Transformer Oils Determined by Using Different Test Methods”, in Annual Report of CEIDP,
Virginia Beach, USA, pp. 608-612 (2009).
[3-9] X. Zhang, J. K. Nowocin, and M. Zahn, “Effects of AC Modulation Frequency and
Amplitude on Kerr Electro-Optic Field Mapping Measurements in Transformer Oil”, in Annual
Report of CEIDP, Montreal, Canada, pp. 700-704 (2012).
[3-10] ASTM, Standard Test Method for Dielectric Breakdown Voltage of Insulating Oils of
Petroleum Origin under Impulse Conditions, ASTM Std. D3300-12 (2012).
[3-11] N. Felici, “High-Field Conduction in Dielectric Liquids Revisited”, IEEE Trans. Electr.
Insul. 20, 233 (1985).
[3-12] R. P. Joshi, J. Qian, S. Katsuki, and K. H. Schoenbach, “Electrical Conduction in Water
Revisited: Roles of Field-Enhanced Dissociation and Reaction-Based Boundary Condition”,
68
IEEE Trans. Dielectr. Electr. Insul. 10, 225 (2003).
[3-13] A. Denat, “Conduction and Breakdown Initiation in Dielectric Liquids”, in Proc. ICDL,
Trondheim, Norway, Jun. 26-30, pp. 1-11 (2011).
[3-14] T. J. Lewis, “Basic Electrical Processes in Dielectric Liquids”, IEEE Trans. Dielectr.
Electr. Insul. 1, 630 (1994).
[3-15] R. P. Joshi, J. Qian, K. H. Schoenbach, and E. Schamiloglu, “A Microscopic Analysis for
Water Stressed by High Electric Fields in the Pre-Breakdown Regime”, J. Appl. Phys. 96, 3617
(2004).
[3-16] X. Lu, Y. Pan, K. Liu, M. Liu, and H. Zhang, “Early Stage of Pulsed Discharge in
Water”, Chin. Phys. Lett. 18, 1493 (2001).
69
70
4
Transient charge injection dynamics in high-voltage
pulsed transformer oil
Synopsis
Transient electrode charge injection in high-voltage pulsed transformer oil is studied with Kerr
electro-optic measurements. Time evolutions of total injected charges and injection current
densities from two stainless-steel electrodes with distinct surface roughness obey a power law
with different exponents. Numerical simulation results of the time-dependent drift-diffusion
model with the experimentally-determined injection current boundary conditions agree with
measurement data. The power-law dependence implies that the electric double layer processes
contributing to charge injection are diffusion-limited. Possible mechanisms are proposed based
on formative steps of adsorption-reaction-desorption, revealing deep connection between
geometrical characteristics of electrode surfaces and fractal-like kinetics of charge injection.
71
4.1 Introduction
Non-polar and weakly polar dielectric liquids (e.g. transformer oil) are widely used for
high voltage (HV) insulation in electrical power systems. Electrical conduction in these liquids
under intense electric fields has been studied for decades [4-1,4-2]. As shown in Figure 4.1,
when flow electrification is negligible (e.g. under impulse HV), bulk dissociation and electrode
injection are the primary physical processes contributing to the conduction current.
Applied Voltage,
Gap Configuration
electrode processes and impurity effects
1
Liquid Ionization
D
1: Integration Law 0 EdxU


2: Gauss’Law dE
dx 
?: Drift and diffusion of charges, various
Electric Field
?
2
Bulk Dissociation
Electrode Injection
(heterocharge distribution)
Space Charge
Figure 4.1. The complexity of electric field determination. Given applied voltage and gap configuration, one has to
know the interactions between electric field and space charge to solve for electric field. However, quantitative
account of the electrode charge injection is difficult.
In the bulk of the liquid, the generation and transport of charge carriers have been
described by a bipolar drift-diffusion ionic conduction model, two simplified scenarios of
72
which, i.e., steady-state conduction [4-3] and unipolar drift-dominated conduction [4-4,4-5],
yielded analytical results. The model assumptions include:
(i)
Electroquasistatic (EQS) approximation, since the ratio of length and time
scales of the system is far less than the speed of light;
(ii)
Drift-diffusion approximation, i.e. ion motion modeled by drift and diffusion
under local field, meaning that the ions immediately relax to a velocity where
the field acceleration balances the momentum losses due to collisions with
other particles;
(iii)
Creation of ions (two types, positive and negative) according to Onsager’s
theory [4-6], in which the ionic conductivity is due to dissociation of ion pairs
and other ionic complexation processes [4-7] are considered insignificant;
(iv)
Recombination based upon the Langevin model [4-8], which, strictly speaking,
is valid for high-pressure gas;
(v)
Einstein relation [4-9], assuming liquid in thermodynamic equilibrium, builds a
connection between diffusion coefficient and mobility for each carrier
Electrode charge injection has been included as boundary conditions in the numerical
simulation of the time-dependent conduction model, e.g. zero [4-10] or field-proportional [4-11]
injected charge densities at the electrode-liquid interfaces. These boundary conditions are
largely hypothetical, and the experimental verifications based on steady-state measurements
(i.e. ac modulation technique) are unsatisfactory [4-11,4-12].
Current density-electric field (J-E) characteristic is a more naturally defined boundary
condition. For example, electronic charge emission from the electrodes can be well described
by vacuum electronic models [4-13] (high-field, typically >
73
V/m, requiring highly
divergent electric fields such as those at a needle tip). In this work we consider equilibrium and
non-equilibrium electric double layer (EDL, thickness much smaller than the inter-electrode
distance) phenomena which includes 1D Onsager effect (ions overcome image charge
attraction) [4-14] and electrode/liquid interfacial charge transfer electrochemical reactions
mediated by EDL. The latter is believed to be the main cause of field-enhanced conduction in
highly insulating liquids in homogeneous fields [4-15].
The structure and dynamics of EDL have been a major topic of modern electrochemistry
[4-16] and colloid science [4-17]. Treating the dielectric liquid as weak electrolyte, previous
works analyzed the steady-state charge injection effects, e.g. field distributions [4-18] and J-E
characteristics [4-19,4-20]. As shown in Figure 4.2, a reaction scheme (of impurity molecules)
consisting of three formative steps, i.e., adsorption, red-ox reaction, and desorption, has been
proposed as a unipolar negative charge injection mechanism [4-19].
EDL
Metal
Adsorption
e-
Neutral molecule
Liquid
Reaction
Electric Field
Desorption
Drift (injection)
Figure 4.2. Illustration of the three-step scheme for charge injection: specific adsorption, charge transfer reaction in
EDL, desorption. While charge transport is drift-dominated in the bulk of the liquid, the EDL processes injecting
charges at the metal-liquid interface are diffusion-limited, which, as will be shown later in this chapter, are closely
related to the roughness of electrode surfaces via fractal geometry concepts and models.
74
Quantitative analysis indicates that it works only under long-term HV applications [4-1].
However, under strong dc electric field, in addition to interfacial electrochemical processes,
turbulent flow resulted from electrohydrodynamic (EHD) instability [4-21] also affects charge
injection [4-7] (like in flow electrification [4-22]). The steady-state analysis may have reflected
the combined effects of electrical, thermal and EHD transport observed on a larger time-scale.
Therefore, it may be problematic when applying the “steady-state” results to the transient
response under short HV impulses with insignificant flow effects.
Actually, the difference between transient (~1 ms) and steady-state (> 1 min) charge
injection patterns in dielectric liquids has been found as early as in 1960s [4-23]. For
electrolyte, the transient injection current density is significantly higher than that in steady state
due to smaller thickness of the Nernst diffusion layer [4-16]. It is of interest to examine if
similar phenomenon can be found in dielectric liquids with a much lower bulk conductivity
under voltages 4~5 orders higher than that applied to electrolyte.
On the other hand, understanding transient charge injection under pulsed excitation is
important since it is the foundation of a promising approach to improving electrical breakdown
strength. Electrical breakdown, as the consequence of sudden increase in applied HV, usually
exhibits impulsive voltage characteristics. Charge injection, modifying the electric field near
the electrodes, may enhance or inhibit breakdown initiation [4-24]. The smart use of charge
injection to improve impulse breakdown strength in transformer oil has been demonstrated in a
recent work [4-25], while a systematic study of the time-dependent charge injection dynamics
remains in demand. The major difficulty lies with the time-resolved measurements of electric
field distribution in transformer oil.
In this chapter, Kerr electro-optic measurements with a high sensitivity camera [4-12,4-
75
25] are conducted to map the electric field profile in a transformer oil-filled gap between
parallel-plate electrodes. The experimental data will be compared with the simulation results of
drift-diffusion conduction model with charge injection boundary conditions. Evidence of
fractal kinetics will be presented for transient charge injection, and physical interpretations of
the fractal kinetics will be made.
76
4.2 Identification of fractal-like charge injection kinetics
The detailed experimental setup of the Kerr measurements including the description of
oil conditions and electrode preparation has been introduced in previous chapters and recent
papers [4-12,4-26]. The differences made in this work are:
(1) The gap spacing between two parallel-plate electrodes is
of interest (ROI) is a
mm, and the region
mm2 rectangle around the center of the gap, corresponding to about
pixels in the imaging area of the charge-coupled device (CCD);
(2) The rise-time and duration of the single square-wave pulses are respectively 1 µs and
1 ms, and the amplitude is adjustable from 10 to 30 kV;
(3) While the HV electrode is made of titanium, there are 2 different grounded stainless
steel electrodes: milled with surface roughness
µm (I) and electro-polished with
µm (II);
(4) The measurements are taken by triggering the pulsed laser and the CCD camera at
μs to 1 ms, in steps of
time
20 μs (the effective exposure time is ~1 ns, the pulse
width of the laser).
Figures 4.3-4.8 present the measured electric field distributions along a line (as stated
above, there are 250 different lines) across the gap (
) at
0.25 ms, 0.5 ms, 0.75 ms,
and 1.0 ms with 10 kV, 20 kV, and 30 kV HV for both cases (I) and (II). The titanium anode
and stainless steel cathode are located at
and
, respectively. Under each condition,
the measurements are repeated 50 times and then the averaged data is used for further
processing.
77
Figure 4.3. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (I), 10 kV.
Figure 4.4. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (I), 20 kV.
78
Figure 4.5. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (I), 30 kV.
Figure 4.6. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (II), 10 kV.
79
Figure 4.7. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (II), 20 kV.
Figure 4.8. Kerr electro-optic measurement results of electric field distributions along a line across the gap
(
) at
0.25 ms, 0.5 ms, 0.75 ms, and 1.0 ms: case (II), 30 kV.
80
Consistent with previous results [4-12], the titanium anode at
injects an
insignificant amount of charges within the time range of the measurements.
In Figures 4.3-4.8, the negative slopes of the field distributions near the cathode at
indicate unipolar negative charge injection from the stainless steel electrodes. The
injected charges will be transported toward the opposite electrode under the action of strong
electric field. An interesting observation of Figures 4.5&4.8 is that as the injected charges
arrive at the opposite electrode, the significantly increased local electric field may be a
precursor of electrical breakdown initiation.
According to the Einstein relation, diffusion is much weaker than drift in the bulk of the
liquid [4-9]. The mobility of the injected negative charges can be estimated from the
propagation speed of the “wave-fronts” in Figures 4.3-4.8, which has to be experimentally
determined to use in the numerical model. The propagation speed is approximately the product
of the electric field and the mobility. To verify this, at
around
and
1 ms, the wave fronts are located
in Figures 4.3 and Figure 4.4, respectively. We see that as the
HV doubles, the propagation speed also increases proportionally. By tracking the advancement
of the wave front position (e.g. every 0.1 ms) under each experimental condition and then
using linear fitting to find the propagation speed, the negative charge mobility is determined as
(4.1±0.4)×10-8 m2/Vs, which is 1-2 orders higher than the previously reported values [43,4-10]. The enhanced mobility may be due to EHD instability [4-27] (to avoid this, low
voltages were used to measure the mobility, which looks paradoxical since the dielectric
liquids are usually under high-voltage work conditions). Besides, considerable amount of highmobility impurities may be suspended in the transformer oil or adhered to the electrode surface,
upgrading the average charge carrier mobility.
81
Our primary goal in this work is to investigate the differences in the charge injection
behaviors of the two electrodes with distinct surface roughness. The information presented in
Figures 4.3-4.8 is less visually clear for this purpose. Now the total injected charge from unit
area on the electrode surface at a given time instant is calculated as follows:
Step 1. Find the charge density at each pixel in the gap from the spatial derivative of the
electric field distribution (Gauss’ law);
Step 2. Integrate the charge densities over the whole gap.
The result will be denoted by
since it has the dimension of surface charge density.
Figures 4.9-4.12 show the total injected charge
as a function of time for cases (I) and (II) in
linear and log-log coordinates.
Figure 4.9. Time evolution of , total injected charge per unit electrode area, plotted in linear coordinates: case (I).
82
Figure 4.10. Time evolution of , total injected charge per unit electrode area, plotted in linear coordinates: case
(II).
Figure 4.11. Time evolution of , total injected charge per unit electrode area, plotted in log-log coordinates: case
(I). The solid lines are the results of linear fitting.
83
Figure 4.12. Time evolution of , total injected charge per unit electrode area, plotted in log-log coordinates: case
(II). The solid lines are the results of linear fitting.
In spite of the fluctuations resulted from measurement inaccuracy, from Figures
4.9&4.10 one can see that in both cases the temporal evolution of
growth rates of
is not a linear one. The
display a damping tendency as increases.
In Figures 4.11&4.12, linear fitting is well made in the log-log coordinate, indicating
power law dependence, i.e.
where the units of
respectively. For case (I),
,
(20 kV);
(10 kV);
The coefficient
,
,
and
(10 kV);
(30 kV). For case (II),
(20 kV);
,
are nC/mm2 and ms,
,
,
(30 kV).
is obviously an increasing function of applied voltage . In this work,
however, this aspect of charge injection will not be explored due to incomplete information
(e.g. chemical composition of the oil and surface layer of the metal) and complexity (e.g.
84
detailed reaction schemes).
There are two key observations regarding the exponent :
Firstly, for the same electrode, either case (I) or (II),
is basically the same under all 3
applied voltages;
Secondly,
for the rougher electrode surface in case (I), greater than
for
the smoother electrode surface in case (II).
Thus it is concluded that surface roughness plays an important role in transient charge
injection dynamics, in addition to physical and chemical properties of electrode and dielectric
materials, oxidation layer and defects on metal surface, impurity composition in the liquid and
on the surface, applied voltages, surface treatments, etc.
It is reasonable to assume that the space charge and current in the bulk of the liquid are
due to electrode injection (the simulations of previous work [4-10] and ours show that without
charge injection, negligible space charge effect appears in tens of milliseconds). Therefore the
charge injection current density is approximately
; for case (II),
(absolute value). For case (I),
. This time-explicit form of charge injection is called fractal
or fractal-like kinetics [4-28,4-29].
85
4.3 Numerical simulations of drift-diffusion conduction
model
In 1D Cartesian coordinates with independent variables x and t, the governing equations
are [4-10,4-11]:
(4.1)
(4.2)
(4.3)
where
Equation (4.1) is the equation for bipolar drift-diffusion current density;
Equation (4.2) is the continuity equation for time-dependent charge transportgeneration-recombination;
Equation (4.3) is Poisson’s equation;
(
) is positive (negative) charge density;
( ) is current density in
and
direction due to transport of positive (negative) ions;
are electric potential and field;
is the permittivity (for our transformer oil
F/m);
are ion mobilities (from previous work [4-3], the positive charge carrier mobility
, while
has been experimentally determined in Section 4.2);
are diffusion coefficients (the Einstein relation [4-9] gives:
is the Boltzmann constant,
is absolute temperature and
86
is the charge per ion);
, where
stands for the rate of charge recombination (according to Langevin model [4-8],
with the recombination coefficient
);
stands for the rate of charge generation (ion-pair dissociation).
the dissociation constant and
where
is
is the concentration of ion pairs. In the absence of applied HV,
the dielectric is assumed to be in thermal equilibrium (all symbols with the subscript ‘0’) with
uniform charge distribution
, which is related to the Ohmic conductivity
. Under this condition, the neutrality of the liquid requires that
by
and
. Field-enhanced dissociation constant takes the form of
(Onsager’s theory [4-6]), where
is the Bessel function of the first kind and order one, and
. The values of the above-mentioned physical parameters are: the lowvoltage equilibrium Ohmic conductivity
S/m, room temperature
and by considering the simplest (also most probable) dissociation case
,
where
C is the elementary charge.
The Equations (4.1)-(4.2) can be transformed to the following advection-diffusionreaction form:
(4.4)
(4.5)
To implement the model Equations (4.4), (4.5) and (4.3), continuous variables such as
and
are sampled with uniform time step
electrodes there are
kth time step (
cells inside which
).
87
and spatial step
and
(
, that is, between the
) are defined at the
The initial conditions (
) are
,
. At the (k+1)th time step,
the charge densities are updated according to Equations (4.4)&(4.5). Then Equation (4.3) is
solved again to update the electric potential distribution under boundary conditions
. With
and
, we can compute the updated current densities and
electric field, and then move forward to the next time step.
The numerical algorithm has two parts:
a) Solution of Equation (4.3) to with first-type boundary conditions
A compact finite difference method [4-30] is used to calculate the spatial derivatives (for
simplicity,
below means the spatial derivative of
at th cell, or the local electric field with
opposite sign):

The first order derivatives can be given at interior cells (
) using a
6th-order tri-diagonal scheme:
(4.6)

At boundary cells
, the 3rd-order formula is as follows:
(4.7)
(4.8)

, the 4th-order formula is as follows:
At boundary cells
(4.9)
For the second order derivatives, we just need to replace
equations with
s and
s and
s in the above
s.
b) Solution of Equations (4.4)&(4.5) to with charge injection boundary conditions
The transport equations for positive and negative charges are discretized using the
88
Crank-Nicolson method [4-31], which is second-order implicit in time, and numerically stable.
It transforms each component of the equations into the following:
(4.10)
(4.11)
(4.12)
We can now write the scheme as:
(4.13)
where
,
,
At boundary cells
.
, charge injection boundary conditions are used:
(4.14)
(4.15)
(4.16)
(4.17)
where
,
as determined experimentally in Section 4.2.
As shown in Figure 4.13, a drawback of the Crank-Nicolson method is that it responds
to jump discontinuities in the initial conditions with oscillations which are weakly damped and
therefore may persist for a long time [4-32]. To reduce the spatial error oscillations, the
89
implicit Euler scheme is used for the first several simulation time steps, in which Equations
(4.11)&(4.12) take the form:
(4.18)
(4.19)
36
36
0.25 ms
0.25 ms
0.75 ms
34
34
32
32
E (kV/mm)
E (kV/mm)
0.75 ms
30
30
28
28
26
26
24
24
0
20
40
60
80
100
120
140
160
180
200
0
Spatial steps
20
40
60
80
100
120
140
160
180
200
Spatial steps
(a)
(b)
Figure 4.13. Numerical solutions of electric field distribution under 30 kV applied voltage at
0.25 ms and 0.75
ms. The number of spatial steps is 200; the number of time steps is 2000. (a) Crank-Nicolson; (b) The CrankNicolson with implicit Euler for the first 10 time steps.
The numerical solutions of the local electric fields near anode and cathode surfaces are
shown in Figures 4.14-4.17. The experimental results are also presented for comparison. The
error bars come from the statistics of measurement data on 250 different lines in the ROI
(along the electrode surfaces). The simulation results of the drift-diffusion model agree
quantitatively with the experiments (note that Kerr electro-optic measurements have a relative
error of 3%~5%).
90
Figure 4.14. Numerical solutions of the local electric fields near anode and cathode surfaces: case (I), anode.
Figure 4.15. Numerical solutions of the local electric fields near anode and cathode surfaces: case (I), cathode.
91
Figure 4.16. Numerical solutions of the local electric fields near anode and cathode surfaces: case (II), anode.
Figure 4.17. Numerical solutions of the local electric fields near anode and cathode surfaces: case (II), cathode.
92
As fast transient response to step excitation, the unique feature of the phenomenon in
insulating liquid compared with that in electrolyte is that the current injection at the electrodes
has a non-local effect, i.e. injected charges will be transported to the bulk of the liquid in a
drift-dominated manner and distort the electric field distribution over the whole gap. For
unipolar negative charge injection, the electric field at the cathode is reduced. However, as the
transient injection current dampens, this tendency may slow down or even slightly reversed
(the 30 kV cases in Figures 4.15&4.17).
93
4.4 Discussions
What is the nature of the injection current? The direct (electronic) charge transfer from
the electrode to the oil requires higher electric field, even after taking into consideration the
field enhancement factor (~10) due to micro-protrusions. So cathode electron emission cannot
be the primary source of the injected charges.
Instead, the injection should be ionic. As illustrated in Figure 4.2, the simplest physical
picture of the origin of injection current is that neutral species like impurity molecule is
specifically adsorbed to electrode/liquid interface and undergoes reduction (accepting electrons)
in the EDL. Then the product is removed from the interface by desorption and transported into
the bulk by electrical force.
The power-law dependence of current density on time indicates that the surface reaction
is diffusion-limited, which may be resulted from: (1) a much lower adsorption rate than
reaction rate; (2) anomalous lateral diffusion of reacting molecules. Correspondingly, there are
two possible interpretations of the fractal-like charge injection kinetics.
For (1), the adsorption-limited current density is given by:
(4.20)
where
is the fractal dimension (FD) of the medium [4-29,4-33]. In this work, the medium is
the part of EDL (of typical thickness
1 nm) where the reaction takes place. For an ideally
smooth electrode surface, in-plane homogeneity of EDL can be assumed.
very close to the result of case (II) above. In case (I),
,
,
, which seems
counterintuitive since the FD of a rough surface is generally greater than two [4-34].
94
,
Figure 4.18. Mechanisms for fractal-like charge injection kinetics. (a) If the surface reaction is adsorption-limited,
on rougher surfaces, the protrusions are dominant in adsorbing neutral molecules (D is the diffusion constant, t is
the duration of HV pulses), while on smoother surfaces, the pores also make significant contributions. (b) If the
surface reaction rate is controlled by lateral diffusion of reacting molecules, anomalous diffusion along fractal
surface may account for the origin of fractal charge injection kinetics.
To resolve this, we find that the active EDL contributing to injection current may cover
only part of the electrode surface (e.g. like the Sierpinski carpet with a FD of 1.89). In Figure
4.18(a), the rough electrode surface is represented by an array of protrusions and pores. If the
reaction is adsorption-limited, for very rough surfaces, the effective adsorption region around a
protrusion is much larger than that inside the pores. The majority of injection charges originate
from the protrusions. The parts of EDL near all protrusions on the electrode surface form a
fractal structure with
.
If adsorption is a fast process compared to reaction or the supply of adsorbed molecules
is sufficient, the current density of a reaction-limited process would be time-independent. In
order to understand the fractal-like kinetics, one need to take into account the sub-diffusion due
to the heterogeneous (fractal) interface structure that slow down the random walk of reacting
95
agents [4-35,4-36], which yields a current density proportional to reaction rate:
(4.21)
where
is the FD of the whole EDL,
diffusion,
is the anomalous diffusion exponent. For normal
, i.e. the mean-square distance of a random walker is proportional to
In case (II), assuming that the EDL can be regarded as a smooth surface,
,
corresponding to a “well-mixed” homogeneous reaction. For case (I),
sub-diffusion
, it follows that
.
,
. Since for
, a general feature of rough surfaces.
In this chapter, the fractal-like charge injection kinetics in HV pulsed transformer oil has
been identified from Kerr electro-optic measurement data and verified by numerical
simulations of the time-dependent drift-diffusion model with the experimentally-determined
injection current boundary conditions. It is demonstrated that while the space charge process
in the liquid bulk is drift-dominated, the charge injection kinetics from the EDL on the
electrode-dielectric interface is diffusion-limited. We propose two mechanisms to reveal the
deep connection between geometrical characteristics of electrode surfaces and fractal-like
kinetics of charge injection. The order of injection current densities is 10-5~10-3 mA/mm2 in
our experiment, corresponding to total current of about 10-2~1 mA in the gap and bulk
conductivity enhanced by 104~106. With such a large magnitude, it seems that the transient
charge injection should be associated with the charging dynamics of EDL. Otherwise, the
formative steps in Figure 4.2 would be the same as in previous studies which work only under
long-term HV applications [4-1,4-19]. A comprehensive consideration of the chemical aspects
of the processes (chemical compositions, reaction schemes, etc.) is out of scope of this work
and may be proposed for further studies.
96
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99
100
5
Electro-optic signal fluctuations as indicator of critical
transitions in dielectric liquids
Synopsis
Motivated by the search for approaches to non-destructive breakdown test and inclusion
detection in dielectric liquids, we explore the possibility of early warning of breakdown initiation
in high voltage pulsed transformer oil from the data of Kerr electro-optic measurements. It is
found that the light intensities near the rough surfaces of electrodes both fluctuate in repeated
measurements and vary spatially in a single measurement. We show that the major cause is
electrostriction which brings disturbances into optical detection. The calculated spatial variation
has a strong nonlinear dependence on the applied voltage, which generates a precursory indicator
of the critical transitions.
101
5.1 Introduction
The behavior of dielectric materials under strong electric fields determines critical
transitions in insulation systems, i.e. the initiation and development of partial or full dielectric
breakdown. When an insulating liquid is stressed by a high voltage impulse, without
breakdown, there are three major phenomena involved:
(1) Electrostriction (a modification of pressure distribution due to changes in the liquid
density) [5-1].
(2) Conduction (including molecular ionization and recombination, electrode-liquid
interfacial processes, and transport of charge carriers) [5-2,5-3].
(3) Electro-hydrodynamic (EHD) flow (as we discussed in Chapter 3, its onset time is
scale dependent) [5-4].
Besides, the presence of inclusions (bubbles and particles adhered to the electrodes and
suspended in the liquid) further complicates the problem [5-5,5-6].
In previous chapters, we mainly discussed the electric field distribution influenced by
space charge due to conduction or charge injection. We now consider electrostriction (this
chapter) and EHD flow (flow). On the one hand, their presence is a major source of error and
fluctuation in the electric field measurement. On the other hand, these phenomena themselves
are of great theoretical and practical interests.
If the applied high voltage pulse duration is very short (sub-microsecond), the
conduction dynamics and flow effects may be weak, and pre-breakdown streamers can be
initiated in the absence of substantial ionization in the bulk of the liquid [5-7,5-8].
Electrostriction becomes the dominant driving force of pre-breakdown phenomena. Under this
102
condition, the following discharge initiation mechanism looks plausible [5-9,5-10,5-11]: as the
electric field exceeds a threshold, electrostriction shock waves may be excited, giving rise to
voids/bubbles that will ionize to form the initial discharge channel.
This physical picture has its implications in the non-destructive detection of
gaseous/metallic inclusions in dielectric liquids. In general, the electric field near inclusions in
the liquid is greatly increased [5-12], resulting in a greater likelihood of electrical breakdown
[5-5,5-9]. The electrostriction effects under short impulses become more significant due to
higher local electric field and increased inhomogeneity of the medium [5-1,5-10,5-11].
Locating the enhanced electrostriction spots with an applied voltage below the threshold for
partial discharge initiation may be a promising approach for inclusion detection.
To capture the electrostriction effects in dielectric liquids, previous works [5-1,5-10,5-11]
have used highly-divergent electrode geometries (e.g. needle-plate) to make sure that the
discharge is initiated at the needle tip where the initial phase of breakdown can be observed via
Schlieren transmission imaging (as refractive index varies spatially in transparent liquid).
Binary in nature, Schlieren imaging is possible only when the voids/bubbles have grown large
enough, which obviously has limited sensitivity under lower electric fields and unavoidably
causes destructive effects due to subsequent breakdown.
In this chapter, we will study parallel-plate electrode configurations in the most widelyused insulating liquid, transformer oil. Compared with the needle-plate geometry in which
almost all detectable phenomena appear near the needle tip, the use of parallel-plate electrodes,
with a quasi-uniform background, can provide a higher “contrast” necessary for the detection
of local electric field enhancement around inclusions or near electrode surfaces. In parallelplate geometry, however, more sensitive optical measurement techniques are needed, since the
103
maximum electric field is much lower than that in highly-divergent geometries with the same
gap spacing stressed by the same voltage.
The Kerr electro-optic measurement with a high-sensitivity charge-coupled device (CCD)
[5-13,5-14,5-15,5-16,5-17,5-18] will be used for our purpose. The image of the electrostriction
pattern may be difficult to acquire, because this effect is much weaker than the Kerr effect and
the electrostriction dynamics has great uncertainty. Nevertheless, an electrostriction wave
induces non-uniform liquid density distribution, which affects the optical detection and may be
identified via statistical data processing.
Enhanced electrostriction effects also exist in the case of electrical breakdown initiation
near the electrode surface, which, with no need for carefully prepared oil samples with
controlled inclusions, will first be tested in this work as preliminary verification of the
principle. By measuring the electrostriction near the electrode surfaces, it may also enrich the
conceptual framework for the transition to electrical breakdown as the applied voltage is
increased. An interesting analogy is the laminar-to-turbulent transition in fluid dynamics [519,5-20,5-21]. When a control parameter of the system (e.g. Reynolds number) becomes large
enough, the transition takes place. Flows in the transitional regime display laminar-turbulent
intermittency, which resembles the statistical behavior of electrical pre-breakdown phenomena
(e.g. may or may not result in breakdown). Furthermore, the effectiveness of passive control
techniques to delay the transition has been demonstrated for fluid flows [5-22], while smart use
of electrode charge injection is shown possible to improve the breakdown strength [5-18].
From an even broader perspective, this work attempts to extend recent research on early
warning signals for critical transitions in complex dynamical systems [5-23]. Generic
indicators predicting the catastrophic shifts (tipping points) are found in slowly-evolving
104
systems, such as population [5-24,5-25,5-26,5-27], climate [5-28], and environmental [5-29]
dynamics. A review of some related concepts will be presented in Section 5.2.
While electrical breakdown is a certain type of critical transition in dielectric liquids
with its time scale in the microsecond to nanosecond range [5-9], little attention has been paid
to exploring the idea of electrical breakdown as a critical transition with predictive indicators.
Apparently, this is because the process of electrical breakdown is so rapid and violent,
characterized by a fast growing current. However, most measurements in dielectric liquids
have been made at electrical terminals of voltage and current, providing no information on
electric field distribution in the bulk, which is important in breakdown initiation and can be
measured by using Kerr electro-optic techniques
In this chapter, statistical analysis of the Kerr measurement data will show that spatial
variance can be a predictive indicator of breakdown in advance of detectable current increase.
The potential applications include an estimation of breakdown voltage without breakdown.
Usually breakdown tests need to be done to evaluate the breakdown strength of a material. If
there do exist early warning signals for breakdown, non-destructive breakdown tests will be
made possible, and as a result some insulation failures may be avoided or have reduced
damage.
105
5.2 Indicators of critical transitions in complex systems
In many complex systems, there are catastrophic thresholds called tipping points across
which the system states experience a sudden shift to distinct regimes. These systems range
from ecosystems and the climate to financial markets and the society. It is of great importance
to predict such critical transitions, though this could be extremely difficult. This is because as
the tipping point approaches, experimentally the state of the system may just change
unnoticeably, and theoretically the model of the system may not work reliably due to
approximations made.
For electrical breakdown in dielectrics, the above features also exist. In this context, the
critical threshold corresponds to breakdown voltage, and the critical transition is breakdown
(insulating state to conducting state). Figure 5.1 shows typical voltage (a) and corresponding
current (b) waveforms when a pair of parallel-plate stainless-steel electrodes are stressed by 1
µs (rise-time) /1 ms (duration) high voltage pulses. The voltage is measured by a capacitive
divider, while the current is measured at the high voltage side with a Rogowski coil. As the
applied peak voltage is increased, the probability of electrical breakdown rises from 0 (case III)
to 1 (case I). The sign of loss of “resilience” means that the insulation becomes increasingly
vulnerable to voltage instabilities (perturbations).
The initial fluctuations seen in the current waveform in Figure 5.1(b) should be
displacement currents interacting with inductive elements in the electrical system. In case II,
once breakdown is initiated, the magnitude of conduction current increases by 5-6 orders in
less than 10 ns, which captures the feature of abrupt (catastrophic) change of state in critical
transitions of complex systems.
106
Figure 5.1. Typical voltage (a) and corresponding current (b) waveforms when a pair of stainless steel electrodes
are stressed by 1 µs/1 ms high voltage pulses.
107
The possibility of using generic statistical early warning signals to indicate if a critical
transition is approaching has been studied extensively. There are generally two categories of
predictive indicators: temporal and spatial. The former is primarily based on a phenomenon
known in dynamical systems theory as “critical slowing down”, i.e. slow recovery from small
perturbations in the vicinity of tipping points. The latter, usually extracting particular spatial
pattern for systems consisting of many coupled units distributed in space, is less generic than
the former and requires details of each system.
The symptoms of critical slowing down include increase in autocorrelation and
fluctuation. As the system approaches critical point, the time it takes to recover from small
perturbations will be longer and therefore the system may become more correlated with its past.
This increase in “memory” can be measured by looking at the autocorrelation of the time series
of the system dynamics. The larger variance or fluctuation is another possible consequence of
critical slowing down. Intuitively, this is the accumulating effect of perturbations since they
decay slowly. Other statistical indicators such as skewness and flickering before transitions
have also been demonstrated, which, however, do not result from critical slowing down.
Early warning of catastrophic transitions based on critical slowing down may correspond
to a fold (catastrophic) bifurcation in the system dynamics, though it also exists for other
classes of bifurcations. Figure 5.2(a) shows the modeled response of semi-arid vegetation to
increasing dryness of the climate. Solid/dashed lines are stable/unstable equilibrium points.
Close to the transition point, a small perturbation is able to drive the system from the upper
(vegetated) to the lower (barren) branch. Figure 5.2(b) is the conceptual counterpart in impulse
dielectric breakdown, in which the phase shift may be either through a catastrophic bifurcation
or across a non-catastrophic threshold.
108
(a)
1
0
Large change
Breakdown Probability
Catastrophic
bifurcation
Non-catastrophic
threshold
Small forcing
Applied Voltage
(b)
Figure 5.2. (a) Bifurcation diagram of a model desert vegetation system undergoing predictable sequence of spatial
patterns as approaching a critical transition (from [5-23], which was modified from [5-29]). (b) The breakdown
probability as a “function” of applied voltage. Catastrophic bifurcation may or may not exist. In either case small
forcing (i.e. increase in voltage) will lead to a distinct state.
109
The width of the transition zone shown in Figure 5.2(b) is typically several kilovolts,
relatively small compared to the absolute value of breakdown voltage. The dashed line
represents unstable “fixed points”, which is unobservable using standard breakdown test
methods. Instead, in high voltage engineering, it is usually assumed that the dependence of
impulse breakdown probability on the applied voltage takes the form of a non-catastrophic
threshold process. However, this does not indicate the impossibility of the catastrophic
bifurcation. In breakdown tests, due to the stochastic nature of the process, the change in
breakdown probability cannot be fine-tuned in a predictable manner by adjusting the applied
voltage. Considerations on sample quality and test cost also prevent us from doing the tests too
many times. Hence the number of measurable breakdown probabilities is always limited. For
example, we may know the voltages corresponding to 50% and 90% breakdown probabilities.
But the details in between remain unclear. Catastrophic bifurcation may exist.
While the studies in time series ignore spatial interactions for real systems, spatial
patterns as early warning signals are much richer. For some systems, critical transitions are
preceded by the appearance of particular spatial patterns or the change of spatial configurations
in a predictable way. The insets in Figure 5.2(a) are some spatial patterns: the dark color
represents vegetation and the light color represents empty soil. The transition of the ecosystem
to a barren state can be predicted by the change of the patterns from maze-like to spots.
Sometimes spatial data are more accessible. This has different meanings in relatively
slow population dynamics and very rapid electrical breakdown process. For the former,
generally long-term observations are necessary to obtain the predictive power of temporal
warning signals. For the latter, when we take Kerr measurements with very short high voltage
pulses, the maximum frame rate of the camera usually allows very limited numbers (in the case
110
of our high-sensitivity high-resolution CCD camera, it's only one) of images, resulting in poor
time resolution.
For our applications, we will mainly discuss spatial indicators. The two reasons are
given below:
Firstly, the dielectric liquid between two electrodes cannot be assumed to be the same
everywhere without spatial coupling. For example, the liquid near the electrode surface is
stressed by higher electric fields due to the existence of electric double layer. And different
parts in the liquid are interconnected by transport processes.
Secondly, the temporal data is ineffective in generating any early warning signal of the
approaching critical transitions. In case II of Figure 5.1(a), with peak voltage ranging from 31
to 39 kV, statistically speaking, the higher the voltage is, the higher the breakdown probability
( ) will be. There is also a time difference ( ) between
1 µs and the instant when
breakdown occurs. The random nature of electrical breakdown is no-good for non-destructive
inclusion detection and breakdown test. The next option, the current shown in Figure 5.1(b),
does not prove to be more useful. The measured conduction currents ( ) are indistinguishable
from noise in both case (II) before breakdown and case (III), since the conductivity of
transformer oil is very low (
). In the absence of measurement techniques or
instruments with exceedingly higher sensitivity, monitoring conduction currents cannot
provide predictive indicators of electrical breakdown.
111
5.3 Electro-optic precursor of breakdown initiation in
transformer oil
The detailed experimental setup of the Kerr measurements has been introduced in
Chapter 2. The description of oil conditions and electrode preparation can be found in Chapter
3. The differences made in this chapter are:
(1) The gap spacing between two parallel-plate electrodes is
mm;
(2) The duration of the high voltage pulses is 1 ms while the rise time
is adjustable
from 100 µs to 10 ns;
(3) The grounded stainless steel electrode is unpolished with surface roughness
µm, while on the high voltage side, the electrode is electro-polished with
µm.
In recent reports [5-17,5-18] on Kerr electro-optic measurements with high voltage
pulsed transformer oil, to reduce the fluctuation due to uncertainty and randomness in the
system, under each experimental condition, multiple images are taken and then averaged. In
order to improve measurement sensitivity, we should identify and correct various errors in the
system. For this purpose, the statistical analysis of the measurement data is necessary.
The detected light intensities both vary from pixel to pixel in a single measurement and
fluctuate at each pixel in repeated measurements. In principle, a laser beam with quasi-uniform
intensity distribution is needed to illuminate the 1 mm gap. Usually one can use a beam
expander to expand part of the laser beam to achieve this goal. However, as shown in Figure
5.3(a), the expanded beam propagates through the gap as if it is in a waveguide. Extra pattern
(bright and dark lines like interference pattern) is generated, possibly due to the light bouncing
back and forth between the two electrodes. The edges of the gap become blurred due to
112
scattering and diffraction effect. One solution is to move the CCD to several meters away from
the test cell, which eliminates the pattern but meanwhile sacrifices the detection sensitivity.
High-voltage electrode
y (j)
1 mm
x (i)
Grounded electrode
(a)
(b)
Figure 5.3. (a) The image of the gap illuminated by an expanded laser beam. (b) The background light intensity
distribution in the gap leaked from crossed polarizers as the 1 mm gap is illuminated by a Gaussian beam (7.6 mm
in diameter). The region of interest (ROI) is recorded in a 120-by-60 (row-by-column) matrix.
Therefore we just use the original Gaussian beam from the pulsed laser. Figure 5.3(b)
shows the light intensity distribution without applied voltage, in which a rectangular area is
chosen as the region of interest (ROI). We use a matrix
to record the light intensity
distribution in ROI, which has 60 pixels in the y (or j) direction (along the electrode surface)
and 128 pixels in the x (or i) direction (across the gap). The location of electrode surfaces in
the x direction has a 2~4 pixel error, so 4 rows of data both on top and bottom of the original
matrix have been discarded (now
).
We first study the shot-to-shot optical signal fluctuation caused by laser beam
scintillation, scattering near the electrode surfaces, and even the influence of high voltage pulse
on the laser and the CCD. Figure 5.4(a) presents the distribution of the fluctuations
113
(normalized by the averages) of the measured pixel light intensities in 1,000 repeated
measurements. The influence of room light has been minimized (<0.5%) by reducing the
exposure time of the CCD to 10 µs (the actual exposure time, however, is about 1 ns, the
duration of the laser pulse) and increasing the laser output power.
(a)
Std./Ave.
0.07
0.06
0.05
0.04
0.03
40
j
(b)
Std./Ave.
0.06
0.07
0.065
0.06
0.06
0.05
0.055
0.05
0.04
20
0 0
40
0.05
60
0.045
80
j
i
30
0 0
40
80
i
Figure 5.4. The distributions of fluctuations (normalized by the averages) of the measured pixel light intensities in
multiple measurements. (a) with no high voltage pulse generated, at most pixels, the standard deviations of the light
intensities in the 1,000 measurements stay below 5% of the averaged light intensities; (b) with high voltage pulses
firing nearby, there is no substantial difference in the fluctuation level compared with (a), indicating that
electromagnetic compatibility is adequate for our measurement system.
Without any applied voltage across the 1 mm gap, optical signal fluctuation level is due
to laser beam scintillation (output power fluctuation and propagation in media with
stochasticity) and possibly the internal errors of the CCD. Since the fluctuation level at the
boundaries is similar to that in the mid-gap, it may be concluded that the effect of random
scattering at electrode surfaces is insignificant.
In Figure 5.5(b), the histograms and fitted normal distributions of the light intensities at
two pixels (#1 and #2 marked in Figure 5.5(a), which is the same as Figure 5.4(a)) are
114
High-voltage electrode
1 mm
presented. The mid-gap (#1) light intensity is about 10% higher
x (i) than that near the electrode
surface (#2). However, we are only interested in the fluctuation level (ratio of standard
y (j)
deviation and average).
Grounded electrode
(b)
Std./Ave.
0.06
0.07
0.06
0.05
0.05
#2
0.04
#1
0.03
0.04
40
j
Probability Density (×10−3)
(a)
1.2
1.0
0.8
0.6
0.4
0.2
80
20
0
40
0
i
(c)
(d)
Figure 5.5. (a) Same as Figure 5.4(a). With no applied voltage, the standard deviations of the light intensities at
most pixels in the 1,000 measurements stay around 5% of the averaged light intensities. (b) The histograms and
fitted normal distributions of the light intensities at two pixels, #1 and #2 marked in (a).
Further, still no applied voltage across the transformer oil gap in the test cell, we apply
high voltage pulses to an air gap (covered with black cloth in order not to send any light to the
optical system) placed close to the test cell (without blocking the light path). When the air gap
discharges, a strong current will spread in the conducting surface of our optical bench on which
the laser and the CCD sit. Besides, every time the Marx generator fires, high frequency
interferences couple into the power cord of both instruments, bringing in additional instability
of their performances.
We insert plastic sheets under the laser and the CCD to insulate them from the optical
115
bench, and use isolation transformers as power supplies for all electronic instruments in the
measurement systems. Consequently, the optical signal fluctuation level has been cut from 10%
to 5% (as shown in Figure 5.4(b)), i.e., no substantial difference from Figure 5.4(a), indicating
that electromagnetic compatibility is adequate for our measurement system. Hence any
upgraded fluctuation level at a pixel (defined as the ratio of standard deviation and average of
detected light intensities in multiple measurements) with high voltage applied to the oil gap
should be attributed to field induced effects, like electrostriction and EHD flow.
We conduct Kerr measurements under 10 ns/1 ms, 1 µs/1 ms, and 100 µs/1 ms pulses
with positive peak voltages of 10 kV, 20 kV, 25 kV, and 30 kV. For Kerr measurements the
results of which will be presented in Figures 5.6 8, the images are taken at
beginning of the high voltage pulses as time
(setting the
). That is, all the images are taken at
approximately the voltage peak.
In each row of the matrix , we first compute the fluctuation level at each pixel in 1,000
repeated measurements, and then find the average of the fluctuation levels of all pixels in the
row. Results of 3 rows with
(cathode surface),
(mid-gap), and
(anode
surface), are shown and compared in Figs. 5.6(a) (c).
It is found that, while the fluctuation levels are generally higher under higher applied
voltages, which can be attributed to field induced effects, like electrostriction and EHD flow,
the upgrading rate of the fluctuation level depends both on position and pulse. Generally, close
to the rougher cathode surface, the increase in the fluctuation level is faster than other positions
in the gap. And for longer rise time pulse, the fluctuation is stronger.
116
(a)
(b)
y
j from 1 to 60
Cathode
x
i from 1 to 120
Anode
(c)
(d)
Figure 5.6. The average fluctuations in row i=1(cathode), 60(mid-gap), and 120(anode) at various stantaneous
voltages with rise-time of the pulses being (a) 100 µs, (b) 1 µs, and (c) 10 ns. (d) is an illustration of matrix ,
which is used to store the pixel light intensity distribution in the ROI.
Figure 5.7 presents the distributions of average fluctuation levels across the gap for three
cases with the same voltage (+30 kV) but different rise times from 10 ns to 100 µs. The pixels
with strongest fluctuations (>10%) are marked in the insets. We choose not to take images after
117
100 µs delay to minimize the space charge behavior and large-scale EHD turbulence [3-16].
The results of the Kerr electro-optic field mapping in all three cases, based on the averages of
detected light intensities, are close to a uniform field distribution with acceptable measurement
errors (two types of errors have been defined in Chapter 2). Now, however, we have two
interesting observations about the distribution of the strongest fluctuations.
Firstly, the cathode surface is rougher than the anode surface, which means that the local
electric field enhancement due to micro-protrusions on the cathode is more significant than that
on the anode. As a result, both electrostriction and EHD flow, though still unable to tell which
one is the major process, will be stronger near the cathode surface, creating more disturbances
and uncertainties in the light intensity measurement (random scattering due to surface
roughness may be a secondary effect also contributing to fluctuations). This explains why the
fluctuations are more intense on the cathode side.
Secondly, strongest fluctuation spots seem more localized to (certain parts of) electrode
surfaces as the rise time of the high voltage pulses decreases. Keep in mind that the rise time of
the pulse is also the time when Kerr measurements are taken. By adjusting the rise time from
100 µs to 10 ns, the fluctuation level in the middle of the gap is lowered. The size of a pixel in
our CCD camera is about 8×8 µm2. Based on the estimation of viscous diffusion time [5-18],
the time for the onset of EHD instability over a pixel size is in the order of 10 µs. This smallscale turbulence may increase the fluctuations in optical measurements. On the other hand,
sub-microsecond pulses are preferred for the generation and detection of electrostriction waves
since these transient patterns tend to damp and diffuse due to relaxation and dissipation over
longer course. For
µs and 10 ns, it may be concluded that the strongest fluctuations near
the two electrode surfaces are primarily due to electrostriction. If the rise time is even shorter
118
(and meanwhile the high voltage impulse generator and other instruments can still work
reliably and accurately), with negligible EHD effect and preserved electrostriction, we may
even be able to locate those spots on the electrodes from which, statistically speaking,
electrical breakdown will be initiated.
Figure 5.7. For 3 cases with about the same instantaneous voltage (+30 kV) but different rise times from 10 ns to
100 µs, the distributions of average fluctuations across the gap are shown, and the pixels with strongest fluctuations
(>10%) are marked.
Figures 5.6&5.7 give us a hint that certain measure of the enhanced shot-to-shot
fluctuations (most likely near the cathode surface) under higher voltages may be an electro-
119
optic precursor of electrical breakdown. However, 1,000 repetitive Kerr measurements will
become less possible since accidental breakdown occurs more frequently as the applied voltage
is getting closer the breakdown voltage (the 50% breakdown voltage is 35~36 kV, and 30 kV
is in fact the highest voltage that we have succeeded without breakdown). Breakdown is
unwanted during Kerr measurements because it till take us a long time to reset the test cell and
more importantly, it causes damage to the imaging parts of the CCD. Instead, we will examine
the light intensity distribution from a single Kerr measurement to identify a more practical (and
economic) warning indicator. The highest voltage for single Kerr measurements reaches 32 kV
(by taking advantage of the relatively low breakdown probability).
Figure 5.8. The slice-by-slice image entropy distributions with zero and 30 kV applied voltages.
120
The amount of information in an image can be quantified as entropy, a statistical
measure of randomness characterizing the “texture” of the image [5-30]. We cut the ROI into
12 slices (each consisting of rows from
to
, where slice number
and use the MATLAB function to find the image entropy
),
for each slice. The results with
zero and 30 kV high voltages are Figure 5.8, which confirms our intuition that an early
warning signal of electrical breakdown is more likely to be found near the rougher cathode
surface.
Figure 5.9. The coefficient of spatial variance of the cathode slice as a function of applied voltage. The error bars
are drawn based on the data from multiple measurements.
121
If we assume the pixel light intensities within a slice are subject to normal distribution
with mean
(
and variance
(analogous to Fig. 5.5(b)), it can be estimated [5-31] that
, or
. According to this, the variance of the cathode slice
and
) grows by about 50% as the applied voltage is increased
from 0 to 30 kV. In Figure 5.9, we use the coefficient of variation,
, to describe the spatial
fluctuations in the optical measurement data. The value of the coefficient of spatial variance is
~3% when there is no applied voltage. The error bars in Figure 5.9 are drawn based on the
results from multiple measurements. When the voltage is over 30 kV, the error is more
significant partly because only 5~10 measurements have been made for each case.
As shown in Figure 5.9, spatial variance rises slowly when the voltage is lower than 30
kV; as the breakdown voltage is approached, there is a significant acceleration in the increase
of spatial variance (at 32 kV which is 90% of the 50% breakdown voltage, the coefficient of
variance jumps over 10%, which can be viewed as an indicator of the vicinity of electrical
breakdown). Electrostriction, interacting with gaseous and solid impurities activated by high
field, may be the underlying mechanism. However, a detailed analysis of these processes
involved is out of scope of the present work.
122
5.4 Discussions
Previous sections explore the possibility of early warning of electrical breakdown
initiation in high voltage pulsed transformer oil from the data of Kerr electro-optic
measurements. Due to electrostriction, the detected light intensities near the rough surfaces of
electrodes both fluctuate in repeated measurements and vary from pixel to pixel in a single
measurement. The calculated coefficient of variation has a strong nonlinear dependence on the
applied voltage, implying that some critical transitions are taking place, at least at some spots
on the electrodes. The results of this work may be helpful to develop new approaches to nondestructive breakdown test and, based on the same physical principle, non-destructive
inclusion detection in dielectric liquids.
As mentioned in Section 5.2, in dynamical systems theory, critical slowing down (slow
recovery from small perturbations in the vicinity of transition) has been suggested as the
leading indicator of whether the system is getting close to a critical threshold. As shown in
Figure 5.10, some phenomenon similar to critical slowing down near transitions in complex
systems has been found. (It has to be pointed out that the analogy regards the high voltage
pulse as some kind of perturbation to the dielectric liquid, which is not true. Strictly speaking,
the voltage fluctuation seen in the waveform of the pulse corresponds to perturbation in
dynamical systems theory.) After the 1 ms pulse has passed, there is essentially no applied
voltage across the gap. However, the detected light intensity will not fall back to the zero field
value immediately as expected by the Kerr measurement principle [5-17]. The transition time
scale (milliseconds) is far beyond any dielectric relaxation process (<nanosecond). On the
other hand, as confirmed by our tests without any applied voltage, flow caused by transient
123
temperature/pressure gradient can only increase the fluctuation level in the detected light
intensity, and cannot increase the mean value of the detected light intensity.
The phenomenon shown in Figure 5.10 may be associated with some kind of relaxation
process, the details of which remain unclear. It might be an interesting topic for continuing
research.
Figure 5.10. A phenomenon similar to critical slowing down. (a) The 1 ms square wave pulse and the ratio of the
detected light intensity and the zero field value. All light intensities have been averaged over the ROI. (b) For 10,
20, 30 kV pulses, the time it takes for the light intensity to drop to the zero field value is approximately 1, 3, 10 ms,
respectively.
124
The initiation and development of partial or full dielectric breakdown remain not fully
understood. Work in this area can be divided into two classes: experiments on breakdown
characteristics and numerical simulation of streamer dynamics. Neither of them can be easily
connected to the physical theory of critical phenomena. This, however, does not necessarily
mean impossibility. Our work exploring the possibility, though inspired by researches in other
fields, is based on statistical processing of the measurement data.
The image shown in Figure 5.11 was taken by fast imaging technique in the early stage
of breakdown development (the full, destructive breakdown is unavoidable). It agrees with our
results in Figure 5.7 that electric field enhancement takes place at localized sites on the
electrode surface. The difference is, our methods with much higher optical detection sensitivity
do not rely on the appearance of visible discharge plasma channel and can predict how close it
is to the breakdown without actually reaching this point.
Figure 5.11. (From [5-32]) Localized discharges (streamers) on cathode on uniform electric field. The gap spacing
is 4 mm. The liquid is n-hexane. The image was taken about 1 µs before breakdown.
Figure 5.12 shows the typical chronogram of interference bands registered under voltage
pulses with an amplitude of 120 kV applied to extended electrodes in de-ionized water (slit
125
scanning, which means the horizontal axis in the image represents time while the top and
bottom dark areas are occupied by electrodes). The electrostrictive excitation originates from
the electrode surface (the formation of the wave pattern is mainly due to the repetitive
application of pulses). This may also viewed as a “collateral evidence” of our work, in which
we interpret the cause of the optical detection fluctuation as enhanced electrostriction.
Figure 5.12. (From [5-9], page 17) Experiment on electrostriction wave excitation in water in the system of
extended electrodes (slit scanning).
Additional work needs to be done to find more evidence that electrostriction is the major
force behind the early warning signal. The influence of a strong electric field on a liquid is
noticeable when the electric field energy density is comparable with the external pressure [5-9].
This condition is usually satisfied in the case of breakdown initiation. We can place the test
cell inside a pressure chamber with a wide range of adjustable pressure. Theoretically, it is
expected that the critical threshold of the applied voltage would be higher under higher
pressures. Under the same applied voltage, the detected fluctuation in electro-optic signal
should strongly depend on the ambient pressure.
126
The influences of applied voltage (peak, rise time, polarity), electrode material and
surface roughness, and ambient pressure on the electrostriction effects need also be
investigated. In the field of dielectric and electrical insulation research, the most common
impulses are microsecond instead of nanosecond. We will start from nanosecond rise-time
pulses and gradually increase the rise-time to the microsecond range. By doing this it is
possible to find a characteristic time beyond which the space charge behavior dominates. Since
parallel-plate electrodes are used, we do not expect any polarity effect if the two electrodes are
‘identical’. This can be a basic check of the reliability of the measurement results and the
processed data.
Finally we would like to propose experimental procedure on the non-destructive
inclusion detection. Prepare transformer oil with conductive inclusions of nm to µm diameter
range. The first type is a dilute nanofluid; the second type is to release a small number of
conducting micrometer-size suspensions between the two electrodes. Test transformer oil
samples with these controlled conducting inclusions to measure the resulting local electric field
enhancement which can be a trigger for electrical breakdown or partial discharge. This method
can easily be extended to larger scale industrial systems by scanning the entire liquid region.
127
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130
6
Electro-optic signatures of turbulent electroconvection
in dielectric liquids under dc and ac high voltages
Synopsis
In this chapter, signatures of turbulent electroconvection in transformer oil stressed by dc and ac
voltages are identified from Kerr electro-optic measurement data. It is found that when the
applied dc voltage is high enough, compared with the results in the absence of high voltage, the
optical scintillation index and image entropy exhibit substantial enhancement and reduction
respectively, which are interpreted as temporal and spatial signatures of turbulence. Under lowfrequency ac high voltages, spectral and correlation analyses also indicate that there exist
interacting flow and charge processes in the gap. This chapter also clarifies some fundamental
issues on Kerr measurements.
131
6.1 Introduction
Electroconvection refers to the flow motion due to injected ionic charges under applied
electric field, which plays an important role in the electrical conduction phenomena in
dielectric liquids [6-1]. It is of practical interests in a wide range of applications such as
electrostatic spraying [6-2], electrostatic precipitator [6-3], and even random number
generation
[6-4].
The
theoretical
framework
for
understanding
the
onset
of
electrohydrodynamic instabilities has been established since the 1970s [6-5, 6-6, 6-7], implying
the ubiquity of electroconvective turbulence in electrical insulation systems (the working
voltages are always much higher than the threshold of instability). Recent numerical studies of
the problem in two [6-8, 6-9] and three [6-10] spatial dimensions have also shown the
existence of turbulent motions as well as ordered patterns in electroconvection.
On the other hand, due to the necessity of keeping the liquid chemically stable and pure
to avoid premature electrical breakdown in the presence of high electric fields [6-6, 6-7],
quantitative flow measurement techniques [6-11, 6-12] are generally not applicable to turbulent
electroconvection. Schlieren visualization was only able to provide some qualitative results [66]; it remains unclear to which extent they can be compared with theoretical results. Kerr
electro-optic technique was used to map the electric field distribution in high voltage (HV)
stressed liquid dielectrics [6-7], but the measurement principle [6-13, 6-14] simply neglects the
effect of flow on the detected light intensities. This is, however, a valid approximation only
when signal-to-noise ratio (SNR) is large. In low Kerr constant liquids like transformer oil
where high sensitivity photo-detectors are required to record weak electro-optic signals, SNR
becomes close to unity. In recent works [6-15, 6-16], to reduce the noise level, multiple
132
measurements are taken and then averaged under each experimental condition. The limitation
of this approach is the loss of information carried by the noise that may be associated with
specific types of noise sources.
In this chapter, we attempt to identify signatures of electroconvective turbulence from
the data of Kerr electro-optic measurements with transformer oil and to find experimental
conditions under which the negative effect of turbulence on optical detection is statistically
insignificant. The two seemingly contradictory goals are actually converging; they are just the
two sides of the same problem. Once one is achieved, clues to the other would also be seen.
133
6.2 Spatiotemporal statistical analysis of Kerr electrooptic signal under dc voltages
The experimental setup has been introduced in Chapter 2. The main difference is that we
no longer use pulsed HV to reduce flow effect. Instead, we use a HV amplifier as the excitation
source. The output dc voltages or ac amplitudes are adjustable from 0 to 20 kV. The two
parallel-plate electrodes are made of stainless steel with polished surfaces and rounded edges.
As shown in Figure 6.1, the region of interest (ROI) is chosen at the center of the
transformer oil-filled gap in view of that optical detection near the electrode surfaces may
bring in additional uncertainty from diffraction and random scattering due to surface roughness.
The ROI corresponds to an array of 128×128 pixels in the imaging area of the high sensitivity
charge-coupled device (CCD).
Figure 6.2 presents the detected light intensity (unit: electron counts) at a pixel within
ROI when there is no applied HV (the liquid is assumed to be at rest, though slight vibrations
of the test cell are unavoidable). A total of
500 samples are taken at 5 Hz sampling rate.
This is done by synchronizing the pulsed laser Q-switch and the CCD camera exposure with a
pulse train at 5 Hz repetitive rate.
As the “inherent” output instability of the pulsed laser, the light intensity fluctuates from
sample to sample. The approximately symmetric distribution of the detected light intensity is
well fitted by both normal and lognormal functions, which means that the disturbance to the
light intensity can be modeled as an unbiased additive noise.
134
Window of the Test Cell
Light Propagation
Laser Beam Profile
Electrode
(HV)
0
d=2 mm
ROI
Electrode
(GND)
CCD Imaging Area
x
Transformer Oil
Figure 6.1. The view as looking into the window of the test cell. The diameter of the pulsed laser beam is 7.6 mm.
The imaging area (8×8 mm2) of the CCD camera has an array of 1002×1004 pixels. The width of the gap between
two parallel-plate electrodes is d=2 mm, corresponding to about 250 pixels. The 1×1 mm2 region of interest (ROI)
is chosen around the center of the gap.
×
8000
6000
PDF
0 20 40 60 80 100
Time (s)
Light Intensity
Figure 6.2. Histogram (bar plot, 500 samples, 5 Hz sampling rate), normal fitting (solid line), and lognormal fitting
(dashed line) of the distribution of detected light intensities without high voltage (HV) application. The inset shows
the light intensity fluctuations in time.
135
On the other hand, it is well-known that lognormal distribution is the statistical
characteristic of the short exposure irradiance (the effective exposure time in our
measurements is ~10 ns, the laser pulse duration) of optical scintillation, i.e. electromagnetic
wave propagation in turbulent atmosphere [6-17, 6-18]. If under certain HV the detected light
intensities display lognormal distribution with substantial deviation from normal distribution,
the existence of scintillation effects may be inferred.
200
150
100
2000
10000
50
2000
5000
S
Skewness
100
8 kV
18 kV
S
(c)
Voltage (kV)
Figure 6.3. The skewness of the detected light intensity distribution as a function of applied HV. The error bars
come from statistics at various pixels in ROI. The three regions partitioned by the two dashed lines indicate that the
data is very likely skewed positively (above), negatively (below), and inconclusively (middle). The two insets of
histograms of light intensities show the slightly (8 kV) and strongly (18 kV) positively-skewed distributions.
136
We then apply dc HV to the gap for about 10 min and then trigger the CCD to acquire
sample images (it has been demonstrated [6-19] that the electromagnetic compatibility of our
current setup is adequate for our purpose, i.e. the application of HV has no obvious
interference with the performance of the laser and the CCD).
In Figure 6.3, the skewness of the detected light intensity distribution as a function of
applied HV is plotted. The error bars come from statistics at various pixels in ROI. The
skewness tends to rise with increasing HV (the absolute value of skewness higher than 0.5
means moderately or highly skewed distributions; otherwise it is called approximately
symmetric [6-20]). The two dashed lines in Figure 6.3 indicate the critical values of the test
statistic [6-21] (approximately
), i.e. the data is very likely skewed positively (top),
negatively (bottom), and inconclusively (middle).
From the above statistical analysis it can be concluded that as the applied HV exceeds 8
kV, the distributions of detected light intensity are positively-skewed. Two examples with
slightly (8 kV) and strongly (18 kV) positively-skewed distributions are shown. For extremely
positively-skewed data, exponential distribution is usually considered [6-17].
In general, for positively skewed data, lognormal distribution is a much better fitting
than normal distribution, implying that the signal has a weak multiplicative noise component
[6-22]. In our case, the only possible source of this kind of noise is optical scintillation due to
turbulent flow of the transformer oil in the gap.
At each pixel, the scintillation index of the detected light intensity is defined as the
normalized variance [6-23]:
, where
is the average over all samples.
Scintillation index, quantitatively characterizing turbulence-induced scintillation effects, is
sometimes considered as a simple indicator of the strength of the turbulence [6-17, 6-23].
137
(d)
S
Electro-optical
Current (µA)
S
Optical
Voltage (kV)
Figure 6.4. The dependence of scintillation index (S) and conduction current on applied HV.
In the top plot of Figure 6.4, the significantly increased
when HV is in the range of 15-
20 kV can be viewed as the signature of electroconvective turbulence in the gap. By removing
the analyzer from Kerr electro-optic measurement setup and adjust laser output accordingly to
avoid saturate the CCD, we repeat the above steps and calculate the scintillation index without
electro-optic modulation. Similar trend is found (the middle plot of Figure 6.4), but the values
of
are about 50% lower, which means lower sensitivity. This can be understood as follows:
besides optical scintillation, turbulence has an additional effect in Kerr electro-optic
measurements. The direction of the HV field is randomly disturbed due to the existence of
electroconvective turbulence, which affects the local electric polarization and electrobirefringence of the liquid.
138
The bottom plot of Figure 6.4 presents the conduction currents measured at the HV
terminal, relatively low and with an approximately linear dependence on the applied HV. Only
with current-voltage relation, one might regard the liquid between the two electrodes as a
stationary ohmic conductor, which is not true since the non-polar transformer oil is subject to
weak charge injection (to be discussed later in this section) and electroconvective turbulence.
For highly insulating dielectric liquids, measurement of terminal currents may not be able to
provide useful information on the physical processes in the liquids.
Note that our experimental setup does not have enough sensitivity and reliability to
accurately determine the onset of turbulent electroconvection; but we are able to reveal the
existence of turbulent electroconvection in the gap under high enough applied voltages (e.g.
the 18 kV and 20 kV cases) via statistical analysis of temporal sequence of detected light
intensities.
In fact, the same conclusion can be reached if one takes a closer look at the spatial
randomness of single ROI images (spatial sequences) under various voltages. A statistical
measure of spatial randomness characterizing the “texture” or the amount of information of an
image is Shannon entropy [6-24]:
, where
is the probability of
light intensity occurring in the image. There is a MATLAB function calculating
for each
image [6-25]. To make the images taken under different voltages comparable, before
calculating image entropy, all the images are normalized so that the average light intensity over
all pixels is the same value (e.g. 1000).
The solid curve in Figure 6.5 shows the ROI image entropy divided by
(the entropy
in the absence of HV) versus applied HV. At first glance, it seems surprising and
counterintuitive that as the voltage exceeds 10 kV, the decrease in
139
begins. However, the loss
of entropy is in accord with the physical picture of turbulent cascade which increases the
spatial correlations [6-26, 6-27].
The output beam of the pulsed laser has a Gaussian profile. Consequently, the
probability distribution of in ROI is approximately normal when the random disturbance field
is unbiased with maximum information content [6-28]. Under higher voltage, however, the
increased spatial correlation in the turbulent flow field may lead to a biased disturbance field
with lower degree of spatial randomness (decrease in entropy). This behavior of image entropy,
though distinct from temporal statistics of scintillation index, can also be viewed as a signature
H/H0
of electroconvective turbulence.
Voltage (kV)
Figure 6.5. ROI image entropy (normalized by H0, the value in the absence of HV) versus applied HV under 3
different experimental conditions.
140
The dashed curve in Figure 6.5 is the case with 4-by-4 binning (i.e., reducing the spatial
resolution by a factor of 4 in each dimension), in which the decrease of
is “postponed”.
While this is actually a loss in sensitivity, it also implies that binning of multiple pixels may be
able to reduce the effect of turbulence on optical detection.
Figure 6.6 shows the scintillation index S evaluated with L-by-L binning (i.e., the
average light intensity in a square region containing L× L pixels). The voltage is 20 KV. The
dashed line indicates the scintillation level corresponding to about 10% measurement
uncertainty, which requres a minimum L of 64 (in this case, there will be only 4 data points
over the whole gap). The bar plot in Figure 6.7 presents the Kerr electro-optic field mapping
S
results.
log2L
Figure 6.6. The scintillation index S evaluated with L-by-L binning (i.e., the statistics is based on the average light
intensity in a square region containing L× L pixels). The dashed line indicates the scintillation level corresponding
to about 10% detection uncertainty. The applied HV is 20 kV.
141
E (×10 kV/mm)
Texp = 10 ms; L = 1
Texp = 10 ns; L = 64
x/d
Figure 6.7. Results of Kerr electro-optic field mapping measurements under 2 different experimental conditions,
both of which are heterocharge configuration with enhanced electric fields near the electrodes. The applied HV is
20 kV.
Figure 6.8. The scintillation index S evaluated with various exposure times. The dashed line indicates the
scintillation level corresponding to about 10% detection uncertainty. The applied HV is 20 kV.
142
Back to laser beam scintillation, the long-exposure beam is approximately diffractionlimited with a smooth Gaussian profile [6-17], which indicates the possibility of reducing
scintillation level by increasing the exposure time
laser with an adjustable pulse width laser (
. To verify this, we replace the pulsed
from 10 µs to infinity). Longer exposure yields
similar results as binning, as shown in Figure 6.5 and Figure 6.8.
Result of Kerr electro-optic field mapping measurements with
ms is
presented in Figure 6.7, showing the heterocharge distribution with enhanced electric fields
near the electrodes [6-13, 6-29]. The non-dimensional injection parameter [6-1] can now be
estimated at the cathode (
):
most previous researches [6-6, 6-7, 6-8, 6-9]
. It is a very low level of injection, while in
was in the order of 1~10. Even when the charge
injection is very weak, with sufficient spatiotemporal resolution it is possible to identify the
signatures of electroconvective turbulence. Conversely, the negative effect of turbulence on
electro-optic measurements can be mitigated by adjusting the resolution.
143
6.3 Spectral analysis of Kerr electro-optic signal under
low-frequency ac voltages
The spectral signature of turbulent electroconvection has been found from electrical
current measurements three decades ago [6-30]. One of the limitations of our CCD is that its
maximum sampling rate is about 100 Hz, which is too low for broadband spectrum analysis of
detected light intensities. As a compromise, we apply very low frequency sinusoidal ac HV to
Light Intensity
Gap
the gap and use Fourier transform to analyze the spectral content of the detected light intensity.
1 2'
2
Number of Samples
Figure 6.9. Detected light intensities at two pixels labeled 1 and 2 (100 pixels or 0.8 mm apart) when the applied
HV is sinusoidal with amplitude 20 kV and frequency fac=0.1 Hz. The sampling rate is 63.53 Hz. A sample image
is presented in the inset, in which the bright band actually bounces between the two electrodes at frequency fac.
144
Figure 6.9 shows the detected light intensities at two pixels labeled 1 and 2 (100 pixels
or 0.8 mm apart) with HV amplitude 20 kV and frequency fac=0.1 Hz. The sampling rate is
63.53 Hz. Pre-semi polariscope [6-31] with crossed polarizers is used. A sample image is
presented in the inset of Figure 6.9, in which the bright band bounces back-and-forth between
the two electrodes.
Pixel #2
P(f)
Pixel #1
Figure 6.10. Fourier spectra magnitude versus frequency at pixels 1 and 2. The dashed lines are the spectra in the
absence of HV.
If the brighter area means higher electric field, then this motion implies an oscillatory
transport of charges in the gap since the gradient in electric field is proportional to the local
145
space charge density (Gauss’ law). In fact, as shown below, the flow driven by the ac HV may
play a more important role.
From the principle of Kerr measurement [6-13, 6-31], if there is no turbulent flow or
unstationary charge distribution in the transformer oil, the only significant harmonic
component is at 2fac.
However, the data presented in Figure 6.9 obviously have much richer frequency
contents. Their different Fourier spectra magnitude
versus frequency
at pixels 1 and 2
are shown in Figure 6.10. At pixel 1, the primary Fourier component is 2fac while the same
frequency component at pixel 2 is a local minima. Additionally, at pixel 2, there seems to be a
significant enhancement of subharmonic components. These phenomena cannot be understood
within the framework of Kerr electro-optic measurement principle. The spectral evidence
suggests that there be interacting flow and charge processes in the gap.
Figure 6.11 shows the coefficient of correlation between the time series of light
intensities at pixels 1 and 2 (2’) as a function of applied HV amplitude. Even under 20kV
(amplitude) ac HV, the data of pixels 1 and 2 are not highly positively-correlated. But there are
two general trends: firstly, due to smaller distance apart, 1-2’ has higher correlation coefficient
than 1-2; secondly, in both cases, under voltages in the range of 15~20 kV, the data sets
become increasingly positively correlated, which may be attributed to eddies of various length
scales developed in electroconvective turbulence.
It is an interesting observation that the results presented in Figure 6.11 are consistent
with Figure 6.5, where the reduced spatial randomness under higher voltages was interpreted
as increased spatial correlation due to turbulence. Here we give an example demonstrating the
assumption made in the previous section.
146
Correlation Coefficient
Voltage (kV)
Figure 6.11. The coefficient of correlation between the time series of light intensities at pixels 1 and 2 (2’, which is
10 pixels away from 1) as a function of applied HV amplitude.
P(f)
2fac Component
f/fac
Figure 6.12. Fourier spectra magnitude versus frequency at pixel 1 with HV amplitude 20 kV and 3 different fac
values. The sampling rate is 80 Hz.
147
The effect of fac on the Fourier spectra can be seen in Figure 6.12. The sampling rate
now is 80 Hz. While only 0.1 Hz and 10 Hz cases have definitive 2fac components, each
spectrum has a main lobe, i.e. “plateau” in low-frequency range (
upper frequency limit of the main lobe reaches
frequency limit of the main lobe is
Hz). For fac=0.1 Hz, the
, while for fac=10 Hz, the upper
. This implies that, the upper frequency limit is not
determined by the ac HV; it should be a property of the liquid itself.
The viscous diffusion time [6-32] τv=
mass density
or fluid viscosity
determines whether fluid inertia with
dominates fluid motions over gap width . This corresponds
to ~10 Hz as the upper frequency limit of the flow effect. The frequency spectrum in the main
lobe is in fact the combined outcome of flow and electro-optic effects. For
Hz, the
component lies outside of the main lobe, the negative influence of electroconvection can
be reduced. This conclusion is consistent with our study on the Kerr electro-optic measurement
technique called ac modulation, which will be discussed in the next section.
148
6.4 Discussions
In this chapter, we have carried out experimental studies to find temporal, spatial,
spectral, and correlation electro-optic signatures of turbulent electroconvection in transformer
oil stressed by dc and ac HV. The implications of this work are two-folded. Combining
theoretical models of optical wave propagation in turbulent medium and statistical
characteristics of simulated electroconvective turbulence fields, it might be possible to test and
verify numerical results with experimental data.
Moreover, this work also clarified some important issues on Kerr electro-optic
measurements. The results presented in Section 6.2 refreshed the understanding of the term
“steady state” in dielectric liquids stressed by HV, which is meaningful only in statistically
averaging sense. The last section demonstrated that to reduce the influence of flow on the
optical detection of harmonic components, the modulation frequency should be high enough;
and the lower ac amplitude is also desirable.
In this section, some elaboration of the second aspect is to be made, which is related to a
technique called ac modulation for Kerr electro-optic measurements with low Kerr constant
liquids like transformer oil [6-33, 6-34]. In this method, the frequency of the ac voltage
superposed on the dc voltage should be high enough so that the ac field does not disturb the
space charge behavior in one cycle. And the modulation voltage amplitude, compared with dc
level, should not be too high. Qualitativly, the requirements of ac modulation method and the
basic conclusions of the previous sections are convergent. To further verify this point, we
conduct a preliminary examination of how high (low) the frequency (amplitude) necessary to
ensure the measurement accuracy which is missing in published works.
149
Figure 6.13. Illustration of experimental setup for Kerr electro-optic field mapping measurements with ac
modulation.
The experimental setup consists of two main subsystems, optical and electrical. A test
cell with transformer oil and a pair of parallel-plate copper electrodes (alloy 110, surface
unpolished) inside is the intersection of the two subsystems. Vacuum pump and filter system
are used to remove suspended bubbles and particles in the oil, which prevents premature
electrical breakdown and improves optical detection accuracy.
There are laser, beam expander, polarizers (P0, P, A), quarter-wave plate (Q), slit and
photodiode in the optical subsystem. The intensity-stabilized He-Ne laser is made by Melles
Griot, model 05-STP-901. The diameter of the output beam is 0.5 mm with wavelength of
632.8 nm, average power 1 mW and linearly polarized. It takes about 15 min for the laser to
lock so that the output light intensity is stable. Any sort of reflection from optical components
back into the laser head should be prevented. The 20× beam expander is made by Special
Optics. It expands the beam diameter to ~1 cm.
150
The pre-semi circular polariscope configuration is used, as shown in Figure 6.13. The
three polarizers are made by Spindler&Hoyer with extinction ratio 500:1 and diameter of 10
cm. P0 is used to attenuate the light to prevent saturation of the photo detector. The output light
intensity of P0 is denoted by
. The angle of the transmission axis of P is at 45° with respect to
the x-axis and that of A (analyzer) is −45° (crossed polarizers). A quarter-wave plate (Q) is
inserted between P and the test cell and its slow axis is along the x-axis.
The photodiode is made by United Detector Technology, Model UDT-455HS. The
bias voltage is 15 V and the detection area is 2 mm by 2 mm. Since the gap between the
electrodes is fixed at 2 mm in width, a 2/3 mm movable slit was used to get spatial resolution,
which means that only 1/3 of the detection area is active for measurement. The light intensity
incident on the slit ( ) is a function of electric field across the gap (and also a function of x).
To reduce the influence of room light, the whole system was covered with a black cloth. The
output of the photodiode is connected to the lock-in amplifier and the oscilloscope to measure
ac (first and second harmonics) and dc components.
In the electrical subsystem, the Hewlett Packard function generator, model 3311A,
generates both ac and dc signals as inputs of the high voltage amplifier. The high voltage
amplifier is made by Trek Inc., model 20/20, which amplifies the combined ac and dc signal by
2000 times in magnitude. The maximum input voltage is 10 V. The output HV is connected to
the feed-through on the top of the test cell. A 1000:1 Fluke high-voltage probe and 5000:1
Pearson capacitive divider was used to measure the high voltage. The attenuated signal is
connected to the oscilloscope to monitor the applied voltage and to the lock-in amplifier as a
reference signal. The lock-in amplifier is EG&G, Model 5210. The time constant is set to 30
seconds for high accuracy and stability of the output.
151
Some constants in the measurement are given below: Kerr constant of transformer oil
m/V2, the electrode length along the light path (z-axis)
gap width
, and the
.
The electric field in the gap (in x direction) is
polariscope with a small Kerr constant (
. For the pre-semi
), the 1st order of
is:
(6.1)
Hence,
,
(6.2)
or equivalently,
,
(6.3)
The dc high voltage applied across the gap is measured by the oscilloscope (with
divider) and denoted by
frequency
. The ac high voltage
. The mean (
) and harmonics (
(peak-to-peak) is at modulation
) of the output of the photo
detector can be read from the oscilloscope and the lock-in amplifier display, respectively.
Then from Equation (6.3), both the dc and ac electric fields are calculated. The slit can
be moved to take measurements at
(
in this case) different positions across the gap: H
(near the surface of the HV electrode), M (in the middle of the gap), and G (near the surface of
the grounded electrode). It should be noted that the spatial resolution in the measurements
with a photodiode is relatively low, and H, M and G are not ‘points’. The light intensity
152
detected at H, M or G actually represents the average level in a 2/3 mm interval determined
from the slit width. Thus the calculated electric field is also the average value in the each 2/3
mm interval.
Measurements under various dc voltages, modulation frequencies and ac amplitudes
are taken. Certain criteria are needed to verify the reliability of the results. Firstly, the ac
electric field across the gap should be uniform. If not, there would be space charge responding
to the ac field and fluctuating at the same frequency, while in the ac modulation method, the ac
field is not assumed to significantly disturb the space charge distribution. So the peak ac field
everywhere in the gap should be close to the mean peak ac field given by:
(6.4)
and a good experimental condition minimizes the deviation:
(6.5)
where the sum is over all
measured points in the gap.
After obtaining the dc field distribution, it is checked by taking the difference between
the integration of dc field across the gap and the applied voltage:
(6.6)
to determine if it is within an acceptable error range (e.g. 5%).
153
2.5
ΔEac/ Eac(m) (%)
|ΔUdc|/ Udc (%)
5
4
3
2
1
2
1.5
1
0.5
0
0
10
1
10
1
2
100
f (H
100
2
3
1k
z)
f (H
53
10k
4
10
2
50
1
Vp
U
p/
53
4
10k
102
50
1
Vp
(a) Udc=1kV
10
6
(%)
8
4
2
6
4
2
0
0
F
F
10
1
10
1
2
100
f (H
z)
2
100
54
1k
3
10
3
4
10k
20
2
50
1
V pp/
Ud
f (H
%)
c(
54
31k
z)
3
10
4
10k
2
20
50
1
(b) Udc=5kV
6
Ud
V pp/
%)
c(
40
ΔEac/ Eac(m) (%)
|ΔUdc|/ Udc (%)
U dc
p/
10
8
ΔEac/ Eac(m) (%)
|ΔUdc|/ Udc (%)
1k
3
z)
(%)
dc
4
2
30
20
10
F
0
F
10
1
0
F
2
100
f (H
z)
F
F
F
10
1
100
2
34
3
1k
53
4
10k
10
2
V pp/
1
20
(
U dc
f (H
%)
34
1k
3
z)
53
4
10k
10
2
V pp/
20
1
(c) Udc=10kV
U
(%)
dc
15
ΔEac/ Eac(m) (%)
|ΔUdc|/ Udc (%)
10
10
5
F
F
0
F
F
z)
4
2
F
F
F
F
F
10
1
100
2
f (H
6
0
F
10
1
8
100
2
31k
33
4
10k
52
10
1
U dc
V pp/
f (H
(%)
z)
31k
33
10k
4
(d) Udc=18kV
Figure 6.14. Errors in measured dc and ac electric fields with dc voltage
kV and various modulation voltages (
) and frequencies ( ).
154
52
10
1
(a)
V pp/
U
(%)
dc
kV; (b)
kV; (c)
kV; (d)
Starting with
50%, 10% and 5% of
kV, the peak-to-peak values of the ac voltage (
) are set to be
. The corresponding ac amplitudes are 250 V, 50 V and 25 V. The
modulation frequency varies from 10 Hz to 10 kHz. There may be difference in values of
different points due to the nonuniformity of the background light field
. But
at
at a fixed
point can be regarded as a constant when changing modulation parameters, as a result of the
stable output of the laser and the irrelevance of
to the applied voltage (approximately).
From Equations (6.5) and (6.6), the errors in measured dc and ac electric fields are computed,
as shown in Figure 6.14(a).
One can see that when
kV all the errors are less than 5%, which indicates that,
when the dc voltage is low, there exists a wide range of modulation frequencies and amplitudes
that make the measurement results reliable. Due to the insignificance of the space charge effect
at this low voltage, even the modulation frequency as low as 10 Hz and ac peak-to-peak value
comparable to the dc voltage yield data of high accuracy.
The measurements and calculations were repeated as the dc voltage was increased to 5
kV, 10kV and 18 kV. The errors in dc and ac electric fields are presented in Figure 6.14(b)-(d).
There is a new feature in these cases of higher dc voltages, as marked by ‘F’ in Figure 6.14(b)(d). This means the failure of the lock-in amplifier to generate a stable output even over a long
period or a correct output with a reasonable order-of-magnitude. Although the causes for the
failure are unclear in detail, it is inferred that the response and feedback of space charge to an
ac electric field may play a destructive role in the establishment of a ‘steady state’ with a set of
relatively stable frequency components.
The failures always occur with low modulation frequencies and relatively high ratio of
ac and dc voltages. To avoid failures, the modulation frequency should be increased or the
155
applied ac voltage be as low as possible. In addition, the errors also tend to decrease. For
example, in Figure 6.14(c), when
10 kV and
, the measurements are not
successful for modulation frequencies of 10 or 100 Hz. The modulation frequency can either
be increased to 1 kHz or the ac amplitude reduced to get stable and reasonable output of the
lock-in amplifier. The former results in a great fluctuation in the ac field profile (
over 40%), which is supposed to be uniform over the gap. It is concluded that
is not suitable for the measurement due to significant errors. To increase the accuracy and
reliability of the measurements the modulation frequency is increased and the applied ac
voltage is made as small as possible. If the results are ‘filtered’ by the criterion of both
less than 5%, then a range of ‘valid’ modulation frequencies and
and
amplitudes for each
can be determined, which is presented in Figure 6.15. In general, there
is an increasingly strict confinement on the applicable range of modulation frequencies and
voltages with the increase of
.
Vpp/ Udc (%)
Udc=5kV
20
Udc=10kV
10
5
3
0
Udc=18kV
10
100
1k
10k
Figure 6.15. Reasonable ranges of ac modulation frequencies and amplitudes for
each
f (Hz)
5 kV, 10 kV and 18 kV. For
, the reasonable range is the set of the parameter pairs at the same side of the corresponding curve as the
arrow.
156
There is a practical implication of the above results. If one wants to replace the
photodiode with a modern computerized CCD camera to increase the spatial resolution and the
efficiency of data acquisition and processing, the restrictions in the frequency and amplitude of
the ac modulation voltage impose requirements on the maximum sampling rate (time
resolution), sensitivity and saturation level of the CCD camera. Typically the modulation
frequency is chosen to be several kHz, and correspondingly, the order of the average ac field
would be 0.1 kV/mm. According to the sampling theorem, in order to detect a double
frequency component, the sampling rate needs to be greater than four times the modulation
frequency. So the CCD camera should be high-speed, capable to take
frames per second.
When a CCD camera is used to record a series of output light intensities
with no high
voltage applied across the gap, a Fourier transform can be done to analyze the frequency
spectrum of the background light field. The typical ratio of the measurement magnitudes of
double frequency component and dc component is
, which requires that, in the
background light spectrum, the same ratio should be much lower. Sensitivity, closely related to
frequency component magnitude in the background, means the minimum distinguishable
signal over the noise level, while saturation level, corresponding to dc component in the
background, means the maximum detectable light intensity. Consideration and test of these two
parameters are necessary as well as the specification of time and spatial resolutions.
In the calculations, the Kerr constant of transformer oil was assumed as
m/V2. Since this parameter is crucial in determining the accuracy of the results, a
verification of this parameter is done. The dc electric field distributions under various dc high
voltages with modulation parameters
check, it was assumed
10 kHz and
0.5 kV are measured. As a basic
kV/mm, and from Equation (6.2), the results
157
show that
holds for every point in all cases. Then
back into Equation (6.2), regarding
and
were substituted
as an unknown variable. The final solution is
m2/V2, which coincides with what was used in the measurements.
E1.4
dcd/Udc
1.2
1
0.8
系列1
H
0.6
系列2
M
系列3
G
0.4
0.2
0
1
Udc=1kV
2
3kV
3
5kV
4
8kV
5
10kV
6
12kV
7
15kV
8
18kV
Figure 6.16. Normalized dc electric field distribution between copper electrodes in transformer oil under various dc
voltages (
) measured with ac modulation
10 kHz and
0.5 kV.
As an application, the dc electric field distributions under various dc high voltages
from 1 to 18 kV are measured with ac modulation parameters:
10 kHz and
0.5 kV.
The dc electric field distribution, after being normalized by the mean dc field across the gap, is
shown in Figure 6.16. When
is relatively small (1 kV and 3 kV), the electric field
distribution in the gap is approximately uniform, since the low electric field cannot produce
enough space charge to distort the field profile. Increasing
to 5 kV or 8kV, bulk
dissociation in the transformer oil takes place. Positive (negative) charges move toward
cathode (anode), creating charge density , or equivalently an electric field gradient according
to Gauss’ law
( is the dielectric constant), at the two electrodes. This forms a hetero158
charge configuration in the gap, with electric field near electrodes enhanced and in the middle
of the gap reduced. At
10 kV, the electric field distribution looks uniform again. It
seems that charge injection from the electrodes balances the bulk dissociation by neutralizing
the charges near their surfaces. Apparently, the growth in electrode injection with increasing
is greater than that of bulk dissociation, for when
is over 10 kV, the so-called homo-
charge configuration with electric field near electrodes reduced maintains. At
18 kV, the
electric fields at H and G are 15% to 20% lower than the average. Since electrical breakdown
often initiates at the electrode surface, this may allow higher applied voltages without
breakdown. Actually, for the pair of copper electrodes used in the measurement, the dc
breakdown voltage is about 20 kV for a 2 mm gap, which is over 15% higher than aluminum
or stainless steel electrodes.
159
References
[6-1] A. Castellanos (ed.), Electrohydrodynamics (Springer-Verlag, Wien, 1998).
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162
7
Concluding remarks
In this thesis, it has been demonstrated both quantitatively and qualitatively that Kerr
electro-optic measurements with a high-sensitivity CCD camera can be used for electric field
mapping. Measurement accuracy and reliability for uniform and fringing space-charge free
fields and field with space charge have been evaluated in Chapter 2. Generally speaking, the
relative errors will be reduced as the applied voltage increases. This may not be true when the
voltage approaches the breakdown threshold, since more uncertainties would be introduced due
to high-field conduction and pre-breakdown phenomena in the liquid dielectrics.
To further improve the sensitivity of the measurements, it is necessary to identify and
quantify various sources of noise in the experimental system, including optical, electro-optical,
and electrochemical processes. Image processing techniques may also be helpful to enhance
the data quality. The most straightforward application of image processing algorithms in our
measurements is edge detection, i.e. identification of the electrode surfaces in the images taken
by the CCD camera. This would be more demanding when the oil gap is smaller, since the
same edge detection inaccuracy (e.g. 5 pixels) takes up a larger portion of the gap.
The smart use of charge injection to improve breakdown strength in transformer oil is
demonstrated in Chapter 3. Hypothetically, bipolar homo-charge injection with reduced
electric field at both electrodes may allow higher voltage operation without insulation failure,
since electrical breakdown usually initiates at the electrode-dielectric interfaces. To find
163
experimental evidence, the applicability and limitation of the hypothesis is first analyzed.
Although further efforts should be made to test more electrode materials, the present work
clarifies a crucial issue regarding the hypothesis. To test the hypothesis, many experimental
details need to be carefully considered, such as appropriate impulse waveform, similar intrinsic
breakdown voltage of different electrode materials, and dynamic Kerr measurement before the
onset of flow. Only under these specific circumstances, the hypothesis is testable and correct.
Impulse breakdown tests and Kerr electro-optic field mapping measurements are then
conducted with different combinations of parallel-plate aluminum and brass electrodes stressed
by millisecond duration impulse. It is found that the breakdown voltage of brass anode and
aluminum cathode is ~50% higher than that of aluminum anode and brass cathode. This can be
explained by charge injection patterns from Kerr measurements under a lower voltage, where
aluminum and brass electrodes inject negative and positive charges, respectively. More
importantly, we worked out a feasible approach to investigating the effect of electrode material
on the breakdown strength, which may be difficult and inconclusive to be directly related to the
electronic, mechanical and thermodynamic characteristics of the metal. The complexity has
been reduced to charge injection patterns and intrinsic breakdown strength.
In Chapter 4, the fractal-like charge injection kinetics in HV pulsed transformer oil has
been identified from Kerr electro-optic measurement data and verified by numerical
simulations of the time-dependent drift-diffusion model with the experimentally-determined
injection current boundary conditions. It is shown that while the space charge process in the
liquid bulk is drift-dominated, the charge injection kinetics from the electrical double layer on
the electrode-dielectric interface is diffusion-limited.
Two mechanisms are proposed to reveal the deep connection between geometrical
164
characteristics of electrode surfaces and fractal-like kinetics of charge injection. The order of
injection current densities is 10-5~10-3 mA/mm2 in our experiment, corresponding to total
current of about 10-2~1 mA in the gap and bulk conductivity enhanced by 104~106. With such a
large magnitude, it seems that the transient charge injection should be associated with the
charging dynamics of EDL. Otherwise, the formative steps in Figure 4.2 would be the same as
in previous studies which work only under long-term high-voltage applications, while the
difference between transient (~1 ms) and steady-state (> 1 min) charge injection patterns in
dielectric liquids has been found as early as in 1960s. A comprehensive consideration of the
chemical aspects of the processes (chemical compositions, reaction schemes, etc.) is out of
scope of this work and may be proposed for further studies.
Chapter 5 explores the possibility of early warning of electrical breakdown initiation in
high voltage pulsed transformer oil from the data of Kerr electro-optic measurements. Due to
electrostriction, the detected light intensities near the rough surfaces of electrodes both
fluctuate in repeated measurements and vary from pixel to pixel in a single measurement. The
calculated coefficient of variation has a strong nonlinear dependence on the applied voltage,
implying that some critical transitions are taking place, at least at some spots on the electrodes.
The results of this work may be helpful to develop new approaches to non-destructive
breakdown test and, based on the same physical principle, non-destructive inclusion detection
in dielectric liquids.
Additional work needs to be done to find more evidence that electrostriction is the major
force behind the early warning signal. The influence of a strong electric field on a liquid is
noticeable when the electric field energy density is comparable with the external pressure. This
condition is usually satisfied in the case of breakdown initiation. We can place the test cell
165
inside a pressure chamber with a wide range of adjustable pressure. Theoretically, it is
expected that the critical threshold of the applied voltage would be higher under higher
pressures. Under the same applied voltage, the detected fluctuation in electro-optic signal
should strongly depend on the ambient pressure.
The influences of applied voltage (peak, rise time, polarity), electrode material and
surface roughness, and ambient pressure on the electrostriction effects need also be
investigated. In the field of dielectric and electrical insulation research, the most common
impulses are microsecond instead of nanosecond. We will start from nanosecond rise-time
pulses and gradually increase the rise-time to the microsecond range. By doing this it is
possible to find a characteristic time beyond which the space charge behavior dominates. Since
parallel-plate electrodes are used, we do not expect any polarity effect if the two electrodes are
‘identical’. This can be a basic check of the reliability of the measurement results and the
processed data.
We would also like to propose experimental procedure on the non-destructive inclusion
detection. Prepare transformer oil with conductive inclusions of nm to µm diameter range. The
first type is a dilute nano-fluid; the second type is to release a small number of conducting
micrometer-size suspensions between the two electrodes. Test transformer oil samples with
these controlled conducting inclusions to measure the resulting local electric field enhancement
which can be a trigger for electrical breakdown or partial discharge. This method can easily be
extended to larger scale industrial systems by scanning the entire liquid region.
In Chapter 6, experimental studies are carried out to find temporal, spatial, spectral, and
correlational electro-optic signatures of turbulent electroconvection in transformer oil stressed
by dc and ac HV. The implications of this work are two-folded. Combining theoretical models
166
of optical wave propagation in turbulent medium and statistical characteristics of simulated
electroconvective turbulence fields, it might be possible to test and verify numerical results
with experimental data. Moreover, this work also clarified some important issues on Kerr
electro-optic measurements. The results presented in Section 6.2 refreshed the understanding
of the term “steady state” in dielectric liquids stressed by HV, which is meaningful only in
statistically averaging sense. The last section demonstrated that to reduce the influence of flow
on the optical detection of harmonic components, the modulation frequency should be high
enough; and the lower ac amplitude is also desirable.
*
*
*
This thesis is an interdisciplinary research involving, in general terms, material science,
electrical engineering, computer science, mechanics and physics. It makes contributions to the
areas of electrostatics, electro-optics, electrochemistry, and electrohydrodynamics. However,
the story is far from finished yet. The goal of constructing an integrated picture of physical
processes in high-field stressed dielectric liquids has not accomplished. On this subject, future
work can be done in three directions:
(a) A detailed analysis of the chemical composition in transformer oil and reaction
schemes involved in electrical conduction;
(b) A numerical model incorporating the dynamics of electrical, chemical, mechanical
and thermal processes with the simulation of electrical birefringence and optical propagation;
(c) An integration and optimization of the optical system based on careful investigation
of the optical property of each component.
The proposed work will advance the knowledge on a more fundamental level. From an
even broader perspective, my thesis provides foundations for a long-term research on advanced
167
materials in power engineering and energy technology. For example, the same measurements
can be done with dilute transformer oil-based nano-fluids, the importance of which has been
recognized by ABB researchers. The behaviors of thin films and colloids in electric field have
received considerable research interests in recent years. Porosity of dielectrics and electrode
coatings, and nano-patterned electrode surfaces may result in unique mechanical and electrical
properties. The use of an ultrafast laser may enable us to explore some more complex electrooptic phenomena. Some semiconductors and inorganic materials may be utilized to make
super-capacitors.
168
Bo Suan Zi: Ode to Plum Blossom
by Lu You (1125−1210), great poet of China’s Song Dynasty
(Translation adapted from Dict.cn)
By a broken bridge outside the post-hall,
Blooming lonely, no care does she gain.
Though drowned in sorrows at night-fall,
She still suffers much from wind and rain.
For the first of spring she has no lust,
Just let spring flowers envy her fame.
Even fallen in mud and ground to dust,
Her fragrance still remains the same.
169
170
A
Physical and chemical parameters of transformer oil
Shell’s Diala® A oil meets the ANSI/ASTM D3478 and the NEMA TR-P8-1975
specifications. It is formulated with refined petroleum oil and a lubricant additive. Their
inherent toxicity is quite low. However, prolonged or repeated contact requires the observation
of good industrial hygiene practices.
Table A.1. Physical and chemical parameters of transformer oil
Properties
ASTM test method
Typical Values
Interfacial tension, 25 °C, dynes/cm
D971
45
Specific gravity, 15/15 °C
D1298
0.886
Viscosity, cSt at 40 °C
D445
9.37
Viscosity, cSt at 0 °C
D445
66
Dielectric breakdown voltage at 60 Hz, kV
D1816
28 (VDE electrodes, 1.02 mm gap)
Dielectric breakdown voltage impulse, kV
D3300
176 (25.4 mm gap, needle-to-sphere GND)
Oxidation inhibitor content, %w
D2668
None
Sulfur, %w
D2622
0.07
Water, ppm
D1533
30
Oxidation stability (164 hrs, sludge %w)
D2440
0.15
Gassing tendency, l/min
D2300
16
Coefficient of expansion, ml/°C /ml
D1903
0.00075
171
Table A.1 (continued). Physical and chemical parameters of transformer oil
Properties
ASTM test method
Typical Values
Dielectric constant at 25 °C
D924
2.2
Thermal conductivity, cal/cm/sec/°C
D2717
0.0003
Molecular weight
D2503
261
Refractive index
D1218
1.4815
Viscosity-gravity constant
D2140
0.865
Carbon type composition: %CA
D2140
7
Carbon type composition: %CN
D2140
47
Carbon type composition: %CP
D2140
46
172
B
Approaches to improving breakdown strength in
liquids
1 Introduction
In the first part of this Appendix, a brief overview of electrical breakdown in liquid
dielectrics is presented, which serves as preliminary knowledge for the subsequent parts. For
more details, one can refer to some textbooks on high voltage engineering [1~4].
Efforts to understand breakdown mechanisms in a variety of liquid insulants have been
continuing for many decades. However, unlike gases and solids, there is no single theory that
has been unanimously accepted. This is because the molecular structure of liquids is not simple
and not so regular. For instance, transformer oil, the most common dielectric liquid, contains
well over 100 chemical compounds, and the fact that liquids tend to be contaminated with
various impurities is a serious problem for fundamental studies. Moreover, the transition from
liquid to gas phase, which takes place during the development of breakdown, still further
complicates the phenomena and hence their interpretations. From the experimental studies of
breakdown process, the breakdown of liquid is influenced by various factors such as
experimental procedure, electrode geometry, material and surface state, presence of chemical
and physical impurities, molecular structure of liquids, temperature and pressure. Several
breakdown theories like electronic theory, suspended particle theory and bubble theory were
advanced in the late 1960s, resulting in. However, it is clear that no single concept in these
173
theories can explain all experimental observations in a unified manner, and it has been
necessary to modify and sometimes even reject them with the emergence of new experimental
evidence. For instance, the electronic breakdown theory which was an extension of electron
avalanche concept in gas discharges has been rejected due to no direct experimental evidence
for the avalanche process. Thus, in the following sections, we will only introduce other more
promising hypotheses based on particle and bubble effects and observation using optical
techniques.
With the advent of fast electro-optic techniques, the understanding of breakdown in
liquids has been advanced tremendously. With these techniques, once a voltage pulse is
applied any perturbations occurring in the electrode gap can be easily visualized under
magnification by taking a photograph of each event. Verification of the bubble theory was
conducted using ultra high speed photography, which confirmed that streamers emerge from
the high voltage electrode grow out in the liquid toward the opposite electrode if the field is
critical, and that actual breakdown is preceded by the formation of secondary streamers which
grow faster than the primary ones. The most popular methods that have been used are
shadowgraph/schlieren techniques, Kerr electro-optic techniques and holographic techniques.
However, the characterization of breakdown process is out of the scope of this research.
2 Suspended particle breakdown theory
Suspended particles are always an integral part of liquids. In spite of rigorous cleaning
techniques imparted both on liquids as well as test cells, submicron sized particles cannot be
removed from the system. The particles could be a fiber, probably soaked with moisture, or it
may be even a droplet of water. The relative permittivity of these particles is higher than that of
174
the liquid. Assuming them to be spherical, then the particles will experience a force that is
directed toward areas of maximum stress. Therefore the particles will align on the high stressed
electrode and start forming a bridge which could lead to gap breakdown. Similarly if
particulate matter is fiber it will get polarized due to the presence of moisture on its surface and
move along converging fields. When a fiber reaches either electrode, its outward tip would act
as extension of the electrode, cause field intensification and thus attract more fibers, thereby
forming a bridge in the gap. This can lead to breakdown via joule heating of the bridge and its
surrounding liquid.
The evidence in support of this theory includes the increased time required to reach dc
and ac breakdown of the liquid with increased viscosity, while under high-frequency or fast
impulse voltages this phenomenon does not occur. Although this theory did explain the
breakdown in liquids containing large amount of particles, it is unlikely to be extended to pure
liquids. Moreover, particles have been seen on several instances to bridge the gap, while
discharge occurs in a different region and still at higher voltages. This means breakdown
involves some other mechanisms. Nevertheless, particles may be instrumental as an aid in the
process of breakdown.
3 Bubble theory of breakdown
According to this theory, a low density vapor is generated in the liquid by the injection
of large leakage currents at the electrode protrusions. By this process local vaporization can
occur in a few milliseconds. Calculation of the heat needed to vaporize a liquid is
straightforward in heat theory. Near breakdown the emission current from the cathode is space
charge limited and is given as proportional to an exponential form of the local field. It then
175
follows that the local energy input during the applied high voltage pulse duration can be
expressed as a function of the local electrical field. The critical breakdown field strength can be
solved by equating the energy input and the energy required to vaporize the liquid. This is the
so-called thermal breakdown criterion and exhibits a marked pressure and temperature
dependence since the boiling temperature increases with pressure. If the liquid is degassed, its
breakdown strength becomes less dependent on the pressure. This theory also explains the
effect of molecular structure of the liquids on breakdown. However, the main objection to this
model has been the simple heat transfer treatment based on the steady state equation for a
phenomenon which indeed needs to be described by transient heat flow dynamics.
In this theory, the concentrated field at electrode protrusions would play a basic role.
Three other alternatives have been proposed to account for the formation of gas bubbles:
release of occluded gases from micro-pores in electrode surface layers; cavitations caused by
mechanical strain of the liquid under the highly concentrated electric field with corresponding
electrostrictive pressure differential; and electrochemical dissociation of some liquid molecules
with the release of gases.
4 Factors influencing breakdown strength of liquid dielectrics
A) Temperature and pressure
The effect of temperature on electrical strength of an insulating liquid depends on its
type and degree of purity. For example, the breakdown strength of dry transformer oil is
insensitive to temperature except slightly below the boiling point, where the breakdown
strength decreases drastically probably because of the formation of vapor bubbles and their
growth aided by the decrease at such temperatures of the oil’s viscosity and surface tension.
The breakdown strength of oils that have a trace of moisture are sensitive to temperature
176
variations over the full range from about -20°C up to their boiling point of about 250°C.
The breakdown strength of an insulating liquid under dc and power frequency increases
significantly with applied static pressure. Raising the pressure from atmospheric to 10 times
higher increases the breakdown strength by about 50%, depending on the type of liquid.
Another effect of pressure is the suppression of pre-breakdown discharges. These observations
support the bubble theory of liquid breakdown. However, under very fast impulse voltages of
duration less than 0.05 μs, breakdown voltage is insensitive to both pressure and temperature.
B) Electrode and gap conditions
The breakdown voltage of a liquid insulated gap depends on its width as well as the
electrode shape and material. For gaps with highly non-uniform fields such as that of a pointto-sphere gap, there is a polarity effect. The negative DC breakdown voltage is lower than the
positive voltage up to a critical gap length above which the relation reverses. This critical gap
length depends on the liquid and the electrode material. There seems to be no simple
explanation for these phenomena. However, the material of the cathode surface layer
determines the electric stress necessary for electron emission. These electrons play a decisive
role in the conduction and breakdown processes.
The size and shape of electrodes determine the volume of liquid subjected to high
electric stress and the degree of field nonuniformity. The bigger this volume is, the higher the
probability of its containing impurity particles. The more of these particles that are present, the
lower would be the breakdown voltage of the liquid gap. Moisture is also an important factor.
The sensitivity of liquid breakdown to these factors is logically higher under DC and powerfrequency AC than fast impulse voltages. Thus the impulse ratios of highly non-uniform gaps
of contaminated or technically pure liquids can reach about 7.
177
It has also been shown that, stressing the oil gap under high-voltage for a long time, and
repeated sparks of limited energy, tend to raise the breakdown voltage of the gap. This is called
conditioning. Particles in suspension collect at zones of field concentration. Points of microroughness on the electrodes get eroded by concentrated discharge currents. A film of discharge
byproducts gradually covers the discharge areas of both electrodes. In the case of the silicon oil,
repeated breakdowns tend to cover the electrodes with a film gel and solid decomposition
products. If a high-frequency arc is allowed to take place in the liquid gap, the arc products
cause the liquid properties to deteriorate.
C) Impurities
Impurities include solid particles of carbon and wax, byproducts of aging and discharges,
cellulose fibers, residual of filtration processes, water, acids, and gases. Impurities usually
cause a reduction in the electrical breakdown strength of an insulating liquid, the largest effect
being that of the simultaneous presence of moisture and fibers. Cellulose fibers are known to
be hygroscopic. Thus, floating moist fibers tend to bridge the oil gap. Under both DC and AC
the effect of a trace of moisture is drastic on meticulously dried liquids, much greater than that
of commercial liquids. The effect of moisture is less pronounced in the case of oil gaps with
strongly nonuniform fields and with liquids containing no fibers. Because water solubility is
considerably higher in silicon oil and phosphate esters than in mineral oil, they need to be
much more carefully dried and kept.
Metal particles may be present in dielectric liquids, particularly those used in
transformers and circuit breakers. Their presence reduces the breakdown strength of oil by as
much as 70%. Longer and thinner particles contribute more to the reduction of the oil’s
breakdown voltage.
178
D) Flow
The behavior of transformer oil and other dielectric fluids used for the cooling and
insulation of power system equipment is significantly influenced by the motion enforced by the
action of circulating pumps. Two important factors affect the situation. First, charges generated
by streaming electrification in critical parts of the hydraulic circuit having high velocity and/or
turbulence can accumulate to distort the electric field in positions where dielectric integrity is
prejudiced. Also, the dielectric strength of the fluid is altered by the actions of the flow. Charge
separation at interfaces between a moving fluid and a solid boundary can give rise to the
generation of substantial electric fields. Either alone or in combination with the existing
electric fields imposed by the energization of the equipment, these can give rise to insulation
failure. The initial response of apparatus manufacturers has been to reduce design velocities
and curtail the operation of pumps.
In apparent contrast, during standard oil testing, the continuous flow of oil was found to
increase the mean breakdown strength. The increase depends on the electrode material and is
larger with steel electrodes than with brass. The increase of breakdown strength can be
explained by assuming either that the oil flow impedes the entry of impurities into the gap, or
that the oil motion delays the establishment of particle bridges between the electrodes. The
change in breakdown strength was significant with an oil velocity of 3 cm/s, although a much
higher velocity is needed to have such an effect. To further complicate the picture, excessive
increase in oil velocity causes the flow to become turbulent, where gas bubbles may then be
created which lead to a reduction in breakdown strength.
5 Review of Ref. [5]
The author had realized that Townsend-type theory was not successful in liquid
179
breakdown. Also in the author’s opinion, the conductivity of liquid insulators is mainly due to
ions while breakdown should be ascribed to coarser particles. The author applied the
electrostatic theory to colloid chemistry, and the insight into the mechanism of breakdown
became much clearer. The key point of this book can be stated as: the electric strength of liquid
insulating material depended mainly on its degree of purity.
According to the author, contamination of insulating oil is unavoidable owing to various
factors. The simplest physics picture is: colloid particles of high permittivity will be charged in
oil, i.e., absorb an amount of positive ions and collect an atmosphere of negative counter ions
and dipoles or absorb soaps. They may tend to unite by flocculation as a result of which the
particles after a collision may adhere, whereas their ion atmospheres unite and form a single
atmosphere enveloping the enlarged complex. This flocculation depends on the relative
magnitudes of the attractive London-van der Waals and chemical binding forces between the
particles and the repulsive electrostatic forces between the ion atmospheres. The repulsive
interaction energy increases in proportion to the particle size, while the breakdown strength
goes downhill. Therefore an equilibrium state with maximum particle size and lowest electric
strength will be reached.
Both theory and experiment indicate that for the formation of a bridge only particles of
high permittivity and larger colloid sizes are responsible. When the particles increase in size
the breakdown strength goes downhill.
The non-uniformity (global or at least local) and impurities of high permittivity are two
factors effectuating breakdown. The non-uniformity of the field in the gap is due to its finite
dimension (the unavoidable existence of edges) and the non-smoothness of the electrode
surface (the protrusions or attached contaminants induce local stress concentration to at least 2-
180
3 times the average value). When impurity particles in non-uniform field have a high
permittivity, they will be polarized with a gradient force proportional to the square of local
field imposed. So they will drift towards a place of maximum stress where they align head-totail to minimize the free energy. If the stress exceeds a certain limit, a bridge will be formed as
a consequence of flocculation which is necessary to cement together the elements of the bridge.
Electrical discharges were observed between parts of a bridge which had been disrupted
by gas bubbles developed by Joule heat or electrolysis. Pre-breakdown discharges may occur
which do not develop into a real destructive breakdown with unlimited carbonization but may
result in development of gas in colloid suspensions. Corona discharges in gas bubbles and local
heating in bridges may cause the amount of carbon particles and the acidity and soap contents
to increase, which lead to deterioration of the dielectrics. Meanwhile, however, the liquid may
be purified by electro-deposition of the impurities at dielectric interfaces or electrodes.
In a breakdown or a pre-breakdown discharge controlled by a large series resistance, no
important additional carbonization and formation of acid in the oil occurs and the impurities
may have disintegrated. This conditioning effect is the opposite of flocculation. In this case a
second breakdown may happen at a stress higher than the first breakdown. A certain
conditioning effect may also take place by electrostatic precipitation of the impurities at a third
electrode. This electro-deposition may be obtained by relatively low field intensities.
To improve the breakdown strength, in addition to efforts to keep the electric field in the
insulation as uniform as possible, the principal advice to be gained from this book is: to see it
that the insulation is pure. A short survey was given of different methods of purifying the
insulating oil, including methods of washing with fuming or concentrated sulphuric acid and
distillation. Good results and extreme purification of hydrocarbon oils were obtained by
181
removal of tiny particles in a Cottrell filter. However, this method failed for oils with a
permittivity close to that of the impurities. Moreover, in this case, centrifugation proved also to
be disappointing.
Addition of a suitable soluble compound to an insulating liquid may increase the
breakdown strength or prolong the life by preventing flocculation. The compounds used should
be added in a definite, minute concentration. A colloid chemical stabilizer (such as
anthraquinone which is a chemically stable, heavy aromatic compound) can prevent the
flocculation, whereas the so-called scavengers (such as tin tetraphenyl) may be applied to
remove deterioration products.
The removal effect of natural inhibitors may increase the breakdown strength, but the
rate if deterioration of the mineral oil may thereby accelerated. The action of several inhibitors
appear to consist of tightly binding acids, oil molecule radicals and iron sludge particles and
forming insoluble compounds, or providing impurities with an aromatic cover to prevent
further flocculation.
The breakdown strength depends on the duration of the application of the field, the
waveform of the applied field vs. time and in general on the past history of the insulation. In
liquid dielectrics, with time-lags of a few microseconds (the time it takes for particles to join
into a bridge), the breakdown strength may be shown to decrease dramatically with the
increase of the duration of application. After about 1 millisecond a more constant value of
breakdown strength is reached.
In a well-controlled breakdown or a pre-breakdown discharge, if no additional
carbonization of the oil has taken place, the complexes consisting of impurities may have
disintegrated, which follows that the diameter of particles decreases whereas their number
182
grows. The author derived relations between breakdown strength EB and characteristic size of
particles r as follows: for long-time cases, EB r3/2 =const; for short-time cases, EB r7/4N1/2 =const
where N is the total number of particles. Owing to the disintegration effect, the original shorttime breakdown strength has decreased (from some intrinsic breakdown strength which is ionic
in origin instead of electronic), while the long-time value has increased.
A phenomenon often reported in the measurements of the breakdown strength is the
influence of the gap width between electrodes. In general the strength decreases with the
increase of the gap width, but after the gap distance has reached a magnitude of a few
millimeters it will remain constant.
The effects of space charge were also discussed. The space charge may be ascribed to
ions as well as to colloid particles and permanent dipoles. Space charge may cause the dc
breakdown strength to increase if the space charges are rigidified at the interfaces, which
strongly retard the flow of the colloid particles toward a place of maximum stress.
6 Review of [6]
In spite of the title of the book, the discussions of liquid breakdown only appear in the
last two chapters. The first 18 chapters were devoted to an excellent establishment and
demonstration of ionization and conduction phenomena in electrically stressed liquid. The
author aimed at explaining various experimental facts from fundamental principles, i.e.
combining the microscopic molecular structure and electronic orbit properties and the
hydrodynamic descriptions and the chemical kinetics on macroscopic level. This is quite
successful. So no wonder the author showed his preference on electronic breakdown theory as
a natural extension of his theory on ionization and high-field conduction. Although this theory
183
for breakdown has been rejected, there remains much valuable information in this classic book.
In Chapter 19, the author did not introduce his theoretical ideas. Instead, he reviewed a
lot of previous experimental investigations. The influence of electrode materials, impurities
and additives in the liquid, gas content, degassing of the liquids and electrodes, the duration of
the voltage applied, the rate of increase of the applied voltage and the frequency of ac voltages,
and the effect of temperature and hydrostatic pressure are included in this chapter. In Chapter
20, the author, according to the known experimental results, developed his theory and
compared it with many other existent theories, which will be commented in a later section.
If not explicitly stated, it is impulse breakdown that serves as the main approach to
investigate the liquid breakdown strength. As shown in Figure B.1, there exists a minimum
pulse duration τ0 for which a constant value of the impulse breakdown is obtained. For very
short pulses with duration smaller than τ0, the electrical strength goes downhill with the
increase of pulse duration.
Figure B.1 (from Ref. [6]). Dependence of breakdown strength Ebd (MV/cm) on time τ (μs) in saturated
hydrocarbons with gap separation of 63.5 μm: a, hexane; b. heptane; c, octane; d, nonane.
Besides the dependence on pulse duration, the great amount of experimental work has
pointed out several other quantitative relationships. The most important are:
Breakdown field stress increase proportionally with increase in the density of the liquid,
as shown in Figure B.2.
184
Figure B.2 (from Ref. [6]). Dependence of breakdown strength Ebd (MV/cm) on liquid density ρ (g/cm3) under
various experimental conditions: a, normal paraffin, τ = 1.4 μs; b, single branched-chain hydrovarbons, τ = 1.4 μs; c,
double branched-chain hydrocarbons, τ = 1.4 μs; d, normal paraffin, direct voltage; e, single branched-chain
hydrocarbon, direct voltage; f&g, straight and branched-chain benzene derivatives, τ = 1.65 μs; h, silicons, dc.
The electrical strength of chemical substances with a molecular structure including
branched chains (isomers) is lower than those with a straight chain molecular structure.
Breakdown strength for liquids belonging to the aromatic hydrocarbons is in general greater
than that of saturated hydrocarbons.
The effects of electrode material have also been shown. In Figure B.3, the relation
between breakdown field and electrode spacing is shown for different electrode (in point-plane
configuration) materials (Al, Cu, Cr) in hexane. When the point electrode is negative, there is
no difference for the three materials, but when the point electrode is positive the breakdown
stress increases from Al to Cu to Cr.
Figure B.3 (from Ref. [6]). Dependence of breakdown voltage Vbd (kV) on electrode separation δ (μm) for a number
of electrode materials and cathode shapes: flat cathode: a, Cr; b, Cu; c, Al (flat cathode); d, Cr, Cu, Al (point
cathode).
185
Very interesting results have been obtained during studies of the relation between the
breakdown strength and the number of breakdowns under dc conditions. As indicated by
Figure B.4, this conditioning effect may cause the breakdown strength to increase by about 50%
-100%. After a large number of breakdowns, due to the contamination of the liquid, there may
be a drop in breakdown stress.
Figure B.4 (from Ref. [6]). Dependence of breakdown strength Ebd (kV/cm) on the number of breakdowns N in
transformer oil. The dashed lines indicate the limits of scatter of experimental results.
An increase in the temperature of the liquid usually causes a reduction in the electrical
strength, which can be explained by the reduction of the density and viscosity. The relation
between breakdown stress and temperature for paraffin and silicon oils is shown in Fig. 5. The
dramatic drop near the boiling point of the liquid can also be observed.
The dependence of breakdown field on hydrostatic pressure relies on the amount of air
dissolved in the liquid and absorbed by the electrodes, and also on the duration and polarity of
applied pulse. For pure liquids, the breakdown strength increases with pressure. This book only
provides experiments under low pressure (< 1 atm). However, later experiments indicated that
at pressure of 25 atm breakdown strength will further increase, whereas the mean free path of
the electron, according to electronic breakdown theory, is hardly altered.
186
At very high fields and with such a great dose of radiation (in megarads) that the effect
of ionizing radiation is comparable with that of the electron emission, a significant irradiation
effects has been observed. For example, irradiation caused an increase in breakdown stress of
about 100%-300% for polyethylene at temperatures above melting point.
Adding different substances to the liquid may lead to a decrease (e.g. water) or increase
in breakdown strength. For instance, it has been reported that the addition of iodine to oil in an
amount of 0.01 g/litre increased the breakdown stress by 18%, but a greater amount (about 0.1
g/litre) reduced the breakdown stress by 5%. Great attention has been paid to the possibilities
of increasing the breakdown strength by adding suitable additives. It was found that the proper
addition of p-nitrotoluene to cable oil may increase its electric strength by 48%. The more
volatile additives proved to be more effective than non-volatile ones in liquid paraffin tests.
The effect of selenium was very pronounced and was attributed to the possibility of the
formation of a protective layer on the electrode surfaces. Two distinct optimum values were
found, the lower one for maximum reduction of conduction current and the higher one (one
order higher) for maximum increase in breakdown stress.
The presence of electronegative oxygen in the liquid may also produce a double layer
next to the electrodes which reduces the emission from the cathode. It has been shown that in
hexane the influence of oxygen causes the electric strength to rise from 0.7 MV/cm to 1.3
MV/cm.
Studies of the effect of frequency on breakdown strength in dielectric liquids are of great
importance in radiotechnology. For low frequencies (dc–power freq. ac) the breakdown
strength for hexane and oil increased with frequency by about 60% to 70%. For high
frequencies (> 1 MHz), the breakdown strength fell toward zero with increased frequency. It
187
was supposed that thermal breakdown took place at very high frequencies. On the other hand,
the effect of impurities and additives is more pronounced at low frequencies than at high
frequencies. For oil, it was found that filtration and removal of water increased the breakdown
strength by about 3 times at 50 Hz but only by 1.3 times at frequencies of the order of 100 kHz.
In general it could be said that some theories explain the breakdown mechanism using a
macroscopic interpretation such as heat production in certain places in the liquid especially at
the cathode, the presence of impurities, colloidal suspensions, gas bubbles and vapor bubbles,
non-uniform distribution of the electric field, irregularities on the cathode surface, etc. Other
theories consider the mechanism from a microscopic view and derive the breakdown criterion
on the basis of molecular structure.
The first group refers to experimental conditions in which liquids of a commercial grade
are used, which are not properly cleaned and degassed, and when relatively large conduction
currents and long duration of the fields are applied. Such conditions are used in most of the
industrial and commercial work, and for this reason these theories are acknowledged and find
application. Theories connecting the phenomenon of breakdown with molecular structure of
the liquid refer to experimental conditions where it is possible to observe the physical
mechanisms of the phenomenon regardless of the purity of the liquid. In the author’s opinion,
they form a basis for establishing a breakdown criterion and their study could lead to very
important future applications.
At the end of this book, the author compared various theoretical hypothesizes with
experimental results, which we think is the most valuable part of this book providing a good
basis for future theoretical development of liquid breakdown.
188
7 Review of [7]
This monograph is the first attempt at a comprehensive consideration of electrical
insulation in high-voltage electro-physical systems. The operating conditions of high-voltage
system insulation and the requirements imposed on it are analyzed and the main insulation
design types are outlined in the first part of this book. In the second part, information on shortand long-term electric strengths of vacuum, gas, liquid, solid and hybrid dielectrics as
functions of various influencing factors is presented. Close attention is also paid to an analysis
of various ways to improve the insulating characteristics of dielectrics. The remaining part of
this book is devoted to the design of high-voltage insulation systems. Methods of increasing
working field strengths and calculating the static, volt-second and statistical characteristics of
the electric strength of insulation and the insulation service lifetime and reliability are
considered here.
This is the English version of a Russian book, most of the references of which were
published in Russian. So, we think what this book tells is actually the results from the Russian
(or more exactly, the former Soviet Union) investigators. Factors influencing the electric
strength, according to the author, include dielectric material properties and states (pressure,
density, viscosity, temperature, molecular and supermolecular structures, mechanical stress
condition, etc.), electrode material and state of the electrode surface, contaminations (solid
particles, moisture, and gases dissolved in the liquid and adsorbed on the electrode), polarity
(for dc and impulse), type (for ac, frequency is also a factor) and duration (for pulses) of the
voltage, insulation gap geometry and other environmental conditions. All the material covered
is of great interest to experts in research areas and industries of power systems and electrical
insulation.
189
We only focus on the contents that indicate comparisons of liquid breakdown strengths
under different conditions, or can be directly related to the improvement of electric strength of
liquid insulations. These contents are summarized in Table B.1.
Table B.1. Dependence of electrical breakdown strength of insulating liquids on various factors (extracted from Ref.
[7]).
Factor
Dependence
Implication or Example
Pressure
a. After careful liquid degassing the influence of pressure
on electric strength sharply decreases, according to the
bubble theory; polar and conducting liquids are
exceptions because liquid gases are rapidly produced as a
result of currents and dielectric losses.
b. The effect is much stronger for a homogenous field
than for inhomogeneous field. In the former case gas
accumulated at electrodes and subjected to pressure has
a major effect on breakdown initiation.
c. For long-term applied voltage, the probability of gas
formation increases. Thus the dependence is also
strengthened.
a. For very pure liquids under short-term voltage
exposure, the main effect of temperature on electric
strength is due to the temperature-dependent density.
The electric strength slowly decreases with the increasing
temperature. And the decrease in voltage duration
weakens this effect.
b. For commercially pure liquids containing impurities
and under long-term voltage exposure, the temperature
dependence is mainly due to the temperature-sensitive
moisture and gas contents. In addition, the viscosity,
surface tension and the hydrodynamic flows must be
taken into account. So the dependence may be rather
complex.
It is often desirable to raise the hydrostatic pressure
to increase the electric strength of liquids in the
following cases: 1) for liquids with high electrical
conductivity (water, glycerin, alcohol, etc.); 2) for
large electrode areas (with more homogeneous field);
3) for long voltage pulses (>1 μs).
a. The dependence of electric strength on electrode
material is perhaps due to the variations in the work
function for electrons going from metals to liquids, the
Young’s modulus and thermodynamic characteristics.
b. There was evidence that, the electric strength of liquid
was mainly affected by the anode material. The reduction
in electric strength of cryogenic liquids with decreased
Young’s modulus of electrodes was also revealed.
Electric strength of purified water and hexane for
hemispherical electrodes (0.2 cm in diameter, and
200 μm in separation) made from indicated materials.
Temperature
Electrode
Material
190
Dependence of electric strength of in-service (1) and
dried (2) transformer oil in a standard breakdown
system.
Factor
Dependence
Implication or Example
State of
Electrode
Surface
a. The effect of electrode contamination and oxidation on
the electric strength is two-fold. For short-term voltage
applied, the oxide film increased the electric strength for
short gaps. For long-term exposure, the reverse effect
occurs.
b. The reduced influence of electrode microgeometry due
to a local increase in electrical conductivity of the
medium can be used to increase the electric strength of
gaps with liquid insulation
Negative effect. Filtration is necessary for the
improvement of electric strength.
1. Careful electrode degassing increases the electric
strength of degassed liquids for dc and ac voltages by
15~20%.
2. Shielding the electrode surface by ionic layers and
heating the volume of liquid adjacent to micro-tips by
high-voltage conduction currents are two means to
increase local electrical conductivity.
Negative effect. Drying process is also essential to ensure
the quality of liquid insulation.
Dependence of Ebr on relative humidity for
commercially pure oil (1) and oil with 0.005% of
cellulose fibers (2).
Gap Width
Generally speaking, the longer the gap is, the lower the
breakdown stress will be. However, certain exceptions
have been reported.
Dependence on center electrode radius of Ubr in
transformer oil for an electrode system comprising
coaxial cylinders with an outer-cylinder radius of 100
mm and ac voltage at 50 Hz.
Electrode
Surface Area
Radiation
This effect decreases with decreasing voltage duration.
Large electrode reduces electric strength (lower-law
relation)
In some cases, the dependence of the electric
strength of liquids on the dose or exposure time is
displayed by a curve with a maximum.
Solid Impurities
Moisture
The physical processes involved and therefore the
dependence are extremely complicated.
191
Electric strength of transformer oil for 50-Hz ac
voltage versus clearing method
Factor
Magnetic Field
Dependence
A transverse magnetic field hinders the multiplication of
charge carriers and hence the onset of breakdown.
Implication or Example
Dependence of breakdown voltage of benzene (1 and
2) and toluene (3 and 4) on transverse magnetic field
induction for interelectrode gap length of 1 (1), 1.15
(3), 1.7 (2) and 2 mm (4).
Flow
A liquid flow significantly influences electrical strength
which decreases when discontinuities arise in the
medium and the gas phase is formed in a turbulent flow,
the number of weak regions in the inter-electrode gap
carried by the liquid flow increases, and electrification of
the liquid, changing of the insulator surface and the
electric field distortion due to this changing dominate. On
the other hand, however, the breakdown voltage
increases when bubbles and gas phase nucleation centers
predominantly escape from the strong field zone and
from the hot liquid zone; bridges between the electrodes
formed by solid and gas impurities and moisture drops
are destroyed, and fragmentation of large gas bubbles
and moisture drops into small-scale ones takes place. For
pulses, the increase effect has been found for dried
transformer oil filling in a coaxial cylinder electrode.
Behavior of Ubr (50 Hz) for purified transformer oil
exposed to voltage pulses
(1), dc (2) and effective ac (3) voltages.
Electrode
Coating
a. The positive effect of this method depends on many
factors, including the coating parameters (thickness and
material), the initial state of the electrode surface, the
properties and state of the insulating medium (mainly its
contamination), the electrode configuration and area,
and the voltage type. The increase in breakdown voltage
due to the use of thin dielectric coatings of the electrodes
results from the joint or individual effect of several
factors.
b. In most cases, a positive effect is observed for DC and
AC voltages. For impulse voltages, when the electric
strength of dielectric liquids approaches that of solid
dielectrics and impurity bridges are not formed, the
effect is manifested only weakly. But there are
publications in which the breakdown voltage in this case
can be increased by 20%-25%.
Generally speaking, it has been found that, both
electrodes must be insulated to increase pulsed
breakdown voltage. The positive effect of electrode
insulation intensifies when aromatic additives (like
anthracene) are injected into the oil.
192
8 Review of [8]
Interest in the liquid breakdown under lightning pulses and in particular, internal surges
has quickened in connection with an expansion of working voltages of electric power
transmission lines and substations and the tendency to a decrease in the insulation level of
high-power electrical equipment systems. The knowledge of the electric breakdown of liquids,
however, has not kept pace with the increasing interest and more and more stringent
requirements on liquid dielectric insulation design. This book is devoted to a description of
physical mechanisms of initiation and propagation of pulsed discharges in liquids as well as to
the basic laws describing impulse electric strength of liquids. It can is a specialization of
another book of the author, which we just reviewed. As the author stated in the preface, in the
process of writing, they had generalized the results of modern research and re-analyzed and reexamined a large volume of data on liquid dielectric breakdown obtained in the last decades.
This has provided their deeper understanding and interpretation.
In our opinion, this book can be regarded as a handbook for theoretically modeling the
electrical breakdown phenomena in liquids. At the current stage, Chapter 6 of this book is what
we concern most, which discussed basic laws describing of the impulse electric strength of
liquids. In the subsequent sections, we will introduce the main results respectively.
Duration, shape, frequency and polarity of voltage pulses
In breakdown of liquids in a uniform field at times approximately by an order of
magnitude greater than in gases, an increase in the electric strength is observed with decrease
in the voltage pulse duration. In addition, a decrease in the duration of the applied voltage
pulse decreases the role of gas formation in the discharge ignition and propagation. In short
193
gaps with a uniform field, this is manifested through changes in the discharge mechanisms for
exposure times less than a certain critical one, namely, transition from the discharge from
cathode (the bubble breakdown mechanism) to the discharge from anode (the ionization
breakdown mechanisms or combined). In long gaps, changes in the voltage pulse duration (and,
correspondingly, in the overvoltage magnitudes) are accompanied by changes in the external
shape of the discharge figure and conditions of bush-like figure transformation into a treelike
figure.
For pulses with duration of several nanoseconds, the electric strength of even
commercially pure liquids exceeds 1 MV/cm; it reaches 4MV/cm in a uniform field for
duration t ≈ 4 ns and gap length d=1.25 mm. Moreover, liquids with radically different
composition have electric strengths close in values.
Under exposure to voltage pulses of equal durations the electric strength of liquids
differs for pulses of different shapes demonstrates that the pulse duration is the important but
not unique parameter of the voltage pulse that determines the electric strength of liquids. This
circumstance stimulated a search for voltage pulse parameters that influence the prebreakdown processes in the liquid and, as a result, its electric strength. It was established that
in long air gaps, the character of discharge processes and the breakdown voltage essentially
depend on the slope of the oblique voltage pulses. An increase in the slope (from 0.4 to 600
kV/μs) causes the discharge ignition voltage to increase. However, for extremely small end
radii of tip electrodes, the discharge ignition voltage increases as the pulse slope decreases.
As shown in Figure B.5, for pulse duration of several tens or hundreds of microseconds,
the dependences of the breakdown voltages in insulating liquids on the pulse slope have
complex character.
194
Figure B.5 (from Ref. [8]). Voltage-time characteristics of a transformer oil with tip-plane gap configuration for d =
5 (1), 15 (2), and 25 cm (3).
Under the joint influence of different voltage types applied in succession, the earlier
voltage significantly affects the electric strength in the presence of the later. The electric
strength increases if the polarity of previously applied voltage (pre-stressing) coincides with
that of the applied voltage (for which the electric strength is measured). The maximum effect
reaches tens of percent and depends primarily on the duration and magnitude of previously
applied voltage, the time interval between the previously applied and applied voltages, and the
type of voltage for which the electric strength is measured.
The electric strength of liquid dielectrics at low frequencies (up to several kilohertz)
depends weakly on the frequency. When dielectric losses in a liquid are insufficient to heat the
liquid to temperatures of electrothermal breakdown, the electric strength of the liquid in a
uniform field is independent of the frequency or slightly increases with the frequency. The
latter is typically recorded for moderately pure liquids. The electric strength of commercially
pure insulating liquids for the voltage at the industrial frequency is slightly (10–20%) higher
than for dc voltages. The frequency dependence under a sharply non-uniform field with intense
cavity processes, typically observed at relatively low ac electric fields, is U-shaped at
frequencies of several hundred Hz, as shown in Figure B.6.
195
Figure B.6 (from Ref. [8]). Dependence of breakdown voltage of perfluorohaxane on the frequency in the tip-plane
gap for an inter-electrode distance of 1.9mm.
At high frequencies (103–106 Hz), the breakdown of even weakly polar liquids results
from the intense heat release in the liquid and is characterized by a significant reduction in
electric strength with increasing frequency.
Table B.2 lists the effect of polarity on the breakdown of liquids for long discharge gaps
used in high-voltage equipment.
Table B.2. Effect of polarity on breakdown initiated in various liquids for a tip-plane electrode system at T = 293 K
(From Ref. [8]).
196
Positive polarity always corresponds to the minimum electric strength and hence is most
dangerous to insulation of high-voltage equipment. Only for inter-electrode distances of several
tens of microns, the breakdown voltage of the majority of liquids for positive polarity of the tip
electrode is higher than for negative one. In addition, the polarity effect is much more evident in
liquids with high permittivity. For breakdown of liquids containing electronegative groups or
molecules (for example, carbon tetrachloride, benzene chloride, etc.), the polarity effect is
essentially nonexistent. From Table B.2, we can also see that, the addition of chlorinated
hydrocarbons (the molecules of which possess considerable electron affinity) to transformer oil,
whose breakdown is accompanied by a sizable polarity effect, eliminates almost completely the
polarity effect.
Chemical nature, composition and volume of liquids
The establishment of a relation between the liquid electric strength and the atomicmolecular structure would allow one to predict the dielectric properties of liquids from the
known physical and chemical constants and to seek for and to synthesize the liquid insulation as
well as to use additives improving the dielectric properties of liquids. However, no reliable
relations have been derived by the present time because of the influence of impurities of different
types that are always present in the liquid, a great variety of processes that affect the liquid
breakdown, and the lack of a well-developed theory of the liquid phase of matter. Under pulsed
voltages, the effect of impurity on the breakdown decreases due to inertia of the secondary
processes, but the results obtained allow one to establish only tendencies of changes of the
electric strength for liquids distinguished by those or other physical and chemical properties.
197
Besides, it was demonstrated that rather inconsistent data on the influence of properties and
structure of liquids on their electric strength were mostly due to difficulties in considering the
influence of the electrode surface state.
Under long-term voltage exposure, the electrical conductivity γ of liquids affects
significantly their electric strength. An increase in γ reduces the electric field strength necessary
for the implementation of the electrothermal breakdown mechanism. However there are
contradictions indicating a complex character of the breakdown strength dependence on γ (it also
depends on the field geometry and pulse polarity). For example, Figure B.7 shows the
dependences of breakdown voltage of aqueous NaCl solution on γ for the nanosecond breakdown
in a uniform (Figure B.7a) and nonuniform fields of the tip-plane electrodes (Figure B.7b).
Figure B.7 (from Ref. [8]). Dependence of the electric strength of the NaCl aqueous solution on the electrical
conduction in a uniform field at td = 70 ns and d = 0.02 cm (a) and in a non-uniform field at td = 90 ns and d = 0.015
cm (b) for −T +P (curve 1) and +T −P electrodes (curve 2).
The working mechanism of various additives injected into liquid dielectrics to increase
their electric strength is primary associated with the two effects: a) a decrease in the field
nonuniformity in the insulation gap due to a local increase in the electrical conductivity, or to
198
polarization processes at the interface between the solid and liquid phases (when solid particles
are introduced into a liquid) and b) the effect of additives on the behavior of charge carriers
produced by emission and ionization.
To reduce the influence on liquid dielectric breakdown of electrode microgeometry and
processes adjacent to electrodes, it has been suggested that surface conducting layers be created
whose electrical conductivity decreases smoothly with depth, and whose effective thickness is
significantly greater than the size of micro-inhomogeneities, but less than the gap distance. If the
voltage duration are not too short, the electric strength of the insulation gap is expected to
increase due to the diminished effect of the near-electrode processes that initiate breakdown.
Figure B.8a shows the behavior of the normalized electric strength E/E0 of water with βalanine as a function of the additive concentration (E and E0 denote the 50% breakdown strength
of water with and without amino acid additives). The data were obtained for a high-voltage
oblique-front pulse width of 5 μs, a distance between the plane electrodes of 1 cm, and areas of
the stainless ferrite steel and aluminum electrodes of 30, 110, and 150 cm2. From Figure B.8a it
can be seen that E/E0 is a complex function of amino acid concentration, with details determined
by the electrode material. For the stainless ferrite steel electrodes, E/E0 = f(c) has a maximum at
c = 0.03 mol/L equal to E/E0 = 1.33. For c ≥ 0.06 mol/L, the electric strength of water with the
additive is the same as that of pure water. For the system with austenitic steel electrodes, E/E0 =
f(c) has two maxima at c1 = 0.03 mol/L (E/E0 = 1.48) and c2 = 0.055 mol/L (E/E0 = 1.41). For
aluminum electrodes, the injection of amino acids into water reduces its electric strength over the
entire range of concentrations examined. An increase in the electric strength of water containing
additives is accompanied by a decrease in the standard deviation σ of the breakdown field
199
strength. Minimum values of σ correspond to maximal values of breakdown electric field (Figure
B.8b).
Figure B.8 (from Ref. [8]). Dependences of the relative electric field strength (a) and standard deviation of the water
breakdown field strength (b) as function of the β-alanine concentration for austenite (curve 1), ferrite stainless steel
(curve 2) and aluminum electrodes (curve 3).
The significant influence of the volume of liquid dielectric in a strong electric field on the
electric strength results from the fact that the in the bulk of the liquid strongly affect the
discharge initiation near the electrodes, and subsequent propagation within the gap. The
relationship between electric strength and liquid volume depends heavily on the elemental
composition of the liquid, the prevalence and nature of impurities, the discharge gap
configuration, the electric field, and the exposure time of the liquid.
In general, breakdown field strength was halved when the dielectric volume increased by
two orders of magnitude. Experimental results have demonstrated that breakdown voltage
increases by approximately 22% when the oil volume in a strong electric field doubles with
electrode area remaining unchanged.
200
9 Recent Progress
The main source of the literature is Proceedings of IEEE International Conference on
Dielectric Liquids (1990-2005). Some papers were later published in IEEE Transaction on
Dielectrics and Electrical Insulation from which more papers are chosen to review.
The power frequency insulation breakdown phenomena in pure hydrocarbon liquids
including straight, branched, and ring-type chemical structures with different electrode shapes
and materials was investigated in [9]. The electric strength of n-pentane, n-hexane, n-heptane,
benzene, toluene, xylene, and 2,2,4-trimethyl pentane was determined using brass, copper, and
aluminum electrodes in sphere-plane, sphere-sphere, tip-plane, tip-sphere and tip-tip
configurations. It was found that, n-hexane with copper sphere-plane arrangement yields
maximum electric strength, while n-pentane with aluminum tip-tip arrangement yields minimum
electric strength. Besides this result, the comparative study method applied in [9] also provided a
good example for designers to obtain maximum breakdown strength when many options are
available.
In [10], the effect of forced flow velocity on the breakdown voltage/gap length
characteristics of transformer oil was studied using a needle point and a mesh plane electrode
system. The velocity of the axial (co-field) oil flow varied from 0 to 280 cm/s. For degassed oil
there was a large increase in the breakdown voltage with increasing oil velocity for both voltage
polarities. For O2- and SF6-saturated oils a similar increase in breakdown voltage was observed
only with the point negative. With the point positive, velocities above 90 cm/s had no effect.
Breakdown voltage versus gap length (1-12 mm) characteristics were obtained in [11] for
transformer oil under uniform field. It was observed that, the breakdown voltage increases with
201
increasing oil gap spacing between electrodes, though the average breakdown field decreases.
The breakdown voltage values are higher for aluminum electrodes than stainless steel. The
breakdown voltage for dehydrated oil was improved by about 100% as compared with oil
containing emulsion droplets of water by (0.2% by mass). Variation of breakdown strength with
temperature is very sensitive between 20 and 40 oC (decrease by about 50%), implying that a
cooling procedure could be effective in this case.
Figure B.9 (from Ref. [12]). Breakdown electric field as a function of distance between electrodes with (a) different
material pairs and (b) different impurity concentrations.
It was shown in [12] that modification of interface properties, whether by electrode
material or by introducing impurities, substantially changes the electric breakdown strength of
the electrode-liquid system. As shown in Figure B.9(a), different combination of electrode
materials results in different electric strength; in Figure B.9(b), when electron donor impurity
concentration (butanol) is 5%, electric strength gains maximum improvement.
202
Theoretical research on the effect of molecular impurities on the development of
ionization electron avalanche and on the electrical strength of atomic liquids (liquid Ar, Kr and
Xe) was presented in [13]. The decrease of pre-breakdown voltage was predicted mainly due to
more efficient vibration excitation of molecules by electron collisions. Another quantitative
theoretical study [14] of the intrinsic dielectric strength of condensed helium under cryogenic
temperatures applied the method of the electron kinetic Boltzmann equation to calculate the
impact ionization coefficients and other related transport quantities, which can be further used to
find the breakdown fields and the breakdown formation times. In [15], the field strength needed
for runaway up to a self-sustaining discharge was calculated using an anti-bubble barrier model
for various electrode surface roughnesses. Cathode surface roughness plays a significant
destructive role in electric strength in the low temperature range 2.5-4.5 K.
Using point-plane geometries, with gaps of 5 mm or larger, it was shown in [16] that
typical transformer oils have higher breakdown voltages when the point is negative than when it
is positive. Perfluorinated polyethers were found to produce opposite results when average gap
size is 5 to 10 mm. For larger gaps the sequence was reversed again. The author of [17]
conducted optical and statistical studies of electrical breakdown of n-hexane under a
quasiuniform field of 0.9-3.5 MV/cm (the duration of voltage exposure ranges from 20 ns to 2 μs)
with gaps 25-150 μm in length. It was established that increase in breakdown field with
reduction in gap length takes place in the case of the bubble breakdown mechanism by reduction
of the local electrical field near the cathode surface.
Ref. [19] reported the effect of enforced cross-field flow on the variation of dc
breakdown voltage for transformer oil and point-to-plane electrode geometry with gap length of
200-900 μm. It was shown that cross-field flow is more effective than co-field to increase the
203
breakdown voltage, whereas in the latter case only when the point is positive this effect is
obvious.
Barrier effect on the prebreakdown and breakdown phenomena in long oil gaps was
investigated in [20]. The experimental setup is illustrated in Figure B.10(a). It was shown that the
effectiveness of an insulating barrier, namely the ratio of the breakdown voltage of oil gaps in
presence of barrier to that one without barrier, in a divergent field, is the higher when the barrier
is placed near the sharp electrode (at 0 to 25% of the electrode gap), and when the polarity is
positive. The results are indicated in Figure B.10(b).
(a)
(b)
Figure B.10 (from Ref. [20]). (a) Scheme of the test cell; (b) 50% lightning impulse breakdown voltage vs.
relative position (a1/a) of the barrier for a=50 mm.
Performance of non-homogenous insulating oil mixtures under dc conditions was studied
in [21], which concluded that mixtures have reduced breakdown strength than that of either of
the two oils. In [22], the authors investigated breakdown characteristics of pressurized liquid
nitrogen (LN2) over a very wide range of electrode size. Experimental results revealed that the
breakdown mechanism changed from an area effect to a volume effect when increasing the
204
highly stressed liquid volume in LN2. Moreover, the contribution of area and volume effects to
the breakdown strength in LN2 was discussed.
The standard ac dielectric breakdown test result is generally used as one of the
acceptance criteria for insulating oil and a maintenance tool for high-voltage power transformers
in service. In [23], oil breakdown results were systematically evaluated and compared using
ASTM and IEC standard procedures and varying many of the test parameters such as the shape
and dimensions of the electrodes, the oil circulation, the voltage application procedure, etc. As
shown in Figure B.11, testing procedures have strong influence on the results.
Figure B.11 (from Ref. [23]). Influence of testing procedures on the breakdown behavior of in-service
contaminated oil.
The increase of the electric stress, in large high voltage dc filter capacitors manufactured
with all polypropylene film dielectric impregnated with synthetic hydrocarbons, is limited due to
the high dispersion of the values of the dc breakdown voltage. The paper [24] described the
results obtained adding to the impregnating liquid a scavenger. The dc breakdown voltage
dispersion is reduced. The capacitor dielectric stress is also increased.
205
The effect of co-field oil flow on the direct breakdown voltage in transformer oil using a
point-to-plane electrode geometry for both polarities of the point was investigated in [25]. Tests
were carried out on degassed oil, oil saturated with O2 and with N2 and oil with 1methylnaphthalene and dimethylaniline as additives. The oil flow velocity varied from 0 to 170
cm/s. For degassed oil, N2-saturated oil and oil with DMA as additive, the results show that for
both point polarities the breakdown voltage increases with increasing oil velocity, attains a
distinct maximum value at a certain velocity and then decreases for higher velocities. For O2saturated oil and oil with MN as additive the breakdown voltage increases with increasing flow
velocity and attains a quasi-saturation value for velocities in the range 100-120 cm/s. With N2
and DMA, breakdown voltages were in general lower than those for degassed oil, where as with
O2 and MN they were substantially higher.
Cryogenic liquids are claimed to have a noteworthy impact on the concept of improved
future power equipment. The low boiling temperature of liquid helium or liquid nitrogen offers
the use of superconducting materials. On the other hand, the liquids seem to be interesting basic
insulators with reasonable dielectric performance. Liquid nitrogen and helium are two common
choices. Figure B.12 from [26] gives typical dielectric strength course of insulators with
comparison with others (a) and long term degradation in ac breakdown strength (b).
The experimental investigation in [27] showed the effect of electronegative dissolved
gases on the conduction current level in transformer oil. The degassed mineral oil containing
C8F18 gas exhibits a reduction in the conduction current levels than that of only mineral oil, and
also the maximum stress reaches a higher threshold. The C8F16O/N2 mixture has this effect even
stronger than C8F18. With a hydrostatic pressure, the effects can be further signified.
206
(a)
(b)
Figure B.12 (from Ref. [26]). (a) Typical dielectric strength course of insulators in insulation systems; (b)
long term degradation in ac liquid breakdown strength.
In [28], the authors made effort to evaluate linear alkyl benzene for a new kind of
transformer oil. It was concluded that electrical, chemical and physical along with ageing
characteristics of LAB are comparable to existent transformer oils (the dielectric strength of
LAB is reported twice that of transformer oil). Effects of bubbles with and without dissolved SF6
gas on the ac and lightning impulse insulation characteristics of perfluorocarbon was studied in
[29]. With the bubbles in perfluorocarbon liquid, breakdown phenomena related to bubbles
crossing a uniform field gap studied. It was found that insulation strength with bubbles is
remarkably lower than without bubbles under ac voltage, but not so remarkable under lightning
impulse.
Ref. [30] reported on measurements investigating the dielectric strength of insulating oil
and from very low (-20°C) to increased temperature (+60°C). Different insulation structure
models-board puncture and creepage-were stressed with 1 hour dc step-by-step voltage increase
of reversed polarity each step, until breakdown. The impact of adhesives and their orientation
207
relative to the electric field was investigated. It was noted that at -20°C, the electric strength of
oil becomes critically low.
The effect of emulsion water in liquid hydrocarbons (benzene, toluene, ethyl benzene, pdiethylbenzene, cyclohexane, and heptane) on the conduction process has been studied in [31].
The content of water in the investigated liquids was changed from 0.1 % to 1.0 %, by weight and
microemulsions of water in liquid hydrocarbons were produced ultrasonically. In general,
conductivity monotonically increases when the concentration of emulsion water increases, but in
case of water mixtures with benzene and toluene a deviation from this monotony was observed,
as shown in Figure B.13.
(a)
(b)
Figure B.13 (from Ref. [31]). Resistivity as a function of water content in (a) benzene and (b) toluene.
In Ref. [32], the performance of ester and mineral oil/ester mixtures concerning the
electric behavior was presented. The breakdown voltage of the mixtures is less temperaturedependent than that of the pure mineral oil. The reason is the difference in the water saturation
208
limit. It was suggested that, if the transformer usually operates at very low temperatures, the
application of the mineral oil and ester liquid mixtures offers increased insulation reliability. The
dielectric strength at low temperatures is higher than that for pure mineral oil. The efficiency of
the hydration was checked using ester liquid as insulation or only as water carrier to fry the paper
in a long or short time period. Investigations on the electrical strength properties of oil gaps were
carried out with uniform electrical fields and electrode distances up to 30 mm [33].
Measurements were performed with alternating current (50 Hz), lightning impulses and
switching impulses. It was shown that it is possible to minimize the dispersion to values of about
5 to 6 percent.
The application of insulating liquids together with a solid insulant immersed therein is
essential for some kinds of applications like power transformers. A dominant risk, reducing the
strength of such insulations, is water, thus drying procedures are required to extend lifetime and
operation reliability. Ref. [34] presented new systems, which perform a continuous desiccation
of the insulating system of power transformers during service and are beneficial for insulating
liquids as well as for solid insulations immersed therein. The requirements on the liquid part of
the insulating system are not only the electric and dielectric performance but also the
performance regarding environmental requirements and dehydration capability as well as low in
flammability. It was reported in [35] that, the use of ester liquid Midel 7131, partly or totally
replacing mineral oil, reduces the risk of environmental pollution, increases the lifetime of the
component and reduces the fire risk. Some results concerning the electric and dielectric behavior
of Midel 7131 is presented and pure Midel 7131 as well as mixtures with mineral oil fulfill the
requirements on the electrical performance of liquid insulating materials.
209
Ref. [36] deals with breakdown voltage characteristics of saturated liquid helium, in the
presence of a metallic particle in shape of needle or sphere to obtain insulation design data for
the pool-cooled low temperature superconducting coil and to find the factors dominating the
breakdown voltage. The main results are: 1) foreign particle in liquid helium causes a high stress
field and the phase change of liquid helium and reduces the breakdown voltage by more than
several tens of percents; 2) at higher pressures, breakdown voltage is improved due to inhibition
of bubbles. Ref. [37] is aimed at the improvement of power transformers through the
improvement of the characteristics of mineral oil by mixing this later with other insulating
liquids for transformers namely silicon and synthetic ester oils. A comparison of breakdown
voltage was presented in Figure B.14. This work gives prominence to the mixture mineral oil /
20% synthetic ester oil as a good compromise to get a liquid better than mineral oil alone. In that
sense, it appears that this mixture could improve the power transformer insulation.
The effect or ice on dc pre-breakdown events was investigated using a needle-to-plane
electrode system in liquid nitrogen at 77.3 K in [38]. It was found that breakdown voltage may
be raised due to the attachment of ice to the electrode. In [39], with respect to the electrical
breakdown mechanism in superconducting coils with a finned wire under quenching conditions,
the bubble dynamics and the correlation between bubble behavior and breakdown voltage
characteristics are investigated using a plane-to-cylinder gap with/without triangular fins. The
results shown in Figure B.15 indicate that the gradient force and Maxwell stress strongly affect
the bubble dynamics and bubble shape in the gap. Especially the pronounced gradient force near
the fin tip reduces the stable growth of bubble there. This results in a smaller effect of thermal
bubble on the breakdown voltage, if the fins are formed to avoid electrically the appearance of
bubble in the shortest gap region at higher applied voltages.
210
Figure B.14 (from Ref. [37]). Breakdown voltage evolution of oils and mixtures with 6 measurements.
[Water content (ppm) / Pollution class (NAS 1638)].
(a)
(b)
Figure B.15 (from Ref. [39]). (a) Bubble distribution and dielectric behavior in three cylinder-to-plane
gaps with different cylinder surface conditions near breakdown voltages; (b) Breakdown voltages of three
cylinder-to-plane gaps with different cylinder surface conditions.
211
The lightning impulse breakdown characteristics of various combinations of insulation
material in silicone oil for use in electric power apparatus were investigated in [40], with the aim
of reducing the amount of oil required and thus the cost. Breakdown characteristics were
investigated in a system in which insulating filler was mixed with silicone oil. The relation
between the breakdown strength and the electric field strength was clarified. Based on the
findings, optimum conditions for the use of silicone oil in electric power equipment are proposed.
Recently ester oil dielectrics have been introduced as substitutes for mineral oil for use in
power transformers. These oils have several advantages over other transformer oils as they are
non-toxic, more biodegradable and less flammable. In [41] samples of one hundred ac
breakdown voltages of esters and mineral oil are analyzed to compare their statistical
distributions, in particular whether the lowest observed breakdown voltages are different. The
results in Table B.3 indicate that these oils can be at least as capable as mineral oil for
transformer insulation.
Table B.3. Comparing withstand voltages of non-parametric and parametric methods (from Ref. [41]).
212
10. Some Concluding Remarks
The electrical strength of all dielectric liquids depends on pressure, the dependence itself
depending on the voltage duration, degree of liquid degassing, electrical conductivity and
electrode configuration. However, an increase in pressure changes the conditions of gas
formation, displaces the equilibrium between molecular dissolved gas and gas bubbles toward
the former, reduces gas bubble size and increasing gas pressure inside the bubbles, thereby
hindering the ionization processes. In this way, higher hydrostatic pressure can lead to an
increase in the electrical strength. This can be regarded as the most straightforward way to
increase the breakdown voltage of a liquid insulation.
Interest in electrode coating, a well-known but seldom used method of increasing
breakdown voltage of liquid insulation gaps, has significantly increased over the past few years.
Data on the influence of electrode coatings on the electrical strength of gaps filled with liquids
are inconsistent.
Space charge control aims at reducing the electric field at electrodes by space charge
injection. Qualitatively, space charge distortion of the electric field distribution between parallel
plate electrodes with spacing d at voltage V so that the average electric field is E0=V/d. When no
space charge exists, the electric field is uniform at E0. Unipolar positive or negative charge
injection so that the electric field is reduced at the charge injecting electrode and enhanced at the
non-charge injecting electrode. Bipolar homocharge injection so that the electric field is reduced
at both electrodes and enhanced in the central region. Bipolar heterocharge distribution where the
electric field is enhanced at both electrodes and depressed in the central region. We need to
choose optimum metal/dielectric material combinations to achieve the bipolar homocharge
injection and therefore increase electric breakdown strength, though the electric field is increased
213
in the center of the gap, but breakdown does not occur because the intrinsic strength of the
dielectric in the volume is larger than at an interface where microasperities are often present.
Electrodes of different metals showing differences in the magnitude and sign of the
injected charge. In highly purified water stainless steel electrodes generally inject positive charge,
aluminum injects negative charge, while brass can inject either positive or negative charge. Thus
by appropriate choice of electrode material combinations and voltage polarity, it is possible to
have bipolar homocharge liquid. Past work has shown that using water between a positive
stainless steel electrode and a negative aluminum electrode resulted in homopolar charge
injection from both electrodes that increased the electric breakdown strength in water by 40%
over the opposite voltage polarity with no charge injection.
Impurities, generally speaking, play a negative role in the breakdown strength of
dielectric liquids. However, there are exceptions. The first example is additive to prevent the
reduction in dielectric strength due to aging. Other work has demonstrated the paradoxical fact
that conducting nanoparticle suspensions in transformer oil have superior positive electrical
breakdown to that of pure oil while insulating nanoparticles offer no insulation advantage over
pure oil. Electrical breakdown testing of magnetite nanofluid found that for positive streamers
the breakdown voltage of the nanofluids were almost twice that of the base oils during lightning
impulse tests. Also, the propagation velocity was reduced by approximately 36% by the presence
of nanoparticles in the oil. This is perhaps because fast electrons from molecular ionization are
collected by conducting nanoparticles which then act as slow charge carriers resulting in higher
breakdown voltages and slower electrical streamers.
214
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218
C
Pictures of the Kerr electro-optic measurement system
As shown in Figure C.1, the small Kerr cell (6 inches tall and 8 inch diameter) was used
for all of the propylene carbonate measurements at the beginning of the research project. The cell
has a fixed rod in the bottom and moveable rod through the top that each electrode screwed onto,
respectively. The top cover can be removed to fill or empty the cell with dielectric fluid. The
high voltage cable is connected to the top moveable rod. The alignment of the electrodes to
provide a parallel surface gap, in line electrodes, and secured electrodes that could not move
when applying high voltage was a tedious process.
Figure C.1. Small Kerr cell with optical components.
219
When conducting transformer oil measurements and breakdown tests the small Kerr cell
quickly resulted in several problematic issues. When voltages were high enough to cause arcing,
there was a high probability that arcing would happen between the electrode and the grounded
test cell because the electrodes were near the sharp edged window viewing ports. The sharp edge
causes a high electric field because the electric field lines want to terminate perpendicular to the
conducting surface of the small test cell. The close proximity of the electrode ends causes nonuniform stressing of the glass windows. The small cell is more susceptible to changes in the
ambient temperature and moisture because the volume contains a small amount of dielectric fluid
causing difficulties in having uniform conditions for taking data. The processing and filtering of
the oil requires the cell to be completely emptied, disassembled, cleaned, refilled, and
reassembled. The small cell size and design make it difficult to add additional sensors. A larger
existing chamber was modified into a larger Kerr cell. Further improvements were made by
adding additional sensors and alignment components that were not able to be incorporated into
the small Kerr cell. The large Kerr cell has an electrode holder that provided some difficulties in
repeatable and accurate alignment of the gap spacing because the top moveable rod was difficult
to secure and adjust accurately to provide the correct gap spacing. The placement of the electrode
gap was horizontal resulting in contamination and suspended particles being trapped in the
region of the gap.
The large Kerr cell shown in Figure C.2 has a larger volume which allows for larger
electrodes making the light path along the electrode surface longer, thereby accurately measuring
the effect of electrical birefringence.
The electrode ends are farther from the viewing window and the opening ports have more
rounded edges. The changes in dielectric fluid condition due to ambient temperature and
220
moisture are less significant than in the small Kerr cell. The large cell can be heated and cooled
via a circular pipe containing cooling fluid that spirals around the outside of the cell, but this
functionality was not used. A filtering process was added to provide more uniform transformer
oil conditions. The variable speed magnetic drive pump was used to circulate the oil. The
circulating path is the pump intake to the cell bottom, 1µm filter, and pump outtake via flexible
tubing to the top of the dielectric fluid level 180° across from the intake. The dielectric fluid can
be filtered for long durations of time. A vacuum process was used to remove air bubbles
suspended in the dielectric fluid before Kerr measurements were taken. The presence of a
vacuum during the test allowed for any suspended particles formed after high voltage was
applied to be removed from the liquid volume between the electrodes. The cell had two vertical
rods inside the bottom that provided approximate alignment to the viewing windows. An
electrode holder was designed and built to provide accurate and precise alignment of the
electrodes. The holder design was an iterative process and the start and final holders are shown
in Figure C.3.
The holder could be adjusted manually, and placed the electrode gap vertical to allow for
suspended particles and bubbles to be easily removed from the measurement region. The large
size of the test cell can incorporate additional sensors such as temperature, conductivity, and
filter oil flow. The disassembly and reassembly of the cell requires bolts on the top cover to be
removed or replaced, respectively. Cell alignment can be difficult due to the size and weight
when dielectric fluid is added. Further cell alignment is provided via a gantry plate and turn
table. The gantry plate slides horizontally along two precision metal guide bars. The turn table
between the cell and gantry plate permits the cell to be rotated. Various ports into the cell allow
entry for additional sensors such as pressure, temperature, etc.
221
Figure C.2. Large Kerr cell with utility grade capacitor used for substation power factor correction.
Figure C.3. Electrode holder (beginning design) and electrode module (final design).
222
A properly conditioned dielectric fluid is one main requirement for repeatable and
reliable Kerr electro-optic measurements. This includes fluid filtering, circulation, and if needed
temperature and moisture control. In this setup fine-tuned temperature and moisture control was
not needed. A flexible input and output pipe circulate the fluid in the cell which can be manually
directed between the electrode gap to clear any particles that may be trapped. The oil is
continually run through a McMaster-Carr standard one cartridge filter (Model: 44185K65) with
canister filter (Model: 44185K41) rating of 3µm to clear any contamination particles that were
suspended in the fluid or introduced via various means. The filter has a gauge (Model:
44185K11) indicator to show when the filter needs replacement. The filter and pump are shown
in Figure 9. The pump is a variable speed magnetic gear pump drive from Cole-Palmer with an
inlet and outlet port of ¼ inch. Two control valves are used to isolate the pump, filter, and tubes
from the cell. This provides easier replacement of oil conditioning equipment, filling or
emptying of fluid.
Figure C.4. Filter canister (3 µm filter rating) and variable speed gear pump drive for oil filtering and
circulation.
223
224
D
List of publications from thesis research
•
X. Zhang, J. K. Nowocin, and M. Zahn (2012), “Effects of AC Modulation Frequency and
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X. Zhang and M. Zahn (2013), “Kerr Electro-optic Field Mapping Study of the Effect of Charge
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X. Zhang and M. Zahn (2014a), “Fractal-Like Charge Injection Kinetics in Transformer Oil
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X. Zhang and M. Zahn (2014b), “Electro-optic Precursors of Critical Transitions in Dielectric
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X. Zhang (2014), “Electro-Optic Signatures of Turbulent Electroconvection in Dielectric
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