Supercritical fluids for High Power Switching

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Supercritical fluids for high power switching
Zhang, J.
Published: 01/01/2015
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Zhang, J. (2015). Supercritical fluids for high power switching Eindhoven: Technische Universiteit Eindhoven
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Supercritical fluids for High Power Switching
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit
Eindhoven, op gezag van de rector magnificus, prof.dr.ir. F.P.T. Baaijens,
voor een commissie aangewezen door het College voor Promoties in het
openbaar te verdedigen op dinsdag 19 mei 2015 om 16.00 uur
door
Jin Zhang
geboren te Jiangsu, China
Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van de
promotiecommissie is als volgt:
voorzitter:
1e promotor:
2e promotor:
copromotor:
leden:
prof.dr.ir. A.C.P.M. Backx
prof.ir. W.L. Kling
prof.dr. U.M. Ebert
dr.ir. E.J.M. van Heesch
Prof.Dr.-Ing. A. Schnettler (RWTH Aachen)
Dr. M. Seeger (ABB Corporate Research)
dr.ing. A.J.M. Pemen
prof.dr.ir. R.P.P. Smeets
dr. R.A.H. Engeln neemt plaats als reservelid
prof.dr. U.M. Ebert neemt tijdens de promotiezitting de taken van wijlen prof.ir. W.L. Kling
over
To my parents and my husband Lei
This research is supported by the Dutch Technology Foundation STW, which is part of the
Netherlands Organization for Scientific Research (NWO), and which is partly funded by
the Ministry of Economic Affairs. Within this context it is also supported by the companies
AnteaGroup, DNV-GL, ABB, and SIEMENS.
Printed by Ipskamp Drukkers.
Cover design by Jin Zhang.
A catalogue record is available from the Eindhoven University of Technology Library.
ISBN: 978-90-386-3840-9
Copyright © 2015 Jin Zhang, Eindhoven, the Netherlands
All rights reserved.
C ONTENTS
Contents
Summary
1
2
3
Introduction
1.1 Plasma in supercritical fluids
1.2 Research goal . . . . . . . .
1.3 Research approach . . . . .
1.3.1 Experimental work .
1.3.2 Modeling . . . . . .
1.4 Dissertation outline . . . . .
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1
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Supercritical fluids and insulating media
2.1 Short review of conventional insulating media . .
2.1.1 Breakdown in conventional media . . . .
2.1.2 Recovery of conventional media . . . . .
2.2 Supercritical fluids . . . . . . . . . . . . . . . .
2.2.1 State equation . . . . . . . . . . . . . . .
2.2.2 SCF properties . . . . . . . . . . . . . .
2.3 Applying supercritical media . . . . . . . . . . .
2.3.1 Chemical applications . . . . . . . . . .
2.3.2 Plasma applications in supercritical media
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High power switching
3.1 The challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Existing solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Vacuum and gaseous state switches for pulsed power applications .
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CONTENTS
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Experimental investigation of breakdown and recovery in SCFs
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Breakdown voltage analysis . . . . . . . . . . . . . . . . . .
4.2.1 Vb under slow pulses (1.66 kV/ms) . . . . . . . . . .
4.2.2 Vb under moderate pulses (2.5 kV/μs) . . . . . . . . .
4.2.3 Vb under fast pulses (2 kV/ns) . . . . . . . . . . . . .
4.3 Dielectric recovery analysis . . . . . . . . . . . . . . . . . . .
4.3.1 Experiment under 1 kHz voltage source . . . . . . . .
4.3.2 Experiment under 5 kHz voltage source . . . . . . . .
4.4 Current interruption analysis . . . . . . . . . . . . . . . . . .
4.4.1 Parameter settings . . . . . . . . . . . . . . . . . . .
4.4.2 Experimental results . . . . . . . . . . . . . . . . . .
4.5 ICCD image of discharge in SC N2 . . . . . . . . . . . . . . .
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Theoretical modeling of discharge and recovery in SCFs
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
5.2 Simple analytic model . . . . . . . . . . . . . . . .
5.2.1 Model description . . . . . . . . . . . . . .
5.2.2 Model Formulation . . . . . . . . . . . . . .
5.2.3 Results and discussions . . . . . . . . . . . .
5.3 Electric field across the gap . . . . . . . . . . . . . .
5.4 Extended physical model for discharge in SCFs . . .
5.4.1 General model description . . . . . . . . . .
5.4.2 Model Formulation . . . . . . . . . . . . . .
5.4.3 Streamer-to-spark transition phase . . . . . .
5.4.4 Discharge and post-discharge phase . . . . .
5.4.5 Numerical conditions . . . . . . . . . . . . .
5.4.6 Results and discussions . . . . . . . . . . . .
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . .
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Comparison of experiment and model
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3.3
3.4
4
5
6
3.2.2 Solid state switches for pulsed power applications .
3.2.3 Circuit breakers in power networks . . . . . . . .
Design of supercritical switches . . . . . . . . . . . . . .
3.3.1 Simple SC switch (A) . . . . . . . . . . . . . . .
3.3.2 Multi-functional SC switch (B) . . . . . . . . . .
3.3.3 SC switch (C) with larger gap width . . . . . . . .
Arc interruption testing circuit . . . . . . . . . . . . . . .
3.4.1 Circuit principle . . . . . . . . . . . . . . . . . .
3.4.2 Real setup . . . . . . . . . . . . . . . . . . . . . .
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CONTENTS
6.2
6.3
6.4
7
Breakdown voltage in SCFs . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2.1 Principle of Paschen’s law . . . . . . . . . . . . . . . . . . . . . . 91
6.2.2 Violation of simple Paschen’s curve . . . . . . . . . . . . . . . . . 93
6.2.3 Comparison of experiments with theories . . . . . . . . . . . . . . 94
Dielectric recovery in SCFs . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.3.1 Validation of simple analytic model - comparison with an air plasma
switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.3.2 Validation of extended physical model - comparison with SC switch
measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Conclusions and Recommendations
103
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.2 Recommendations for future work . . . . . . . . . . . . . . . . . . . . . . 105
Appendix
A1. State Equation of nitrogen . . . . . . . . . . . . . . . . .
A2. Integrator of the triggering signal generator . . . . . . . .
A3. Calibration of current measured by Rogowski coil . . . .
A4. Cylindrical coordinate in Euler system . . . . . . . . . . .
A5. Simulation of electron-ion recombination in N2 discharge
A6. Ionization and dissociation mechanisms . . . . . . . . . .
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107
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113
114
Bibliography
119
List of publications
139
Acknowledgement
143
Curriculum Vitae
145
S UMMARY
Supercritical fluids for high power switching
For high power switching media the most important properties are high dielectric strength
and fast dielectric recovery. The performance of the popular insulating media: gases, liquids, and solids, is limited by specific disadvantages. The dielectric strength of gases is
relatively low. Although liquids have higher dielectric strength, the performance of liquid
insulators is affected by bubble formation and chemical degradation. Solid insulators can be
damaged by the thermal and electrochemical breakdown. In high voltage power networks,
a discussion about replacing the dominating insulating medium for circuit breakers (CBs)
- Sulphur hexafluoride (SF6 ), due to its global warming potential and toxic degradation
products, is ongoing. Enormous research has been carried out for exploring new insulating
media, while no promising alternatives have yet been found.
In this thesis work we propose a new medium for high power switching: supercritical
fluid (SCF). SCF refers to a state of fluid where the temperature and pressure are both
above a critical value. In the SC phase fluids have special characteristics, superior to those
in either gas or liquid phase: high density and high heat conductivity, large mass transfer
capability such as low viscosity and high diffusivity. The superiority of SCFs has already
been highlighted in the field of chemistry, due to the unique property around the critical
point: significant change of the density, diffusivity, and solubility with a minor variation
of pressure or temperature. Based on these properties, we foresee significant advantages of
SCFs as switching media in switches for high pulsed power applications.
In this thesis work we investigate the three most important properties of SCFs in high
power switching from both an experimental and a theoretical perspective:
• dielectric strength;
i
ii
S UMMARY
• dielectric recovery;
• current interruption capability.
SC nitrogen (N2 ) is chosen to be the studied medium in our work, because of its relatively low critical pressure (3.396 MPa), critical temperature (126 K), environmental harmlessness, and its easy availability.
Via a literature survey, SCF with its basic properties is introduced. State-of-the-art
applications of SCFs in the conventional chemistry field and in the plasma discharge area
are reviewed and discussed. Based on the data obtained from a literature survey and from
the prediction of a simple analytic model, several SCF insulated switches are designed and
manufactured.
Various pulsed voltage sources are designed and built for the experimental analysis
of the SC switches. The dielectric strength and subsequent dielectric recovery of the SC
switches are investigated under these sources. The impact of the parameters such as the
SCF pressure, flow rate, gap width, and voltage rise rate on the breakdown voltage and
recovery is studied under repetitive operation.
Arc quenching capability is an important property for the high-energy switches in the
power system. A simple synthetic circuit is designed and built, to investigate the current
interruption capability of a SC switch. The experimental results reveal that the SC switch,
though with non-moving electrodes and small gap width, can successfully interrupt the
current at a low current amplitude. Higher medium pressure, larger gap width, and more
intense flushing through the gap help the current interruption in the SC switch.
The experimental results show good switching performance of SC N2 switches:
• dielectric strength of 60 − 180 kV/mm (obtained in low repetition rate situation),
which is higher than most of the dielectric media;
• dielectric recovery completed within 200 μs after short pulse breakdown in a submillimeter gap;
• successful interruption of oscillating current (peak amplitude 20 − 40 A and damps
to zero at a few milliseconds) within 2 ms after the breakdown in a millimeter gap.
For the in-depth understanding of the breakdown and recovery in SCFs, an extended
physical model has been developed to simulate the complete discharge and recovery process
in a SC N2 switch. The time and spatial evolution of the temperature, pressure, density, and
velocity during the discharge process is investigated. The recovery breakdown voltage of
the SC switch has been estimated from the results of the model.
iii
We compared the experimental results of breakdown and recovery in SC N2 switches
with the simulated values. Good consistency exists between the measured values and the
theoretical calculations. The Paschen’s curve calculated from discharge constants is consistent with the measured dielectric strength in SC N2 at low pd values (product of pressure and
gap width). At high pd values Paschen’s curve gives too high values, whereas the streamer
inception criterion with enhanced ionization gives good prediction of the dielectric strength
in SC N2 for high pd. The modeled recovery breakdown voltage in SC N2 is slightly lower
than in the experimental results. Possible reasons are discussed and improvement of the
present model is proposed.
Conclusions are drawn based on the work carried out in this dissertation, and recommendations for the future work regarding the application of SCFs in high power switching
area are given.
C HAPTER 1
I NTRODUCTION
1.1
Plasma in supercritical fluids
Supercritical fluid (SCF) refers to a state of fluid where the temperature and pressure are
above the critical point. In this SC area, liquid and gas states are united and undistinguishable. SCFs have been studied since long in chemistry fields, as an alternative to the
traditional solvents [1–3]. Besides the conventional chemical application, SCFs recently
attracted attention in the area of plasma discharges, due to the combined superior transport
properties of SCFs with the high reactivity of plasmas [4].
Plasma in various SC media has been observed and studied, for different purposes. Figure 1.1 illustrates the images of plasma in several SCFs [5–7]. Plasma in SCFs is an interesting subject which covers applications for a wide area: SC plasma chemistry, SC plasma
power switches, and dense planet atmosphere, etc.. Figure 1.2 gives a diagram of the application fields of plasmas in SCFs.
Plasma chemistry studies in SCFs mainly focus on the near-critical region, where the
properties of the fluid change significantly with a minor variation of pressure or temperature. Reported work concerning plasma chemistry in SCFs comprises conversion of organic compounds [8] and plasma microreactor for synthesis of nanomaterials and diamondoids [9–11]. The research on plasma discharges in SCFs also involves lightning phenomena on extra-terrestrial planets such as Venus and Saturn, where the surface atmosphere is in
SC condition due to the temperature and pressure [12]. The potential of SCFs in high power
switching applications, though less explored, is attractive to us, because of the expected
unique breakdown and recovery characteristics of SCFs.
1
2
1. I NTRODUCTION
(b)
(a)
(c)
(c)
(d)
Figure 1.1 – Plasmas generated in different SCFs. (a) lightning in the Saturn interior atmosphere
[5]; (b) in SC argon [6]; (c) in SC carbon dioxide; (d) in SC nitrogen [7].
1.2
Research goal
The goal of this work is to explore the potential of SCFs for applications in high power
switching. The research area is indicated by the highlighted parts in figure 1.2. SCFs
combine the advantages of liquids and gases, therefore, SCFs have high dielectric strength
and fast dielectric recovery. Density of a SCF is liquid like and the viscosity is gas like.
Heating a liquid above boiling conditions causes vapor bubbles, while heating a SCF does
not cause vapor bubbles. This is the important property for applications in high power
equipment. Other important advantages of SCFs for high power applications as a switch
include high heat capacity, high diffusivity, and high heat conductivity.
The main potential applications of SCFs in high power switching area are insulating
media in high repetition rate pulsed power switches and replacement for sulfur hexafluoride
(SF6 ) in high voltage circuit breakers (HVCBs) in power networks. SCFs operated pulsed
power switches are expected to allow higher power and higher repetition rates than those
achievable with gaseous spark gaps, based on the advantages of SCFs mentioned above. For
pulsed power applications such as pollutants treatment with plasma discharges, high peak
voltage and high operation frequency help improve the efficiency of pollutant treatment
[13]. Therefore utilization of SCFs as switching media for the pulsed power switches in
plasma purification systems can achieve more compact switches. In power networks there
is the desire of replacing SF6 in HVCBs, because SF6 is an extreme greenhouse gas with
global warming potential 23,900 times that of carbon dioxide (CO2 ) [14]. Besides, the
3
1.3. R ESEARCH APPROACH
Plasmas in
supercritical fluids
SC plasma power
switch
Power
networks
SF6 free switch
gears
Supercritical
plasma chemistry
Pulsed power
systems
Synthesis of nanoparticles
[9-11]
Dense planetary
atmosphere [12]
Conversion of
chemical
compounds
Pulsed power
processing [7]
Conversion of
organic
compounds [8]
Ignition &
stabilization in
combustion [136]
Plasma
purification
Figure 1.2 – Application area of plasmas in supercritical fluids. The research area in this thesis
work is high-lighted.
decomposition products of SF6 are extremely toxic. SCF could be an ideal alternative to
SF6 , due to its high dielectric strength, expected fast dielectric recovery, and environmental
harmlessness.
In this thesis work we investigate the dielectric strength and recovery capability of SCF
switches from both an experimental and a theoretical perspective. SC nitrogen (N2 ) is
chosen to be the studied medium, because of its relatively low critical pressure (3.396 MPa),
low critical temperature (126 K), environmental harmlessness, and its easy availability.
1.3
1.3.1
Research approach
Experimental work
The experimental work on an insulating medium includes investigation of the dielectric behavior such as dielectric strength and dielectric recovery, inspection of the parameters of the
medium such as the temperature, density, and electron/ion mobility during/after discharges,
and inspection of the parameters of the switch materials such as materiel electrode erosion.
The dielectric strength of a medium is tested by applying high-voltage waveforms across
two electrodes separated by the medium. Various waveforms can be applied: positive or
negative polarity; direct current (DC), alternating current (AC), or pulsed voltages. The
mechanisms and conditions that determine the dielectric strength have been investigated and
reported extensively in literature. For example, geometry of the electrodes [15], electrode
4
1. I NTRODUCTION
surface roughness [16], rate-of-rise of the voltages, voltage polarity [17], gas pressure [18],
gas temperature, and gas flushing velocity, etc.. The main experimental approach for the
dielectric recovery investigation in power switches is a two-pulse technique [19, 20]: the
first pulse causes the breakdown of the switch and the second pulse tests the dielectric
recovery voltage.
The inspection of the plasma parameters is also important for the study of the high power
plasma discharges. Laser shadowgraph [21], Schlieren imaging [22], and spectroscopic
investigation [23] are the common experimental approaches.
Recent data about the breakdown voltage in SCFs, e.g. SC CO2 , SC argon (Ar), SC
helium (He) and SC N2 , have shown the very high dielectric strength of SCFs [17, 24–27].
But the performance of SCFs concerning dielectric recovery has rarely been studied.
In this thesis work we have chosen the following approaches for the experimental study
of the SCFs switching:
• investigating the dielectric strength of SC N2 switches by applying different pulsed
sources at low repetition rates;
• testing the dielectric recovery of SC N2 switch under repetitive operation mode with
pulsed voltage sources up to 5 kHz;
• estimating the current interruption capability of the SC switch with an arc interruption
testing circuit;
• investigating the discharge radius in SC N2 using an intensified CCD camera, providing important data for the theoretical modeling.
1.3.2
Modeling
In plasma discharge research, modeling is an important approach to gain insight in the
processes and interactions. A number of modeling tools have been developed to explain
the phenomena of plasma in various insulating media, especially in gases. According to the
time evolution of a discharge, the models focus on separate discharge stages:
avalanche-to-streamer stage: from the avalanche initiation by a single electron to the
formation and propagation of streamers [28, 29];
sparking (arcing) stage: from the streamer bridges the gap onward, until the formation
of a complete conducting channel in the gap [30–37];
discharge and post-discharge stage: after the spark (arc) channel formation, until the
energy decay and dielectric recovery of the switch gap [38–40].
In the early stage of a discharge, the generation of avalanches and streamers concerns complicated plasma physics and gas dynamics. Literature on modeling methods for this stage
includes: Monte-Carlo-collision [41, 42], Particle-in-cell [43], Boltzmann equation solving [44, 45], etc.. The time scale of the streamer stage is normally nanosecond to several
1.4. D ISSERTATION OUTLINE
5
microseconds, depending on the studied media and applied electric stress. The modeling
work found in literature concerning this time range is mainly devoted to the breakdown
process in atmospheric pressure gases and studies of plasma processing.
The arcing stage and discharge and post-discharge stage have a much longer time scale
than the streamer stage. Simulation of arcing and recovery in CBs is a typical example. The
time evolution of the properties of the gases in CBs is inspected till the turbulent mixing
phase, which is normally in millisecond to second range. Methods for modeling of discharges in CBs include: Computational fluid dynamics [46] and Turbulent modeling [47].
Since the nanosecond time scale of the streamer stage is rather short compared to the whole
simulation time, the complicated streamer phase is mostly neglected in the modeling of
discharge in CBs.
Among the well-studied numerical models, few of them have combined the modeling
of these stages and simulated the complete discharge process inside the media. There is no
published report on modeling of the discharge processes in SCFs. A model covering the
complete discharge process in SCFs would be very interesting in order to learn the impact
of the early stage on the late recovery phase in an electric switch.
In this thesis work we have developed two models to simulate the complete discharge
process in SCFs:
• a simple analytic model which employs the mechanisms of adiabatic expansion and
heat transfer in succession, aiming on roughly predicting the recovery time in a SCF,
hence providing important design data for the SC switches;
• an extended physical model, taking the simulation results in streamers and experimental results in SC N2 as input parameters, which simulates the complete discharge
process in SCFs.
1.4
Dissertation outline
Chapter 2 briefly reviews the starting point of the thesis work: conventional insulating media and SCFs with their present applications. The breakdown and recovery mechanisms of
gases, liquids, and solids in electric switches are generally discussed. Via a literature survey, SCF with its basic properties is introduced. State-of-the-art applications of SCFs in the
conventional chemistry field and in the plasma discharge area are reviewed and discussed.
Chapter 3 discusses the main challenges of high power switching. The existing solutions
for high power switches in pulsed power switching and power networks are reviewed. As
an alternative, the design and experimental layout of SCF insulated switches is introduced.
Chapter 4 studies the switching characteristics of SCFs experimentally. The dielectric
strength and the subsequent dielectric recovery in SC N2 switches are investigated. The
capability of current interruption of the SC switch is investigated under an arc interruption
testing circuit. Additionally the spark channel radius in a SC N2 switch is estimated by an
6
1. I NTRODUCTION
intensified CCD camera, providing important input parameters for the theoretical analysis
in chapter 5.
Chapter 5 develops two physical models for the theoretical analysis of the discharge and
recovery process in a SCF switch. A simple analytic model roughly predicts the recovery
time in SC N2 , and provides design data for the SC switches applied in this work. The electric field across the gap is estimated from the measured arc current. An extended physical
model simulates the complete discharge and recovery process in SC N2 . The time and spatial evolution of temperature, pressure, density, and velocity of the SCF during the discharge
process is investigated.
Chapter 6 compares the theoretical estimation with the experimental results. The breakdown voltage in SC N2 is observed to deviate from the prediction by the simple Paschen’s
curve in high pd region, while matching well with the calculations based on the streamer
inception criterion with enhanced ionization. The validation of the two physical models introduced in chapter 5 is tested by comparing the simulation results with the measurements
in real plasma switches.
Chapter 7 summarizes the main conclusions and gives recommendation for future work.
C HAPTER 2
S UPERCRITICAL FLUIDS AND
INSULATING MEDIA
2.1
Short review of conventional insulating media
The breakdown and recovery processes differ in each insulating medium. High dielectric
strength and fast subsequent recovery are considered as the most important criteria for an
insulating medium in high power switches. The performance of the popular insulating media: gases, liquids, and solids, is limited by specific disadvantages. The dielectric strength
of gases is relatively low. Although liquids have higher dielectric strength, the performance
of liquid insulators is affected by bubble formation and chemical degradation. Solid insulators can be damaged by the thermal and electrochemical breakdown. In this section the
breakdown and dielectric recovery in gaseous, liquid, and solid state insulators is briefly
surveyed and discussed.
2.1.1
Breakdown in conventional media
The dielectric strength of an insulating medium depends on its specific characteristics, and
is influenced by the external environment. Figure 2.1 summarizes the dielectric strength of
the selected gaseous, liquid, and solid state insulators under two types of voltage sources:
lightning pulse and 50 Hz AC source. In the following the breakdown mechanisms in these
conventional insulating media as well as the factors affecting the dielectric strength are
reviewed.
7
8
2. S UPERCRITICAL FLUIDS AND INSULATING MEDIA
Breakdown
voltage
[kV/mm]
Lightning pulse
AC breakdown
Mineral Air
oil
Liquid
N2
SF6
Liquid PTFE
He (thin film)
Figure 2.1 – Summary of the dielectric strength for selected insulators: air (0.5 − 4 bar) [48],
mineral oil [49, 50], Liquid N2 [51, 52], SF6 (1 − 3 bar) [53], liquid He [54], and Solid (PTFE
thin film) [55,56] under AC source and lightning pulses. The solid line and dashed line represent
the envelope of breakdown voltage under 50 Hz AC source and lightning pulse, respectively.
Gas insulators
Leaving lightning aside, gas discharges have been studied since the 18th century, with early
reports dating back to 1705. Only till about two centuries later, the explanations were
founded that we know today, aided by the discoveries of the breakdown law in 1889 by
Paschen, the electron concept in 1897 by Thomson, and the ionization and discharge laws
in 1900 by Townsend. The streamer breakdown mechanism was discovered and explained
in 1939 and in 1940 by Loeb, Raether and Meek [57], [58]. The dielectric strength of gases
is dependent on the density/pressure, and in practical applications is influenced by various
factors such as the electrode shape, the electrode surface condition, the rising slope of the
applied voltage, and the polarity of the impulses, etc.. In the scenario of gas mixtures, the
dielectric strength depends also on the fractions of gas components [59].
Electrical breakdown of a gas is the result of self-sustained avalanche processes that
depends on the relative activity of electron generation and loss mechanisms [60]. The
breakdown mechanism can be classified into two types: Townsend breakdown and streamer
breakdown. The criterion for distinguishing Townsend and streamer mechanism is the electron number in the first avalanche: if the number of electrons is larger than a critical value
Ncr , then the breakdown transits from Townsend to streamer mechanism. For both breakdown mechanisms, the famous similarity law: Paschen’s law [61] states that the breakdown
voltage is a function of the product of pressure and gap width (the pd value). Under high
pressure and small gap width, the breakdown voltage of gases tends to be lower than prediction by the Paschen’s law [53]. Similar effects are reported from breakdown studies in
2.1. S HORT REVIEW OF CONVENTIONAL INSULATING MEDIA
9
liquids at normal pressure. Extra factors need to be considered when calculating the dielectric strength of gases under elevated pressure and micro gaps. We will discuss this issue in
detail in chapter 6.
Air, N2 , CO2 [62, 63], and SF6 are applied for high power switches. SF6 is widely
employed in the power networks as an excellent insulating and arc quenching medium for
HVCBs and gas insulated substations (GIS) [64,65]. However, due to the greenhouse effect
of SF6 , many countries have noticed the huge impact of SF6 on the environment. Efforts
to reduce the emission of SF6 are ongoing, among which the replacement of SF6 in CBs
is a major task. Mixing of SF6 with other gases such as N2 or Ar reduces the amount
of SF6 needed. Research on the mixture of SF6 with inert gases includes SF6 +air [66],
SF6 +CO2 [67], SF6 +Ne (neon) [68], SF6 +N2 [69], SF6 +He [70], SF6 +Ar, and SF6 +H2
(hydrogen) [71]. At present a SF6 -N2 mixture is often applied. Such mixtures are nonflammable and those containing 50 − 60 % of SF6 have dielectric strength up to 85 − 90 %
that of pure SF6 [59].
Investigations have also been proceeded to study other insulating media for full replacement of SF6 [62,72–77]. No promising alternative has yet been found within the same pressure and temperature range. However, the main relative superiority of SF6 over other gas
species like N2 and CO2 in dielectric strength diminishes when pressure is above 9 bar [78].
Liquid insulators
Liquids such as liquid He [79, 80], liquid N2 [51, 52], and mineral oil [49, 50] are applicable
for high power switches. The breakdown phenomena in liquid dielectrics have been extensively studied in the past a few decades [81, 82]. Although being complimented for higher
dielectric strength compared to gaseous insulators, liquid dielectrics have their own disadvantages, which make their applicability less common in switches (mineral oil has been
applied but been replaced by gaseous insulators completely). The main disadvantages of
liquids in switches are bubble formation during the breakdown process [83–85], chemical
degradation, poor self-healing properties, and field emission from small protrusions on the
electrode surfaces [85–87].
Under short impulses with pulse duration up to several hundred nanoseconds, the formation and propagation of the ionization waves is the main mechanism of breakdown in liquids [88]. For longer impulses, the formation of gas bubbles due to the liquid evaporation
becomes the dominant process [88]. Bubbles, i.e. gas cavities with lower dielectric strength
than liquids, are generated a few microseconds after the voltage is applied [89]. During the
discharge process, streamers first develop in these bubbles rather than in the liquid phase,
which process is known as partial discharge [90]. After the bubbles deform due to ionization and plasma phenomena therein, the breakdown transits from lower density region into
liquid phase, and finally leads to the breakdown of the liquid medium.
The dielectric strength of liquid insulators is dependent on the properties of the liquid (pressure, temperature, and impurities), and on the external environment (applied field
strength, pulse duration, and electrode surface material, roughness, and area). In general,
the longer the pulse duration, the more the breakdown field of liquids decreases [91]. Under
10
short impulses (< 0.1 μs), the dielectric strength has a weak dependence on the temperature
and pressure, but a strong dependence on the pulse duration [88]. The temperature, pressure, and pulse duration play more significant role under pulses longer than 1 μs: higher
temperature [92], lower pressure [93], and longer pulse duration [91] deteriorate the dielectric strength of the liquids. The bubble formation process happens at lower temperature in
a liquid with impurities than that in a pure liquid [88]. With more rough electrode surface,
larger effective surface area, lower work function and higher hardness of the electrode, the
dielectric strength of the liquid decreases [87, 94].
Solid insulators
Breakdown strength
Solid insulators are used almost in all electrical equipment, forming an integral part of electrical devices especially when the operating voltage is high [95]. The breakdown field of
a solid insulator is in order of 10 − 100 kV/mm, depending on the thickness of the used
dielectrics [55, 96]. Regarding the number and duration of repetitive voltage applications,
the breakdown mechanisms in solid dielectrics are classified in figure 2.2 [95]. For short
pulses, time of the order of 10−8 seconds, breakdown in the solids can be caused by the
migration of the free electrons through the lattice of the dielectric, named ’intrinsic breakdown’. Under longer duration of the electric field, when the continuously generated heat
due to conduction currents and dielectric losses is greater than the heat dissipated, the solid
undergoes so called ’thermal breakdown’ [95].
Intrinsic breakdown
streamer
thermal
electrochemical
ͳͲି଼ s
‫ ݃݋ܮ‬time
Figure 2.2 – Breakdown mechanism of solids with time of repetition of applied voltage.
The dielectric strength of solid insulators might be affected by the material quality (e.g.
cavities in the solid) [97] and by the external factors (e.g. temperature [98] and humidity [99]). Under situation of gas cavities in the solid, the electric field in the cavities will
be εr times higher than that in the solids, which makes the gas cavities break down at lower
voltage. Under repetitively applied voltages, the breakdown in the cavities develops step by
step and finally leads to the complete breakdown of the solid. It is known as breakdown
due to treeing [100]. Accompanied by the cavities breakdown, local thermal instability and
chemical degradation of the material may occur, resulting in the slow erosion of the material
and cause a breakdown below desired value. This breakdown process is known as ’electro-
2.1. S HORT REVIEW OF CONVENTIONAL INSULATING MEDIA
11
chemical breakdown’ [95]. Thermal breakdown becomes increasingly more important at a
temperature above 400 K [98]. The environment humidity enters the dielectric by diffusion
processes, resulting in a remarkable change of both permittivity and dielectric losses, which
reduces the dielectric strength of the solid materials [99].
2.1.2
Recovery of conventional media
The dielectric recovery of an insulating medium can be defined as the re-establishment of the
dielectric strength after breakdown. Insulating media have their specific dielectric strength
in undisturbed situations, as mentioned in section 2.1.1. Under applied electric field, a
medium goes from insulating to breakdown, accompanied by conducting channels building
up in the inter-electrode gap. During the discharge process the temperature of the medium
in the channel increases dramatically due to the energy input. After the arc extinction, the
total energy of the medium changes due to the gas dynamic expansion and heat transfer
from the hot channel to the environmental medium. The thermodynamic properties of the
medium in the discharge channel recover and finally the dielectric strength of the medium
can recover.
The experimental results of the recovery time in selected insulating materials are summarized in table 2.1 [20,101–105]. Typical gas insulators like air, N2 , and Ar have recovery
times typically in the order of ten to hundred milliseconds [106]. Various factors e.g. gas
pressure, gap width, gas flushing velocity, and input energy can influence the recovery time
of the gases. Chemical decomposition products and metallic vapor from the electrodes also
play a crucial role in recovery of the media.
Flushing of liquids through the gap can help remove the vapor bubble, hence reduce
the recovery time of liquids [107]. However, too much flushing in a liquid reduces the
dielectric strength, due to the transition from laminar to turbulent flow [91]. From data
collected in various experiments [91, 101, 107], it is found that even though with optimized
flow, the maximum available repetition rate of a water discharge switch can only reach
around 2 kHz [101].
The repetition rate of the solid-state switches can be in the MHz range with average
power in the order of kilo Watts [108–110]. In solid switches such as IGBTs with voltage
rate above 4.5 kV, the practical switching frequency is generally lower than 1 kHz, due to
switching loss limitations [111,112]. Intensive cooling by bulky forced air or liquid cooling
systems is required for these solid-state switches during operation [113].
Gap width [mm]
Pressure [MPa]
Flow rate [cm3 /s]
Current [kA]
Recovery time [ms]
Max. repetition rate [Hz]
Condition
Gap width [mm]
Pressure [MPa]
Flow rate [cm3 /s]
Current [kA]
Recovery time [ms]
Max. repetition rate [Hz]
Condition
9
110
0.79
0.13
1.48
0.3
−
7
143
Ar [102]
2
500
2.96
0.06 − 0.13
0.1
0
0.4
0.6
−
−
−
−
1k
1.4 k < 1 k
Water [101]
Propylene carbonate
(C4 H6 O3 ) [105]
0.2
0.1
0.3
−
−
< 10
160
6.3
0.1
0.8
70
14.3
0.4
Insulator
200
5
0.1
1.2
0.4
−
−
100
10
0.14
900
1.1
0.1
2.7
700
1.4
0.4
1000
1
3.7
0.1
65 − 70
0.26
−
2
11
>8
> 10
< 125 < 100
Synthetic air [103]
2
> 2.5
< 400
N2 [104]
Insulator
Ar-H2 mixture [102]
SF6 [20]
(95% − 5%)
0.13
≤ 80
0.1
0.79
2.96
0.5
0.3
−
−
3
25
40
15
8
0.6
0.6
0.3
>1
67
125
1.7 k 10 k 3.3 k < 1 k
Table 2.1 – Overview of the recovery rates in water, hydrogen, SF6 , air, Ar, Propylene carbonate, and N2 .
12
13
2.2. S UPERCRITICAL FLUIDS
2.2
Supercritical fluids
Pressure
A fluid can be found in three states: gas, liquid or supercritical fluid (SCF), depending on the
combination of the fluid parameters. Above the critical temperature Tc and critical pressure
pc , specific for each fluid, a fluid becomes supercritical, as can be seen in figure 2.3. Many
pressurized gases are actually in SCF sates, for example N2 in a gas cylinder above 3.4 MPa
is acting as a SCF.
Solid
Pc
Fluid
Critical
pressure
[MPa]
Critical
temperature
[K]
H2 O
CO2
He
H2
Ar
N2
Air
21.8
7.38
2.27
1.28
4.90
3.40
3.77
647
303
5.20
33.3
151
126
132.6
Supercritical
fluid
Liquid
Critical point
Gas
Triple point
Tc
Temperature
Figure 2.3 – Idealized phase diagram of a single substance and the critical pressure (pc ) and
critical temperature (Tc ) of the selected fluids.
The critical point is the point corresponding to the critical temperature Tc and critical
pressure pc , above which the distinction between the liquid and gas (or vapor) phases diminishes. The values of these parameters slightly vary across reports due to the experimental
difficulties in the critical region as well as the modeling problems [114]. In this work we
use the values of N2 reported in [114]:
Tc = 126 ± 0.01 K;
pc = 3.3958 ± 0.0017 MPa;
ρc = 313.3 ± 0.1 kgm−3 (= 11.1839 ± 0.014 mol · m−3 ) .
(2.1)
In the SC phase a fluid has special characteristics that are superior to those either in gas or
liquid phase, as will be discussed in detail in the following.
2.2.1
State equation
The general state equation of a fluid can be expressed using the Helmholtz energy α with
independent variables of density ρ and temperature T by equation [114]:
α (ρ, T) = α 0 (ρ, T) + α r (ρ, T),
(2.2)
14
where α 0 (ρ, T) stands for the ideal gas contribution to Helmholtz energy; α r (ρ, T) is the residual Helmholtz energy corresponding to the influence of inter-molecular forces. Pressure
of the fluid p can be calculated as the ideal gas contribution plus a correction term given by
the derivative of the residual Helmholtz energy:
r ∂α
,
(2.3)
p = ρRT 1 + δ
∂δ
τ
Pressure [MPa]
in which R is the molar constant, δ = ρ/ρc the reduced density, and τ = Tc /T the reduced
temperature. The detailed equations for α 0 (ρ, T) and α r (ρ, T) for N2 (the studied medium
in this work), and the partial derivatives in equation (2.3) are given in appendix A1.
Pc:
3.3958
Figure 2.4 – Phase diagram of N2 in the range of temperature 86 − 306 K and pressure up to
20 MPa, calculated by state equation (2.3).
Figure 2.4 illustrates the phase diagram of N2 in form of pressure versus density up to
20 MPa, within the temperature range of 86 − 306 K. Below the critical temperature Tc ,
N2 has either gas status (when above critical pressure) or liquid status (when below critical
pressure). N2 changes from other phases to the SC phase when the temperature and pressure
satisfy T > 126 K, p > 3.4 MPa.
The parameter range of SC N2 in the case of electrical discharge applications is in the
region: 300 K < T < 104 K, 5 MPa < p < 50 MPa, because we work at room temperature
but during discharges temperature and pressure will increase considerably. A reference
equation was developed, valid for SC N2 between 250 K and 350 K and pressure up to
30 MPa [114]:
10
p = ρRT(1 + ∑ ik Nk δ ik τ jk ),
k=1
with the parameters given in table 2.2.
(2.4)
15
Table 2.2 – Parameters used in the state equation of N2 , equation (2.4).
2.2.2
k
Nk
ik
jk
1
2
3
4
5
6
7
8
9
10
−0.409226
0.583733818
−0.132040812535 × 101
0.854602646673 × 10−1
0.207794266769
0.112593667 × 10−1
−0.604379290 × 10−1
0.567224683 × 10−2
−0.496167879 × 10−2
0.572786636 × 10−2
1.0
1.0
1.0
2.0
2.0
3.0
3.0
4.0
6.0
6.0
−1.0
−0.875
1.625
0.125
3.5
0.0
2.875
−0.125
−1.0
−0.875
SCF properties
Properties attractive in traditional applications
The unique properties of SCFs open the way for applications such as efficient reaction
media in chemical applications. In the near-critical region of a fluid, properties change
significantly with a minor variation of pressure or temperature [1]. The most well-known
property of SCFs in this term is their controllable solvent strength.
Solubility represents the solvent strength of a substance in a solvent. The solubility
parameter δ can have a direct impact on the reaction rate, yield, design, and economy
of the process [115]. Depending on the processes of interest, either high solubility (e.g.
in supercritical extraction process) or extremely low solubility (e.g. in supercritical antisolvent precipitation processes for particles manufacture) is required [115].
Around the critical point, the solubility parameter of a fluid can be finely tuned over
a wide range, with a small variation in either isothermal pressure or isobaric temperature
[116]. This unique feature of the solubility in SCFs makes them important reaction media
in chemical reactions that need precise process control or reversibility. Extreme examples
of this feature are processes in which SC CO2 extracts a bond component into the CO2 .
After releasing the pressure, the dissolved material can easily be separated (used e.g. in
decaffeination, dry cleaning, and herbal extraction).
Properties attractive in high power switching
The performance of a high power switch strongly depends on the characteristics of the
insulating medium. SCFs have the following favorable characteristics that are relevant to
high power switching:
– similar to gases: low viscosity, high diffusivity, and self-healing;
16
– similar to liquids: high dielectric strength, high heat capacity, and high thermal conductivity.
A comparison of the order of magnitude of the physical properties for common insulating
media in the three phases is given in table 2.3. Figure 2.5 plots the profiles of the viscosity, thermal conductivity, diffusivity, and specific heat of N2 in the range of temperature
of 110 − 290 K and pressure up to 40 MPa (covering gas, liquid and SC phases). In the
following these properties are briefly introduced and the advantages of SCFs are discussed.
Table 2.3 – Comparison of the order of magnitude of the properties for common insulating
media in gas (at standard temperature and pressure) and liquid phases and SC N2 . The value of
diffusivity is the order of magnitude figure for N2 in range of T = 70 − 500 K, p = 0.1 − 80 MPa.
Gas at STP
SC N2
Liquid
Density
Viscosity
Diffusivity
[m2 /s]
Heat
capacity
[106 J/m3 /deg]
Thermal
conductivity
[10−3 J/m/s/deg]
[kg/ m3 ]
[μPa · s]
1
100
500
10
50
100
10 − 300
2 − 60
1−2
1
100
500
20
100
200
Viscosity of a fluid measures the tendency to dissipate energy when disturbed from equilibrium by the imposition of a flow field [1]. The viscosity of a fluid η can be expressed
with equation [118]:
η = η 0 (T) + η r (τ, δ ),
(2.5)
in which η is the dynamic viscosity, η 0 the dilute viscosity corresponding to low pressure
gas (typically one atmospheric pressure), η r the residual fluid viscosity, δ and τ the reduced
density and reduced temperature. The detailed calculation of η 0 and η r of N2 can be found
in [118]. Viscosity for a SCF is almost the same as in a gas and it is 10 times less than a
liquid [119]. The viscosity of liquids has weak dependence on the temperature, while for
SCFs temperature can affect the viscosity in a considerable way [1].
Thermal conductivity of a fluid is defined to be the quantity of heat transmitted through
a unit thickness in a direction normal to a surface of unit area, due to a unit temperature
gradient under steady state conditions. Similar to the calculation of viscosity, thermal conductivity λ of a fluid can be calculated as the function of temperature and density with
equation:
λ = λ 0 (T) + λ r (τ, δ ) + λ c (τ, δ ),
(2.6)
in which λ 0 is the dilute gas thermal conductivity, λ r the residual fluid thermal conductivity,
λ c the thermal conductivity critical enhancement. Detailed calculation of λ 0 , λ r and λ c for
N2 can be found in [118]. The thermal conductivity of a fluid is significantly enhanced in
17
−4
1.4
x 10
(a)
1.2
100 K
Viscosity [Pa*s]
1
110 K
0.8
130 K
0.6
170 K
0.4
250 K
210 K
0.2
290 K
0
0
5
10
15
20
25
30
35
40
0.16
(b)
Thermal conductivity [W/m/K]
0.14
0.12
100 K
0.1
110 K
0.08
130 K
0.06
170 K
250 K
210 K
0.04
290 K
0.02
0
0
5
10
15
20
25
30
35
40
(c)
3
Diffusivity [m2/s]
10
2
10
290 K
250 K
1
10
210 K
170 K
130 K
100 K
110 K
0
10
0
5
10
15
20
25
30
35
40
3
10
Heat capacity cp [J/mol/K]
(d)
2
10
130 K
100 K
110 K
170 K
210 K
250 K
290 K
1
10
0
5
10
15
20
25
Pressure [MPa]
30
35
40
Figure 2.5 – Comparison of the (a) viscosity, (b) thermal conductivity, (c) diffusivity, and (d)
specific heat of N2 in gaseous (blue dots), liquid (green dots) and SC states (red dots), reproduced
from the NIST Standard Reference Database [117].
18
the ’near-critical region’ (T ∼ Tc , p ∼ pc ) as well as in the ’extended critical region’ (up to
T/Tc = 2) [1].
Diffusivity stands for the capability of the random movement of a fluid from an area of
higher concentration to an area of lower concentration. In a gas undergoing breakdown, the
higher the diffusivity (υ), the faster the heat is transferred from the high temperature gas in
the spark channel. Diffusivity of a SCF, though lower than a gas, can be considerably higher
than a liquid [120]. The diffusivity of N2 used in this work is reproduced from [117].
Heat capacity is the measurable physical quantity of heat energy required to change the
temperature of the fluid by a given amount. The higher the heat capacity (cp for isobaric
value and cv for isochoric value), the smaller the temperature changes under given deposited
energy. The detailed equation for the heat capacity of SC N2 is given in appendix A1.
From the survey of the properties we can see that the properties of SCFs combine the
advantages of gases and liquids. The combined properties lead to the favorable capability of
high dielectric strength and fast dielectric recovery. In the following the traditional chemical
applications of SCFs as well as the research proceeded in the plasma discharge area are
discussed.
2.3
2.3.1
Applying supercritical media
Chemical applications
SCFs have drawn much attention in the chemistry field as alternatives to the traditional reaction media. The clustering phenomenon or local density enhancement is regarded as a
fundamental feature in SCFs and their mixtures. In the clusters the member molecules are
bounded to each other with relatively weak inter-molecular forces. The life time of an average cluster (∼ picoseconds) is much shorter than that in solids and liquids [121]. Cluster
formation generally influences the solution structure and affects transport properties such
as mass transfer coefficients. This characteristic makes SCFs applicable in sensitively controlled reaction conditions (e.g. rates and pathways), which is impossible with traditional
solvents. In industrial applications the SCFs are employed as separation, material production and reaction media [1].
The industrial applications for SCFs as solvents include SCF extraction [122], SCF
drying [123], polymer processing using SCFs [124], oxidative destruction of toxic waste
[125], hydrogenation of organic compounds, [126], chemical synthesis for nano-particles
[127], and other applications. SC CO2 is the most utilized SCF in such applications, due
to the advantage of convenient critical temperature, non-inflammability and non-explosive
properties.
2.3. A PPLYING SUPERCRITICAL MEDIA
2.3.2
19
Plasma applications in supercritical media
Besides the traditional chemical applications, SCFs, typically SC CO2 , also attracted attention in the electrical discharge area, due to the unique characteristics of plasmas generated
in SCFs. Research on plasma discharges in SCFs focuses on experimental investigations,
while the theoretical analysis is less explored. The studies on plasma discharges in SCFs
can be classified into two main groups, based on the temperature of plasma: non-thermal
plasmas and thermal plasmas.
Non-thermal plasmas in SCFs
Non-thermal plasmas generated in SCFs, which combine the superior transport properties
of SCFs with the high reactivity of plasmas, have been extensively studied. The mostly
studied SCFs for non-thermal plasma are SC CO2 [3, 128, 129], SC Xe (Xenon) [9], SC
water [8], and SC Ar [130]. The reported applications comprise the conversion of organic
compounds [8] and plasma micro-reactors for synthesis of nano-materials and diamondoids
[9–11]. In this section we give a short overview of the state-of-the-art applications of nonthermal plasmas in SCFs, as well as the research carried out on non-thermal SCF plasmas.
Low temperature plasma in sub-critical water generates active species (.H, .OH, ion,
and free electron) which have high reactivity, thus can be used for the conversion of organic
compounds such as phenol and aniline. [8] proceeded the experiments of the degradation of
phenol in a sub-critical water solution (in non-catalytic condition) with plasma discharges.
During the experiment 60 − 150 kV peak voltages were applied to a gap of 0.1 mm width,
in a reaction cell (900 mL total volume) filled with solution. The feed solution was prepared
by dissolving of phenol or aniline using the distilled water. Experimental results show that
the degradation of phenol increases with the number of plasma discharges, and reaches a
conversion percentage of 17 % after 4000 shots.
In contrast to atmospheric-pressure CO2 environments, in which no carbon materials
could be fabricated, it is possible to fabricate various carbon materials, such as amorphous
carbon, graphite and nanostructured carbon materials, using SC CO2 as a processing medium on a raw starting material [10]. Experimental results reveal that in the vicinity of the
critical point, fabricated carbon nanostructured materials have the largest quantity. Varying
voltage frequency has impact on the conversion percentage of nanostructured materials.
Besides surveying the industrial applications, numerous research work on non-thermal
plasma discharges in SCFs has been carried out. The studied aspects of SCFs in non-thermal
plasma include corona onset, and streamer formation and propagation.
The corona inception phenomenon in SCFs and its dependence on voltage polarity and
electrode configuration are important for the design of efficient plasma reactors. Measurements of corona onset voltages in CO2 in various phases, under negative and positive polarities were performed in [3,17]. The results with point/plane electrode under negative polarity
reveal that the corona onset voltage in CO2 is independent on the medium pressure in the
gas and SC phase, while in liquid phase it increases with higher liquid density [131, 132].
20
For negative polarity, very little corona or other partial discharge activity was observed for
voltages below the breakdown voltage.
Streamers are essential components in pulsed corona discharge applications. The initiation and branching of streamers in the reaction medium are considered to have impact
on the process efficiency. Via methods of fractal analysis and Schlieren experiments, the
streamer initiation, streamer branching, and streamer length in SC CO2 were investigated [133–135]. The streamer initiation voltage under negative pulses is found to be lower
than that under positive pulses. Under both positive and negative voltage polarities the
streamer initiation voltage increases with the density in gas phase, while in liquid and in
SC phases it is independent on the density and keeps almost constant [134]. The complexity of the streamer branching is observed to be higher in SC phase than that in liquid and
in gas phases. The streamer length in SC CO2 is reported to be dependent on the applied
voltage, the fluid density, and the polarity of applied voltage, varying from a few to tens of
micrometer (at applied peak voltage 20 kV and gap width 5 mm): the larger the density, the
shorter the streamer length [133, 134].
Thermal plasmas (breakdown in SCFs)
The complete breakdown in SCFs leads to a thermal plasma. Thermal plasma in SCFs is
less explored compared to non-thermal plasma. A reported application is the supercritical
mixing and combustion in rocket propulsion [136]. Studies on the breakdown phenomena
in SCFs have been done mostly in SC CO2 [129, 131, 137, 138] and a few in SC He [139],
SC H2 O [140], SC air [141], and SC Xe [142]. In the following the breakdown delay
time, breakdown voltage, and the influencing factors on the breakdown voltage in SCFs are
reviewed.
Breakdown delay time was investigated in SC CO2 [131]. Experiments were performed
under two different CO2 temperatures: 305 K and 373 K. The experimental results in SC
CO2 show that up to a density of 90 kg/m3 (pressure 4 − 5 MPa), the breakdown delay
time increases with the density, while beyond this point the delay time suddenly drops to a
value which is much lower than that at 90 kg/m3 [131]. This phenomenon is observed in
near-critical region at CO2 temperature of 305 K, and in SC region at temperature 373 K.
Although the reason for the sudden drop of the breakdown delay time is not clear yet,
random molecular clustering around the critical point might be responsible for the speeding
up of breakdown process.
Breakdown voltage in CO2 up to the SC state at around room temperature was experimentally investigated [137, 143, 144]. The measured breakdown voltage in CO2 reveals
that the dielectric strength of CO2 increases with the density [143]. Experimental results
in [137, 143] show that under both DC and pulsed voltage, in low gas density, the measured breakdown voltage agrees with the prediction by Paschen’s law, while in higher density region, the measured value deviates from Paschen’s curve and tends to saturate in SC
phase [137]. The breakdown voltages in the SC phase are more scattered compared to the
gas phase, and seem not to be dependent on the density anymore. The possible reasons for
the lower than calculated breakdown voltage are suggested to be the influences of the mo-
2.3. A PPLYING SUPERCRITICAL MEDIA
21
lecular clusters and space charges [137, 145]. The reason for the saturation of breakdown
voltage in SC phase was assumed to be the field emission on the tip of protrusions on the
electrode surface.
Experimental results in CO2 including the SC phase also show that the breakdown
voltage experiences a local minimum near the critical point of a fluid under DC voltages
[128]. The local minimum dielectric strength near the critical point is presumed to be caused
by the locally enhanced ionization phenomena caused by the molecular clusters with lower
ionization potential or accelerated electrons in in-homogeneous (low density) region [141].
An interesting observation must be pointed out that under pulsed voltage sources, the local
minimum on breakdown voltage around the critical point is not obvious in CO2 [143]. However, the experiments of micro-discharge (with gap width of 25 μm) in SC air [141] observe
a local minimum on breakdown voltage around the critical point, under nanosecond-pulses.
A possible explanation for the conflicting observations in [143] and [141] might be: the
locally enhanced ionization near the critical point is not sufficient to reduce the breakdown
voltage in a gap larger than millimeter range. But in a micro-gap such as 25 μm, the locally enhanced ionization did play significant role, which causes the local minimum of the
breakdown voltage also under pulsed voltage.
C HAPTER 3
H IGH POWER SWITCHING
3.1
The challenges
High power switching is essential in high power applications to control and limit the power
flow and to protect the power network against abnormal situation. The development of
modern industry demands larger and faster high power switches. The technical requirements such as current rating, voltage rating, and maximum repetition rate (for pulsed power
switch) are continuously increasing, although the emphasized parameters may vary with
specific applications. For example the development of high voltage and extra high voltage
transmission systems demands switches e.g. circuit breaker (CB) with larger power capability. In pulsed power applications such as corona gas purification pulsed power switches
with higher repetition rates are desired.
In the pulsed power technology field the pulsed switch is an essential element in the
chain that generates and transmits high voltage pulses. The load can be a plasma reactor, a
switch requiring triggering signals, or equipment under high voltage/current test, etc.. The
technical requirements for these switches are: high insulation strength during off-mode, low
resistance during on-mode, large current rating, high voltage rating, fast switching time (low
jitter), allowing high repetition rate switching, fast recovery after switching, low inductance,
self-healing medium, long life time, and accepting large overloads.
The vital characteristics of CBs include: short switching time, high current rating, fast
arc quenching, rapid dielectric strength regaining, long service time, and safe operation. In
modern power networks, the development of direct current (DC) transmission systems and
the increasing distributed energy generation bring more challenges to the power switches in
the systems [113,146]. CBs in DC systems are more difficult to operate compared to the AC
CBs. The reasons are: 1) there is no natural current zero-crossing point in the DC system,
and 2) DC CBs need to dissipate large amount of energy stored in the inductance of the
system [147]. The increased short-circuit power resulting from increased distributed energy
23
24
3. H IGH POWER SWITCHING
generation requires faster reaction time, higher current rating, and more frequent current
interruption of CBs than before, especially in MV and HV networks [113, 146]. In addition
to the technical requirements, from environmental conservation point of view, CBs should
minimize the use of environmentally hazardous switching media, typically, SF6 in HV and
EHV CBs.
3.2
Existing solutions
In pulsed power systems, both gaseous (and vacuum) state switches and solid state switches
are widely employed and have their own advantages and drawbacks. A comparison of the
switching voltage, switching current, repetition rate, firing jitter, and turn-on/-off time of
selected gaseous and solid state switches in pulsed power applications can be found in table
3.1.
Gas and vacuum pulsed switches have relatively simple design, higher power capability
and longer service time compared to the solid state pulsed switches. The disadvantages of
gas insulated pulsed switches are the large jitter, strong dependence on the switch design
and insulating material, and massiveness. Solid state pulsed switches have advantages of
stable operation, compact design, low maintenance cost, low jitter, and high repetition rate.
However, the maximum capable switching current and voltage of solid state pulsed switches
are lower than those of gaseous and vacuum pulsed switches. In practical applications the
favorable property of high repetition rate of solid state pulsed switches has to be weighted
against the high dissipation and either low switching speed or low current capability [148].
Since the first prototype described by Thomas Edison in 1879, high energy switches
such as CBs in power networks have been developed for over one hundred years. The
rated switching capabilities increased dramatically with generations of CBs. Classic CBs
are mechanical switches insulated with gases or liquids. Solid-state CBs nowadays are
also more and more popular in low and medium voltage level power networks, due to their
advantage of shorter switching time (microsecond range) than that of the mechanical CBs
(millisecond range) [146]. However, the material cost and the cost caused by losses and
maintenance of solid state CBs are higher than those of the mechanical CBs. Furthermore,
extra costs for cooling and system controls is another disadvantages of solid CBs compared
to the mechanical CBs [146].
In section 3.2.1-3.2.2 we give a brief overview of the state-of-the-art gaseous and solid
state pulsed power switches. The development of CBs in power networks is surveyed in
section 3.2.3.
3.2.1
Vacuum and gaseous state switches for pulsed power applications
The exciting period for development of vacuum and gaseous state switches for high power
applications was from beginning of the last century till the 1980s. Various types of gas
switches appeared and all have their own characteristics. The commonly employed vacuum
and gaseous state switches include:
SiC Schottky diode
MOSFET
SI Thyristor
ETO Thyristor
SiC GTO
(optically triggered)
20 A
1A
165 A
< 1 kA
100 A
∼ 100 A
20 A
100 − 360 A
≤ 6.5 kV
15 kV
1 − 2.2 kV
80 kV
1.2 kV
1.2 kV
6.5 kV
10 kV
12 kV
700 kA
−
30 kV
100 kV
1 kHz
1 MHz
1 kHz
5 kHz
-
20 kHz
100 Hz
1 kHz
-
∼ kHz
∼ kA
30 kV
-
-
2 − 40 ns
< 1 ns
> 5 ns
∼ kHz
100 kV
20 − 250 μs
100 kA
2 − 10 kA
≤ 10 kA
2 − 30 kA
5 − 20 kV
≤ 100 kV
3 − 32 kV
-
Jitter
50 − 100 ns
1 − 5 ns
5 ns
-
< 1 kV
Cold cathode
switch
Vacuum tubes
Thyratron
Pseudo
spark gap
Gas filled
spark gap
Laser triggered
spark gap
Ignitron
Corona
stabilized switch
IGBT
SiC n-IGBT
SOS diode
JR diode
Repetition
rate
10 Hz
1 kHz
1 kHz
Current
Voltage
Switch type
200 ns
toff = 5 − 10 ns
∼ ns;
toff = 0.5 − 2 ns
∼ ns;
1.25 − 40 ns
35 ns
∼ 200 ns
70 ns
-
-
-
-
-
Turn-on time
Table 3.1 – Comparison of the properties of selected pulsed power switches.
[161]
[110, 162, 163]
[164, 165]
[166]
[167]
[108]
[109]
[158, 159]
[160, 161]
[156]
[153, 157]
[155]
[154]
[150]
[150, 151]
[152, 153]
[149]
References
3.2. E XISTING SOLUTIONS
25
26
Cold cathode devices - a category of vacuum insulated switches with very simple
design, normally for triggering other larger devices. The typical operation voltage is several
hundred Volt [149]. The disadvantage of such a switch is the large firing jitter: typically
20 μs in day light and a 250 μs in darkness. Triggered vacuum gaps are applied up to
50 kV, have very short and constant trigger delay but repetition frequency of approximately
1 Hz.
Thyratron - a type of gas filled tube used as a high power electrical switch and controlled rectifier. The H2 thyratron is a typical example. A H2 thyratron can switch up to
100 kV voltage, a peak current of few kilo amperes, with firing jitter of 1 − 5 ns [150, 151].
The repetition rate of the H2 thyratron is up to 1 kHz [150].
Pseudo spark gap [152] - a new thyratron-type of switch capable of high speed switching. Commercial pseudo sparks have switching parameters of: voltage 3 − 32 kV, peak
current 2 − 30 kA, and pulse repetition rate 1 kHz [168]. The jitter of a pseudo spark gap is
normally a few nanosecond [150].
Gas filled spark gap - a type of switch with simple design, usually applied in high
voltage pulse generators. The insulating media can be high or atmospheric pressure N2 ,
air, SF6 , H2 , or even liquids. The operation parameters are up to 100 kV voltage, 100 kA
current [154], and a few kHz repetition rate. Laser triggered [155] and field-distortion
triggered [169] spark gaps have jitters in the sub-nanosecond range.
Ignitron - a mercury vapor switch in which an arc is induced between an anode and a
mercury pool cathode. The structure of the switching tube and the mechanism of ignition
play dominant roles in the performance of an ignitron. Typical ignitrons can switch up to
100 kA current, 10 kV voltage, with low repetition rates [150]. With optimal design of
tube size, an ignitron can switch peak currents of 700 kA and charge transfer ratings of
250 C [156].
Corona stabilized switch - a type of switch filled with electronegative gases e.g. air or
SF6 . Under a strongly non-uniform electrical field supplied by DC or slowly rising voltage,
space charges develop around the highly stressed electrode, redistributing the electric field
such that the non-uniform electrode is shielded from the rest of the gap. This phenomenon
can be used to reduce the recovery time of the withstand voltage and thereby can have
an increased repetition rate. A corona stabilized switch has a breakdown voltage in the
range of 15 − 100 kV, and the jitter can be less than 5 ns if the gas pressure is carefully
chosen [153, 157].
3.2.2
Solid state switches for pulsed power applications
Solid state switches appeared since the middle of last century, initially were just designed
for low voltage and communication systems. From the 1990s due to the availability of new
materials the voltage and power capability of solid state switches have been dramatically
improved. The list of recent solid state switches includes:
3.2. E XISTING SOLUTIONS
27
Diode - a crystalline piece of semiconductor material with a P-N junction connected to
two electrical terminals. Diodes are used as important nanosecond opening switch for high
power switching [170]. Two modes of diodes are popular: junction recovery (JR) diode and
silicon opening switch mode (SOS) diode [158]. JR mode diodes are preferable as bases
for generators with a pulse rise-time of 0.5 − 3 ns and a peak power of ≤ 50 − 80 MVA.
An example of application of JR model diodes can be found in [160], which introduces
a powerful drift step recovery diode (DSRD)-based generator with switching properties of
80 kV, 0.8 kA, 1.0 kHz, and 0.8 ns turn-off time. The turn-on time for an ultra-fast recovery
diode is typically in nanosecond range [161]. SOS diodes are preferable at a pulse rise-time
higher than 5 ns for any power and at any pulse rise-time if the peak power is higher than
100 MVA.
Thyristor - a type of solid-state semiconductor device with multiple layers of alternating N and P-type material. Static-induction (SI) thyristors, emitter turn-off (ETO) thyristors, and silicon carbide gate turn-off thyristors (SiC GTOs) are widely applied. Maximum
voltage rating of SI thyristors is 6.5 kV with current in the range of a few kA [164]. The
ETO thyristors have a switching voltage up to 10 kV [166]. SiC GTOs have highest blocking voltage of 12 kV and are believed to have a potential of above 15 kV [167]. The turn-on
time for thyristors varies between 35 ns (SI thysitor [165]) and 200 ns (ETO thyristor).
IGBT - abbreviation for insulated gate bipolar transistor. The highest commercially
available Silicon (Si) IGBT has a switching voltage of 6.5 kV, a current of several kA
[108]. Other state-of-the-art IGBT technology using silicon carbide (SiC) can switch 15 kV,
at 20 A [109], and as a turn-on time of 200 ns. The available repetition rate for IGBTs
nowadays is about 20 kHz [171].
MOSFET - refers to metal-oxide-semiconductor field-effect transistor. A modern SiC
MOSFET has a typical switching voltage of 1.2 kV, switching frequency as high as 1 MHz,
and power capacity of 1.2 kVA [110]. The turn-on time of a MOSFET is in the range of a
few nanosecond [163] to tens of nanosecond [162, 172].
3.2.3
Circuit breakers in power networks
The first electricity transmission systems were DC systems. However, in the early days,
DC power could not be transformed to higher voltages for efficient transport over long
distances. Since the three-phase AC was introduced around 1910, it has been the dominant
option for the transmission and distribution of electric power. Circuit breakers are critical
to the safe operation of power networks. They are responsible for the regular switching
of circuits in operation, and for the disconnection of components in case of overload or
short-circuit [173]. CBs can be classified according to:
− the voltage level: low voltage (LV), medium voltage (MV), and high or extra high
voltage (HV or EHV);
− the insulating media: water, oil, air, SF6 , vacuum, and solid state, etc.;
28
− the switching current: alternating current (AC) and direct current (DC).
We focus on the survey of (E)HV CBs. In (E)HV networks CBs are designed for either
indoor or outdoor applications. The outdoor (E)HV CBs are more often seen in our daily
life. There are two types of outdoor CBs: dead tanks (enclosure grounded) and live tanks
(enclosure at working voltage). They both have their own advantages and drawbacks. Dead
tanks allow easy installation of current transformers and they are completely assembled with
factory made adjustment. But dead tanks are more expensive and require larger volume of
insulating media than live tanks. Live tanks have advantages of lower cost, more compact
structure, and less insulating media. However, live tanks are at high voltage level, so they
need careful isolation from ground [174].
The insulating media for CBs have made great developments in the past century; meanwhile, the capacity rating of the CBs increased dramatically. Figure 3.1 gives an overview
of the development of the insulating media in CBs [173]. Water and bulk oil insulated CBs
are the earliest products applied on low current and voltage levels. Due to the problems of
massiveness and explosion risks of oil, bulk oil CBs are no longer manufactured anymore
since the last quarter of the 20th century.
Figure 3.1 – Development of the insulating media for circuit breakers in power system networks,
reproduced from [173].
The minimum oil CBs are simple in design and have low need of mechanical power.
They are based on the principle of oil CBs, but reduce the oil volume to about 10 % of that
in bulk oil CBs. The minimum oil CBs were applied until the 1980s and had a voltage rating
of 3 − 420 kV and an interruption capacity of 250 − 25000 MVA [175]. In the meantime
the compressed air CB, as a competitor, became also popular as an clean device, easy in
maintenance [176]. The switching parameters for a single unit of an air blast CBs (CBs
employ a high pressure air blast as an arc quenching medium) reached a voltage of 400 kV
and a breaking current of 87 kA [177]. However, both of these two types of CBs had
their drawbacks: minimum oil CBs required periodic maintenance and replacement; air
CBs required powerful compressors and made noise during operating. Demanding of more
frequent maintenance is another disadvantage of air CBs.
In the 1970s, SF6 CBs, having high dielectric strength and excellent arc quenching
capability, were introduced in HV systems. Meanwhile, in MV systems, vacuum CBs were
3.3. D ESIGN OF SUPERCRITICAL SWITCHES
29
widely applied for the level up to 72 kV [178]. Nowadays SF6 CBs are widely applied
in high/extra and ultra-high voltage systems up to 1200 kV with power up to 800 MVA
[179, 180]. Commercial vacuum CBs are developed up to 145 kV, 40 kA (per single-break)
[181].
In an AC system basically CBs interrupt the current at current zero-crossing. Enormous
switching technologies and CB designs have been developed over the past hundred years.
The majority of the CBs mentioned above were designed for AC systems. In the recent
decades, the development of high voltage converters made the transmission of DC power at
high voltages and over long distances possible, thus reviving the interest in HVDC transmission systems [182]. With the conventional two-terminal HVDC transmission system, more
and more converter stations are required with the increasing number of HVDC lines. Multiterminal (MT) HVDC transmission systems can effectively reduce the number of converter
stations needed, thus save cost, increase reliability and reduce conversion losses. DC CBs
were not required in HVDC transmission systems with two-terminal scheme [147, 183].
However, unlike the two-terminal scheme, the reliability, controllability, and efficiency of
the MT HVDC transmission systems strongly depend on HVDC CBs [147].
As mentioned before, the current commutation and energy absorption are the two critical
requirements for DC CBs. The detailed implementation of these requirements differs in
LV/MV and HV systems. But the principles are the same: a mechanical interrupter working
together with the auxiliary circuits [147]. So far the HVDC CBs have only been realized
in very limited numbers, with limited ratings. The first HVDC CB was an air-blast breaker
reported in 1959, which was capable of interrupting 100 kV voltage and 250 A current
[183].Today the maximum ratings of HVDC CBs are 250 kV, 8 kA, with interruption time
of 28 − 30 ms (SF6 insulation) [184] or 500 kV, 4 kA, with interruption time of ≤ 20 ms
(air blast) [185].
Recently, hybrid breakers composed of a mechanical CBs in the nominal path and a
solid-state switch in the auxiliary circuit, are presented as a new concept for fast switching
(< 3 − 5 ms) in (E)HV systems, independent of AC or DC systems [147].
3.3
Design of supercritical switches
The existing solutions for high power switching all have their specific strong and weak
points. Based on the combination of excellent properties of SCFs (high dielectric strength,
high heat transfer capability, and possible low cost), we should expect very good performance of SCFs for high power switches.
We have designed and manufactured three SCF insulated switches and tested their
dielectric strength and recovery capability in different experimental setups. The key points
when designing a SCF insulated switch include:
• Sufficiently high mechanical strength
• Compact design with minimum stray inductance
• Precise gap distance adjustment and measurement
30
• Necessary inspection and diagnostic components for SCF parameters
• Optimized gas flow design for flushing and pressurizing the switch.
Table 3.2 – Comparison of the design parameters of the three SC switches denoted with (A), (B),
and (C) in our work.
SC switch
A
B
C
Gap width
Max. SCF pressure
0 − 0.5 mm
200 bar
0.05 − 5.0 mm
200 bar
Structure compactness
Simple
Diagnostic components
No
SCF parameter
inspection
Pressure gauge
0 − 1.2 mm
200 bar
Integrated capacitor & TLT
(transmission line transformer)
Optical window;
Embedded I & V sensor
Flow meter;
Pressure gauges;
Heat ex-changer;
Air driven booster
Simple
No
Flow meter;
Pressure gauges;
The three SC switches: simple SC switch (A), multi-functional SC switch (B), and
high voltage SC switch (C), were designed for different purposes, hence the focused design
parameters have distinct differences. Table 3.2 compares the design parameters of the three
SC switches. Later we will describe the switch designs and the experimental setups in detail.
3.3.1
Simple SC switch (A)
In order to get a first impression about the dielectric strength of SCFs, a simple SC switch
(A) was designed and manufactured. The cross section of this switch is shown in figure 3.2.
The switch consists of three major parts: two metal electrode bodies with plane electrode
heads (1), two Ertalyte (an un-reinforced semi-crystalline thermoplastic polyester based on
polyethylene teraphalate (PET-P)) insulator bodies (2), and a metal housing (3). The sealing
of SCF inside the switching chamber is realized by O-rings embedded in the slots (4) on
the electrode surface as well as on the inside of the metal housing. Via engagement of the
threads on the insulator bodies and on the inside of the metal housing, the inter-electrode
gap distance can be adjusted in a range of 0 − 0.5 mm, with accuracy of ±0.01 mm. A fluid
inlet and an outlet hole with threads are employed on the metal housing, axially aligned
with the switching gap. This switch has a very simple design and compact structure, but
sufficient mechanical strength for SCF with pressure up to 200 bar. There is no optical
access in this simple SC switch. Diagnostic components for SCF temperature and flushing
rate through the switch are not available.
Figure 3.3 gives a sketch of the SCF flow through SC switch (A). The SC N2 comes from
a N2 cylinder (with purity of 99.9%), with maximum pressure of 200 bar. The pressure of
31
(1)
(2)
(3)
(4)
a
(5)
b
cd
Figure 3.2 – Cross section of simple SC switch (A). (1)-Electrode body; (2)-Ertalyte insulator;
(3)-Metal housing; (4)-Slots for high pressure sealing O-rings; (5)-Inlet/outlet hole for insulating
SCF. In the enlarged view of the electrodes part: a. Ertalyte insulator; b. Gap width; c. Electrode
body; d. O-rings for high pressure sealing.
3UHVVXUH
5HJXODWRU
1HHGOH9DOYH
6&6ZLWFK
1
1HHGOH
9DOYH
7RRSHQDLU
Figure 3.3 – Schematic of the SCF loop for the simple SC switch (A).
SC N2 supplied to the SCF loop is controlled via a pressure regulator. The accuracy of the
pressure regulator is ±1 bar. Pressure drop of the SCF in the loop due to friction (major
loss) in stainless steel tubes is neglected, so the pressure of the SC N2 in the switch gap was
read from the value on the outlet gauge of the pressure regulator. We measure the distance
between the ends of the cathode and anode when they touch each other (gap width equals
zero) by a vernier caliper and take it as a zero value. When the electrodes are separated, the
distance between the two ends after pressurization of the gap is taken as the status value.
The difference between the status value and the zero value is the gap width of the switch, at
certain gap pressure. Due to the deformation of the insulator material under high pressures,
the inter-electrode gap distance of the switch filled with SCFs is larger than that before the
pressurization. So the gap width of the switch has to be measured each time again after the
pressurization.
The experiments with SC switch (A) were carried out in the situation of no-flow and
forced SC N2 flushing respectively. The flushing of SC N2 through the switching gap was
32
simply realized by opening the valve denoted as ’2’ on the downstream side of the switch. In
the forced flushing scenario, since no flow meter is applied in the SCF flow circuit, the flow
rate and flow velocity is estimated from the open section of the needle value 2. Two types of
impulse voltage: a slow charging circuit with voltage increasing slope of 1.66 kV/ms and
a fast charging circuit with slope of 2 kV/ns are applied to SC switch (A). In the following
these two circuits are introduced.
Slow charging circuit (1.66 kV/ms)
The circuit diagram of a slow charging source with charging rate of 1.66 kV/ms is given in
figure 3.4.
5 ੬
&
Q)
9
5 ੭
&
Q)
6&VZLWFK
5

Figure 3.4 – Schematic of the slow charging circuit (1.66 kV/ms) for SC switch (A).
In this circuit an adjustable (up to 230 V) sinusoidal voltage (50 Hz) is transformed to
high voltage by two transformers with ratios of 3 : 1 and 1 : 360 in succession. Capacitor C1
is charged to high-voltage DC via the leakage inductance of the transformers, the resistor
R1 , and a rectifying diode. In a second charging process, capacitor C2 is charged from
capacitor C1 via a resistor R2 and a diode, to a peak value of 40 kV. Since C1 C2 , C1
acts like a constant voltage source. Once the SC switch breaks down, energy dissipates into
the resistive load R3 . A resistor R2 prevents the discharge of C1 into R3 . After breaking
down, C2 discharges almost completely and the next charging process can start again. The
repetition rate of this sequence is slow and is determined by the R2 · C2 time (33.2 ms), gap
setting and adjustable initial sine wave amplitude.
Fast charging circuit (2 kV/ns)
A faster charging circuit with charging rate of 2 kV/ns is illustrated in figure 3.5. This circuit supplies an impulse voltage with 50 kV peak value. In this circuit the 230 V sinusoidal
voltage source with two transformers is used again (see the slow charging circuit in figure
3.4). The capacitor C1 is charged via the transformers, a resistor R1 and a diode. Resonant charging of C2 from capacitor C1 occurs (differently from the slow charging circuit)
via a diode, an inductor L1 and an air spark gap X1 . Via the breakdown of a second air
plasma switch X2 , voltage pulses with rising rate of 2 kV/ns are generated and amplified
by a 4-stage transmission line transformer (TLT). Under these pulses, breakdown voltages
33
of SC switch (A) are measured by a voltage probe on the high voltage side, with experimental situations of either a 200 Ω resistive load connected behind the SC switch or a direct
short-circuit to ground behind the switch.
5
੬
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6&VZLWFK
VWDJH
7/7
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Q)
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੭
Figure 3.5 – Schematic of fast charging circuit (2 kV/ns) for SC switch (A) with experimental
situation of 200 Ω load connected.
4
x 10
4
x 10
Breakdown voltage [V]
10
Breakdown voltage [V]
8
6
4
2
8
6
4
2
0
-5
0
5
Time [s]
10
15
-8
x 10
0
directly connect to ground
connected with 200 : load
-2
-5
0
5
10
Time [s]
15
20
-7
x 10
Figure 3.6 – Typical voltage waveforms measured in simple SC switch (A) under fast charging
circuit (2 kV/ns) as shown in figure 3.5. The voltage waveforms till 150 ns are enlarged in the
subfigure.
The purpose of these two grounding situations is to investigate the influence of load on
the measured breakdown voltage of SC switches. Figure 3.6 explicitly shows that the measured voltage has different values under situations of the load connected and short circuited.
This is because the voltage measured before the switch is composed of two components
in series: 1) the voltage across the switch and 2) the voltage across the load. In the scenario of a 200 Ω load connected behind the switch, there is some temporary voltage building
up across the load during the fast charging process of the switch capacitance. Hence, the
voltage drop across the switch at breakdown is lower than the charging voltage measured
before the switch. In the scenario of a direct short-circuit to ground, most of the charging
34
voltage appears across the switch, so the measured voltage before the switch in this case
more closely represents the breakdown voltage of the switch.
3.3.2
Multi-functional SC switch (B)
In order to gain an in-depth knowledge of the breakdown and subsequent dielectric recovery, installation of inspection and control components needs to be considered when designing a SC switch and its setup. The SCF parameters like pressure, temperature, and flow
rate should be controllable and measurable; the switch gap distance should be precisely
adjustable; the stray inductance in the experimental circuit should be minimized; optical
observation of the spark generated in SCFs should be possible in order to provide valuable
information about the discharge generated in the SC medium. Based on these considerations we have designed and manufactured a SC switch with multiple functions, named as
SC switch (B).
b a
1
2
c3
4
de
f
5
6
Figure 3.7 – Versatile SC switch (B) and the schematic of its setup. a. cable for voltage supply
to high voltage capacitor Ch ; b. trigger pin; c. integrated high voltage capacitor Ch (total capacitance in the range of 1 − 12 nF); d. Rogowski coil; e. copper plate for voltage sensor; f. stainless
steel plate for connection to load (TLT & resistive load); 1. Adjusting knob for trigger electrode;
2. Adjusting knob for main electrode; 3. Flexible aluminum disk for gap width adjustment; 4.
optical sight plug; 5. SCF inlet tube; 6. SCF outlet tube.
Figure 3.7 gives a 3D plot of the SC switch (B). The aluminum switch housing provides
sufficient mechanical strength for the SCF up to pressure of 200 bar; the integration of
the high voltage capacitors in the switch minimizes the stray inductance in the circuit; the
35
S
WULJJHUJDS
Figure 3.8 – Schematic cross section of the electrode part in SC switch (B). The switch is cylindrical symmetric. SC N2 flows through the path indicated by dash line arrows. 1. Stainless
steel electrode body; 2. Tungsten copper (WCu 75/25) anode; 3. Quartz filled epoxy insulator;
4. WCu 75/25 trigger electrode; 5. WCu 75/25 cathode; 6. Typical region of spark channel when
switch breaks down; 7. O-ring for SCFs sealing; 8. Insulator body; 9. Metal screw to fix the
cathode to the electrode body.
movable anode facilities variable gap widths in a range of 0 − 1.2 mm, with accuracy of
±0.01 mm; replaceable heavy duty electrode heads (WCu 75/25) provide option for the
electrode erosion investigation; quartz windows allow optical observation of the SCF discharge; integrated current and voltage sensors provide high band-width current and voltage
measurements; the flange on the right, attached to the 4-stage TLT, is the output connection. To the load it supplies a 4-fold voltage amplification [186], i.e. 120 kV peak value,
facilitating further study of higher voltage SC switch breakdown in the future.
The detailed electrode part of SC switch (B) is sketched in figure 3.8. The anode (2)
has an annular configuration with inner diameter of 10 mm and outer diameter of 24 mm.
N2 flows through the gap between the trigger pin (4) and anode (2), and then flushes the
gap between the anode and the cathode (5). The cathode is a planar electrode with the same
corresponding area as the anode. After the breakdown of the main gap the spark channel
develops randomly in the gap, e.g. (6) between the two electrodes.
Figure 3.9a gives the drawing of the SCF loop for SC switch (B). SC N2 (with purity of
99.9 %) is supplied from the N2 cylinder. A pressure regulator controls the pressure of SC
N2 going to the SCF loop. An air driven gas booster is used to facilitate the N2 flow in the
loop in the scenario of forced flushing; a balance vessel is used to smooth out the pressure
fluctuation caused by pulsed operation of the gas booster; a pressure relief valve with set
pressure of 200 bar is mounted to prevent the over-pressure in the loop; a water cooled tubein-tube heat ex-changer keeps the SCF temperature constant at room temperature (300 K);
36
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1
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5HOLHI9DOYH
EDU
3UHVVXUH
JDXJH
3UHVVXUH
JDXJH
)ORZ
PHWHU
+HDW
H[FKDQJHU
(a) Schematic of SCF loop for SC switch (B).
(b) Picture of the SCF loop for SC switch (B).
Figure 3.9 – Design and real setup for the SCF loop of multiple functional SC switch (B).
a flow meter as well as two pressure gauges monitor the SCF volume velocity and pressure
flowing through the SC switch.
Two repetitive voltage sources with repetition rate of 1 − 1000 Hz and 1 − 5000 Hz respectively are employed to test the dielectric strength and dielectric recovery of SC switch
(B).
Moderate repetition rate circuit up to 1 kHz and charging rate 2.5 kV/μs
A charging circuit with voltage rise slope of 2.5 kV/μs and repetition rate in the range of
1 − 1000 Hz is shown in figure 3.10.
37
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VQXEEHU
5
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6&VZLWFK
VWDJH7/7
PDJQHWLFFRUH
3XOVHYROWDJH
VRXUFH
N9N+]
5
5/
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&K
Q)
'
Figure 3.10 – Schematic of the 1 kHz charging circuit with voltage rise rate of 2.5 kV/μs and
repetition rate of 1 − 1000 Hz. Ch - high voltage capacitor (in real setup it is integrated in the SC
switch, denoted as ’c’ in figure 3.7); L1 - air core inductance; TLT - transmission line transformer;
RL - resistive load matching the impedance of TLT.
35
1200
30
25
1000
15
Current [A]
Voltage [kV]
20
10
5
0
−5
600
400
200
−10
−15
−10
800
−5
0
5
10
15
Time [μs]
20
25
30
0
0
100
Time [ns]
200
300
Figure 3.11 – Typical voltage (measured with a North Star PV 5.0 HV probe) and current (measured by a single turn Rogowski coil) waveforms of SC switch (B) under the 1 kHz charging
circuit shown in figure 3.10. The pressure of SC N2 is 80 bar, the gap width 0.3 mm, and the
temperature 300 K.
In the circuit a repetitive voltage source with 1 kV peak value and 1 − 1000 Hz variable
repetition rate is connected to a 1 : 30 ratio pulse transformer. The resonant circuit (Ch represents the capacitor integrated in the SC switch (B)) applies voltages with increasing slope
of 2.5 kV/μs and peak value of 30 kV to the anode of SC switch (B). A LCR triggering circuit [186] connects the anode with the trigger pin of the switch. During the charging process
of Ch (in real setup it is integrated in the SC switch, denoted as ’c’ in figure 3.7) the voltage
on the trigger pin increases simultaneously with, and in a certain proportion (depending on
the value of L, R, and C) to the voltage on the anode. After the charging is finished, the
voltage on the trigger pin decays with a time constant of R · C, while the voltage on the
anode keeps almost constant. The purpose of the trigger pin is to initiate the breakdown of
the main gap at a voltage below its nominal static breakdown voltage. When the potential
38
difference between the main electrode and the trigger pin reaches the dielectric strength of
the trigger gap, the trigger gap fires. The plasma generated by the trigger gap firing initiates
the breakdown of the main gap.
Figure 3.11 gives an example of the voltage on the anode measured by a HV voltage
probe (North Star 5.0) and the current through the switch measured by a single turn Rogowski coil. The signal integrator circuit for the Rogowski coil is given in Appendix A3.
A second peak at time about 150 ns is observed in the measured current. This is due to the
reflection from the incorrectly matched TLT mounted behind the SC switch.
High repetition rate charging circuit up to 5 kHz and charging rate 1 kV/μs
From the measurements which will be described later in chapter 4.3.1, the recovery time of a
SC N2 switch is less than 1 ms. Hence a voltage source with high repetition rate exceeding
1 kHz should be used to further experimentally investigate the dielectric recovery in SC
switches. Therefore we use an up to 5 kHz charging circuit that provides 30 kV charging
voltage at rise rate of 1 kV/μs. Figure 3.12 gives the charging circuit of this 5 kHz pulsed
voltage source. The detailed circuit design and operation will be published in the Ph.D.
dissertation of my colleague F.J.C.M. Beckers.
6Z
50
6Z
(0&ILOWHU
0DLQV
/
/LQH
5HDFWRU
'
&0
/
7U
&K
6Z
&
'
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&
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6Z
Figure 3.12 – The charging circuit for the high repetition rate voltage source with 30 kV peak
value and 1 − 5000 Hz repetition rate. Ch is the high-voltage capacitor integrated in the SC
switch (B).
A typical voltage waveform measured on the anode of SC switch (B) under this charging
circuit is given in figure 3.13. The voltage applied to the switch has a rate of rise of 1 kV/μs
and a peak value of 25 − 30 kV.
3.3.3
SC switch (C) with larger gap width
As mentioned in chapter 3, CBs in power networks can only interrupt the arc at current zero
crossing, and the electrodes must be separated wide enough, in order to quench the arc. We
want to study the arc interruption behavior of the SCFs insulated switches. For this reason
we have designed and manufactured the larger gap SC switch (C). Since this work is the
39
4
3
x 10
2.5
2
Voltage [V]
1.5
1
0.5
0
−0.5
−1
−1.5
−40
−30
−20
−10
Time [μs]
0
10
20
Figure 3.13 – Typical voltage waveform measured on the anode in the SC switch (B) connected
to the 5 kHz charging circuit shown in figure 3.12. Gap pressure and gap width: p = 75 bar,
d = 0.25 mm.
starting point of the arc interruption study, we made the structure of the switch as simple
as possible. Hence, the construction of this switch differs considerably from the layout of
normal mechanical CBs:
− the electrodes in switch (C) are stationary, while in CBs moving electrodes are applied;
− the flushing direction in the switch (C) is perpendicular to the arc generated in the
gap, while in CBs the flushing of insulating media is in an axial direction, parallel to
the arc.
The main structure of SC switch (C) is similar to the simple SC switch (A), but with
larger inter-electrode gap distance and higher sustainable voltage. The SCF pressure in SC
switch (C) can go up to 200 bar and the gap width is adjustable in the range 0.05 − 5 mm.
Figure 3.14 gives a drawing of SC switch (C). The switch housing (1), the cylinder with
screw thread on the outside for gap width adjustment (2), and the electrodes (3) are all
made of brass. The plane-plane electrode heads have a diameter of 25 mm, while the rest
of the electrode bodies have a diameter of 10 mm. The material of the insulator bodies (4)
is Ertalyte. The surface of the insulator between the high voltage electrodes and grounded housing has a corrugated structure, to increase the creeping distance. O-rings (5) are
employed for the high pressure sealing inside the switching chamber. Connections for gas
tubes are embedded on the housing of the switch. Compared to the design of SC switch (A)
in section 3.3.1, the cylinder body (2) creates a smooth electric field inside the insulator,
which prevents the possibility of partial discharge or breakdown of the insulator under high
electric stress.
40
(5) (6) (1) (3) (2)
(4)
Figure 3.14 – The schematic of appearance and cross-section area of high voltage SC switch
(C). (1)-switch housing, (2)-metal sheath, (3)-anode and cathode, (4)-Ertalyte insulator bodies,
(5)-O-rings for high pressure sealing. In this drawing the (adjustable) gap is in the zero width
position, (6)-SCF in/outlet.
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5HJXODWRU
1HHGOH9DOYH
3UHVVXUH
JDXJH
3UHVVXUH
JDXJH
)ORZ
PHWHU
1
1HHGOH
9DOYH
5HOLHI9DOYH
EDU
7RRSHQDLU
Figure 3.15 – Schematic of SCF loop for high voltage SC switch (C).
41
3.4. A RC INTERRUPTION TESTING CIRCUIT
The SCF loop for SC switch (C) is sketched in figure 3.15. The design of the N2 cylinder
and pressure regulator are the same as those of switch (B) introduced before. A flow meter
with maximum pressure of 195 bar and volume velocity in the range of 70 − 500 L/h is
employed to detect the flow rate of SCF in the loop, in the scenario of experiments with
forced flushing. Two pressure gauges, one upstream and one downstream of the SC switch
are applied to inspect the pressure inside the switching chamber. A pressure relief valve
with set pressure of 200 bar is employed to prevent over-pressure in the system. In the
scenario of forced flushing SC N2 , the flushing of SCF through the switch is realized by
opening the valve (2) and releases N2 in to the open air.
We have built a circuit for the investigation of the arc interruption and dielectric recovery
in SC switch (C).
3.4
3.4.1
Arc interruption testing circuit
Circuit principle
We used a prototype to inspect the arc interruption and dielectric recovery characteristics of
SC switch (C). The simplified circuit in figure 3.16 describes the basic principle of the arc
interruption testing circuit.
6
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/
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LW
6&
VZLWFK
Figure 3.16 – Simplified circuit for the arc interruption experiments.
A capacitor C1 is charged by a DC voltage source consisting of a transformer and a
rectifier, and is manually isolated from the source after being fully charged. Once the switch
S1 is closed, a capacitor C2 with value of C2 C1 is charged by C1 via an inductance L1 .
When the voltage on C2 reaches the breakdown voltage of the SC switch, the SC switch
breaks down and the current flows through the SC switch, oscillating with a frequency
depending on the value of L2 and C2 . The energy stored in C1 and C2 is deposited into
the SC switch and the resistor R2 as long as the arc channel in the switch exists. Current
and voltage traces in case of successful interruption will be different from the ones in case
of continued conduction in the switch. Figure 3.17 sketches the waveforms of these two
scenarios.
If the SC switch is able to interrupt the current and can recover to a non-conducting
state before all the energy in the capacitors is dissipated, the capacitor C2 will be charged
again by C1 . A transient recovery voltage will be observed on the anode of the SC switch
is shown in 3.17(a), (b). The SC switch will break down again if the voltage applied to the
42
(a)
SC breakdown
SC switch re-ignition in
recovery phase
(b)
I=0
SC breakdown
No re-ignition in recovery
phase
I=0
Current interrupted
V=0
V=0
Current interrupted
SC breakdown
current
voltage
(c)
No current interruption
I=0
V=0
Figure 3.17 – Examples of voltages and currents (i(t)) appearing at pin 1 in the circuit of figure
3.16, in various situations. (a) successful arc interruption, SC switch undergoes re-ignition; (b)
successful arc interruption, SC switch does not re-ignite; (c) SC switch does not interrupt the arc.
switch is higher than the recovered dielectric strength, see the example in figure 3.17(a).
If the dielectric strength of the SC switch recovers faster than the voltage applied to it, no
re-ignition in the SC switch will be observed, and the typical voltage waveform given in
figure 3.17(b) will be measured.
On the other hand, if the SC switch cannot interrupt the current, all the energy in C1 and
C2 will be deposited into the discharging loop of the switch, and C2 will not be recharged by
C1 . The current through the SC switch will decay to zero. The example current and voltage
waveforms under failure of current interruption is given in figure 3.17(c).
3.4.2
Real setup
The schematic of the real testing circuit is given in figure 3.18. In the circuit the capacitor
C1 is charged by transformer T1 via a large resistor R1 = 120 MΩ. Diode group D1 with
snubber circuits provides uni-directional energy flow from capacitor C1 to C2 and the rest
of the components. A grounding switch SG connected with resistor RG = 1 MΩ has been
inserted to discharge the remaining energy in the circuit after the test. A self-breakdown air
spark gap X1 acts like the switch S1 in figure 3.16. The output voltage from the resistor R2
is supplied to the SC switch (C).
The testing circuits with various groups of parameters values were simulated in MicroCap circuit Simulator. By choosing the value of C1 and C2 , we can determine the maximum
energy that will be deposited into the SC switch. L1 determines the rising slope of the
voltage applied to the SC switch. The current oscillation frequency, peak amplitude, and
damping time constant are controlled by the value of L2 and R2 . The values of the parameters are chosen to be C1 = 16 nF; L1 = 115 mH; C2 = 1 − 2 nF; L2 = 800 μH − 9.8 mH;
43
3.4. A RC INTERRUPTION TESTING CIRCUIT
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7
5
/
;
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5
+9SUREH
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5*
9
&
&
6&
VZLWFK
6*
&XUUHQWSUREH
Figure 3.18 – Schematic of the arc interruption testing circuit for SC switch (C).
R1
SC
switch
L1
D1
RG
C1
C2
T1
L2
Figure 3.19 – Picture of the arc interruption testing circuit for SC switch (C).
R2 = 10 Ω. The current rate-of-rise and current frequency supplied by this setup are in the
range of di/dt = 0.14 − 29 A/μs and f = 83 − 285 kHz, respectively.
Figure 3.19 gives the picture of the real charging circuit. An example voltage waveform
measured on the anode of the SC switch as well as the current waveform are given in figure
3.20. The pressure of N2 under this situation is 50 bar and the gap width is 0.986 mm.
44
Voltage [kV]
60
40
20
0
−20
0
20
40
−20
0
20
40
60
80
100
120
140
160
60
80
Time [μs]
100
120
140
160
Current [A]
100
0
−100
−200
Figure 3.20 – An example of the voltage and current waveforms measured with SC switch
(C) under the arc interruption testing circuit. The N2 pressure is 50 bar and the gap width
is 0.986 mm. Circuit parameters are C1 = 16 nF, L1 = 115 mH; C2 = 1.3 nF; L2 = 800 μH;
R2 = 10 Ω.
C HAPTER 4
E XPERIMENTAL INVESTIGATION OF
BREAKDOWN AND RECOVERY IN SCF S
4.1
Introduction
We have discussed the crucial characteristics of SCFs for high power switching and introduced the design of several SC switches and their experimental setups in chapter 2-3. In this
chapter the dielectric strength and subsequent dielectric recovery of the SC switches under
various voltage sources are tested and the experimental results are discussed.
In section 4.2 the dielectric strength of the SC N2 switches is tested and its dependence
on pressure and gap width is investigated. The dielectric recovery of a SC N2 switch is
experimentally analyzed in section 4.3, by using repetitive voltage pulses up to 5 kHz. For
the utilization of SCFs in CBs in power networks, the current interruption capability of a
SC N2 switch is investigated in section 4.4. The radius of the discharge channels in SC N2
is optically observed by an intensified CCD camera in section 4.5, providing valuable data
for the theoretical modeling, which will be introduced later in chapter 5. Conclusions of the
experimental analysis in SC N2 switches are given in section 4.6.
4.2
Breakdown voltage analysis
The dielectric strength of a switching medium is influenced by the combination of various
parameters: medium pressure, gap width, medium flow rate, and applied voltage waveform.
The charging circuits introduced in chapter 3 generate different voltage impulses, which we
classify into three types: fast pulses with charging rate of 2 kV/ns, moderate pulses with
charging rate of 2.5 kV/μs, and slow pulses with charging rate of 1.66 kV/ms. The typical
waveforms of these voltage impulses are illustrated in figure 4.1.
45
46
4. E XPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCF S
4
x 10
fast pulse, p= 80 bar, d=0.4 mm
Voltage [V]
6
4
2
0
16.5 ns
-2
-6
-4
-2
0
2
Time [s]
4
6
8
10
-8
x 10
4
Voltage [V]
6
x 10
moderate pulse, p=80 bar, d=0.25 mm
4
2
0
11.3 μs
−2
−1.5
−1
−0.5
0
0.5
1
Time [s]
−5
x 10
4
Voltage [V]
3
x 10
slow pulse, p=80 bar, d=0.24 mm
2
34.1 ms
1
0
−0.035
−0.03
−0.025
−0.02
−0.015 −0.01
Time [s]
−0.005
0
0.005
Figure 4.1 – Waveforms of the fast (2 kV/ns), moderate (2.5 kV/μs), and slow (1.66 kV/ms)
voltage pulses applied to the SC switches.
4.2.1
Vb under slow pulses (1.66 kV/ms)
The dielectric strength of SC switch (A) (introduced in chapter 3.3.1) is tested under the
slow voltage pulses with charging rate of 1.66 kV/ms. During the experiment various combinations of parameters were tested. The N2 pressure in the switch varied in a range of
10 − 80 bar, covering the gas and SC phases. The gap width (measured after the switch
is pressurized) of the switch covered a range of 0.1 − 0.5 mm. Scenarios of no flushing
or slightly flushing of the N2 through the inter-electrode gap were both investigated. With
the SCF loop described in figure 3.3, the flushing rate of the SC N2 could only be roughly
estimated, due to the setup limitation. The flow rate was calculated from the flow coefficient, which is dependent on the wheel setting (sections) of the needle valve, and from the
SCF pressure. In the needle valve one sect is 1/80 turn of the wheel. For 80 bar SC N2 ,
in the scenario of valve 1 sect opening, the flow rate and flow velocity are approximately
2.8 × 10−4 m3 · s−1 and 14 m/s in a 0.2 mm gap, respectively.
Breakdown voltages were recorded under different experimental conditions by a high
47
4.2. B REAKDOWN VOLTAGE ANALYSIS
30
Breakdown voltage [kV]
25
20
15
10
no flushing
1 sect
2 sect
3 sect
5
(a)
0
0
10
20
30
40
50
Pressure [bar]
60
70
80
30
25
20
15
10
5
0
0
no flushing
1 sect
(b)
0.05
0.1
0.15
0.2
Gap width [mm]
0.25
0.3
0.35
Figure 4.2 – Averaged breakdown voltage of SC switch (A) under slow voltage slope with charging rate of 1.66 kV/ms. (a) Breakdown voltage versus the N2 pressure at a fixed gap width of
0.14 mm. (b) Breakdown voltage versus the gap width at a fixed pressure of 70 bar. The relative
unit ’1 sect’ in the legend means the needle valve in the SC N2 loop is opened by 1 scale division.
For 80 bar SC N2 , in the scenario of 1 sect, the flow rate and flow velocity are approximately
2.8 × 10−4 m3 · s−1 and 14 m · s−1 in a 0.2 mm gap, respectively.
voltage probe (North Star PVM 5.0) placed on the high-voltage side of the switch. For
each condition the averaged values for over 200 breakdowns were estimated, see figure 4.2.
From the figure, it is clear that under slow voltage pulses, generally the breakdown voltage
of SC switch (A) increases at higher N2 pressure, larger gap width and higher N2 flushing
rate. A dip of averaged breakdown voltage is observed at a N2 pressure around 40 bar. This
voltage dip near the critical pressure coincides with the reports about such phenomenon in
the breakdown voltage of SC CO2 under DC source [128]. The reason of this dip is assumed
to be the molecular clusters generation around the critical points (microscopic view) and gas
density inhomogeneity around the critical point (macroscopic view). Detailed investigation
48
of this phenomenon and related mechanisms are beyond the scope of the present thesis
work.
4.2.2
Vb under moderate pulses (2.5 kV/μs)
The breakdown voltage of SC switch (B) (introduced in chapter 3.3.2) under voltage pulses
with a charging rate of 2.5 kV/μs is tested. During this experiment the voltage source (seen
in figure 3.10) operated at a low repetition rate of 10 Hz.
The breakdown voltage was measured under situation of no forced N2 flushing through
the gap, by a high voltage probe (North Star PVM 5.0) placed on the high-voltage side of
the switch. Figure 4.3(a) represents the breakdown voltage of SC switch (B) versus the N2
pressure at two gap widths: 0.25 mm and 0.3 mm. From the measurements we can see that
the breakdown voltage increases with N2 pressure, and no obvious tendency of saturation
was observed up to a pressure of 80 bar. Another interesting phenomenon is that no obvious voltage dip around the critical point of N2 was observed. This observation coincides
with the measured breakdown voltage in SC CO2 under pulsed voltage sources [143]. The
possible reasons as been discussed in chapter 2 are briefly repeated here: the locally enhanced ionization phenomena caused by the molecular clusters or accelerated electrons in
low density region [141] are responsible for the local minimum of the breakdown voltage
around the critical point.
The influence of the gap width on the dielectric strength of SC switch (B) is also investigated. The measured breakdown voltage, breakdown field, and reduced breakdown field
as a function of the gap width at pressure of 37.5 − 90 bar are plotted in figure 4.3(b)-(c).
From the figures we can see that the increase of the pressure has less significant influence on
the breakdown voltage at smaller gap widths (e.g. 0.2 mm) than that at larger gap widths.
We expect that at small gap widths the field emission from small protrusions dominates the
breakdown behavior over a wide pressure range, whereas at larger gap widths the effect of
field emission is much less pronounced. In high pressure gases including the SC phase,
positive ions produced in the fluid can accumulate the positive space charge in the electrode
gap, and this process leads to substantially lower breakdown voltages [27, 187].
4.2.3
Vb under fast pulses (2 kV/ns)
The breakdown voltage of SC switch (A) was tested under very fast pulses with charging
rate of 2 kV/ns. N2 pressure in the switch was adjusted in a range of 5 − 180 bar, and the
gap width changed between 0.3 mm and 0.52 mm (after the pressurization of the switch).
Figure 4.4(a) shows the breakdown voltages of SC switch (A) as a function of the N2
pressure at a fixed gap width of 0.37 mm. Each point in the figure represents the averaged
value over 200 shots. The values in the conditions of a 200 Ω load connected and the switch
short-circuited to ground were both included. The results explicitly show that the measured voltage has different values under situations of load connected and short-circuited.
As discussed in section 3.3.1, the values with the switch short-circuited to ground represent the real breakdown voltage. We can notice the characteristics of breakdown voltage of
49
4.2. B REAKDOWN VOLTAGE ANALYSIS
4
4
x 10
d=0.3 mm
d=0.25 mm
Breakdown Voltage [V]
3.5
3
2.5
2
1.5
1
0.5
(a)
0
0
20
40
80
60
Pressure [bar]
100
120
140
0.22
0.24
0.26
Gap width [mm]
0.28
0.3
0.32
Breakdown Voltage [kV]
35
90 bar
70 bar
50 bar
37.5 bar
30
25
20
15
(b)
10
0.18
0.2
90 bar
70 bar
100
bd
[kV/mm]
120
E
50 bar
80
37.5 bar
2.2
2
1.8
1.6
1.4
1.2
1
50 bar
40
70 bar
20
0.18
(c)
90 bar
0.2
0.22
0.24
0.26
Gap width [mm]
0.28
0.3
Ebd/p [kV/mm/bar]
37.5 bar
60
0.32
Figure 4.3 – Breakdown voltage of SC switch (B) under moderate voltage slopes with charging
rate of 2.5 kV/μs. (a) Breakdown voltage versus pressure at gap widths of 0.25 mm and 0.3 mm.
(b) Breakdown voltage versus gap width at pressures 37.5 − 90 bar. (c) Breakdown field and
reduced breakdown field versus gap width at various pressures.
SC switch (A) under fast pulses: with increasing gas pressure, the breakdown voltage increases, and tends to saturate under high pressure situation. The scattering of the breakdown
voltages constricts at a pressure nearby the critical value. The measured voltages with load
connected behind the switch have larger difference from the real breakdown values above
50
90
80
70
60
50
40
30
20
10
0
0
load short−circuited
with load
(a)
20
40
60
80 100 120
Pressure [bar]
140
160
180
200
75
no flushing
1 sect
Breakdown Voltage [kV]
70
65
60
55
50
45
0.25
(b)
0.3
0.35
0.4
0.45
Gap width [mm]
0.5
0.55
Figure 4.4 – Breakdown voltage of SC switch (A) under fast voltage slopes (2 kV/ns). (a)
Breakdown voltage versus the pressure at a fixed gap width of 0.37 mm. (b) Breakdown voltage
versus the gap width at a fixed pressure of 70 bar. Each data point represents the average value
for 200 shots; ’1 sect’ means the needle valve in the SC N2 loop is opened by 1 scale division.
For 180 bar SC N2 , in the scenario of 1 sect, the flow rate and flow velocity are approximately
4 × 10−5 m3 /s and 1 m/s in a 0.4 mm gap, respectively.
the critical pressure. The reason of this phenomenon is unclear. Possible effects are mentioned here: above the critical pressure the switch capacitance may be higher but also the
plasma resistance might be higher, which result in the higher voltage drop across the spark
in the SC state.
The measured breakdown voltage of SC switch (A) as a function of the gap width under
a fixed pressure of 70 bar is illustrated in figure 4.4(b). During the experiment the switch
was short-circuited to ground. Scenarios of no N2 flushing and slightly flushing through the
gap were investigated. According to the experimental results, under fast voltage pulses, the
breakdown voltage of SC switch (A) does not increase with larger gap width below 0.4 mm.
However, at gap widths in the range of 0.4 − 0.5 mm, a slight increase of the gap width and
4.3. D IELECTRIC RECOVERY ANALYSIS
51
higher flushing rate (in low repetition rate situation) bring significant improvement of the
breakdown voltage.
4.3
Dielectric recovery analysis
Due to the gas-like high diffusivity, viscosity and liquid-like high thermal conductivity, the
heat transfer in SCFs is considered to be faster than that in gases. The experimentally
observed dielectric recovery time in an air insulated plasma switch is in the range of a few
to tens of millisecond, depending on the air flushing rate, while from rough prediction by
a simple analytic model, the recovery time in SC N2 is about 1.5 ms at the pressure of
150 bar [188]. We tested the recovery breakdown voltage of SC switch (B) under repetitive
pulses. The experimental circuits have been introduced in section 3.3.2.
4.3.1
Experiment under 1 kHz voltage source
Due to the LC resonant charging circuit of figure 3.10, the rise time of the voltage from 0 to
its peak value of 30 kV supplied by the circuit is almost constant. Under repetitive operation
mode of SC switch (B) in this testing circuit, we classify the breakdown of the switch into
two categories:
• Normal firing: at the plateau of the pulse the switch is triggered and breakdown occurs;
• Pre-firing: the breakdown occurs too early, during the rising edge of the excitation.
In figure 4.5, examples of the voltage waveforms under situation of a normal firing and a prefiring are illustrated. When SC switch (B) undergoes a normal breakdown, it is considered
that the dielectric strength of the switch is fully recovered. The percentage of the shots
undergoing ’normal firing’ to the total shot number is defined as the recovery percentage of
the switch.
Due to the estimated fast dielectric recovery, testing was performed under the highest
repetition rate: 1 kHz. Figure 4.6 gives the recovery percentage of SC switch (B), as a function of the combinations of pressure and gap width pd, under no forced flushing situation.
A few collected experimental results at pd < 15 bar · mm revealed that below 15 bar · mm
the percentage of normal firing will become too low, so we performed the experiment only
above this value.
The experimental results in figure 4.6 show that at gap width d > 0.2 mm, the recovery
percentage of the SC switch achieves 80 % within 1 ms, when the pressure is above 45 bar
(corresponding to pd ≥ 18 bar · mm). Figure 4.6 also shows an interesting phenomenon
distinguished by pd. For pd less than 20 bar · mm, a larger gap width d contributes to faster
recovery, while at pd > 20 bar · mm, the effect of d on the recovery percentage vanishes.
52
35
30
ʼNormal firingʼ
25
Voltage [kV]
20
15
Not fully recovered
10
5
0
−5
−10
−15
−10
5
0
−5
10
Time [μs]
25
20
15
30
Figure 4.5 – Examples of the voltage waveforms measured on the anode of SC switch (B), in the
situations of fully recovered (normal firing) and not fully recovered (pre-firing).
Recovery percentage [%]
100
80
d=0.4 mm
d=0.3 mm
d=0.2 mm
d=0.45 mm
60
40
20
0
0
5
10
15
pd [bar⋅mm]
20
25
30
Figure 4.6 – The recovery percentage of SC switch (B) estimated with experiment, under 1 kHz
repetitive source.
4.3.2
Experiment under 5 kHz voltage source
The recovery time of SC switch (B) proves to be less than 1 ms, as concluded from the
experimental results under 1 kHz repetitive voltage source. It is worthwhile to test the recovery breakdown voltage of the SC switch under shorter time lags between two succeeding
pulses. The voltage source introduced in figure 3.12 supplies repetitive voltage pulses with
a time lag of ≥ 200 μs between two succeeding pulses, which allows us to investigate the
dielectric recovery of the SC switch to investigate the recovery at short times between the
pulses.
53
4.3. D IELECTRIC RECOVERY ANALYSIS
The recovery breakdown voltage of SC switch (B) is tested under the source with variable repetition rates in range of 1 − 5000 Hz (corresponding to a time lag between the two
succeeding pulses in range of 200 μs − 1 s) and peak voltage reaches 30 kV. In this group of
experiments we use pre-firing mode, which means the breakdown occurs below the charging
voltage reaches the peak value. No SCF flushing is supplied in this group of experiment.
N2 pressure between 10 bar and 70 bar, and gap width of 0.15 mm and 0.25 mm were used.
Figure 4.7 gives the measured recovery breakdown voltage of SC switch (B) at pressures
of 30 − 75 bar and gap width of 0.25 mm. Generally the recovery breakdown voltage, at
any time lag between pulses, increases with the N2 pressure. The difference of recovery
breakdown values at various time lags is not significant with 0.25 mm gap width. But from
the envelope line regarding to 5 Hz and 5000 Hz repetition rate, we can still observe that
the recovery breakdown voltage decrease at higher repetition rates.
The results with gap width of 0.15 mm and pressure in range of 20 − 70 bar are given
in figure 4.8. From the results we find that the recovery breakdown voltage at the gap width
of 0.15 mm increases with pressure. At the same pressure, the measured values have larger
scattering regarding the repetition rate, and seems not to be linear with the repetition rate.
Comparing the recovery breakdown value at different gap widths, we find that at the same
pressure the recovery breakdown voltage at 0.25 mm has almost twice the value of that at
0.15 mm.
Recovery breakdown voltage [kV]
26
24
5 Hz (0.2 s)
100 Hz (10 ms)
22
1000 Hz (1 ms)
2500 Hz (400 μs)
5000 Hz (200 μs)
20
18
60
16
14
12
10
8
6
20
30
40
50
Pressure [bar]
60
70
80
Figure 4.7 – Results from the 1 − 5000 Hz pulse source: the recovery breakdown voltage of SC
switch (B) versus pressures at a gap width of 0.25 mm in pre-firing mode, as a function of the
time lag between pulses. No SCF flushing is supplied during the experiment.
54
15
Recovery breakdown voltage [kV]
14
13
12
1 Hz (1 s)
250 Hz (4 ms)
70 2500 Hz (400 μs)
5000 Hz (200 μs)
11
10
9
8
7
6
5
10
20
30
40
50
Pressure [bar]
60
70
80
Figure 4.8 – Results from the 1 − 5000 Hz pulse source: the recovery breakdown voltage of SC
switch (B) versus pressures at a gap width of 0.15 mm in pre-firing mode, as a function of the
time lag between pulses.
4.4
4.4.1
Current interruption analysis
Parameter settings
The arc interruption characteristics of SCFs are investigated by experiments presented in
this section. The working principle of a synthetic source circuit has been introduced in
section 3.3.3. The oscillation frequency and amplitude of the arc current going through the
SC switch after the breakdown can be tuned by adjusting the inductance L2 and capacitance
C2 in the circuit shown in figure 3.18.
We applied various values of L2 during the tests: 800 μH, 3.8 mH, 6.8 mH, and 9.8 mH.
The value of C2 is set to be 1 nF, 1.3 nF, or 2 nF. The examples of the current waveforms
with different settings of L2 at C2 = 1.3 nF are given in figure 4.9. From the figure it is
clear that with a fixed C2 , larger L2 results in lower oscillation frequency of the arc current
and longer duration of the current. Under a fixed L2 , different C2 causes only slightly
different current waveforms. Figure 4.10 gives the examples of the current waveforms with
C2 = 1.3 nF and C2 = 2 nF, respectively, at L2 = 800 μH. We tested the current interruption
performance of SC switch (C) at various pressures and gap widths under this circuit. The
influence of the SC N2 flushing through the gap on the current interruption performance is
investigated. In the following the experimental results are given.
4.4.2
Experimental results
The experimental results of the current interruption testing for SC switch (C) (introduced in
chapter 3.3.3) under combinations of various parameters are summarized in table 4.1. From
55
4.4. C URRENT INTERRUPTION ANALYSIS
Current [A]
50
3 A/μs
0
50
Current [A]
0.14 A/μs
(a)
-50
-100
0
100
200
300
400
500
600
700
800
900
4.2 A/μs
1000
L2=3.8 mH
0
0.3 A/μs
(b)
-50
-100
50
Current [A]
L2=9.8 mH
0
200
100
400
300
600
500
900
800
700
29 A/μs
1000
L2=800 PH
0
1.4 A/μs
(c)
-50
-100
0
100
200
300
400
500
Time [Ps]
600
700
800
900
1000
Figure 4.9 – Current through the SC switch (C) with different settings of inductance L2 in
the arc interruption testing circuit (figure 3.18), under N2 pressure of 50 bar and gap width of
0.986 mm. The value of C2 is 1.3 nF. The measured current rate-of-rise and current frequency
is di/dt = 0.14 − 3 A/μs, f = 100 kHz for L2 = 9.8 mH; di/dt = 0.3 − 4.2 A/μs, f = 83 kHz for
L2 = 3.8 mH; di/dt = 1.4 − 29 A/μs, f = 285 kHz for L2 = 800 μH, respectively.
100
C2=1.3 nF
Current [A]
50
0
−50
−100
0
50
100
150
200
250
100
C =2 nF
2
Current [A]
50
0
−50
−100
0
50
100
Time [μs]
150
200
250
Figure 4.10 – Current through the SC switch (C) with different settings of capacitance C2 in
the arc interruption testing circuit (figure 3.18), under N2 pressure of 50 bar and gap width of
0.986 mm. The value of L2 is 800 μH.
the results we find that under the current waveform shown in figure 4.9(b)-(c) (corresponding to L2 ≤ 3.8 mH), the SC switch was not able to interrupt the current at a gap width of
d ≤ 1 mm. However, at a gap width of d ≥ 1.2 mm, we observed temporary current interruptions at the current zero crossing point, at t = 30 μs or later after the breakdown of the
56
switch.
An example current waveform at p = 60 bar and d = 1.29 mm is illustrated in figure
4.11. The circuit parameters are L2 = 3.8 mH and C2 = 1 nF. No forced N2 flushing was
supplied during the experiment. From the enlarged view of the selected time region in
figure 4.11, we see that from 29.4 μs after the breakdown onward, at every current zero
crossing point, the current is interrupted temporarily, both in positive and negative slopes.
The arc current measured by the current probe indicated in figure 3.18 is influenced by the
current flowing in C2 , and also by the current induced by the stray capacitance of the SC
gap. This explains the slightly negative current during the charging process of capacitor C2
(in the time between −10 μs and 15 μs in figure 4.11), and the displacement of the current
interruption from zero crossing in the measured current waveforms.
60
2
-5
40
0
-10
-2
29.3
29.4
29.5
29.6
53
Current [A]
20
53.5
54
0
-20
2
0
-2
-40
190
0
50
100
150
192
200
Time [Ps]
194
250
196
300
198
350
400
Figure 4.11 – Measured current through SC switch (C) under the arc interruption testing circuit
given in figure 3.18. Pressure 60 bar, gap width 1.29 mm, L2 = 3.8 mH, and C2 = 1 nF. No
forced N2 flushing was supplied during the experiment.
In case of the arc current shown in figure 4.9(a), a successful interruption was observed
at 2 ms after the breakdown in a gap of d > 1.7 mm, with forced flushing estimated to be
50 Liter/h (corresponding to 2.73 m3 /h at STP), i.e. flow velocity approximately 0.05 m/s
in a 1.7 mm gap. Examples of the arc voltage and arc current under the situation of successful arc interruption are illustrated in figure 4.12 and figure 4.13, in the scenario of forced N2
flushing with volume of 50 Liter/h and no flushing, respectively. In the arc voltage measurements the voltage induced in the measurement loop by the oscillating current, though
not shown here, is measured to be 10 % of the signal.
Figure 4.12(b) gives the enlarged view of the selected two time regions for the temporary current interruptions: t = 901.8 μs and t = 906.4 μs. From the figure we can see that
the current was temporarily interrupted, which can be identified by a short duration rise of
57
Voltage [V]
500 V
Temporary interruption
500
Successful interruption
0
-500
0
1000
2000
0
1000
2000
3000
4000
5000
6000
4000
5000
6000
6
Current [A]
4
2
0
-2
-4
3000
Time [Ps]
6
Current [A]
4
2
0
-2
-4
900
950
1000
Time [Ps]
1050
1100
(a) Voltage and current waveforms in SC switch (C). An enlarged view of a half cycle of the current
waveform, in the range of t = 900 − 1100 μs, is plotted as well.
0.5
200
Current [A]
Voltage [V]
400
0
-200
-400
0
-0.5
902
904
906
Time [Ps]
908
910
902
904
906
Time [Ps]
908
910
(b) Enlarged view of three selected time regions where temporary current interruptions are observed:
t = 901.8 μs and t = 906.4 μs. The other current interruption moments are not enlarged here.
Figure 4.12 – Voltage and current waveforms measured in SC switch (C) in the arc interruption
circuit. Pressure 50 bar, gap width 1.814 mm, L2 = 9.8 mH, and C2 = 1 nF. Forced N2 flushing
of about 50 Liter/h (2.73 m3 /h at STP), i.e. flow velocity approximately 0.05 m/s in the gap,
was supplied during the experiment.
transient recovery voltage. After a temporary interruption of 0.2 − 0.3 μs , the SC switch
undergoes a re-ignition, which is represented by the sudden voltage collapse and continu-
58
Voltage [V]
500
Successful interruption
0
-250 V
2.35 ms
-500
0
1000
2000
3000
4000
5000
6000
0
1000
2000
3000
Time [Ps]
4000
5000
6000
6
Current [A]
4
2
0
-2
-4
Figure 4.13 – Voltage and current waveforms measured in SC switch (C) in the arc interruption circuit. Pressure 50 bar, gap width 1.814 mm, L2 = 9.8 mH, and C2 = 1 nF. No forced N2
flushing was supplied during the experiment.
ation of (arc) current. The sudden collapse of the voltage indicates that the switch undergoes
a dielectric breakdown, i.e., the arc was interrupted thermally before the re-ignition of the
switch. After about 2 ms the current is successfully interrupted, and the voltage on the anode of the switch rises up to 500 V and remains almost constant. By comparing figure 4.12
and figure 4.13 we observed that the current was interrupted 0.15 ms later without flushing
than with forced N2 flushing through the gap. Without forced flushing, the arc voltage in
SC N2 switch has a value of ≥ 100 V from 100 μs onward after the breakdown. Under
situation of forced flushing the value of arc voltage is higher than that without flushing, and
increases after each temporary interruption in the scenario of forced flushing. This increase
might reflect the negative current-voltage characteristics of arcs in gaseous media.
The dependence of the interruption capability on the pressure of the medium and on the
flushing situation was investigated next. The current and voltage slopes at the moment of
successful arc interruption di/dt and du/dt at the pressure of 10 − 40 bar are illustrated in
figure 4.14. The value of the current rise slope di/dt first slightly increases with pressure,
then for p > 20 bar, decreases slightly with pressure, while in conventional gas media the
behavior is a monotone increase with pressure. This abnormality needs more investigation. The rate-of-rise of transient recovery voltage du/dt increases with pressure, which is
consistent with the observations in gas media. The results under forced flushing condition
presented in figure 4.14 suggest that forced flushing results in faster recovery of the former
arc channel. However, from the rate-of-rise of the dielectric recovery voltage corresponding
to the temporary arc interruption shown in figure 4.15, we observe that the value of du/dt,
at 0.9 ms and 0.43 ms after the current initiation, decreases with the media pressure. This
phenomenon needs further investigation as well.
59
6000
d=2.112 mm
5000
d=2.139 mm
d=2.151 mm
di/dt [A/s]
4000
Forced flushing
3000
2000
Non-flushing
d=2.195 mm
1000
0
0
5
10
15
20
25
Pressure [bar]
30
35
40
45
6
6
x 10
d=2.151 mm
d=2.195 mm
5
d=2.139 mm
du/dt [V/s]
4
d=2.112 mm
Forced flushing
3
Non-flushing
2
1
0
0
5
10
15
20
25
Pressure [bar]
30
35
40
45
Figure 4.14 – The rate-of-rise of current di/dt and rate-of-rise of recovery voltage du/dt at the
moment of successful arc interruption in SC switch (C), under situation of forced flushing and
no flushing situation, at various pressures.
8
x 10
12
0.89 ms from current intiation
0.43 ms from current intiation
du/dt [V/s]
10
d=1.744 mm
8
d=1.763 mm
d=1.79 mm
6
d=1.814 mm
4
15
20
25
30
35
40
Pressure [bar]
45
50
55
Figure 4.15 – The rate-of-rise of recovery voltage du/dt as the function of the pressure at different moment after the initiation of the arc in the switch gap, under the situation of forced flushing
in the gap.
No flushing
Forced flushing
Current
Interruption
No flushing
Forced flushing
SC switch
(C)
0.956
×
×
40
40
1.473
T
T
1.458
T
T
1.496
T
T
50
d > 1.4 mm
0.941
×
×
30
30
0.917
×
×
20
d ≤ 1 mm
1.513
T
T
60
0.986
×
×
50
1.24
T
T
30
L2 = 9.8 mH, C2 = 1.0 nF
d > 1.7 mm
p [bar]
20
30
40
50
d [mm]
1.744 1.763 1.790 1.814
T
1.21
T
T
20
d > 1.2 mm
p [bar]
40
50
d [mm]
1.25
1.265
T
T
T
T
L2 = 3.8 mH, C2 = 1.2 nF
2.112
10
1.29
T
-
60
2.136
20
50
2.151
30
1.496
T
T
d > 2.0 mm
1.496
T
T
50
d > 1.4 mm
2.195
40
1.513
T
T
60
L2 = 6.8 mH,
C2 = 1.0 nF
d > 1.4 mm
Table 4.1 – Experimental results of the arc interruption testing of SC switch (C). ’×’: failure of current interruption; ’T’: capable of
temporary current interruption; ’’: successful current interruption.
60
61
4.5. ICCD IMAGE OF DISCHARGE IN SC N2
4.5
ICCD image of discharge in SC N2
Discharge imaging inside the SC switch provides valuable information for the theoretical
analysis of the breakdown and recovery in SCFs. In this section the photographs of the
discharge channels in SC N2 switch are taken with an intensified CCD camera mounted
with a microscope lens. The ICCD camera is a 4 Picos from Stanford Computer Optics
with 780 × 580 pixels, 8.3 × 8.3 μm pixel size.
5
'
/
/
'
3XOVH
YROWDJH
VRXUFH
N9N+]
&L
5
'
/
6
VWDJH7/7
PHWHUOHQJWK
&
5
0LFURVFRSLF
OHQV
5&
VQXEEHU
&
,&&'
FDPHUD
9VLJQDO
JHQHUDWRU
ILOWHU
2VFLOORVFRSH
FRPSXWHU
Figure 4.16 – Schematic of the electric circuit for triggering of ICCD camera.
The camera is synchronized with the pulsed voltage supplied to the trigger electrode
of the SC switch, using a triggering circuit sketched in figure 4.16. Simultaneously with
the charging of capacitor Ch in the main circuit (capacitor embedded in SC switch (B)),
the capacitor C2 in the triggering circuit, via an inductance L2 = 21 mH, is charged with a
relatively slower voltage increasing slope, but to higher amplitude than that on Ch . During
the charging process of Ch , the voltage on the trigger pin also increases due to the LCR
system explained in section 3.3.2. In order to prevent the voltage increases on the right
side of S1 (2-stage TLTL side), an isolating capacitor Ci = 200 pF is applied. From the
impedance equation Z = 1/(ω · Ci ) we can see that impedance of Ci is high at low frequency,
hence it can block the energy flow from the trigger pin to S1 during the slow charging
process of Ch .
At a time moment after the voltage on Ch reaches the plateau, the voltage on C2 reaches
the threshold voltage of the air switch S1 . Once S1 breaks down, a voltage impulse is
generated and transmitted to the trigger electrode of SC switch (B) through a 2-stage TLT.
The 2-stage TLT has two functions: 1) to amplify the peak-voltage of the impulse by two
62
times, and 2) to introduce a delay of 100 ns for the impulse to reach the trigger electrode of
SC switch (B). Ci , under this high frequency pulse, has low impedance, hence the voltage
pulse can transmit through Ci , and be applied to the trigger pin.
4
4
4
x 10
x 10
spark gap S1
3
Voltage [V]
4
Voltage [V]
3
2
1
trigger pin
SC switch anode
camera opening
0
signal sent to camera
2
-1
-400
1
-200
0
Time [ns]
200
400
0
-1
-2
-1
0
1
2
3
4
x 10
Time [ns]
Figure 4.17 – The typical voltage waveforms measured on the main capacitor Ch , trigger capacitor C2 , isolating capacitor Ci , and the trigger pin of the SC switch.
Discharge channel at camera opening
Gap width
0.32 mm
800
700
600
Current [A]
500
Camera opening
400
Current through SC switch
300
Camera monitoring signal
200
100
0
-100
0
100
200
300
Time [ns]
400
500
600
Figure 4.18 – Imaging of discharge in the SC switch (B) with an ICCD camera. The N2 pressure
is 70 bar and the gap width 0.32 mm. The exposure time of the camera is 0.3 ns; the ND filter
intensity is 100 X. The camera opening signal illustrated in figure 4.18 represents the feed back
signal from the ICCD camera to the oscilloscope. The time delay for the waveforms caused by
the cables has already been deducted.
At the moment of S1 firing, a noise pick up coil placed nearby S1 induces a voltage sig-
4.5. ICCD IMAGE OF DISCHARGE IN SC N2
63
nal. Via an integrator circuit shown in appendix A2 and a buffer circuit, this signal serves
as the triggering signal for the ICCD camera. The trigger signal is sent to the camera about
100 ns earlier than the firing of the main gap. This 100 ns compensates the reaction time of
the camera, in practice ≈ 97 ns (including the delay of signal generator and internal delay
of ICCD camera). Once the voltage pulse reaches the trigger electrode and superimposes
on the originally induced voltage, the trigger gap (toroidal gap width ≈ 0.1 mm) fires and
initiates the breakdown of the main gap. The opening of the ICCD camera is synchronized
with the breakdown of the SC switch, hence to capture the discharge channel in SCF. The
time sequence of the typical voltage waveforms measured on the main capacitor Ch , the triggering capacitor C2 , the isolating capacitor Ci , and on the trigger electrode of the SC switch
during the operation is illustrated in figure 4.17. The time delay of the signal transmission
caused by the cable has been deducted from the waveforms shown in figure 4.17.
Td:
0 ns
5 ns
10 ns
60 ns
80 ns
Pressure:
70 bar
Gap width:
0.38 mm
Breakdown voltage: 25 kV
Exposure time:
1 ns
ND filter intensity:
100 X
Pressure:
40 bar
Gap width:
0.35 mm
Breakdown voltage: 25 kV
Exposure time:
3.5 ns
ND filter intensity: 200 X
Figure 4.19 – Images of the discharge channels in the SC N2 switch (B) taken by an ICCD
camera. Td : time moment after the current appearing in the gap.
The light emission from the SC N2 breakdown is very strong. In order to prevent the
overexposure of the camera, a neutral density (ND) filter (filtering intensity 2 − 400 X) is
placed between the optical window of the SC switch and the microscope lens of the ICCD
camera. At the moment of current detected in the SC N2 gap, the discharge diameter measured as full width at half maximum (FWHM) of the peak intensity is estimated to be 70 μm,
as can be seen in figure 4.18. This value is larger than the predicted streamer diameter by
the similarity law (∼ 3 μm at 70 bar, as calculated from the parameters in table 5.2 given in
chapter 5), indicating that the images we captured is somewhat after the streamer has bridges
the gap and expanded. Here the possible explanation is given. The streamer propagation
velocity in N2 at a pressure of 1 bar was measured to be 7 × 104 m/s under the applied elec-
64
tric field of 0.31 kV/mm [189], and the velocity increases with the applied electric field.
Results in [190] indicate that the streamer velocity is inversely proportional to the medium
pressure. If we assume a linear increase of the streamer velocity versus the electric field,
the streamer velocity at the pressure of 70 bar under the electric field of 80 kV/mm is estimated to be 2.58 × 105 m/s, i.e., the streamer transition time across a 0.32 mm SC N2 gap
is 1.2 ns. Fast expansion of the streamer channel is assumed to happen, from the streamer
bridging the gap till the current is detected by our current sensor. We observe typically
only one spark channel during the breakdown of the SC switch, at varying positions of the
electrode ring.
Figure 4.19 shows the images of the discharge at Td = 0 − 80 ns (Td means time after
the current appeared in the gap) at p = 70 bar, d = 0.38 mm; as well as at Td = 100 − 600 ns
at p = 40 bar, d = 0.35 mm. From the images we observe that the bright channel expands
in the time span of Td = 0 − 80 ns. From Td = 100 ns onward, the diameter of the bright
channel keeps almost constant, while only the intensity of light emission becomes weaker.
It is reasonable to conclude that for the discharge channel in SC N2 , fast expansion happens
at time Td ≤ 100 ns. It agrees with the observation in [191, 192] that fast expansion of the
spark radius happens within the first few hundred nanoseconds after the spark onset.
4.6
Conclusions
In this chapter we investigated the dielectric strength, dielectric recovery, and current interruption capability of SC N2 switches. The electric field across the SC gap and the discharge
radius were observed, providing important data for the theoretical simulations which will be
introduced later in chapter 5. The following conclusions are drawn from the experimental
results.
Dielectric strength
The dielectric strength of SC N2 have been recorded under different voltage pulses: slow
(1.66 × 103 kV/s), moderate (2.5 × 106 kV/s), and fast (2.0 × 109 kV/s) pulses.
Figure 4.20 summarizes the breakdown field of SC N2 under theses pulses at a regime
of gap width for N2 pressure of 70 bar. Data for other pressure values are not available.
From the dashed line in the figure we can clearly see that at fixed gap width and pressure
e.g., p = 70 bar and d = 0.3 mm, the breakdown field in SC N2 increases under increased
voltage slope of the impulses. Under the same voltage pulse, the breakdown field is higher
at smaller gap width.
Dielectric recovery
The dielectric recovery characteristics of a SC N2 are derived from the experimental results:
• The recovery breakdown voltage increases with N2 pressure and gap width;
65
4.6. C ONCLUSIONS
200
180
Breakdown field [kV/mm]
160
140
120
݀ ൌ ͲǤͳ݉݉
100
݀ ൌ ͲǤʹͷ݉݉
݀ ൌ ͲǤͷʹ݉݉
݀ ൌ ͲǤ͵݉݉
80
60
40
ͳǤ͸͸ ൈ ͳͲଷ kV/s
ʹǤͷ ൈ ͳͲ଺ kV/s
ʹǤͲ ൈ ͳͲଽ kV/s
Figure 4.20 – Breakdown field of SC N2 under slow (1.66 × 103 kV/s), moderate
(2.5 × 106 kV/s), and fast (2.0 × 109 kV/s) charging slopes, at the pressure of 70 bar. Each
bar represents a regime of gap width. The dashed line represents the breakdown field at gap
width of 0.3 mm under the three voltage rising rates.
• The recovery breakdown voltage decrease at higher repetition rate at gap width of
0.25 mm;
• The recovery breakdown voltage at smaller gap width (0.15 mm) show less significant
relationship to the repetition rate compared to that at larger gap width (0.25 mm).
Current interruption capability
The current interruption capability of high-frequency (≥ 7 kHz) and low (< 500 A) current of SC N2 is investigated experimentally. From the experimental results, we draw the
following conclusions:
I. Under the charging voltage supplied by our testing circuit (50 − 70 kV), the current with rate-of-rise in the range of 0.14 − 3 A/μs and oscillation frequency up to
100 kHz can be successfully interrupted in a SC switch with fixed electrodes, at approximately 2 ms after the current initiation;
II. Higher pressure results in a slight decrease of di/dt at the moment of successful arc
interruption, and an increase of the rate-of-rise of transient recovery voltage du/dt;
III. Forced flushing results in faster recovery of the former arc channel: increased arc
voltage, earlier successful current interruption, and increased rate-of-rise of transient
recovery voltage du/dt.
At the current interruption the returning voltage was between 200 − 500 V at 1.5 mm
gap width. The current slope di/dt at the interruption moment was between 2000 and
5000 A/s, in a 40 bar, 2.2 mm gap.
66
Higher arc voltage is beneficial to limitation of di/dt and thus arc current crosses current
zero earlier. The increased arc voltage observed in SC switch under forced N2 flushing
situation indicates the advantage of SC N2 in arc interruption. Successful arc interruption
within 2 ms in non-moving contacts and small inter-electrode distance in present work also
provides evidence of high arc interruption capability of SC N2 .
C HAPTER 5
T HEORETICAL MODELING OF
DISCHARGE AND RECOVERY IN SCF S
The content of this chapter is based in parts on two recent publications by the author and
co-authors of this work, see publications [188] and [7]. The writer of this thesis is first
author and acknowledges the contributions from the co-authors of these papers.
5.1
Introduction
The dielectric strength and subsequent dielectric recovery in SC N2 have been studied by
experimental investigations (chapter 4). The dielectric strength of SC N2 is in the range of
60 − 180 kV/mm, which is as high as most solid dielectrics. The dielectric strength of a SC
N2 switch recovers to 80 % of the cold breakdown value within 200 μs after the breakdown.
In order to verify the superiority of SCFs in high power switching, theoretical analysis is
also an important approach to understand the discharge characteristics of SCFs.
In this chapter we introduce two models for the simulation of the discharge and recovery
processes in SCFs. In section 5.2 we introduce a simple analytic model. The purpose of this
simple model is to get a rough idea about the recovery time of a SCF switch, thus to provide
design data for the SC switches introduced earlier in chapter 3. The electric field across the
gap during the discharge of SC N2 is analyzed with simplified circuits in section 5.3. In
section 5.4 an extended physical model is generated, aiming on deeply understanding the
discharge and recovery characteristics of a SCF.
67
68
5.2
5.2.1
5. T HEORETICAL MODELING OF DISCHARGE AND RECOVERY IN SCF S
Simple analytic model
Model description
The physical model of a SC switch in this model is introduced in figure 5.1. The switch is
composed of an anode (a), a hollow-cylindrical trigger electrode mounted inside the anode
(b), and a plane cathode (c). The anode is a 40.0 mm cup with a hole of 21.0 mm in diameter. A cylindrical trigger electrode with inner diameter of 9.0 mm and outer diameter of
18.0 mm is mounted in the hole of the anode, forming a gap distance of 1.5 mm between
the trigger electrode and the anode. The axial thickness of the plane cathode is 50 mm, and
distance between anode and cathode is in the range of 0 − 10 mm. The medium is blown
into the spark gap from both the trigger gap and the center of the trigger electrode, then
flows out via six symmetrical exists, with the arrow indicating the gas flow direction.
Figure 5.1 – Schematic of the switch for the simple analytical model. (a) anode; (b) hollow
cylindrical trigger pin; (c) cathode; (d) example of spark channel generated in the switch.
When the switch breaks down, we assume that all the energy from the external source is
deposited into the spark channel (d) generated in the inter-electrode gap shown in figure 5.1.
In order to analyze the recovery performance of the switch, we calculate the temperature
decay of the spark channel by assuming two separate processes: adiabatic expansion and
heat transfer (the latter being adapted from a model with spherical electrodes in [193]).
The process of volume expansion is much faster than that of the heat transfer, so these two
processes are assumed to happen in succession. The criterion of recovery of the switch is
defined as the moment at which the temperature inside the spark channel drops to a value
of 550 K, corresponding to a breakdown voltage equal to ≈ 80 % of the static dielectric
strength [194].
This simple thermodynamic model is assumed to be suitable for an estimate of the recovery time in a SCF, because:
I) In our range of temperature T and pressure p the behavior is near the behavior of an
ideal gas. Although SCF has density ρ similar to liquids, its compressibility is high
5.2. S IMPLE ANALYTIC MODEL
69
as in gases. This makes the adiabatic expansion law applicable for SCF.
II) The heat transfer model is general and applies to both gases and liquids.
5.2.2
Model Formulation
Once the switch breaks down, a finite amount of energy E (in our simulation we take the
value as 0.7 J) suddenly releases into a cylindrical spark channel developed in the interelectrode gap [195]. The initial condition of our simulation follows Plooster’s assumption:
a very rapid heating of a column of gas in very short time, before it starts to expand [196].
This means we assume a cylinder with homogeneous temperature and density, following
the state equation of a real gas. The external gas pressure, temperature and flow velocity
are kept constant in time and space. Gas inside the cylindrical spark channel undergoes a
rapid temperature rise while the gas density remains constant and equals to the background
density, following the equation:
E = cv ρ0 V0 (T0 − Tg,0 ),
(5.1)
in which cv [J/(kg · K)] is the isochoric specific heat capacity of gas, Tg,0 = 300 K the temperature of the gas before energy deposition, T0 [K] the temperature of the channel after
heating, ρ0 [kg/m3 ] the gas density after heating (equaling to the background density), V0
[m3 ] the initial volume of spark channel.
The volume of the cylindrical spark channel has to be given as an initial parameter. It
was reported that limiting temperature exist for specific gases, which is reached in a sufficiently strong discharge [197]. As the limiting temperature is reached (in air 43000 K and in
N2 41000 K), the discharge emission spectrum is close to that of the blackbody, and further
released energy does not lead to an increase in the discharge plasma temperature. Instead,
the channel diameter increases, causing a larger activated gas volume [198]. So the initial
radius of the spark channel R0 can be calculated from equation (5.1) with T0 = 41000 K (for
N2 ). If the calculated radius R0 is less than 50 μm, then R0 is set to be R0 = 50 × 10−6 m.
V0 is adapted to the new value according to R0 , and the value of initial pressure p0 [Pa]
before expansion can be calculated from the gas state equation. It is clear that with constant
density, increasing temperature causes large increase of gas pressure. The theory of cylindrical strong shock waves gives the asymptotic solution for a strong shock radius versus
time [196]:
R20
,
(5.2)
Rc · a
in which Rc = E/(lgap Bγpg,0 ) [m] is a characteristic value determined by the initial conditions; B is a dimensionless constant specific to the characteristics of gases: 3.94 for air
and 3.37 for N2 ; γ = cp /cv is the ratio of specific heats; a [m/s] is the velocity of sound in
the background gas; lgap [m] is the inter-electrode gap width; pg,0 [Pa] is the gas pressure
before the energy deposition. A time of t0 [s] is needed for the spark to expand from the
characteristic value Rc [m] to the initial radius R0 [m] in our situation.
t0 =
70
Following this initially very rapid heating, the spark channel starts to expand due to the
pressure difference between the in- and outside of the channel, in which process, conservation of mass is applicable. During the volume expansion process, no heat transfer between
the spark channel and the environmental gas is considered (adiabatic expansion). The pressure and temperature change due to the adiabatic expansion is described by equation (5.3):
V0 γ
;
V1
γ−1
V0
T1
=
,
T0
V1
p1
=
p0
(5.3a)
(5.3b)
in which notation 0, 1 stands for before and after expansion respectively; γ = cp /cv is the
ratio of specific heats. The adiabatic expansion stops when the pressures in and outside the
channel are equal p1 = pg,0 , i.e., the left side of equation (5.3a) equals pg,0 /p0 . The radius
of the spark channel after adiabatic expansion R1 [m] can be calculated with the equation:
V1
R1 =
.
(5.4)
π · lgap
This adiabatic expansion is assumed to follow the the theory of moderate shock waves, so
the time duration of the expansion, denoted as t1 [s], can be calculated as equation [199]:
R21
E
t1 =
+
.
(5.5)
pg,0 · lgap γ · B · a2 a2
After the adiabatic expansion, the model continues with the start of the heat transfer
phase. Now, heat transfer from the channel to the surroundings is seen as the only contribution to the temperature decay of the spark channel. In the heat transfer process the governing
equation is:
Q = (Tg (t2 ) − Tg,0 )S = −cp · m
dT
,
dt2
(5.6)
where Tg (t2 ) [K] is the gas temperature in the spark channel; S [W/K] is sum of the products
of heat transfer coefficients and surface areas; m [kg] is the mass of gas inside the spark
channel. The term S is composed of the heat convection part (to the environmental gas)
with surface area Aconv [m2 ], and heat conduction part (to the electrodes) with surface area
Acond [m2 ], and the details are given by equation:
S=
kaver
Nu · kf
Aconv +
Acond ,
L
x
(5.7)
where kf [W/(m · K)] is the coefficient of thermal conduction at film temperature Tf [K]
(arithmetic mean of the spark channel wall temperature and the far-end gas temperature);
71
5.2. S IMPLE ANALYTIC MODEL
kaver [W/(m · K)] is the averaged thermal conductivity coefficient of the hot gas over the
temperature decay range; x = 5 × 10−2 m is the length of the electrodes; Nu (Nusselt number ,dimensionless) is calculated with physics of forced heat convection across a circular
cylinder [200]:
Nu = C · Rem Pr1/3 ;
Pr = υ/D;
Re = uL/υ,
(5.8a)
(5.8b)
(5.8c)
in which Pr is Prandtl number (dimensionless); Re is Reynolds number (dimensionless); u
[m/s] is the velocity of gas flowing through the gap; υ [m2 /s] is the kinetic viscosity of the
gas; D [m2 /s] is the thermal diffusion coefficient of the gas. The constants C and m for
equation (5.8) can be found in table 5.1.
Table 5.1 – Constants for equation (5.8) for circular cylinders in cross flow [200].
Re
0.4 − 4
4 − 40
40 − 4000
4000 − 4 × 104
4 × 104 − 4 × 105
C
m
0.989
0.330
0.911
0.385
0.683
0.466
0.193
0.618
0.027
0.805
The analytic solution for the gas temperature Tg (t2 ) in equation (5.6) is expressed as:
Tg (t2 ) − Tg,0
−t2
= exp
,
(5.9)
T1 − Tg,0
cp ρV/S
in which τ = cv ρV /S is the time constant of the exponential decay of the gas temperature in
the heat transfer stage; T1 is the gas temperature after adiabatic expansion.
5.2.3
Results and discussions
The recovery time of a SC N2 switch after breakdown is calculated with this simple model.
Figure 5.2 gives the prediction of the recovery time of a SC switch insulated with 300 K,
150 bar SC N2 , at a gap width of 0.4 mm and various flow rates after breakdown accompanied by 0.7 J energy deposition. The recovery time shown in figure 5.2 consists of three parts:
1) t0 : the time needed for the spark channel to expand from the characteristic radius Rc to
the initial radius R0 ; 2) t1 : the time needed to expand from R0 to the radius after the adiabatic expansion R1 ; 3) t2 : the time needed for the cooling of the gas temperature to 550 K.
The value of t0 and t1 are found be in nanosecond and microsecond range, respectively.
Hence the time of heat transfer is the major part of the total recovery time.
With flow rates up to 0.675 m3 /h (flow velocity equals to 6 m/s in a 0.4 mm gap) at
actual pressure and temperature (corresponding to 98 m3 /h at STP) we see the following
phenomenon: a larger flow rate results in faster recovery of the SC switch. The recovery
time in a SC N2 switch is predicted to be about 1.5 ms after the energy deposition. The
72
9
Estimated recovery time [ms]
8
7
6
5
4
3
2
1
0
0
20
40
60
Flow rate at STP [m3/h]
80
100
Figure 5.2 – Estimated recovery time of a SC N2 switch after the energy deposition of 0.7 J. Gap
width 0.4 mm, flow rate at STP 8 − 98 m3 /h, corresponding to 0.05 − 0.675 m3 /h at working
pressure of 150 bar (flow velocity equals to 0.4 − 6 m/s at 0.4 mm gap width).
discontinuity of the curve at 55 m3 /h STP volume flow corresponds to the critical Reynolds
number Re (part of the Nusselt number Nu that appears in equation (5.7)) transition from
laminar to turbulent flow [200]. The recovery time in an air plasma switch with the same
amount of energy deposition and flushing volume velocity at STP was also calculated by
this simple model (later in chapter 6.3.1). The simulation results reveals that the recovery
time inside SC N2 of 150 bar is about 5 times shorter than that in a 2.5 bar air switch.
This simple model provides important design data for our SC switches. However, the
model is too simple to produce accurate data on the recovery process. Therefore the calculated recovery time is an order of magnitude estimate, which for example can be seen from
a comparison with the measured data given later in chapter 6.3.1. Hence we have to develop
an extended physical model for the discharge and recovery in SCFs.
5.3
Electric field across the gap
For the extended physical modeling which will be described later in section 5.4, the electric
field E across the gap during the discharge of SC N2 is an important input parameter. From
the measured current i(t) through the gap, we can calculate the time evolution of E by using
the simplified discharge circuit of the switch [201]. The simplified discharge circuit (marked
with dotted box in figure 3.10) is given in figure 5.3.
In the simplified circuit, the SC switch and the spark channel generated in the gap is
replaced by the series connection of an inductance La and a resistance Ra . The electric field
73
5.3. E LECTRIC FIELD ACROSS THE GAP
9E
/D
&K
5D
LW
/V
5R
Figure 5.3 – Simplified circuit of the dotted box in figure 3.10. i(t): measured current in the circuit; Vb : measured breakdown voltage; La : arc inductance; Ra : arc resistance; Ch : high voltage
capacitance; Ls : stray inductance in the circuit; R0 : total resistance in the circuit (including stray
resistance and load resistance).
across the switching gap can be calculated with the following formulas:
1
Ra (t) = i(t)
;
dLa (t)
× Vb − C1 0t i(t)dt − [Ls + La (t)] di(t)
−
R
+
i(t)
0
dt
dt
(5.10)
h
E(t) =
di(t)
1
i(t) · Ra (t) + La (t)
.
d
dt
(5.11)
In the equations above the variables are explained here:
− Ra (t): the resistance of the arc generated in the gap of SC switch;
− i(t): measured current through the gap, with a typical waveform shown in figure 3.11;
− Vb : the measured breakdown voltage of the SC switch;
− Ls : the stray inductance in the circuit. SC switch (B) in this case can be seen as a
set of coaxial cables with different diameters of the inner conductors, outer metal shield,
and insulators. So the value of Ls can be taken as the equivalent inductance of the co-axial
cables in series. The value of Ls is calculated to be Ls = 104 nH.
− R0 : the total resistance of the circuit, which consists of the input impedance of the
4-stage TLT: RTLT = 12.5 Ω, the resistance of the electrode heads (W/Cu 75/25) Rcopper , the
resistance of the electrode bodies (stainless steel) Rss1 , and the resistance of the stainless
steel plate denoted as ’6’ in figure 3.7 Rss2 . The resistance of the grounded return path
(aluminum housing) of the switch is negligible, because the surface area is very large. Hence
the total resistance of the circuit can be calculated as R0 = RTLT + Rcopper + Rss1 + Rss2 .
− La : the arc inductance which can be calculated from equation [202, 203]:
La = l
rc
μ0
ln
,
2π rs (t)
(5.12)
in which rc is the radius of the return path of the current to ground, rs = 35 μm is the radius
of the discharge channel generated in the gap. The value of rs is estimated by imaging with
an intensified CCD camera, as described in section 4.5. La (t) is found to be much smaller
than the value of Ls .
74
7
8
x 10
(a)
7
Electric field [V/m]
6
5
4
3
2
1
0
−1
0
100
200
300
400
500
Time [ns]
7
8
x 10
(b)
7
Electric field [V/m]
6
5
4
3
2
1
0
−1
0
100
200
300
400
500
Time [ns]
Figure 5.4 – (a): Estimated average electric field E from the measured arc current i(t) in figure
3.11, with applied voltage of 25 kV and gap width of 0.3 mm; (b): Smoothed electric field E in
(a) with a span of 10 %.
With the current given in figure 3.11, the calculated electric field E across the gap up
to 500 ns after the start of the current is shown in figure 5.4(a). The oscillation in the tail
of the curve is due to the resonance oscillation between the inductance and capacitance in
the circuit. We use the smoothed curve of the calculated E with moving average of 10 % of
the total number of data points, shown in figure 5.4(b), as the electric field profile that will
be applied as the input parameter in the extended physical model for discharge in SCFs in
chapter 5.
5.4
5.4.1
Extended physical model for discharge in SCFs
General model description
The goal of this model is to study the complete breakdown and subsequent recovery processes in SC N2 . The physical model is of SC switch (B), which has been introduced in
chapter 3. If the switch undergoes a breakdown, the discharge is assumed to occur in the region (6) in figure 3.8, i.e., in the region of a rather uniform background field. We use results
of previous work in streamer propagation as input parameters, and simulate the streamer-to-
75
5.4. E XTENDED PHYSICAL MODEL FOR DISCHARGE IN SCF S
spark transition phase and discharge and post-discharge phase of the discharge. The rough
time scale for physics during these processes and the estimated temperature of neutral N2 is
given in figure 5.5.
300 K
5000 K
20000 K
Temperature on axis
Streamer stage
0
Conservation of mass,
momentum,
total energy
Streamer-spark transition stage
ns
Spark-decay stage
μs
Time defined in the model
Figure 5.5 – Stages in our extended physical model and the estimated temperature on the axis of
the spark channel in SC N2 .
The modeled discharge phases in our work are briefly introduced here, while the detailed
explanation is given in section 5.4.3-5.4.4. In the streamer-to-spark transition phase the
streamer forms and propagates, and electric energy from the external source is deposited
into the gap. The discharge energy is transferred to different levels: translational motion,
rotational levels, vibrational levels, and electronically excited levels as well as dissociation
and ionization of N2 molecules. Energy in some excited levels is relaxed to gas heating
instantaneously, while the energy in the other excited levels takes time to relax fully. All
energy going into gas heating is denoted as Qin . During the relaxation process there is
energy output due to heat conduction and radiation, denoted as Qout . The total energy ε is a
result of the energy input, energy output and the gas dynamics.
We assume the streamer-to-spark transition phase ends when the gas temperature in the
discharge center is larger than 5000 K, then the discharge and post-discharge phase begins.
In this stage the remaining energy in excited levels continues relaxing with a certain time
constant; the total energy of the spark channel changes under combined mechanisms; the
thermodynamic properties of the N2 in the spark channel recover and finally the dielectric
strength of SC N2 can recover. During the discharge and post-discharge phase, the forced
flushing of the N2 might push the spark channel to the outer-edge of the inter-electrode gap,
where turbulent flow cools down the spark channel more fast. For the simplicity, we neglect
this effect during our simulation.
σe E2
μ i small
μ e n eq
(ηrot ηele ηV ηion ) QR
σe
Energy
ε
Energy loss Qout
Relaxed to gas
kinetics Q ET
Relaxed to gas
kinetics Q VT
Via W VT
Gas dynamics p·dV
Via W ET
Vibrational energy ε V
ηV Q R
εE
Electronic excited
+ ionization energy
(0.7ηele ηion ) QR
Stored in electronic levels
+ spent on ionization
Electric conductivity
Goes to excited level
+ spent on ionization
Neglect Q ion
Relaxed to gas kinetics Immediately relaxed
(ηrot 0.3ηele ) QR
Stored in vibration level
Qe
Kinetic modeling
dne /dt Fion Frecomb
Figure 5.6 – Flow chart of the energy transition in the numerical model of discharge and recovery process inside a SCF. E: electric field
estimated from equation (5.11); ne : number density of electrons; Fion and Frecomb : the ionization and recombination coefficients of N2 ;
QR : the electric power density; Qe and Qion : electron and ion component of the discharge power input density; σe : electrical conductivity
of the electrons; μe : electron mobility; qe : electron charge; ηtrans , ηrot , ηV , ηele , and ηion : fractions of energy that go into translational
level, rotational level, vibrational level, electronic excited level, and ionization of N2 ; QT : electric power density going directly into the
gas heating; QVT : the power density relaxed from vibrational to translation energy level of N2 ; QET : the power density relaxed from
electronically excited levels as well as from dissociation and ionization of N2 molecules; τVT and τET : time scales of the vibrational
relaxation and the electronically relaxation in N2 ; Qin and Qout : the local power input and output density; ε: the total energy density; εV :
the vibrational energy density; εE : the sum of the electronic excited energy and energy spent on ionization of N2 ; p · dV: gas dynamics
contribution to the total energy density.
Energy input Qin
Goes to gas
heating Q T
ηtrans QR
Goes to gas kinetics
QR
Electric energy
Presumed electric field E
76
77
The numerical modeling of the discharge process follows the flow chart of the energy
transition shown in figure 5.6. From the detailed streamer simulations [204–206], it is
known that in the interior of streamer channel the electron density can be assumed to be
uniform in the axial direction far from the electrodes. Since we do not take into account
the effect of the electrodes, we assume a 1D configuration (in the radial direction) to be
sufficient for the present work.
5.4.2
Model Formulation
The Euler equations [30, 207, 208] which cover the equations of conservation of mass, momentum, and energy are applied in the model. The balance equations of the vibrational
energy and electronic excited energy of N2 are included in the following set of equations:
⎡
⎡
⎡ ⎤ ⎡
⎤
⎤
⎤
ρu
ρ
0
0
⎢ ρu ⎥
⎢ ρu2 ⎥
⎢ p ⎥ ⎢
⎥
0
⎢
⎢ ⎥ ⎢
⎥
⎥
⎥
∂ ⎢
⎢ ε ⎥ + 1 ∂ r ⎢ u(ε + p) ⎥ + ∂ ⎢ 0 ⎥ = ⎢ Qin − Qout ⎥ ,
(5.13)
⎢
⎢
⎢
⎥
⎥
⎥
⎥
⎢
∂t ⎣
r ∂r ⎣
∂r ⎣ ⎦ ⎣
ηV QR − QVT ⎦
εV ⎦
0
εV u ⎦
εE
ηE QR − QET
0
εE u
where ρ [kg · m−3 ] is the mass density, u [m · s−1 ] the velocity, p [Pa] the pressure, ε [J · m−3 ]
the total energy density, εV [J·m−3 ] the vibrational energy density, εE [J·m−3 ] the electronically excited energy density, Qin [J·s−1 ·m−3 ] the local power input density, Qout [J·s−1 ·m−3 ]
the local power output density, QR [J · s−1 · m−3 ] the external discharge power input density,
QVT [J · s−1 · m−3 ] the power density relaxed from vibrational to translational energy level
of N2 , and QET [J · s−1 · m−3 ] the power density relaxed from electronically excited levels
as well as dissociation and ionization of N2 molecules, ηV the fraction of the energy which
goes into vibrational excited level, ηE the energy used for ionization together with the part
of electronic excited energy which will not be relaxed immediately. The detailed derivation
for the Euler equations in cylindrical coordinate can be found in appendix A4. All the units
listed in this work are SI unit, unless otherwise specified, and the terms and units in the
equations below will not be repeatedly described.
The total energy per unit volume ε is defined as ε = ρu2 /2 + p/(γ − 1), where γ is the
specific heat ratio depending on gas temperature and pressure [209]. The input power density Qin is expressed as
Qin = QT + QVT + QET ,
(5.14)
where QT is the electric power density going directly into the gas heating; QVT and QET
have been introduced before. The output power density Qout is described by
Qout = Qrad + Qcond + Qelectrode .
(5.15)
where Qrad is the output power density due to radiation heat transfer, Qcond the output due
to heat conduction in the radial direction of the spark channel, and Qelectrode the output due
78
to heat conduction to the metal electrodes. Energy dissipation due to heat convection is
neglected, since the temperature in the outer domain of the spark channel is almost equal to
the background temperature.
5.4.3
Streamer-to-spark transition phase
The critical electric field that can initiate a breakdown in N2 is normally Eb = 20N/N0 kV·
cm−1 [210], in which N0 is the density under standard temperature and pressure (STP) and
N is the density at working pressure. At voltage below Eb , streamer model is able to explain
the breakdown mechanism, while at electric fields much higher than Eb , runaway electrons
from the main avalanche lead to a broad channel breakdown [211]. Since the electric field
applied in this work (seen figure 5.4) is lower than Eb , the streamer mechanism is applicable
in our model. Streamer properties like radius, maximum field on tip, propagation velocity,
electron density distribution etc., are very well studied [204, 212–214]. Results of previous
work [215, 216] in streamer propagation are taken as input parameters for our modeling.
In [217, 218] scaling (or similarity) laws have been derived. We use these laws to obtain
streamer properties in SC N2 by scaling of literature values at STP. However, as corrections
to scaling law at pressure substantially above one bar have been suggested in [213], and
as the radius of the discharge channel briefly after the streamer phase has been measured
to be 35 μm in chapter 4.5, we use 35 μm as the initial radius applied in our model. The
streamer develops into a conducting channel and electric energy from the external source,
with power density denoted as QR , deposits into the channel. When the N2 temperature
in the channel heats up to Tg = 5000 K [30, 34], we move to the next modeling domain:
discharge & post-discharge phase.
QR is composed of the ion and electron contributions, denoted as Qion and Qe respectively. The ion component of the energy is neglected, as for the time scales considered in
the present work ion mobility is negligible compared to the electron mobility. So the electric energy input is considered to be equal to the electron component of the electric energy
QR = Qe . After the streamer bridges the gap, the electric field E is assumed as uniform in
the gap [219]. For a given E, the electron energy deposition rate can be calculated with
the equation Qe = σe E2 = qe μe ne E2 , where σe is the electrical conductivity due to electron
mobility; qe , μe and ne are the electron charge, mobility, and number density of electrons,
respectively.
The electron mobility μe is dependent on the reduced electric field E/nN2 and was obtained from [220]. The balance of the electron density ne can be analyzed through the
kinetic processes governing the species reactions such as direct ionization, step-wise and
associative ionization, attachment, detachment, etc.. In present work we consider only ionization and recombination mechanisms. We write the kinetic equation in the following form
dne (r)
= nN2 (r)ne (r)Fion (r) − ne (r)n+ (r)Frec (r) ,
dt
(5.16)
where Fion (r) [m3 · s−1 ] and Frec (r) [m6 · s−1 ] are the ionization and recombination coeffi-
79
cients of N2 , obtained from [220, 221]. In appendix A5 we use a zero-dimensional model
to analyze detailed temporal dynamics of species in a streamer channel. The results reveal
that during the discharge N2 + is converting very rapidly to N4 + , and the dominant electron
loss mechanism in the streamer channel is electron-ion dissociative recombination between
N4 + and electrons [222]. In equation (5.16) the drift and diffusion of the electrons and ions
are justified to be neglected in the nanosecond time range in our situation. 1
As described before, part of the discharge power density QR is transferred into the excited levels and needs time to relax. Figure 5.7 gives the fractions of energy that go into
translational level ηtrans , rotational level ηrot , vibrational level ηV , electronic excited level
ηele , and ionization of N2 ηion , as a function of the reduced electric field E/nN2 obtained
from BOLSIG+ [225]. From the figure we can see that at E/nN2 < 300 Td, sum of energy
fractions equals 100 %, while above 300 Td the sum is less than 100 %. This is probably
because the difference between calculated electron transport coefficients in N2 and the experimental results increases at higher E/nN2 [226]. In the range of electric field concerned
in our model (less than 100 Td), the sum of energy fractions equals 100 %, indicating that
all the energy has been taken into account. Flitti and Pancheshnyi [227] reported insignificant sensitivity of the energy fractions to pressure changes, so figure 5.7 is considered to be
applicable for the SCF situation.
The fraction of energy expanded on translational level ηtrans and rotational level ηrot can
be considered to equilibrate instantaneously [30, 32, 34, 228]. In a large range of reduced
electric fields E/nN2 = 60 − 300 Td, about 30 % of the energy distributed in the excitation
of electronic levels with fraction ηele is directly transferred to gas heating [32, 34, 228, 229].
The main source of N atoms is via the routes of electronic excitation and subsequent dissociation [229, 230]. This implies that the fraction ηele already contains the electron induced production of atoms (dissociation). 30 % is directly converted to heat (heat release
in dissociative de-excitation), 70 % is delayed (heat release in de-excitation and atom recombination). The fraction of the energy which goes into vibrational excited level ηV also
needs time to be relaxed to gas heating. This process is known as a vibrational relaxation
with time constant τVT . Depending on the applied reduced electric field E/nN2 , a small
fraction ηion of energy is expanded on the ionization of N2 molecules. This fraction is
found to be ηion ≤ 2.5 % for a value of value of E/nN2 ≤ 200 Td. The energy expanded
for ionization together with the rest 70 % of the electronic excited energy, which sum we
denote by ηE = ηion + 0.7ηele , takes time to be relaxed to the gas heating, which is a com1 We mention here a discussion with a referee about the assumption that the electron density is uniform along
the streamer channel after the streamer bridges the gap. The referee referred to reference [223], stating that the
electrons would be rapidly lost due to recombination at high pressure. The motivation of [223] that streamers
would not obey scaling relations with pressure [224], can be resolved by taking the scaling of streamer lengths
with pressure into account. The results in [223] reveal that the degree of ionization increases linearly with gas
density, and so does the ratio of molecules that are excited, ionized or dissociated by electron impact. Recombination rates of electrons and molecules will certainly change when many molecules are vibrating or electronically
excited. Furthermore in [223] it is implicitly assumed that the gas stays weakly ionized, whereas according to our
simulations the gas is highly ionized (40 %), therefore the ground state recombination rates suggested in [223] do
not apply. In the present work we have chosen the simplified 1D approximation and refer to possible future work
for a 2 dimensional model.
80
2
Figure 5.7 – Energy fractions for discharge in N2 as function of reduced electric field E/nN2 at
ambaint pressure. ηtrans : fractions of energy that goes into translational level, ηrot : rotational
level, ηV : vibrational level, ηele : electronic excited level, and ηion : ionization of N2 .
plicated process [229]. For the sake of simplicity we don’t track the detailed processes such
as dissociative ionization, dissociative recombination, atomic recombination, etc.. Instead
we assume that this part of energy will be relaxed into gas heating with an assumed time
constant τET .
In summary: the discharge energy that goes directly into gas heating can be expressed
as equation
QT = ηT QR ,
(5.17)
with the fraction of energy contributing directly to the gas heating ηT written as
ηT = ηtrans + ηrot + 0.3ηele .
(5.18)
The discharge energy that relaxes from vibrational level to gas heating is expressed with
equation
QVT =
εV − εV,eq (Tg )
,
τVT
(5.19)
in which εV,eq (Tg ) [J·m−3 ] is the equilibrium value of εV at temperature TV = Tg given by
the following expression [231]
εV,eq (Tg ) = nN2 ·
EV
E
/kB ·Tg
V
e
−1
,
(5.20)
81
and the time scales of the vibrational relaxation τVT in N2 can be written as [232, 233]
−1/3
τVT = (pg /105 ) −1 · 3.4 × 10−12 e195×Tg
.
(5.21)
In the equations above EV is the vibrational energy of one N2 molecule and equals to
0.29 eV; kB is Boltzmann’s constant, kB = 1.38 × 1023 J · K−1 ; pg is the gas pressure [Pa].
The discharge energy that relaxes from electronic excited level as well as releases by recombination mechanisms is expressed by equation
QET = εE /τET
(5.22)
in which εE = 0t ηE (τ )QR dτ is the integrated energy with fraction ηE over the simulation
time τ. [221] reported the relaxation of electronic-excited N2 within 20 μs in air discharge
under ambient pressure, and the relaxation time tends to be smaller in higher density gas
[234]. Since the modeling results is found to be insensitive to the precise value of τET , we
assume the relaxation time to be τET = 20 μs.
Around the axis of the spark channel, the heat transfer is dominated by radiation [235].
We split the channel into infinitively thin annular zones with thickness of δ r, which volume
calculated to be V = πδ r2 · d. The selection of δ r will be described later in section 5.4.5.
The heat transfer by radiation can be expressed by
Qrad = ξ · σ
(T4g − T4N2 ) · S
,
V
(5.23)
where ξ is the net emission factor dependent on the gas temperature and pressure in the discharge zone, σ = 5.671 × 10−8 W · m−2 K−4 Stefan-Boltzmann constant, TN2 = 300 K the
environmental temperature, S = 2πr · d the radiation surface area. The expression of ξ is
taken from [235] and reads
ξ = 1 − e−(C·pg
1.2 r0.5 )/T
g
,
(5.24)
where C is a constant C = 4.2 × 10−3 Pa−1.2 m−0.5 K. This expression of ξ is valid for SF6 ,
but since we assume the spark channel reaches local thermal equilibrium soon (details seen
in section 5.4.4), the difference of ξ for SF6 and N2 is considered to be not significant.
Due to the faster temperature rise in the inner discharge channel, there is a temperature
gradient in the radial direction. Energy is transferred by heat conduction from the high
temperature to low temperature gas by expression
Qcond = −k ·
∂ Tg
2πrd
,
2
∂ r π (rj+1 − r2j )d
(5.25)
where k [W·m−1 ·K−1 ] represents the thermal conductivity of the N2 ; rj and rj+1 are inner
and outer radius of the annular zones, with relation rj+1 = rj + δ r. In this stage the thermodynamic parameters of the SCF below 2000 K are calculated precisely with [209], while above
82
this temperature no existing references can be found. However, from [236] we can find that
for temperatures above 2000 K, the thermal conductivity of the gas is almost independent of
the gas pressure, i.e., k keeps almost constant with increasing pg . So for temperature higher
than 2000 K, k is calculated from the equation in air [196] and assumed to be applicable for
the SC N2 situation. Hence the thermal conductivity k of N2 can be expressed by equation
k = 14.88σ Tg + 2.2 × 108 ρ
dA0
+ 0.01(1 − A1 ) Tg ,
dTg
with Tg ≥ 2000K;
(5.26a)
k = k (Tg ) + k (τ, δ ) + k (τ, δ ) ,
0
r
c
with Tg < 2000K,
(5.26b)
where σ = 5.671 × 10−8 W · m−2 K−4 is Stefan-Boltzmann constant; the detailed description of dimensionless numbers A0 , A1 as well as the sub terms of thermal conductivity
k0 (Tg ), kr (τ, δ ), kc (τ, δ ) can be found in [196, 209].
Energy loss to the metal electrodes (part 1, 2, and 5 in figure 3.8) by heat conduction
is considered in our model. Since the system is axially symmetric, we calculate the heat
transfer to the anode side and multiply the results by 2 to get the value of heat transfer to
electrodes Qelectrode . The equation is formulated as
Qelectrode =
2(Tg − T∞ )
1
·
,
2
Rheat
π (rj+1 − r2j )d
(5.27)
in which T∞ = 300 K is the electrode temperature on the far distance surface; Rheat [m2 W−1 ]
is the total thermal resistance of the spark channel, the electrode head (part 2 in figure 3.8),
and the electrode body (part 1 in figure 3.8). The equation of Rheat can be written as
1/4d L1 L2
1
Rheat =
+
+
·
,
(5.28)
2
k
k1 k2
π (rj+1 − r2j )
in which the characteristic lengths of the thermal resisting layers are respectively 1/4d for
the high temperature spark, L1 = 10 mm for the electrode head, and L2 = 126 mm for the
electrode body; the thermal conductivity of the layers are respectively k obtained from
equation (5.26) for the high temperature medium, k1 = 189 [W · m−1 · K−1 ] for the electrode
head, and k2 = 21 [W · m−1 · K−1 ] for the electrode body.
5.4.4
Discharge and post-discharge phase
In discharge and post-discharge stage the spark channel expands due to the pressure rise
and shock waves formation under the combined changes of the kinetic and heat energy.
The total energy of the spark channel decreases and the channel cools down. The dielectric characteristics of the gas are restored and finally the thermal recovery of the gap will
complete.
83
Many works have discussed the modeling of the spark discharge in this stage based on
different mechanisms. Taylor [237] and Lin [238] modeled the strong shock wave generated with an infinitely small initial radius. The similarity assumptions of an expanding blast
wave of a constant total energy are applied and the heat transfer term is ignored. Authors
used Rankine-Hugoniot relations to calculate the parameter profiles versus time and radius.
Plooster [196] estimated the blast wave from line sources, in which the conservation of momentum, mass and internal energy are applied. For the energy conservation, heat exchange
between the blast wave and the environment is neglected. Akram [39, 239] developed the
hydrodynamic equations by adding heat transfer terms and correcting the momentum equation in Plooster’s work. In both Plooster and Akram’s work artificial viscosity from von
Neumann-Richtmyer [240] is implemented in the models in order to solve the discontinuity
problem in the shock region.
In our model since the profile of the parameters is already known from the results of
the previous stages, the artificial viscosity term is not needed in the modeling. Comparing
to the models of Plooster and Akram, the equation of conservation of energy in this model
has additional terms of energy relaxation from excited levels to the neutral gas heating. Following the assumptions made by Akram, we assume that a local thermal equilibrium (LTE)
exists all the time; the discharge column is straight and cylindrical symmetric; the conduction portion of the plasma column is electrically neutral; the interaction of the discharge
current and own magnetic field as well as the body forces in short gaps are negligible.
The hydrodynamic equations in this stage can be expressed again by the formula (5.13).
The electric power input QR with the same expression as previous section is assumed to
exclusively contribute to the gas heating, i.e. QT = QR . The fraction of energy transferred
into vibrational excited and electronic excited levels in formula (5.13) is now set to be
ηV QR = ηE QR = 0. Energy previously stored in the excited levels continues to be relaxed
into gas heating by the terms QVT and QET , with time constant τVT and τET respectively, as
given in equations (5.19-5.22). The heat radiation Qrad , heat conduction in N2 Qcond , and
heat conduction to electrodes Qelectrode can again be expressed by equations (5.23-5.28).
Thermal dissociation and ionization of N2 molecules become significant under high gas
temperature. However, in our modeling the high temperature zone vanishes with a time
scale much shorter than the establishing time of dissociation and ionization equilibrium, as
can be seen from the information given in appendix A6. Hence we neglect the impact of
thermal dissociation and ionization in our modeling. Detailed discussion will be given in
section 5.4.6.
5.4.5
Numerical conditions
The initial values of the input parameters are adapted from streamer modeling results mentioned in section 5.4.3. Table 5.2 gives the initial parameters at STP as well as the corresponding scaling properties. The initial parameters at the working pressure in this paper:
80.9 bar, are calculated from the values given in table 5.2. We assume in the radial direction
84
the initial electron density ne (r, t) has a Gaussian shape
ne (r, 0) = ne,0 · e−r
2 /r2
s,0
,
(5.29)
where rs,0 and ne,0 are the initial channel radius and the maximum electron density on the
axis of the channel. Initial N2 density, velocity and pressure are assumed to be constant
from table 5.2. The set of equations (5.13) is discretized using a second-order Lax-Wendroff
numerical scheme [241], with the numerical parameters presented in table 5.3.
Table 5.2 – The initial parameters for the model.
Parameter
Symbol
Electron mobility
Initial gas temperature
Initial vibrational temperature
Quantum of vibrational energy
Applied voltage
Gap distance
Initial gas density
Initial electron density
Initial channel radius
μe,0
TN2
TV,0
EV
V
d
nN2 ,0
ne,0
rs,0
Value at ground pressure
Scaling property
∼ 4.4 × 10−2
∝ (N/N0 ) −1
∝ (N/N0 ) 0
∝ (N/N0 ) 0
∝ (N/N0 ) 0
∝ (N/N0 ) 0
∝ (N/N0 ) −1
∝ (N/N0 ) 1
∝ (N/N0 ) 2
∝ (N/N0 ) −1
2 V−1 · s−1
m
300 K
300 K
0.29 eV
30 kV
24.3 mm
2.4 × 1025 m−3
8.87 × 1020 m−3 [242]
100 μm [213]
Table 5.3 – Numerical settings of the modeling. a is the sound velocity inside SCF.
5.4.6
5.4.6.1
Parameter
Symbol
Value
Initial domain size
Initial space step
Space step
Domain size
Time step
Lr,0
δ r0
δr
Lr
δt
10 × rs,0
rs,0 /100
∝ 1/ρ
∑δr
0.01 × min(δ r/a, τVT )
Results and discussions
General results
The modeling results based on the initial parameters defined in section 5.4.5 are given as
below. Figure 5.8 gives the results of neutral N2 temperature Tg and vibrational temperature
TV on the axis of the spark channel in the early stage of the discharge. The phenomenon that
TV increases faster than Tg is due to the larger fraction of energy stored in the vibrational
level than in the translational level. At a time of 1.5 ns, Tg heats up to 5000 K, while TV
has a value of about 18000 K. The time needed for Tg heating up to 5000 K decreases with
85
increasing reduced electric field, and for the same value of reduced electric field, higher E
and p result in shorter formation time. Following the Toepler’s spark law [243], the time
dependent resistance of the spark channel can be calculated with equation
kT d
,
i(τ
)dτ
0
RF (t) = t
(5.30)
in which i(t) is the measured current across the gap, RF (t) [Ω] the resistance of the spark
channel at time point t, kT the empirical spark constant, and d the gap length. The spark is
assumed to be formed when RF (t) ≤ 100 Ω, which moment we denote as the spark formation time. Figure 5.9 gives the calculated spark formation time as function of the reduced
electric field E/p, as well as the time needed for gas temperature building to Tg ≥ 5000 K
according to our simulation results. The time needed for Tg ≥ 5000 K in our model matches
well with the spark formation time calculated from Toepler’s law, while disparity appears
when ≤ 0.1 mm, and with smaller gap width, this disparity becomes more significant.
Simultaneously with the temperature rise, the N2 pressure pg also increases in the discharge channel. Figure 5.10 gives the ratio of the pressure on the axis of the discharge
to the background pressure paxis /pback . From equation (5.21) we can see that the value of
vibrational energy relaxation time τVT decreases with increasing Tg and pg . With smaller
τVT , the energy relaxes faster from vibrational level to gas heating. From figure 5.8 it is
clear that immediately after the spark is formed, TV starts to decrease while Tg increases
more dramatically, and they merge with each other at ∼ 1.6 ns, TV = Tg = 13000 K. LTE
status is assumed to be achieved at this moment. Since this time is almost the same as the
time needed for Tg ≥ 5000 K, the assumption of LTE during the modeling of discharge and
post-discharge stage is fairly accurate.
20000
Tg
18000
T
vib
16000
Temperature [K]
14000
12000
10000
8000
6000
4000
Tg=5000 K
2000
0
0
2
4
6
8
10
Time [s]
12
14
16
18
−10
x 10
Figure 5.8 – Gas temperature and vibrational temperature on the spark axis in the streamer-tospark transition stage. Initial parameters given in section 5.4.5.
Figure 5.11 gives the radial distributions of the N2 temperature Tg , the neutral partial velocity u, the N2 density ρg , and the ratio of N2 pressure to the background pressure pg /pback ,
86
Spark formation time [ns]
4.5
Toeplerʼs spark law
0.2 mm, 80 bar
0.13 mm, 80 bar
0.1 mm, 100 bar
0.07 mm, 150 bar
0.15 mm, 60 bar
4
3.5
3
2.5
2
1.5
1
0.5
0
0
5
10
15
20
25
E/p [kV/(cmbar)]
30
35
40
Pressure ratio Paxis/Pback
Figure 5.9 – Streamer-to-spark transition time calculated by Toepler’s law [243] and modeling
results with different pd settings.
50
40
30
20
10
0
0
0.5
1
Time [ns]
1.5
2
Figure 5.10 – N2 pressure increase on the axis of the spark channel. Paxis : N2 pressure on the
axis; Pback = 80.9 bar: background N2 pressure.
at various time instants after the streamer bridges the gap, denoted as td . It can be seen that
Tg in the discharge channel heats up to 21000 K at td = 3 ns, while the ρg in the channel
does not show a significant change. The pressure pg in the channel builds up rapidly due to
the unchanged ρg and increased Tg .
Later on the temperature curve becomes broader and flatter. In the meanwhile the N2
moves outer-wards with increasing peak velocity u which becomes supersonic at a time
of 49 ns. Shock waves form after the extinction of the electric energy input, i.e. after
td = 220 ns. The distribution of the gas density ρg changes so that ρg in the center of the
channel becomes smaller, while high density exists in the shock region. The pressure at
the shock boundary is an order of magnitudes higher than that of the background pressure.
From about 10 μs onward, Tg in the whole discharge channel is below 1500 K, the Tg decay
versus time becomes slower. This is because the gas does not transport much energy by heat
87
5
Temperature [K]
10
3 ns
49 ns
4
220 ns
10
1 μs
10 μs
3
10
50 μs
100 μs
2
Velocity [m/s]
10 −7
10
−6
10
−5
−4
10
10
−3
−2
10
Radius [m]
−1
10
10
0
10
220 ns
600
49 ns
1 μs
400
10 μs
200
3 ns
0 −7
10
−6
10
−5
50 μs
−4
10
10
−3
−2
10
Radius [m]
10
100 μs
−1
10
0
10
Density [kg/m3]
250
200
1 μs
150
49 ns 220 ns
3 ns
100
10 μs
50 μs
100 μs
50
0 −7
10
−6
10
−5
10
−4
10
−3
−2
10
Radius [m]
10
−1
10
0
10
49 ns
3 ns
g
Pressure ratio P /P
back
2
10
220 ns
1
10
1 μs
10 μs
0
50 μs
100 μs
10
−7
10
−6
10
−5
10
−4
10
−3
10
Radius [m]
−2
10
−1
10
0
10
Figure 5.11 – Parameters of the N2 temperature Tg , velocity u, density ρg , and pressure ratio
to the background pressure Pg /Pback , in the radial coordinate of the spark channel at different
moment after the streamer bridges the switch gap.
conduction, due to the flatter temperature profile and smaller thermal conductivity. The
shock wave propagates further during this time region. The gas density ρg in the channel
recovers to the background density. The peak values of velocity u, the gas density ρg ,
and pressure pg propagate together with the shock wave and decrease with time. From
88
td ≈ 20 μs onward, the temperature decay becomes very slow. The peak temperature in the
channel is about 800 K at td = 50 μs. From microsecond time range on the temperature on
the axis of the discharge is lower than the temperature further from the axis. This might be
due to the implementation of the net emission coefficient in equation (5.24) in the annular
zones inside the channel. From 50 μs onward, the temperature on the axis of the spark
channel is higher again than the temperature on the outer region of the spark channel. This
is probably due to the fact that after 50 μs the system is equilibrated, and strong gradient
effects like the nonmonotonic temperature profile disappear.
The distance of the shock wave is several centimeter away from the discharge axis.
Compared to the observed millimeter shock region in experimental work with 60 kV in a
50 mm gap under atmospheric pressure [244], the propagation of the shock front in our
work is further from the axis. One of the important reasons is explained here. The experiment in a N2 discharge [245] shows that from tens of microsecond after the spark forms,
the spark channel becomes a turbulent mix of excited and cold, recirculating gases. The
hydrodynamic instability of the gas due to the turbulent mixing would cause the compression of the spark channel [246], while in our simulation the turbulent mixing is missing.
Besides, with turbulent mixing the intensity of the channel cooling process will increase
more sharply than only taking into account heat transfer [246]. Since in our model the temperature decrease is already convincingly fast in the first 20 μs after the discharge, we do
not take the turbulence energy transport into account. We should be aware that the recovery
process of the SC N2 would be faster than the results shown by this model.
0
10
1/eTaxis
−1
10
500 K
−2
10
1000 K
2000 K
Radius [m]
−3
10
5000 K
−4
10
10000 K
−5
20000 K
10
−6
10
−7
10
−8
10 −10
10
−9
10
−8
10
−7
10
−6
10
−5
10
−4
10
−3
10
Time [s]
Figure 5.12 – Radius of spark channel with the region defined as temperature above 1/e · Taxis ,
500 K, 1000 K, 2000 K, 5000 K, 10000 K, and 20000 K and respectively.
Figure 5.12 gives the modeling results of the high temperature region of the spark channel for Tg equals to: 1/e · Taxis , 500 K, 1000 K, 2000 K, 5000 K, 10000 K, and 20000 K
respectively. It can be seen that the kernel of the discharge for Tg ≥ 20000 K shrinks after
89
40 ns, whilst the Tg = 1000 K boundary compresses after several tens of microseconds. The
characteristic time needed for establishing the thermal ionization equilibrium for N2 at a
temperature of 20000 K is in the range of about 1 μs to 6 μs, as calculated with our specific
initial electron density and the data given in [247]. For temperature of 20000 K, the fraction
of thermally dissociated N2 is about 10−5 at a time of 1 μs, as reported in [248]. Since the
time scale for establishing thermal dissociation and ionization equilibrium is much longer
than the time duration of the high temperature zone in our modeling results, it is acceptable
to exclude the two mechanisms from our model.
5
Temperature [K]
10
4
10
3
10
2
10 −11
10
−10
10
−9
−8
10
−7
10
−6
10
Time [s]
−5
10
−4
10
10
Figure 5.13 – N2 temperature on the axis of the spark channel with pd = 24 bar · mm,
TN2 = 300 K, and d = 0.3 mm.
29 kV
4
10
3
10
2
10 −10
10
−9
10
−8
10
−7
10
−6
Time [s]
10
−5
10
−4
10
−3
10
Figure 5.14 – The recovery breakdown voltage of the SC N2 with pd = 24 bar · mm,
TN2 = 300 K, and d = 0.3 mm.
The N2 temperature on the axis of the spark channel Taxis is plotted as the function
of time, seen in figure 5.13. It can be seen that Taxis drops to 1000 K at 6 μs. In order
to transfer the information of temperature decay to the dielectric recovery of the SCF, the
streamer inception criterion is applied. The details of the calculations will be given in
chapter 6, while here we only give the simulated results. Figure 5.14 gives the calculated
breakdown voltage Ubr during the recovery process. The dielectric strength of the gap Ubr
90
decreases from cold breakdown value Ucold = 29 kV to about 300 V when the discharge is
fully developed. After the extinction of the electric energy input, Ubr starts to increase again.
The value of Ubr recovers to 10 kV within 10 μs. After that the recovery of Ubr becomes
slower, and Ubr recovers to 17 kV at 200 μs. The slower rate of rise of Ubr corresponds to
the more flat temperature decay in the radial direction, and no significant increases of Ubr is
expected after 20 μs.
5.5
Conclusions
We developed two models for the simulation of discharge and recovery process in a SC
switch. A simple analytic model gives the prediction of the recovery time in a SC N2
switch to be 1.5 ms after an energy deposition of 0.7 J, at gap width of 0.4 mm and flow
rate of 98 m3 /h at STP (corresponding to 0.675 m3 /h at working pressure of 150 bar). The
prediction of this simple model provides important design data for the SC switches in our
work. However, due to the simplified heat transfer mechanisms and radial distribution of
parameters, the simulation results is only an order of magnitude estimate.
An extended physical model for the simulation of the discharge inside SC N2 covering
the streamer-to-spark transition and discharge & post-discharge stages is developed. The
results of the modeling show that the gas temperature in the spark channel increases from
background temperature to 5000 K within 1.5 ns after the streamer bridges the gap, and in
the meanwhile the dielectric strength of the SC N2 drops to about 300 V. During spark development the temperature rises to the peak value of 22000 K at 3 ns after start of the spark
formation. The spark formation time is much smaller than that in atmospheric pressure,
although with comparable reduced electric field. Due to the high heat transfer capability of
the SCF, the N2 temperature on the spark axis decays to 1500 K at about 10 μs after the
breakdown. After 70 μs the dielectric strength of the gap recovers to about half of the cold
breakdown value, and the recovery of the dielectric strength slows down afterwards because
of slower temperature decay. The obscene of a turbulence mechanism might be responsible
for the slower temperature decay in the late stage. The influence of the thermal conductivity
on the simulation results is investigated. Different settings of thermal conductivity result in
distinct temperature profiles along the time axis, but the differences are very small. Both
experimental and numerical investigations indicate that SCF is an environmental harmless
insulating medium with proven high breakdown voltage and fast recovery speed.
C HAPTER 6
C OMPARISON OF EXPERIMENT AND
MODEL
6.1
Introduction
In chapter 4 we have measured the breakdown voltage and dielectric recovery in SC switches
under various voltages sources. The simulation of the discharge and recovery in SCFs has
been introduced in chapter 5. In this chapter, by comparing the experimental results with
the calculations, we test the validity of the models generated in our work, and verify the
properties of SCFs as switching media in depth.
In section 6.2 the dielectric strength of SC N2 is calculated by simple Paschen’s law
and by streamer inception criterion with enhanced ionization, respectively. The measured
breakdown voltages are compared with the theoretical calculations. Section 6.3 tests the two
theoretical models introduced in chapter 5, by comparing the measured recovery breakdown
voltages of SC N2 switches with the simulation results. Conclusions are given in section
6.4.
6.2
6.2.1
Breakdown voltage in SCFs
Principle of Paschen’s law
As described in chapter 3.2, the breakdown mechanisms of a gas insulator: Townsend mechanism and streamer mechanism, can be described both by the Paschen’s law. Here the principle of the Paschen’s law is generally introduced.
In a homogeneous field, if an avalanche is developing from a single electron at the
cathode, the number of the electrons Ne at distance x from the cathode can be described
91
92
6. C OMPARISON OF EXPERIMENT AND MODEL
by [243]:
Ne = exp
0
x
(α − η )dx = exp[(α − η )x],
(6.1)
in which α is the ionization coefficient and η the attachment coefficient. The number of
the positive ions Ni left in the avalanche tail can be calculated from the value of Ne , using
equation
Ni =
x
0
αNe dx =
α
{exp[(α − η )x] − 1}.
α −η
(6.2)
Townsend mechanism
If the electron number Ne in the first avalanche is lower than a critical number Ncr , the
positive ions as well as the photons emitted from the avalanche lead to the start of a next
avalanche at the cathode. New initial electrons are released from the cathode, according to
the secondary emission law, with the coefficient denoted as γ. The number of the new initial
electrons Ne can be calculated with:
Ne = γNi = γ
α
{exp[(α − η )d] − 1}.
α −η
(6.3)
If the number of the new electrons satisfies the relation Ne ≥ 1, the successive avalanche
developed from the new electrons will be larger than the previous one. And so on, the
following avalanches grow steadily, finally causing the breakdown of the gap. The breakdown following this mechanism is called ’Townsend mechanism’. So the criterion for the
Townsend breakdown can be expressed by equation:
γ
α
{exp[(α − η )d] − 1} ≥ 1.
α −η
Equation (6.4) can be rewritten as
α −η
(α − η )d ≥ ln
+1 .
αγ
(6.4)
(6.5)
In a gas with small or negligible electron attachment, we have relation α >> η. So the
right side of equation (6.5) can be simplified to be:
α −η
ln
+ 1 ≈ ln(1/γ + 1) = KTown ,
(6.6)
αγ
in which KTown is the discharge constant corresponding to Townsend breakdown mechanism. The value of (α − η ) can be measured empirically and the measured value can be
described by
−Bpd
(α − η )
= A · exp(
),
p
V
(6.7)
6.2. B REAKDOWN VOLTAGE IN SCF S
93
in which p is the gas pressure; d is the gap width; A and B are constants depending on the
gas composition, related to the primary ionization coefficient. A is the saturation ionization
in the gas at particular E/p (electrical field stress/pressure), and B is related to the excitation
and ionization energies [249].
At the breakdown voltage Vb the relation in equation (6.5) must be fulfilled. Combining
equations (6.5)-(6.7), the breakdown voltage of a gas undergoing Townsend mechanism can
be calculated by
Vb =
Bpd
Bpd
=
.
Apd
Apd
ln
ln
KTown
ln(1 + 1/γ )
(6.8)
Streamer mechanism
On the other hand, if the number of electrons Ne in the first avalanche reaches a critical value
Ncr , the spatial distribution of the electron in the avalanche head and positive ions in the
avalanche tail will generate a space charge induced electric field EL . Under the combination
of EL and the external field, the total electrical field is locally enhanced. Ionization is
increased at the place of the locally enhanced electric field and new avalanches are initiated
and propagate. Streamer is formed by the coalescence of these avalanches. Eventually when
the streamer bridges the inter-electrode gap, breakdown occurs. This breakdown mechanism
is called ’streamer mechanism’.
In a homogeneous electric field the criterion of streamer breakdown can be written as:
Ne = exp[(α − η )xcr ] ≥ Ncr , with xcr ≤ d.
In a non-homogeneous electric field the relation is expressed by:
x
cr
Ne = exp
(α − η )dx ≥ Ncr , with xcr ≤ d.
(6.9)
(6.10)
0
If we write ln(Ncr ) = Kstreamer in equations (6.9) and (6.10), we can easily find that actually
the criteria for Townsend mechanism and streamer mechanism can be expressed by the same
equation, only with different discharge constants: Kstreamer for streamer mechanism and
KTown for Townsend mechanism. Hence equation (6.8) is also applicable for the calculation
of breakdown voltage following streamer mechanism (in a homogeneous electric field), if
we implement the constant Kstreamer instead of KTown in the equation.
For a gap width of several to tens of centimeter the value of the critical electron number
is assumed to be Ncr = 106 − 108 . The constant for streamer mechanism breakdown has
then the value of Kstreamer = 13.8 − 18.4 [243].
6.2.2
Violation of simple Paschen’s curve
In high pressure gases including SCFs, the measured breakdown voltage is found to be
lower than the calculated value by the Townsend mechanism. The possible reasons are:
94
1) The electron-field emission from the cathode under high density situation [18, 27];
2) The ionization is enhanced at the protrusion on the electrode surface roughness
[53];
3) Particles or dusts are responsible for the micro-discharge generated near by the
electrodes [53, 250].
Simply calculating the breakdown voltage from equation (6.8) using the constant KTown or
Kstreamer cannot precisely predict the breakdown voltage in high pressure gases. In order to
more precisely calculate the breakdown voltage in SCFs, in our work we take the factor of
enhanced ionization into consideration. The breakdown voltages in N2 calculated from two
approaches: I. Paschen’s curve calculated from the Townsend breakdown mechanism and
II. streamer inception criteria taking into account surface roughness (enhanced ionization
coefficient), are compared with the measurements in SC N2 switches obtained in chapter 4.
6.2.3
Comparison of experiments with theories
Approach I. Paschen’s curve in N2
The Paschen’s curve in N2 can be calculated from equation (6.8). The constants in equation (6.8) are A = 112.50 ionization/(kPa · cm) and B = 2737.50 V/(kPa · cm) [251]. The
discharge constant KTown [251] has the form of:
⎧
A
pd
⎪
⎪
, with 0.0133 ≤
≤3
⎪
⎪
−0.0514
kPa
· cm
⎪
exp
2.5819
×
(pd)
⎪
⎨
A
pd
,
≤ 100
with 3 ≤
.
(6.11)
KTown =
0.1030
⎪
kPa
· cm
exp
2.4043
×
(pd)
⎪
⎪
⎪
A
pd
⎪
⎪
,
with 100 ≤
≤ 1400
⎩
exp (3.8636)
kPa · cm
Approach II. Streamer inception taking into account surface roughness
If a gap filled with SC N2 (density nN2 ) is applied with an electric field of E, avalanches
are initiated from the places where have highest reduced electric field E/nN2 and start to
propagate. These places can be either a small protrusion on the electrode surface or the low
density region of the discharge channel. Usually these are the hottest regions in the center
of the channel, but with the varying pressure in the channel, in reality it might also be at the
boundaries. If the avalanche attains a critical electron number Ncr within xcr ≤ d, it leads
to fast moving streamers from its head. These streamers can result in partial or complete
breakdown in non-uniform field gaps.
We calculate the breakdown voltage according to the discharge parameters on the axis,
by assuming a streamer initiating from a semi-ellipsoid protrusion on the electrode surface,
seen in figure 6.1. The major semi-axis of the protrusion is 20 μm, and the minor semi-axis
6.2. B REAKDOWN VOLTAGE IN SCF S
95
Figure 6.1 – The geometry of the protrusion on the surface of the electrode [16].
10 μm. So the electric field distribution can be calculated with [16]
⎫
⎧
1 x+a+c
(x + a)c ⎪
⎪
⎪
⎪
ln
−
⎬
⎨
2 x + a − c (x + a) 2 − c2
,
E(x) = E0 1 −
1 a+c c
⎪
⎪
⎪
⎪
ln
−
⎭
⎩
2 ac
a
(6.12)
in which E0 is the averaged electric field; a√and b are the parameters of the protrusion
geometry, seen in figure 6.1; c is given as c = a2 − b2 .
The streamer inception criterion can be expressed by [252]
xcr
0
α (E(x)) dx = ln(Ncr ),
(6.13)
in which E(x) is the electrical field at the distance x from the tip of the protrusion; Ncr is the
critical number of the electrons; α [m−1 ] is the ionization coefficient dependent on E/nN2
and is got from BOLSIG+ [225] (more detailed discussion can be found in [103]). The
value of ln(Ncr ) for N2 is a function of the pd, which can be calculated by [253]
⎧
⎪
⎨ 13.4 + 1.74ln(pd), 2 × 10−3 ≤ pd ≤ 0.05
bar · cm
.
(6.14)
ln(Ncr ) =
pd
⎪
⎩ 5.75 − 0.76ln(pd),
0.05 ≤
≤ 10
bar · cm
The criterion of breakdown of the gap in this work is defined as: under an electric field
E0 = Ebd in equation (6.12), if equation (6.13) is satisfied at xcr ≈ d, we say that the streamer
can bridge the electrodes hence cause the breakdown of the whole gap.
Comparison with experimental measurements
The simple Paschen’s curve as well as the breakdown voltage calculated from the streamer
inception criterion with enhanced ionization are plotted in figure 6.2 and figure 6.3. The
discontinuity of the dashed line in figure 6.2 is caused by the dependence of ln(Ncr ) on the
value of the pd, as shown in equation (6.14). The measured dielectric strength of SC N2
96
switches are plotted in the figure as well. The calculated breakdown electric field Ebd and
reduced breakdown electric field Ebd /p are compared with the measurements.
The measured Ebd in SC N2 is as high as 180 kV/mm at pd = 50 bar · mm. This is
comparable to solid insulating materials which have dielectric strengths reported to be
10 − 150 kV/mm for our gap width range. In the case of very thin films, some materials have a higher dielectric strength (around 400 kV/mm for 40 μm film of Kapton) [254].
From the measurements we can find that in general Ebd increases with higher value of pd,
but the gain slows down for higher pd values. This observation confirms the description by
Cohen [255] in his work on electric strength of highly compressed gases.
250
Simple Paschen’s curve
200
Breakdown field E
bd
[kv/mm]
300
150
Fast pulse, 0.6 - 0.66 mm
Fast pulse, 0.37 mm
100
Fast pulse, 0.26-0.32 mm
50
Moderate pulse, 0.3 mm
Streamer inception criterion
Slow pulse, <=0.16 mm
0
0
10
20
30
40
pd [bar*mm]
50
60
70
80
Figure 6.2 – Comparison of the experimental data on the breakdown field Ebd in SC N2 switches
with theoretical calculations. Solid line represents Paschen’s curve in N2 ; dashed line represents
the calculated breakdown field following the streamer inception criterion with enhanced ionization at the small protrusion on electrode surface.
At pd value below 15 bar · mm the measured Ebd matches the prediction by Paschen’s
law. Above this value deviation from Paschens’s curve is observed, and the value of Ebd
tends to rise more slowly from pd = 40 bar · mm onward. No obvious distinction regarding
to the steepness of the voltage sources is observed. Except for d > 0.6 mm, the measured
Ebd does not show much difference at different gap widths. The failure of Paschen’s law
under high pd value was reported as associated with field emission of electrons from the
cathode, as described in [27].
The measured Ebd /p of SC N2 switches is plotted in figure 6.3. Ebd /p in SC N2 is
found to decrease fast with increasing pd below 10 bar · mm, after then the slope becomes
more steady. By comparing with the Paschen’s law we find that the measured Ebd /p in
SC N2 matches the Paschen’s curve for fast rising pulses at pd < 5 bar · mm only. For the
97
6.3. D IELECTRIC RECOVERY IN SCF S
8
Fast pulse, 0.6 - 0.66 mm
Fast pulse, 0.37 mm
7
Reduced breakdown field [kV/mm/bar]
6
5
Slow pulse, <=0.16 mm
4
Simple Paschen’s curve
3
2
1
0
0
Streamer inception criterion
10
20
30
40
pd [bar*mm]
50
60
70
80
Figure 6.3 – Comparison of the experimental data on the reduced breakdown field Ebd /p in SC
N2 switches with theoretical calculations. Solid line represents Paschen’s curve in N2 ; dashed
line represents the calculated reduced breakdown field following the streamer inception criterion
with enhanced ionization at the small protrusion on electrode surface.
moderate and slow pulses as well as the fast pulses at pd > 5 bar · mm the measured Ebd /p
is lower than the prediction by Paschen’s law. For pd above 20 bar · mm, the dielectric
strength calculated by the streamer inception criterion with enhanced ionization matches
the measured values.
6.3
6.3.1
Dielectric recovery in SCFs
Validation of simple analytic model - comparison with an air plasma
switch
The recovery time in air predicted by the simple analytic model introduced in chapter 5.2
is compared with the experimental results of an air-flushed plasma switch with pressure
of 2 − 8 bar. The air plasma switch was tested under a voltage source with repetition rate
of 10 − 1000 Hz and peak voltage of 30 kV. The criterion of defining the recovery of the
switch δ is the same as that of the SC switch (B) under 1 kHz source (introduced in section
4.3). The reciprocal of the repetition rate at which δ ≥ 80% is taken as the recovery time of
the air plasma switch [194].
The recovery time of the air plasma switch estimated by this model is plotted as function
of the air flow rate in the range of 0 − 40 m3 /h at working pressure 2.5 bar (corresponding
to flow velocity 0 − 19 m/s in a 7.35 mm gap) in figure 6.4. The experimental results of the
98
35
Recovery time [ms]
30
25
20
Modeling results
15
10
5
0
0
Experimental results
20
40
60
3
Flow rate at STP [m /h]
80
100
Figure 6.4 – Predicted recovery time of the air plasma switch after the energy deposition of
0.7 J, and comparison with the experimental results. Gap width 7.35 mm, flow rate at STP zero
to 98 m3 /h (corresponding to flow rate of 0 − 40 m3 /h and flow velocity of 0 − 19 m/s in the
gap at working pressure 2.5 bar).
recovery time are also plotted in the figure. From figure 6.4 we can find that the calculated
recovery time is in the same order of magnitude, and is almost twice of the measured values.
There are several factors that might cause the deviation of the modeled value from the
experimental results. First of all, the heat transfer coefficient is taken from the value corresponding to the average temperature of the hot gas over the temperature decay range, and is
kept constant in the process. Secondly, the simple model assumes homogeneous temperature T, density ρ, and pressure p profiles inside the channel, whereas in practice the profiles
have peak values on axis or on outer radius. Thirdly, heat conduction to the electrodes is not
included. This lack of heat conduction mechanism is partly compensated by the heat convection between the gas on the spark channel outer edge and the environmental gas under
situation of larger temperature difference than that in reality. Moreover, radiation, which is
not accounted for as well, also reduces the recovery time. Last but not least, the breakdown
energy is taken as a constant input parameter, whereas from the experimental measurements
we observed that the breakdown voltage varies slightly with the experimental settings such
as repetition rate and gap width.
6.3.2
Validation of extended physical model - comparison with SC switch
measurements
Effects of thermal conductivity
The temperature decay inside the spark channel strongly depends on the thermal conductivity k of the medium. The impact of k on the simulation results of the extended model
99
6.3. D IELECTRIC RECOVERY IN SCF S
introduced in chapter 5.4 is inspected here.
6
k
16(a)
Thermal conductivity [Wm−1K−1]
k
16(b)
5
4
3
2
1
0
0
0.5
1
1.5
Temperature [K]
2
2.5
4
x 10
Figure 6.5 – Thermal conductivity of N2 calculated with the two sub-equations in (5.26). Solid
line - equation (5.26(a)), Dash line - equation (5.26(b)).
4
2.5
x 10
Tg for k16(b)
Tg for k16(a)
Temperature in the axis [K]
2
1.5
1
0.5
0 −11
10
−10
10
−9
10
−8
10
Time [s]
−7
10
−6
10
−5
10
Figure 6.6 – Modeled N2 temperature in the axis of the spark channel with thermal conductivity
k introduced in equation (5.26(a)) and equation (5.26(b)) respectively. The initial parameters are
taken from table 5.2.
Figure 6.5 gives the k of N2 calculated with sub-equation (5.26(a)) and (5.26(b)) in the
temperature range of 300 − 25000 K. The value of the thermal conductivity calculated from
100
the two equations differs when Tg > 2000 K, and the largest disparity happens at temperatures around 7000 K and 15000 K. The modeled gas temperatures on the axis of the spark
channel obtained with the two different thermal conductivity values are given in figure 6.6.
The figure shows that temperature is not very sensitive on the choice of thermal conductivity
model.
Effects of working pressure
With the thermal conductivity given in equation (5.26), the pressure dependence of the recovery process in N2 after breakdown is investigated with the extended model introduced
in chapter 5.4. The dielectric recovery breakdown voltage of the SC switch gap is calculated with the streamer inception criterion with enhanced ionization, as been introduced in
section 6.2.3. Three working pressures: 80 bar, 10 bar, and 5 bar are simulated. The basic
parameters of the models are given in table 6.1, while the other initial parameters can be
calculated by the scaling properties given in table 5.2. Due to the unsolved numerical instability at larger spark radius in the simulation, we choose the same initial radius: 35 μm
for the various pressures.
Table 6.1 – Background parameters of the modeling.
Pressure
Gap width
Temperature
Initial radius
80 bar
10 bar
5 bar
0.3 mm
2.0 mm
2.0 mm
300 K
300 K
300 K
35 μm
35 μm
35 μm
The simulated recovery breakdown voltage in N2 at these three working pressures are
given in figure 6.7. The simulated cold breakdown voltage has a value of 29 kV at p = 80 bar,
d = 0.3 mm, 22 kV at p = 10 bar, d = 2 mm, and 11.8 kV at p = 5 bar, d = 2 mm, respectively. After the breakdown of the medium, the withstand voltages at p = 80 bar and p = 10 bar
s predicted to decrease to approximately 300 V, while at p = 5 bar the value drops below
100 V.
After the extinction of the applied energy (current lasting about 200 ns), the breakdown
voltages at the three working pressures start to recover. At a time moment of 200 μs after
the breakdown, the breakdown value at 80 bar recovers to approximately 50 % of the cold
breakdown value. The recovery breakdown voltage at p = 10 bar and at p = 5 bar, however,
recovers to less than 25 % of the cold breakdown voltage at the moment of 200 μs after the
breakdown.
The measured recovery breakdown voltages of SC switch (B) at time lags between
two pulses in the range of 200 μs − 1 s are also plotted in figure 6.7. The values at time
lags shorter than 200 μs could not be measured with the existing setups. The measured
recovery breakdown voltage increases with larger medium pressure, which is consistent
with the modeling results. The simulated cold dielectric strength at 80 bar, d = 0.3 mm is
96.7 kV/mm, while the experimental results at 75 bar, d = 0.25 mm is 96 kV/mm at the
101
6.4. C ONCLUSIONS
5
10
Experimental, 75 bar, d=0.25 mm
29 kV
Modeling, 80 bar, d=0.3 mm
22 kV
4
10
11.7 kV
Experimental, 10 bar, d=0.25 mm
3
10
2
10
−10
10
−9
10
−8
10
−7
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
10
Time [s]
Figure 6.7 – Comparison of the experimental and modeling results of the recovery breakdown
voltage in SC N2 switch at various N2 pressures.
repetition of 5 Hz (time lag between pulses 0.2 s). Good consistency is found between the
simulation and measurements of the cold breakdown voltage.
The simulated recovery breakdown voltages are compared with the measured values.
From the comparison we can find that at a similar gap width, the simulated breakdown
voltages have good consistency with the experiments, though are slightly lower than the
experimental measurements. The percentage of the simulated recovery breakdown voltage
(at p = 80 bar, d = 0.3 mm) to the cold breakdown value at 200 μs is 50 %. The experimental results of 75 bar, 0.3 mm at 5 kHz repetition rate (time lag between pulses 200 μs)
are 80 % of the value at 5 Hz. The possible reasons of the lower calculated recovery breakdown voltage than measured values have been discussed in chapter 5.5.
6.4
Conclusions
We calculated the dielectric strength in SC N2 using two approaches: Paschen’s law using
simplified discharge constants and streamer inception criterion with enhanced ionization.
The measured breakdown voltages in SC N2 switches are compared with the calculations.
The deviation of the dielectric strength from the simple Paschen’s curve at high pd value is
observed. Breakdown voltage calculated by streamer inception with enhanced ionization is
found to match the measurements in SC N2 in the high pd range.
The simple analytic model is validated by comparing the simulation results in air with
the measurements of an air plasma switch. The validation of the extended physical model is
done by comparing the simulation results in SC N2 with the measurements in a SC switch.
The dependence of the extended model on the thermal conductivity of the insulating me-
102
dium is investigated. The modeled recovery breakdown voltages at different pressures are
compared. The simulation results are compared with the experimental measurements in SC
switch (B) (under repetition operation mode up to 5 kHz.
Table 6.2 compares the experimental and theoretical results of the dielectric strength
and recovery time in SC N2 switches. Good consistency exists between the experimental
measurements and theoretical calculations. The Paschen’s curve calculated from simplified
discharge constant is consistent with the measured dielectric strength in SC N2 , in the range
of p · d ≤ 20 bar · mm. Above this value the Paschen’s curve gives too high values, whereas
the streamer inception criterion with enhanced ionization mechanism gives good prediction
of the dielectric strength in SC N2 at higher pd values. The modeling results of the recovery
breakdown voltage are slightly lower than the experimental values, and improvement of the
present model could be researched.
Table 6.2 – Comparison of the experimental and theoretical results of breakdown and recovery
in SC N2 switches.
Parameter
Experiment
Model
p · d ≤ 18 bar · mm follows
Paschen’s curve
(with simplified constant);
Breakdown field
60 − 180 kV/mm
p · d > 18 bar · mm follows
streamer inception mechanism
(with enhanced ionization)
Recovery time
< 200 μs at 75 bar
200 μs at 80 bar
(Vrecov = 80 %)
(Vrecov = 50 %)
C HAPTER 7
C ONCLUSIONS AND R ECOMMENDATIONS
7.1
Conclusions
This thesis work studies the characteristics of supercritical fluids applied to high power
switching. This is a new field that has rarely been explored. Literature about the physical properties and applications of SCFs in multiple applications were reviewed. Based on
the data provided by a simple analytic model, we designed and manufactured three SCF
insulated switches. Under different voltage sources: fast rising pulses, moderately rising
pulses, slowly rising pulses, high repetition rate pulses up to 5 kHz, and a simple synthetic
arc current source, the breakdown and recovery characteristics of the SC N2 switches are
extensively studied. With an extended physical model the discharge and recovery process in
SC N2 was investigated theoretically. The modeling results were compared with the experimental measurements. Good consistency between the experimental and theoretical results
was observed, while the disparities were discussed. Table 7.1 gives a short summary of the
work that has been carried out within this dissertation.
Properties of SCFs
The state equation of a SCF is introduced and the physical parameters of SCFs such as
viscosity, density, diffusivity, heat capacity, and thermal conductivity are extrapolated from
literature. SCFs have liquid like properties such as high density and high thermal conductivity; gas like properties such as low viscosity and high diffusivity. Via literature survey,
the breakdown voltage in SCFs is proven to be very high. Although few research on the
dielectric recovery of SCFs has been carried out, the combined advantages of liquids and
gases indicate the capability of fast dielectric recovery of SCFs.
103
104
7. C ONCLUSIONS AND R ECOMMENDATIONS
Table 7.1 – Summary of the work on SCF switching in this thesis work.
Realized
Various SC
switch setups
Analysis
Experimental analysis
Experimental analysis of
of breakdown and recovery
current interruption capability
⇑
comparison
⇓
Two models
Analytic and numerical
−
results of discharge and recovery
Experimental measurements in SCF insulated switches
Several SCF insulated switches as well as their experimental setups are designed and manufactured. The dielectric strength of SC N2 switches is studied experimentally. SC N2
shows excellent insulation properties: insulation strength of 60 − 180 kV/mm is observed
in sub-millimeter gaps.
The dielectric recovery of SC N2 switches is analyzed under repetitive voltage pulses
with repetition rates up to 5 kHz. The experimental results prove that the recovery breakdown voltage in SC N2 increases with pd value, while too small gap width deteriorates the
recovery percentage of the switch. In high repetition rate mode, the recovery breakdown
voltage of SC N2 (at a pressure above 50 bar and gap width of 0.25 mm) is found to be
80 % of the cold breakdown value within 200 μs in non-flushed pre-firing mode. The recovery breakdown voltage at smaller gap width (0.15 mm) show less significant relationship
to the repetition rate compared to that at larger gap width (0.25 mm).
The current interruption capability of high-frequency (≥ 7 kHz) and low (< 500 A) current of SC N2 is investigated experimentally. SC N2 switch with fixed electrodes and small
inter-electrode distance can successfully interrupt the current with rate-of-rise in the range
of 0.14 − 3 A/μs and oscillation frequency up to 100 kHz at approximately 2 ms after the
breakdown. At the current interruption the returning voltage has a value of 200 − 500 V at
1.5 mm gap width. The current slope di/dt at the interruption moment is between 2000 A/s
and 5000 A/s, in a 40 bar, 2.2 mm gap. Forced flushing results in faster recovery of the
former arc channel, increased ac voltage, earlier successful current interruption, and increased rate-of-rise of transient recovery voltage du/dt. The experimental results indicate
the high arc interruption capability of SC N2 .
Modeling of the discharge in SCFs
Two models are developed to theoretically study the breakdown and recovery process in
SCFs. A simple analytic model utilizes the theory of gas cooling by adiabatic expansion
7.2. R ECOMMENDATIONS FOR FUTURE WORK
105
and the subsequent heat transfer mechanism. The predicted recovery time of SC N2 gives
reference parameters for the design of the SC switches.
Via an extended physical model, the discharge formation, temperature decay, and dielectric recovery in a SC N2 switch are simulated. The simulation results in a 80 bar SC N2
switch reveal that at 200 μs after the breakdown, the dielectric strength of the gap recovers
to about half of the cold breakdown value. Afterwards the recovery of the dielectric strength
slows down, because of the slower temperature decay. The absence of the turbulence mechanism might be responsible for the slower temperature decay in the late stage.
Comparison of experiment and model
The theoretical results of the breakdown and recovery in SC N2 switches are compared with
the experimental measurements. The Paschen’s curve calculated from simplified discharge
constant coincides with the measured dielectric strength of SC N2 in low pd range. At high
pd values Paschen’s curve gives too high value, while the streamer inception criterion with
enhanced ionization gives good prediction of the dielectric strength in SC N2 . The modeling
results of the recovery breakdown voltage have good consistency with the experiments,
though are slightly lower than the experimental results, and possible reasons are discussed.
7.2
Recommendations for future work
Experimental work
• In the present work the thermodynamic parameters of the SCFs during discharge can
be only theoretically estimated. Diagnostic components could be added, measuring
the pressure inside the discharge channel. The plasma temperature can be measured
optically by e.g. spectroscopic methods.
• There are no reports yet about the kinetic parameters of plasmas in SCFs such as
the initial electron density, electron-ion recombination rate, and ionization rate. The
method in present work is scaling up the values at ground pressure to the working
pressure by the similarity law. It is interesting to do some experimental research on
the parameters of plasmas in high pressure gases including SCFs.
• For the study of arc interruption characteristics, non-moving electrodes and flushing
perpendicular to the arc channel are basic ingredients of the SC switch in this work.
For the future research on the arc interruption of SCFs, moving electrode contacts
and axial SCF flushing need to be considered in the SC switch design. Circuits that
can produce power frequency currents could be considered as well.
Theoretical analysis
The theoretical models generated in this work use some simplified methodologies e.g. simplified kinetic mechanisms and one-dimensional geometry. These simplifications allow us
106
7. C ONCLUSIONS AND R ECOMMENDATIONS
to make the first step in theoretical study of discharges in SCFs, but have influence on the
accuracy of the simulation results. For further development of the theoretical models, the
following recommendations are made:
• The kinetic mechanisms need to be improved in the future theoretical models. More
reaction species need to be taken into account.
• Under continuous energy deposition, which mimics the discharge situation in a SC
switch applicable for circuit breakers, the mechanisms of thermal dissociation and
thermal ionization need to be considered.
• In the late stage of the extended physical model, mechanism of turbulent mixing
would be helpful to model the recovery of the spark channel more precisely.
• A two dimensional model would be able to more precisely study the streamer propagation and the subsequent heat transfer phenomenon in SCFs, in both in radial and axial
coordinates.
• Heat loss due to melting, evaporation, or direct sublimation of electrode materials
would mean a faster loss of thermal energy and thus a faster recovery. It would be
interesting to take this loss mechanism into account in a next research step.
A PPENDIX
A1. State equation of nitrogen
The general state equation of a fluid can be expressed using the Helmholtz energy α [J/mol]
with independent variables of density ρ [mol/m3 ] and temperature T [K] by [114]
α (ρ, T) = α 0 (ρ, T) + α r (ρ, T),
(A-1)
where α 0 (ρ, T) [J/mol] stands for the ideal gas contribution to Helmholtz energy; α r (ρ, T)
[J/mol] is the residual Helmholtz energy corresponding to the influence of inter-molecular
forces. Ideal gas Helmholtz energy can be written as
α 0 = lnδ + a1 lnτ + a2 + a3 τ + a4 τ −1 + a5 τ −2 +a6 τ −3 + a7 ln [1 − exp(−a8 τ )],
(A-2)
in which a1 = 2.5, a2 = −12.76952708, a3 = −0.00784163, a4 = −1.934819 × 10−4 ,
a5 = −1.247742 × 10−5 , a6 = 6.678326 × 10−8 , a7 = 1.012941, and a8 = 26.65788.
The function form for the residual Helmholtz energy is expressed by:
αr =
6
32
k=1
k=7
∑ Nk δ ik τ jk + ∑ Nk δ ik τ jk exp(−δ lk )
+
36
∑ Nk δ ik τ jk exp(−Φk (δ − 1)2 ) − β (τ − γk )2 ,
(A-3)
k=33
in which the coefficients are given in table A-2 and table A-3.
Pressure of the fluid p [Pa] can be calculated as the ideal gas contribution plus a correction term given by the derivative of the residual Helmholtz energy:
r ∂α
p = ρRT 1 + δ
.
(A-4)
∂δ
τ
107
108
A PPENDIX
The isochoric capacity cv [J/(mol · K)] and isobaric capacity cp [J/(mol · K)] of N2 are
calculated with
2 0 2 r ∂ α
∂ α
2
+
cv = −Rτ
;
(A-5)
∂ τ2 δ
∂ τ2 δ
r
2 r 2
∂α
∂ α
1+δ
−δτ
∂δ
∂ τ∂ δ
cp = cv + R r τ
2 r ,
∂α
∂ α
−δ2
1 + 2δ
∂δ τ
∂δ2 τ
(A-6)
in which R [J/(mol · K)] is the molar constant, δ = ρ/ρc the reduced density, and τ = Tc /T
the reduced temperature. The partial equations of α 0 and α r used in the equations above
are
6
32
∂ αr
= ∑ ik Nk β ik τ jk + ∑ ik Nk β ik τ jk exp(−β lk ) × (ik − lk β lk )
∂ δ τ k=1
k=7
36
∑ ik Nk β ik τ jk exp(−φk (β − 1)2 ) − βk (τ − γk )2 [ik − 2δ φk (β − 1)];
+
(A-7)
k=33
τ2
τ
2
∂ 2 α0
∂ τ2
∂ 2 αr
∂ τ2
= −a1 + 2a4 τ −1 + 6a5 τ −1 + 12a6 τ −3 − a7 a28 τ 2
δ
δ
=
6
32
k=1
k=7
(A-8)
∑ jk (jk − 1)Nk δ ik τ jk + ∑ jk (jk − 1)Nk δ ik τ jk exp(−β lk )
36
+
exp(a8 τ )
;
[exp(a8 τ ) − 1]2
∑ Nk β ik τ jk exp
−φk (β − 1) 2 − βk (τ − γk ) 2 [jk − 2τβk (τ − γk )];
(A-9)
k=33
δ
∂ αr
∂δ
+
τ
=
6
32
k=1
k=7
∑ jk Nk β ik τ jk + ∑ jk Nk β ik τ jk exp(−β lk ) × (ik − lk δ lk )
36
−φk (β − 1) 2 − βk (τ − γk ) 2 ×[ik − 2δ φk (δ − 1)];
(A-10)
k=33
δτ
+
∂ 2 αr
∂δ∂τ
36
=
6
32
k=1
k=7
∑ ik jk Nk β ik τ jk + ∑ jk Nk β ik τ jk × exp(−β lk )(ik − lk δ lk )
∑ Nk β ik τ jk × exp
−φk (β − 1) 2 − βk (τ − γk ) 2 × [ik − 2δ φk (δ − 1)][jk − 2τβk (τ − γk )];
k=33
(A-11)
109
Table A-2 – Parameters used in state equation of nitrogen.
k
Nk
ik
jk
lk
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
0.924803575275
−0.492448489428
0.661883336938
−0.192902649201 × 101
−0.622469309629 × 10−1
0.349943957581
0.564857472498
−0.161720005987 × 101
−0.481395031883
0.421150636384
−0.161962230825 × 10−1
0.172100994165
0.735448924933 × 10−2
0.168077305479 × 10−1
−0.107626664179 × 10−2
−0.137318088513 × 10−1
0.635466899859 × 10−3
0.304432279419 × 10−2
−0.435762336045 × 10−1
−0.723174889316 × 10−1
0.389644315272 × 10−1
−0.212201363910 × 10−1
0.408822981509 × 10−2
−0.551990017984 × 10−4
−0.462016716479 × 10−1
−0.300311716011 × 10−2
0.368825891208 × 10−1
−0.255856846220 × 10−2
0.896915264558 × 10−2
−0.441513370350 × 10−2
0.133722924858 × 10−2
0.264832491957 × 10−3
0.196688194015 × 102
−0.209115600730 × 102
0.167788306989 × 10−1
0.262767566274 × 104
1.0
1.0
2.0
2.0
3.0
3.0
1.0
1.0
1.0
3.0
3.0
4.0
6.0
6.0
7.0
7.0
8.0
8.0
1.0
2.0
3.0
4.0
5.0
8.0
4.0
5.0
5.0
8.0
3.0
5.0
6.0
9.0
1.0
1.0
3.0
2.0
0.25
0.875
0.5
0.875
0.375
0.75
0.5
0.75
2.0
1.25
3.5
1.0
0.5
3.0
0.0
2.75
0.75
2.5
4.0
6.0
6.0
3.0
3.0
6.0
16.0
11.0
15.0
12.0
12.0
7.0
4.0
16.0
0.0
1.0
2.0
3.0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
4
4
4
4
2
2
2
2
110
A PPENDIX
δ2
∂ 2 αr
∂ τ2
τ
=
6
∑ ik (ik − 1)Nk β ik τ jk
k=1
+ ∑ jk Nk β ik τ jk × exp(−β lk ) (ik − lk δ lk )(ik − 1 − lk δ lk ) − l2k δ lk
32
k=7
+
36
−φk (β − 1) 2 − βk (τ − γk ) 2 × [ik − 2δ ϕk (δ − 1)]2 − ik − 2δ 2 ϕk .
k=33
(A-12)
Table A-3 – Parameters used in state equation of nitrogen.
k
φk
βk
γk
33
34
35
36
20
20
15
25
325
325
300
275
1.16
1.16
1.13
1.25
A2. Integrator of the triggering signal generator
Pick-up antenna
Figure A-1 – Integrator of the triggering signal generator for the ICCD camera.
111
A3. Calibration of current measured by Rogowski coil
From figure A-2 we can derive the relation between signal Vcoil , which comes out of the
Rowgowski coil and signal Vout collected by the oscilloscope
Vcoil − Vout Vout
1
Vout =
−
dt.
(A-13)
Ci
Ri
R1
in which Vout is the signal read from oscilloscope, and τ = Ri · Ci with Ri and Ci respectively
1060 Ω and 879 pF. With known output voltage, the real voltage on the coil can be rewritten
with
Ri
Vcoil dt = τVout + 1 +
Vout dt.
(A-14)
R1
Vout
Ri
Vcoil
Ro
Ci
R1
Figure A-2 – Circuit diagram of integrator of current measurement.
The arc current can be calculated from the voltage on the Rogowski coil
i(t) =
1
M
Vcoil dt,
(A-15)
where M is the mutual inductance of the Rogowski coil. By interpreting equation (A-14)
into equation (A-16), we can get the expression of arc current:
Ri
Vout
Vout τ
+ 1+
dt.
(A-16)
i(t) =
M
R1
M
112
A PPENDIX
A4. Cylindrical coordinate in Euler system
The Euler equations which covers the equations of conservation of mass, momentum, and
energy are
∂ρ
+ · (ρu) = 0;
∂t
∂ (ρu)
+ · (u
(ρu)) + p = 0;
∂t
∂ε
+ · (u(ε + p)) = 0.
∂t
(A-17a)
(A-17b)
(A-17c)
In cylindrical coordinate, we have the expression:
1 ∂ (A1 r) 1 ∂ (A2 ) ∂ (A3 )
+
+
;
r ∂r
r ∂Φ
∂z
∂ (A)
1 ∂ (A)
∂ (A)
+ e2
+ e3
.
A = e1
∂r
r ∂Φ
∂z
·A =
(A-18a)
(A-18b)
The total energy of the gas satisfies ∂∂εt + · (u(ε + p)) = Qin − Qout , with Qin and Qout
representing the energy per unit time which comes in and goes out of the system. Also we
have energy stored in the vibration excited level εV and electronic excited level εE . Combining equation (A-17) and (A-18), we can write the equation of conservation in cylindrical
coordinate as:
∂ ρ 1 ∂ (ρur)
+
= 0;
∂t r ∂r
∂ (ρu) 1 ∂ (ρu2 r) ∂ p
+
+
= 0;
∂t
r ∂r
∂r
∂ ε 1 ∂ (u(ε + p)r)
+
= Qin + Qout ;
∂t r
∂r
∂ εV 1 ∂ (uεV r)
+
) = ηV QR + QVT ;
∂t
r ∂r
∂ εE 1 ∂ (uεE r)
+
) = ηE QR + QVT .
∂t
r ∂r
(A-19a)
(A-19b)
(A-19c)
(A-19d)
(A-19e)
113
A5. Simulation of electron-ion recombination in N2 discharge
We use a zero-dimensional modeling platform ZDPlasKin [256] to model the dynamics of
species in a streamer channel. The description of dynamics is given by
d[ni ]
= Si ,
(A-20)
dt
where the source term Si represents the total rate of production and destruction of species i in
various processes. We use N2 kinetics from [227,256] which includes the following species
and states: e, N, N2 , N+ , N+2 , N+3 , N+4 , N2 (A3 Σu+ , B3 Πg , C3 Πu , a
1 Σu− ), N2 (X1 , v = 1 − 8).
The rate constants for electron-neutral interactions are calculated using BOLSIG+ solver
[225].
For self-consistent coupling between the electric field and the equation (A-20) we use
the approach proposed in [257], where the electric field obeys the equation
dE ε0
=
μ (|E|) E ne .
(A-21)
dt
e
Essentially we apply the same initial conditions as in [257], but scaled up to 80 bar.
The maximum electric field is assumed to be 150 kV · cm−1 at standard temperature and
pressure (STP), which scales to E(0) = 12 MV · cm−1 at 80 bar according to the similarity
laws. Maximum electric field E(0) corresponds to the initial electron density from the table
5.2 and reads as ne (0) = ne,0 = 8.87 × 1020 m−3 . The equations (A-20) and (A-21) are integrated together to obtain a decay of the electric field consistent with the conductivity. The
integration is continued up to the electric field reaches the value of 0.4 MVcm−1 . Afterwards, we continue integration with a constant electric field of 0.4 MVcm−1 until end of
the pulse (total pulse duration is taken to be equal to 100 ns), and then in a vanishing field.
The results of ZDPlasKin run are imported and analyzed in an open source software
package PumpKin [222], which is freely available at www.pumpkin-tool.org. PumpKin
automates the process of finding all principal pathways, i.e. the dominant reaction sequences, in a chemical reaction system. We run PumpKin for the time interval of [0.01, 1]
ns and for the species of interest of electron. The result of analysis shows that the lifetime
of N+2 is very short about 12 fs, while N+4 has much longer lifetime of about 9.1 ps. Under these conditions, the dominant electron loss mechanism is a electron-ion dissociative
recombination given by
e + N+4 → N2 + N2 .
(A-22)
According to PumpKin, this reaction is responsible for the 100 % of the destruction of
electron with a rate of 1.4 · 1022 cm−3 s−1 . On the other hand, the electron impact ionization
e + N2 → N+2 + 2e ,
(A-23)
2.0 · 1015
cm−3 s−1 .
is responsible for 98 % of the production of electrons with a rate of
This is the reasoning why we, under the assumption that the similarity laws are applicable at 80 bar pressure, consider the kinetic equation in form of (5.16).
114
A PPENDIX
A6. Ionization and dissociation mechanisms
Here we only consider the ionization up to double ionization stage, while the higher level
is neglected. We assume that all the molecules are assumed to be completely dissociated
before ionization begins, and all atoms are assumed to be singly ionized before the number
of doubly ionized particles becomes noticeable [38].
In this approach the state of equation and caloric equation are derived from references [258]. The difference between the calculation here and the reference is that the concentration of molecules is also taken into account. The indexes used in the calculations are
given in table A-4 .
Table A-4 – The indexes used in the calculation.
Parameter
Number of total particle
Number density of
total particle
Electron mass
Nitrogen atom mass
Nitrogen ion mass
Nitrogen molecular mass
Concentration of molecule
Concentration of atom
Concentration of electron
Concentration of single ion
Concentration of double ion
Total Pressure
Electron Pressure
Statistic weight
of ion on stage n
Statistic weight of atom
Boltzmann’s constant
Plank’s constant
Dissociation energy
Single ionization energy
Double ionization energy
Gas constant
Temperature
Symbol
Value
Ntotal
ntotal
Me
M0
Mi
MN2
CN2
C0
Ce
C1
C2
P
Pe
gn
NN2 + N0 + Ne + N1 + N2
MN2 NN2 + M0 N0 +
Me Ne + M1 N1 + M2 N2
9.10 × 10−31 [kg]
1.163 × 10−26 [kg]
≈ 1.163 × 10−26 [kg]
2.326 × 10−26 [kg]
NN2 /Ntotal
N0 /Ntotal
Ne /Ntotal
N1 /Ntotal
N2 /Ntotal
−
P × Ce
g1 = 9; g2 = 6
g0
k
h
I0
I1
I2
R
T
g0 = 4
1.38 × 10−23 [J/K]
6.626 × 1034 [J·s]
3.3484 × 104 [kJ·kg−1 ]
9.9806 × 104 [kJ·kg−1 ]
2.0321 × 105 [kJ·kg−1 ]
R = 2.8809 × 102 [J·K−1 ·kg−1 ]
−
We know Saha’s equation for dissociation
n0 n0 g0 · g0 [2πMN /2kT]3/2 −I0
=
e RT ,
nN2
gN2
h3
(A-24)
115
and Saha’s equation for ionization
ni+1 ne ge · gi+1 [2πMe kT]3/2 −Ii+1
=
e RT .
ni
gi
h3
(A-25)
If we write the Saha’s equations in the format of concentration of different particles, we
have equation for dissociation
CN2
=
C0 C0
in which
C0 C0
CN2
1
0
g0 ·g0 [2πMN /2kT]3/2 −I
e RT
gN2
h3
=
Ci
=
Ci+1 Ce
n0 V n0 V ntotal V
ntotal V ntotal V nN2 V
=
· ntotal ,
n0 n0 1
nN2 ntotal ;
1
i+1
ge ·gi+1 [2πMe kT]3/2 −IRT
e
gi
h3
(A-26)
and Saha’s equation for ionization in format:
· ntotal ,
(A-27)
V
Ce
ni+1 ne 1
= nni+1 VV · n ne VV · ntotal
in which Ci+1
Ci
n0 V = n0 ntotal . In the equation above if we write ntotal = P/kT,
total
total
then equation (A-27) actually is the same as the one given in [258].
The summary of all the particle concentrations should be
1 = CN2 + C0 + Ce + C1 + C2 + ...
(A-28)
The generation of electrons due to ionization satisfies the relation
Ce = C1 + 2C2 + 3C3 ...
(A-29)
Combining equation (A-28) and (A-29), we have
1 = CN2 + C0 + 2C1 + 2C2 ...
(A-30)
All the concentrations can be expressed by the value of C0 and other parameters, seen as
1 P
· C2 ;
·
S0 kT 0
C0 S1 kT
;
C1 =
Ce P
C1 S2 kT C0 S1 · S2 (kT) 2
=
C2 =
.
Ce P
C2e
P2
CN2 =
(A-31a)
(A-31b)
(A-31c)
The values of S0 , S1 , and S2 are
g0 · g0 [2πMN /2kT]3/2 −I0
e RT ;
gN2
h3
(A-32a)
S1 =
ge · g1 [2πMe kT]3/2 −I1
e RT ;
g0
h3
(A-32b)
S2 =
ge · g2 [2πMe kT]3/2 −I2
e RT .
g1
h3
(A-32c)
S0 =
116
A PPENDIX
If we substitute equation (A-31a)-(A-32c) into equation (A-30), we can derive the solution,
though with an unknown value Ce inside. By assuming a value of Ce , we can calculate a
value of C0 . The values of CN2 , C1 ,C2 can be calculated with equation (A-31a)-(A-31c).
With equation (A-29) a new value of Cepre can be calculated. If the calculated Ce differs
larger than 0.1 % from the presumed value, a new value Ce−new = (Ce−pre + Ce )/2 is used
for the new round of calculation. The iterative process continues until the value of Ce
convergences to the required accuracy 0.1 %.
120
Particle concentrations [%]
100
80
Catom
Cion1
60
Cion2
CN2
40
C
Ne
total concentration
20
0
0
0.5
1
1.5
Temperature [K]
2
2.5
4
x 10
Figure A-3 – Concentrations of particles in air for temperature up to 25000 K, pressure at 1 bar.
120
Particle concentrations [%]
100
80
C
atom
C
ion1
60
Cion2
CN2
40
CNe
total concentration
20
0
0
0.5
1
1.5
Temperature [K]
2
2.5
4
x 10
Figure A-4 – Concentrations of particles in air for temperature up to 25000 K, pressure at 80 bar.
117
Figure A-3 and figure A-4 show the value of C0 , C1 , and C2 as function of temperature
at different pressures. From the figures we can see that thermal dissociation and ionization
happen at higher temperature when the pressure is higher. In both 1 bar and 80 bar situation,
the mechanisms become significant when the temperature is above 5000 K. However, from
literature survey, we learn that the establishing time scale of the ionization equilibrium for
nitrogen is quite long. The time scales of ionization equilibrium of several species against
the temperature can be found in [247]. According to the calculation, the time needed for
establishing ionization equilibrium in nitrogen in our case is between 1.5 − 60 μs. From
the time development of N2 dissociation under different temperatures given in [247], we
can see that for the temperature of 10000 K, the fraction of dissociation in nitrogen reaches
about 10−12 at the time of 1 μs. For temperature of 25000 K, the fraction reaches about
10−3 at 1 μs.
In our simulations given in chapter 5.4, the high temperature zone of the discharge channel (at 80 bar) vanishes with a time scale much shorter than the establishing time of dissociation and ionization equilibrium, hence it is reasonable to neglect the impact of thermal
dissociation and ionization in our simulations.
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L IST OF PUBLICATIONS
Journal Publications
2015
• J. Zhang, A.H. Markosyan, M. Seeger, E.M. van Veldhuizen, E.J.M. van Heesch,
U. Ebert.
Numerical and experimental investigation of dielectric recovery in
supercritical N2 , Plasma Sources Sci. Technol., vol.24, no.2, pp. 025008, 2015.
• J. Zhang, E.J.M. van Heesch, F.J.C.M. Beckers, T. Namihira, A.J.M. Pemen, A.H.
Markosyan, R.P.P. Smeets. Breakdown Strength and Dielectric Recovery Investigation
in High Pressure Nitrogen Switch up to Supercritical Status (accepted for publication),
IEEE Transactions on Dielectrics and Electrical Insulation.
2014
• J. Zhang, E.J.M. van Heesch, F.J.C.M. Beckers, T. Huiskamp, A.J.M. Pemen.
Breakdown Voltage and Recovery Rate Estimation of a Supercritical Nitrogen Plasma
Switch, IEEE transactions on Plasma Science, vol.42, no.2, pp.376-383, 2014 .
Conference publications
2014
• J. Zhang, E.J.M. van Heesch, Takao Namihira, F.J.C.M. Beckers, and A.J.M. Pemen.
Breakdown strength and dielectric recovery investigation inside a supercritical switch.
Proceedings of 14th International Symposium on High Pressure Low Temperature
Plasma Chemistry (HAKONE XIV), Germany, 2014.
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L IST OF PUBLICATIONS
• E.J.M. van Heesch, J. Zhang, T. Namihira, A. Markosyan, A.J.M. Pemen, F.J.C.M.
Beckers, T. Huiskamp, and U. Ebert. Voltage recovery in supercritical switching
media. Proceedings of IEEE International Power Modulator and High Voltage Conference,
Santa Fe, June 1-5, 2014.
• E.J.M. van Heesch, W.F.L.M. Hoeben, J. Zhang, F.J.C.M. Beckers, T. Huiskamp and
A.J.M. Pemen. Pulsed Power Applications Research: From Super Critical Switches
to Renewable Fuels. Proceedings of IEEE International Power Modulator and High
Voltage Conference, Santa Fe, June 1-5, 2014.
2013
• J. Zhang, E.J.M. van Heesch. Recovery rate analysis of plasma switch and comparison
with experimental results. Proceedings of XXth Symposium on Physics of Switching
Arc-FSO 2013, Czech Republic, Sep. 2013.
• A.H. Markosyan, J. Zhang, B. van Heesch, U. Ebert. Streamer to spark transition in
supercritical N2 . Proceedings of XXth Symposium on Physics of Switching ArcFSO 2013, Czech Republic, Sep. 2013.
• J. Zhang, T. Furusato, F.J.C.M. Beckers, E.J.M. van Heesch, E.M. van Veldhuizen.
Study of breakdown inside a supercritical fluid plasma switch. Proceedings of IEEE
Pulsed Power & Plasma Science Conference, San Francisco, CA USA, June. 2013.
2012
• J. Zhang, F.J.C.M. Beckers, E.J.M. van Heesch. Breakdown voltage study of a
supercritical medium switch based on experiment. Proceedings of EAPPC-BEAMSConference, Karlsruhe, Germany, 2012.
ACKNOWLEDGEMENT
After the long hard time, I am so glad and proud about what I have managed to do. But I
know that I couldn’t have gone so far without the great help from my colleagues, my friends,
my family and everyone else who has given me help within the past five years.
First of all, I want to give my sincere appreciation to my first promoter prof.ir. Wil
Kling. When my husband Lei got a chance of interview for a Ph.D. candidate position in
EES-group in TU/e, Wil kindly invited me for a visit to the group. The encouragement and
care from Wil in our regular discussion during my Ph.D. study always gave me impetus to
work hard and cruise to the happy ending of the thesis.
Dr. Bert van Heesch is my daily supervisor and co-promoter. My highest thanks go
to Bert for his patient guidance. You gave me huge help throughout my five-year study,
from the collection of the initial materials for this project to the design and operation of the
supercritical switches. Thanks to the kind help from Bert, my contract of Ph.D. study was
successfully extended for extra six months.
I would like to give my acknowledgement to my second Promoter prof. Ute Ebert. She
gave me huge support in the theoretical modeling of my thesis. I am enlightened by her
intelligence and diligence.
My great thanks also go to Dr. Martin Seeger from ABB, Switzerland. You ceaseless
advertising is an indispensable part of my thesis. My appreciation to your patient guidance
and friendly attitude.
I would also like to appreciate prof.dr.ir. René Smeets. Thanks so much for your
kind patient guidance during the past years. During all the discussion and meetings, you
always gave me essential suggestions, and your kindness always made me feel relaxed and
confident.
I want to thank colleagues Tomohiro and Dr. Takao Namihira from Kumamoto University,
Japan. Thank you a lot for the useful discussion and sharing of information during your visit
to our group.
With this chance, I want to express my thankfulness to all the other committee members,
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ACKNOWLEDGEMENT
Prof.Dr.-Ing. A. Schnettle, dr.ing. A.J.M. Pemen, and dr. R.A.H. Engeln for their precious
time to review my thesis. Their useful comments help me improve this thesis so much.
My gratitude also goes to my cooperator Aram from CWI, Amsterdam. I enjoyed all
those hard working weekends when we built the theoretical models and prepared the papers.
Other colleagues from CWI, Anbang, Ashutosh, and Jannis also gave me kind support
during those days. My appreciations to all of you.
I would like to thank all the other colleagues from EES-group. I feel so lucky to
work with you during my Ph.D. student life. Thank you so much for creating the joyful
environment and your support whenever I need. I especially want to thank Anna, Annemarie,
Ballard, Bart, Chai, Eloy, Frank, Gu, Hennie, Jerom, Marcel, Pavlo, Tom, Vindhya, Wilfred,
Yan, Yin, Yu. My sincere appreciation goes to Ad, Rene, and Sjoerd, who have given me so
much technical support and warm care.
Last but not the least, I want to thank my parents and my husband. Thank you for being
around and supporting me.
C URRICULUM V ITAE
Jin Zhang was born in Jiangsu, China, on 12. Dec. 1985. She obtained her Bachelor
of Science of thermal power and dynamic engineering from Nanjing Normal University
in Nanjing, China, in 2007. She graduated from RWTH-Aachen University in Aachen,
Germany, as a Master of Science of electrical power engineering in 2010. In the same year,
she joint the Electrical Energy System group at Eindhoven University of Technology, as a
Ph.D. candidate under the supervision of prof.ir. W.L. Kling and dr.ir. E.J.M. van Heesch.
Her research topic is "Supercritical fluid for high power switching".
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