Supercritical fluids for high power switching

Transcription

1 Supercritical fluids for high power switching Zhang, J. Published: 01/01/2015 Document Version Publisher s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. The final author version and the galley proof are versions of the publication after peer review. The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA): Zhang, J. (2015). Supercritical fluids for high power switching Eindhoven: Technische Universiteit Eindhoven General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 02. Apr. 2018

2 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 uur door Jin Zhang geboren te Jiangsu, China

3 Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van de promotiecommissie is als volgt: voorzitter: prof.dr.ir. A.C.P.M. Backx 1 e promotor: prof.ir. W.L. Kling 2 e promotor: prof.dr. U.M. Ebert copromotor: dr.ir. E.J.M. van Heesch leden: 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

4 To my parents and my husband Lei

5 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: Copyright 2015 Jin Zhang, Eindhoven, the Netherlands All rights reserved.

6 CONTENTS Contents Summary i 1 Introduction Plasma in supercritical fluids Research goal Research approach Experimental work Modeling Dissertation outline Supercritical fluids and insulating media Short review of conventional insulating media Breakdown in conventional media Recovery of conventional media Supercritical fluids State equation SCF properties Applying supercritical media Chemical applications Plasma applications in supercritical media High power switching The challenges Existing solutions Vacuum and gaseous state switches for pulsed power applications. 24

7 CONTENTS Solid state switches for pulsed power applications Circuit breakers in power networks Design of supercritical switches Simple SC switch (A) Multi-functional SC switch (B) SC switch (C) with larger gap width Arc interruption testing circuit Circuit principle Real setup Experimental investigation of breakdown and recovery in SCFs Introduction Breakdown voltage analysis V b under slow pulses (1.66 kv/ms) V b under moderate pulses (2.5 kv/μs) V b under fast pulses (2 kv/ns) Dielectric recovery analysis Experiment under 1 khz voltage source Experiment under 5 khz voltage source Current interruption analysis Parameter settings Experimental results ICCD image of discharge in SC N Conclusions Theoretical modeling of discharge and recovery in SCFs Introduction Simple analytic model Model description Model Formulation Results and discussions Electric field across the gap Extended physical model for discharge in SCFs General model description Model Formulation Streamer-to-spark transition phase Discharge and post-discharge phase Numerical conditions Results and discussions Conclusions Comparison of experiment and model Introduction... 91

8 CONTENTS 6.2 Breakdown voltage in SCFs Principle of Paschen s law Violation of simple Paschen s curve Comparison of experiments with theories Dielectric recovery in SCFs Validation of simple analytic model - comparison with an air plasma switch Validation of extended physical model - comparison with SC switch measurements Conclusions Conclusions and Recommendations Conclusions Recommendations for future work Appendix 107 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 N 2 discharge A6. Ionization and dissociation mechanisms Bibliography 119 List of publications 139 Acknowledgement 143 Curriculum Vitae 145

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10 SUMMARY 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 (SF 6 ), 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

11 ii SUMMARY dielectric recovery; current interruption capability. SC nitrogen (N 2 ) 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 N 2 switches: dielectric strength of 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 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 N 2 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.

12 iii We compared the experimental results of breakdown and recovery in SC N 2 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 N 2 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 N 2 for high pd. The modeled recovery breakdown voltage in SC N 2 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.

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14 CHAPTER 1 INTRODUCTION 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

15 2 1. INTRODUCTION (a) (b) (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 (SF 6 ) 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 SF 6 in HVCBs, because SF 6 is an extreme greenhouse gas with global warming potential 23,900 times that of carbon dioxide (CO 2 ) [14]. Besides, the

16 1.3. RESEARCH APPROACH 3 Plasmas in supercritical fluids SC plasma power switch Supercritical plasma chemistry Dense planetary atmosphere [12] Power networks Pulsed power systems Synthesis of nanoparticles [9-11] Conversion of chemical compounds SF6 free switch gears 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 SF 6 are extremely toxic. SCF could be an ideal alternative to SF 6, 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 (N 2 )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 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

17 4 1. INTRODUCTION 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 CO 2, SC argon (Ar), SC helium (He) and SC N 2, 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 N 2 switches by applying different pulsed sources at low repetition rates; testing the dielectric recovery of SC N 2 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 N 2 using an intensified CCD camera, providing important data for the theoretical modeling 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

18 1.4. DISSERTATION 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 N 2 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 N 2 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 N 2 switch is estimated by an

19 6 1. INTRODUCTION 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 N 2, 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 N 2. 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 N 2 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.

20 CHAPTER 2 SUPERCRITICAL 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 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

21 8 2. SUPERCRITICAL FLUIDS AND INSULATING MEDIA Breakdown voltage [kv/mm] Lightning pulse AC breakdown Mineral oil Air Liquid N2 SF6 Liquid He PTFE (thin film) Figure 2.1 Summary of the dielectric strength for selected insulators: air (0.5 4 bar) [48], mineral oil [49, 50], Liquid N 2 [51, 52], SF 6 (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 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 N cr, 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

22 2.1. SHORT 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, N 2,CO 2 [62, 63], and SF 6 are applied for high power switches. SF 6 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 SF 6, many countries have noticed the huge impact of SF 6 on the environment. Efforts to reduce the emission of SF 6 are ongoing, among which the replacement of SF 6 in CBs is a major task. Mixing of SF 6 with other gases such as N 2 or Ar reduces the amount of SF 6 needed. Research on the mixture of SF 6 with inert gases includes SF 6 +air [66], SF 6 +CO 2 [67], SF 6 +Ne (neon) [68], SF 6 +N 2 [69], SF 6 +He [70], SF 6 +Ar, and SF 6 +H 2 (hydrogen) [71]. At present a SF 6 -N 2 mixture is often applied. Such mixtures are nonflammable and those containing 50 60%ofSF 6 have dielectric strength up to % that of pure SF 6 [59]. Investigations have also been proceeded to study other insulating media for full replacement of SF 6 [62,72 77]. No promising alternative has yet been found within the same pressure and temperature range. However, the main relative superiority of SF 6 over other gas species like N 2 and CO 2 in dielectric strength diminishes when pressure is above 9 bar [78]. Liquid insulators Liquids such as liquid He [79,80], liquid N 2 [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

23 10 2. SUPERCRITICAL FLUIDS AND INSULATING MEDIA 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 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 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]. Breakdown strength Intrinsic breakdown streamer thermal electrochemical s time 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 ε r 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-

24 2.1. SHORT 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] 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 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, ]. Typical gas insulators like air, N 2, 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 [ ]. 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].

25 12 2. SUPERCRITICAL FLUIDS AND INSULATING MEDIA Table 2.1 Overview of the recovery rates in water, hydrogen, SF6, air, Ar, Propylene carbonate, and N2. Condition Insulator Water [101] Ar-H2 mixture [102] SF6 [20] Synthetic air [103] (95% 5%) Gap width [mm] Pressure [MPa] Flow rate [cm 3 /s] Current [ka] Recovery time [ms] > 1 > 2.5 > 8 > 10 Max. repetition rate [Hz] 1 k 1.4 k < 1 k k 10 k 3.3 k < 1 k < 400 < 125 < 100 Condition Insulator Ar [102] Propylene carbonate N2 [104] (C4H6O3) [105] Gap width [mm] Pressure [MPa] Flow rate [cm 3 /s] Current [ka] Recovery time [ms] Max. repetition rate [Hz] <

26 2.2. SUPERCRITICAL FLUIDS Supercritical fluids 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 T c and critical pressure p c, 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 N 2 in a gas cylinder above 3.4 MPa is acting as a SCF. Pressure Pc Solid Liquid Gas Triple point Tc Supercritical fluid Critical point Temperature Fluid Critical Critical pressure temperature [MPa] [K] H 2 O CO He H Ar N Air Figure 2.3 Idealized phase diagram of a single substance and the critical pressure (p c ) and critical temperature (T c ) of the selected fluids. The critical point is the point corresponding to the critical temperature T c and critical pressure p c, 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 N 2 reported in [114]: T c = 126 ± 0.01 K; p c = ± MPa; ρ c = ± 0.1 kgm 3 (= ± 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 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)

27 14 2. SUPERCRITICAL FLUIDS AND INSULATING MEDIA 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: p = ρrt [ 1 + δ ( )] α r δ, (2.3) τ in which R is the molar constant, δ = ρ/ρ c the reduced density, and τ = T c /T the reduced temperature. The detailed equations for α 0 (ρ,t) and α r (ρ,t) for N 2 (the studied medium in this work), and the partial derivatives in equation (2.3) are given in appendix A1. Pressure [MPa] Pc: Figure 2.4 Phase diagram of N 2 in the range of temperature K and pressure up to 20 MPa, calculated by state equation (2.3). Figure 2.4 illustrates the phase diagram of N 2 in form of pressure versus density up to 20 MPa, within the temperature range of K. Below the critical temperature T c, N 2 has either gas status (when above critical pressure) or liquid status (when below critical pressure). N 2 changes from other phases to the SC phase when the temperature and pressure satisfy T > 126 K, p > 3.4MPa. The parameter range of SC N 2 in the case of electrical discharge applications is in the region: 300 K < T < 10 4 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 N 2 between 250 K and 350 K and pressure up to 30 MPa [114]: p = ρrt( k=1 with the parameters given in table 2.2. i k N k δ i k τ j k ), (2.4)

28 2.2. SUPERCRITICAL FLUIDS 15 Table 2.2 Parameters used in the state equation of N 2, equation (2.4). k N k i k j k 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 CO 2 extracts a bond component into the CO 2. 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;

29 16 2. SUPERCRITICAL FLUIDS AND INSULATING MEDIA 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 N 2 in the range of temperature of 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 N 2. The value of diffusivity is the order of magnitude figure for N 2 in range of T = K, p = MPa. Density Viscosity Diffusivity Heat Thermal capacity conductivity [kg/ m 3 ] [μpa s] [m 2 /s] [10 6 J/m 3 /deg] [10 3 J/m/s/deg] Gas at STP SC N Liquid 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 N 2 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 N 2 can be found in [118]. The thermal conductivity of a fluid is significantly enhanced in

30 2.2. SUPERCRITICAL FLUIDS x (a) K Viscosity [Pa*s] K 130 K K 210 K 250 K K (b) Thermal conductivity [W/m/K] K 110 K 130 K 170 K 210 K 250 K 290 K (c) Diffusivity [m 2 /s] K 250 K 210 K 170 K 130 K 100 K 110 K (d) Heat capacity c p [J/mol/K] K 110 K 170 K 130 K 210 K 250 K 290 K Pressure [MPa] Figure 2.5 Comparison of the (a) viscosity, (b) thermal conductivity, (c) diffusivity, and (d) specific heat of N 2 in gaseous (blue dots), liquid (green dots) and SC states (red dots), reproduced from the NIST Standard Reference Database [117].

31 18 2. SUPERCRITICAL FLUIDS AND INSULATING MEDIA the near-critical region (T T c,p p c ) as well as in the extended critical region (up to T/T c = 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 N 2 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 (c p for isobaric value and c v for isochoric value), the smaller the temperature changes under given deposited energy. The detailed equation for the heat capacity of SC N 2 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 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 CO 2 is the most utilized SCF in such applications, due to the advantage of convenient critical temperature, non-inflammability and non-explosive properties.

32 2.3. APPLYING SUPERCRITICAL MEDIA Plasma applications in supercritical media Besides the traditional chemical applications, SCFs, typically SC CO 2, 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 CO 2 [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 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 CO 2 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 CO 2 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 CO 2 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 CO 2 is independent on the medium pressure in the gas and SC phase, while in liquid phase it increases with higher liquid density [131, 132].

33 20 2. SUPERCRITICAL FLUIDS AND INSULATING MEDIA 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 CO 2 were investigated [ ]. 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 CO 2 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 CO 2 [129, 131, 137, 138] and a few in SC He [139], SC H 2 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 CO 2 [131]. Experiments were performed under two different CO 2 temperatures: 305 K and 373 K. The experimental results in SC CO 2 show that up to a density of 90 kg/m 3 (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/m 3 [131]. This phenomenon is observed in near-critical region at CO 2 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 CO 2 up to the SC state at around room temperature was experimentally investigated [137, 143, 144]. The measured breakdown voltage in CO 2 reveals that the dielectric strength of CO 2 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-

34 2.3. APPLYING 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 CO 2 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 CO 2 [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.

35

36 CHAPTER 3 HIGH 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

37 24 3. HIGH 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, SF 6 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 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 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:

38 3.2. EXISTING SOLUTIONS 25 Table 3.1 Comparison of the properties of selected pulsed power switches. Switch type Voltage Current Repetition Jitter Turn-on time References rate Cold cathode < 1 kv μs - [149] switch Vacuum tubes 5 20 kv 2 10 ka 10 Hz ns - [150] Thyratron 100 kv 10 ka 1 khz 1 5 ns [150, 151] Pseudo 3 32 kv 2 30 ka 1 khz 5ns - [152, 153] spark gap Gas filled 100 kv 100 ka khz >5ns - [154] spark gap Laser triggered 30 kv ka khz <1ns - [155] spark gap - Ignitron 30 kv 700 ka [156] Corona 100 kv ns - [153, 157] stabilized switch IGBT 6.5 kv 100 A 20 khz - [108] SiC n-igbt 15 kv 20 A ns [109] SOS diode kv A 100 Hz - toff = 5 10 ns [158, 159] JR diode 80 kv 1 khz - ns; [160, 161] toff = 0.5 2ns SiC Schottky diode 1.2 kv 20 A 1 khz - ns; [161] MOSFET 1.2 kv 1 A 1 MHz ns [110, 162, 163] SI Thyristor 6.5 kv 165 A 1 khz - 35 ns [164, 165] ETO Thyristor 10 kv <1kA 5 khz ns [166] SiC GTO 12 kv 100 A ns [167] (optically triggered)

39 26 3. HIGH POWER SWITCHING 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 H 2 thyratron is a typical example. A H 2 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 H 2 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 N 2, air, SF 6,H 2, 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 SF 6. 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 kv, and the jitter can be less than 5 ns if the gas pressure is carefully chosen [153, 157] 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:

40 3.2. EXISTING 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 ns and a peak power of 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] 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, SF 6, vacuum, and solid state, etc.;

41 28 3. HIGH POWER SWITCHING 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 kv and an interruption capacity of 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, SF 6 CBs, having high dielectric strength and excellent arc quenching capability, were introduced in HV systems. Meanwhile, in MV systems, vacuum CBs were

42 3.3. DESIGN OF SUPERCRITICAL SWITCHES 29 widely applied for the level up to 72 kv [178]. Nowadays SF 6 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 ms (SF 6 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

43 30 3. HIGH POWER SWITCHING 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 mm mm mm Max. SCF pressure 200 bar 200 bar 200 bar Integrated capacitor & TLT Structure compactness Simple (transmission line transformer) Simple Optical window; Diagnostic components No Embedded I & V sensor No Flow meter; SCF parameter Pressure gauge Pressure gauges; Flow meter; inspection Heat ex-changer; Pressure gauges; Air driven booster 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 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 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 N 2 comes from an 2 cylinder (with purity of 99.9%), with maximum pressure of 200 bar. The pressure of

44 3.3. DESIGN OF SUPERCRITICAL SWITCHES 31 (1) (2) (3) (4) (5) a b c d 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. Figure 3.3 Schematic of the SCF loop for the simple SC switch (A). SC N 2 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 N 2 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 N 2 flushing respectively. The flushing of SC N 2 through the switching gap was

45 32 3. HIGH POWER SWITCHING 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. 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 C 1 is charged to high-voltage DC via the leakage inductance of the transformers, the resistor R 1, and a rectifying diode. In a second charging process, capacitor C 2 is charged from capacitor C 1 via a resistor R 2 and a diode, to a peak value of 40 kv. Since C 1 C 2,C 1 acts like a constant voltage source. Once the SC switch breaks down, energy dissipates into the resistive load R 3. A resistor R 2 prevents the discharge of C 1 into R 3. After breaking down, C 2 discharges almost completely and the next charging process can start again. The repetition rate of this sequence is slow and is determined by the R 2 C 2 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 C 1 is charged via the transformers, a resistor R 1 and a diode. Resonant charging of C 2 from capacitor C 1 occurs (differently from the slow charging circuit) via a diode, an inductor L 1 and an air spark gap X 1. Via the breakdown of a second air plasma switch X 2, 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

46 3.3. DESIGN OF SUPERCRITICAL SWITCHES 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. Figure 3.5 Schematic of fast charging circuit (2 kv/ns) for SC switch (A) with experimental situation of 200 Ω load connected. Breakdown voltage [V] 10 x Breakdown voltage [V] x Time [s] x 10-8 directly connect to ground connected with 200 load Time [s] x 10-7 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

47 34 3. HIGH POWER SWITCHING voltage appears across the switch, so the measured voltage before the switch in this case more closely represents the breakdown voltage of the switch 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 c 3 4 d e 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 C h ; b. trigger pin; c. integrated high voltage capacitor C h (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

48 3.3. DESIGN OF SUPERCRITICAL SWITCHES 35 Figure 3.8 Schematic cross section of the electrode part in SC switch (B). The switch is cylindrical symmetric. SC N 2 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 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. N 2 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 N 2 (with purity of 99.9 %) is supplied from the N 2 cylinder. A pressure regulator controls the pressure of SC N 2 going to the SCF loop. An air driven gas booster is used to facilitate the N 2 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);

49 36 3. H IGH POWER SWITCHING 3UHVVXUH UHJXODWRU %DODQFH YHVVHO 1 *DV ERRVWHU 5HOLHI 9DOYH 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 Hz and 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 Hz is shown in figure 3.10.

50 3.3. DESIGN OF SUPERCRITICAL SWITCHES 37 Figure 3.10 Schematic of the 1 khz charging circuit with voltage rise rate of 2.5 kv/μs and repetition rate of Hz. C h - high voltage capacitor (in real setup it is integrated in the SC switch, denoted as c in figure 3.7); L 1 - air core inductance; TLT - transmission line transformer; R L - resistive load matching the impedance of TLT. Voltage [kv] Time [μs] Current [A] Time [ns] 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 The pressure of SC N 2 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 Hz variable repetition rate is connected to a 1 : 30 ratio pulse transformer. The resonant circuit (C h represents the capacitor integrated in the SC switch (B)) applies voltages with increasing slope of 2.5kV/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 C h (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

51 38 3. HIGH POWER SWITCHING 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 N 2 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. Figure 3.12 The charging circuit for the high repetition rate voltage source with 30 kv peak value and Hz repetition rate. C h 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 The voltage applied to the switch has a rate of rise of 1 kv/μs and a peak value of kv 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

52 3.3. DESIGN OF SUPERCRITICAL SWITCHES 39 3 x Voltage [V] Time [μs] 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 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 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.

53 40 3. HIGH POWER SWITCHING (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. Figure 3.15 Schematic of SCF loop for high voltage SC switch (C).

54 3.4. ARC INTERRUPTION TESTING CIRCUIT 41 The SCF loop for SC switch (C) is sketched in figure The design of the N 2 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 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 N 2, the flushing of SCF through the switch is realized by opening the valve (2) and releases N 2 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 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. Figure 3.16 Simplified circuit for the arc interruption experiments. A capacitor C 1 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 S 1 is closed, a capacitor C 2 with value of C 2 C 1 is charged by C 1 via an inductance L 1. When the voltage on C 2 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 L 2 and C 2. The energy stored in C 1 and C 2 is deposited into the SC switch and the resistor R 2 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 C 2 will be charged again by C 1. 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

55 42 3. HIGH POWER SWITCHING (a) SC breakdown SC switch re-ignition in recovery phase (b) SC breakdown No re-ignition in recovery phase I=0 I=0 V=0 V=0 Current interrupted Current interrupted (c) SC breakdown current voltage 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 C 1 and C 2 will be deposited into the discharging loop of the switch, and C 2 will not be recharged by C 1. 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) Real setup The schematic of the real testing circuit is given in figure In the circuit the capacitor C 1 is charged by transformer T 1 via a large resistor R 1 = 120 MΩ. Diode group D 1 with snubber circuits provides uni-directional energy flow from capacitor C 1 to C 2 and the rest of the components. A grounding switch S G connected with resistor R G = 1MΩ has been inserted to discharge the remaining energy in the circuit after the test. A self-breakdown air spark gap X 1 acts like the switch S 1 in figure The output voltage from the resistor R 2 is supplied to the SC switch (C). The testing circuits with various groups of parameters values were simulated in Micro- Cap circuit Simulator. By choosing the value of C 1 and C 2, we can determine the maximum energy that will be deposited into the SC switch. L 1 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 L 2 and R 2. The values of the parameters are chosen to be C 1 = 16 nf; L 1 = 115 mh; C 2 = 1 2 nf; L 2 = 800 μh 9.8 mh;

56 A RC INTERRUPTION TESTING CIRCUIT 5& VQXEEHU 7 5 / ; / 5 +9 SUREH ' 5* 9 & & 6& VZLWFK 6* &XUUHQW SUREH 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 = A/μs and f = 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 The pressure of N2 under this situation is 50 bar and the gap width is mm.

57 44 3. HIGH POWER SWITCHING 60 Voltage [kv] Current [A] Time [μs] Figure 3.20 An example of the voltage and current waveforms measured with SC switch (C) under the arc interruption testing circuit. The N 2 pressure is 50 bar and the gap width is mm. Circuit parameters are C 1 = 16 nf, L 1 = 115 mh; C 2 = 1.3 nf; L 2 = 800 μh; R 2 = 10 Ω.

58 CHAPTER 4 EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS 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 N 2 switches is tested and its dependence on pressure and gap width is investigated. The dielectric recovery of a SC N 2 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 N 2 switch is investigated in section 4.4. The radius of the discharge channels in SC N 2 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 N 2 switches are given in section 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 2.5kV/μs, and slow pulses with charging rate of 1.66 kv/ms. The typical waveforms of these voltage impulses are illustrated in figure

59 46 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS 6 x 10 4 fast pulse, p= 80 bar, d=0.4 mm Voltage [V] ns Time [s] x 10-8 Voltage [V] Voltage [V] 6 x Time [s] x x moderate pulse, p=80 bar, d=0.25 mm slow pulse, p=80 bar, d=0.24 mm 34.1 ms 11.3 μs Time [s] 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 V b 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 N 2 pressure in the switch varied in a range of bar, covering the gas and SC phases. The gap width (measured after the switch is pressurized) of the switch covered a range of mm. Scenarios of no flushing or slightly flushing of the N 2 through the inter-electrode gap were both investigated. With the SCF loop described in figure 3.3, the flushing rate of the SC N 2 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 N 2, in the scenario of valve 1 sect opening, the flow rate and flow velocity are approximately m 3 s 1 and 14 m/sina0.2 mm gap, respectively. Breakdown voltages were recorded under different experimental conditions by a high

60 4.2. BREAKDOWN VOLTAGE ANALYSIS Breakdown voltage [kv] no flushing 1 sect 5 2 sect (a) 3 sect Pressure [bar] 30 Breakdown voltage [kv] (b) no flushing 1 sect Gap width [mm] 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 N 2 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 N 2 loop is opened by 1 scale division. For 80 bar SC N 2, in the scenario of 1 sect, the flow rate and flow velocity are approximately m 3 s 1 and 14 m s 1 ina0.2 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 N 2 pressure, larger gap width and higher N 2 flushing rate. A dip of averaged breakdown voltage is observed at a N 2 pressure around 40 bar. This voltage dip near the critical pressure coincides with the reports about such phenomenon in the breakdown voltage of SC CO 2 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

61 48 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS of this phenomenon and related mechanisms are beyond the scope of the present thesis work V b 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 N 2 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 N 2 pressure at two gap widths: 0.25 mm and 0.3 mm. From the measurements we can see that the breakdown voltage increases with N 2 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 N 2 was observed. This observation coincides with the measured breakdown voltage in SC CO 2 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 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] V b 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. N 2 pressure in the switch was adjusted in a range of 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 N 2 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

62 4.2. BREAKDOWN VOLTAGE ANALYSIS x 104 d=0.3 mm d=0.25 mm Breakdown Voltage [V] (a) Pressure [bar] Breakdown Voltage [kv] bar 70 bar 50 bar 37.5 bar (b) Gap width [mm] E bd [kv/mm] bar 70 bar 50 bar (c) 37.5 bar 50 bar 70 bar 90 bar 37.5 bar Gap width [mm] 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 bar. (c) Breakdown field and reduced breakdown field versus gap width at various pressures E bd /p [kv/mm/bar] 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

63 50 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS Breakdown voltage [kv] (a) load short circuited with load Pressure [bar] no flushing 1 sect Breakdown Voltage [kv] (b) Gap width [mm] 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 N 2 loop is opened by 1 scale division. For 180 bar SC N 2, in the scenario of 1 sect, the flow rate and flow velocity are approximately m 3 /sand1m/s ina0.4 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 N 2 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 mm, a slight increase of the gap width and

64 4.3. DIELECTRIC 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 N 2 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 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.

65 52 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS ʼNormal firingʼ Voltage [kv] Not fully recovered Time [μs] 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 [%] d=0.4 mm d=0.3 mm d=0.2 mm d=0.45 mm pd [bar mm] Figure 4.6 The recovery percentage of SC switch (B) estimated with experiment, under 1 khz repetitive source 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.

66 4.3. DIELECTRIC RECOVERY ANALYSIS 53 The recovery breakdown voltage of SC switch (B) is tested under the source with variable repetition rates in range of 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. N 2 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 bar and gap width of 0.25 mm. Generally the recovery breakdown voltage, at any time lag between pulses, increases with the N 2 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 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. 26 Recovery breakdown voltage [kv] Hz (0.2 s) 100 Hz (10 ms) 1000 Hz (1 ms) 2500 Hz (400 μs) 5000 Hz (200 μs) Pressure [bar] Figure 4.7 Results from the 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.

67 54 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS 15 Recovery breakdown voltage [kv] Hz (1 s) 250 Hz (4 ms) 2500 Hz (400 μs) 5000 Hz (200 μs) Pressure [bar] Figure 4.8 Results from the 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 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 The oscillation frequency and amplitude of the arc current going through the SC switch after the breakdown can be tuned by adjusting the inductance L 2 and capacitance C 2 in the circuit shown in figure We applied various values of L 2 during the tests: 800 μh, 3.8 mh, 6.8 mh, and 9.8 mh. The value of C 2 is set to be 1 nf, 1.3 nf, or 2 nf. The examples of the current waveforms with different settings of L 2 at C 2 = 1.3 nf are given in figure 4.9. From the figure it is clear that with a fixed C 2, larger L 2 results in lower oscillation frequency of the arc current and longer duration of the current. Under a fixed L 2, different C 2 causes only slightly different current waveforms. Figure 4.10 gives the examples of the current waveforms with C 2 = 1.3 nf and C 2 = 2 nf, respectively, at L 2 = 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 N 2 flushing through the gap on the current interruption performance is investigated. In the following the experimental results are given 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

68 4.4. CURRENT INTERRUPTION ANALYSIS 55 Current [A] Current [A] Current [A] A/μs 0 (a) 4.2 A/μs (b) (c) 3 A/μs 1.4 A/μs 0.3 A/μs L 2 =9.8 mh 0.14 A/μs L 2 =3.8 mh L 2 =800 H Time [ s] Figure 4.9 Current through the SC switch (C) with different settings of inductance L 2 in the arc interruption testing circuit (figure 3.18), under N 2 pressure of 50 bar and gap width of mm. The value of C 2 is 1.3 nf. The measured current rate-of-rise and current frequency is di/dt = A/μs, f = 100 khz for L 2 = 9.8 mh; di/dt = A/μs, f = 83 khz for L 2 = 3.8 mh; di/dt = A/μs, f = 285 khz for L 2 = 800 μh, respectively. Current [A] C 2 =1.3 nf Current [A] C 2 =2 nf Time [μs] Figure 4.10 Current through the SC switch (C) with different settings of capacitance C 2 in the arc interruption testing circuit (figure 3.18), under N 2 pressure of 50 bar and gap width of mm. The value of L 2 is 800 μh. the results we find that under the current waveform shown in figure 4.9(b)-(c) (corresponding to L 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

69 56 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS switch. An example current waveform at p = 60 bar and d = 1.29 mm is illustrated in figure The circuit parameters are L 2 = 3.8 mh and C 2 = 1 nf. No forced N 2 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 C 2, 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 C 2 (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 Current [A] Time [ s] Figure 4.11 Measured current through SC switch (C) under the arc interruption testing circuit given in figure Pressure 60 bar, gap width 1.29 mm, L 2 = 3.8 mh, and C 2 = 1 nf. No forced N 2 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 m 3 /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 N 2 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 = μs and t = μs. From the figure we can see that the current was temporarily interrupted, which can be identified by a short duration rise of

70 4.4. CURRENT INTERRUPTION ANALYSIS 57 Voltage [V] Temporary interruption Successful interruption 500 V Current [A] Time [ s] 6 4 Current [A] Time [ s] (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 = μs, is plotted as well Voltage [V] Current [A] Time [ s] Time [ s] (b) Enlarged view of three selected time regions where temporary current interruptions are observed: t = μs and t = 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 mm, L 2 = 9.8 mh, and C 2 = 1 nf. Forced N 2 flushing of about 50 Liter/h (2.73 m 3 /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 μs, the SC switch undergoes a re-ignition, which is represented by the sudden voltage collapse and continu-

71 58 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS 500 Voltage [V] Successful interruption -250 V 2.35 ms Current [A] Time [ s] Figure 4.13 Voltage and current waveforms measured in SC switch (C) in the arc interruption circuit. Pressure 50 bar, gap width mm, L 2 = 9.8 mh, and C 2 = 1 nf. No forced N 2 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 N 2 flushing through the gap. Without forced flushing, the arc voltage in SC N 2 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 bar are illustrated in figure 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.

72 4.4. CURRENT INTERRUPTION ANALYSIS d=2.112 mm d=2.139 mm d=2.151 mm di/dt [A/s] Non-flushing Forced flushing d=2.195 mm du/dt [V/s] Pressure [bar] 6 x d=2.112 mm d=2.139 mm d=2.151 mm d=2.195 mm Forced flushing Non-flushing Pressure [bar] 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. du/dt [V/s] x d=1.744 mm d=1.763 mm 0.89 ms from current intiation 0.43 ms from current intiation d=1.79 mm d=1.814 mm Pressure [bar] 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.

73 60 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS 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. L2 = 3.8 mh, C2 = 1.2 nf L2 = 6.8 mh, C2 = 1.0nF SC switch d 1mm d > 1.2 mm d > 1.4mm d > 1.4mm (C) p [bar] Current d [mm] Interruption No flushing T T T T T T T T Forced flushing T T T T - T T T L2 = 9.8 mh, C2 = 1.0 nf d > 1.4 mm d > 1.7 mm d > 2.0mm p [bar] d [mm] No flushing T T T T T Forced flushing T T T T

74 4.5. ICCD IMAGE OF DISCHARGE IN SC N ICCD image of discharge in SC N 2 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 N 2 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 pixels, μm pixel size. 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 Simultaneously with the charging of capacitor C h in the main circuit (capacitor embedded in SC switch (B)), the capacitor C 2 in the triggering circuit, via an inductance L 2 = 21 mh, is charged with a relatively slower voltage increasing slope, but to higher amplitude than that on C h. During the charging process of C h, the voltage on the trigger pin also increases due to the LCR system explained in section In order to prevent the voltage increases on the right side of S 1 (2-stage TLTL side), an isolating capacitor C i = 200 pf is applied. From the impedance equation Z = 1/(ω C i ) we can see that impedance of C i is high at low frequency, hence it can block the energy flow from the trigger pin to S 1 during the slow charging process of C h. At a time moment after the voltage on C h reaches the plateau, the voltage on C 2 reaches the threshold voltage of the air switch S 1. Once S 1 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

75 62 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS times, and 2) to introduce a delay of 100 ns for the impulse to reach the trigger electrode of SC switch (B). C i, under this high frequency pulse, has low impedance, hence the voltage pulse can transmit through C i, and be applied to the trigger pin. 4 3 x 10 4 Voltage [V] 4 x spark gap S1 SC switch anode camera opening trigger pin Voltage [V] signal sent to camera Time [ns] Time [ns] x 10 4 Figure 4.17 The typical voltage waveforms measured on the main capacitor C h, trigger capacitor C 2, isolating capacitor C i, and the trigger pin of the SC switch. Discharge channel at camera opening Gap width 0.32 mm Camera opening Current [A] Current through SC switch Camera monitoring signal Time [ns] Figure 4.18 Imaging of discharge in the SC switch (B) with an ICCD camera. The N 2 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 S 1 firing, a noise pick up coil placed nearby S 1 induces a voltage sig-

76 4.5. ICCD IMAGE OF DISCHARGE IN SC N 2 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 C h, the triggering capacitor C 2, the isolating capacitor C i, and on the trigger electrode of the SC switch during the operation is illustrated in figure The time delay of the signal transmission caused by the cable has been deducted from the waveforms shown in figure 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 N 2 switch (B) taken by an ICCD camera. T d : time moment after the current appearing in the gap. The light emission from the SC N 2 breakdown is very strong. In order to prevent the overexposure of the camera, a neutral density (ND) filter (filtering intensity 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 N 2 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 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 N 2 at a pressure of 1 bar was measured to be m/s under the applied elec-

77 64 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS 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 m/s, i.e., the streamer transition time across a 0.32 mm SC N 2 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 T d = 0 80 ns (T d means time after the current appeared in the gap) at p = 70 bar, d = 0.38 mm; as well as at T d = ns at p = 40 bar, d = 0.35 mm. From the images we observe that the bright channel expands in the time span of T d = 0 80 ns. From T d = 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 N 2, fast expansion happens at time T d 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 N 2 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 N 2 have been recorded under different voltage pulses: slow ( kv/s), moderate ( kv/s), and fast ( kv/s) pulses. Figure 4.20 summarizes the breakdown field of SC N 2 under theses pulses at a regime of gap width for N 2 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 N 2 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 N 2 are derived from the experimental results: The recovery breakdown voltage increases with N 2 pressure and gap width;

78 4.6. CONCLUSIONS Breakdown field [kv/mm] kv/s kv/s kv/s Figure 4.20 Breakdown field of SC N 2 under slow ( kv/s), moderate ( kv/s), and fast ( 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 N 2 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 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 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, 2.2mmgap.

79 66 4. EXPERIMENTAL INVESTIGATION OF BREAKDOWN AND RECOVERY IN SCFS 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 N 2 flushing situation indicates the advantage of SC N 2 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 N 2.

80 CHAPTER 5 THEORETICAL MODELING OF DISCHARGE AND RECOVERY IN SCFS 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 N 2 have been studied by experimental investigations (chapter 4). The dielectric strength of SC N 2 is in the range of kv/mm, which is as high as most solid dielectrics. The dielectric strength of a SC N 2 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 N 2 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

81 68 5. THEORETICAL MODELING OF DISCHARGE AND RECOVERY IN SCFS 5.2 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

82 5.2. SIMPLE 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 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 = c v ρ 0 V 0 (T 0 T g,0 ), (5.1) in which c v [J/(kg K)] is the isochoric specific heat capacity of gas, T g,0 = 300 K the temperature of the gas before energy deposition, T 0 [K] the temperature of the channel after heating, ρ 0 [kg/m 3 ] the gas density after heating (equaling to the background density), V 0 [m 3 ] 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 K and in N 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 R 0 can be calculated from equation (5.1) with T 0 = K (for N 2 ). If the calculated radius R 0 is less than 50 μm, then R 0 is set to be R 0 = m. V 0 is adapted to the new value according to R 0, and the value of initial pressure p 0 [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]: t 0 = R2 0 R c a, (5.2) in which R c = E/(l gap Bγp g,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 N 2 ; γ = c p /c v is the ratio of specific heats; a [m/s] is the velocity of sound in the background gas; l gap [m] is the inter-electrode gap width; p g,0 [Pa] is the gas pressure before the energy deposition. A time of t 0 [s] is needed for the spark to expand from the characteristic value R c [m] to the initial radius R 0 [m] in our situation.

83 70 5. THEORETICAL MODELING OF DISCHARGE AND RECOVERY IN SCFS 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): p 1 = p 0 T 1 = T 0 ( V0 V 1 ( V0 V 1 ) γ ; (5.3a) ) γ 1, (5.3b) in which notation 0, 1 stands for before and after expansion respectively; γ = c p /c v is the ratio of specific heats. The adiabatic expansion stops when the pressures in and outside the channel are equal p 1 = p g,0, i.e., the left side of equation (5.3a) equals p g,0 /p 0. The radius of the spark channel after adiabatic expansion R 1 [m] can be calculated with the equation: V 1 R 1 =. (5.4) π l gap This adiabatic expansion is assumed to follow the the theory of moderate shock waves, so the time duration of the expansion, denoted as t 1 [s], can be calculated as equation [199]: E t 1 = p g,0 l gap γ B a 2 + R2 1 a 2. (5.5) 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 = (T g (t 2 ) T g,0 )S = c p m dt, (5.6) dt 2 where T g (t 2 ) [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 A conv [m 2 ], and heat conduction part (to the electrodes) with surface area A cond [m 2 ], and the details are given by equation: S = Nu k f L A conv + k aver x A cond, (5.7) where k f [W/(m K)] is the coefficient of thermal conduction at film temperature T f [K] (arithmetic mean of the spark channel wall temperature and the far-end gas temperature);

84 5.2. SIMPLE ANALYTIC MODEL 71 k aver [W/(m K)] is the averaged thermal conductivity coefficient of the hot gas over the temperature decay range; x = 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 Re m Pr 1/3 ; 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 [m 2 /s] is the kinetic viscosity of the gas; D [m 2 /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 C m The analytic solution for the gas temperature T g (t 2 ) in equation (5.6) is expressed as: T g (t 2 ) T g,0 T 1 T g,0 ( ) t2 = exp, (5.9) c p ρv/s in which τ = c v ρ V /S is the time constant of the exponential decay of the gas temperature in the heat transfer stage; T 1 is the gas temperature after adiabatic expansion Results and discussions The recovery time of a SC N 2 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 N 2, 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) t 0 : the time needed for the spark channel to expand from the characteristic radius R c to the initial radius R 0 ;2)t 1 : the time needed to expand from R 0 to the radius after the adiabatic expansion R 1 ;3)t 2 : the time needed for the cooling of the gas temperature to 550 K. The value of t 0 and t 1 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 m 3 /h (flow velocity equals to 6 m/s ina0.4 mm gap) at actual pressure and temperature (corresponding to 98 m 3 /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 N 2 switch is predicted to be about 1.5 ms after the energy deposition. The

85 72 5. THEORETICAL MODELING OF DISCHARGE AND RECOVERY IN SCFS 9 8 Estimated recovery time [ms] Flow rate at STP [m 3 /h] Figure 5.2 Estimated recovery time of a SC N 2 switch after the energy deposition of 0.7 J. Gap width 0.4 mm, flow rate at STP 8 98 m 3 /h, corresponding to m 3 /h at working pressure of 150 bar (flow velocity equals to 0.4 6m/s at0.4 mm gap width). discontinuity of the curve at 55 m 3 /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 N 2 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 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 N 2 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 L a and a resistance R a. The electric field

86 5.3. ELECTRIC FIELD ACROSS THE GAP 73 Figure 5.3 Simplified circuit of the dotted box in figure i(t): measured current in the circuit; V b : measured breakdown voltage; L a : arc inductance; R a : arc resistance; C h : high voltage capacitance; L s : stray inductance in the circuit; R 0 : total resistance in the circuit (including stray resistance and load resistance). across the switching gap can be calculated with the following formulas: R a (t) = { i(t) 1 V b C 1 t h 0 i(t)dt [L s + L a (t)] di(t) dt [ R 0 + dl a(t) dt ] } ; (5.10) i(t) E(t) = 1 [ i(t) R a (t) + L a (t) di(t) ]. (5.11) d dt In the equations above the variables are explained here: R a (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; V b : the measured breakdown voltage of the SC switch; L s : 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 L s can be taken as the equivalent inductance of the co-axial cables in series. The value of L s is calculated to be L s = 104 nh. R 0 : the total resistance of the circuit, which consists of the input impedance of the 4-stage TLT: R TLT = 12.5 Ω, the resistance of the electrode heads (W/Cu 75/25) R copper, the resistance of the electrode bodies (stainless steel) R ss1, and the resistance of the stainless steel plate denoted as 6 in figure 3.7 R ss2. 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 R 0 = R TLT + R copper + R ss1 + R ss2. L a : the arc inductance which can be calculated from equation [202, 203]: L a = l μ 0 2π ln r c r s (t), (5.12) in which r c is the radius of the return path of the current to ground, r s = 35 μm is the radius of the discharge channel generated in the gap. The value of r s is estimated by imaging with an intensified CCD camera, as described in section 4.5. L a (t) is found to be much smaller than the value of L s.

87 74 5. THEORETICAL MODELING OF DISCHARGE AND RECOVERY IN SCFS Electric field [V/m] Electric field [V/m] 8 x Time [ns] 8 x 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 %. (a) (b) 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 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 N 2. 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-

88 5.4. EXTENDED PHYSICAL MODEL FOR DISCHARGE IN SCFS 75 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 N 2 is given in figure K 5000 K K Temperature on axis 0 Streamer stage Conservation of mass, momentum, total energy ns Streamer-spark transition stage μs Spark-decay stage 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 N 2. The modeled discharge phases in our work are briefly introduced here, while the detailed explanation is given in section 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 N 2 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 Q in. During the relaxation process there is energy output due to heat conduction and radiation, denoted as Q out. 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 N 2 in the spark channel recover and finally the dielectric strength of SC N 2 can recover. During the discharge and post-discharge phase, the forced flushing of the N 2 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.