Insulation of High-Voltage Equipment [1 ed.] 9783540207290, 9783662079188

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Power Systems v.Y. Ushakov Insulation of High-Voltage Equipment

Springer-Verlag Berlin Heidelberg GmbH

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v. Y. Ushakov

Insulation of High-Voltage Equipment With 226 Figures

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Springer

Prof. Vasily Y. Ushakov Tomsk Poytechnic University Lenin Ave. 30 634034 Tomsk Russia

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ISBN 978-3-642-05853-0 ISBN 978-3-662-07918-8 (eBook) DOI 10.1007/978-3-662-07918-8 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH.

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Preface

Over the past two or three decades, investigations of thermonuclear fusion, the effects of high-power energy fluxes on matter, generation of superstrong magnetic fields, and other branches of applied physics have motivated the development of high-power electrophysical systems, including electrodischarge and electroionization lasers, high-current accelerators, sources of electromagnetic radiation, etc. The demand for these promising fields of physics and engineering has raised the long-term priority of high-power pulse engineering, and attracted the attention of many academic, institutional, and university scientific groups to such investigations. The major thrusts and problems in the development of high-power pulse engineering, and the scientific and technical level achieved in this field, have repeatedly been summarized in monographs, reviews, and scientific conference proceedings [1--6]. In the early stages of such investigations, new high-voltage sources with stateof-the-art parameters were based on long-standing experience in the development of high-voltage engineering systems. However, high-voltage electrophysical systems (HES) respond continuously and rapidly to complex conditions in all constituent components, not the least being their electrical insulation. The extent to which the electrical insulation problem is addressed in pulsed HES determines not only the cost and engineering characteristics of the systems, but also the feasibility of generating power pulses with the specified parameters. The advent of these systems calls for elevated working gradients of electrical insulation, most often paying a penalty in service lifetime, reliability, and high cost. Over the past decade, HES previously used for physical investigations have expanded into engineering applications. A start has been made on the mass production of engineering lasers, accelerators, and systems using spark discharge in condensed media as a working tool. The electrical insulation of these systems must exhibit rigorous technical and economical characteristics and long service lifetime. The present monograph is the first attempt at a comprehensive consideration of electrical insulation in high-voltage electrophysical systems. The operating conditions of HES insulation and the requirements imposed on it are analyzed and the main insulation design types specially developed for HES are outlined in Part 1. Information on short- and long-term electric strengths of vacuum, gases, and liquid, solid, and hybrid dielectrics as functions of various influencing factors is presented in Part 2. However, it is impossible to provide all types of factual evidence required for practical needs in a single book. In addition, the nomenclature of electrical insulating materials (ElM) is continuously expanding. All this calls for testing the ElM electric strength and service lifetime under various conditions including non-specialized laboratories. In this regard, the author provides some recommendations on ElM test procedure at the beginning of Part 2 of the mono-

VI

Preface

graph. In combination with national and international standards that regulate highvoltage and service-lifetime ElM tests, these recommendations will help the designers of high-voltage systems to properly plan such tests. Noting that certain characteristics of the electric strength of various dielectric media have much in common (the influence of voltage duration, interelectrode gap, electrode area, voltage polarity, electrode aging, etc.), the author eschewed a conventional presentation of the material, in which the electric strength of gases, liquids, and so on is addressed in a monograph, with each taken in tum, or in which a number of monographs are devoted to electrical breakdown in each medium. The author's approach-step-by-step consideration of various factors that affect the electric strength of all dielectric media-makes the presentation of the material more compact and convenient for practical applications. In this part, particular attention is paid to the influence of strong external factors, typical of RES operation, on the electric strength of ElM and dielectric media. Close attention is also paid to an analysis of various ways to improve the insulating characteristics of dielectrics. Part 3 is devoted to the design of high-voltage insulation systems. Methods of increasing working field strengths and calculating the static, volt-second, and statistical characteristics of the electric strength of insulation and the insulation service lifetime and reliability are considered here. It is demonstrated that the design and operation of RES and power systems call for the probabilistic and statistical approach to the isolation coordination. Only this approach ensures high technical and economical levels of the HES development and their high reliability and specified service lifetime. Due to a lack of experimental data and HES operating experience, the author often examines power systems insulation. In some cases, this enables the problem of HES design to be solved satisfactorily. The author hopes that the material on power systems insulation is of interest to experts in areas of power and in the electrical engineering, electrical insulation, and cable industries. This is an English version of the Russian book "Insulation of High-Voltage Equipment." In addition to the basic references, I also present additional references to acquaint the reader with the most recent information on the subject. This additional list of references includes papers published in English on the insulation of high-power equipment over the past 7-10 years. The author acknowledges the Rector of Tomsk Polytechnic University, Prof. Yurii P. Pokholkov, for financial support in preparation of the English version of this monograph, and Dr. Sergei A. Lopatkin and Engs. A. Yu. Khudonogova and A. Yu. Tushina, Tomsk Polytechnic University, for their assistance in preparing the manuscript. I especially wish to thank Dr. Lyudmila G. Shamanaeva, Institute of Atmospheric Optics of the SB RAS, Tomsk, who translated my monograph into English. Finally I wish to thank Springer-Verlag for their efficient cooperation. October 25, 2003

Professor V. Ya. Ushakov

Contents

Preface ........•.......................................................................................................... V Part 1 Requirements on Insulation and Methods of Determining the Electric Strength Chapter 1 Insulating Materials and System Design Selection ................•...•....... 3 1.1 Operational Conditions and Requirements on Insulation ............................ 3 1.2 Typical Design of Electrophysical Systems Insulation ................................ 9 Chapter 2 Insulation and Media Test Techniques ............................................. 13 2.1 Testing Electric Strength ........................................................................... 13 2.2 Lifetime and Treeing Tests ........................................................................ 19 Part 2 Short- and Long-Term Electric Strength of Insulating Materials and Media Chapter 3 Influence of Dielectric Properties, State, and Electrodes on Electric Strength •.......................•........................................................ 27 3.1 Pressure, Density, and Mechanical Stresses .............................................. 27 3.2 Temperature ............................................................................................... 42 3.3 Molecular and Supermolecular Structure .................................................. 60 3.4 Electrode Material ..................................................................................... 65 3.5 State of the Electrode Surface .................................................................... 71 Chapter 4 Influence of Contamination and Structural Defects ........................ 83 4.1 Solid Particles ............................................................................................ 83 4.2 Structural Defects and Impurities in Solid Dielectrics ............................... 93 4.3 Moisture ..................................................................................................... 97 Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage .....•..................•...•................................................... 103 5.1 Voltage Duration ..................................................................................... 103 5.2 Shape of a Voltage Pulse ......................................................................... 113

VIII

Contents

5.3 Frequency and Periodicity ....................................................................... 122 5.4 Voltage Polarity ....................................................................................... 132 Chapter 6 Influence of Insulation Gap Geometry on Electric Strength ••••.•.• 141 6.1 Field Configuration in an Insulation Gap ................................................ 141 6.2 Interelectrode Gap Length ....................................................................... 150 6.3 Electrode Surface Area ............................................................................ 156 6.4 Dielectric Volume in an Electric Field .................................................... 164 Chapter 7 Flashover Voltage at the Interface between Two Dielectric Media •..•••••••...•.•••••••••..•.•••••••...•••••••••••..•.••••••••••...•••••••.•...••••••••••••••••••• 169 7.1 Orientation and Dimensions of an Insulator in an Electric Field ............. 169 7.2 Geometry of the Electrodes and the Character of Their Contact with the Insulator ............................................................................................. 176 7.3 Properties and State of the Insulator Surface and Ambient Medium ....... 182 7.4 Parameters of the Applied Voltage .......................................................... 191 Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment ••••••.••••.•.••••••••••.•••••••••••••••••••.••••.•••••••.•..•.••••••••••..•.•.•••••• 195 8.1 Ionizing Radiation ................................................................................... 195 8.2 Electron and Ion Beams ........................................................................... 204 8.3 Laser and UV Radiation .......................................................................... 215 8.4 Magnetic Field ......................................................................................... 227 8.5 Electric Strength ofInsulation and Intercontact Medium in Explosive Commutators .......................................................................... 234 8.6 Electric Strength of Gases and Liquids in a Flow ................................... 244 8.7 Recovery of Electric Strength after Spark and Arc Discharges ............... 251 Chapter 9 Methods for Improving the Dielectric Properties of Electric Insulating Materials and Media ...................................................... 265 9.1 Mixing and Injection of Additives and Fillers ......................................... 265 9.2 Radiation Modification ............................................................................ 283 9.3 Conditioning of the Electrodes and Dielectric Medium .......................... 292 9.4 Orientational Extension of Polymers ....................................................... 302 9.5 Unconventional Insulation ....................................................................... 304 Part 3 Insulation Design Chapter 10 Methods for Increasing the Working Field Strength of Insulation •••••••.••••••••••••••••.•••.••••••••..•.••.•.••••••••••..••.•••••••..•••.•.•••.•••••••• 311 10.1 Electric Field Control ............................................................................ 311 10.2 Electrode Coating .................................................................................. 335 10.3 Combination Insulating Materials ......................................................... 340

Contents

IX

Chapter 11 Calculation of Insulation ............................................................... 351 11.1 Calculations of Short-Term Electric Strength (Static and VoltageTime Characteristics) ............................................................................ 351 11.2 Statistical Characteristics of the Electric Strength and Coordination of Insulation .......................................................................................... 372 11.3 Calculation ofInsulation Reliability and Operating Lifetime ................ 378 11.4 Choice of the Working Field Strength ................................................... 385 References .......................................................................................................... 393 Additional References ................................................................................... 41 0 I Vacuum Insulation ........................................................................... 410 II Gas Insulation .................................................................................. 41 1 III Liquid Insulation ............................................................................. 413 IV Solid Insulation ................................................................................ 414 V Composite Insulation ....................................................................... 418 VI General Problems ofInsulation Design .......................................... .420

Part 1

Requirements on Insulation and Methods of Determining the Electric Strength

Chapter 1 Insulating Materials and System Design Selection

1.1 Operational Conditions and Requirements on Insulation Operational conditions for HES insulation differ from those for insulating power and electrotechnical systems. Operating voltages in certain high-current accelerators and x-ray sources exceed 10 MY, i.e., they lie far beyond the limits of not only working, but also testing voltages of high-voltage systems of power engineering. Heavy demands are imposed on the specific power deposited into dielectric materials of energy-storage capacitors and on the inductance of all parts of transient HES circuits, defmed primarily by their overall dimensions (insulation gaps). The bulk of HES insulation is exposed to voltage pulses, which in terms of their field effects differ significantly from the effects of dc and ac voltages. For example, the short-term dielectric strength for voltage pulses is higher than for dc or ac voltages (especially for condensed media), and the service lifetime of solid dielectrics exposed to many voltage pulses is shorter than for dc or ac voltages. Insulation of most HES is subject to a number of powerful effects that can impair operation. Among these are: Intense shock waves generated by the expanding discharge channel or detonation products of explosives that affect liquid insulation in spark gap switches and insulation in explosive switches; in some cases, the dielectric medium (gas or liquid) flows at high velocity. Elevated temperatures that affect materials, including dielectrics, in cw gas lasers, tokamaks, magnetohydrodynamic generators, and high-frequency electrodischarge engineering systems. Radiation in various spectral ranges, high-energy charged particles, and products of decomposition of the working medium and sputtering of the electrode material affect dielectric media of lasers, gas-filled spark switchers, and highvoltage vacuum diodes. Magnetic fields affect dielectric media simultaneously with electric fields in a number ofHES elements. Depending on the specific model and operating conditions of a high-voltage system, certain individual requirements prevail among those typically levied against ElM. Among these are high electric strength, small tano, efficient heat re-

4

Chapter I Insulating Materials and System Design Selection

moval, high mechanical strength, chemical and radiation resistance, resistance to the action of partial discharges (PD), low or zero flammability, nontoxicity, low gas absorption, high resistance to effects of spark and arc discharges, good arcquenching properties, and adaptability to industrial production. Many of these requirements are mutually inconsistent. Most resistant to the action of the majority of unfavorable factors are the ceramic materials. However, because of economical and technological reasons, ceramics are not widely used in manufacturing bulk HES. Polymeric materials (polymethylmethacrylate (PMMA), polyethylene (PE), and acryl) and certain compound materials (glass-epoxy compounds etc.) are most often selected. This choice is based on a comparison of the operative factors with physical, mechanical, and thermal ElM properties, as well as on a generalization of operating experience and results of systematic experiments. Thus, for example, the stability of acrylic plastic, layered asbestos cement material (transit), pyrex, and quartz glass used as materials for manufacturing of a high-voltage spark-discharger housing was tested in [7]. All the materials (except quartz glass) are cheap and adaptable to industrial production. The discharger switched an energy of 8 kJ and transferred a charge of 0.4 C per pulse. A current of 40 kA ran through it, and the switching frequency was some tens of hertz. Its housings withstood tens of thousands of discharges. The main reasons for fracture differed for different materials. The acrylic housing was emolliated, and a significant part of its material was ablated from the interior surface; a discharge in the interlayer space fractured the transit housing; the pyrex glass housing melted, darkened by metal deposited on its surface, but survived for a long time. Quartz glass possesses good properties: it is thermally stable and has good dielectric properties and reasonably good mechanical stability. The quartz glass housing withstood more than 40,000 discharges grouped in series lasting several minutes each. Its failure was due to mechanical fracture. Quartz glass is too expensive for manufacturing of discharger housings. It is advantageous to use it when the spark gap is illuminated by ultraviolet light from an external source. The development of an energy-storage capacitor with enhanced specific accumulated energy, low inductance, and large pulse charge time calls for a dielectric medium with high E br (~15 MY1m for f ~ I J..Ls) and e (several tens or hundreds), and a long time constant 't (the Maxwell relaxation time). The first two characteristics (Ebr and e) enter into the equations matching the impedance of the shaping circuit to its load. High e enables the circuit length to be reduced and reasonable geometry for a low-impedance «10 Q) load to be chosen. High E br and high e ensure high stored energy density (W = eeo£212). The third electric characteristic 't ('t = eeo/y) plays an important role in the choice of a method of shaping circuit charging. The parameter 't determines the efficiency of the charging cycle. When the circuit is charged for a time feh' the ratio of energy expended on ohmic heating of the liquid Wsp to stored energy Wae is WspfWae = a(fehh ).

1.1 Operational Conditions and Requirements on Insulation

5

The coefficient a is independent of circuit geometry and is determined by the parameters ofa charging voltage pulse. In typical charging systems, a = 0.5-I. Rapid charging of the circuit (small feh) reduces ohmic losses and enables circuit operation at elevated working field strengths E work • However, practical implementation imposes more stringent requirements on the charger, thereby making One use complicated and expensive systems, including Marx-connected voltage pulse generators and intermediate peaking shapers (energy concentrators). For charging times of the order of 100 Ils, a double resonance transformer can be used as a charger. By increasing feh to a few milliseconds without significant impairment of other electrical characteristics of the insulation medium, we could obviate the need for a voltage rectifier and primary energy-storage capacitor, and charge the system directly from a rotating electrical machine. Vacuum insulation in high-current electron accelerators (HEA) operates under extremely severe conditions. This operating mode is chosen not only to reduce system weight and dimensions, but also to implement explosive electron emission from the cathode, which is the most efficient source of electrons [8]. Among all types of insulation used in HEA (vacuum, gases at elevated pressure, liquids, and solid dielectrics), vacuum insulation is characterized by the lowest electric field gradients at the vacuum surface of the solid insulation. Vacuum insulators of electron guns operate at Ework = 15-20 kV/cm for microsecond pulses and at Ework = 40-50 kV/cm for nanosecond pulses. The electric strength of HEA vacuum insulation depends heavily on gas-dynamics and vacuum engineering conditions in the evacuated volume, because in these systems one must deal with the so-called technical vacuum. The specific features of the breakdown characteristics of such insulation are the following: • The increase in the residual gas pressure in gaps between the electrodes with large working area to 10-1_10-2 Pa essentially doubles the electric strength. • The replacement of diffusion oil pumps with non-oil pumps considerably increases the electric strength. • Electrode cooling from room temperature to liquid nitrogen temperatures almost doubles the electric strength. • Electrode erosion in technical vacuum reduces the electric strength by much less than pure vacuum. • Electrical and primarily vacuum insulation of HEA is subject to intense external backfluxes of electrons from the vacuum diode, high-power magnetic fields, x-ray pulses, and fluxes of electrode material. Electron bombardment of insulation structures engenders desorption of gas and impurities, secondary emission, bremsstrahlung, and field deformation by space and surface charges of primary and secondary charged particles. Magnetic fields used to confine electron beams can engender discharge processes. The designer must solve two competing problems in the development and operation of certain HES (HEA and electrical discharge technological systems). On the one hand, electrical breakdown must be avoided in systems of voltage supply to the main working element (vacuum diode or spark gap); on the other,

6

Chapter I Insulating Materials and System Design Selection

Table 1.1. Specific gassing rates for certain materials

Material Polytetrafluoroethylene (teflon) Polyeth,ylene 7889 vacuum rubber Organic glass 22XC ceramics Soda glass

Gassing rate [m3.PaI(m2.s)] 3·10-4 2·10-4 5.3.10-5 HO-3 4·1O--{i

Measurement conditions At room temperature after 2-h evacuation Same Same Same After holding in vacuum at 630 K and cooling to 293 K After holding in vacuum at 470 K for 2 h

the electrical breakdown or the high-current stage of vacuum discharge must be initiated to produce pulsed disturbances or electron fluxes. For REA, the first requirement is imposed on the operation of dielectric vacuum gaps between cathode holders and grounded elements of the vacuum diode housing, and the second is imposed on the operation of vacuum diodes and vacuum transmission lines. The materials used in manufacturing vacuum insulators must not just be good dielectrics, they must also meet the requirements of vacuum technique. They must have high vacuum density, low saturated vapor pressure at the working temperature, minimum gassing in vacuum, and easy degassing. Many ElM, including plastic and compounds, glass and ceramics, pyroceramic and porcelain have been tested in the design of vacuum insulators of electron guns of accelerators (Table 1.1). The choice of material is dictated not only by the requirements enumerated above, but also by its adaptability to industrial production, and in particular to large-scale construction, which is especially important for the development of high-energy HEA. In addition, ElM of REA operating in periodic pulse mode under high thermal loading must possess high thermal stability. The construction of thermonuclear reactors of the tokamak type, magnetohydrodynamic generators, chemical-element cw lasers, plasmatrons, plasmochemical reactors, and thermal emission transducers calls for a rise in the operating temperature of the insulation to 1500-2500 K. The output power of the majority of gas-discharge systems and devices can be increased by increasing the energy deposited into plasma, thereby raising the operating temperature and sometimes the temperature of its structural elements to thousands of degrees. Thus, for example, shunting in plasmatrons due to breakdown dictates the basic plasma parameters, output system power, and the character of electrode erosion. Breakdown in near-electrode regions of magnetohydrodynamic generators, along with charge constriction, significantly influence their service lifetime and basic characteristics. In lasers with electrical pumping, the time the space charge exists and its subsequent constriction determine in many respects the efficiency with which stored energy is converted into coherent radiation. In these systems, the working and structural elements, including insulation, are subjected to the combined influence of strong thermal, electric, and magnetic fields. In this regard, high-temperature dielectrics, in addition to their high operating temperatures, must

1.1 Operational Conditions and Requirements on Insulation

7

in addition to their high operating temperatures, must meet a number of specific requirements: high mechanical strength, ability to withstand thermal shock waves, good thermal conductivity, small dielectric losses, radiation and chemical stability, vacuum density, and low pressure of compound vapors. Over the past 20-25 years, the need for materials with high operating temperatures and the development of corresponding divisions of chemical engineering have spawned the development and production of radically new materials with wide-ranging thermal stability-organic polymers, organic silicates, metal phosphates, glass ceramics, various compounds, plastics, hard-fiber materials, etc. [10-12]. Only some types of carbide oxides and nitride ceramics conform to the most stringent requirements imposed on these insulating materials. The most important role among these chemical compounds is played by the nitrides-metals or metalloids combined with nitrogen. The nitride materials and products, in addition to high thermal and chemical stability, possess excellent semiconductor and insulating properties. Hexagonal boron nitride produced by the pyrolytic method (PBN) is the best of the nitride materials (boron nitrides, aluminum, and silicon) possessing electrical insulating properties at high temperatures [13]. One pressing problem in operating such systems is the high-temperature behavior of the main components of the working body--electronegative O2, CO, CO2, H 20, CClzF2 and SF6 gases, as well as Ar, N2 , He, air, etc. Interest in the operation of high-voltage insulation at cryogenic temperatures has been fueled by the steadily rising application of low-temperature superconductivity (superconducting cables, superconducting magnet coils, high-Q microwave generators, etc.) to high-voltage electrophysics. Mechanical stresses are also important. They determine the choice of solid ElM and insulation systems design. The majority of HES internal insulation structural elements are prepared from modular polymeric materials (polyethylene, organic glass, caprolactam, etc.) or fused epoxy compounds. Specific operating conditions of these insulators include high average electric fields (4-10 kVlmm), large insulating layer thickness (from tens to hundreds of centimeters), high internal thermal and mechanical stresses when current-conducting elements are potted with some compound, and mechanical loading due to large overall dimensions and mass. These severe operating conditions impose more stringent requirements on electric and mechanical strengths of insulators, and hence on manufacturing quality. Stringent requirements are simultaneously imposed on the mechanical and electrical strength of materials used to manufacture the draw pins of segmented housings for gas-filled spark dischargers. The ultimate tensile strength and the sparkover voltage Uso in the insulating oil medium in certain ElM suited to this purpose [14] are presented in Table 1.2. The vacuum values of Uso obtained for samples preliminarily impregnated with oil are indicated in parentheses. Samples 3 cm high were tested in transformer oil upon exposure to pulses of 50/160 J.1S duration. Withstood mechanical stresses depend heavily on the character of surface breakdown. In insulators prepared from epoxy glass materials, the discharge develops primarily in the bulk of dielectric along its layers, leading to a significant charring of the layer surface or even to

8

Chapter I Insulating Materials and System Design Selection

Table 1.2. Mechanical strength and Uso in certain ElM

Parameters Ultimate tensile strength [MPa] Uso ± (J [kV]

Fabric glass laminate 175-200

Epoxy glass Glass plastic Caprolon Steatite Superhigh tube 80 mm rods 10 mm rods 30 mm rods 30 mm modulus in diameter in diameter in diameter in diameter fiber 170-200

170-200

70-120

75-100

170-230

230 ± 40 200 ± 25 (240 ± 30)

215 ± 30

300 ± 25

280 ± 25

(340 ± 30)

cleavage into layers. Deep discharge channel penetration into the sample with its subsequent fracture is typical of caprolon and steatite. These materials have higher electric strength than layered materials, but the discharge along their surface impairs their mechanical strength. From the data in Table 1.2 it follows that the best combination of mechanical and electrical characteristics among the materials tested has a core of superhigh modulus fiber with the removed cotton braid impregnated with oil in vacuum. Not only statistical loading from the excess gas pressure, but also shock wave loading from the expanding discharge channel affect the housing of a gas-filled discharger. When switching kiloampere currents, these loads can reach several megapascals. The electrical insulation of superconducting magnetic coils (SCMC) used in high-power thermonuclear reactors is subjected to huge tensile stresses and compression stress with amplitudes of the order of 400 MPa. During a sudden SCMC switch off, the accumulated energy, which reaches lOll J, is dissipated in an ohmic protective resistor. In this case, the voltage drop across the protective resistor can exceed the breakdown voltage of the insulation, which has reduced electric strength due to high mechanical loading. The insulation of transmission striplines in high-power pulse systems, the latter being plane conductors with solid or composite insulation, is exposed to strong electric fields. Calculations [15] show that mechanical loads in this case can be sufficient to cause insulation strain or fracture. These calculations were carried out for plane busbars with identical mica insulating layers (I:: = 8) of thickness d l = d2 = 1 cm. For an exciting field at the resonant frequency COl = 9.10 9 Hz and maximum linear current density Jmax = 107 AIm, the field component normal to the dielectric surface is En = 3.77.109 V1m, and the pressure preaches (2.22.8)-108 Pa. If one layer of mica is replaced by vacuum, En= 7.5.109 Vim. In lowfrequency fields (co« c/ ~I::ldl or co« c/ ~1::2d2 ), that is, for COo= 108Hz (coo --

o

f

___~-+--+----i

2

J

Fig. 3.4. Dependence on relative gas density of initial self-maintained discharge voltage (curves 1 and 2) and breakdown voltage (3 and 4) in SF6 gas (1 and 3) and air (2 and 4) for positive voltage polarity. The gap was formed by a sphere I cm in diameter and a plane segment 10 cm in diameter

Table 3.3. Value of 8CT for three gases and the indicated electrode radius of curvature "0

[cm]

1 2 3 5 10

8cr itrogen 7 75 35 25 15 7.2

Air 4.5 2.9 2. 1 1.55 1.05

Ter is most likely due to the thermionic emission which increases the concentration of charged particles and contributes to the gas transition into the plasma state. The latter redistributes the field within the gap, thereby facilitating gas discharge initiation and evolution. Similar results were obtained by the authors for air and nitrogen breakdown under applied dc and ac (50 Hz) voltages applied between the planar electrodes fabricated from Pt, PtRh, MoSiz, zr02 , and Ah03. For T< 1500 K, the dependences Ubr =.f{T) are described by the expression U br = 24.55 0.5 mm. In air, the minimum Ubr for zr02 and Ah03 cathodes at T = 2000 K is about 500 V irrespective of gap length. The approximation for nitrogen has the same form as for the other gases, and merely takes different numerical coefficients: U br = 270d +6.44../&i,

(3.15)

where Ubr is in kV. From a comparison of Ter and Ubr(T) for four gases, it follows that the role of electron attachment to neutral particles as a factor yielding high electric strength of electronegative gases decreases at high temperatures. Given that Paschen's law holds for the four gases examined, their critical temperatures Ter satisfy

The generalized form of Paschen's law is also applicable to a description of Uer of a heated gas flow when T= 300-2100 K and d < 1 mm [52]. In argon, for example, the available experimental data can be summarized by the empirical formula

3.2 Temperature

Ubr. V

.L

6000 'fOOD ZOOO

fOOD "\ 600

'100 200

51

"

6 10-3 2

-- - -

./

. / I'"

V

V

L.

Fig. 3.17. Generalized dependence on pdl T of breakdown voltage pulses in argon

Ubrcp = f(pd IT), cP = [1-(I-d I d o)(0.06- pd IT)r with an error of ±30%. For do= 10- 3 m, we have 4.10-3 100 Pa) in the temperature range examined, surface breakdown is governed by processes in the gaseous medium, but at p < 100 Pa the surface properties of ceramics and gas adsorbed by those ceramics play a prominent role. The dependence Eft=j(pd) as a function of temperature has the U-shaped form typical of the generalized form of Paschen's law Ubr= j(pd/T). A temperature decrease shifts the dependence Eft(Pd) toward larger pd, which corresponds to an increase in Eft(Pd) at small pd and a decrease in Eft(Pd) at large pd. The U-shaped form of the dependence Eft(Pd) is maintained in inert gases at room temperature, but the similarity law no longer holds. For pressures between 103 and 105 Pa, Eft decreases with increasing temperature in nitrogen as well, whereas at lower p, a temperature increase to 1300 K does not influence Eft. Further increase in T is accompanied by a slight decrease in Eft. A constricted discharge in atomic gases becomes diffuse at T> 1000 K. Moreover, the delay of the discharge initiation decreases with increasing temperature. To estimate Uft under conditions corresponding to the right branch of the Paschen curve and close to those realized in [53], empirical relations similar to Eqs. (3.14) and (3.15) can be used. For the flashover voltage in nitrogen,

3.2 Temperature

53

Uft = 689.18d + 70.77.J&i

or Uft = 1. 993pd IT +3.806.JPd IT.

For the flashover voltage in argon, Uft = 1.46.Jpd IT -0.415pd IT.

Here Uft is in kV, d is in m, and p is in Pa. For ac voltages, the dependence Uft = 1(T) has a complex character (Fig. 3.19) [59]. When the temperature increases to T r::: 110 K, Uft decreases monotonically, and its rate of decay is greater than that for the air gap (cf. curves 1 and 3). An anomalous increase in Uft is observed at T> 1000, and at Tr::: 1200 K, it approaches Uft for the air gap. The less the difference between Uft and Ubr, the greater the sample height. For 1= 7 mm, these voltages become equal at T r::: 1200 K. Upon heating to temperatures above T r::: 1300 K, Uft rapidly decreases irrespective of the sample dimensions. When the gas temperature decreases to that of liquefaction, the electric strength changes in agreement with the generalized form of Paschen's law. For electrical breakdown of liquids (short-term voltage exposure and high degree of clearing and degassing), the electric strength slowly decreases when the temperature increases from 273 K to the temperature near the boiling point of the examined liquid (curve 2 in Fig. 3.20). Moreover, the decrease in the voltage duration weakens the influence of T on E br• Good qualitative agreement of curves illustrating the dependences Ebr= 1(1) and the density as a function of the temperature demonstrates that in this case, the main effect of T is due to the temperature-dependent density. For commercially pure liquids containing impurities of different types and long-term voltage exposure (regions II and III in the voltage-time characteristics; see Sec. 5.1), the temperature dependence of their electric strength is primarily due to the temperature dependence of moisture and gas content and their redistribution between the emulsified and molecular dissolved states. In addition, the thermal decomposition of liquids and changes in their viscosity, surface tension, density, and hence the rate of electroconvective processes and electrohydrodynamic flows must be taken into account. The rate of liquid flow influences its electric strength, increasing it at the expense of breaking the bridges formed by the impurity particles, liquid drops, and gas bubbles. However, the rate of liquid flow can also reduce the electric strength when large bubbles are carried into the region of large E by this flow (see Sec. 8.6). Bubbles will grow with increasing temperature and decreasing viscosity at the given energy, and the pressure inside them will decrease, thereby reducing their Ebr• Large bubbles have high probability of being elongated along the electric field lines or coalescing with other bubbles. Bubbles 50 I-lm in diameter, or even larger, with internal pressures up to 0.4 MPa are typical of oil.

54

Chapter 3 Influence of Dielectric Properties, State, and Electrodes

,

t

\ 9

8 1

\

*i\ ,

-I(.

\

l~i5

J.

,, )

3 \.

*\i

,

-,

v' ,

"

!\

\

2

,,

21I

If.

;t.~

JOO

500

.... on

~1.t

~~ ~J..~ ~b

,t,. 900

1

11

0-1

• -1

i:J.-J

\

~'rlot.

700

•

I

" ' ...\ o* --5If " ....... ............ r\

~

1

....1 J

I

~A

J

+

I

1\

*1

~

o

\,

0

6 5

,

9

~.o A*

~

I

1

~\ '

~.

• ffOO

1300

f500

r, K

Fig. 3.19. Dependence of breakdown voltage Ubr on the air temperature (1) and Un for AhO) (3) and Zr02 (4) samples. Curves 2 and 5 illustrate the calculated thermal breakdown voltages Ur for the AI 20) and zr0 2 samples, respectively; D = 12 mm and 1= 5 mm; first heating of sample No. I (1), cooling of sample No. I (2), second heating of sample No.1 (3), heating of sample No.2 (4), and heating of sample No.3 (5)

A great number of factors influence the temperature dependence of breakdown processes, resulting in a complex temperature dependence of the electric strength of actual liquid insulation (curve 1 in Fig. 3.20) [18]. When cold insulating oil is not in contact with ambient air, its electric strength has no local minimum at temperatures -273 K. For less pure liquid, the difference between Ebr at T"", 273 and 353 K can reach 200%. Qualitative behavior of the dependence E br = .f(D is maintained not only for liquids with different degrees of clearing but also for composite insulation. For this insulation type the effect of temperature on electric strength also depends on the rate of gas release during decomposition of a solid dielectric

3.2 Temperature

55

.

Ebr kV/mm

20

2

b..

1G

12 6

1/ 6......

"

0233

V"

>-..

...... ......, ""'r:

'/~

27J

J/J

151

7; /(

Fig. 3.20. Dependence of electric strength of in-service (1) and dried (2) transformer oil in a standard breakdown system

RW~~~~~~~~~

JOO

700

f100

f500

r, K

Fig. 3.21. Dependence of PBN electric strength (in the direction C) on temperature for sample 2-mm thick for an oscillating damped pulse with a period of 300 ns and a damping decrement of2 in a homogeneous field

and moisture liberation, on the amount of moisture and gas the solid dielectric can absorb, and on the charge transfer mechanism in the composite insulation. The temperature dependence of short-lived electric strength of solid thermostable inorganic dielectrics is characterized by two well-defined regions that can be referred to as low-temperature and high-temperature. The lowtemperature region is characterized by electric strength that is essentially independent of the temperature; in the high-temperature region, Ebr rapidly decreases with increasing temperature. Even in such superthermostable insulation as PBN, heating a sample from room temperature to 1800 K halves E br (Fig. 3.21). (The 0.95 confidence level is indicated in the curve in Fig. 3.21.) The temperature dependence of the electric strength for some of the commonest heat-resistant composite electrical insulation types can be inferred from Table 3.6. The table represents the author's sample from a large amount of data on the heat-resistant insulation characteristics presented in [10]. From Table 3.6 it follows that heating to 1073-1123 K reduces the electric strength of most ElM by a

56

Chapter 3 Influence of Dielectric Properties, State, and Electrodes

Table 3.6. Dependence of electric strength E br [MV/m] in highly heat-resistant composite electrical insulation Material Mica sheets

Fluorophlogopite flexible materials Hardened imEreS!!ants Coatings: organosi licone metallophosphate Filling and sealing compounds

omenclature FlmFV FFAV FMAV FlmKV GlsKV L1cKV SPV-8 SPV-20 OS-52~

OS-92-19 AFS-2 AFSA AF-5 AF-8 BMK-I AF -4

293 26 40 43 38 15 15- 17 6-8 5- 12 47 40 4-6 6-8 2.3- 2.7 2. 1- 2.4 2- 3 1.7

Laminated plastics: 13 AGVN asbomicarta 3-3.5 SK-9A glasstextolite >20 micaceous micarta SGVN PKO-2-2-7 7 Composite plastic {molded silicone2 Glasses and glassbased materials: 18 glass 3 1 26 glass 4 1 15 novomycalex 19 mica glass ·ceramics 17M Ceram ic materials: > 18 microlite 19 GB-7 19 uralite ote: Empty rows imply a lack of data.

623

TemEerature [K] 973 1073 873 16 14 23 16 34

1123

10 10 5-4 6-1 0

5- 7 5- 7

8 1.8 3

0.5-0.8 0.5-0.7 0.6-0.8 0.7

1.3- 1.6 0.7-0.9 1.5 10 3 > 16 5

3.2 5.0

1.5

12

4

3.2 4.6 6.0 1.5

6.0 6.0 3.0

factor of 2-5. The least decrease in Ebr is observed for hardened impregnants with organic silicon binders and thermostable fillers (alundum, quartz, mica, chromium oxides, and cobalt). Complex and highly diverse behavior of the electric strength on the temperature is typical of polymer insulation.

3.2 Temperature

57

Ebr • MV/cm

f7J

Z73

373

T,K

Fig. 3.22. Dependence of E br for high-density polyethylene (HOPE) doped with I % of the surface-active substance AS = 1 (3 and 4) for a dc voltage (l and 3) and voltage pulses (t p = 5 Jls) (2 and 4)

The short-term electric strength and treeing stability of the majority of polymer compounds at cryogenic temperatures slightly exceed those at room temperature. This is especially true of polar polymer compounds. The electric strength of the polar polymer compounds lies in the range (11-15).10 8 Vim, and that of nonpolar ones is in the range (5-8).108 V1m. The maximum Ebr were obtained for polyvinyl alcohol, which has a polar (-OH) group in a side chain. At low temperatures, the cohesion energy of polymer compounds and the electric strength are correlated, which to some extent is similar to the correlation between E br and the lattice energy of the alkali metal halides. With increasing temperature, Ebr for the majority of polymer compounds decreases by a factor of 2- 5 or more at critical temperature (the glass transition temperature for amorphous polymer compounds or the melting point for crystalline polymer compounds). Depending on the structure of polymer compounds, the presence and type of additive agents, and the voltage type, the temperature rise from cryogenic to critical is accompanied by an increase or decrease in E br • In most cases, the temperature dependence of Ebr (or Ubr) is nonmonotonic. Figure 3.22 shows the electric strength of polyethylene films (with and without dopants) for a dc voltage over a wide temperature range [56]. A maximum in curves Ebr = fiT) can be seen at a temperature of about 198 K. It is of interest to note that E br for dc voltage and polyethylene doped with a surface-active substance (AZ-l) is higher than for voltage pulses at T < 198 K. At higher temperatures, the decay rate of the breakdown dc voltage is greater than for voltage pulses. The maximum in the curve Ebr=f(I) for a polyethylene film (50 !-lm) was recorded in [57] at an elevated temperature of 353 K. The authors explained this by noting fact that the temperature rise reduces the dimensions of amorphous regions in low-density polyethylene (LOPE) (see Sec. 3.3).

58

Chapter 3 Influence of Dielectric Properties, State, and Electrodes

Under long-term and simultaneous exposure to an electric field and elevated temperatures on polymer compounds, thermal aging is in many cases the key factor for insulation degradation, which determines its service lifetime. The rate of thermal insulation aging is determined by rates of chemical reactions, which depend on the temperature according to the Arrhenius equation (3.16) where v' is the chemical reaction rate, that is, the amount of matter which enters the reaction per unit of time, and Wa is the activation energy of the reaction. The service lifetime with thermal aging can be set approximately inversely proportional to the rates of chemical reactions. This enables us, using Eq. (3.16), to relate the service lifetime to the temperature: (3.17) where t, and t2 is the insulation service lifetime at temperatures T, and T2 , respectively; IlT is the temperature increment which halves t. For many insulation types, IlT can be setto 10°. Equation (3.17) is the mathematical expression of the ten-degree rule which states that the service lifetime of insulation of class A halves when the temperature increases by 10° (in the range of working temperatures). Equation (3.17) is well-confirmed experimentally and under conditions of ElM operation, except when the contribution of chemical reactions of second or higher order to the aging process becomes significant. Equation (3.17) fails for polymer compounds if their glass transition temperature falls within the working temperature range (the chemical reaction activation energy is no longer temperatureindependent). Equation (3.17) also fails in inhomogeneous dielectrics. For polymeric films whose aging in an electric field is primarily due to the evolution of partial discharges intensifying chemical degradation of polymer compounds, the temperature dependences logt = j{UT) are depicted by straight or broken lines so that the formula t = to exp( -Wa / kT) is valid for each straight line segment, where to is the service lifetime at standard temperature (293 K) and Wa is the activation energy. For large thickness of polymer insulation, the dependence of the lifetime on the temperature for ac and dc voltages and voltage pulses is determined by the incubation and treeing stages of aging [25]. The dependence of the time before treeing origin in PE and PMMA for ac voltage in a tip (r = 5 J.UD)-plane (d = 2-5 mm) electrode system on the voltage and temperature is described in [60] by the equation Id.t =

A(T)exp[-B(T)U],

3.2 Temperature

59

Table 3.7. Coefficients A and B as functions of temperature T [K]

PE

PMMA

303 323 353 373

kl0 3 1.9 1.26 0.84 0.55

A·IO J 11 .00 3. 15 0. 11

3.71 3.00 2.90

B·IO

4.15 3.95 2.02

n, pulses

JfJ

JJJ

3537;1(

Fig. 3.23. Temperature dependence of PE service lifetime as a function of the pulse repetition rate f (oscillating pulse with 'ft = 0.3 /ls, 'half = 0.6 /ls, and a damping decrement of 1.4). Needle-plane electrode system with r = 20 /lm and d = 2.5 mm

where A and B are temperature-dependent coefficients (Table 3.7), td.t is in s, and Uis in V. Figure 3.23 illustrates the dependences of the PE service lifetime on the temperature as functions of the high-voltage pulse repetition rate. Three tendencies are clearly discernible:

60

Chapter 3 Influence of Dielectric Properties, State, and Electrodes

- the temperature dependence of the service lifetime on a semilogarithmic scale represents a smooth curve with a minimum, - the minimum becomes more prominent with increasing pulse amplitude and repetition rate, - the difference between low- (298 K) and high-temperature (353 K) service lifetime increases with the pulse repetition rate. The temperature dependence of short- and long-term ElM electric strengths can be regulated by various technological means. In particular, special dopants, fillers, radiation, and preliminary heat treatment are most widely used for polymer insulation (see Secs. 9.1and 9.2).

3.3 Molecular and Supermolecular Structure Establishing a correlation between the electric strength of dielectrics and their structure is an important facet of searching for and systematically synthesizing of insulating materials and media, and of predicting their dielectric characteristics based on known physicochemical parameters. One experimentally confirmed regularity is that the greater gaseous electric strength, the slower the process of energy accumulation by the electron in the field, that is, the greater the electron energy losses due to inelastic collisions. This follows immediately from the concept of shock ionization considered the basic gas-discharge mechanism. In heavy gases containing easily polarized molecules, the inelastic energy losses of the electron are greater, and hence such gases have greater electric strength. Table 3.8 [18] compares breakdown voltages in certain gases and their constants. Except for O2, all gases examined exhibit the aforementioned behavior: the greater the molecular mass, the greater the electric strength. In addition, the analogous correlation of electric strength with critical temperature is observed. This correlation also extends to other gases, namely CO2, C2H 2 , N02, H 2S, C1 2 , and S02'

Table 3.8. Gas breakdown voltages and constants (breakdown between spheres 8.6 mm in diameter for d = 4 mm)

Gas Hz

O2 2

0

HCI HBr HJ

[kV]

Vbr

Molecular mass

1.06 1.46 1.66 1.7 2.48 3.66 5.22

2.0 16 32 28.0 16 30.0 1 36.455 80.924 127.93

Mean free path [lO~ em] 11.23 6.47 5 9. 9 5.7 4.33

Ionization potential [V]

Critical temperature

[K]

Dis oeiation energy [eV]

16 12.5 15.5 9.5 13.8 13.2 12.8

33.2 155. 1 127. 1 177.4 325.4 364.17 423 .9

4.4 5.1 9 6.8 4.4 3.7 3 .1

3.3 Molecular and Supermolecular Structure

61

However, there is a group of sulfur gases (SiF4, S02F2, S02, and SOF2) for which the electric strength increases with decreasing molecular weight. Following the logic of these observations, B. M. Gokhberg et al. carried out a large number of investigations in the 1930s and 1940s to find heavy molecular gases suitable for electrical insulation of high-voltage gas-filled equipment. They must have not only high electric strength, but must also meet a number of requirements, namely: - low liquefaction temperature, so that they can be used at standard temperatures under high pressure - chemical inertness relative to insulation and structural materials placed in the gas atmosphere - stability when subjected to electric discharge - nontoxicity - low cost. They chose sulfur hexafluoride SF6 and freon CClzF2. Over the following few years, only SF6 gas and its gas mixtures were widely used as insulation, first in systems with small volumes and than in large systems of high-voltage metal-clad switchgear. Since the basic types of liquid insulation used in high-voltage engineering are mineral oils comprising paraffin, naphthene, and methane hydrocarbons in various proportions depending on their group, it is of interest to track the dependence of their electric strength on the molecular constants. In addition, these liquids are convenient objects of investigation, since some particular molecular constants can be changed by choosing liquids of the same series, with other parameters remaining unchanged. An analysis of this problem [61] shows that for dc and ac voltages and microsecond voltage pulses, the influence of liquid properties (in particular, their density) on electric strength is masked by a stronger influence of impurities (see Sections 4.1 and 4.3) and electrode state (see Sections 3.4 and 3.5). For this reason, this influence was detected in some studies but not in others. For liquid paraffin hydrocarbons with a modest amount of clearing, a linear dependence of the discharge time (for E = const) on the density and other physicochemical parameters determining the intermolecular bond force was established in [61] using nanosecond pulses and long discharge gaps, whereupon the role of secondary effects engendered by impurities and electrode state decreased significantly. However, this dependence was only a special case, because it was detected solely for normal hydrocarbons of the paraffm series. The density cannot be the key parameter governing the electric strength of hydrocarbons, because isomers possessing higher density have lower electric strength than normal hydrocarbons. At the same time, the electric strength of normal hydrocarbons and their isomers is directly proportional to the length of molecular chains. This dependence can be satisfactorily explained by the bubble and intrinsic electrical mechanisms of liquid breakdown. The liquid breakdown mechanism depends mainly on electrical conductivity and voltage duration (and hence on the field strength related to it). For liquids whose molecular structure and physicochemical properties differ significantly, the

62

Chapter 3 Influence of Dielectric Properties, State, and Electrodes

r

.

If

,/

10

D.9 0.0 la-II 2

.... ~ ~ ~i-"

V

(;

iP'"

~~

"~

Nact d,

~

r--

"6810- 3 2 "6 810- t Z 'I 58 (0-12 If 6 Y. S/m

Fig. 3.24. Dependence of electric strength of aqueous NaCl solution on electrical conductivity in homogeneous field for nanosecond voltage pulses (tp = 70 ns and d = 0.02 cm)

discharge characteristics are uncorrelated with the electrical conductivity when exposed to voltage pulses lasting tens of microseconds or less. For water and aqueous electrolytes with electrical conductivity in the range 10-4-1 Slm, the dependence Ebr = f(y) is complicated. In a homogeneous field, it is displayed by a curve with a maximum (Fig. 3.24). With increasing voltage duration, the maximum is shifted toward lower electrical conductivity. In the field of tip-plane electrodes, the dependence Ubr= f(y) differs significantly for positive and negative electrode polarities. For the negative polarity, it is a straight line on a semilogarithmic plot, whereas for negative polarity in the range y = 10-4_ 10-1 Slm, Ubr is essentially independent of y, and only for y > 10-1 Sim does Ubr increase (slightly) with any further increase in y. These results demonstrate that contrary to widespread belief, reducing the electrical conductivity of water by very careful clearing is an inefficient way to increase its electric strength for voltage pulses. The optimal value of y for water must be selected taking into account the allowable resistance of a specific system with water insulation and the total cost of preparing and maintaining water with low y. For aqueous salt solutions, the dependence of their electric strength on the cation charge was also observed for nanosecond voltage exposures (40-220 ns). Salt solutions with smaller cation charges have greater electric strengths. No prominent dependence of E br on the anion parameters was detected in experiments with salt solutions having identical cations but different anions. Liquids possessing high intrinsic conductivity, as a rule, have high permittivity E. For long-term voltage exposure, high E and hence high y make gas formation easier due to effervescence and electrolysis, that is, they lead to the bubble breakdown mechanism with typically lower E br • As demonstrated in [61], the elevated value of E facilitates breakdown evolution and reduces Ebr for purely electrical liquid breakdown. This dependence was first established in [62] for a set of liquids comprising xylene, toluene, transformer oil, tricresyl phosphate, nitrobenzene, and

3.3 Molecular and Supermolecular Structure

63

glycerin. The strongest influence of I> on Ebr was observed under long-term voltage exposure. More recently, the dependence of Ebr (kV/cm) on I> in the form

Ebr = -0.05881> + 3.026 was established in [63] based on test results for 22 well-purified liquids with I> in the range 1.88-15.06 for ac and dc voltages. For gaps with highly inhomogeneous fields (+T -P) and 1.2170-J..Ls pulses, the dependence of the average breakdown electric strength (Eav.br = Ub/d), in kV/cm, on I> is [61] 10gEav .br = -0.0921>+4.67.

For negative tip polarity, this dependence is complicated (it is described by a U-shaped curve) due to the abnormally strong effect of polarity on the breakdown of water and some other liquids with high 1>. With decreasing voltage duration, the difference between the electric strengths of polar and nonpolar liquids decreases, and for t < 10-7, no well-defmed I> dependence of Ebr is observed. For nanosecond voltage exposure, liquids whose physicochemical properties differ significantly have nearly the same electric strength. A consequence of the above discussion important for the design of high-voltage nanosecond pulsed systems is the fact that the electric strength of liquids cannot be the main criterion for choosing insulation of such devices. Depending on specific conditions, the choice is determined by electrical conductivity, permittivity, stability in an electric field and when exposed to a spark, nontoxicity, low cost, etc. For solid dielectrics characterized by highly diverse physicochemical properties, production technologies, etc., the case in point is a correlation between, on the one hand, molecular and supermolecular structure, and on the other, electric strength for materials of the same class. This correlation is most significant in model solid dielectrics-monocrystals. Among dielectrics that are most widely used as ElM in highvoltage engineering, this problem has received the most study for solid polymers. For crystalline polymers containing crystalline and amorphous phases, the shortand long-term electric strengths depend on the extent of crystallization; for example, Ebr increases by a factor of 2.5-3 when the extent of solid-state polyethylene crystallization increases from 3 to 52%. The same effect was observed for polyethylene at different densities, copolymers of ethylene with propylene, and mixtures of low- and high-density polyethylene (Fig. 3.25). However, this correlation type is not always observed. The opposite dependence is observed when sample production and testing processes change slightly-the electric strength decreases with increasing crystallization. These inconsistent results indicate the strong influence of the size and type of supermolecular structures on electric strength. The electric strength of intraspherulite space decreases with increasing spherulite size and saturates when the spherulite size exceeds 230 J..Lm. The maximum stability against electric discharge [64] is found in polyethylene samples with the smallest spherulites, greatest degree of crystallization, and lowest concentration of stressed bonds at the interface between the amorphous and crystalline phases

64

Chapter 3 Influence of Dielectric Properties, State, and Electrodes

fa

9

6

6

G

7

'I

6

2

S

.Y-

D

oOU

Y

~

/.r

I!

~

n

n

r--o

o ¥ Ii

1

0

/

0-2 " -J

so

JO

/(,·/0

70

Fig. 3.25. Dependence of treeing stability (1) and electric strength (II) of polyolefins on the degree of crystallization K for polyethylene with intermediate (1), high (2), and low density (3)

p(")

0

bo

0.6 0

2 '0 0 0

. ... . 0

00 0 0

o.z

0" 0

o •

0

..

o

'eo ",cP ••:

.

0

00 0

0

• •-

.·~f

00

0

. obtained in [67] for a dc voltage remains essentially unchanged for breakdowns of short (several tenth of millimeter) vacuum gaps by nanosecond pulses. In [68], the series of metals was molybdenum, copper, aluminum, lead, and graphite. For pulses 1.2/50 J.Ls and long interelectrode gaps (up to 35 mm), the sequence was aluminum, stainless steel, and copper [69]. Taking into account discrepancies in the results obtained by various authors under similar and radically different experimental conditions, at least four characteristics of the electrode metal can be identified that affect strongly the electric strength of vacuum gaps, namely, hardness, corrosion resistance, gas liberation rate, and degree of bulk and surface metal impurity. In this case, not only the elemental composition of the material but also its structure and the amount and distribution of impurities are important (see Sec. 3.5). With a certain amount of care, the electrode metal for high-voltage vacuum equipment can be chosen based on the following series of metals in order of decreasing electric strength: tungsten, molybdenum, tantalum, stainless steel, iron, nickel, aluminum, copper, lead, and graphite. One more requirement imposed on the electrode material-highly stable electric strength-is also of great practical importance. According to [34], this requirement is best satisfied by a stainless steel, titanium, molybdenum, and a titanium alloy (89% titanium, 5-7% aluminum, 3-4% vanadium, and 0.3% iron). Copper, nickel, and tungsten are much less stable. When the cathode and anode are prepared from different materials, the electric strength can be influenced predominantly by the material of the cathode, anode, or both electrodes, depending on breakdown conditions. The anode material is dominant only when it is transported to the cathode, that is, under conditions of multiple breakdowns and long-term application of near-breakdown voltage to the vacuum gap. The cathode material has the most obvious effect on the voltage of first breakdown (for unconditioned electrodes) when exposed to voltage pulses and short-term dc and ac voltages, as well as for large electrode areas and few breakdowns per unit area. At low gas pressure, when processes at the cathode surface play an important role in the breakdown according to the Townsend theory, the breakdown conditions (or the conditions of self-sustained discharge in an inhomogeneous field) can be written in the form

Y[ exp( ad -l)J = 1. The strong dependence of the second Townsend coefficient y on the cathode material and state of its surface dictates the dependence of the electric strength of low-pressure gases on the work function of the cathode material. Due to a number of secondary effects associated with the impurity of the electrode surface (see Sec. 3.5) and gases, as well as with the small difference in work function for various metals, it is difficult to obtain this dependence experimentally. For alkali metals, which possess very small work functions (tenths of an eV), Ubr has half the value found in conventional metals (

ocn deviation from the similarity law is observed, the gas breakdown voltage at standard temperature again depends on the electrode material for each specific interelectrode gap length. The cathode materials in order of decreasing Ebr for compressed gases are stainless steel, copper, iron, mild steel, brass, silver, zinc, aluminum, nickel, and carbon. The difference between E br for electrodes prepared from stainless steel and aluminum can reach 80% [70]. The farther along the cathode material is in the above sequence, the smaller the value of Ebr at which the deviation from Paschen's law starts and the greater the number of required training breakdowns. The anode material influences Ebr only when it is deposited on the cathode surface as a result of previous breakdowns or when loosely bound particles are detached from the anode surface. The higher the pressure and strength of the electric field applied to the gap, the greater the influence of the material. At cryogenic temperatures, the influence of the electrode material on E br of gases is qualitatively similar to that at standard temperature. The influence of electrode material on electric strength intensifies with increasing gas temperature (see Sec. 3.2). In [51] it was shown that CO2 electric strength depends on the emission characteristics of the cathode and is independent of the properties of the anode material (when the discharge gap is formed by planar electrodes) for electrodes prepared from Pt, PtRh (work function = 10), PtRh (work function = 30), Alz0 3, and zr02 at T> 1400-1600 K. Cathodes with smaller work functions (Alz0 3 and Zn02) exhibit smaller Ubr and higher pre-breakdown currents than cathodes with larger work functions (Pt, PtRh, and PtRh). For cathodes prepared from zr02 and Alz0 3 at T ~ 2000 K, the values of Ubr for short gaps (d=0.25-10mm) differ only slightly and are about 0.45kV, which is several times less than the values calculated by Paschen's law. For cathodes prepared from platinum and its alloys, this difference does not exceed 50%. When a solid dielectric is present in the interelectrode gas gap and breakdown is initiated at its surface or in its immediate neighborhood, no influence of the electrode material on Ubr can typically be discerned. This can be explained by a stronger influence of the solid dielectric (field distortion, influence of impurities adsorbed on the electrode surface, etc.). In many theories of liquid dielectric conductivity and breakdown, it is assumed that electrons are emitted in the same way as in vacuum, and the influence of the liquid is taken into account only via a corresponding correction factor for the permittivity of the medium. However, this correction factor does not ensure satisfactory agreement of the experimental results, even those obtained under extremely pure conditions, with calculations using the Fowler-Nordgame and Schottky equations. Low experimental values of the work function for electrons going from metals to liquids that are within the range 0.025-1.25 eV called for more de-

3.4 Electrode Material

69

Table 3.9. Dependence of electric strength of certain gases on the electrode material

Electrode material Stainless steel Brass Copper Gold Platinum

Ebr [MY/cm] h 1.4 1.01 1.4 1.16 1.1

Cd = SO /fm and O.S-cm electrode diameters) ~

~

2.38 1.44 1.81 1.24 2

1.88 1.62 1.S 2.24

tailed analysis of this problem. In [61] it is shown that lower than calculated values of

0.1 %, the dependence Ubr = j( C) is complicated (Fig. 4.4). Suspensions should be considered systems of noninteracting particles-weak elements-that can be described by the insulation reliability equation (4.6). As can be seen from Fig. 4.4, the breakdown voltage first decreases with increasing C and then increases and saturates when the concentration exceeds a certain critical value. The concentrations corresponding to the characteristic points in the curve depend on the suspension properties. Thus, in the region of the minimum C= 0.35-l.2%, while in the saturation region C= l.2-2%. When the particle material is conductive (soot), the dependence Ubr = j(C) exhibits a maximum. The most probable reason for the increase in Ubr as C increases

92

Chapter 4 Influence of Contamination and Structural Defects

J

mo~--~--~--~--~

0.'1

0.8

f.Z

C, %

Fig. 4.4. Dependence on solid-phase concentration of Vb, for glass spheres suspended in glycerin for voltage pulse slopes A = 1.15.106 (1), 6.1.104 (2), and 2.88.104 V/IlS (3) and a tip-tip electrode system with d = 3 cm

to 6-7% is that the conducting particles are charged in the electric field and make it less inhomogeneous in the region adjacent to the tip electrode. Vorob'ev and Ushakov [95] suggested using these effects to increase the breakdown voltage of insulation gaps filled with a liquid and possessing an inhomogeneous electric field. For C > 6-7%, the decrease in Ub, can be explained by the fact that the increase in electrical conductivity of the medium dominates at these concentrations, causing the probability of thermal breakdown of the suspension to increase. One important practical problem is monitoring the impurity content in liquids. Based on a study of the influence of mechanical impurities on the electric strength of transformer oil and oil-barrier insulation for U with a frequency of 50 Hz, Kuchinskii and Kalent'ev [96] demonstrated that the Russian Standard "Method for Determining Mechanical Impurity Content," which defines oil clarity in terms of content by weight of mechanical impurities, does not take account of a potentially significant decrease in the electric strength of oils containing impurities when their content by weight is below the critical (permissible) value. For example, they demonstrated that for a number density N = 200 cm- 3 of particles with 50 ~m average diameter in oil, their content by weight can increase from 10 to 40 glt. According to the Standard, oil with these amounts of impurities is classified as pure. However, the electric strength of this oil can be half that for N = 50 cm-3 . Kuchinskii and Kalent'ev [96] drew the following conclusions, which are important in the operation of oil-filled insulation equipment: the volume concentration N of mechanical impurity particles rather than their mass concentration primarily affects the electric breakdown of oil; the dependence of Eb, on N in the range 50 cm-3 ::;; N::;; 240 cm- 3 is described by the equation Eb,= Eo]-klnN, where

4.2 Structural Defects and Impurities in Solid Dielectrics

93

Table 4.2. Values of the parameters Eo!> Eo, and k for different materials of impurity

particles Impurity type Aluminum particle Cellulose fiber, W1,, = 7% ilicon oxide particle ell ulo e fibe r, WI" = 0.2%

Interelectrode gaE length 6 8

4 EOI 3 1.5

k

k

I

k

10 k

4

Ell I 21.6

3.0

20.9

2.5

17.7

1.9

2.3

19.0

2.2

17.8

2.0

2.2

19.0

2

13.8

1.0

4.7

EOI 29.4

4.4

27.0

30.5

4.2

22.7

2.8

26.9

3.5

20.9

25.2

3.0

20.6

EOI

Eo= 13.9 kV/mm IEo= I1.5 kV/mmlEo= 10.7kVllnm IEo= 10.OkV/mm

and k are parameters that depend on the impurity type and interelectrode gap length (Table 4.2). For N ~ 50 cm-3, Ebr = EbrO ; for high-voltage oil-filled transformers, the maximum permissible concentration of mechanical impurities must be ~50 cm-3, and the liquid water content Wiw in solid cellulose must be g .O%. A method and device (developed by the Alsthom Corpomtion) for monitoring and calculating the impurity particles in transformer oil was suggested in [108]. It was approved by Committee lOA of the International Electrotechnical Commission (IETC). The method enables particles with diameters from 1.5 to 90 !lm to be calculated and classified into nine groups. A special breakdown tester with an interelectrode gap length of 2.5 mm (like a conventional tester) but much greater oil volume in the range of field action was also developed. The results obtained with this special tester better reflect the actual influence of impurity particles on the electric strength of oil-filled system insulation. The IETC standard ASTMF-661 unifies measurements of the number and size of particles contained in a liquid.

EOI

4.2 Structural Defects and Impurities in Solid Dielectrics The kinetics of formation and dimensions of embryo submicrocracks in actual solids having supermolecular structure and defects are closely related to the inhomogeneity of their structure for long voltage exposure. For this reason, even in amorphous-crystalline polymers with typically stable regions of material discontinuity origin-amorphous interlayers in fibrils-local cracking in regions of individual defects is more probable than mass uniform pouring of submicrocracks. The supermolecular structure with weak defect regions is typical not only of crystallizing polymers. Block polymethylmethacrylate (PMMA) has microstructure containing individual domains with well-defined centers and fibril-like structures separated by amorphous regions. The energy density required to separate domains with average radii of 10- 5 m along these amorphous regions is 2-5 J/m2 ,

94

Chapter 4 Influence of Contamination and Structural Defects

which is much less than the energy density required to break the C-C bond (70 J/m2 ). The supermolecular structure of block polystyrene (PS) is globular in character. The space between globules is filled by a loose amorphous polymer. Globules are bonded by van der Waals interaction forces. They form larger structures-zones of various dimensions-that are bonded more weakly than globules. Boundaries of these zones are weak regions where cracks originate under applied mechanical stresses and electric voltages. Spherulite structures of polypropylene are predominantly bodies of revolution (spheres, ellipsoids, cylinders, etc.). Spherulite boundaries are least resistant to voltages and mechanical stresses. When the strain exceeds the critical value, they fracture with the formation of voids. The discharge probability in these voids increases, because gas penetrates rapidly. The discharge channel, as a rule, develops along spherulite boundaries. Moreover, if a tip electrode enters a spherulite, a breakdown (or dendrite) channel originates from interspherulite interlayers closest to the tip rather than from the needle. As pointed out in Sec. 3.3, the degree of imperfection of molecular and supermolecular polymer structures affects their electric strength. Actual dielectrics with inhomogeneities on molecular and supermolecular levels contain macroscopic defects with characteristic dimensions of tens of microns. An elucidation of their role in electrical aging and breaking down the polymer insulation is important not only for an understanding of the insulation failure mechanisms but also for a formulation of technically and economically justified requirements on the insulation production process. The role of existing defects of this type and defects newly formed by an electric field in LDPE and PMMA failure and breakdown was studied in [98] for multipulse voltage exposure. To this end, scattering phase functions and diagrams were analyzed and photographs of imperfections arising in the electric field in PMMA were taken in scattered light. The influence of the number, dimensions, and spatial distributions of original inhomogeneities on the service lifetime of PMMA and LDPE samples was also investigated. The examined samples were prepared from blocks of commercial polymers. LDPE samples contained many inhomogeneities with sizes ~100 J..lm. There were also individual inhomogeneities of larger sizes. It has been found that the service lifetime does not correlate with the number and sizes of the original inhomogeneities. The service lifetime and the distribution of inhomogeneities over the interelectrode gap volume are also uncorrelated. Shapes and dimensions of the inhomogeneities remain essentially unchanged over the course of aging. The breakdown channel in most cases did not intersect the original inhomogeneities, even when they formed chains that traversed the interelectrode gap, given that distances between individual inhomogeneities exceeded their dimensions. Initial failures originate irrespective of the original inhomogeneities in the interelectrode gap, and trajectories of their development are close to the electric field lines. Zones of failure are formed in the weakest regions of the interelectrode gap as a result of

4.2 Structural Defects and Impurities in Solid Dielectrics

95

more intense (compared to the entire volume) growth of submicrocracks with dimensions from some tens to hundreds of nanometers. Investigations into the influence of micropores with an average diameter of 1.2 J..IIIl in cross-linked polyethylene on its pulsed electric strength have shown that it decreases with increasing pore concentration when the latter exceeds 230 nm-2 • For lower concentrations, the electric strength and the number of pores are uncorrelated. Thus, not all original inhomogeneities in polymers can be considered defects that influence their failure in an electric field. Since polymers have a very high degree of structural imperfection on molecular and supermolecular levels, the role of local microinhomogeneities against the background of these structural imperfections is insignificant. For this reason, the dimensions of these inhomogeneities rather than their concentrations are the key factors in the polymer breakdown initiation. A high electric field on the inhomogeneities does not initiate breakdown, because PD cannot develop due to small dimensions (several microns and even less) of these inhomogeneities. The next group of large-scale defects, which more strongly influence short- and long-term electric strength, can be subdivided into three types: gaseous inclusions inside an insulating material or on its boundary with the electrodes in which PD may arise - defects that cause the local electric field to increase compared to the electric field in the bulk of material (conducting inclusions) regions with very low electric strength compared to that of the main dielectric (for example, agglomerations of the hardener). Studies of the influence of PD on electric strength in air voids of various dimensions, configurations, and locations inside an interelectrode gap are summarized in [101,102]. The main sources of impurities and inclusions in solid dielectrics are raw materials and production processes, whereas in polymers they are fillers and additives that ensure the desired polymer properties. The simplest dielectric model is a system containing spherical inclusions localized at the comers of cubes. From the Rayleigh formulas it follows that the maximum field strength can be many times the average, and hence the breakdown voltage for a dielectric with inclusions will be less than that for a homogeneous dielectric. The greater the decrease, the larger the difference between the permittivities or electrical conductivities of the basic material and the filler. For example, the service lifetime of polyethylene containing 0.2% of a copper powder is halved, while a 5% admixture of butyl rubber reduces its service lifetime by only a few percent. The influence of the material of inclusions on the insulation service lifetime is illustrated by the data in Table 4.3 [99]. Cables with polyethylene insulation were tested. Steel, wooden, and glass needles were inserted into polyethylene in the process of its extrusion. The needles were 0.7-1 mm long and 0.1-0.2 mm in diameter, the radii of their tips were :S;5 J..IIIl. The experiments were performed with PE having different flow indices and percentage of antioxidants and other additives. The test field strength was 13.5 kV/mm.

96

Chapter 4 Influence of Contamination and Structural Defects

Table 4.3. Service lifetime of PE with various inclusions Conventional PE grade

Service lifetime, in h, with indicated needles Gla s Wood teel 10 23 1200 2 0.02 1.5 0.1 3 20 5 0.0)

Cable without inclusion 1200 1000 0.5 5

Ebr • kV/mm

o

25

50

7S

C,%

Fig. 4.5. Dependence of Ebr in polyethylene on the concentration of titanium oxide (Ti02). Test frequency SO Hz; standard samples were I mm thick

Figure 4.5 shows the typical dependence of the electric strength of solid dielectrics on the concentration of the additive whose properties differ significantly from the dielectric ones for small and large concentrations of the additive. The filler not only disturbs the macroscopic homogeneity of the material but can also change the supermolecular structure of filled polymers compared to the polymers without fillers. Pores and cracks can arise at high filler concentrations. In these cases, the electric strength decreases even when the difference between the permittivities and electrical conductivities of the filler and the polymer is small. Plasticizers also significantly influence the electric strength of polymers. In most cases, an increase in the plasticizer content reduces the electric strength of the polymer [100]-the higher the polymer breakdown temperature, the stronger the dependence (Fig. 4.6). The plasticizer influences the temperature dependence of the electric strength of polymers (see Sec. 3.2). The electric strength of plasticized polymers starts to decrease sharply at lower temperatures than unplasticized polymers. Organic additives to polymers, mainly glycerides, cause agglomerates of carbon particles with sizes between 100-300 nm to be formed. This is a reason for a thermal breakdown of such insulation. However, as demonstrated in Sec. 9.1, in some cases fillers and plasticizers increase, rather than reduce, the electric strength of polymers. This enables not only thermomechanical properties of polymers to be improved and their cost to be reduced but also their insulating properties to be improved.

4.3 Moisture

97

Ebr • kV/mm

GO t---T-~--+-------1

O.Z

0.5

C. %

Fig. 4.6. Dependence of E br of polyvinylchloride (PVC) on the plasticizer (DAF-789) content at the indicated temperatures. Test conditions are the same as in Fig. 4.5

4.3 Moisture Moisture most strongly influences the dielectric properties (including the electric strength) of liquid, solid, and combined insulation. When moisture that appeared in insulation as a result of its operation cannot be removed by reasonably simple methods (for example, this is the case of oil-paper insulation of cables, output leads, etc.), wetting is frequently considered a special form of insulation aging. The influence of moisture on the electric strength of gases in relatively short (tens of centimeters or less) gaps with homogeneous or weakly inhomogeneous field is insignificant until it condenses and forms drops. This influence is primarily due to the electrons captured by water vapor molecules, which is accompanied by a decrease in the number of electrons involved in the ionization processes. The decrease in the effective collisional ionization coefficient aeff due to the increased adhesion probability 11 (aeff= a-l1) is especially appreciable for small Elp, when the probability of creation of negative ions increases. The results of investigations into the influence of humidity were summarized for these gaps by the IETC and were included as correction factors Icy in the Russia Standard. The influence of the relative air density 8 and humidity is given by

In long discharge gaps, the electron flux along streamer channels decreases as 11 increases with the humidity. This impedes the transformation of the streamer

98

Chapter 4 Influence of Contamination and Structural Defects

1, t.Q6

\

z· ~.\ .....

1.0" 1.00

496 1U2

o

"

I

'"

~,

1Z

~ ..... 'fa. g/m 3

Fig. 4.7. Dependence of correction coefficient Icy on absolute humidity for voltage pulses 1150 !-Is, rod-rod gap of length 1-3 m, and positive (1) and negative (2) polarity of voltage pulses

into the leader, which also increases the electric strength of the gap. This effect weakens with increasing interelectrode gap length. Aleksandrov et al. [103] established that for gaps with a sharply inhomogeneous field, d > 2 m, and the moisture content Y. > II g/m 3, the breakdown voltage at a frequency of 50 Hz becomes essentially independent of the humidity. For short gaps and voltage pulses, the influence of humidity on Ubr is smaller than for voltage at the mains frequency, whereas for long gaps it is greater. Moreover, for voltage pulses with negative polarity the influence of humidity on Ubr is much weaker than for pulses with positive polarity (Fig. 4.7). While establishing the relationship of the electric strength of gases with the absolute humidity, it is well to bear in mind that the humidity is a temperature-dependent parameter. The absolute humidity increases with the temperature. The results of systematic measurements of air temperature absolute humidity during measurements of Ubr at the Laboratory of High-Voltage Engineering of Saint Petersburg Technical University are summarized in [103]. The breakdown voltage of a gas gap Ubr and the flashover voltage of an insulator Un decrease substantially when the moisture content in the gas filling the high-voltage system is so high that water condenses on the electrode and insulator surfaces and forms drops. However, if the gas dew point is low and water vapors are sublimated, form hoarfrost on the insulator, and the hoarfrost is then vaporized by melting and does not form drops as the temperature rises, Ubr and Un scarcely decrease at all. Considerable recent attention has been focused on the influence of various impurities (primarily moisture) on the electric strength of SF6 and its mixtures with other gases. Senouci et al. [104] demonstrated that the deviation from the discharge similarity law in SF6 for relatively large pd results from the influence of not only inhomogeneities of the electrodes (see Sec. 3.5) but also from the moisture. Breakdown was initiated by the dc voltage in the positive rod (d = 8 mm)-

4.3 Moisture

/1.26

0.20 0.12

~

~

,

99

.

~ o

a2

0.1f

aG

0.6 C, %

Fig. 4.8. Dependence on moisture content of Ebr in transformer oil for ac and dc voltages (summary of results obtained by various authors)

plane electrode system with gaps of length 2-40 mm and gas pressure in the range 0.1-0.3 MPa. Pure (with a volume impurity concentration of ~40 ppm), natural (300 ppm), and moist SF6 (up to 2000 ppm) was used. Deviations from the similarity law were observed at relatively large d (or high p): the greater the gas contamination, the greater the deviations. Based on optical investigations, Senouci et al. concluded that the deviation from the similarity law results from a change in the discharge type. The deviation is not observed for a streamer discharge; it arises when the conditions for the streamer-leader transition are realized. In particular, these conditions are created when water vapor is added. In this regard, information on the discharge type is needed in each particular case to predict Ubr of the gap. The low-voltage electric characteristics of transformer oil and its electric strength depend substantially on the moisture content (Fig. 4.8) [105]. Therefore, determination of the moisture content of the transformer oil and its efficient drying are important for oil and oil-bearing insulation (including oil-paper and oilbarrier insulation types). Now it can be considered well established that in addition to molecular dissolved and emulsion water and water settled at the bottom of the system housing, the oil contains water bound to definite groups of hydrocarbons and surface-active impurities. When the oil is heated, water settled at the bottom can be transformed into emulsion or molecular dissolved state; in tum, emulsion water can be transformed into the dissolved state. Emulsion, dissolved, and bound waters cause the electric properties (y and tano) of oil and other hydrocarbons to deteriorate markedly; however, the main contribution to the decrease in the electric strength with increasing moisture content comes from emulsion water. These effects cause Ebr of liquids to increase as the temperature rises to a certain critical value; other factors come into play at higher temperatures, and Ebr decreases with any further increase in the temperature (see Sec. 3.2). Bound water cannot be tested by the conventional methods; in this regard, considerable difficulties arise in measuring the total moisture of oil. Deep drying of oil enables bound water to be removed, thereby significantly improving the oil characteristics. In addition to water, other low-molecular substances (formic, acetic, and

100

Chapter 4 Influence of Contamination and Structural Defects

80 60

"

~ 100 J.ls, Vbr depends only weakly on the shape of the tail of pulses (that is, on the rate of voltage decay). The influence of high-frequency oscillations on Vb" superimposed on the aperiodic pulse component or the dc voltage, is stronger. The increase in the high-frequency component from 0 to 100% reduces Vbr by a factor of 1.5-2 and Vfl by a factor of 2.5-3 . (By the percentage of oscillations we mean the ratio of the rms component of ac voltage to the average value of the dc voltage.) Under the combined influence of different voltage types applied in succession, the earlier voltage significantly affects the electric strength in the presence of the later. The electric strength increases if the polarity of previously applied voltage (pre-stressing) coincides with that of the applied voltage (for which the electric strength is measured). The maximum effect reaches tens of percent and depends primarily on the duration and magnitude of previously applied voltage, the time

5.2 Shape of a Voltage Pulse

119

interval between the previously applied and applied voltages, and the type of voltage for which the electric strength is measured. In general, the voltage-time characteristics of solid dielectrics, for which breakdown occurs in oblique pulse fronts, are analogous to those of liquid dielectrics. Curves illustrating the dependence Ebr = j(t) are undulatory: for t < IOns, Ebr increases sharply as t decreases; for 10 ::;; t::;; 100 ns, Ebr is virtually independent of the pulse width; for t > 1 /-ls, Ebr increases and reaches its maximum at t = 1-10 /-ls. With any further increase in t, Ebr decreases and approaches the long-term electric strength of the examined insulating material. The undulatory voltage-time characteristics are typical of gaps with homogeneous and inhomogeneous fields. The increase in Ubr when t exceeds a certain critical value is associated with the accumulation of a space charge, which attenuates the electric field near the electrode. For solid dielectrics, as for gases and liquids, the critical slope of the voltage pulse front at which Ubr reaches its minimum remains approximately unchanged and independent of the discharge gap length. Thus, gases and liquid and solid dielectrics are characterized by approximately identical behavior of the dependence Ubr = j(t) when breakdown occurs in the oblique pulse front. For each medium there exists an approximately constant critical pulse slope at which Ubr reaches its minimum and the maximum variance in its values is observed. For gases, Acr = 5-8 kV/s, for liquids, Acr = 120160 kV/s, and for solid dielectrics, Acr = 25-35 kV/s. Since two stages of electrical aging-incubation and treeing-differ strongly in their physical nature, it is important to know the influence of the voltage parameters on each of them. This creates essential prerequisites to the objective interpretation of the dependences of the long-term (multipulse) electric strength on the voltage parameters and to their prediction. In [120] it was established that the number of pulses applied to LDPE before the onset of treeing is essentially independent of the pulse shape, polarity, and repetition rate. Tests were carried out with O.3I1.2-J..Ls aperiodic pulses and damped oscillations with a front of 0.3 /-lS, duration at half amplitude of 0.6 /-lS, a damping decrement of 1.33; and pulse repetition rate of 2-50 S-l. The tests were carried out for a tip-plane electrode system with an end radius of the tip electrode of 2·1 0-5 m and the interelectrode gap length in the range (2.5---6)-10-3 m. Analogous results were obtained in [121] during tests of radio-frequency cables with a monolithic polyethylene insulation (type 1) and high-voltage pulsed cables with a monolithic polyethylene insulation (type 2) and with a laminated insulation (type 3). Due to their different design, these cables differ with respect to relative contributions of the incubation and treeing aging stages to the total insulation service lifetime. Thus, for type 2 cables, the number of pulses before treeing ntr is much greater than the number of pulses ng necessary for the dendrite growth and breakdown. Thus, the insulation service lifetime n of type 2 cables is determined by the incubation stage processes. For cables of the two other types, ntr and ng are compara-

120

Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage

'tr· 1 150

150

100

100

b

50 1.11

2.6

J,Z E max ·l

, Vim

02.0

2.It

1.6

J.Z ElIUlx·1

V im

Fig. 5.13. Dependence of treeing length on Emax for oscillating (a) and aperiodic voltage pulses (b) with a pulse repetition rate of 2 (1), IO (2), and 50 pulsesls (3). Empty symbols are for positive polarity, and filled symbols are for negative polarity

ble, and their service lifetime is determined by the sum of ntr and ng• It was found that the insulation service lifetime of type 2 cables is essentially independent of the applied pulse shape and is determined only by the pulse amplitude. For type 1 and type 3 cables, the pulse shape significantly influences the insulation service lifetime. Damped sinusoidal voltage pulses with a frequency of 30 kHz and a damping decrement of 1.35 were used for tests. High-frequency if = 1 MHz) overvoltages of multiplicity kov = 1-2.4 were superimposed on the pulse front. Long-term voltage exposure, in which the polarization, accumulation, and relaxation of the space charge processes are fully developed, changes the parameters of the incubation aging stage. The incubation stage duration and the treeing voltage decrease with increasing rate of the dc voltage rise, because the formation of the space charge, which shields the tip electrode, is impeded. A similar effect is observed for pulses with long rise times. The treeing voltage decreases for both pulse polarities as the slope of the pulse front increases. It can be suggested that the increase in the rate of voltage rise in the region of its very large values, when the effect of the discharge delay starts to manifest itself, will cause the treeing voltage to increase. The parameters of the treeing aging stage are more sensitive to the parameters of the applied voltage. The data shown in Fig. 5.13 demonstrate that for the identical maximum field strengths, the dendrite length for aperiodic pulses is less for negative tip electrode [120]. The difference in the rate of growth of dendrites for positive and negative polarities ranges from a few percent to several hundred percent, depending on the type and state of the polymer and experimental conditions (see Sec. 5.4).

5.2 Shape ofa Voltage Pulse

121

Fast sign changes in the voltage applied to the sample lead to electric field amplification, due to addition of the applied voltage and space charge fields. This significantly increases the rate of growth of treeing. The treeing length increases considerably when we proceed from unipolar pulses to ac or damped oscillating pulses, with all other factors being the same. Thus, the incubation aging stage processes are less sensitive to the parameters of the applied voltage than the processes responsible for the growth of the treeing. This causes the dependence of the insulation service lifetime on the parameters of the applied voltage to differ for systems with different degrees offield inhomogeneity. The service lifetime of composite insulation is especially sensitive to the parameters of the applied voltage. Aging is primarily due to PD. In [101, 123] it was demonstrated that the service lifetime and the working electric field gradients of insulation in high-voltage pulsed capacitors depend on the magnitude and the rate of voltage change from the maximum of one polarity to the maximum of the opposite polarity. For example, capacitors with paper-oil insulation, with a service lifetime of 105-108 discharges, operate at a working insulation field strength Ew = 40--60 kVImm in oscillatory discharge mode, while in aperiodic discharge mode they operate at Ew= 70-100 kV/mm. Capacitors with a service lifetime in the range of 103_105 discharges operate at Ew= 70-100 kV/mm in oscillatory discharge mode, and Ew= 85-120 kV/mm in aperiodic discharge mode. This means that the charging voltage of a capacitor operating in aperiodic discharge mode can be approximately 1.8 times that of a capacitor intended to operate with the same service lifetime in oscillatory discharge mode with a damping decrement of -1.4. In this case, it is also assumed that the insulation of the housing (for capacitors with metal housings) and terminals has the required electric strength. For paperfilm insulation, the service lifetime increases approximately by an order of magnitude when the discharge time (in aperiodic discharge mode) increases from 30 to 300 J.1s. The short-term electric strength of such insulation increases by -20% when the rate of voltage rise slows from 1 to 0.1 kV/s. The electric strength of solid dielectrics depends on the field history, that is, on the preliminary voltage exposure, even stronger than for liquid dielectrics. The increase in Ebr for identical polarities of preliminary applied and applied voltages and the decrease in E br for opposite polarities was revealed for the examined solid dielectrics of small (tens of microns) and large (tens of millimeters) thickness. Quantitatively, this effect depends on the same parameters as indicated above for liquid dielectrics as well as on the properties of solid dielectrics. It is most clearly manifested in materials capable of efficiently trapping charge carriers and accumulating space charge. As an example, Fig. 5.14 shows the dependence of the pulsed breakdown voltage of epoxy resin on the number and amplitude of pulses of preliminary applied voltage ofthe same polarity [122].

122

Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage Ubr5 0"1o

.~------r-------r-----~

tOO

50

120

U, kV

Fig. 5.14. Dependence of 50% breakdown voltage UIJr on amplitude U and the number of pre-

liminary applied voltage pulses for samples prepared from epoxy resin. The electrodes are spheres 8 mm in diameter, the interelectrode gap length is 0.5 mm, and the pulse width is 5 J.1s

5.3 Frequency and Periodicity The influence of the applied voltage frequency on the breakdown characteristics of vacuum insulation becomes appreciable at high frequencies when the specific features of charged particle motion in a high-frequency electric field come into play, including particle hitting the opposite electrode at different voltage phases and returning to their own electrode, secondary emission, etc. A summary [79] of the results of many experimental studies demonstrates that for ac voltages at frequencies up to several hundred hertz, the maximum breakdown voltage only slightly exceeds its dc value (by 10-15%). The main features of the breakdown characteristics in this frequency range, compared to the corresponding characteristics for dc voltages, are: - longer aging of electrodes is required to obtain reasonably high and stable breakdown voltage - the dependence of the breakdown voltage on the interelectrode gap length is more nonlinear than for dc voltages (see Sec. 6.2) - the pressure dependence of the breakdown voltage becomes apparent above 10-3 Pa. Basic peculiarities of the vacuum breakdown mechanism and the breakdown characteristics are expected at frequencies such that the particle transit time between the electrodes becomes at least comparable to the HF-voltage half-period. Estimates performed in [34] showed that electrons in HF fields have had time to acquire considerable amount of energy, and the time they traverse actual interelectrode gaps is less than the voltage period. In addition, low inertia of the field emission process and high inertia of the thermal processes engendered by it should be borne in mind. Therefore, processes involving field emission and the action of electrons at the cathode and anode remain essentially unchanged at frequencies of up to several hundred megahertz compared to the action of ac voltages at the

5.3 Frequency and Periodicity

123

ages at the industrial frequency, dc voltages, and voltage pulses. Significant changes should be expected in processes resulting from the motion of ions and charged microparticles of the electrode material. Even the lightest ions (protons) in HF fields acquire only very low energy, whereas microparticles can be considered fixed. At the same time, the electrostatic energy of charged micro- and macroparticles will be manifested for HF voltages in the same way as for voltages of the other types, if the HF field (rather than a single field period) acts fairly long so that the particles have had time to traverse the gap between the electrodes. The fact that the processes in the stage of disruption of the electric strength of a vacuum gap under applied HF voltage and voltages of the other types differ only slightly leads to a small difference in the breakdown characteristics for the meter wavelengths range. When we proceed to even higher frequencies, a certain increase in the electric strength is observed, and its dependence on the interelectrode gap length weakens. To estimate the electric strength of a vacuum gap EHF when even the lightest ion has had no time to traverse the interelectrode gap (d> 4.85.106 EHF/f2), we can take advantage of the empirical criterion

E~f-l exp(-8.5.106 I ENF)~ 6·105 v 2 1m 2 • In the gigahertz frequency range, experimentally measured electric fields significantly exceed the values calculated according to this criterion. In gases, and in particular in air, a frequency increase beyond the industrial value causes the character of the pre-discharge and discharge processes and the breakdown characteristics to change. Air breakdown under the influence of highfrequency voltages is studied in [124]. Unlike vacuum insulation, gas insulation is characterized by a considerable decrease in the electric strength (to half its initial value) as the frequency increases from the industrial value to 109_10!2 Hz. (The electric strength of gases, by analogy with that of vacuum, differs for dc voltages and ac voltages at a frequency of 50 Hz only negligibly.) Over a wide range of frequencies, the frequency dependence of the electric strength is nonmonotonic and is characterized by six segments (zones) (Fig. 5.15). In a low-frequency zone (zone A), Ubr is essentially independent of the frequency and is Ubr for the voltage at the industrial frequency. In zone B, Ubr decreases with increasingf due to the space charge accumulated in the gap, which changes the initial distribution of the electric field. The space charge at these frequencies amplifies the field near the electrode during the negative voltage half-period and facilitates the ionization and discharge evolution. The position of the right boundary of zone A (!crt) depends on the gas properties, its density, and the interelectrode gap length. For example, when d decreases from 2 to 0.1 cm,/crl will increase from 10 to 1000 kHz. In [124], the relationship of the first critical frequency /cr! to the corresponding gap length der! and the breakdown field strength Ebr is I'

~eqEbr

Jcrl=-d-' 1t crt

124

Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage

r' 2.0

If\. fert

f.5

(,0

Ii

I I I fer I I

A

18:C~1

Ii i i i

E

Z

/,.

I~fcr J

i,

Ii

F

Fig. 5.15. Frequency dependence of Ubr for an air gap 0.4 mm long with a homogeneous field at atmospheric pressure (105 Pa)

where l1eq is the equivalent mobility ratio, which takes into account the processes determining the space charge accumulation. In the frequency range 10-1000 kHz, the equivalent mobility ratio I-leq of gaps with homogeneous and inhomogeneous fields in air at standard atmospheric conditions can be calculated by the empirical formula

l1eq = 2lgfcrl , where !erl is in kilohertz. At frequencies above 20 kHz, the positive space charge influences Ubr only after accumulating over several periods, whereas at frequencies below 20 kHz, the charge produced during the first half-period influences the discharge evolution. The critical frequency!erl decreases as the gas density increases. In zone C, the breakdown voltage is essentially independent of the frequency, because the space charge in the gap ceases to increase due to the eqUilibrium established between the rate of production of new ions and the rate of their annihilation through diffusion. In zone D, the voltage half-period becomes at most comparable to the time in which electrons transverse the gap. Some electrons remain in the gap and take part in ionization processes; as a result, Ubr decreases. In zone E, the number of electrons ceases to increase, because an equilibrium is established between the electron accumulation and their diffusion from the gap. In this frequency range, the breakdown voltage is essentially independent of the frequency. Starting with the third critical frequency!er3 (in zone F), Ubr increases with J, because for such half-period duration, some electrons have had no time to accumulate energy sufficient for ionization. Positions of right boundaries of zones C and E, like!erh depend on the gas properties, its density, and the gap length. Paschen's law breaks down at frequencies above!erh but the U-shaped dependence of the breakdown voltage on the pressure (at d = const) is preserved. For gaps with a sharply inhomogeneous field, the dependence of Ubr on f is stronger and differs from the above patterns for homogeneous and inhomogeneous fields

5.3 Frequency and Periodicity

f20 tOO

-r-K r- t----

60 60

6

20

0.050.1

- -:'\\"\\

i'"-" ~' i'--

y.

M

o

\'

J

/5

0.5 f

125

......

- --f::::-........ l"-

~

5 10

50 100 J, kHz

Fig. 5.16. Frequency dependence of Ub, for air gaps formed by tip-plane electrodes for interelectrode gap lengths of 40 (1), 30 (2), 20 (3), 10 (4), 6 (5), and 4 cm (6)

(Fig. 5.16). By convention, the frequency dependence of Ub, in such gaps can be subdivided into two frequency ranges. The first extends to !erl or slightly higher frequencies, and results from the influence of the frequency on the motion of ions in the gap. The second starts at the second critical frequency!e,2, and results from the influence of the frequency on the motion of electrons. The breakdown characteristics for the first frequency range were studied in most detail in [124], and for the second frequency range they were analyzed in [18, 125]. The influence of the air pressure on Ub, at elevated frequencies can be taken into account by the same method as for the voltage at the industrial frequency (see Sec. 3.1), that is, by introducing the correction coefficients K(8) depending on the relative density 8. For gaps with homogeneous and weakly inhomogeneous fields,

the coefficient K(8) is

K(o)=Eoo I Eo), where E06 is the initial field strength for the relative density 8, and E01 is the same but for 8 = 1. For gaps with a sharply inhomogeneous field, the correction coefficient is

K (8) =

Ubro I Ubr ) •

According to [124], the correction coefficient K(8) for 8 in the range 0.2-1 and gaps with a homogeneous field at p = 20-100 kPa, T = 293 K, and frequencies of 11.5 and 45 kHz can be found from the formula

K(8)=0.1+0.98. At high frequencies and reduced gas pressure, when space charge accumulation in the gap can be neglected, the discharge processes are well described theoretically.

126

Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage

At pressures below 0.1 hPa in the centimeter wavelength range, the resonant theory of gas breakdown holds; for large p and A., the discharge processes are described by the simplest theory of collisional ionization; and, for still larger p and A., the diffusion theory of high-frequency breakdown works well. These theories developed by different authors are systematized in [18]. At frequencies in the range 103-106 Hz, Vbr of gases at moderately low pressures decreases monotonically with increasing frequency. At very low pressures and frequencies of tens of megahertz, the frequency dependence of Vbr is V-shaped. The electric strength of liquid dielectrics at low frequencies (up to several kilohertz) depends weakly on the frequency. Moreover, the effect of the frequency depends on electrical conductivities (both intrinsic and impurity) and permittivities of liquids as well as on the geometry of the discharge gap. When dielectric losses in a liquid, determined by the well-known expression

p_ eftano E2 - 1.8.1012

'

are insufficient to heat the liquid to temperatures of electrothermal (bubble) breakdown, the electric strength of the liquid in a homogeneous field is independent of the frequency or slightly increases with the frequency. In the above formula, P denotes specific losses (the power dissipated in 1 cm3 of the dielectric) in W/cm3;fis the frequency in S-I; tano is the tangent of the loss angle, and E is the electric field in V/cm. The increase in the breakdown field Ebr is typically recorded for moderately pure liquids. The electric strength of commercially pure insulating liquids for the voltage at the industrial frequency is slightly (10-20%) higher than for dc voltages. The frequency dependence of Vbr of gaps with a sharply inhomogeneous field with intense cavity processes typically observed at relatively low electric fields is V-shaped at frequencies of several hundred hertz (Fig. 5.17) [126]. At high frequencies (10 3-106 Hz), the breakdown of even weakly polar liquids results from the intense heat release in the liquid and is characterized by a significant reduction in electric strength with increasing frequency. Thus, for example, the breakdown voltage of a pure transformer oil in the gap with a homogeneous field amounts to 27 kV for d= 5 mm andf= 50 Hz, whereas atf~ 5·105 Hz, it is equal only to 19.5 kV (its maximum values are given). Figure 5.18 shows the character of the frequency dependence of Vbr at high frequencies. The increase in frequency alters a number of laws describing the electric strength of liquids. At high frequencies, the influence of impurities on Ebr of liquids is much weaker than at low frequencies. At positive temperatures, the maximum of Vbr= f(D (see Sec. 3.2) shifts toward higher temperatures with increasing frequency. (This somewhat surprising result can be explained by the detailed behavior of the relaxation minimum of the tangent of the loss angle.) With increasing frequency, the pressure exerts less of an influence on the electric strength of liquids, and likewise the degree of liquid degassing has less of an effect on the pressure dependence of the breakdown voltage.

5.3 Frequency and Periodicity

127

\

5

z 1

SO

\0 \

~

15"0

"'

~

250

/

J50

f, Hz

Fig. 5.17. Frequency dependence of Ubr of perflu orohexane in the gap fonned by tip-plane electrodes for an interelectrode gap length of 1.3 mm

Ubn,. ::k:.. :V_ _ _ _- r_ _ _ _ _-.-_-----, ~r---~--~~----~-r--~ ~r---~~~~--~~~+----1

8r---------+---~~~~~~

4~--------~---=----~~~

OfOS Fig. 5.18. Frequency dependence of Ubr of xylene (1) and transfonner oil (2) in a gap fonned by spherical electrodes for d = I mm

As the repetition rate of microsecond pulses increases from 1 pulse per minute to 30 pulses per second, the electric strengths of a transformer oil and deionized water remain unchanged. Whereas for liquids the frequency dependence of the electric strength is determined mainly by the two processes, including the heating due to dielectric losses and the disruption of phase homogeneity due to the cavitation processes, for solid dielectrics this dependence is completely determined by the heat release process. If the loss factor (the product c;·tan8) in Eq. (5.5) had been independent of the frequency and electric field, in the context of the theory of thermal breakdown of solid dielectrics, their electric strength would have decreased with increasing frequency in proportion to/ l12 at high frequencies. However, the law Ebr-/1/2 actu-

128

Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage Ebl"l

kV/cm

"

'"

fGO f20

60

oG

G.Z

6#

I'"

G.G G.6

...........

i"

7.0 log!

Fig. 5.19. Frequency dependence of Ebr in mica samples with a homogeneous field. The samples were 0.13 mm thick

ally holds, if at all, only over a narrow frequency range. For low frequencies, the electric strength of high-resistance solid dielectrics is essentially independent of the frequency, because breakdown is not thermal, and a minor temperature rise cannot markedly influence the breakdown. As for other dielectric media, transition from dc voltages to the ac voltage at the industrial frequency increases the electric strength by only 10-15%. At high frequencies, the frequency dependence of the loss factor E·tan8 becomes significant. In addition, with increasing frequency, when the temperature of the dielectric significantly exceeds its standard value, E·tan8 depends only slightly on the frequency, and a further temperature rise to the point of thermal breakdown is determined by the active losses. Both of these effects weaken the frequency dependence of the electric strength. As a result, it deviates even more from the theoretically predicted behavior. For low-resistance dielectrics, the key role of the active losses in the initiation of a thermal breakdown spreads toward high frequencies. For polymer dielectrics, the frequency dependence of the electric strength is influenced by changes in their supermolecular structure due to the increasing temperature (see Sec. 3.2). Obviously, in actual practice the frequency dependence of Ebr will differ from the theoretical prediction due to the foregoing effects, and its specific form will depend on the dielectric properties, conditions of heat removal, ambient temperature, etc. Figure 5.19 illustrates the typical frequency dependence of the electric strength of solid inorganic materials, in this case in mica. The influence of the periodic voltage frequency or of the pulse repetition rate on the service lifetime of solid insulation must be known not only to correctly choose working gradients of electric fields in insulation of systems operating in the pulse frequency mode but also to substantiate a choice of modes for accelerated service lifetime tests. Many papers devoted to electrical aging acceleration by the method of frequency increase have been published. In many of them, unlike the previous publi-

5.3 Frequency and Periodicity

129

log (if)

)(-1

o-z .-]

10 8

ctb

I~ ~ he.. ~

G

7.0

,

o-/f

--5 IJ,.-G

zz

"~ , \

~"\..~ ~J lI".I(",~

-

,

"""" "-

"~

7,1f

7.&

7.6

1/.0

I/.Z

I(

logE

Fig. 5.20. Lifetime curves of polystyrene film at 0.05 (1), 0.9 (2), 16 (3), 50 (4), 104 (5), and 240 kHz (6)

cations, the proportionality between aging acceleration and frequency remains unconfirmed. A linear dependence of the service lifetime on the frequency of ac voltages is clearly manifested only for polymer films under conditions of their ionization aging. Over a wide frequency range for E > Eion (the electric field at which ionization begins), the service lifetime of the polymer films is inversely proportional to the frequency, that is, if = const for E = const .

For E < E iom this proportionality breaks down, and the service lifetime increases sharply (Fig. 5.20) [100]. In most cases, at elevated frequencies one fails not only to predict the quantitative parameters of the effects due to the frequency increase but also to detect even the direction of any change in the laws describing ElM aging. This is due to the fact that depending on the ElM type, the field configuration, and the number of external factors, the dominant effect on the change in the aging rate attendant upon frequency variations will make for one frequency-dependent effect or another. This affects the aging differently for different ElM (Sec. 3.2). The treeing pattern, the dynamics of space charge accumulation, and the space charge influence on the field strength and the rate of ElM disruption processes also depend on the voltage frequency [25]. The determination of the frequency dependence of the number of pulses withstood by insulating high-voltage pulsed systems before breakdown faces engineering problems-a test facility must generate voltage pulses at several hundred kilovolts with repetition rates ranging from several pulses per second to thousands of

130

Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage

pulses per second. The source power must be sufficient for simultaneous testing of many samples to obtain statistically representative data. The dependences of the service lifetime on the pulse repetition rate were found in [25, 127] based on extensive studies of statistics offailures of various polymer dielectrics. The requirements on the accelerated insulation tests were also formulated in these papers. These data, complemented by the results of physical experiments, enabled the nature of the frequency dependence to be explained. The tests were carried out with samples prepared from LDPE, fluoroplastic, and epoxy-filling compound. The electrode configuration ensured weakly or sharply inhomogeneous field in the working zone of the sample. Pulsating and aperiodic voltage pulses were used in tests. The pulse repetition rate varied from 0.1 to 103 S-1. The number of pulses withstood before breakdown was satisfactorily described by the Weibull distribution. Based on the parameters of the Weibull distribution, the frequency dependence of the number of pulses withstoond before breakdown was analyzed. Three probabilities of failures were considered: P(n) = 0.1,0.5, and a value in the range 0.7-0.9 (which depended on the truncation length of individual samples). The corresponding characteristics were denoted by no.I. nO.5, and nO.r-nO.9. An analysis of the service lifetime distribution functions and the plots of their dependences on/test showed the following: In the region of primary failures, the effect of the pulse repetition rate on n was not observed. The influence of/on the service lifetime was observed in the subsequent aging stages (for high probability of failure). The dependence had the form shown in Fig. 5.21. For the examined materials, ne increased with/especially quickly at low frequencies. LDPE exhibited the greatest stability under multipulse voltage exposure. The physical pattern of electric aging of monolithic polymer insulation suggested in [28] enabled the nature of the main laws of insulation failures to be explained for different frequency ranges. In particular, it was demonstrated that the increase in the temperature of the dielectric (at least in the region adjacent to the tip electrode) with increasing/increased the mobility of charge carriers and hindered the space charge formation. At high frequencies in the stage of treeing evolution, the influence of the ac voltage frequency was manifested through the specific features of the ionization process in the treeing channel. The discrete character of ionization with time in the gas treeing channel caused successive disruptions of the material near the channel head and ensured the treeing spread toward the opposite electrode. For low pulse repetition frequencies, each pulse causes nearly the same disruption of the material in front of the treeing channel head. The disrupting effect of the subsequent pulse will be independent of the frequency only when the conditions for the disruption evolution completely return to their initial state before voltage application. This primarily implies that the gas pressure in the treeing channel, the space charge, and the temperature of the material near the treeing channel head will decrease to their initial levels. For high/, the system will be unable to return to its initial state between voltage pulses. The increase in

5.3 Frequency and Periodicity

131

nc, pulses

y "

1

-~

0

rr

Z -'

..",- ~

"Y""

3 ",.,

r7

".

>if

)(

tO Z

o

200

'100

f, pulses/s

Fig. 5.21. Dependence on pulse repetition rate of service lifetime for PE (1), fluoroplastic (2), and EZK-7 compound (3) in a weakly inhomogeneous field, with P(n) = 0.632

gas pressure reduces both the ionization intensity and the disruptive effect of a single voltage pulse, and consequently increases the service lifetime of the insulation system. Experiments with a hollow needle used in addition to the conventional tip electrode showed that the rapid release of excess pressure in the treeing channel through the hollow in the needle preserves the high ionization intensity, and hence significantly shortens the insulation service lifetime (by as much as a factor of 100). Since wide-ranging variations in the pulse repetition rate have essentially no effect on the service lifetime of defect insulation, that is, insulation with short service lifetime, rejection efficiency can be improved by testing at elevated frequencies. The complex character of the frequency dependence of the service lifetime (for high failure probabilities) precludes linearly frequency accelerated tests of insulation systems to estimate their service lifetimetime. The frequency acceleration method should be used to obtain quality series of different materials or to assess insulation systems of the same types based on long-term stability with fields applied. When the engineering factors enable one to change modes of operation of a high-voltage facility, it is desirable to adjust them with allowance for the dependence of the rate of ElM aging on the mode of high-voltage loading. The concept of relative duration of loading TrJ can be introduced by analogy with [128]. The aging period can be represented as T=

tload

+ t res! ,

132

Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage

where fload is the period of loading and fres! is the period of rest. The system state after n aging cycles can be represented as a sum of effects from individual Tr.l: n

n

v=!

v=!

A" = L r..~1 = L t10adv 1Tv

.

The aging accelerates when the rest period shortens, the number of loading cycles increases, and the pulse width increases. Generally speaking, aging is an irreversible process, but in some particular modes for some individual cycles depending on Tr.l it can be considered partially reversible. Unfortunately, these cycles are a priori unknown in practice and must be found experimentally. In [128], an LDPE film 30 J..Ull thick in a sphere (d = 20 mm)-plane electrode system was subjected to aging tests in xylene exposed to various numbers of 1/50 and 570/3000 J.1s pulses with different rest periods. The amplitude of test pulses Utes! was 0.8 or 0.9 Uhr of the film with no preliminary exposure voltage pulses. It was found that the short-term electric strength of the LDPE film recovered after a certain rest period. Long pulses accelerated its aging. After loading of the dielectric by long pulses, it recovers its properties for a longer period (250 min against 30 min for loading with short pulses), but the recovery is incomplete. When the initial aging states are largely determined by the space charge accumulation processes and field redistribution in the dielectric due to these processes rather than chemical degradation of the dielectric, the influence of voltage periodicity differs from the behavior described above. The service lifetime of certain ElM decreases as the applied voltage pulse separation increases. This can be explained by the fact that as the treeing channel grows, its walls acquire an excess charge whose sign coincides with that of the initiating electrode. The field of this charge reduces the electric field in the channel and impedes PD development, which causes channel growth toward the opposite electrode. The space charge decreases in the period during which the external field does not act, thereby recovering the PD intensity and the rate of treeing growth [25].

5.4 Voltage Polarity A common feature of different vacuum breakdown models is the dominant role of electron emission from the cathode in breakdown initiation under the overwhelming majority of experimental conditions [42,66, 129]. A consequence of this mechanism of vacuum breakdown initiation is the least value of the breakdown voltage for a vacuum gap with a sharply inhomogeneous field, when the electrode with a larger surface curvature is the cathode (Fig. 5.22) [130]. The fact that the difference between the breakdown voltages of +T -P and - T +P gaps increases with the interelectrode gap length when the electrode dimensions remain unchanged has engaged our attention. (The difference between the breakdown voltages for positive and negative electrode polarities is referred to as the polarity effect.) For d = 4 em, the difference between the values of Ubr reaches a factor of 5.

5.4 Voltage Polarity

133

Ubn kV

r----,-----,-----,----~

12 00 t----;~t_----____!.!;.L---_+----___I

BOO 'fOOI-'-----+-------+--- T·-=-~----_i

o

8

12

d, cm

Fig. 5. 22. Dependence of pulsed Vb, on the length of tip (anode}-plane (cathode) (1), plane-plane (2), and tip (cathode}-plane (anode) vacuum gaps (3) for copper electrodes and 't p = I I!S

The polarity effect becomes less appreciable when the electrode surface curvature decreases while the interelectrode gap length remains unchanged (Fig. 5.23). It should be noted that Fig. 5.23 shows a somewhat distorted pattern of the polarity effect. This is due to the fact that the electrode polarity in the experiment was changed by a physical flip-flop of the electrode system rather than by changing the polarity of the applied voltage pulse. Because the chamber walls serve as grounded electrodes and terminate some fraction of the electric field lines, the field strength at the grounded electrode will be lower than at the ungrounded one. This is taken into account when electrode system configurations and test chambers are chosen, or in air when the dimensions of high-voltage laboratories and location of test fields in them are chosen. In addition, this effect is taken into account in the lEe recommendations for high-voltage measurements by spark gaps. In gaps formed by coaxial cylinders, the reversed polarity changes not only the absolute value of the breakdown voltage but also the character of the dependence of Vb, on the geometry of the discharge gap, in particular, on the ratio of the outer and inner electrode radii Rand r (Fig. 5.24) [130]. From Fig. 5.24 it follows that for positive polarity of the center electrode, the dependence Vb, = j(Rlr) increases and then saturates at Rlr > 7.5-8.0. For negative polarity, Vb, decreases and then saturates with increasing Rlr for Rlr > 2.7. The behavior of curve 1 can be explained by the increase in the interelectrode gap length and of the degree of field inhomogeneity. The character of curve 2 corresponds to the change in the maximum field strength in the coaxial gap accompanying the change in its geometry:

V Emax = rln ( R Ir) .

(5.6)

l34

Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage Ubr>

kV,:-_ _--r-_ _---,--:-_ _"'"T"""_ _----,

fZOO I------,,.......,'r+-~-

600~~~~~~-----+-----;

o

8

12

d, em

Fig. 5.23. Dependence of Ubr on the interelectrode gap length for electrodes of different configurations. The numbers adjacent to sketches of the electrodes denote the diameter of the spherical electrode, in cm

200~--~--~~~~----r----;

o

2.5

7.5

IZ.5

17.5

Rfr

Fig. 5.24. Dependence of pulsed Ubr of the coaxial vacuum gap formed by steel electrodes with R = 6.10-2 m on the ratio of the electrode radii for positive (1) and negative (2) polarities of the center electrode under conditions of technical vacuum at p = 1.3.10-3 Pa

According to Eq. (5.6), the field strength at the surface of the center electrode is minimized when Rlr = e. The largest value of Ubr corresponds to minimum electric field. Similar behavior is observed for breakdown initiated in gases, liquids, and solid and hybrid dielectrics under conditions of the minimum field distortion in the gap by pre-discharge processes (primarily, by SC accumulation; see Sec. 6.1).

5.4 Voltage Polarity

135

The polarity effect for vacuum breakdown is essentially independent of the shape and duration of the applied voltage. The state of the electrodes, in particular their temperature, has a stronger effect. As follows from the data tabulated below [131], the effect of polarity is close to 3 for a dc voltage at standard temperature of the electrodes. When the temperature of the tip electrode decreases to 83 K, the breakdown voltage for positive and negative polarities and their ratio remain unchanged. Cooling the planar anode increases Ubf by more than a factor of 1.5, while cooling the planar cathode leaves Ubf unchanged. Thus, the polarity effect decreases to 1.75. Anode temperature [K] Cathode temperature [K] Ubd kV]

one, 300 73

one, 3

78

Cone, 300

120

Cone, 300 Di k,300

207

Cone, 300 Di k,83

210

The experimental conditions in [131] were the following. Copper electrodes were disks 100 mm in diameter with a rounded edge and a cone with a vertex angIe of 48° and a vertex radius of 0.2-1 mm. The electrode gap length was 6 mm, and the residual gas pressure was ~1O--6 Pa. When breakdown is initiated in gases, liquids, or solid dielectrics, Ubf in gaps with a nonuniform asymmetric electric field also depends on the polarity of the electrode that determines field inhomogeneity. However, the effect of polarity is the opposite of that observed for breakdown initiated in vacuum gaps, that is, Ubf for positive polarity of the electrode with a larger surface curvature is lower than for negative polarity. For the vacuum breakdown, electron emission from the cathode is the main factor in the polarity effect. However, the particulars in gases, liquids, and solid dielectrics differ from those in vacuum. In gases, the polarity effect results from the much greater mobility of electrons than positive ions, and by the fairly long lifetime of electrons in the free state. The physical nature of the polarity effect in gas breakdown is described in detail in many monographs devoted to gas breakdown, and in university textbooks devoted to high-voltage engineering. Quantitatively, the polarity effect depends on the factors that influence the SC accumulation in the interelectrode gap, including the gas composition and density, the parameters of applied voltage, and the geometry of the discharge gap. The influence of these factors can be so strong that for some combinations of experimental conditions, the polarity effect can inversely affect the breakdown voltage, that is, r > Ubr . The data on the effect of polarity on the breakdown of all the dielectric media under different experimental conditions can be extracted from illustrations in other paragraphs of Chapt. 2 of this book. This section presents only the results that are most interesting from the practical viewpoint. For example, it is important to bear in mind that the breakdown voltage of air gaps whose length ranges from tens of centimeters to meters depends only weakly on the pulse polarity for lightning-type pulses (1.2/50 ~s). Under exposure to long

U:

136

Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage

I

ZOO 160

-

f20

f

2

80 'HJ

Ubr for r = ,

'-1~-

o10- 1

J

7 f

00

~ V_ -

~

...... 7ubr for r '=

I 00

r-..: ~/+r

~ ~'

fO

r

I

mm

Fig. 5.25. Dependence of 50% Ubr of SF6 gas (1 and 2) and air (3 and 4) at atmospheric pressure on the radius of curvature of the electrode for negative (1 and 3) and positive (2 and 4) voltage polarities

pulses (commutation pulses, for example) and dc voltages, Ubr is much higher for negative polarity than positive. The polarity effect is reversed in mixtures of SF6 gas with other gases for nanosecond voltage exposures (see Sec. 5.1), when the degree of field inhomogeneity decreases to a certain critical value (Fig. 5.25) [31]. In the gap of length d = 20 mm formed by a plane and an electrode with a variable vertex radius of curvature r, the polarity effect for a lightning pulse is inverted in SF6 gas at r = 6.5 mm [(d + r)/r = 4.1] and in air at r = 10 mm [(d + r)/r = 3]. The breakdown voltage for positive polarity depends more strongly on the geometry of the electrodes than Ubr for negative polarity. In [31] it was pointed out that for weakly inhomogeneous fields [(d + r)/r::::: 2], for which Ubr increases monotonically with p (without anomalies indicated in Sec. 3.1), the increase in the pulsed breakdown voltage for negative polarity in SF6 gas slows down for p ~ 4.105 Pa. In air, this effect is observed for p ~ 5.10 5 Pa and positive voltage polarity. The pulse width ratio in these cases slightly exceeds unity. In most studies, for breakdown in liquid and solid dielectrics by a dc voltage and moderately short voltage pulses, the polarity effect was also associated with the SC accumulation by mechanism close to that for gases outlined above. The main specific features of SC accumulation are a much lower charge-carrier mobility in condensed media and a short lifetime of free electrons. Electrons emitted by the cathode are either captured by molecules of the liquid or by traps (in solid dielectrics) and form a negative SC having low mobility. In addition, intense emission of positive charge carriers from the anode (emission of holes or the extraction of electrons) is observed in condensed media. In [132], the distribution of prebreakdown fields in nitrobenzene was investigated upon microsecond voltage exposure based on the Kerr effect. Emission of charge carriers from the tip electrode of both polarities was detected. For negative tip polarity and E ~ 6.105 V/cm, SC uniformly covering the tip surface was detected. Its density preached

5.4 Voltage Polarity

137

Table 5.3. Effect of polarity on breakdown initiated in various liquids for a tip-plane electrode system at T= 293 K Liquid

Voltage

Toluene n-oetane hlorobenzene arbon tetrachloride Tran former oil

0.9/401-15 0 .9/4O l-ls 0.9/40 p 0.9/401-15 1.5/40 l-ls, dc vo ltage 1.5/401-1 , de vo l ta~e

Dodecylbenzene

egalive polarity d[mm] Vbr [kV] 3 42.3 3 49.8 3 27.3 3 2 1.8 12.7 86 9.6 100 12.7 175 9.6 110

Positive po larity d [111 111 ] V br [kV] 3 21.8 3 18.4 3 25.5 3 21 25.4 60 9.6 42 25.4 122 9.6 62

7·10-4 C/cm 3 for Eo= 1.2.106 V/cm. This halved the field near the tip, whereas the electric field maximum Emax shifted deeper into the discharge gap. The SC boundary moved with a velocity of (2-4)-10 3 crn/s. Emission from the anode was pointlike. The threshold emission electric field was 106 V/cm. Apart from field distortion, charge-carrier emission in the liquid can be accompanied by cavitation or gas-vapor bubbles, hydrodynamic perturbations, etc. [133, 134]. For nanosecond pulses in trichlordiphenyl in a quasi-homogeneous field of strength E = 0.83 MV/cm [135] and in water at E = 1.2 MV/cm [136], the initial (electrostatic) field was not distorted until discharge initiation. Since pre-breakdown phenomena, their intensities, and even their sequence can change significantly when breakdown conditions change, the quantitative polarity effect will also depend on these conditions, and can reverse sense for certain combinations of these phenomena. In particular, the breakdown voltage of micronlength point-plane gaps at a negative polarity point is greater than at a positive one. The critical length at which the polarity effect changes is smaller in liquids with the highest electron mobility. In most cases, the breakdown voltage for positive tip-electrode polarity is lower than for negative polarity. This difference ranges from several percent to several hundred percent, and depends on the same factors as for gas breakdown. However, the properties of liquids have a more prominent effect on the difference between U:r and U br . As indicated in Sec. 3.3, the polarity effect is much more evident in liquids with high permittivity. For breakdown initiated in liquids containing electronegative groups or molecules (for example, carbon tetrachloride, benzene chloride, etc.), the polarity effect is essentially nonexistent. This suggests that electrons injected from the cathode are captured by electronegative compounds and transformed into negative ions possessing the same mobility as positive ions in these liquids. SC field distortion and its effect on the discharge processes and the breakdown voltage become independent of the tip-electrode polarity. The results demonstrating the effect of polarity on the breakdown of various liquids are tabulated in Table 5.3 . The addition of chlorinated hydrocarbons (the molecules of which possess considerable electron

138

Chapter 5 Dependence of Electric Strength on the Parameters of Applied Voltage

U,kV

60

IiU

~

I"-- ~

40

"

~ /: ..... '( r--...... Jo

-

.U-

20

2

2

~ tU"a, VI

Fig. 5.26. Initiation voltage of for positive (1) and negative (2) treeing in PE as a function ofthe rate of voltage rise for a tip-plane electrode system (ro = 5 f.lm) with d = 5 mm

affinity) to transfonner oil, whose breakdown is accompanied by a sizable polarity effect (Table 5.3), eliminates the polarity effect almost completely. In this case, Ub, remains unchanged for positive polarity, whereas Ub, decreases when the tip polarity is negative. The polarity effect in liquid dielectrics depends on the degree of electric field inhomogeneity. For example, for transfonner oil in highly inhomogeneous fields with inhomogeneity coefficient Jl > 25-30, the pulsed breakdown voltage for negative polarity is 1.4-1.7 times Ub, for positive polarity, while for K < 16 U:, it can even slightly exceed U b, . In condensed gases, the polarity effect is the same as in conventional liquids; liquid helium, however, exhibits the opposite polarity effect under all experimental conditions. In [75] and many other studies, the nature of the polarity effect in breakdown of solid dielectrics is associated with the streamer breakdown mechanism for solid dielectrics, similar to the streamer discharge in gases. Subsequently, in [137, 138] the polarity effect for breakdown of solid dielectrics was explained by invoking the electron-hole mechanism of electrical conductivity in solid dielectrics in strong electric fields, and nonequilibrium thennodynamics. Despite significant differences between these physical concepts, they predict the same polarity effect-higher breakdown voltages Ub, for negative tip polarity electrode than for positive polarity. This is confinned by numerous experimental data obtained over a wide range of breakdown conditions. The interelectrode gap length varied from some tens or hundreds of microns to several centimeters, the voltage duration varied from several nanoseconds to dc, and the temperature varied from cryogenic to thousands of degrees (in ceramics). The polarity effect in two limiting cases of applied voltage, namely breakdown with nanosecond time delay and speciment failures resulting from electrical aging, can be judged from Figs. 5.8, 5.26 [139],

5.4 Voltage Polarity

139

n, pulses

2

J

5

d 103, m

Fig. 5.27. Number of pulses n withstood before breakdown as a function of d for LDPE with various supermolecular structures: amorphous (1 and 5), small spherulite (2 and 4), and large spherulite (3 and 6) for pulses of positive (1-3) and negative (4- 6) polarities, U = 15 kV, andf= 2 S- l

and 5.27 [25]. These results demonstrate that ignition and breakdown voltages are lower in solid dielectrics, as in liquid, and the breakdown channel evolves faster for positive tip polarity electrode than for negative polarity. In rare instances, the sense of the polarity effect in solid dielectrics is reversed.

Chapter 6 Influence of Insulation Gap Geometry on Electric Strength

6.1 Field Configuration in an Insulation Gap Gases, liquids, and solid and hybrid dielectrics in gaps with homogeneous electric fields have the highest breakdown voltages. The breakdown voltage decreases with increasing field inhomogeneity. Insulation gaps with a sharply inhomogeneous asymmetric field, such as tip-plane electrode gap, have the lowest breakdown voltages. As indicated in Sec. 5.4, the vacuum, unlike other dielectric media, has the maximum electric strength for inhomogeneous asymmetric fields rather than homogeneous fields, when the positive electrode surface has the smaller radius of curvature. Analogous gaps with negative polarity exhibit the least strength. The decrease in the radius of curvature of the electrode determining the field inhomogeneity in the first case increases, and in the second case reduces the breakdown voltage, with all other parameters remaining unchanged. A change in the cathode configuration, especially its surface curvature, significantly affects electron emission, because the field strength at the cathode and the number of emission centers change. As a result, the dependence of the breakdown voltage of a vacuum gap on cathode geometry becomes dominant. Since processes at the anode also take part in the initiation of a vacuum breakdown, the geometry of the anode influences the breakdown voltage of the vacuum gap. For a system of coaxial cylinders with a negative center electrode, the dependence Ubr = .f{Rlr) is depicted by a curve with a maximum at Rlr = 2.7, that is, when the ratio of the radii ensures the minimum field strength in the gap (see Fig. 5.25). For positive polarity, the decrease in r at fixed R is accompanied by a monotonic increase in Ubr' The radius r in [130] was varied from 0.25 to 5 cm for a fixed outer electrode radius of 6 cm. When the ratio of the radii remains fixed at approximately 2.7 while the overall dimensions of the electrode system increase, Ubr will also increase almost linearly for either polarity of the center electrode (Fig. 6.1). When the coaxial gap length increases by a factor of six, the electric field at the center electrode surface corresponding to the breakdown voltage will vary only slightly, ranging from 183 to 203 kV/cm. For ac voltage (50 Hz) and much shorter gaps, we can rely on the data [140] in Fig. 6.2 to assess the effect of

Chapter 6 Influence ofInsulation Gap Geometry on Electric Strength

142

'toot---+--+-~~f-7'I"t---i

o~~--~--~--~--~

J

10

15

20 r, mm

Fig. 6.1. Dependence of Vbr on r for coaxial vacuum gap with R/r = 2.7, and positive (1) and negative (2) polarities of the center electrode

electrode geometry on field inhomogeneity, as well as the effect of field inhomogeneity on breakdown voltage. As follows from this figure, the difference between the curves Ubr=j(d) for small (r= 1 mm) and large (r= 19mm) hemispherical end radii of the rod electrode is significant. At small rand d> 2 mm, the positive slope of Ubr decreases abruptly. This causes curves 1 and 2 to intersect at r = 1 and 19 mm. It was found that for r = 1 mm and d> 1 mm, breakdown always occurs during the negative voltage half-period, whereas for r = 19 mm, this effect is observed for d> 10 mm. For smaller d, breakdown is equally probable during both positive and negative voltage half-periods. Calculations of the macroscopic field strength

E::;

(on the basis of the macrogeometry of the electrode sys-

tem), and of the local field E~r with allowance for hemisphere surface inhomogeneities, demonstrated that for r = 19, 1, and 0.02 mm,

E!;

increases with

decreasing r, and E~r remains virtually unchanged. The breakdown voltage and the breakdown field strength of vacuum gaps for the indicated hemispherical electrode radii are tabulated below. r

[mm]

19 0.02

Vbr [kV)

E{; [k Y/cm]

!l

E~r kV/cm)

112 71 41

1.7. 10 2

620 170 30

1.05·10' 1.1 0·10' 1.62·10'

6.7. 10 2 54. 10 2

The electric field gain Il was calculated based on the Fowler-Nordgame curves. The results confirm the crucial importance of the idea that vacuum breakdown occurs when the local field near cathode surface microinhomogeneities reaches its critical value, independent of the electrode configuration and discharge gap length. The latter two parameters influence the electric field gain, and thereby the macroscopic breakdown field strength and voltage.

6.1 Field Configuration in an Insulation Gap

o

to

143

IS d, mm

Fig. 6.2. Dependence of Ubr (50 Hz) on interelectrode gap length for a vacuum gap fonned by a rod electrode with a hemispheric end and a plane electrode fabricated from electrolytic copper, with hemisphere radius r = I (1) and 19 mm (2). Measurements made in vacuum at p= I mPa

A change in field inhomogeneity, or more precisely, a transition from homogeneous and weakly inhomogeneous fields to highly inhomogeneous fields in gases is accompanied by radical changes in the discharge mechanism. In the first case (~ < 2), a spark breakdown occurs without preliminary corona discharge when the condition of a self-sustained discharge is realized. For pulsed voltage exposure, streamers of the initial spark (the primary corona) traverse the entire gap in a short time. The greatest portion of the streamer charge is carried to the opposite electrode, the field near the electrode with the larger radius of curvature remains essentially unchanged, and a spark breakdown (a streamer or a leader) [141] occurs in the gap. Moreover, the initial voltage Uo coincides with the breakdown voltage Ub" and the Townsend theory can be used to estimate the electric strength, even though the breakdown mechanism for such gaps at normal and elevated pressures is streamer or leader rather than avalanche (for long interelectrode gaps). This approach is applicable to air, SF6 gas, and gas mixtures containing SF6 gas. Bazelyan and Rozhanskii [141] suggested that the contact of streamers with the opposite electrode does not necessary lead to the formation of a leader, because the excess charge in nitrogen is uniformly distributed across the streamers of the primary corona. In this case, the initial and breakdown voltages differ. In the second case (~ 2! 4), spark breakdown is preceded by a corona discharge, whose effect on the breakdown voltage becomes more prominent as ~ increases. In this case, the initial voltage Uo is much lower than the breakdown voltage (Fig. 6.3) [124]. The dash~ot curve in Fig. 6.3 shows the maximum electrostatic field strength at the wire surface in kVlcm, calculated with the Pieck formula

144

Chapter 6 Influence of Insulation Gap Geometry on Electric Strength

Eo, kV/cm

'. 60

\

,\

20 1/

/

,,

/

, ,

', ...... ~

K~

k

12

,

10 G5 If

J.O

--

~

2.5

-

Eo

fG 2.0

r---

-=- 50

--JO

20

2ro mm

20

f.8

Fig. 6.3. Dependence on the wire diameter 2ro and field inhomogeneity IJ of breakdown (1) and initial (2) voltages in an air gap 3 cm long comprising a wire electrode and a plane electrode under standard atmospheric conditions (voltage at the mains frequency)

where ro is the wire radius in cm, and 8 is the relative air density. The initial voltage was d

Uo =Eo-· Il

The boundary of the region of highly inhomogeneous fields in Fig. 6.3 is at the point where the curves Ubr(ll) and Uo(ll) start to diverge. The region of highly inhomogeneous fields is usually subdivided into two subregions. In the first (from the interface between the homogeneous and highly inhomogeneous fields to the minimum of Ubr in Fig. 6.3), the corona discharge preceding the spark breakdown develops as a streamer. In the second (to the left of the minimum of Ubr in Fig. 6.3), the corona discharge develops as an avalanche. In [124], based on the available experimental data, generalized dependences were suggested for calculating the breakdown voltages of wire-plane and coaxial cylinder gaps for Il typical of a streamer corona discharge. Initial voltages in this case are calculated using the same relations as for homogeneous fields. At very large fl, deep SC penetration due to avalanche corona discharge increases Ubr with decreasing ro (increasing fl). The random character of a streamer channel at an electrode surrounded by an avalanche corona discharge leads to a wide spread in Ubr' The spread is especially large for dc voltages, low frequencies, and carefully polished electrodes. For SF6 gas and gas mixtures containing SF6 gas, the minimum of the dependence Ubr = j(ro) is more apparent due to their stronger electronegative properties, which influence SC formation. Generally, lar-

6.1 Field Configuration in an Insulation Gap

145

ger differences between the breakdown voltages of gaps with homogeneous and inhomogeneous fields are typical of electronegative gases. For long (meter) air gaps, the electrode shape influences only weakly the breakdown voltage, because the initial (electrostatic) field is distorted by the SC field which penetrates the near-electrode region with the corona discharge. A criterion for estimating the minimum critical anode radius rer for which the minimum electric strength of an air insulation system does not depend on the anode radius was determined in [141] by analyzing mechanisms in all stages of discharge evolution for long air gaps between a positive rod and negative plane electrodes. When interelectrode gaps exceed a certain critical value den which for a given gas and the applied voltage shape depends on the radius of the electrode with the larger surface curvature, Ubr for asymmetric gaps (sphere-plane and cylinder-plane electrodes, etc.) is close to Ubr for tip-plane gaps. As demonstrated in [18], the ratios rider are approximately equal for spheres of differing radii r. For 2r=25 and 75cm, this ratio is 0.15, whereas for 2r=50cm, it is 0.14. The maximum electric field (at the spherical electrode surface) at which breakdown of gaps formed by spherical electrodes of different diameters occurs decreases with increasing electrode diameter. When the diameter increases from 25 to 50 cm, EID1lX decreases by a factor of 1.08. This means that for gaps with an inhomogeneous field, breakdown in gases, as in liquid and solid dielectrics, is determined by the electric field applied over a certain volume of the interelectrode gap, rather than by the maximum field strength at any point or set of points on the electrode surface. A higher degree of field inhomogeneity due to the reduced electrode radius of curvature ro does not lead to an unbounded decrease in Ubr. When ro reaches a certain minimum value, no breakdown occurs near the electrode for the given electric field Eo, because Eo must span a certain volume of the dielectric to initiate breakdown. If this volume is small, a voltage higher than that calculated for the given Eo near the electrode with small ro is required to initiate a dielectric breakdown. Repeated attempts have been undertaken to develop methods for recalculating the breakdown characteristics obtained experimentally for electrode systems with the given geometry of the electrodes for pulses with critical fronts (see Sec. 5.1) for other electrode system configurations and pulses of arbitrary shapes. To this end, for example, the geometrical factor-the ratio of the 50% breakdown voltage for a gap with the given geometry to UbrSOOIo of the rod-plane gap--was introduced. The results obtained for pulses with the critical factor are then used to calculate Ubr for pulses with other parameters. As was clearly demonstrated in [141], this procedure of determining Ubr introduces gross errors, at least for anode radii less than rer. As indicated in Sec. 3.5, stronger dependence ofthe electric strength on microand macro inhomogeneities of the electrodes is more typical of liquids than gases, because in the evolution of liquid breakdowns, there is no discharge stage analogous to the streamer or avalanche-type corona discharge in gases that is capable of rapidly carrying the space charge into the gap, thereby transforming the initial field near the electrode with the larger surface curvature [61]. In addition, because

146

Chapter 6 Influence of Insulation Gap Geometry on Electric Strength

of the high density of liquids, local fields near electrode microinhomogeneities affect small volumes and can initiate a discharge. However, to cause the discharge channel to propagate toward the opposite electrode and initiate breakdown of the insulation gap, the critical field strength must appear in a certain volume of the interelectrode gap. As in other dielectric media, a decrease in the electrode radius of curvature reduces the breakdown voltage, and the breakdown field strength near this same electrode, which corresponds to the breakdown voltage, increases. For example, for transformer oil and applied dc, the breakdown field strength at spherical electrode surfaces (a sphere-sphere gap) with radii of 50, 3.5, and 0.5 mm is 250, 260, and 310 kV/cm, respectively [18]. When the electrode radius of curvature is much less than the interelectrode gap length, Ubr depends only weakly on roo The pulsed breakdown voltage of insulation gaps with d = 1-10 cm, filled with the transformer oil, varies by some tens of percent (but no more than 3~0%) when ro varies over two to three orders of magnitude. The breakdown voltage of tip-plane gaps depends not only on the tip end radius of the electrode but also on the rake angle a. (For this reason, a correct comparison of the experimental data for Ubr ofT-P gaps calls for complete data on the geometry of the electrodes.) Since the maximum field strength for such a gap decreases with increasing a (when other parameters remain unchanged) according to the expression U cosa Emax = d sin 2 aln(cot(a/2))'

we expect that Ubr will increase with a. In most cases this conclusion has been confirmed experimentally. However, some data are indicative of a more complex dependence of Ubr on a. For insulation gaps between the coaxial electrodes that are important in practice, the dependence of the breakdown voltage of liquid dielectrics on inner electrode diameter (given that the outer electrode diameter remains unchanged) is depicted by a curve with a maximum (Fig. 6.4) analogous to curve 2 in Fig. 5.25 obtained for the vacuum gap. However, unlike the vacuum gap, the maximum of Ubr for transformer oil and ac voltage is observed at Rlr = 5 rather than Rlr = 2.7. For microsecond voltage pulses, the maximum is observed at Rlr = 3.5-4. One important feature of liquid breakdown in a highly inhomogeneous field is the less prominent influence of humidity, pressure, and temperature on Ubr with increasing field inhomogeneity. As a result, no correlation of the breakdown characteristics in transformer oils, for example, was observed between a homogeneous or slightly inhomogeneous field and a highly inhomogeneous field. For macrohomogeneous solid dielectrics, the influence of the field configuration on breakdown voltage is approximately the same as for liquids when breakdown is initiated by voltage pulses, and the motion of the liquid in the electric field does not influence Ubr • For macroinhomogeneous dielectrics (porous, laminated, or fibrous with large supermolecular structure), these dependences are somewhat different, because their breakdown voltage depends not only on elec-

6.1 Field Configuration in an Insulation Gap

100 80

147

./ ~

1

"' \

GO

20

\

'10

\\ 50

I

"

r, mm

Fig. 6.4. Dependence on center electrode radius of Ubr in transfonner oil for an electrode system comprising coaxial cylinders with an outer-cylinder radius of 100 mm and ac voltage at 50 Hz

Table 6.1. Breakdown voltages of glass-plastic samples for the indicated electrode geometry Radius of curvature [mm] 2.5 2.5

0.1 0.04

A verage breakdown voltage [k V] 53 ± 8.5 53 ± 8.5 55.8 ± 5.6 56.2 ± 7.6

trode geometry but also on their location relative to macroscopic structures. For example, it follows from the data in Table 6.1 [142] that the pulsed breakdown voltage increases with the end radius of curvature of the tip electrode (the thickness of the breakdown layer was 10 mm, and a positive pulse of 0.1 IlS duration had oblique fronts) . For homogeneous dielectrics, this dependence is analogous to that for other dielectrics: Ubr increases with the electrode radius of curvature. Under long-term or multipulse voltage exposure, the two components of the insulation service lifetime, namely, the incubation stage duration and the time of treeing through the insulation thickness, depend differently on the initial electrostatic field configuration. The first component is very sensitive to the local field strength near the initiating electrode and responds only weakly to changes in the average electric field in the interelectrode gap. In contrast, the second component depends only weakly on local field strength. It depends strongly on the average field strength. Both local and average field strengths change as the insulation ages (given that the potential difference remains unchanged). The local field strength changes due to SC accumulation and treeing channel propagation. The change in the field configuration during electrical aging makes the prediction of the depen-

148

Chapter 6 Influence oflnsulation Gap Geometry on Electric Strength

n, pulses

1

~ L

6

5:.. . .

--

'+* - ........ ...... --...........

1~ I--

-t

o

--- ----~ ' ...... r - - - - -

r_-~

x

-

:;..

~--~

--:;:::::-~

V

*

;'

'"- f--- L...-A

':;'"/fill" __

-

....

~

~

7"

/"

I 10

20

JO

Fig. 6.5. Dependence of number of pulses withstood before breakdown at the end radius of the tip electrode for LDPE with amorphous (1 and 5), small-spherulite (2 and 4), and largespherulite (3 and 6) supermolecular structures, positive (1-3) and negative polarities of voltage pulses (4-6), U= 15 kV,f= 2 S- I, and d= 2.5 mm

dence of insulation service lifetime on the geometry of insulation difficult and calls for experimental investigations of the insulation service lifetime for electrode systems with differing configurations. When the interelectrode gap length and the potential difference remain unchanged, the decrease in the end radius of the tip electrode significantly curtails the incubation stage of aging, but influences the treeing channel propagation only slightly. On the whole, this shortens the insulation service lifetime. The decrease in ro from 60 to 5 /lm reduces Emax approximately by an order of magnitude and only slightly reduces the LDPE service lifetime for an interelectrode gap length of 2.5 mm (Fig. 6.5). From the figure it can be seen that the dependence n = j{ro) has a minimum at ro - 20 /lm. The decrease in the interelectrode gap length from 6 to 1 mm increases Emax only slightly (from 210 to 280 kV/mm) for ro= 20 Jlffi, but reduces the service lifetime by about three orders of magnitude due to the significant increase in E.v. The left rising branch of the curves n = j{ro) can be explained by the fact that many treeing channels start to propagate simultaneously from the tip electrode for large Emax (small ro). They tend to bunch, and further development is delayed by mutual shielding of numerous channels [25]. The fact that in Fig. 6.5 the effect of polarity has reversed has engaged our attention. We suggest that this phenomenon is due to the fact that the effect of tip--cathode shielding by the space charge field produced by injected electrons becomes less prominent with increasing ro (decreasing Em.x). In the electrode system comprising coaxial cylinders, the service lifetime, like Ubr of all dielectric media, depends strongly on the ratio of the diameters of the

6.1 Field Configuration in an Insulation Gap

/f / 2

A

\\ 'K

149

~

\

\2

I

3

~

S

R/r

Fig. 6.6. Dependence of number of pulses withstood by LDPE before breakdown on Rlr for variable inner (1) and outer (2) electrode radii and chopped pulses of positive polarity with 'efr = 0.25 )ls and a damping decrement of 1.8

inner and outer cylinders. The maximum service lifetime of polyethylene insulation is reached at Rlr = 2.73-5.47. Figure 6.6 shows the results of experimental testing of the service lifetime of LDPE samples after exposure to many voltage pulses, for two experiments in which 1) the diameter of the inner electrode was varied (2R = const and U = const) and 2) the diameter of the outer electrode was varied (2r = const and Emax = const). In the first experiment, the maximum service lifetime was recorded for Rlr = 2.73-3.27 (curve 1). In the second experiment, when the field strength near the outer electrode surface (Emax) remains unchanged, the service lifetime is also depicted by the curve with a maximum. Analogous results were obtained when the average field strength in the interelectrode gap remained unchanged [143]. These results demonstrate that the electric field for coaxial electrode systems does not unambiguously determine the optimal ratio Rlr from the standpoint of service lifetime. An analysis of the dependence on Rlr of the Wei bull distribution parameters band ne enables the factors governing insulation service lifetime to be identified. The dependence of ne on Rlr is depicted by the curve with a maximum (ne is the service lifetime for a failure probability p = 0.632). Figure 6.7 shows the behavior of the parameter b for the first (b l ) and second (b z) segments of the Weibull distribution on Rlr. It can be seen that the behavior of curves b l for the two cited experiments is analogous to Emax = j(Rlr). Since the first segment of the Weibull distribution corresponds to the rejection of samples with gross defects, this suggests that the service lifetime of such samples is determined by the electric field. The parameter bz behaves analogously to the insulation volume. This means that the service lifetime of preliminary rejected insulation depends not only on the electric field but also on the insulation volume (see Sec. 6.4).

150

Chapter 6 Influence ofInsulation Gap Geometry on Electric Strength

x"

8,8

~ ......

• ?I

..... o

..... x'l"l

./

/

~

12 fO

I

2

8,6

IJ,Z

V

,

f,O

Vl(

/,5

~I /J

~

G

A

I

1---

_x

-

-8 )(

r\ J

fi

1,/

"z

J

5 R/r

2

Fig. 6.7. Parameters of the Weibull distribution b l (1 and 2) and b2 (3 and 4) and the material volume (5 and 6) as functions of Rlr

6.2 Interelectrode Gap Length The scaling effect, that is, the dependence of electric strength on interelectrode gap length, electrode area, and volume of the insulating medium exposed to an electric field, is a common property of all insulating media. In insulation systems, it shows up as a decrease in the mean breakdown field strength with increasing overall dimensions of the system and increasing number of individual insulation units. The electric strength of all dielectrics increases with decreasing electrode gap length, all other conditions remaining unchanged. Only for solid insulation containing defects might Ebr decrease with d when the interelectrode gap length becomes comparable in size to defects. When breakdown results from electron collisional ionization (breakdown of gases and probably of liquid and solid dielectrics under certain specific combinations of experimental conditions), Ebr increases with decreasing d, since the increase in the number of electrons in an avalanche obeys the familiar exponential law n = noexp( a.d). Thus, for short interelectrode gaps, a stronger electric field is needed to produce the critical SC required to transform the avalanche into a streamer. In condensed media, this factor most likely acts in micron interelectrode gaps. Numerous experimental data demonstrate that the strongest electric hardening is observed in precisely such gaps. The dependence of Ebr on d is also attributable to other factors.

6.2 Interelectrode Gap Length

151

An increase in d for fixed electrode area is accompanied by a corresponding increase in dielectric volume exposed to a strong electric field, and the number of weak regions facilitating breakdown also increases. This effect is observed in the breakdown of liquid, solid, and composite dielectrics. In actual experiments, an increase in d implies either an increase in electrode area, when experimenters endeavor to preserve the field inhomogeneity coefficient, or an increase in field inhomogeneity, when the electrode areas remain unchanged. In both cases, Ebr decreases with increasing d. The decrease in Ebr with increasing d also follows from a consideration of the physical pattern of discharge evolution. The breakdown voltage for long gaps in gases and liquids is largely determined by the leader stage of the discharge. The rate of discharge channel propagation in a dielectric medium is primarily determined by the field strength near its head, which depends on the voltage applied to the gap and the voltage drop across the discharge channel. As d and the discharge channel length increase, the voltage drop across the channel also increases. It follows that the voltage applied to the gap must be increased to compensate for this additional voltage drop. However, the increase in gap and discharge channel length, and hence in channel propagation time, heats the channel and reduces the longitudinal potential gradients in it. This means that the voltage increase required to compensate for the voltage drop across the gap depends nonlinearly on the gap length. The dependence E br = j(d) for solid polymer dielectrics of small thickness is influenced by changes in the molecular and supermolecular structures when the dielectric layer thickness decreases, whereas for solid dielectrics oflarge thickness it is influenced by the SC field distortion (see Sec. 6.4). Generally, the dependence of breakdown voltage on interelectrode gap length for all dielectric media can be written

where B and n are constants that depend on the properties of the dielectric medium and breakdown conditions. Moreover, n can be set to 1 only when d varies between relatively narrow limits. In most cases, n < 1. For example, the value of n for vacuum obtained in various studies lies in the range 0.2-1.2; however, n is overwhelmingly confined to the range 0.5-0.7. A decrease in the electric strength of vacuum with increasing gap length is often referred to as the total voltage effect in the specialized literature. Figures 5.22 and 5.23 show the dependence of the voltage pulse (a wave with oblique edges and tfr= 0.5 J.ls) on the interelectrode gap length for insulation gaps with varioius configurations and technical vacuum. Kassirov [9], based on a large volume of data on the influence of different factors on the electric strength of vacuum and on the, physical processes determining this influence, concluded that the total voltage effect is manifested only when the surface area of the cathode (from which desorbed gases are supplied to the gap) increases. We believe that as in other dielectric media, the total voltage effect is also a consequence of changes in the field configuration or electrode areas in experiments designed to determine Ubr in vac-

152

Chapter 6 Influence ofInsulation Gap Geometry on Electric Strength

10'

I",

I

HO~

~~ l 0

Fig. 6.S. Dependence on the interelectrode gap length of breakdown field macrostrength at the cathode for vacuum gaps with homogeneous or weakly inhomogeneous fields

Table 6.2. Coefficients B and n in the equation for Ubr Voltage Dc voltage Ac voltage of the main frequency High-frequency voltage (f~ 106 Hz) icrosecond vo ltage pul es

Interelectrode gap length d[mm] 2 0.05- 1.5 1.5- 2.8 1- 3.6

8 [kV·m-1j

n

40-45 45 57 31

0.4-06 0.85 0.3 0.7

1.5 2

40 64

1 0.5

uum gaps. The great diversity of experimental conditions leads to the fact that in some studies the total voltage effect was detected, whereas in others the breakdown field macrostrength at the cathode was constant. Figure 6.8 dramatically illustrates this circumstance [130]. The results obtained in 14 studies are shown in this figure (each curve segment or point was taken from a different source). The data in Fig. 6.8 were obtained for gaps with homogeneous or weakly inhomogeneous fields . It should also be noted that the dependence Ubr = j(d) for vacuum breakdown is influenced by the differing behavior of oxide films on the electrodes for breakdown of short and long gaps. For millimeter gaps, the film on the oxidized cathode surface is essentially destroyed after the first breakdown, and the breakdown voltage decreases sharply. For centimeter gaps, oxidized cathodes withstand tens of thousands of breakdowns. Table 6.2 summarizes the data reported in [79] for the dependence of Ubr on d in vacuum gaps with homogeneous or weakly inhomogeneous fields and varioius types of applied voltage.

6.2 Interelectrode Gap Length

153

~5~--+---~---+~~

o

as

f.O

1.5

d, m

Fig. 6.9. Dependence of 50% values of Vb, as a function of interelectrode gap length of a rod-plane electrode system in air for 1.2/50 (2 and 3) and 250/2500 f.ls (1 and 4) voltage pulses of positive (1 and 2) and negative polarity (3 and 4)

For gases, the dependence of breakdown voltage on interelectrode gap length is completely determined by the Paschen curve (see Sec. 3.1). At constant pressure, the increase in Eb, with decreasing d is clearest in millimeter and submillimeter gaps with homogeneous fields, when satsifying the conditions for avalanchestreamer transition becomes important. As follows from the data reported in [18] and presented below, the electric strength of a 25-llm reaches 200 kV/cm.

d [cm) E b , [kV/cm]

1 31

0.4 0.1 36 45

0.06 53

0.04 59

0.02 74

0.01 0.008 97 107

0.006 125

0.0025 200

As the gas pressure decreases, the interelectrode gap length at which electric hardening commences increases. For much longer gaps, Ub, increases virtually in proportion to d when the field in the gap remains homogeneous, or when it is so inhomogeneous that the increase in d has essentially no effect on field inhomogeneity (Fig. 6.9) [85]. These discharge gaps are usually called short, although the interelectrode gap lengths in air can reach tens of centimeters. According to (85), short gaps are taken to mean gaps in which the discharge evolves as a streamer rather than a leader. For the overwhelming majority of electrode shapes, the discharge type changes at gap lengths between 1.5 and 2 m. For long gaps, the dependence Ub,(d) is nonlinear. Nonlinearity becomes especially prominent under exposure to long voltage pulses (see Fig. 5.10). For pulses with tf,= 1.2 J..lS, the dependence Ub,(d) can be treated as linear:

Ub, = 0.525d , where Ub, is in kV and d is the interelectrode gap length.

154

Chapter 6 Influence of Insulation Gap Geometry on Electric Strength

As indicated in Sec. 5.2, the fastest decrease in the average breakdown field strength for long air gaps Eav with increasing d is observed for pulses with the critical rise time. For gaps many meters long, the average breakdown field strength decreases significantly when subjected to pulses whose parameters differ from those at which the voltage-time characteristics reach their minima. Information on the breakdown of air gaps with length ranging from several tens to several hundreds of meters, when the average breakdown field gradients are only several hundred volts per centimeter, can be found in the literature. The increase in Ubr slows down markedly with increasing d when going from short to long gaps, that is, from streamer to leader discharge in SF6 gas. Moreover, for electronegative gases and gaps with highly inhomogeneous fields, the dependence Ubr = j(d) has a minimum [31]. For liquid dielectrics it is worth considering E br = j(d) over two ranges of interelectrode gap length. Millimeter gaps comprise the boundary between these two ranges. Shorter discharge gaps are conventionally called short, and longer discharge gaps are called long. Experimental data for short gaps are inconsistent. G.!. Skanavi [18] thoroughly studied a large collection of published experimental data and concluded that E br is independent of layer thickness over a wide range of time and thickness. For very small thicknesses (less than 50 J.Ull), Ebr increases with decreasing thickness. Therefore, he suggested that the hardening typical of breakdown, due to collisional ionization, occurs in thin layers as well. The results obtained in different studies for long discharge gaps are unambiguous: an increase in interelectrode gap length is accompanied by a decrease in E br • Ambiguous results for short gaps can be explained by the fact that in addition to the factors indicated at the beginning of this section that lead to electric hardening, bridges of impurity particles are formed faster and at lower electric fields in the gap as d decreases, electrode microgeometry has a stronger effect on Ebr, and the breakdown probability of foreign inclusions (solid particles, gas bubbles, and moisture drops) increases. With decreasing d, the conditions for electrohydrodynamic, convective, and thermal process evolution, accompanied by the violation of the condition of continuity of the medium and by the decrease in the electric strength, also change. As for gases, the change in d is accompanied by the change in the mechanism and laws of the discharge evolution. In particular, when going from centimeter (and longer) to millimeter (and shorter) gaps, the leader discharge is not realized. For gaps with homogeneous fields, when going to micrometer gaps, the anode mechanism of discharge initiation becomes the cathode mechanism [72] instead. An analysis of works published after [18] allows us to conclude that when the effect of secondary processes is minimized by careful preparation of the liquid and electrodes before testing and by applying voltage pulses, Ebr decreases with increasing d over essentially the entire range of gap lengths. In particular, Fig. 6.10 [61] shows the nanosecond electric strength of transformer oil and distilled water obtained by various authors for gaps with homogeneous fields and different lengths. The dependence of the electric strength of distilled water on the length of gaps with homogeneous fields is shown in Fig. 6.11 for microsecond pulses [22].

6.2 Interelectrode Gap Length Ebro

155

MY/cm

5r---~~----~~----~ ~~--~-+~~--+-----~ J~----~~~--~~~--~

2r------+~~~~~~~

fr------+------+-----~

d,cm Fig. 6.10. Dependence of Ubr on d for transfonner oil (1) and distilled water (2) homogeneous fields at lbr = IOns

220 2f}O

f'..:"",

r---. ;--.....,

180 (50

0.2 0.'1 0.6

ae 1

.......

~

2

If

~

In

r--...I'-

6 d, cm

Fig. 6.11. Dependence of E br in water exposed to a single pulse as a function of the length of the gap fonned by plane electrodes

Experimental investigations of the dependence of electric strength of solid dielectrics on their thickness face considerable methodological difficulties. In fabricating thin films or samples with small thickness of the breakdown layer, it is difficult to ensure the homogeneity of the material and hence to avoid a decrease in Ebr due to breakdown of weak regions. For very large thickness of the examined samples, it is difficult to ensure the field homogeneity and to avoid edge and surface discharges that reduce Ebr and distort the results of measurements. Not until the late 1950s and early 1960s did experimenters obtain robust data indicating a decrease in E br with increasing d over a wide range of interelectrode gap lengths. The electric strength of hyperfine films (d = 30-700 nm), which are typically prepared in a glow discharge, is characterized by certain specific features [100] : Ebr of polymer and organosilicon films is independent of the temperature over a wide range, but the greater the work function of electrons leaving the metal cathode, the greater the value of Ebf'

156

Chapter 6 Influence of Insulation Gap Geometry on Electric Strength

E bn MV/cm

7 5 J

:-

,

max

f

"-....... av

mm r---=- r=-:- -}z --t--_

~-

o 50

ISO

2S0

d, Ilm

Fig. 6.12. Dependence of Ebr on d for PE samples in a homogeneous electric field for a dc voltage (J) and voltage pulses with 'tfr = 10-6 S

The electric strength continues to increase with decreasing d and, for example, for polypropylene films 200 om thick reaches 5.10 7 V/cm, which exceeds E br for d = 10 f.lm almost by an order of magnitude. For commercial polymer films tens of microns thick, as for capacitor paper, Ebr decreases when d decreases below a certain threshold due to the increasing influence of defects like a through pore, a weak region, etc. Figure 6.12 illustrates the behavior of Ebr(d) for films whose thickness ranges from several tens to several hundreds of microns, using polyethylene as an example (100]. It can be seen that the maximum and average values of E br increase by 2~0% as d decreases from 450 to 25 f.lm; in this case, the minimum values of E br depend on d only slightly. For large film thickness, the dependence EbcCd) for different solid dielectrics and experimental conditions is similar to that shown in Fig. 6.12. Moreover, the dependence Ebr(d) shows up especially clearly in edge and surface discharges. For breakdown of dielectrics in highly inhomogeneous fields, the dependence E br = j(d) is also lower, but its location and detailed shape are strongly influenced by the polarity and geometry of the electrode that governs field inhomogeneity. Figure 6.13 shows the dependence of the pulsed breakdown voltage for a plastic in the field of tip-plane electrodes with positive (1) or negative (2) electrode polarity [75].

6.3 Electrode Surface Area An increase in electrode area reduces the electric strength due to the increased number of weak regions produced by geometrical surface inhomogeneities, polishing agent residues, electrode metal oxidation products, and adsorbed gas and moisture. In addition, as indicated above, an increase in electrode area increases the volume of dielectric medium in a strong electric field. This factor becomes most important for breakdown of liquid, solid, and composite dielectrics (see Sec. 6.4).

6.3 Electrode Surface Area

200 f50 fOO

5U

o

/

f

II f

/

,/'

V

157

."".,.. 2

--'

V

2

J

4 d, mm

Fig. 6.13. Dependence of pulsed Ubf in a plastic as a function of the length of the gap between tip-plane electrodes for positive (1) and negative (2) polarity of the tip electrode

The influence of electrode area is especially strong when processes at the electrodes and adjacent regions dominate processes deep in the dielectric medium. The breakdown field strength distribution then obeys the Weibulllaw. The general relation between electric strength and electrode area is given by an empirical relation of the form (6.1)

where n is a coefficient that depends on dielectric type and breakdown conditions. To consider the effect of electrode area for gaps formed by electrodes of arbitrary configuration and not just flat electrodes that create a homogeneous field, the concept of the effective electrode area is introduced. The effective electrode area for gaps with an inhomogeneous field is defined as the electrode area in a homogeneous field of strength E max , with the same number of weak regions as the actual gap. In laboratory tests, the effective (frequently called strong-field) area is usually considered to be the electrode area with field strength exceeding 0.9 of its maximum value. In calculations of large insulation systems, a somewhat greater value Seff = 0.7-0.85 of the actual physical area is taken to be the effective area. In vacuum, electrode area becomes an influence for all types of voltages, discharge gaps of different lengths, different degrees of pumping to vacuum, and different qualities of electrode surface treatment. Quantitatively, the effect of electrode area is described by Table 6.3 [144]. The data in Table 6.3 are described by Eq. (6.1) with n = 0.05 for an oxidized aluminum cathode and n = 0.1 for a stainless steel cathode.

158

Chapter 6 Influence ofInsulation Gap Geometry on Electric Strength

Table 6.3. Effect of electrode area on the breakdown voltage of vacuum gaps with homogeneous fields athode material Oxidized alumi num tainless steel

I nterelectrode gap length [m m]

Pressure [mPa]

6 6 10 10 10

0.1 100 100 0.1 100

Electrode area [cm~l

7 215 280 450 235 290

10 215 480 290

50 195 250 415 200 250

300 185 240 375 170 200

700 175 240 360 180 185

Uhf' kV

o

75

ISO

Fig. 6.14. Dependence of vacuum breakdown voltage Ubr for a system of coaxial cylinders on the area of electrodes with variable lengths of cylinders, R = 60 mm, and r = 22.5 rom for a pulse with oblique fronts of duration 'tfr = 0.5 JlS and negative (1) and positive (2) polarities of the center electrode

Since the desorption of gas from the electrode surface and its subsequent separation are the important factors governing this effect in vacuum breakdown, the breakdown field strengths depend not only on electrode surface area but also on the conditions of gas separation [9]. Gas separation is impeded in so-called closed electrode systems--coaxial electrodes and flat electrodes that are large relative to the interelectrode gap length (several dozen times the latter). The electric strength of these gaps is less than that of open gaps, and electrode area exerts less of an effect. The breakdown voltage in coaxial gaps with the optimal ratio Rlr = 2.7 is a factor of 2-3 less than in plane-plane gaps that have the same electrode area and interelectrode gap length (Fig. 6.14). The increase in the electrode area makes the breakdown electrode aging more labor intensive (many breakdowns are required) and less efficient, because vapors and particles of eroded material are deposited on the electrode surface rather than on the walls of the test chamber. Various side effects (which alter the electrode configuration, maximum electric field, effective rather than actual electrode area, capacitance of the gap and hence the stored energy, etc.) that occur in the course of experimental investigations of

6.3 Electrode Surface Area

159

o a7~~--~--~~--~~-

as

1.0

1.5 2.0 log(S/So)

Fig. 6.15. Relative breakdown voltage for a vacuum gap with cylindrical spacer-insulator as a function of the ratio of the electrode areas

the scale effect, and in particular of the effect of electrode area, make it difficult to obtain objective data. Important practical manifestations of the scale effect were considered in [145] for a flat vacuum gap with a base insulator-spacer accompanying changes in electrode area, and for a coaxial vacuum line accompanying changes in the number of insulator-spacers. Diameters of electrodes with Rogowski profiles varied from 8 to 190 mm. The ceramic insulator-spacer was 8 mm in diameter and 5.7 mm high. Measurements were carried out for voltages of the mains frequency in vacuum below 8 MPa. Figure 6.15 shows the measured data for this case. In this figure, U~r is the breakdown voltage for the gap formed by electrodes equal in diameter to the spacer diameter 2Ro (the area of this electrode is denoted by So). The solid curve corresponds to an expression analogous to Eq. (6.1): (6.2)

where Sj and U~r are current values of the electrode areas and breakdown voltages corresponding to them, and n = 0.036. For a coaxial electrode system with fixed center electrode area equal to 1300 cm 2, increasing the number of insulators to 21 reduces Ubr by 55%. The breakdown voltage conforms to a Wei bull distribution. The dependence of Ubr on the number of insulators N for the given breakdown probability is (6.3) where U~r is the breakdown voltage for a system with a single insulator, and b = 3.7 is the parameter of the Weibull distribution. Taking both effects into account and combining Eqs. (6.2) and (6.3), we obtain the dependence of the breakdown voltage for the insulation system on the break-

160

Chapter 6 Influence ofinsulation Gap Geometry on Electric Strength

0.3

6

9

12

15

f6

21 N

Fig. 6.16. Dependence of relative breakdown voltage . for a vacuum coaxial line on the number of insulator-spacers, with allowance for simultaneous changes in electrode area from 0.5 to 1300 cm 2

down voltage of the system with a single spacer, with allowance for the electrode area and the number of spacers:

ubri = U brO

(SiS )-n No

llb

.

(6.4)

The dashed curve in Fig. 6.16 shows the dependence given by Eq. (6.4). The solid curve passes through experimental points obtained when S varied from 0.5 to 1300 cm2 and N varied from 1 to 21. The very strong scale effect for vacuum breakdown can be a serious obstacle to the construction of extended vacuum highvoltage transmission lines and large insulation systems. As a rule, changes in the electrode area in vacuum, as in other media, are accompanied by corresponding changes in the breakdown voltage distribution from normal (for small S) to a Weibull or double exponential law (for large S). The effect of electrode area for a gas breakdown is primarily associated with an increase in the number of microinhomogeneities with increasing electrode area, and a rising probability of fairly large inhomogeneities on the electrode surface. The latter are not only capable of initiating breakdown, but they can also alter the discharge type (for example, changing a streamer discharge into a leader). As the high-field electrode area grows, deviations from the discharge similarity law start to show up at lower electric fields, and their values are greater [146]. Usually, the data obtained by different authors for gaps with large electrode area (100 cm2 and larger) differ significantly. This can be explained by the strong influence of the care exercised in carrying out a particular experiment: controlling large insulation systems is much more difficult than controlling the small ones used for laboratory discharge gaps. Since the influence of electrode surface micro geometry increases with the gas pressure, the effect of electrode area will also be much more strongly manifested (Fig. 6.17) [147]. At P = 0.34 MPa and for voltages at the mains frequency, Ebr

6.3 Electrode Surface Area

2S0 200

150 fOO 50

-.......

r- ....

-

.... 1"-

-

1--1"-

l....... :::..:: ~

..... .....

'- ,-I-

tr-~

'-

--

I-

-

r-.::: :::::- ~I'r- r-I'-

161

r- r-8 ~7

r--.... G r--

'(:"5

r-.... r---3 _2 .:.::: -1

fOO 1000S, cm 10 " Fig. 6.17. Electric strength of SF gas as a function of electrode area at 2

p = 98 (1 and 2), 6 196 (3 and 4), 294 (5 and 7), and 343 kPa (6 and 8) for 1.5/40 J.1S voltage pulses (- - -) and 50-Hz ac voltages (- )

decreases by a factor of 1.7 when S increases by a factor of 103 • Nearly the same rate of Ebr decay with increasing S was observed in compressed nitrogen and air. In nitrogen at p = 2-3 MPa, Ebr was halved when S increased by a factor of 10 3 • The effect of electrode area on voltage pulses is weaker than its effect on dc and ac voltages. This causes the pulse width ratio to increase with increasing electrode area. For example, for SF6 gas and a 25% SF6 + 75% N2 mixture, the pulse width ratio for lightning pulses and S < 10 cm2 was at most 1.1-1.15, whereas for S > 100 cm2 , the pulse width ratio climbed to 1.2-1.4 [148]. Greater values correspond to gaps with lower electric strength for ac and dc voltages. For larger electrode area (l05 cm 2 and larger), the electric strength becomes essentially independent of the electrode area, and approaches the so-called lower electric strength limit Eo, which depends on gas pressure and composition (Fig. 6.18). The value of Eo can be used to estimate the minimum electric strength for separate units of gas-filled insulation equipment, and to find the electric strength as a function of electrode area. According to [148], (6.5) where Ems is the average electric strength (mode) for a gap with electrodes of area S, Eml is the mode of the breakdown field strength for electrodes of unit area, and n is a coefficient analogous to that of Eq. (6.1). Its numerical value for certain gases, including SF6 and N2 mixtures, lies in the range 0.11-0.13. The average breakdown field for a 50% SF6+ 50%N2 mixture as a function of electrode surface area, as calculated with Eq. (6.5), agrees fairly well with the published experimental data of various authors.

162

Chapter 6 Influence of Insulation Gap Geometry on Electric Strength Ebr>

kV/cm

~or+----r---~L---~~-+~ mO~--~-r~~~--~~'---~

~r+--~~~7S~~~~-4~ M~~--4S~~~--~~--~~

~r+~~;-~~~~~~~-r~

20 H---+---+----=.+----=+~ f

2

J

4 p·5.1O- 5 , Pa

Fig. 6.18. Gas pressure dependence of the lower limit on Ebr for SF6 gas, N2> and their mixtures

Pr--'r---r---~~

O.90t-----If---+-~~~ arot-----If---~~~~

O~t-----If-~~~~~

040t-----I~~~~~~

O.oOf L - - - L_ _--L_.....L.._ _.....J 1110 ISO 160 E kV/cm Fig. 6.19. Electric field dependence of breakdown probability for coaxial gaps with SF6 gas (p = 0.25 MPa): S = 4 (1), 12 (2), and 40 cm2 (3) (double exponential distribution)

In the range of electrode surface areas of greatest practical interest (10 2_ the breakdown voltage distribution function (DF) obeys the Weibulllaw [146]. In a number of studies (for example, see [30]), the double exponential distribution was preferred. The increase in the electrode area there was accompanied by the displacement of the probability curves (in the appropriate coordinates depicted by straight lines) toward higher breakdown probabilities (Fig. 6.19) [30]. For small electrode areas typical of laboratory tests, the DF is satisfactorily described by a normal distribution. The effect of electrode area on gas breakdown decreases significantly when the electrodes are coated with a thin homogeneous insulation layer (see Sec. 10.2). 105 cm2),

6.3 Electrode Surface Area

163

EIII 3

2.0 f.O

0.6 0.'1 0.2 0.1 0.08

Z

-

£tWla Et'/3

f

-

o.OG

0.0'f

to

0

Fig. 6.20. Dependence on S of Et"3 for transformer oil with weakly inhomogeneous (1) and homogeneous (2) fields

Thus, in [149] it was demonstrated that Ubr does not change at an SF6 gas pressure of 0.4 Pa with 1.2/50 J.ls pulses when the electrode area increases from 1 to 105 cm2, if the electrodes are coated with a 25-J.lm epoxy resin and fluoroplastic insulating layer. In polystyrene and aluminum oxide coatings, Ubr decreases only slightly with increasing S. For uncoated electrodes, Ubr decreases by 40%. In liquid dielectric breakdown, the influence of electrode area depends on the voltage duration even more than in gas breakdown. For microsecond pulses and ac voltages, this effect becomes evident even when S changes by a factor of 5. For long-term applied voltage, bridges can be formed by foreign inclusions. Breakdown is facilitated either through or along them. For microsecond or longer pulses, when the impurity particles can be considered fixed, they have time to be polarized (this includes slow polarization processes), thereby causing local field distortions and reducing the electric strength. In that event, the scale effect results from the combined influence of electrode area and the volume of the liquid in the electric field. For nanosecond breakdowns, only weak regions at the electrode surface play a major role in the electrode area effect, which comes into play only when S varies over a wide range. Figure 6.20 shows the generalized dependence on electrode area of pulsed electric strength for insulating oil, which varies by five orders of magnitude [150]. The dependences were generalized as follows: 1) all electrodes were assumed similar (to this end, the field inhomogeneity coefficient J.l was introduced); 2) a certain monotonically increasing pulse with duration 'teff' defined as the time of voltage rise from 0.63Ebr to Ebr. was used to construct these dependences. The value of the exponent n in Eq. (6.1), according to these data, is 0.1. The value of this coefficient was repeatedly refined over subsequent years in numerous studies of electric strength for liquids (mainly of the insulating oil and purified water) under conditions corresponding to their use as insulation in coaxial and strip shaping lines of high-power and high-voltage generators intended for accelerators and xray sources. For water and microsecond voltage pulses, n = 0.1 was reported, in

164

Chapter 6 Influence ofInsulation Gap Geometry on Electric Strength Ebr>

kV/cm

280 .......

2~0

ZOO

........

160

'90

120 tOO f

2

~

10 10 W 100 200 S, cm 2

Fig. 6.21. Dependence on electrode area S of E br for water exposed to a single voltage pulse in a homogeneous field for d = 1 cm

particular, in [22,61,133]. For water and nanosecond pulses (7.10- 9-3.10-8 s), n = 0.06 was obtained in [151]. In [150], n = 0.1 was recommended to consider the effect of electrode area for transformer and castor oils, ethyl and methyl alcohol, water, and glycerin. From this brief consideration we conclude that quantitatively, the effect of electrode area is independent or only slightly dependent on the specific properties of particular liquids having approximately identical degrees of purity. It decreases with decreasing voltage duration. Figure 6.21 [22] illustrates the agreement between the available experimental data and their approximation by a power-law dependence given by Eq. (6.1). Results analogous to those obtained for the cited normal liquids were also obtained for cryogenic liquids. In general, the two components of the scale effect on Ebr--effects of the electrode area and the volume of dielectric medium in the electric field--cannot be separated for solid dielectrics. It is convenient to analyze their combined influence as the effect of volume (see Sec. 6.4).

6.4 Dielectric Volume in an Electric Field For vacuum and gas breakdown, the effect of volume is manifested only slightly and results from solid impurity particles in the interelectrode gap, which are capable of initiating breakdown while approaching the electrode (see Sec. 4.1). As a consequence and due to the fact that it is difficult to separate the effect of volume from the total voltage effect and the effect of electrode area, scant information on this problem can be found in the literature. When SF6 gas in a system of coaxial cylindrical electrodes was tested with 1.2/50 J..ls voltage pulses and the gas volume exposed to a strong electric field varied, the following behavior was reported in [153]: the discharge time lag decreased with increasing gas volume, irrespective of the gas pressure; the primaryelectron production rate no per unit volume per unit time was independent of the

6.4 Dielectric Volume in an Electric Field E. kV/mm

cr, kV/mm

0\

a

\

~1

20 fO

o

-

-

~

165

~ 0 2

~

K

2

~

• ~ ~ t'o

1

I'"

b 'I(>

""-Z~'\ :~ ,/1

'bb: ~ o

0

-

Fig. 6.22. Dependence of Ebr (a) and its spread (b) on dielectric volume in a strong field for oil of types I (curve 1) and II (curve 2)

gas volume, and slightly increased with the slope of the voltage pulse leading edge; and a pressure rise from one atmosphere to 250 kPa did not alter no. Setting no constant at 0.4 Ils-I'cm-3, the order of magnitude of the discharge time lag can be estimated to be

as a function of the gas volume enclosed in coaxial electrode systems for microsecond voltage pulses with an oblique leading edge. Here to is the voltage leading edge rise time to the statistical breakdown level, tso-to is the period during which 50% of breakdowns occur, and Vc is the corrected gas volume for coaxial cylindrical electrodes. The significant influence of the volume of a liquid dielectric in a strong electric field on the electric strength results from the fact that processes in the bulk of the liquid strongly affect discharge initiation near the electrodes, and subsequent propagation within the interelectrode gap. The relationship between electric strength and liquid volume depends heavily on the elemental composition of the liquid, the prevalence and nature of impurities, the discharge gap configuration, the electric field, and the exposure time of the liquid. Figure 6.22 [152] shows the typical behavior as a function of dielectric volume of the electric strength and its spread for transformer oil of two types. The tests were carried out for voltages at the mains frequency by the stepwise method of voltage application, with ten or twenty voltage rises at each step and I-min exposure (see Sec. 2.1). The voltage at the initial step was 30% of the predicted breakdown voltage, and the voltage was raised by increments equal to -5% of the breakdown voltage. As follows from Fig. 6.22a, Ebr was halved when the dielectric volume in the strong electric field increased by two orders of magnitude. The experimental dependences E br( V) and cr( V) are described well by the empirical equations

166

Chapter 6 Influence of Insulation Gap Geometry on Electric Strength

Table 6.4. Influence of dielectric volume on E br of transformer oil (electrode areas held constant) I nterelectrode Electrode area [cm l ] gap length [mm]

8 16

1120 1120

Oil volume Number Breakdown voltage [kY/mm] enclosed between of test for breakdown ~robabilit~ [%] electrodes [cm 3] 10 SO

900 1800

EIO%

= 8.95V- 1I7

SO

50

7.74 5.60

8.73 5.59

+ 2.33,

cr = 3.25V- 1I6 for oil of type I, cr = 2.36V- 1/ 7 for oil of type II, where E is in kV/mm and Vis in cm3• Experiments also compared effects due to liquid dielectric volume and electrode area. The results in Table 6.4 demonstrate that Ebr decreases by approximately 22% when the oil volume in a strong electric field doubles, with electrode areas remaining unchanged; that is, the influence of dielectric volume in a strong electric field is greater than that of electrode area. For voltage pulses, when many processes responsible for the behavior of EbrU') under long-term voltage exposure can be neglected, the most important factor is the increasing probability of occurrence of weak regions with increasing liquid dielectric volume in a strong electric field. In this case, an attempt has been made [154] to use the distribution function of the breakdown field strength probability obtained in [94] for solid dielectrics. After some simplifications for a coaxial electrode system, the dependence of the maximum breakdown field strength on the liquid dielectric volume in a strong electric field assumes the form

E;?;:2 = A+ Blog (Ir2 In ~).

(6.6)

where A and B are parameters describing the properties of the dielectric, I is the electrode length, and rand R are the radii of the inner and outer electrodes, respectively. The applicability of the statistics of extreme values to a description of Ebr(V) for voltage pulses was tested for three coaxial electrode systems (R = 19, 28, and 40 mm, r = 2-30 mm, and 1= 70 mm) and commercially pure transformer oil. Breakdowns were initiated at the leading edge of a single voltage pulse of positive polarity with a slope of 1700 kV//.l.s. Figure 6.23 shows the resulting measurements. In coordinates chosen according to Eq. (6.6), they are satisfactorily approximated by a straight line, which confirms the validity of Eq. (6.6). In this case, A = -0.0161 and B = 0.0147 kV/mm.

6.4 Dielectric Volume in an Electric Field

167

EI

102/0. 2 brmax

~

0

~ ,'Xx

JO

xJI'

2.'1

x

1.6 2.3

/

•

~

'if:

/

r.1

x - f o -z • -3 L

2.7

~

3.1

.J.5

1

J.9

log(l?log(RJr»

Fig. 6. 23. Effect of liquid dielectric volume on 28 (2), and 40 mm (3)

Ebrmax

for transformer oil and

R =

19 (1),

The dependence of the short- and long-tenn electric strength on solid insulation volume follows directly from the physical mechanisms of electric aging and solid dielectric breakdown, and from the statistical theory of extreme values describing these phenomena. This dependence is referred to as the statistical volume effect. If the insulation lifetime curve is represented as

or log E = A -

(1 In) log 't ,

(6.7)

to consider the insulation volume, Eq. (6.7) should be refined by introducing the volume coefficient kv, equal to the ratio of the insulation volume VI to the volume V2 , for which the service lifetime is known. Then the insulation service lifetime becomes

or logE = A = (lin )log(kv't) ,

(6.8)

where E is the field strength, 't is the predicted insulation service lifetime for a field of strength E, and n is the exponent, which for polymer, epoxy, and many other insulation types lies in the range 10-15. An increase in insulation volume leads to a parallel shift of the straight line 10g(E) = .f{logt) toward smaller E. When the insulation volume increases due to increased sample thickness, the so-called physical volume effect ensues after long-tenn voltage exposure. This effect is associated with SC accumulation in layers adjacent to the electrodes due to emission of charge carriers near the anode as the field strength increases (when

168

Chapter 6 Influence of Insulation Gap Geometry on Electric Strength

80

........ ..........

60 'fO

20

10

.........

.............

-.......

(I

Fig. 6.24. Ebr(50 Hz) of an epoxy compound as a function of dielectric volume in a strong field electrons are emitted from the cathode). With increasing sample thickness, SC accumulated in the dielectric occupies larger and larger regions adjacent to the electrodes. These regions grow as the thickness increases. The physical volume effect further reduces insulation service lifetime (or the allowable field strength for a fixed service lifetime). This leads to a decrease in the exponent n in Eq. (6.8) and an increase in the slope of the straight line logE = j(logt) relative to the time axis. Numerous experimental data can be considered unambiguous, because all of them indicate a decrease in short- and long-term electric strength of solid dielectrics with increasing dielectric volume in a strong field. Only the rate at which Ebr decreases with increasing V is different. Figure 6.24 shows the behavior of short-term electric strength of an epoxy compound as a function of dielectric volume in a strong field [16]. For cables, the scaling effect, which includes the dielectric volume effect, shows up as a strong dependence of electric strength on cable length. In the literature it is most often claimed that the electric strength of cables with extruded insulation decreases by 40-60% when the cable length increases by a factor of 100. For voltage pulses, the insulation service lifetime depends more heavily on dielectric volume than on electric strength. For example, with E = 100 kVlmm, a 30 J.ls pulse width, and a pulse repetition rate of 8 S- l, the service lifetime ofLDPE samples increases by three orders of magnitude when their volume is halved (the volume is altered by changing the sample thickness). In studying the dependence of service lifetime on dielectric volume that is altered by changing the sample thickness, manufacturing processes must be carefully monitored, as production variations can significantly distort the characteristics of the desired functional dependence. The dependence of the distribution of the failure parameters on the volume of the material for the compound, changed by changing the electrode area, was detailed in [25].

Chapter 7 Flashover Voltage at the Interface between Two Dielectric Media

7.1 Orientation and Dimensions of an Insulator in an Electric Field One often fails to achieve high electric strengths of vacuum, compressed gases and gas mixtures, and dielectric liquids to manufacture compact insulation equipment, because the electric strengths of insulation gaps considerably decrease when solid insulation is inserted into them. When solid dielectrics are used as barriers or parts of multilayer insulation systems, their surfaces are perpendicular to the electric field lines and hence the breakdown voltage increases. However, in spacers and base and through insulators, the dielectric surface is often parallel to the electric field vector, and the electric strength of a composite dielectric is much lower than that of individual dielectrics. Nowadays, a lower electric strength of the interface is explained mainly by three factors: the field distortion due to different dielectric characteristics (E, y) of the medium and solid insulation, the influence of sorbates in the dielectric medium and atmosphere (before pressurization), and additional feeding of the propagating discharge channel by the insulator capacitance. The largest electric field distortion (gain) is observed at the triple point, where the electrode, the solid insulation, and the dielectric medium are in contact. By virtue of the aforementioned effects, the flashover voltage Ufl is determined by combinations of many factors: the character of electrode contact with the insulator, the size and shape of the insulator surface, its orientation relative to the electric field lines, the properties of the solid dielectric and ambient medium, the parameters of the applied voltage, etc. Since Ufl of insulators determines the short-term electric strength of insulation equipment, the electric strength of dielectric medium and solid insulation must be coordinated in the design stage, the structural parameters of the insulator must be optimized, and the solid insulating material must be chosen with allowance for its electric and mechanical strength. One additional requirement is some degree of immunity to a number of diverse factors (see Sec. 1.1 and Chapter 8). Over the past few years, interest in flashover through a gas (in the form of a creeping discharge) has been fueled by prospects for application in commutators and lasers as an efficient ultraviolet preionizer. For this source ofUV radiation, a

170

Chapter 7 Flashover Voltage at the Interface between Two Dielectric Media

60~--I--R---1

x-J

40

/

201....-----'----"----'--........---" o 0.1 o.Z 0.3 0.1# p , MPa Fig. 7.1. Dependence of Vbr and Vn on SF 6 gas pressure for breakdown of a pure gas gap (1), and for flashover between clamped (2) and potted (3) nonaxial cylindrical electrodes

high rate of gap electric strength recovery after creeping discharge plus retention of discharge emission characteristics at current pulse repetition rates up to 104 Hz are typical. Advances in fracture and treatment of solid nonconducting workpieces by electric discharges-in electrical pulse technology-have stimulated research into flashover processes at the interface between dielectric media. The behavior of Ufl in various dielectric media as a function of the principal applied factors are considered below. Flashover at the humidified, contaminated surface of an outdoor insulator is not considered here, as it is beyond the scope of this monograph. As indicated in Sec. 1.2, methodologically it is convenient to reduce the great diversity of orientations of the solid dielectric surface relative to the electric field lines to three reference insulation configurations (see Fig. 2.3). The least field distortion is observed for a dielectric inserted in the interelectrode gap with configuration shown in Fig. 2.3a; moreover, in this case the flashover voltage is described by the discharge similarity law and Un is essentially equal to Ubr (Fig. 7.1) [30]. In calculations, the flashover path length must be substituted for the interelectrode gap length. For other configurations (see Fig. 2.3b and c), the electric strength of the interface is much less than the strength calculated and measured in actual discharge gaps (Fig. 7.2) [30]. The maximum decrease in Ufl compared to Ubr is typical of configurations with inhomogeneous fields when the normal component of the electric field vector prevails over most of the interface. This effect, according to the Toepler hypothesis and the specific features of the flashover mechanism developed in succeeding years, can be explained in two ways. The normal component of the electric field vector En maintains charges that move by virtue of the field near the dielectric surface. The heat liberated increases the plasma temperature and conductivity in the discharge channel. For configurations with a dominant normal component, the propagating discharge channel is additionally fed by displacement currents that close the circuit via the capacitance formed by the

7.1 Orientation and Dimensions of an Insulator in an Electric Field

171

Ebr , En, kY/cm

J

"" mo~==~~~~~~ 80~--~~~-;~~-r~ ~~--~~~~--;--r~ *O~--~----~--~~~

0.05

0.10

0.20 o.JOp, MPa

Fig. 7.2. Dependence of Ebr and Eft on SF 6 gas pressure: calculated value of Ebr (1), and E br measured for 1.2/50 fls voltage pulses (2) and 50-Hz ac (3); value of Eft measured for 1.2/50 fls pulses (4) and 50-Hz ac (5)

Un, kY 80

50

t---:t-7"""~~-\-

20 H--+t--+---+--+--4---l 100 JOO 900 500 I, mm Fig. 7.3. Dependence of

Un

on flashover path length of solid insulation in air for

50-Hz applied voltage and configurations with dominant tangential (1) or normal (2) electric field components

channel and the opposite electrode. This causes the plasma temperature in the channel to rise and longitudinal gradients in the channel to fall. As a result, surface discharge propagation is facilitated. Obviously, the larger the capacitance Csp per unit insulator surface from which the discharge propagates to the opposite electrode and the greater the rate ofvoitage change dU/dt, the larger the currents. The value of Csp is varied by changing the dielectric thickness ~ or choosing dielectrics with the required permittivity. Both effects can be discerned in Fig. 7.3. For small flashover length, curves Ufl = j(t) for configurations with prevailing normal and tangential components of

172

Chapter 7 Flashover Voltage at the Interface between Two Dielectric Media

Un max' kV 1

Z 1--........+---+-

Fig. 7.4. Dependence of Un max on the thickness of CaTi03 samples for dc voltage (1) and ac voltages at frequenciesf= 50 Hz (2), 135 (3), and 1025 kHz (4)

the electric field vector coincide. For large I, the first configuration is characterized by a low rate of increase in Un with increasing I. Efficient methods for increasing Un in these configurations are to increase insulation thickness or to use semiconducting coatings that reduce field inhomogeneity near the outer electrode edge (see Sec. 10.1). According to [155], Un can be described for I > 10 by an empirical relation of the form

_ (11 )0.45 (-:-1 )0.2 ,

Un -k -

E

10

where k is a constant. The contribution of the capacitive component to the total current that flows through the flashover channel in the transformer oil exposed to microsecond pulses was calculated and measured experimentally in [71]. It was found that the current through the solid dielectric, which depends on C sp, accounts for a considerable fraction of the total flashover current and hence the total current (approximately 60%) flowing through the propagating flashover channel, and the flashover voltage of dielectrics can be varied widely by changing this current. Experimental results demonstrate that with decreasing dielectric thickness 11 (increasing Csp), the greater the rate of voltage change, the faster Un decreases. For ac voltages, the higher the frequency, the faster Un decreases (Fig. 7.4) [18]. Figure 7.5 [61] shows the influence of Csp on the pulsed flashover voltage for plastic samples in transformer oil, 1.8/80-IlS positive-polarity voltage pulses, and a flashover path length 1= 10 cm. Un decreases with increasing Csp over the entire range of voltage pulse width examined . For essentially all combinations of solid dielectrics with insulating media, the dependence of Un on Csp is given by

7.1 Orientation and Dimensions of an Insulator in an Electric Field

173

I

2

J q. flO

5

10

20

15

25

t, /ls

Fig. 7.5. Voltage-time flashover characteristics of a plastic sample in transformer oil in an electric field, with dominant normal component, as a function of specific capacitance (sample thickness~) Csp = 0.86.10- 13 (1), 1.7-10- 13 (2), 3.1.10- 13 (3), and 5.1.10- 13 F/cm2 (4)

:~

A

90

•I

IX

80 70

Ii 0.2

I

•~

0

r-./1

-.

~ l"-

[J"-

• - f

.. -2 /:. -3

4

x

-'f.

o -5

o.S

(.0

1.'1

Fig. 7.6. Decrease in electric strength of a gap with an inserted solid dielectric as a function of the permittivity ratio sliqll'sol for pressboard (1), polyphenylene oxide polycarbonate (2), polycarbonate (3), permal (4), and perspex solid dielectrics (5)

where k and n are constants that depend on the properties of the dielectric and medium, and on flashover conditions. Changing Csp by changing I': rather than the solid dielectric thickness produces the same effect. The flashover voltage Un decreases for insulators fabricated from materials with larger 1': , the parameters of the dielectric medium remaining unchanged. When the difference between I': of the solid dielectric and the medium increases, Un decreases, and the flashover probability also increases compared to the liquid breakdown probability. For cylindrical insulators in a liquid in the field of flat electrodes, the dependence of Un on the ratio of the permittivity of the solid dielectric to that of the liquid is more complicated (Fig. 7.6) [156].

174

Chapter 7 Flashover Voltage at the Interface between Two Dielectric Media

En kY/mm ~

12

1

10

6

G

2

a

lq

~ }

~ !'\ rJ i'. r-..... \

,~

~ r--....

I"'.....

1

;-- 15 mm, the pulsed values of Ufllie below the static values. In most cases, voltage polarity affects the flashover voltage less than the breakdown voltage. For a flashover in a liquid, it is most prominent when the difference between the dielectric characteristics of the liquid and the solid dielectric is minimal. The greater statistical spread of the experimental values is more typical of Ufl than Ubr because there are far fewer controllable factors governing the flashover. When field distortions at the triple point strongly affect Ufl and PDs or microdischarges arise regularly, the distribution of Ufl is described well by a normal distribution. If the field distortion at the triple point is negligible, Ufl is described by a double exponential law or a Weibull distribution. Since the effect of local field distortions on Ufl intensifies with increasing gas pressure, the range of insulating system geometric parameters for which the normal distribution law is applicable to the description of Ufl expands as well.

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

8.1 Ionizing Radiation Radiation-induced effects in dielectric media. In connection with the fact that dielectric materials used to fabricate various parts of high-voltage electrical equipment systems, nuclear and thermonuclear reactors, and electronic devices often operate in ionizing radiation fluxes, problems of radiation resistance and charging of insulating materials and devices are urgent. The researchers involved in the development of accelerator technology and nuclear power engineering from the outset search for radiation-resistant insulation and structural materials, and develop ways to improve the radiation resistance of novel and conventional materials (by the radiation resistance of materials is meant their ability to maintain their basic properties during and a:fter irradiation). Considerable attention has recently been paid to the study of physical processes in dielectrics, supporting the construction of empirical models and the development of engineering methods for predicting the behavior of dielectrics in ionizing radiation fluxes [168]. Exposure to ionizing radiation considerably alters dielectric materials; the most intense and profound changes occur in polymer dielectrics and hydrocarbon liquids. Long chains of molecules can join and form rigid three-dimensional grids, or they can decompose, chemical bonds can break and separate, free radicals can be formed, etc. These processes usually proceed simultaneously; and the dominant process largely determines the way in which material properties change. In this case, the main factors are the nature of the polymer and the absorbed radiation dose rate. For example, when the absorbed ionizing radiation dose is less than 105 Gy, sructuring (joining) of polymer chains dominates for PE. When doses exceed 105 Gy, destructive processes prevail over constructive processes, thereby leading to irreversible deterioration of polyethylene properties. When ionizing radiation acts on dielectrics, electrons with high kinetic energies, created by ionization and the Compton effect, are displaced from their standard sites in the dielectric in the direction of the incident photon flux. Electric fields between the displaced electrons and the remaining massive positive ions can reach breakdown values and initiate an electrodeless breakdown. If no breakdown is initiated (in either the presence or absence of an external field), the electrical characteristics of dielectric materials after the termination of irradiation and de-

196

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

ionization usually recover or come close to their original values. This happens when radiation does not alter the structure of the material. For this reason, all characteristics of the material-dielectric (Ebn E, tan 0, and Y), mechanical, and chemical-depend on the radiation parameters (its nature, intensity, and dose), on the nature and thickness of the material (longer or shorter than the mean free path), and whether these characteristics are measured during irradiation or afterwards. The initial electrical conductivity Yo changes under exposure to ionizing radiation, and these changes, like changes in many other characteristics of the material, can be reversible or irreversible. A reversible increase in conductivity results from ionization of atoms and molecules exposed to ionizing radiation. Moreover, the concentration of newly formed charge carriers depends primarily on radiationinduced chemical yield, radiation dose, concentration of traps and their distribution with depth, temperature, and exposure time. Radiation-induced conductivity YR of polymer materials is primarily electron-hole in character. The lifetime of photoinduced charge carriers can be large due to centers of localization of these charges-traps-in actual polymers. The time of YR relaxation to Yo after irradiation termination depends on the concentration and depth of trap localization. Traps might comprise impurities with charge affinity (for example, molecules of donor-acceptor additives and free radicals), as well as polymer structural defects (for example, broken chemical bonds and microvoids). The concentration of traps varies over the range 1022_10 26 m-3 in various materials. The kinetics of radiationinduced electrical conductivity of polymer and composite materials is described by the Rose-Fowler theory, which relates the radiation-induced electrical conductivity YR to the dose rate D:

YR=AU, where A and k are the parameters of the material. The parameter k characterizes the distribution of traps as a function of depth, and for the majority of polymers it lies in the interval 0.5-l.0. The lower the temperature of the irradiated material, the greater the number of electrons accumulated in traps, and hence the lower the value of YR. For larger absorbed doses that lead to irreversible changes in the material, the kinetics of residual radiation-induced conductivity is not described by the Rose-Fowler theory. The value of YR as a function of depth, and the character of radiation-induced chemical changes can be greater or smaller than Yo. As can be seen from Fig. 8.1, for polymer dielectrics there is a maximum in the dependence of Y on the exposure time or on the total dose. For PE, Y increases by an order of magnitude, whereas for teflon and polystyrene, Ychanges only negligibly. Ionizing radiation also changes the surface conductivity of dielectric materials Ys. Whereas Y8 of nonirradiated dielectrics increases linearly with the relative humidity, Y8 of irradiated dielectrics can decrease with increasing relative humidity when the latter exceeds 50%. A decrease in moisture absorption by polymers is also observed after Yirradiation (for more detail, see Sec. 8.2). The dependence of Ebr on the parameters of ionizing radiation is no less complex.

8.1 Ionizing Radiation

197

o.f 1.0 fa faD t, h Fig. 8.1. Dependence of electrical conductivity of polyethylene (1), teflon (2), and polystyrene (3) on the y radiation (Co60) exposure time for a radiation intensity of 100 RIh at T= 393 K

Apart from electrical properties, ionizing radiation can alter essentially any other property of materials, including chemical, physical-mechanical, etc. For long exposure times or very intense irradiation, any polymer finally fails. For example, teflon irradiated by a dose of 50 kGy becomes very brittle and crumbles, and polyisobutylene is transformed from a rubber-like material into a viscous liquid whose molecular mass is a factor of 15 less than the original value. Inorganic dielectrics have much greater radiation resistance than organic materials. The radiation resistance of inorganic material structures depends on their material composition, that is, on the cross section for radiative interaction with structural elements, along with their crystal structure, packing density, and chemical bond type. Dense and symmetric structures with strong ionic bonds are most stable under irradiation. More symmetric structures are formed after irradiation due to the accumulation of ordered atomic displacements. Some chemical bonds in irradiated glasses break and form other chemical bonds, electrons are captured by excited atoms (color centers are formed), and crystallization occurs even without subsequent thermal treatment. Lead glasses are less resistant to irradiation. Structural and chemical changes after irradiation are specific to each type of ceramic. These are described in a number of monographs (for example, see [169]). The electrical conductivity of inorganic materials is altered by ionization and structural changes. The first effect exists only during irradiation, and the second effect has reversible and irreversible components. The reversible component results from an excess concentration of point defects compared to their equilibrium level; the defects produced by radiation cause the ionic conductivity component to increase during irradiation and afterwards. The irreversible component results from transmutation doping that produces donoracceptor energy levels in the forbidden band. These levels, due to thermal excitation, supply the conduction band with charges. The values of tan 8 and I:: of inor-

198

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment E bn kV/mm 6lf

56 ~ 46

1

""'- - '

-0.. .....

40

32 2'1 16 6

o

~

I

........

3

.~~

.L_

_J:!-

-

fO

2 ......... 20

JO P, Gy/s

Fig. 8.2. Dependence of Ebr of steatite (curves 1 and 2) and mullite-corundum ceramics (curve 3) on the dose rate for dc voltage, sharply inhomogeneous field, and sample thickness d = 0.1 (2),0.6 (1), and 1.0 mm (3)

ganic materials after y and neutron irradiation at doses up to 10 17 cm-2 and pure y irradiation at doses up to 10 MGy typically revert to their initial levels immediately after irradiation ends. For higher doses (10 18_1020 cm-2 or greater), tan 8 increases irreversibly, from severalfold to several orders of magnitude. The electric strength of ceramic materials and glasses after y irradiation with doses up to 3.7.107 Gy and y plus neutron irradiation with doses up to 10 19 cm-2 maintains its original value. After irradiation with larger doses, Ebr of electrical porcelain and glass, pyroceramic, and forsterite ceramics decreases by 30, 75, and 55%, respectively [170]. The value of Ebr in electrical porcelain and steatite passes through a minimum at P = 10 Gy/s and decreases for P> 20 Gy/s with increasing dose rate; E br of mullite-corundum ceramics uniformly decreases with increasing P (Fig. 8.2). The mechanical strength of ceramics remains virtually unchanged at doses up to 10 19_1020 cm-2 . At D = 1020 cm-2, ultimate compression and bending strengths increase slightly, and upon further irradiation, decrease quickly. High-silica materials exhibit the greatest strength after irradiation. Upon exposure to ionizing radiation in liquid dielectrics, many processes, similar to those in polymers, proceed in them, including 1) ionization of atoms and molecules; 2) excitation of atoms and molecules to higher electronic, vibrational, oscillatory, and rotational energy states; 3) dissociation of molecules into neutral components or ions; 4) formation of free radicals and a number of accompanying processes involving these radicals (oxidation, reduction, etc.). Changes in the structure of hydrocarbon molecules induced by radiation can lead to the formation of gases (hydrogen and methane), breaking of C-C and C-H bonds, association of molecules into novel complexes with additional cross-links and gratings, production of unsaturated hydrocarbons, derangement of pseudocrystalline liquid structure, oxidation, etc.

8.1 Ionizing Radiation

199

r>

6 [j

z

~ x"'x

~

~

~~ ~ -~

o

.A.

0.1

1

V

/

,A/

.£.-

X ~

,0 Py> Oy/s

Fig. 8.3. Dependence of Vb, in air gaps fonned by tip-plane (1 and 2) and sphere-sphere electrode systems (3 and 4) on the dose rate of the y component of reactor emission for dc voltage (1 and 3) and 50-Hz ac (2 and 4)

At high (supercritical) radiation doses, such macroscopic characteristics of liquids as density, viscosity, electrical conductivity, electric strength, etc. change, that is, liquid dielectrics completely degrade. At doses and radiation intensities below the critical value, which do not cause catastrophic changes in liquids, their high-voltage conductivity and electric strength change only negligibly. In most published works, after irradiation of liquids by cobalt and radium sources, no changes in these characteristics are detected for any applied voltage type. In some cases, the dependence of the electric strength of liquids on the dose or exposure time is displayed by a curve with a maximum. Upon gas exposure to ionizing radiation, the main effects are ionization and excitation of molecules and atoms. After irradiation, the gas reverts to its initial state via recombination and emission processes. Irreversible changes may take place only in complex gases. For example, after y irradiation of the SF6 gas, stable SOF6 and S02F2 compounds are produced. Under simultaneous exposure to an electric field and radiation, the electric strength of gases decreases. The amount of this decrease depends not only on the radiation parameters, the properties and the state of the gas, and the electrode material but also on the discharge gap configuration [171]. As can be seen from Fig. 8.3, Vb, of the gap with a homogeneous field decreases monotonically with increasing y radiation dose rate. Qualitatively similar effects produce x-rays. The dependence Vb,= j(P) for a gap with a sharply inhomogeneous field has a clearly defined minimum. In [171] the parameters of radiation were changed in the following limits: the y radiation dose increased from 2.5 mOy to 250 Oy and the thermal neutron fluence increased from 2.109 to 2.10 13 s-l·cm- 2. For a maximum specific rate of ion formation of about 5.2.10 13 (ion pairs)'s-t, the stationary ion concentration in air reached approximately 5.6.109 (ion pairs)·cm-3 • The electric strength of gases at low pressures (in the region of the Townsend discharge) depends on irradiation only weakly.

200

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

The effect of irradiation sharply intensifies under simultaneous exposure to other unfavorable factors, including elevated temperature, vapor, chemical substances, etc. This mode of operation is typical, for example, of insulation of cables and electric motors in emergency situations at atomic power stations. The problem area is the protective shield of a nuclear reactor, where insulating materials are exposed to radiation both during emergency and normal operation. During routine operation, insulation is irradiated by y rays and slow neutrons, and insulation failure is almost completely due to y rays. The dose rate depends on the arrangement of insulation (for example, of cable insulation) and lies typically in the range 0.11 Gy/h. At a dose rate of 0.5 Gy/h, the tota140-year dose (the planned service lifetime of nuclear reactors) will be approximately 0.2 MGy. In an overheating emergency, the dose rate varies with time, and a few seconds after the accident, it reaches 0.1 Gy/h; then it slowly returns to its initial value over about a year. In this case, the total radiation dose will be 5 MGy. When containers of one or more fuel rods rupture because of coolant loss, fission products penetrate the housing zone, and J3 and y rays are emitted. In this case, emergency pumps must continuously pump water out, and ventilators must continuously decontaminate the atmosphere, operating under full load under conditions of high-power radiation, high temperature, vapor, and chemical agents used for decontamination. The duration of operation under such extreme conditions can exceed a year before deactivation is complete. Notwithstanding the probability of this event being very low, standards relating to the choice and testing of ElM intended to operate under such conditions have been carefully prepared. Tests of ElM and electrical equipment modeling of coolant loss are very complicated and expensive, since the examined objects must be simultaneously subject to the cited factors. For this reason, researchers must model exposure to fewer factors, such as, for example, radiation and temperature. In this case, aging is accelerated by increasing the y radiation dose, but it still seldom exceeds doses observed in emergency situations. Sometimes, aging is accelerated by increasing the temperature and oxygen concentration (tests in an oxygen atmosphere at elevated emergency situation, the temperature, relative hupressures). When modeling midity, and elemental composition of the ambient medium must correspond to actual emergency situations. Laboratory tests on radiation resistance are regulated by the lEe and National Standards. However, even after simplified laboratory tests, the development of practical recommendations is a complicated problem. Under the combined influence of radiation and temperature, ElM service lifetime differs considerably from that recorded under exposure to one of these factors or after repeated exposure. Different materials respond differently to such actions. Polyimide, polyvinylformal, and polysiloxane are aged much more slowly due to simultaneously elevated temperature and radiation than due to elevated temperature alone. On the other hand, teflon, polyimide, and complex polyethers rupture much faster under the simultaneous action of both factors, that is, significant synergetic effect is observed for them. A polytetrafluorethylene and hexafluoropropylene conjoint is decomposed by exposure to radiation at room temperature because of breaking of its

an

8.1 Ionizing Radiation

201

molecular chains. However, at temperatures exceeding its glass-transition temperature (Tgi = 353 K), the cross-link formation process dominates. If a sample is irradiated in a nitrogen atmosphere at the temperature Tgh the processes are compensated, and no significant changes in polymer properties are observed. The above examples demonstrate that even for ElM of one type (polymers), the type and rate of viable reactions under the influence of external factors are virtually unpredictable. Each individual material must be investigated. The ambient atmosphere and rate of dose absorption significantly influence ElM radiation resistance. Rates of oxidizing reactions with the formation of peroxides and hydroperoxides can increase under exposure to radiation. Moreover, an important factor here is the rate of oxygen diffusion into the polymer, due to which the rate of dose absorption influences the total dose producing the given effect. If a sample is irradiated for a long time with a small dose in the presence of oxygen, the resistance of the material to radiation damage is 2-3 orders ofmagnitude less than for sample irradiation in vacuum or an inert gas atmosphere. This implies that accelerating aging by increasing the dose absorption rate might yield results inconsistent with actual conditions. The sequence in which aging factors are applied is important for radiationinduced changes in materials. Aging at an elevated temperature after y irradiation produces stronger degradation than aging under simultaneous exposure to these factors. Thermal treatment of a polymer after irradiation produces intermediate products of radiation decomposition-free radicals, unsaturated compounds, hydrogen peroxide, etc. Thermal aging followed by y irradiation produces nearly the same effect as irradiation alone. As shown in [172], for cross-linked PE (Tme1t = 383 K, P - 0.92 g/cm3, and 50% crystallization) subject to y radiation from a C060 source at elevated temperatures, the combination of these factors can be ordered in terms of increasing oxidation effect as follows: radiation-temperature, then radiation-radiation, then temperature-the two factors act simultaneously. Mechanical stresses that arise during production of polymer parts or during their operation strongly affect the polymer behavior under exposure to radiation. The dielectric characteristics (tan 8 and E) and electric strength of mechanically stressed LDPE (d= 55 J..LIfl) and PK-2 and PK-4 grade polycaprolactam films (d= 60 J..LIfl) were investigated in [173] under irradiation with y rays from a Co60 source with a dose rate of30 kGylh, energy of 1.25 MeV, and doses up to 1 MGy. Simultaneous exposure to radiation and mechanical stress intensify radiationinduced effects-an increase in E and tan 8 and decrease in Ebr (Fig. 8.4). This can be explained by the intensification of oxidation-destructive processes. The increase in Ebr of unloaded PE with increasing y radiation dose results from radiation-induced cross-linking. Preliminary orientational pulling has essentially no influence on the dependence of Ebr in PE films exposed to y radiation, and weakens it in polycaprolactam films. Thus, we can conclude that dose and dose rate effects that accompany changes in other factors-temperature, O2 content, moisture, etc.-are ambiguous. Oxygen

202

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

o

20

40

60 D'lO-4, Gy

Fig. 8.4. Behavior of Eb,lEo in PK-2 (1), PK-4 (2), and PE films (3). Curves 1'-3' illustrate the same behavior but under a 20 MPa load

is the key factor in chemical degradation processes under exposure to radiation. When the radiation dose increases, oxygen is quickly consumed, and hence the damage to insulation decreases. The foregoing effects make the prediction of ElM behavior under multiple influences difficult. High radiation resistance of inorganic dielectrics is also maintained under the combined influence of the aging factors, although additional factors (especially elevated temperatures) influence the properties of dielectrics exposed to radiation. For example, for a fixed intensity of reactor emission (y rays + neutrons), a lower temperature exists (approximately 800-1100 K), beyond which radiation effects are enhanced by heating-the higher the radiative intensity, the stronger the effects. For static reactors, the electrical conductivity of ceramic materials depends linearly on the dose rate of gamma and neutron radiation. For pulsed reactors, the resistivity of ceramic materials also decreases with increasing dose rate, but nonlinearly. Thus, according to [174], Pv of a porcelain sample decreased by 20% when the dose rate doubled (over the full range of elevated temperature), whereas for an CNT sample (a certain kind of ceramic) it decreased by 1.5 orders of magnitude. The samples were irradiated in a pulsed reactor with two levels of gamma/neutron radiation. The y radiation dose rates were 35 and 17 kGY'S- I, the fluences of neutrons with energies exceeding 0.1 MeV were 6.8.10 14 and 3.4.10 14 S- I'cm- 2, the pulse width at half maximum was in the range 0.1-2 ms, and the average energies of neutrons and y rays were 1 MeV. Insulation exposure to high-power fast neutron fluxes is typical of thermonuclear reactors. Without significantly increasing shielding cost, insulating materials will accumulate a dose of the order of 108-109 Gy over 20-30 years of operation of tokamak thermonuclear reactors. In this regard, investigations of the behavior of various insulating materials under such exposure acquire new significance. It is difficult to correctly assess the contribution of neutrons to ElM degradation under exposure to radiation emitted by conventional and pulsed nuclear reac-

8.1 Ionizing Radiation

500

T 'HlO - A JOO

1

203

t i-I-at~ 11 t A

~

200 100

o Fig. 8.S. Dependence of Ebr in an LDPE film (d = 20 J.1m) on the absorbed dose of neutron radiation for pulsed voltage

tors because of accompanying y radiation. In addition, the spectrum of fission neutrons differs considerably from the spectrum of neutrons spawned by thermonuclear fusion. In this regard, to predict the ElM behavior in thermonuclear reactors, pure sources of fast neutrons are required. Studying collective ion acceleration by high-power electron beams, with concomitant development of sources of high-power pulsed neutron radiation for thermonuclear fusion, enable one to obtain neutron beams with an intensity of 1021 S-I· m- 2 or higher. In tum, this enables the radiation resistance of materials that are promising for thermonuclear power engineering to be investigated under repeated irradiation by high-power pulsed neutron flux. The problem of electrical insulation for thermonuclear reactors can be addressed by using radiation-resistant inorganic insulation. However, this method increases reactor cost. In addition, not all reactor systems can be insulated by inorganic ElM because of inferior suitability of inorganic ElM for industrial production as compared to organic ElM. At neutron irradiation doses up to 105_10 6 Gy, the electric strength of polymer insulation changes negligibly (Fig. 8.5), whereas radiation-induced conductivity increases by about an order of magnitude [175]. LDPE samples 30 /lm thick with deposited aluminum electrodes 20 mm in diameter were investigated in [175]. Breakdown was initiated at a pulse leading edge with slope 10 kV/l-ls. The pulsed neutron flux with a fluence of 10 16 S- I· m- 2 (E> 0.5 MeV) corresponded to a reactor power of 100-300 kW, and the radiation dose reached 5.106 Gy. It was established that the increase in electrical conductivity is attributable to neutron activity, and that ElM radiation aging in nuclear reactors is attributable to neutrons rather than y rays. Until recently, because conventional polymers have insufficient radiation resistance, attention of researchers have been focused on composite ElM (convention-

204

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

ally, epoxy resins filled with inorganic materials) possessing high radiation resistance. Advances in space materials science led to the synthesis of new aromatic polymers that exhibit high thermal stability. Analysis of their chemical structure predicts high radiation resistance. Novel materials like polyphenylene sulfide (PPS) and polyaryl etheretherketone (PEEK) exhibit good mechanical properties at cryogenic temperatures. Investigations of their radiation resistance compared to the polyethylene terephthalate (PETP) and polypyromellite imide (PM) stabilities at cryogenic temperatures have shown that both materials have high stability at doses up to 8 MGy and T> 20 K. However, PEEK exhibits enhanced brittleness at cryogenic temperatures even without irradiation. For this reason, using it in superconducting magnets of thermonuclear facilities is undesirable. The PPS material, like PM, is a good ElM for these applications. Figure 8.6 summarizes the data on the resistance of various polymers to y-ray damage, and their suitability for insulation at doses from 102 to 108 Gy [177].

8.2 Electron and Ion Beams Alteration of the dielectric characteristics of solid insulating materials. Insulation elements of electron and ion accelerators and materials coating the exterior surface of space vehicles orbiting in the Earth's radiation belts are exposed to electron and ion fluxes with broad energy spectra. Just as when they are exposed to y rays and neutrons, dielectrics exposed to electrons and ions undergo reversible or irreversible changes in the material structure and properties, which depend on the radiation parameters and the properties of the material. However, during irradiation of dielectrics by charged particles the key factor in many cases becomes the accumulation of radiation-induced charges that can markedly alter the high-voltage electrical insulating properties, create internal fields exceeding the electric strength of the dielectric material, initiate breakdown, and cause insulation failure [180]. Both with a potential difference and without it, the charged dielectric can produce electromagnetic fields that cause radio and electronic equipment to fail. Insulation of space vehicles is irradiated by electrons and ions with energies in the range 10-20 keY. Electrons that penetrate the subsurface insulation layer are most dangerous for insulation, because they can initiate breakdown. This problem is presently under study in many countries. Research results have been discussed at many conferences, and presented in hundreds of papers. By now various methods have been developed to diagnose fields induced by SC upon irradiation of dielectrics [178]. The influence of electron irradiation on ElM electric strength under conditions of efficient charging of materials can be discerned in investigations of laminar plastics possessing high radiation resistance performed in [181]. A significant change in the electric strength occurs when the absorbed doses of ionizing radiation exceed 106 Gy. The two kinds of foil fabric glass laminate samples with thicknesses of 0.2 and 0.5 mm, respectively, and fabric glass laminate with a

8.2 Electron and Ion Beams

,

RIlZlzzZ2zz,

Extent of damage

Utility of organic materials

Incipient to mild Mild to moderate Moderate to severe

Nearly always usable Often satisfactory Limited use

205

Gamma dosa. rad (8i) (1 rad=10·2 J!kg)

,

10·

Phenolic, glass laminate Phenolic, asbestosfilled Phenolic, unfilled Epoxy, aromatic-type curing agent Polyurethane Polyester, glass filled Polyester, mineral filled Diallylphthalate, mineral filled Polyester, unfilled Mylar Silicone, glass filled Silicone, mineral filled Silicone, unfilled Melamine-formaldehyde Urea-formaldehyde Amiline-formaldehyde Polystyrene Acrylonitrile!butadiene! styrene (ABS) Poly,mide Polyvinyl chloride Polyethylene Polyvinyl formal Polyvinylidene chloride Polycarbonate Kel-F polytrifluorochloroethylene Polyvinyl butyral Cellulose acetate Polymethyl methacrylate Polyamide Vinyl Chloride-acetate Teflon (TFE) Teflon (FEP) Natural rubber Styrene-Butadiene (SBR) Neoprene rubber Silicone rubber Polypropylene Polyvinylidene fluoride (Kynar 400)

,

10"

10'

,

10' I

10'

10' I

J

I I

I

,

I

I,

,

I

~I

I ,

I I

I

I

I

Fig. 8.6. Resistance of the indicated materials to y irradiation, and their suitability for insulation under different doses

thickness of 0.5 mm placed between the flat electrodes 10 and 20 mm in diameters with rounded edges were investigated. The sample dimensions were 60 x 60 mm. The breakdown voltage Ubr was measured for dc voltages and ac voltages at a frequency of 50 Hz. The "Tonus" (with radiation pulse width of 50 ns and electron energies in the range 0.5-1.0 MeV) and ML-1 (with pulse width of 10 ns and

206

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

--t--+--~J

o

10

D'IO-4 Gy

Fig. 8.7. Dependence of Ubr (50 Hz) on the dose absorbed by foil glass laminate (1), foil fabric glass laminate with d=0 .5 mm (2), and d=0.2 mm (3) samples

electron energy of 0.2 MeV) accelerators were used as radiation sources. The beam current density varied over the range 0.1-4 kA/cm 2; the examined samples were irradiated in air through a collimator 20 mm in diameter. Figure 8.7 shows the dependence of Ubr at 50 Hz on the dose absorbed by three plastics. For all of them, the breakdown voltage decreases with increasing dose, although at different rates. At doses of about 105 Gy, foil fabric glass laminate samples fail (foil peels off the substrate). All the examined materials are charged upon irradiation; electrization is especially efficient for fabric glass laminate. Upon irradiation by pulses of electrons with energy of 0.8 MeV and current density of about 2 kA/cm2 , a spontaneous breakdown occurs. Measurements of Ubr at different times after irradiation, that is, for different levels of the residual SC, have shown that for dc voltages, the SC significantly influences the electric strength, whereas for ac voltages, Ubr is virtually independent of the pause duration. The greatest decrease in the breakdown voltage Ubr is observed when the particle mean free path is less than the ElM sample thickness and the sample is irradiated from the anode side. As indicated above, breakdown of an irradiated dielectric can be initiated spontaneously, without an external field, during irradiation or after irradiation termination when a metal needle comes in contact with the dielectric surface, a nonmetallic object strikes it, high-velocity microparticles hit it, laser radiation acts on it, etc. If the dielectric has a very high electric strength, the ponderomotive forces in a charged dielectric can reach the mechanical strength of the dielectric and disrupt the material continuity, thereby initiating a spontaneous mechanoelectric breakdown. Under simultaneous mechanical and electrical loading, the ponderomotive and mechanical stresses are summed; therefore, acharged dielectric fails at lower mechanical loads than an uncharged dielectric. In turn, the electric strength of solid dielectrics under mechanical loads may decrease (see Sec. 3.1). Provoking actions on charged dielectrics are probable not only during various experiments with HES but also during operation of space vehicles whose external parts are subject to the micrometeor bombardment. Electrical breakdown initiation in radiatively charged glass was investigated in (182] by simulating micrometeor

8.2 Electron and Ion Beams

207

bombardment using micron-sized solid (aluminum) particles with masses of the order of 10-12 g, accelerated to speeds of several kilometers per second. The production of isolated discharge figures was detected in the sample after every exposure to particles. As in collisions with an uncharged dielectric, plasmoids containing partially ionized particle and target materials and emitted electron and ion fluxes are formed. The electron component of the secondary emission from charged glass exceeded that from uncharged glass by an order of magnitude, and when breakdown was initiated, this excess reached two orders of magnitude. Akishin et al. [182] pointed out the following factors of breakdown initiation: - decrease in the electric strength of a mechanically loaded dielectric due to a particle collision - formation of a local shock wave with a pressure at the shock front of 1081011 Pa (for a particle velocity of 2-4 km!s), at which the electrical conductivity of a number of dielectrics (teflon, PE, and glass) increases by 12-14 orders of magnitude - ionization at the shock front and current generation in the presence of a strong SC field in the dielectric lead to discharge propagation. The main mechanism of laser breakdown initiation in charged glasses is the distortion of the homogeneity of an electric field, created in the dielectric volume by the space charge, by the optical breakdown. Two main factors of field distortion due to the optical breakdown were pointed out in [183]: the crack growth in the optical breakdown region and the plasma formation due to the optical breakdown. By the time the laser pulse terminates, the length of the crack which grows in a borosilicate glass with maximum rate of 1.5.105 cmls reaches about 10 J.11ll. Microcracks of such sizes not only play the roles of microtips strengthening the field but also weaken the dielectric. The optical breakdown plasma in the dielectric volume is equivalent to a conductive inclusion which distorts the electric field. In addition, the plasma supplies free charge carriers and hence makes a discharge formation easier. When the optical breakdown initiates shock waves with a pressure in the wave front equal to several hundred gigapascals, breakdown can be initiated due to the many-fold increase in the electrical conductivity of the dielectric (virtually up to the metallic conductivity). In the experiments described in [183], the laser radiation energy was less by three orders of magnitude than the energy required for metallization. Widespread use of high-current electron beams (HEB) in experiments and a start of engineering beam applications have made the study of the behavior of dielectrics under such actions urgent. In [184, 185] a failure of high-ohmic materials (dielectrics and semiconductors) exposed to high-power electron beams was investigated. As a possible mechanism of failure, an electrical breakdown initiated outside of the region of beam propagation in the field created by the injected HEB SC was suggested. For some materials, the threshold energy densities leading to a failure Wr were found in modes of single and repeated HEB actions. For different materials they lie in the limits from several hundredths to several joules per square

208

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment F(n)

Fig. 8.8. Distribution function of the number of pulses withstood before breakdown of nonirradiated LOPE (1) and LOPE irradiated with a dose of 1.95.105 (2), 3.9.105 (3), and 7.10 5 Gy (4)

centimeter. Naturally, in the mode of a single HEB event, failure occurs at larger values of Wf • Since the fonnation of SC capable of creating fields sufficient for a sharp decrease in E br or even for breakdown without application of an external potential difference is detennined by the dynamics of radiation-induced conductivity of the material, many publications were devoted to this problem (see Sec. 8.1). When electrization of a dielectric upon irradiation by charged particles is not dominant (above all, when the particle mean free path is greater than the dielectric layer thickness), reversible and irreversible radiation-induced changes, on the whole, are similar to those observed during reactor irradiation. Figure 8.8 shows the data obtained on LDPE irradiation by lO-MeV protons with mean free paths longer than the sample thickness (d= 0.4-0.7 mm) for 2.5-9 min (the absorbed dose was in the range 2.105-7.105 Gy) [179]. The samples were tested with aperiodic pulses of 3/4 JlS duration with positive polarity and a pulse repetition rate of 400 pulses/so The average electric field in the sample was 75 kV/mm (the diameter of the high-voltage electrode was 10 mm, and its radius of curvature was 0.5 mm; the diameter of the grounded electrode was 35 mm). Along with other properties, the PE electric strength was also measured under exposure to radiation. The number of pulses withstood before breakdown (for breakdown probability of 0.632) decreased by more than an order of magnitude when the absorbed dose increased from 2.10 5 to 7.10 5 Gy. Moreover, the distribution function of the number of pulses withstood before breakdown also changed: for 10 3_10 5 pulses it in-

8.2 Electron and Ion Beams

209

creased, whereas for 106-107 pulses it dropped to approximately half the value in nonirradiated samples.

Effect of beams on the electric strength of vacuum gaps. In high-current electron and ion accelerators, above all in coaxial diodes with magnetic insulation, a number of electrons escape the accelerating electron beam from different sections of the beam acceleration trajectory and bombard the surfaces of structural elements, including insulation surfaces. In this case, electrons and ions with broad energy spectra are produced via secondary emission. In turn, they affect surfaces of electrodes and insulating materials. In segmented through insulators of diodes, the sections adjacent to a grounded bearing flange are most strongly affected by electrons in the reverse current of the cathode holder. The greatest decrease in flashover voltage in vacuum results from electrons with relatively low energies (approximately 10 keY). Such electrons affect ElM surface layers and intensify desorption and secondary emission processes. Higher-energy electrons penetrate deep into ElM and do not produce prominent surface effects. In the bombardment of the anode surface of a vacuum gap, the temperature rises and bremsstrahlung is produced. Heating is accompanied by desorption of impurities and direct action of electrons on adsorbed gas and impurity molecules. In this case, these molecules can be ionized or excited, and their sorption bond can be changed, which is also reduced to desorption. Each incident electron can release up to 7-12 molecules, that is, the electron-stimulated desorption has a high yield. Anode exposure to high-power electron fluxes can lead to melting and vaporization of the anode material. The ion bombardment of the cathode of a vacuum gap changes considerably the cathode surface state and its emission properties. This intensifies the surface self-diffusion processes leading to changes in the cathode microtip shapes, that is, to their tapering. In this case, singly and multiply charged ions of the cathode material and desorbed impurity molecules leave the surface. The intensity of this process increases approximately linearly with increasing energy of bombarding ions. The ratio of the number of molecules of the material leaving the unit surface element and transforming into the gas phase during the ion bombardment to the number of bombarding ions TJ also depends on the flux intensity, the cathode temperature, and the duration of the ion bombardment process. For ion energies of several keY, h is in the approximate range 10-40. At cryogenic cathode temperatures, the intensity of the ion-stimulated desorption is extremely small. For high-power ion fluxes, the cathode-material sputtering process becomes significant. In the bombardment of the electrodes of a vacuum gap by charged particle fluxes, the processes related to microdischarges in desorbed gases and to the exchange processes (mutual emission) are the key factors in breakdown initiation. In the steady state (I> 10-5 s), the anode breakdown mechanism dominates, and the anode surface state and material significantly influence the electric strength of the vacuum gap. A procedure and programs for computation of the vacuum gap characteristics, including the dependence of Ubr (or E br) on d, the voltage-time characteristics under exposure to beams, the parameters describing different mechanisms

210

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment Ebr

kV/mm

35

f

z

J

'r d, mm

Fig. 8.9. Dependence of Ebr of a vacuum gap on the gap length when the anode was irradiated by an electron beam with the current 1=0 (1), 0.51 (2),0.73 (3),1.16 (4), and 1.51 rnA (5). The exposure time was 1 s

of fonnation of charged particles at the anode and cathode, etc. were developed in [186]. Numerical calculations were carried out for vacuum gaps fonned by molybdenum and steel electrodes with various adsorbed gases for voltages increasing in the range 0.1-1000 kV, current densities up to 50 mA/cm2, and the anode temperatures T= 125-1750 K. The calculated maximum breakdown field strengths under exposure to electron beams (Ebr::::: 3.4.10 7 VIm or with allowance for the field amplification on inhomogeneities, E odA.l0 8 V/m) are much less than the

threshold ones for field and explosive emissions (5.10 9 Vim). The results of calculations were confinned by the experiments in which the anode was bombarded by an electron beam with currents increasing in the range 0.51-1.51 rnA through the cathode aperture. The dependences Ebr(d) and tl.Ubr(d) have extrema (Figs. 8.9 and 8.10). Ion beams reduce the electric strength of vacuum gaps stronger than electron beams. Moreover, the electric strength (1-15 kV/mm) is comparable to (and in some cases even less than) the flashover strength. This adds the specifics to coordination of vacuum insulation in systems with charged particle beams. Bremsstrahlung, like electron and ion beams, affects essentially all structural elements of the diode, including the insulator, housing, electrodes, and cathode holder. Upon exposure to x-rays, gases desorb from surfaces and structural changes occur in materials, primarily polymer insulation. By the time the electron energy reaches 400 eV, between 2.5.10-2 and 4.5.10-7 gas molecules might be desorbed by each x-ray photon. Desorption processes intensify with increasing xray intensity and dose, possibly leading to vacuum insulation breakdown at reduced electric field gradients. A consequence of the action of electrons and ions on the structural elements of high-voltage vacuum systems is the charge accumulation on their surfaces. This causes reconfiguration of electric fields, and under certain conditions reduces the

8.2 Electron and Ion Beams

211

___......... 5

o

1

2

J

If d mm

Fig. 8.10. The same as in Fig. 8.9 but for the relative decrease in the breakdown voltage

°

i

/l,.Vb, = Vb,V-OVb, . 100%0 (Vob, and Vbi , are the breakdown voltages of nonirradiated and b,

irradiated gaps, respectively)

flashover voltage for the insulator surfaces exposed to vacuum. The reason of charging can be either deposition of primary electrons and ions or the secondary emission from the insulator surface under the bombardment by primary electrons. In [187] it was demonstrated that the ion surface charge with density in the range 10-4_10- 3 C/m2 reduces Ufl by a factor of 1.5-2. A flashover occurred in the system of electrodes with the dominant normal component of the electric field vector (the model of a lead-out). Breakdown was initiated at the negative pulse front with the slope a = 0.5-5 kV/f.!s for dc voltages. The high voltage was applied from several seconds to several minutes after switching off the ion source. The characteristic spreading times for charges with densities in the range 10- 5-10-4 C/m2 have the order of 102_10 3 s. On the periphery, the charge leaves faster. In external electric fields up to 4.10 4 Vim, the drift velocities of ions are (2-5).10- 5 mls. The ion source (the moving plasma) ensured ions with energies in the range 0.23 keY, ion currents up to 80 rnA, ion concentrations up to 108 cm-3 , and a beam diameter at the exit from the source of 8 cm. From Fig. 8.11 it follows that Ufl in the presence of a charge over the entire surface between the electrodes is much less than in the absence of a charge, and depends only weakly on the interelectrode gap length. The strong dependence of Ufl on the pulse front slope and the weak dependence on the charge density cr are observed when the latter exceeds 0.25·10-4 C/m2 . When a flashover occurs, the charge vanishes almost completely from the dielectric surface. The voltage-time characteristic has an exotic overturned shape, that is, Ufl decreases from 2.3 to 1.3 kV when the voltage duration decreases from 10 to 1 f.!s for 11 = 0.1 mm, d = 10 mm, and cr = 10-4 C/m2• When only a part of the surface (for example, a

212

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

Un, kV \

J

2 1

\

S~ "-

o

0.25 0.5

1

Z J

(J' )

04, C/m 2

Fig. 8.11. Dependence of Ufl on the precipitated charge density for different slopes of the high-voltage pulse a = 7.10 9 (1), 2.109 (3), and 109 Vis

spot) is charged rather than the entire surface, Ufl decreases only when the charged surface area is in contact with the cathode. As soon as this contact breaks, Ufl increases sharply and reaches the value of Ufl in the absence of a charge. Based on the Tramp-Van de Graaf criterion, the expression for calculating the voltage at the onset of a flashover was derived in [187]. After simplifications, it has the form

where W. is the binding energy of physical adsorption of particles at the surface (in calculations, W.= 0.5 eV). The above equation ensures good agreement with the experimental data reported in [187] and the data of other authors. Control of a gas discharge. Upon exposure to an electron beam in gases, neutral atoms are ionized by direct collisions with electrons of the injected beam (primary electrons). Under certain conditions, the resulting positive ions and secondary low-energy electrons can cause further ionization of the gas in avalanche-type processes, described for model representations by the following equations [188]:

ane(t) ns(t) ne(t) ne(t) at te te ts an;(t) ns(t) ne(t) --=--+-at te te '

---=--+-----,

where te is the characteristic time of electron collisional ionization (te = 1/nr-==6~.,.. ~f 363'

+.1303" - 4-

60

50 ~=-=+=--+-~-+----1

o

0.1

0.2

0.3

0.'" B , T

Fig. 8.15. Behavior of Vbr in vacuum gaps 3 nun long (p '" 10- 7 Pa) while exposed to dc voltage in various configurations, as a function of transverse magnetic field induction

(8.3)

Extrapolation of Eqs. (8.2) and (8.3) to larger H.L, for example to H.L = l.2 mAIm, leads to an increase in Vbr by a factor of 5-10 in the first case and 2-4 in the second. The electric strength of coaxial vacuum diodes with magnetic insulation is analyzed in detail in [207]. By now the record electron-beam parameters (140 kJ) have been obtained exactly with these diodes. However, in these systems the efficiency of energy transfer from the storage device to the beam remains only 2026%. One of the main factors limiting the output parameters of vacuum diodes is breakdown initiated transverse to the magnetic field. Based on an analysis of many experimental and theoretical investigations, Bugaev and Kim [207] conclude that the breakdown of forward-biased diodes (in which the center electrode of the coaxial system is the cathode) is initiated because of the centrifugal instability due to cathode plasma motion transverse to the magnetic field. To increase the electron beam energy, they recommend using reverse-biased diodes in strong magnetic fields and forward-biased diodes in inhomogeneous magnetic fields, with the field strength B rapidly increasing in the direction from the cathode to the anode. In this case, special measures must be undertaken to suppress the reverse current.

230

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

Un,kY

ISO

J20

'tOO H !eNm

Fig. 8.16. Behavior of Uf! for cylindrical organic-glass (1), teflon (2), and polycaprolactam (3) insulators in vacuum (p = 10-4 Pa) as a function of the transverse magnetic field strength for dc voltage and h = 2 (1 and 2) and 4 mm (3)

In reverse-biased diodes, one reason for electric strength failure is anode plasma propagation transverse to the insulating magnetic field due to centrifugal instability as well, but in a plasma layer adjacent to the anode. As a consequence, the electric strength and the diode withstand time prior to breakdown depend on the material used in the center electrode, and on magnetic field characteristics. The flashover voltage of solid insulation in vacuum is a complex function of the magnetic field parameters. In most cases, transverse magnetic fields reduce Uf!; in this case, the behavior of Uf! as a function of H1- depends on the orientation of the insulator surface relative to the electric and magnetic field vectors. A longitudinal magnetic field whose strength varies over a wide range has essentially no influence on Uf!. For example, Avdienko [208] shows that a magnetic field ranging from 160 to 240 kAlm perpendicular to the electric field reduces Uf! by a factor of 1.5 in coaxial electrode systems with cylindrical and conical insulators. Further increase in H to 3.2 MAIm has essentially no effect on Ubr (Fig. 8.16). In this case, breakdown propagates only in a direction orthogonal to both the electric and magnetic fields, and the electron drift velocity vector is directed toward the insulator surface. These specific features are typical of dc voltages and voltage pulses, and insulators fabricated from a variety of materials, including organic glass, polycaprolactam, and teflon. The dependence of Ubr on the height and rake angle of an insulator in a magnetic field is the same as without a magnetic field, but with reduced absolute values. The influence of H on Uf! derives from the bending of electron trajectories by the magnetic field. A magnetic field parallel to the dielectric surface returns some of the electrons that have left a desorbed gas cloud to their original state. The relative number of such electrons increases with H until diffusion losses are fully compensated (at H = Her). Further increases in H do not influence the discharge processes or Uf! (Fig. 8.16). The numerical value of Her can be estimated by equating the Larmor radius to the thickness of the layer adjacent to the dielectric surface:

8.4 Magnetic Field

Her ~ 3.4~We fA,

231

(8.4)

where We is the average electron energy in the gas, and D is the gas layer thickness. The values Her = 240-400 kAlm, obtained from Eq. (8.4), agree satisfactorily with the available experimental data [209]. Figure 8.17 illustrates the magnetic field effect on Uf! of insulators in various configurations. It can be seen that when H1- increases to 0.5 T, Uf! of a conical insulator is 30% than without a magnetic field. Further increase in H1- to 1.7 T has essentially no effect on Uf!. For insulators consisting of a flat or slot washer, Uf! increases with H when it exceeds 0.5 T. The magnetic field markedly affects the gas discharge characteristics, and in particular, the electric strength when the radius of the Larmor orbit is less than or equal to the particle mean free path. For the right branch of the Paschen curve, the critical magnetic field Her at which it affects the gas discharge is given by the expression

Her =(mfe)Avp,

(8.5)

where A is a constant defming the relationship between a. and the gas pressure p, and v is the charged particle velocity, equal to the vector sum of the thermal velocity and the drift velocity in the electric field. Since the average velocity v does not depend on the pressure, according to Eq. (8.5), the magnetic field H is proportional to p. The available experimental data [209] confirm this conclusion. A model of overlap between electron avalanches propagating from the anode to the cathode explains the effect of H. At atmospheric pressure in electric fields of -40-45 kVfcm, the transverse magnetic field can significantly influence gas discharge characteristics only when Her is at least 4 MAIm. The application of transverse magnetic fields leads to an apparent gas pressure rise. The gas pressure in combined magnetic and electric fields is given by

PH

=0.5Po(I+~(EPO + 16.1O-4 H 2 )/(Epo) ),

(8.6)

where Po is the gas pressure in the absence of a magnetic field. According to Eq. (8.6), PH is 102.4 kPa, 107.2, or 123.1 MPa at Po = 101.3 kPa in a magnetic field of 2.4, 5.6, or 11.2 MAIm, respectively. Since the principal characteristics of avalanche-type processes, such as the collisional ionization coefficient a. and electron velocity ve, depend on the gas pressure, the application of a transverse magnetic field causes the discharge onset time lag to vary, and for fixed voltage duration, it causes the electric strength to change.

232

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

Un kY r",

JOO

,

",r

I

.L

t

\,

200

_

- .+

LJ.

r>-,

" ,,

::----> ~!~ +~

,.oJ(

J(

u

"', fOO

.~

LJ.

' .............

1..-Ir--' ..

T

1

Sf mm

h"

_'I

-

-~o

0.5

1.0

1..f

HT

Fig. 8.17. Behavior of UII in organic-glass insulators with various configurations in vacuum (p :580 mPa), as a function of H for 1.5 Ils voltage pulses

Figure 8.l8 illustrates the calculated (solid curve) and experimental (open circles) behavior of the discharge onset time lag in air at atmospheric pressure, as a function of H1-, when the discharge is initiated by multielectron processes. The electron concentration here is of the order of 104 cm-3, d= O.l cm, and E = 42 kY/cm. The effect of magnetic field on the breakdown characteristics of liquid and solid dielectrics has very seldom been addressed in the literature, for want of practical applications. Paul, in a series of papers (for example, see [210]), analyzed the influence of a static, transverse magnetic field on the high-voltage conductivity and electric strength of liquid dielectrics. He demonstrated theoretically that irrespective of the bubble or purely electric mechanism of liquid breakdown, a transverse magnetic field hinders the multiplication of charge carriers and hence the onset of breakdown, because it bends the charge-carrier trajectories, and thus reduces their free paths. The available experimental data confirmed this conclusion. The electric strengths of benzene and toluene in discharge gaps formed by the Rogowski electrodes with interelectrode gap lengths of 1-2 mm were measured for dc voltages (Fig. 8.19).

8.4 Magnetic Field

233

J50~-+---+U-~--~

o

J.Z

II, MN m

5.~

Fig. 8.18. Behavior of discharge onset time lag in air at atmospheric pressure as a function of transverse magnetic field strength

"

2'1

20

--

)(

~

2_ ~

---

j

1

....x J x,..A 1 i.6--""" l. I.l.

)(

16 A

t

12 0

~-

0.2

0.11

0.6

0.6 B, T

Fig. 8.19. Dependence of breakdown voltage of benzene (1 and 2) and toluene (3 and 4) on transverse magnetic field induction for interelectrode gap lengths of I (1), 1.15 (3), 1.7 (2), and 2 mm (4)

Effects of transverse and longitudinal magnetic fields on the electric strength and dielectric characteristics (tan 8, e, and Pv) of new organic materials polyphenyl quinoxalines and polyoxadiazoles as well as on polypropylene were studied in [211]. The electric strength was measured for smoothly rising ac voltages. The electrodes were disks 25 and 75 mm in diameter. The results tabulated in Table 8.3 demonstrate that the magnetic field significantly influences the characteristics of the examined dielectrics only when B> 1.5-2 T. In this case, E br increases and tan 8 and e decrease with increasing B I , and all three parameters are essentially independent of B~. For polyphenyl quinoxaline, pv increases negligibly with B~, that is, the magneto resistive effect is manifest. It was not observed for polypropylene.

234

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

Table 8.3. Electric strength and dielectric characteristics of polymers in longitudinal and transverse (.1) magnetic fields Mate rial

Magnetic nux densiti es BII and BJ. [Tl Polypheny l 0 quinoxal ine 0.5 1 1.4 2 3 3.7 Polyoxad iazoles 0 0.5 1 1.4 2 3 3.7

Ebr

II

[MV/m] .1

2 10 2 10 2 10 2 10 220 226 230 0 0 83 5 90 95

210 210 210 210 210 21 1 212 80 0 0 0 80 I 2

tan 0 [10

J]

II

.1

5 5 5 4 3 2 1 30 30 30 30 20 10 9

5 5 5 5 5 5 4 30 30 30 30 ~O

20 10

(II)

I:

.1

3 3 2.7 2.7 2. 2.9 2.7 2.6 2.6 2.6 2.6 2.5 2.5 2.3

3 3 3 3 3 2.9 2.6 2.6 2.6 2.6 2.5 2.5 2.5

8.5 Electric Strength of Insulation and Intercontact Medium in Explosive Commutators Electric strength of detonation products of condensed explosives. Unique energy parameters of explosives lead to their wide use in different fields of science and engineering, including high-voltage electrical equipment and high-voltage engineering. Explosives are characterized by extremely high energy density. They can release energy with high power density at time ascertained to 10-{i s. Their use in magnetocumulative and magnetoexplosive generators enabled the development of high-power sources of superstrong magnetic fields, beams of charged particles, etc. High initial densities of detonation products (DP) and their high expansion velocities are successfully used in explosive commutators (EC), including breakers and contactors based on nontraditional principles. Fields of their most efficient application are bighvoltage electrical equipment (in particular, high-voltage and high-power pulse generators with inductive energy storage devices) and high-power electrical engineering (including protection of semiconductor transformers, clipping of short-circuit currents, protective breaking of emergency circuits, switching of responsible users to reserve feeders, etc.). Using explosive commutators, the ultimate parameters of pulses from generators with inductive energy storage devices are bounded from above by the voltage being restored in voltage commutators. In this case, the main commutator parameters are the speed of response and the electric strength. Among the processes governing the basic characteristics of closing commutators and their

8.5 Electric Strength of Insulation and Intercontact Medium

235

subsequent operation, a highly important role is played by recovery of the electric strength of gaps (see Sec. 8.7). The key process for breaking low-voltage circuits of "fast" HES commutators and synchronized Ee is recovery of DP electric strength. An important problem of "slow" commutators for high-power circuits in which transformer oil is used as the insulation medium is the electric strength not only of DP but also thermal oil decomposition products (exposed to the arc), mixture of these products with DP, and transformer oil contaminated by these products. The first studies of DP electric strength of condensed explosives were not published until the early 70s. Even now, only a few papers have been published on this subject. There are two main reasons for this-the complexity and laboriousness of the experiments, and difficulties in modeling the processes in actual commutators under laboratory investigations. Although just after detonation the DP electric strength is of the same order as that of solid dielectrics, the electric strength of DP in actual systems is nearly two orders of magnitude less (10-25 kV/cm) [212, 213]. This difference is primarily due to the fact that detonation products in commutators expand. In this regard, it is important to know the DP electric strength at different times as well as the dependence ofDP electric strength on various factors (for example, the DP type, the concentration and type of additives, etc.). The rate of increase in the electric strength within the intercontact gap of an explosive commutator is determined by the rate of energy dissipation in the arc when it interacts with shock waves and detonation products. As shown in [212, 214], in breakers based on conductivity decay behind the detonation front, the growth of the voltage being restored can initiate a DP breakdown. After breaking, when repeated ignition can only result from detonation products, the restoring electric strength of the gap can be determined without preliminary passage of a current through the gap. Modeling the actual propagation of detonation products in a breaker due to charge explosion and considering that the electrodynamic forces do not affect the character of the DP separation, the curve depicting the restoring electric strength of the breaker can be identified with the voltage-time characteristic of the model explosive gap. Figure 8.20 [214] shows the voltagetime characteristic of a discharge gap filled with expanding pentaerythritol tetranitrate (PENT) detonation products. It can be seen that Uhr is essentially independent of t when it increases from 30 to 100 f.ls. Then Uhr decreases rapidly, and is roughly proportional to the decrease in the detonation product density. This suggests that the t-independence of Uhr over the curve segment in question is due to the approximately equal but opposite effects of two factors-an increase in gap length due to electrode displacement due to the explosion, and a decrease in the DP electric strength due to a decrease in their density. To determine DP electric strength, the shape and length of the discharge gap before breakdown initiation must be known, because the discharge gap length changes due to asymmetric electrode displacement under exposure to DP. The rates of interelectrode gap length increase recorded in [214] are in good agreement with calculations of the mass velocity of the electrode material behind the shock wave.

236

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment Ubr>

kY

60 50 IHJ

30 20 fO

o

ZO '10 60 60 fOO f201'l0 t, j..ls

Fig. 8.20. Behavior of Ubr in expanding PETN detonation products (bulk density 1 glcm 3) as a function of the time lag between the trigger pulse and interelectrode gap breakdown. An interelectrode gap 2.5 mm long was formed by the flat ends of cylindrical electrodes 42 mm in diameter

Fig. 8.21. Ubr ofpentaenythritol tetranitrate DP as a function ofthe time since explosion for

d 1 = 10 (1), 20 (2), and 30 mm (3)

The fast decrease in Ubr for t ~ 80-100 f.lS probably results from the low rate of interelectrode gap lengthening and the high rate at which the DP density decreases. In this time interval, the DP density is less than I % of the density of the detonation wave; Ebr decreases roughly linearly from 120 kY/cm at t = 30 f.ls to 20 kV/cm at t = 150 j..ls. DP breakdowns at average field gradients less than 20 kV/cm can be due to a DP pressure drop below atmospheric pressure due to their inertia. Before the radial DP separation (at t ~ 15 f.ls), their electric strength was about 180 kY/cm. Detailed investigations [215] of DP breakdowns for small time lags between the explosive ignition time and the time of high-voltage pulse application (when DP expand to distances greater than ten charge radii) show that the time dependence can be depicted by curves with maxima (Fig. 8.21). An exploding spherical PENT charge with a mass of 1.8 g and a density of I g/cm 3 was used in [215]. The high-voltage pulse was synchronized with PD ignition by using an ionization sen-

8.5 Electric Strength ofInsulation and Intercontact Medium

237

10r----------r--~~~~F_--_4

10 1--------,~'____if__-------+--_4 x-I

.

0-2 C) -J

-"-

• -s

o

o.s

1.0 p, MPa

Fig. 8.22. Static breakdown voltage Ubr of the DP of PENT (2), hexogen (3), ammonite (4), and EW 8G explosive (5) as a function of pressure, compared to the breakdown voltage of air (1)

sor at a distance d2 from the charge. A 160 kV sounding pulse with 'tfr= 0.2 J..Ls was applied across the gap, located at a distance dl from the charge. The breakdown voltage of the gap Ubr was measured 5-30 IlS after the explosion at points d l = 10-50 mm when d2 = 15-80 mm. A gap 5 mm long was formed by coaxial electrodes with end curvature radii of 0.15 cm. As can be seen from Fig. 8.21, Ubr increases from 35 to 95 kV as t increases from 5 to 17 IlS due to the pressure (DP density) increase resulting from interaction between rarefaction waves and the DP compression wave. The decrease in Ubr for t > 15-20 Ils results from the pressure decrease in expanding DP, which also causes Ubr to decrease with increasing d l • The electric strength of DP from the explosive chamber was investigated in a separate discharge chamber for a slowly rising voltage. It depended only weakly on the explosive type and increased almost linearly when the pressure rose in the range 0.1-1 MPa (Fig. 8.22). It can be seen that the DP electric strength is less than that of air over the entire range of pressures examined. DP electric strength can be increased by injecting explosive additives containing molecules with higher electron affinity. In this case, the electric strength increased by a few percent to some tens of percent. For example, this effect was observed in [214] when fluoroplast, which decomposes into fluorine molecules, was injected into PENT.

238

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

, M~----r---~~~~~ 1Dt--~~

~~--~----~----~

SDk~~~~k.!--l

1

2

J

1, IlS

Fig. 8.23. Temporal behavior of the pulsed breakdown voltage of detonation products of PETN (1), hexogen (2), and a 90% PETN + 10% talc mixture (3). The gap was formed by tip electrodes with d = 0.5 mm

Electric strength of a mixture of transformer oil decomposition and detonation products. When transformer oil is used as the arc-suppression medium in explosive commutators, the intercontact gap is separated from hot DP by a dielectric liquid. By virtue of low compressibility of the latter, the DP action on the arc is transmitted essentially unchanged. In addition, the energy absorbed by the liquid is expended on its decomposition. Gaseous products increase the pressure in the pressurized chamber, and heat removal from the arc is intensified. At the same time, the improvement of the commutation characteristics so obtained is accompanied by the complication of the commutation process and a wider variety of phenomena taking place in the intercontact gap. The composition of the intercontact medium can vary over a wide range that depends on the structural elements of the device, the volume of the working chamber, the degree of chamber filling with the transformer oil, the mass of explosive, and its location relative to the liquidgas interface. Successful breaking of an electric circuit depends on the electric strength of either the vapor-gaseous mixture of DP containing transformer oil particles at various concentrations, or the pure transformer oil at high-pressure or in high-velocity flow. In the initial stages (t ~ 1.5-4 IlS), the electric strengths of solid DP and PETN are similar (Fig. 8.23) [216]. For an interelectrode gap 0.5 mm long, breakdown of detonation products of a PETN charge with a density of 1 g/cm 3 is initiated at a distance I behind the detonation wave front between the hemispherical ends of cylindrical electrodes I mm in diameter immersed in transformer oil. Breakdown was initiated in the rectilinear segment of the leading edge of a 100-kV sounding pulse with rise time 'tfr= 0.2Ils. For a charge diameter of 7 mm, 1.7-1.81ls after the detonation front had passed through the discharge gap, the DP electrical conductivity decreased and breakdown was initiated at the pulse front. Figure 8.23 demonstrates that Ubr(t) exhibits maxima. A decrease in Ubr with increasing I results from the pressure decrease in separating DP.

8.5 Electric Strength ofInsulation and Intercontact Medium

o

20

GO

239

v,%

Fig. 8.24. Behavior of Ubr of the gap formed by two tip electrodes as a function of the degree of chamber filling with (vM/v)·100% transformer oil for time lags between ignition and high-voltage pulse application equal to 22 (1),47 (2), 85 (3), 410 (4), and 1500 JJS (5)

Since the high-conductivity zone behind the detonation wave front is boundec} by the center of symmetry of the incoming rarefaction wave, the maximum DP electric strength is shifted to the right proportionally to the conduction zone growth. The change in the breakdown voltage of the medium in a closed volume with various filler concentrations was investigated in [217] under explosive action of DP on the oil. The length of the gap between the conical copper electrodes (d = 4 mm) was derived by requiring breakdown initiation in an oblique pulse front with a slope of 0.85 MV//ls. A PETN charge with a mass of 1.7 g was placed symmetrically about the electrodes 30 mm from the longitudinal axis of a strong explosive chamber with a volume of 890 ml. Maximum filling of the chamber with (v m/v)·100% transformer oil was limited to 80% by the chamber strength. The electric circuit of the facility allowed high-voltage pulses to be applied with specified time lags after ignition, and actual changes in the composition of the cold medium in the intercontact gap of the explosive breaker to be imitated (without breaking the high-current circuit). The breakdown voltage of the gap increased as the chamber filled with transformer oil (Fig. 8.24), and depended only slightly on the lag between the pulse arrival time from a pulsed voltage generator and the ignition time (Fig. 8.25). The latter can be explained by the increase in static pressure in the chamber, from ~1.7 MPa for (VM/VPOO% = 6% to 30 MPa for (vM/v)-100% = 80%. A small decrease in Ubr 400-600 /ls after the explosion is due to a pressure decrease resulting from leakage through poorly fitting parts. Curves 1 and 2 in Fig. 8.25 are for measurements with a discharge gap located above the oil level in the chamber. The gap was filled with pure DP immediately after charge ignition. When both electrodes were immersed in oil, the overall behavior of Ubr(t) was unchanged. This indicates the presence of a vapor-gas mix-

240

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

V

100

~

o

*'

""""0

J-

10/

50

r"- r--r-

h' ".

P"

1--'0

P"

Z

~ i"'"

/ Q 1000, Ufl is essentially independent of v. In all test modes, the fimctions Ufl(V) for cone insulators are the same as those illustrated by curves l' and 3' in Fig. 8.35. The observed dependence can be ex-

8.7 Recovery of Electric Strength after Spark and Arc Discharges

*OO~~~

J50 0

o

251

:.. 2 mm), and electrode material. The electric strength of the gap after a spark discharge with Q < 0.1 C was restored to Ur = (0.85-O.9)Uo (modes 3 and 4 in Table 8.4) approximately exponentially. Further increase in Ur slowed down. The ESR period for hydrogen was 35 ms, for air and argon it was 4-7 ms, and for SF6 gas and compressed air it was 10-12 ms. It did not depend on electrode material and increased only slightly with increasing interelectrode gap length. After a high-power spark discharge with Q> 0.25 C (modes 1 and 2 in Table 8.4), the electric strength was first restored at the same rate as in the mode with Q < 0.1 C, but then the recovery rate decreased sharply. In the first stage, the ESR rate did not depend on the electrode material, and depended only weakly on

8.7 Recovery of Electric Strength after Spark and Arc Discharges

255

Table 8.4. Parameters of current pulses traversing a discharge gap during spark and arc

discharge Label in First halfOscillation Fig. 8.38 \ a e ampl i- frequency tude 1m [kA] f[kHz] 90 250

o cillation damping constant 11 1.33

2 3 4 5

2.7 1.87 2.3 1.08

60 20 4 0.65

200 600 1600 1 .2

Pulse width

IectTic Comments charge

1~ [I:!S]

Q[

15 10 3 1500

0.25 0.05 0.003 0.3

40

J

High-power discharge Q > 0.25 C Spark discharge, Q Tcp

(8.8)

where na is the concentration of neutral particles in the gap; CI is a constant factor (units of y-I) that depends on gas type; Ter is a certain critical temperature (approximately 2.103 K) at which the curve finad) assumes a different form .

8.7 Recovery of Electric Strength after Spark and Arc Discharges

257

Ur kV 40r---~/L~~~~~~~~

~~~~~~~~~~~

20r-~~~~~~--~~ m~~~~~~~~~~

o

0.5

f.2

f.8

2/# I, ms

Fig. 8.40. Time dependence of the RES of a discharge gap for the circular frequency of the movable electrodes n = 46.6 revolutions/s and the radial component of the air flow velocity pumped through the discharger v, = 18 mls. Curves 1-7 are for the currentlm = 5, 8.7, 15, 30, 67, 98, and 150 kA. Curves 8 and 9 indicate the boundaries of the regions of hot and cold electric strengths of the gap

The curve depicting the dependence Ji(nad) is conventionally referred to as the "cold electric strength" curve. It is observed at temperatures for which the generalized form of Paschen's law is satisfied and thermal gas ionization can be neglected (for air Tp ~ 2.103 K). Otherwise, the applicable curve is the one for h(nad), referred to as the "hot electric strength" curve. In [230] it was suggested that one approximate the data for Ur in spark gaps in various media at T > Tcr with the expression

cpr = 0 .8(C2K)O.6 , where

K

=nad/(nad)o and (nad)o=2.71 ·1023 m-2 ; for air, cl=0.8·10 2 y -l and

C2 = 2.22.103.

For air we can write

where Ur is in kY. Assuming that an analogous dependence applies to commutators with movable electrodes for T ~ Tor. and noting that

the formula

was derived in [229], where To is the temperature on the axis of the arc column, equal to (2-5).104 K, ST is a constant factor that depends on the discharge column radius, the tangential component of the oncoming air flow velocity vq> (which re-

258

Chapter 8 Electric Strength of Dielectric Materials in a Hostile Environment

suIts from electrode circulation and passes through the discharge channel in the longitudinal direction), and the radial component of the air flow velocity Vr (which is produced by ventilation blades and flows in the transverse direction). The unknown parameters A, m2, To, and 8T were derived from empirical curves 5-7 in Fig. 8.40. It was found that A = 25 kV, m2 = 0.6, To = 3.104 K. The functions 8 T = fUm) and To= fUm) were also measured experimentally. It was found that changes in To resulting from variations in 1m can be neglected over the temperature range in question. Curves that specify interfaces between the regions of hot and cold restored electric strength were calculated using Eq. (8.9) and the expression 1

Ur = - fi (nad). cl

The dependence of 8 r on the main applied factors ro, v 323-333 K, the electric strength of cross-linked silane PE for a dc voltage becomes greater than E br of non-cross-linked PE. For voltage pulses, the difference between E br of non-cross-linked and cross-linked PE decreases with increasing temperature. Aromatic compounds with a conjugate system of 1t-electrons and additives containing polar groups are capable of absorbing and scattering the energy of accelerated electrons while keeping their structure intact. The ability of 1t-bonds to distribute the absorbed energy throughout the entire molecule and thereby to prevent local accumulation of energy, leading to dissociation of molecules, increases for aromatic compounds as the number of condensation nuclei in the molecule increases. This is confirmed by the correlation between this parameter and the ionization energy of molecules that include benzene (9.4 eV), naphthalene (8.1 eV), pyrene (7.5 eV), and anthracene (7.5 eV). The system of 1t-bonds also accepts energy absorbed by the polymer and converts the energy of the excited molecule into other energy types, for example, into thermal or luminous energy. The following data illustrate the effect produced by introducing a particular aromatic compound, namely naphthalene chloride, into PE. 20 25 35 40 30 Applied voltage [kV] 30/22 11 /2 23/6 29/ 19 Number of breakdowns 311 Notes. The numerator here is for samples without additives, and the denominator is for samples with a concentration ofthe naphthalene chloride additive of 1.5 mole fraction.

280

Chapter 9 Methods for Improving the Dielectric Properties

A positive effect was also observed in [245] after introducing cable oil containing aromatic and naphthenic compounds, and of N- and N - substituted nphenylenediamines and quinolene into PE. The positive effect due to electron energy absorption with benzene rings can be achieved using the ethylene and styrene copolymer. For a styrene content of 22%, E br is 25% greater than that of LDPE. However, Ebr decreases with any further increase in the styrene content. These results can be explained in terms of the combined influence of electron energy absorption by benzene rings (a positive factor) and a rise in 'Y due to the negative effect of styrene on crystallization, yielding a lesser degree of crystallinity. Products of decomposition of the aromatic additives or specially introduced additives either have elevated electrical conductivity themselves (anthracene), or decompose with concomitant formation of ions (acetophenone). For long voltage exposure, the diffusion of stabilizing additives (which attenuate local fields and thereby hinder treeing) into strong field zones starts to affect the service lifetime significantly. The disadvantages of polymers, including PE, include destructive oxidation processes engendered by various factors (primarily E and 1). As a result, polymers lose their positive qualities in oxygen-bearing media. Such processes include the decomposition of polymer molecules followed by free-radical chain reactions forming new end groups and, as a consequence, altering their mechanical and electrical properties. To prevent or even decelerate these processes, antioxidants are injected into polymers. These additives suppress the production of pyroxene radicals and prevent further decomposition of the material. Thermal oxidation destruction, as one of the important reasons for polymer degradation in an electric field, becomes especially prevalent when PD are initiated in treeing channels. Diphenylamine (DEA) injected via thermal diffusion is an efficient PE stabilizer. Any particular type of additive injected into polymers to increase luminous and thermal stability and plasticity, and to improve antistatic properties, will influence E br and the dielectric characteristics in some characteristic fashion. Luminous and heat stabilizers not only improve polymer resistance to corresponding deleterious factors, but also increase the electric strength somewhat. The injection of plasticizers reduces Ebr. as a rule [100]. This decrease is roughly proportional to plasticizer content and the higher the temperature at which Ebr of the polymer is measured, the stronger the effect. The injection of a plasticizer alters the temperature dependence of electric strength, which starts to decrease sharply with increasing T at lower values of T than in polymers without plasticizers. However, in some cases, introducing small amounts of a plasticizer does not degrade Ebr. and can even increase it. Thus, Ebr of polyvinylchloride was found to increase after the introduction of up to 15% of dibutyl phthalate, dioctyl phthalate, or tricreosyl phthalate [100]. It was assumed that this was due to reorganization of supermolecular structure during plastification. After antistatic additives (electron sources) have been introduced into a polymer, Ebr remains essentially constant at cryogenic temperatures, but at normal and

9.1 Mixing and Injection of Additives and Fillers

I !I'

80 60 40

20 10

5

10- 3

;t

~1

, ',f 10- 2

2-

f

:l

281

If

--Y

;/ 10

10- 1

tOO

10

t, h

Fig. 9.11. Treeing probability of PE (1) and PE with 20% ZnO (2) as a function of lO-kV voltage pulse width for an interelectrode gap length of 5 mm and tip-electrode end radius of5 Jlm

elevated temperatures it decreases due to an increase in 'Y and increased probability of thermal breakdown. An urgent problem for insulating materials science is the behavior of Ebr and the dielectric characteristics of materials after injection of finely-dispersed solid fillers. Such fillers are injected to improve mechanical characteristics (durability under wear, hardness, etc.), reduce the cost and density of the material, increase its permittivity, give it piezoelectric properties, etc. Loading of the filler, in particular, at high concentrations, is accompanied by the formation of pores and cracks, due to local mechanical stresses at the boundaries of inclusions. In these cases, Ebr can decrease even when the electrophysical characteristics of the filler are close to those of the basic material. However, this is not a particular obstacle to the use of solid heterogeneous dielectrics as high-voltage insulation when one of the aforementioned properties is more important. Thus, for example, a combination of £0-20 epoxy resin and acetonic furfural monomer with an MSO-grade glass microsphere filler was used at the Scientific Research Center of the AIIRussian Electrotechnical Institute to manufacture support insulators intended for high-voltage pulsed facilities. A certain loss in electric strength due to the microspheres was compensated by the enhanced mass utilization factor (the ratio of the failure load to the insulator mass) of the polymeric insulators, which for these insulators is twice that of porcelain insulators in the same voltage class. On the other hand, some finely-dispersed additives engender homogeneous finely-dispersed structure in the material and thereby increase short- and longterm electric strengths of polymers (Fig. 9.11) [247]. The electric strength of teflon containing titanium dioxide filler with 5-/lm particle diameter was examined in [248]. Samples of a composite material with dimensions 1.5 x 100 x 130 mm 3 were prepared by mixing, molding at room temperature, and subsequent sintering at 643 K. The titanium dioxide content was varied between 5% and 50%. The breakdown field strength E br was measured in transformer oil for mains-frequency voltage that rose smoothly at 2-3 kV/s and

282

Chapter 9 Methods for Improving the Dielectric Properties Ebr>

kV/mm

10

20

JO

JHJ crOf,

Fig. 9.12. Ebr in teflon as a function of titanium dioxide content brass disk electrodes 10 and 25 mm in diameter. As can be seen from Fig. 9.12, the dependence of Ebr on filler concentration peaks at c = 5-20%. In the vicinity of the maximum, Ebr of the composite exceeds that of pure teflon by 20-25%. The electrical conductivity of polymers can be enhanced by filling them with finely-dispersed high-conductivity powders (most frequently, technical carbon). After injection of acetylene black into PE, the electrical conductivity of the composite increases not only with filler concentration but also with the degree of crystallinity and isothermal fluidity of the polyethylene compound (single- and bicomponent matrices). In this case, matrix fluidity is a very important factor. The parameter y decreases with increasing T more strongly for HDPE than for LDPE. The resistivity of polyethylene systems filled with acetylene black can be varied over a wide range by altering their matrix composition. The need for capacitive storage devices with enhanced energy content stimulates the search for solid heterogeneous systems and study of their dielectric properties for use as insulation. Of fundamental importance is the behavior of sand Ebr as the concentration and properties of fillers and matrices change. The quantitative electrophysical characteristics of these materials are described in the context of the theory of an effective medium. The percolation effects characterized by a threshold increase in the active or reactive component of the electrical conductivity of the material as the concentration of the filler whose properties differ radically from those of the matrix approaches a certain critical value are peculiar to randomly nonuniform heterogeneous materials. The behavior of the principal electrophysical parameters of such systems (s, Pv, tan 8, and Ebr ) as a function of filler concentration was analyzed in [249]. It was demonstrated that the effective permittivity s* of a composite with a metal filler increases infinitely as the volume concentration of the metal approaches the critical value Ccn and the decrease in p* is inversely proportional to the increase in s* : c*p* ~ SdielPdieh as confirmed experimentally in a PE system with a coarsegrained forming ceramic compound and conductive filler. In this case, Khari-

9.2 Radiation Modification tonov [249] managed to obtain heat-shrinkable materials with p* ~ 107 n·cm and

e; ~ 60 at p* ~ 10 n·cm.

283

e; ~ 200-250 at

9

The concentration dependence of Ebr was analyzed in [249] for thermal and electrical breakdown mechanisms. For the thermal breakdown mechanism, E br of dielectrics with metal fillers decreases monotonically with increasing filler concentration and vanishes as the metal concentration approaches its threshold value. For the electrical breakdown mechanism, E br = .f(c) is a power-law function. An analysis of the concentration dependence of the stored energy density in a capacitive device whose insulation is fabricated from heterogeneous materials demonstrated that the product e*· E~r for the thermal mechanism of insulation breakdown is independent of c up to c = Ccr. For higher c, this product decreases rapidly. For the electrical breakdown mechanism, the energy density peaks at a certain concentration Cm < Ccr. Moreover, a significant gain in energy content can be achieved by virtue of having used heterogeneous materials. Heterogeneous systems make it possible to grade resistance of continuously monolithic polymer insulation (see Sec. 10.1). Heterogeneous systems based on polymer matrices with ferroelectric ceramic or piezoceramic fillers have been developed and assiduously studied since the late 1970s and early 1980s, resulting in the production of cables and transducers that record mechanical vibrations of extended objects such as soil, water, and engineering structures. The technology used to produce piezocomponents and cables with piezocomposite insulation, and further development of heterogeneous systems theory stimulated by this technology, can be used to produce insulation for energy storage devices and shapers for high-voltage systems that generate highpower pulses.

9.2 Radiation Modification Changing the bulk properties of dielectrics. Radiation treatment has been successfully used for several decades to improve the physical, chemical, and mechanical properties of polymers and to alter their elemental composition. Due to the high reactivity of the products produced by irradiating various materials, radiation reactions can run at very low temperatures, thereby enabling materials that are typically incompatible with other methods to be combined without chemical initiators or catalysts, yielding very pure materials. Radiation reactions that can be implemented in a solid enable one to modifY molded parts of machines, mechanisms, and structures, with occasional concomitant engineering gains. It is important to note that essentially no nuclear reactions take place during treatment, and the irradiated material exhibits no induced radioactivity. Polymerization and cross-linking dominate certain polymer irradiation methodologies, rather than destruction (see Secs. 8.1 and 8.2).

284

Chapter 9 Methods for Improving the Dielectric Properties

Polymerization, that is, addition of repeated unsaturated molecules of lowmolecular compounds (monomers), is intensified under exposure to ionizing radiation and proceeds in the liquid, gas, or solid phase as well as in solutions and emulsions. Radiation polymerization can occur at temperatures optimal for the growth of macromolecules. For high-power radiation, the concentration of newly formed radicals can be so high that the effect of any inhibitor contained in the material is offset. Under exposure to ionizing radiation, a number of polymerization reactions that traditionally require high pressure run at standard pressure. Radiation technology also facilitates radiation-grafted copolymerization and polymerization in heterogeneous systems. In the former, side polymer chains are formed on free radicals and secondary ions produced under irradiation in the main molecular chains. Depending on the energy of photons or charged particles, the graft can occur either in the bulk of the material or only in the subsurface layer. Nowadays, several methods of radiation-grafted copolymerization have been developed and mastered. Moreover, copolymerization is applied not only to synthetic polymers, but also to cellulose (wood, paper, etc.). To produce new materials with unique properties (for example, wood and concrete polymers), the polymerization process is implemented in heterogeneous systems. To this end, preliminarily dried and degassed material is impregnated with a monomer and then irradiated at a dose of 10-15 kGy in an inert atmosphere, or in monomer vapors at a pressure of -1 MPa. Some polymers, in particular many polyolefins, form cross carbon--carbon (or other) bonds under exposure to ionizing radiation. These bonds produce a spatial lattice that combines all molecules in a common system, i.e., radiation crosslinking. An empirical rule states that if each alternating carbon atom of the monomer link of the main chain is bound to at least a single hydrogen atom, that is, if the polymer has (CHr-CHR)n structure, the dominant effect after irradiation will be cross-linking; if the alternating carbon atoms of the main polymer chain are bound to CHr-CRR radicals or atoms of other elements, these polymers will predominantly be destroyed. However, it must be borne in mind that there are polymers that do not obey this rule. In addition, the relationship between the probability of polymer bond breaking and cross-linking depends on the irradiation conditions. Cross-linking dominates for irradiated PE, polypropylene, polyvinyl chloride, difluoropolyvinyl, polyacrylamide, polystyrene, some types of rubber, polyamides, and polyethers. The destruction process is dominant for irradiated polyisobutylene, polymethylmethacrylate, polytetrafluoroethylene, and cellulose. The efficacy of radiation cross-linking depends only weakly on the type of high-energy radiation employed (photons, electrons, or heavy particles) and the dose rate. The most important characteristic of irradiation is the absorbed dose D, which determines two main characteristics of the cross-linked polymer, namely, its molecular mass and molecular topology. Radiative transformations in crystallizing polymers are determined not only by processes at the molecular level, but also by the supermolecular structure of the polymers.

9.2 Radiation Modification

285

o~--~--~--~--~ J7J S7J T, I( "73

Fig. 9.13. Temperature dependence of Vbr in nonirradiated (1) and irradiated LDPE; radiation dose D = 460 kGy (2) and 2 (3) and 4 MGy (4)

For high-voltage insulation technique, the effects of radiation modification such as the increasing electric strength at standard and in particular at elevated temperatures, the improved dielectric characteristics, the higher thermal stability and mechanical strength, and the memory effect are most important. After irradiation of PE by a dose of the order of 50 kGy, the extension of its molecular chains increases by a factor of 4-5, thereby increasing its mechanical strength. Moreover, PE thermal stability jumps from 378 to 473 K, and the PE electrical properties improve. PE high-temperature stability at T > Tme1t improves with increasing absorbed radiation dose (Fig. 9.13). For very high radiation doses (10 MGy), Ebr decreases only negligibly as the temperature increases to the point of thermal decomposition. However, at such high radiation doses, PE cannot be used as insulation because of its brittleness. The bulk resistivity of radiation cross-linked high- and low-density PE is two orders of magnitude higher than that of nonirradiated PE over the full range of operating temperatures. Even at temperatures above the melting point of noncross-linked PE, its Pv exceeds 108 Q .. Radiation modification affects tan 8 only weakly, increasing it slightly. This effect becomes most prominent at low frequencies and extreme temperatures. Sensitizers (monomers) injected into PE before irradiation to improve and stabilize its physical/mechanical properties have no appreciable effect on its dielectric characteristics. This enables radiation cross-linked PE to be used as electrical insulation for systems in severe insulation operating environments, including elevated temperature and high-power radiation. It can be used at temperatures above the melting point of nonirradiated PE. The most serious problem for the application of radiatively cross-linked polyolefins as insulation is their physical and mechanical characteristics. The way in which some of them are altered by irradiation is not always consistent with highvoltage insulation requirements. If the tensile strength increases somewhat or remains essentially constant with increasing (but low) radiation dose, the relative

286

Chapter 9 Methods for Improving the Dielectric Properties

elongation decreases at room temperature and higher. At room temperature, the relative elongation of polyolefins decreases most significantly at doses up to 0.50.7 MGy, while at elevated temperatures it decreases by doses up to 0.2-0.3 MGy. Young's modulus at temperatures below the melting point is a complex function of the absorbed radiation dose [250]. At elevated temperatures, the absorbed radiation dose corresponding to the minimum Young's modulus shifts toward lower doses, while at T ~ Tmelt. Young's modulus increases monotonically. Even if the absorbed radiation doses are relatively small (0.1-0.2 MGy), PE cracking stability in a stressed state increases significantly (by a factor of 2-10). For doses in the range 0.5-0.6 MGy, it increases by more that two orders of magnitude. PE irradiated by small doses has slightly greater immunity to various climatic factors, especially after injection of small amount of soot. At high radiation doses, this property deteriorates. Thus, radiation treatment that improves polymer properties simultaneously impairs some operating characteristics of polymers. This calls for a careful analysis of the most efficient application fields for radiation-modified polymers. Special techniques to ameliorate the negative effects of radiation treatment must also be developed. The basic restriction on the use of irradiated polyolefins as high-temperature insulation is their high-temperature oxidation destruction, which primarily impairs their elasticity. Such materials must be used without mechanical loads or in an oxygen-free medium; they must also be protected from the adverse effects of oxygen. Polyolefins can be protected either by special hermetic coatings and films or by stabilizers that inhibit oxidation. A broad class of substances (see Sec. 9.1) can be used as such stabilizers. Effective complex stabilizers increase the operating lifetime of radiation-modified PE in air by factors of hundreds at T> Tmelt • As emphasized in [168], considerable success in the area of radiation modification over the past few years has been due to the use of new polymers, such as polymers with conjugated double bonds in the main chain, new treatment techniques (in particular, radiation doping of polymers), and unconventional types of ionizing radiation, such as accelerated ions. Change in the surface properties of dielectrics. A recent trend in the development of radiation physics of polymer dielectrics is irradiation of polymers with high-energy (tens to hundreds ofkeV) ions, that is, ion implantation (or ion doping). This enables their properties to be modified. These changes result from ion (impurity) injection and radiation-induced defects. A specific feature of treating solid dielectric, semiconductor, and metal surfaces with ion beams is the copious transfer of atoms-mass transfer-through vacancies; therefore, essentially all basic relations describing the mobility of atoms in the exposure zone can be derived, based on the modem concept of forming and spreading vacancies. Notwithstanding the fact that essentially all of the elements in the periodic table, molecular ions, and particles in various charge states can be used as bombarding particles, ion beams are more flexible means of treating samples, because they enable the properties of particles in the beam to be varied over wider limits. Vari-

9.2 Radiation Modification

287

ous types of structural defects and chemical modification depend on ion energy and mass, while the degree of transformation depends on the radiation dose. Heavier ions produce higher defect densities, and lead to more significant changes in the properties of polymers than lighter ions. At low radiation doses (10 10_10 13 cm-2), ion beams initiate cross-linking and bond breaking in polymers, polymerization of monomers, and dissociation. They also change the diffusion constant of polymers. At radiation doses in the range 10 13_10 15 cm-2 , the optical characteristics of polymers change, oxygen atoms are captured, the homogeneity of polymers is disrupted, and they are saturated with carbon. For higher radiation doses (exceeding 10 15 cm-2), the electrical conductivity of the implanted layer increases sharply, and polymers are subject to graphitization at a depth comparable to the projected ion mean free path. The use of ions instead of fast electrons has a number of advantages when one relies on irradiation alone, especially when the doping effect comes into play. Doses of accelerated ions decrease by more than two orders of magnitude. Ion treatment can convert an organic polymer into an inorganic one. It induces the formation of polymer films in low-molecular organic compounds, converts conventional diamagnetic polymers irradiated by iron ions into ferromagnetic ones, etc. Ion implantation amounts to a clean method of injecting impurity centers into a dielectric at some desired concentration, thereby significantly altering its electrical properties, especially the electrical conductivity. Moreover, polymer electrical conductivity enhanced by 12 orders of magnitude via ion implantation has more stable temporal behavior than electrical conductivity enhanced by conventional doping, which deteriorates with time due to desorption of injected impurities. The higher kinetic energy of impurities injected via ion implantation reduces the rate of impurity desorption. Since ion implantation is a surface phenomenon for dielectrics with thickness typical of high-voltage engineering, it is a good method for adjusting the surface resistivity of insulation systems in order to redistribute the electric field, give them antistatic properties, etc. For example, implantation of ions into polyimide increases its surface conductivity by 14 orders of magnitude (Fig. 9.14) [251]. After implantation of Ar+ ions with energies of 50 keY, Y8 of Si02 increases by 10 orders of magnitude. The results of investigations into the surface conductivity of certain organic and inorganic materials treated with fluxes of 0+, Ar+, and AI+ ions [251] are summarized in Table 9.5. An increase in Y8 of polyimide films by 15 orders of magnitude after irradiation by Ar+ and N" ions with energies in the range 40-90 keY and doses up to 3.1017 cm-2 was established in [252]. The metal electrical conductivity Y = 200 n-I·cm- I was reached. The modified layer depth was estimated to be 10-5 cm. Impurity ions implanted into organic dielectrics can produce localization centers responsible for hopping electron transfer in regions of polyconjugation. Since the concentration of implanted localization centers n varies with depth in the material, we cannot use the traditional equation

288

Chapter 9 Methods for Improving the Dielectric Properties

1~~------~~~--~~~~--------------~

7 8

11

23

Fig. 9.14. Electrode measurment system and temperature dependence of the conductivity of PBN (0), silicon nitride (+), and aluminum nitride ceramic layers (~) without irradiation (1-3) and after irradiation by carbon ions at doses of 1013 (4), 10 15 (5), 10 16 (6 and 8), 10 17 (7 and 10), and 10 18 cm-2 (9). Here E denotes the electrodes, Sdenotes the sample, and PS denotes the power supply unit

(9.5) to calculate y in the case of hopping electrical conductivity. In the above equation a is the radius of the localized state, a is the percolation constant, and Yo is a temperature-dependent pre-exponential factor. In most cases, the distribution of ion-implanted impurity concentration with depth of the irradiated material can be described by a Gaussian. Moreover, to describe the dependence of the electrical conductivity of ion-doped organic materials, the effective thickness of the doped layer and the effective concentration of impurity centers can be considered. This enables one to use Eq. (9.5). Modification of structure and properties by implantation of ions is increasingly used to improve the surface properties of inorganic dielectrics. A number of severe and quite often inconsistent requirements are imposed on dielectrics that operate in high-temperature regions of high-power electrical systems. For example, nitride insulation ceramics that operate in contact with gas-discharge plasma (in channels of magnetohydrodynamic generators and in CO2 lasers) must have high

9.2 Radiation Modification

Table 9.5. Effect of ion flux on the surface conductivity of dielectrics for D Trad = 293 K Initial 0+ conductivity Yo [~rl .""'] Ys [n- I. ~] Y /Yo < 10 17 > \.3.10 8 1.3 . 10 9 LiF < 10- 17 9.1.10- 12 >9.10 5 MgO 1.10- 11 2.5.10- 17 4. 10 5 5.6.1025 Si02 9 6 16 1.25.103.9.10 3.2.10UF-46 3.1.10-9 2.10- 16 1.5.107 MK 5.10- 2 5·10-4 5.10 13 Pol yimide < I 0-17 < 10- 17 4 .7· 10- 1600 K slightly increases Ps and TRC, and it reduces the heat stability of the semiconducting layer. TRC in the above experiments lay within the range (0.9-5.8)-10-4 deg- I . The resistance characteristics of the modified layer deteriorate with increasing mass of ions implanted in PNB, and with decreasing radiation dose (compared to an optimal dose of _10 17 cm-2) and current density in the beam. When the specifications for modified dielectrics are not so stringent, simple technologies are used, including treatment of dielectric surfaces with UV radiation or cold gas-discharge plasma, instead of the rather complex technology of ion implantation using accelerators. Because the energy ofUV photons (~1O eV) is low, excited molecules are concentrated near the irradiated surface of the dielectric, and no complex reactions run along fast-particle tracks, due to the low concentration of excited or ionized molecules. Treatment of dielectric materials (mainly polymers) with cold plasma in which the UV radiation is only one of the applied factors is more widespread. Such treatment increases humidity resistance and adhesiveness, causes the memory effect, and improves some dielectric characteristics. By analogy with exposure to high-power radiation and particles, plasma treatment at T < Tmelt causes crosslinking of polymer molecules. This method enables one to inject hydrogen, inert gases, and metals into polymers and ceramics, thereby creating a surface concen-

9.2 Radiation Modification

291

tration of alloy elements as high as 5.1026 m-2. Even at room temperature, the rate of mass transfer exceeds the equilibrium value many times. Free radicals are formed in the surface layer of many polymers exposed to cold plasma. The nature of these radicals depends on the polymer type and the composition of the gas medium in the reactor. If the ambient gas medium or the gas absorbed by the polymer contains oxygen, peroxide radicals are formed. Alkyl radicals are produced in the absence of oxygen. As a rule, they are short-lived radicals, especially at elevated temperatures. The formation of free radicals leads to cross-linking of polymer molecules. The deepest and fastest modification on treatment with the cold plasma is observed in polymers with ether, carbonyl, and hydroxyl groups. Depending on the technology, the surface to be treated is subjected either to the direct action of the gas glow- or corona-discharge plasma or only to the action of gas-discharge products. To improve the quality of polymer films, a glow discharge is initiated in gaseous monomers surrounding the surface to be treated. In this case, the diffusion rate and reaction rates between monomer ions and polymer molecules increase. This technology is used, for example, for PE, PS, and PMMA fluorination with NF 3 • The depth of LDPE fluorination is 400-600 nm, and the period of fluorine retention in PE is several months. The quality of HDPE, polycarbonate, and teflon surfaces can be improved by polymerization with a glow discharge in tetramethyl silane and tetramethoxylane. Indirect exposure to a discharge is more efficient for large surface areas or large, complex surface configurations. In this case, the surface to be treated is blasted by a gas containing molecules and groups excited by a glow discharge. For example, treatment of polymer films with an O2+ N2 gas mixture for only 1530 s significantly improves their adhesion properties. Choosing of the optimal treatment time ttreat is important for the above technology, since not only the concentration of implanted impurities but also the relationship between modification and degradation depends on it. For t> ttreat. the second process can dominate. In most reports on polymer processing with glow discharges at mains-frequency voltages, this time is estimated to be 200-300 s. For t> ttreat. most of the polymer characteristics deteriorate rapidly. This is confirmed, for example, by the decrease in the breakdown voltage of polypropylene treated with a glow discharge (Fig. 9.16) [255]. If the mode of treatment and the parameters of materials to be treated differ radically from those used in [255], ttreat can either increase or decrease significantly. The composition of dopants also depends on the treatment time, because gaseous decomposition products are liberated when the polymer interacts with the plasma. As a consequence, the composition of the gas mixture in the reactor differs from the initial gas composition, and the longer the time of contact between the plasma and the polymer, the greater the difference. Now the time ttreat cannot be estimated a priori, because it depends on many factors, including the voltage magnitude and type, the composition of the gas medium, the gas-discharge gap length, the material to be treated, etc.

292

Chapter 9 Methods for Improving the Dielectric Properties

• -1

0-2 o

G

nO D

5

Il.

0

-J

C2D

~.oco

100200

\

0 0

~ 00

1000

t s

Fig. 9.16. Dependence of Vb, of a polypropylene film on the time of treatment with a glow discharge in air (1), O2 (2), and N2 (3) media

9.3 Conditioning of the Electrodes and Dielectric Medium Mechanical methods of treating electrode surfaces and cleaning them with solvents do not enable one to eliminate microroughness, traces of contamination, or adsorbed gases from the electrodes. These methods of treatment are used only for high-power HES (for example, high-current accelerators, HCA) with large vacuum volumes and large-scale and massive electrodes. For the majority of physical experiments and production of high-voltage sealed-off vacuum devices, a modern technology-conditioning-is used to treat the electrodes. Conditioning is performed immediately in a vacuum medium. To a lesser extent, conditioning of the electrodes and dielectric medium is applied to insulation equipment with gas, liquid, and solid insulation. Nowadays, various methods of conditioning electrodes and dielectric media are used. In some cases, they significantly increase the electric strength and stability of the discharge characteristics. The most widespread way to condition electrodes in vacuum insulation systems is to process them with spark or glow discharges, dark pre-breakdown currents, radiation, or charged-particle beams (mainly ions of inert gases), or to subject them to thermal treatment. Various conditioning methods for vacuum insulation gaps are compared in [79, 256] . In [256], conditioning was performed in a gap 2 mm long between plane-parallel electrodes for a dc voltage. The residual pressure in the vacuum chamber was 10-3 Pa. It was demonstrated (Fig. 9.17) that the greatest increase in electric strength was secured by electrode aging with discharges that decontaminate the electrode surface and destroy (etch) microtips. Conditioning effects were observed for dc, ac, and pulsed high voltages. However, long-term voltage exposure can be recommended only for vacuum systems under conditions of pure vacuum. In vacuum systems with vapors of organic compounds or other contaminants, long-term passage of even small currents de-

9.3 Conditioning of the Electrodes and Dielectric Medium

293

Fig. 9.17. Effect of various electrode conditioning methods on Uhr in a vacuum gap as a function of the number of aging pulses: 1) nonconditioned electrodes; 2) electrodes annealed in vacuum at T= 1173 K; 3) electrodes bombarded with hydrogen ions; 4) electrodes bombarded with argon ions; 5) electrodes treated with pre-breakdown currents; 6) electrodes treated with high-voltage discharges in vacuum

posits carbon-bearing and other films on the working electrode surface, thereby making conditioning difficult. The effect of microtip explosion on an electrode surface subject to nanosecond voltage pulses [129] demonstrates that the efficiency of electrode aging with these pulses can exceed that of aging under exposure to dc or ac voltage. In this case, microtip explosions smooth the electrode surface relief, reduce the effective field gain, and as a result, increase the electric strength. Figure 9.18 [257] illustrates the dependence ofthe conditioning effect on applied pulse width. According to [34], it is desirable to vary the interelectrode gap length or the pulse amplitude during aging so that the electric field in the gap smoothly increases from pulse to pulse before breakdown initiation by the subsequent pulse. For several subsequent pulses, the field strength should not be changed. If no breakdown occurs, the field strength can be further increased. In contrast, if breakdowns are initiated by almost every pulse, the field strength should be reduced until breakdowns vanish completely; then the procedure must be repeated. The discharge characteristics of vacuum gaps improve only when the number of breakdowns does not exceed a certain critical value. The number of breakdowns required for conditioning depends on many factors. The larger the surface electrode area, the higher the degree of surface roughness and contamination, the higher the refractoriness and mechanical strength of the electrode material, and the less the energy liberated into the gap during each breakdown, the greater the number of breakdowns required. It is essentially impossible to determine this number a priori; an experiment is required. For copper, stainless steel, and molybdenum electrodes with sizes typical of high-voltage testing, the number of aging breakdowns with low energy release (from some tens to hundreds of joules) ranges from a few to a few dozen. The electrodes of high-power RES cannot be conditioned via complete discharge initiated by the main power supply, as they would experience considerable erosion and sputtering. It can be performed using an auxiliary low-current power

294

Chapter 9 Methods for Improving the Dielectric Properties

10

15

20

Uaging. k V

Fig. 9.18. Dependence of static Vb, of a vacuum gap on aging pulse amplitudes for pulse width 't = 100 (1). 150 (3), and 200 ns (2)

supply unit. In so doing, the energy of training discharges must be optimized. Deviation from the optimal energy will either not produce the expected effect (at lower energies), or it will reduce the electric strength (at higher energies) because the electrode microrelief worsens. Aging with breakdowns is not always applicable to large systems even if the liberated energy is limited. Conditioning with dark currents, microdischarges, and

interrupted discharges yields good results for vacuum insulation gaps of HCA. Dark currents used for electrode aging depend on the same parameters as the number of aging breakdowns. For large gaps in technical vacuum, pre-breakdown currents are pulsed microdischarges, and their critical values can be as high as a few amperes. In this case, aging is performed by applying to the vacuum gap voltage pulses at 25-30% of the working voltage. As currents decrease during conditioning, voltages increase in small steps up to the working voltage, or even -25% higher; in the process, microdischarge currents are controlled. If the electrode polarity changes, the same aging procedure must be repeated with the opposite polarity. Even more efficient aging is provided by interrupted discharges. To this end, a voltage pulse with the working amplitude is cut off by a high-speed discharger in parallel with the vacuum gap. Treatment of the electrode surface with glow discharges and its conditioning with currents in partial vacuum yield good results. Both methods rely on the bombardment of the electrode surface by ions. This is accompanied by three effects: the injection of ions, which alters the surface properties of the metal by making it denser and stabilizing sorption and diffusion processes on the electrodes; smoothing of microtips; and decontamination of the surface. This treatment remains effective for many months. Upon treatment of a vacuum system with glow dis-

9.3 Conditioning of the Electrodes and Dielectric Medium

295

charges, the pressure is increased to 0.1-1.0 Pa to ignite and maintain a glow discharge. The best results are obtained for ac voltages of the mains frequency for a treatment period of about 1 h and a current of a few tens of milliamperes (typically 20-40 rnA). The efficacy of the treatment depends heavily on the gas in which the glow discharge is initiated. Most experts consider helium to be the best gas, with nitrogen ranking second. Conditioning with a current in partial vacuum ("gas conditioning") differs in terms of its greater influence at the cathode surface, especially its emitting regions. The vacuum chamber is filled with inert gas, usually argon at a pressure of 0.1 Pa, through which a current of -50 rnA is transmitted. Ions generated by collisions of emitted electrons with atoms are accelerated by the strong field in the vicinity of microtips, and bombard the latter. As a result, microtips are smoothed and Ubr increases by a factor of 3-5 [79]. Thermal electrode treatment can also be an efficient way to increase Ubr of vacuum gaps. Like the aforementioned methods, this requires an optimal mode to be chosen carefully. Exposure to elevated temperatures not only intensifies degassing and decontamination from vapors that cause Ubr to increase, but also leads to ion-induced sputtering of the cathode material, yielding cathode material and contamination vapors in the gap. The latter reduce Ubr • It is important that even when the cathode and anode consist of identical materials, their thermal treatment modes differ. Electrode annealing at high temperature in combination with glowdischarge processing in an inert gas atmosphere for a few hours enables one to obtain short-term electric strengt4 of 1.1 MY/cm, and long-term electric strength (for a few dozen hours) of 0.55-0.6 MY/cm. Working gradients of vacuum insulation systems, limited by the flashover voltages of solid dielectrics, can also be increased by first conditioning not only the electrodes but also the insulator surfaces. Conditioning with surface breakdown is an efficient method of treating inorganic insulators. In this case, Ufl continues to increase through dozens (or even hundreds) of flashovers (Fig. 9.19) [46]. Aging organic ElM insulators by means of surface breakdown requires particular care, due to possible irreversible changes to their surface material. A few to perhaps a few dozen flashovers are typically used, so that in many cases the aging curve for polymer insulators saturates after a few flashovers (Fig. 9.20) [9]. The optimal breakdown number is determined by the type of dielectric and the quality of its surface treatment, discharge circuit parameters, and the type of conditioning voltage. Conditioning with dc voltages and nanosecond pulses is most efficient. To increase the efficiency of conditioning and to reduce the required number of flashovers, it is advantageous to use breakdowns with polarity opposite that of the operating system. This effect can be explained by the more thorough decontamination of the anode surface by flashovers, the anode having been transformed into the cathode by the reversal of polarity. Radiation treatment of an ElM surface in vacuum is one method of surface aging. There exist optimal wavelength, intensity, and vacuum conditions to ensure a maximum rate of gas desorption for any insulating material without destruction of its surface. An electric spark can be used as the source. One method of treating the

296

Chapter 9 Methods for Improving the Dielectric Properties Un,kV

2D 'HJ 60 80 tOO 12D 1'11/ N Fig. 9.19. Un for cylindrical glass samples (diameter 25 mm, length 10 mm) in vacuum (p = 1.3 mPa) as a function of the number of successive breakdowns for dc voltage and brass Rogowski electrodes

Un,kV

II

190

GO

o

/

/

~

20

""

n

Fig. 9.20. Ull of polyethylene ring insulation section as a function of the number of aging flashovers

insulator surface with radiation from a spark discharge (up to 80,000 sparks) in vacuum is described in [259]. After such treatment, Un doubled in a number of polymer (lucite, lexane, delrin, and PE) and ceramic materials (macor). The effect results from a modified surface layer -2 om thick, including its secondary electron emission coefficient. The simplicity and remote nature of this method are among its advantages. However, it is difficult to apply it to vacuum insulation systems with complex geometry (segmented housings of vacuum-tube diodes, accelerating tubes, generator lamps, and so on). Mutual shielding of the parts and difficult access to regions of metal and dielectric contact make the efficiency of this method low. The methods for decontaminating vacuum insulator surfaces based on the interaction of strong electric fields with surface currents are of interest in such systems. A positive effect is observed for both dc and ac voltages; however, ac voltage is more efficient. Aging with dc voltage in nearly optimal modes roughly halves the subsequent outgassing from the vacuum volume formed by LDPE or PMMA cylinders, whereas aging with ac voltages reduces it almost fourfold.

9.3 Conditioning of the Electrodes and Dielectric Medium

~

~

a

297

1 ~

~--.

::a

MO~----~--~----~~--~~--~

o

to

20

JO

'10 f IlS Fig. 9.21. Voltage-time characteristics of an insulator section after breakdown-free aging (I) and aging with discharges (II) for positive voltage polarity. The section comprises insulation rings (1), conducting spacers (2), a high-voltage electrode (3), a grounded electrode (4), and a current carrier (5)

One method of interest is breakdown-free aging of vacuum insulation for pulses with steep trailing edges. In this method, one applies n voltage pulses (n = 40--60) with duration less than that of the working pulse and amplitude defined by the empirical relation

u=~u 2 w

(l+N-l) 40'

where Uw is the amplitude of pulses in the rated working mode and N is the serial number of the training pulse. Figure 9.21 shows breakdown voltage-time characteristics of a vacuum segmented insulator (also sketched in Fig. 9.21) after breakdown-free aging (I) and aging with electric discharges (/I). A 25-30% increase in Ubr due to degassing of solid dielectrics can be achieved simply by holding them in vacuum for a few hours. Degassing of the dielectric surface intensifies with pulsed heating, thereby significantly increasing Ubr and reducing the preliminary treatment period. Dielectrics can be heated by radiation [9]. On irradiation by a few light pulses of a xenon lamp with an output power density of the order of lO2 W/cm 2, Ufl of a ring PE section is doubled. Combined aging ensures good results. It includes initiation by light pulses of aging breakdowns for voltages less than working ones by an order of magnitude, thereby preventing possible irreversible surface damage of solid dielectrics.

298

Chapter 9 Methods for Improving the Dielectric Properties

'60 f60 0000"

f'lO

f20 fOO

80 60

o '0 00 1,,0

o

o

0 1,,00

.., 0

0

_00

U

o

0

0

U

" fO

20

n

Fig. 9.22. Dependence of Vb, of the gap formed by a plane and a sphere lying on the plane as a function of the number of breakdowns in air at a pressure of 3 MPa. The interelectrode gap length is 8 mm and the electrode area is 1963 mm 2 At low (atmospheric and lower) gas pressures, the electric strength depends on the number of previous breakdowns, assuming that the electrode area is fairly large (a few square centimeters or more), and that the discharge energy does not significantly damage the electrodes. At elevated pressures, when Eb, reaches 100 kV/cm or more, Ub, increases with the number of breakdowns and essentially saturates. The surface state of a steel sphere 4 mm in diameter as viewed by an electron scanning microscope before and after breakdown shows [83] that low values of U b, for the first breakdown result from various contaminants and microtips on the electrode surface (the electrode system was formed by a plane and a sphere located on the plane) (Fig. 9.22). Contaminants and microtips have been eliminated by the time subsequent breakdowns occur, and surface damage due to the discharge plasma does not produce inhomogeneities with high field gain; therefore, the insulation gap ages. The number of breakdowns in gas required to obtain high, stable breakdown voltages depends on the same factors as in vacuum. Dust in the gas and on the electrode requires more aging breakdowns. Conditioning without breakdowns is more widespread in large-scale gas-filled systems (for example, SF6 insulated switchgear). The value of Ub, increases by a few tens of percent (in [70] this increase reached 80%) when a slowly increasing dc or ac voltage is applied to the gap for several hours. For slowly increasing voltage (for example, when it rises to Uw in half an hour), free conducting particles move to regions of weak electric field, where they do not appreciably affect the electric strength of the system. For small systems, conditioning also reduces electrode surface roughness due to burning out of microtips by low-power discharges. Conditioning of insulation gaps with liquid and solid insulation includes effects on the electrodes and dielectric medium due to exposure to an electric spark (in a liquid), an electric field, and pre-breakdown currents. It is difficult to isolate the individual contributions of these effects to resultant conditioning.

9.3 Conditioning of the Electrodes and Dielectric Medium

ZS 20 15

o

v n

0

00

5

0

,., 0

299

00 0

10

n

Fig. 9.23. Dependence of Ebr in liquid nitrogen on the serial breakdown number for plane stainless steel electrodes with an area of 1963 mm 3 and an interelectrode gap length of O.5mm

Aging with discharges causes Ebr of a gap in a liquid to increase or decrease. In the former case, elimination of dissolved gas and initiating centers (microinhomogeneities and regions with reduced work functions) from the electrode surface prevails. A positive effect of preliminary breakdowns is most likely in liquids that decompose under exposure to a spark discharge without forming solid products. A positive effect is also observed when the energy released into the gap during each breakdown is small. In [61], the breakdown voltage Ubr of a discharge gap with purified water increased and stabilized after the application of 15-20 nanosecond voltage pulses that initiated breakdown. In [22] it was found that the electric strength of purified water increased upon exposure to the first 7-10 breakdowns initiated by microsecond pulses, and then saturated during the subsequent 100150 breakdowns (the volume of the examined liquid was 600-700 L). A fairly stable increase in the electric strength of condensed gases subjected to conditioning with breakdowns was observed in [260] (Fig. 9.23). Breakdowns in hydrocarbon liquids, as a rule, did not improve the state of the electrode surface. Conditioning of the electrodes in transformer oil was not observed if the oil was replaced after each breakdown. It is believed that products of hydrocarbon decomposition accumulate on the electrodes during aging discharges in addition to the disruption and welding of microtips. These products hinder stabilization of surface electrode properties. If the transformer oil is not replaced and its volume is small, previous breakdowns reduce its electric strength because of contamination by products of its decomposition and by the electrode metal [61]. Non-breakdown aging methods are more suitable for liquid dielectrics and are the sole methods of aging of solid dielectrics. An increase in the electric strength of liquid and solid dielectrics under preliminary voltage stress of insulation gaps (prestressing) was discovered in the 1940s. It is still of interest to researchers, because it enables them to investigate the processes of polarization, emission, injection, and relaxation of charge carriers, their transfer, etc. This effect has yet to be incorporated into practical system operation. It has, however, figured in one attempt to assess the operating conditions of insulation exposed to alternating-sign

300

Chapter 9 Methods for Improving the Dielectric Properties

fjElL

1

,..-- ....l-'x" " 1-- i-"'2

'"

/. ~,x

1/.3

2

1.7

1 r tG lL L'. I '/ ~ r--1.5

J

)(

I

1.2 f. f 0.15 0.10 ON 0

til II

,il

0.3 .f( 0.8

0.7

0.05 0.10 0.15 J, mNcm

\V J

'"""-

Fig. 9.24. Dependence of E/Eo on current density for stainless steel (1), titanium (2), and aluminum (3) electrodes

voltage pulses or voltage of composite shape (for example, pulses superimposed on a dc voltage). In liquids with elevated electrical conductivity, preliminary voltage exposure caused stronger effects, including an increase in electric strength under certain conditions. In [87] it was suggested to increase the electric strength of highly conductive liquids, especially water, by first electrically heating the electrodes using the pre-breakdown conductivity. The authors explained the increase in electric strength observed under these conditions in terms of an increase in the electrical conductivity of the liquid during heating, and a decrease in the electric field near microtips where the current density and temperature are highest. Figure 9.24 shows the results of investigations of pulsed electric strength ofpurified water after passage of a direct current through the gap [261]. The test pulse width was 1.5 IlS, the interelectrode gap length was 1 cm, and the area of the plane electrodes ranged from 30 to 150 cm2 • For the positive direction ofthe abscissa in Fig. 9.24 we took the direction of current for which the plus terminal of the direct current source was connected to the anode of the examined gap, and for the negative direction of the abscissa we took the direction of current at which the plus terminal of the source was connected to the cathode. As can be seen from Fig. 9.24, there are optimum conditions under which Ebr of water increases by a factor of -1.7 and the spread in breakdown voltages decreases by a factor of 2-3. The authors explained this effect in terms of the influence of space charge accumulated near the electrodes, and conduction layers produced by the enhanced concentration of charge carriers near the electrodes. For current densities higher than the optimal density, the combination of electrical hydrodynamic instabilities developed here and outgassing during electrolysis cause Ebr to decrease.

9.3 Conditioning of the Electrodes and Dielectric Medium

F(nJ 0.3

o.Z

aOJ

3

./i

~ -1

V - /

D.f

/'

301

10'

2

J

3 n, pulse

Fig. 9.25. Operating lifetime distribution for experimental cable

Long-term voltage exposure of solid polymers can not only alter their charge state, like prestressing, which vanishes in a relatively short time, but also their structure. For PE exposure to multipulse voltages, structurization was observed in addition to degradation of its state (electrical aging) [268, 263]. The structurization and an increase in electric strength and operating lifetime of insulation were observed only when the number of pulses did not exceed a certain threshold value. With any further increase in the number of pulses, electrical aging dominated. Improved insulating properties-diminished breakdown probability for a fixed voltage duration after preloading by an electric field-were recorded for samples of cast epoxy insulation and cable products. A method of preliminary heating for polyethylene cable insulation suggested in [264] to close by melting dendrites propagating from the cable core can be considered a kind of conditioning to increase the long-term electric strength of thermoplastic dielectric insulation. Experiments were performed using an experimental cable and commercial cable of similar design. For example, the experimental cable is designed as follows: a continuous aluminum core 9 mm in diameter, insulation 24 mm in diameter, a semiconducting shield, a copper braid, and a protective casing. To close by melting dendrites, a current at a frequency of 50 Hz was conducted through the core to heat it up to the PE melting point, and the current duration was chosen so that a thin PE layer had time to melt. The feasibility of increasing the operating lifetime of the cable using this method was studied on the example of the experimental cable for pulsed voltage with an amplitude of 180 kV. The length of the examined segment of the sample disregarding cable terminations was 1.6 m. The results are shown in Fig. 9.25. Samples of the first group were tested in the initial state (curve 1); the second group of samples (curve 2) was subjected to three heating procedures. Samples of the third group (curve 3) were subjected to analogous heating procedures, but only after 900, 1800, and 2700 current pulses. It can be seen that heating procedures during testing increased the cable operating lifetime especially significantly for periodic heating procedures. For the given Utes!> this heating procedure completely eliminated breakdowns. The efficacy of this method was confirmed only for cables with solid metal cores.

302

Chapter 9 Methods for Improving the Dielectric Properties

N-M 2

--

3

o

= 5 Fig. 9.26. Modification of LOPE film structure in various stages of extension: initial state (1); first stage (extension up to the elastic limit) (2); second stage (near the fluidity limit)

(3); third stage (4); fourth stage (5)

9.4 Orientational Extension of Polymers Since the electric strength of polymers depends not only on the structure of their molecules but also on the structure of various aggregates formed by them (see Sec. 3.3), structural changes, and especially changes in supermolecular structure, can be used to modify the properties of the material over wide limits. Different structures of materials also result from different structural defects: grain boundaries, internal strains, voids, and cracks. The structure of the material can be changed by mechanical means. Orientational extension is one of the most widespread methods of modifying supermolecular structure. For example, when a PE film is extended, crystalline lamellae are rotated; with any further extension, these lamellae slip relative to each other, and the C axis is oriented in the extension direction, as shown in Fig. 9.26 [57]. In this case, the breakdown field strength in the direction perpendicular to the extension axis increases (Fig. 9.27) along with the operating lifetime of insulation for all voltage types (see Sec. 3.1). The orientation causes the packing density of molecular chains to increase, thereby intensifying intermolecular interactions and making the diffusion of gaseous discharge products into a polymer difficult. The orientational PE extension causes the rate of C=C bond formation to increase in a sample exposed to discharges. In this case, rates of change in tan 8, E, and Pv of polymers and the rate of electrical aging decrease upon exposure to discharges in air. The orientation and denser packing cause the short-term electric

9.4 Orientational Extension of Polymers

303

E b" MY/cm

f

5.0

M

J.o 2.0

).-~

f-t.J.Jf---'"

I

~

. 1.5 it propagates above the insulator surface. When ko increases from -1.5 to 15, Uf! remains unchanged, to within the measurement error. However, the discharge trajectory and the location of its main points on the electrodes depend on ko and the electric strength of the ambient medium. Adhesion of the discharge to the insulator surface with increasing Ebr occurs at large ko. For compressed N2 and SF6, the threshold values of these two parameters are: 1) ko= 1.5 and Ebr = 85 kV/cm; 2) ko= 3.2 and E br = 120 kV/cm; 3) ko= 7 and Ebr= 150-175 kV/cm. Further increase in ko leads to discharge propagation far from the insulator surface. To choose an optimal shape for the generatrix of the dielectric surface, initial discharge voltages were calculated for a set of field lines in the vicinity of interior electrodes of various geometry. Figure 10.6 shows the results for compressed N2 in terms of the ratio of the breakdown voltage in the vicinity of the interior electrodes as a function of x to the breakdown voltage of the main insulation gap: TJ = Udisch(X)IUdisch.gap. An intermediate maximum and a minimum in the curves indicate that when choosing the insulator generatrix, the discharge voltage of the support insulator near the maximum will be higher than in the ambient medium, because the region with a reduced discharge voltage (ky= 1.2) is near the insulator surface. When generatrices are made coincident with lines of force to the left of

10.1 Electric Field Control

1 1.5). It follows from Fig. 10.6 that Ufl increases significantly as the degree of field inhomogeneity in the dielectric surface decreases; that a discharge is initiated in the middle of the gap rather than at the electrodes; and that for ky= 1.2 and leo> 7, the discharge propagates in the medium surrounding the insulator rather than along its surface. To ensure the conditions of discharge initiation and propagation far from a support insulator and hence the maximum electric strength of the system, the minimum surface discharge voltage must exceed the maximum breakdown voltage of the main gap, that is, U main.br max

::; U surf min .

(10.3)

Choosing the confidence level p = 0.995 and assuming that the discharge voltage is normally distributed, the necessary excess of calculated Ubr at the insulator surface over the calculated voltage of the coaxial gap can be estimated using the 3cr rule: U main.br max = Ueale.br + 3crl, U surf min

= Ueale.surf - 3cr2,

where crl and cr2 are the standard deviation of the discharge voltages of the main gap and insulator surface, respectively. Transforming inequality (10.3), we obtain

11 ~ I + 3 (WI + W2 ) • 100% ,

320

Chapter 10 Methods for Increasing the Working Field Strength ofInsulation

where WI and W2 are the coefficients of discharge voltage variation (the meaning of subscripts 1 and 2 is the same). The parameter " is unambiguously related to Icy for a specified ratio of the coaxial system radii. An insulation design procedure that enables one to eliminate surface discharges with reasonable assurance and obtain the maximum possible electric strength of the insulation system was briefly formulated in [275] as follows. The desired value of " is determined for the known coefficients of discharge voltage variation in the main insulating medium. Then geometrical parameters are chosen for which the electric field distribution is characterized by the value of Icy corresponding to the given value of". In order that a discharge initiated in the vicinity of the insulator not propagate close to its surface, the condition ko> 7 must be satisfied in regions adjacent to the electrodes that depend on the strength of the ambient medium. As indicated in Chap. 7, when the voltage duration decreases with other conditions unchanged, the probability that the discharge trajectory will pass above the insulator surface rather than through the ambient medium increases. However, an interior shield with optimal geometry enables one to increase Un, due to the displacement of the maximum field strength zone and the region of discharge initiation from the triple point to the center of the insulation gap. In systems with stringent requirements on Ew , Un can be increased with simultaneous interior and exterior shielding, and by choosing an optimal profile for the insulator surface and adjusting the insulating material. In part, this approach was taken, for example, in [276], where the electric field distribution in the vicinity of cylindrical insulators with only interior, only exterior, or both kinds of shields (Fig. 10.7) was calculated by the method of ring charges (the number of rings was 110-136) as a function of 8 in the insulator material, the heights of rod shields (5 mm), depth of insulator embedding in the electrode d, and tilt angles of the lateral walls of the groove 1. For inhomogeneous insulation containing gas cavities in the initial state, the mechanism of electrical aging can be considered identical for the entire range of field strengths from Ecr to E br. For such insulation, the failure distribution can be described by a two-parameter Weibull equation

where y is a coefficient with a fixed confidence interval. According to [119], the experimental dependence of the coefficient ~ on the applied field strength for macroinhomogeneous insulation is described by the expression

~=

exp(aE) b

'

where E is the average field strength in insulation and a and b are coefficients that depend on the aging rate of insulation and are determined experimentally. With allowance for the above assumptions, the equation for the electrical reliability assumes the form t J3

InP(t) =-exp( aE). b

The above equation can be used not only to calculate the reliability for the given field strength and operating lifetime but also to solve inverse problems, namely, to calculate the operating lifetime for the given reliability and average working electric field and the average permissible field strength for the given operating lifetime and reliability. For E < Eon the equation for the lifetime curve is a particular case of the equation of electrical reliability. The important advantage of the method of determining the parameters of the lifetime curve suggested in [318] is that it can be used to calculate the operating lifetime and reliability of insulation under thermal and mechanical loads, including their combination with an electrical load. The ElM operating lifetime under a thermal load t, can be described by the equation of the form

11.4 Choice of the Working Field Strength

385

t~ = Aexp(BIT),

which agrees well with the Arrhenius law. Here A and B are constant factors. In most cases, the reciprocal power law N=kF- m

,

is applicable under cyclic mechanical loads (for the fatigue failure), where N, F, k, and m are the number of cycles before fracture, the mechanical stress, and the corresponding constant factors, respectively. If mechanical stresses are periodic, N can be changed by the operating lifetime t. Although these equations are empirical and describe the action of a single factor, they can be used to model aging under simultaneous actions of several independent factors. Using them, the expression for the average operating lifetime -:r can be written In-:r=A+BIT-nlnE-mlnF.

The equation holds under assumption that plots of the dependences of the electrical field strength on the time (E on t) and of the mechanical stress on the number of loading cycles (F on N) undergo parallel translations in log-log coordinates when other aging factors are changed.

11.4 Choice of the Working Field Strength The working field strength of an insulation system Ew is chosen based on the permissible working field strength Ep.w. and the safety factor ks• The latter takes into account the influence of technological factors on insulation systems and the action of different operating factors disregarded in the experimental determination of Epow: Ew

=

Epow I ks ,

where Epow is the maximum average field strength permissible for the insulation system under exposure to one or several factors determining its aging and ensuring some specified reliability over the required operating lifetime. Choosing Epow for an insulation system which ensures the required operating lifetime and acceptable figures of merit is a rather complicated problem which requires a large volume of experimental investigations, because in most cases calculations are based on empirical fmdings. This problem is simplified for RES, since Epow is determined by the condition for the reliable system operation for working voltages. As is well known, one more requirement is imposed on electrical engineering equipment, namely, for its reliable operation under exposure to internal and lightning overvoltages. The most reliable values of working voltages Epow are obtained when the laboratory tests are very similar to the operating conditions and the volume of experimental data and the data processing algorithms enable one to determine the statistical aging characteristics. In many cases, it is impossible to

386

Chapter

11

Calculation of Insulation

detect the most important aging mechanism, to obtain the dependences of its characteristics on the field strength and other applied factors, and based on these dependences, to choose Ep.w for the given operating lifetime. Efficient methods of determining Ep.w are its calculations using the experimental reliability equation or the lifetime curve. The method of determining Ep.w using the experimentally measured parameters of the operating lifetime distribution can be demonstrated on the example of epoxy insulation [320]. The experimentally measured distribution of the operating lifetime of these insulation systems 't obeys the Weibull distribution with the lower limit 'to. The distribution function can be written

for t > 'to. The coefficient a is equal to 1, that is, in this case it represents an exponential distribution which is a particular case of the Weibull distribution. The empirical reliability function Q(t) = 1-P(t) can be written Q(t) = Nt = exp[ -A(t-'tO)]' No

(11.49)

where No is the number of the examined samples for the given value of Eav' Nt is the number of samples that withstood without breakdown by the time t = 't, and A is the failure rate, in h- 1• The coefficient A entering into Eq. (11.49) satisfies the relation VA = 't-'to, where 'to is the time during which breakdowns of approximately 37% of the samples occur, which follows from the definition of the average of an exponential function. We note that A specifies the slope of a straight line P(t) to the time axis in the coordinates 10gN!No and t. The value of 'to can be determined from a plot as the time at which the straight line representing P(t) intersects a vertical line at N!No = 100%. The range of field strength within which no breakdown occurs can be determined from the plot of 'to(E) (Fig. 11.7). With increasing operating lifetime, the curve in Fig. 11.7 asymptotically approaches the average field strength Eo at and below which no breakdown occurs, at least for 3.104 h (the maximum testing period for Eo in [320)). In an epoxy compound, Eo was 2-2.1 kV/mm. If the required operating lifetime of the insulation system does not exceed the above value, Eo can be set to Ep.w. For Etes! = Eo, treeing channels that had not yet been propagated to the opposite electrode were observed for all samples. If the treeing is inadmissible, the maximum field strength for insulation Emax must be reduced to values at which the treeing is not initiated. To find these values, the distribution parameter A is used, since Emax cannot be determined from the parameter 'to, because Emax of insulation gaps is independent of 'to for a wide range of its variations when Eav = const. The parameter A is a probabilistic function of the electrode radius of curvature ro, Eav' and Emax. Since ro determines the surface area S which initiates the treeing, we can write

11.4 Choice of the Working Field Strength

387

E kY/mm

to

'-." --"

8 G

¥ J

E,

.... ~

.-

0.1

1

......

--

to

~-

-. .-

~

tOO tUOO tUUUD

r". h

Fig. 11.7. Lifetime curve ofan epoxy compound

A. =

f( S,Eav,Emax) '

(11.50)

where S represents the surface area of the needle for which E ::; 0.8 Emax. In [320] it is demonstrated that Ep.w at which the treeing is not initiated can be calculated using the experimentally measured dependence described by Eq. (11.50). The value of Ep.w can be calculated for homogeneous and inhomogeneous (composite) insulation, as well as for short-term voltage exposure, using the reliability equation. To implement this approach, it is required not only to conduct a large volume of measurements and prolonged testing of the operating lifetime, but also to take into account the scale effect when proceeding from the results of laboratory sample tests to the actual insulation systems, or in applying lessons learned by operating insulation systems with scaled-down overall dimensions to the required ones. To consider the scale effect, the dependence of the electric strength DF of insulation on the electrode area and the insulation thickness and volume should be considered. Designating by S. the electrode area during the laboratory testing (or the electrode area for the system with smaller dimensions) and by S2 = nS. the electrode area of the system with larger dimensions (n> 1) and using the probability multiplication theorem, we can write Eq. (11.31). Since 0< [1-P.(U)] < 1, for n> 1 and U = const we obtain P2(U) > p.(U). Therefore, with increasing electrode area, the curve of the distribution function of Ubr in the coordinates P( U) and U is shifted at the top left. The same effect is observed when the insulation volume increases n times. If the function P( U) represents, for example, a double exponential distribution, then using Eq. (11.36), we obtain the relationship

J6

S2

Up. 2 =Up. I --crlnS 1t

I

between the permissible voltages of the system with electrode areas S. and S2: as indicated in [49], this expression was confirmed by the experiments in which the electrode area was changed by three to four orders of magnitude.

388

Chapter 11 Calculation ofInsulation

A decrease in Ebr with increasing d for insulation thicknesses typical of RES is primarily due to an increasing degree of field inhomogeneity m and an increasing volume of insulating material in the region exposed to the electric field (see Sections 6.2 and 6.4). The influence of d due to field distortions can be considered using the maximum field strength rule which states: the maximum field strength in insulation gaps is independent of d for any specified insulation breakdown or failure probability. From this rule, the relationship Up. 1

d ~l

- - : : 2- U p.2 d1 ~2 follows for Up of two systems with insulation of the same type. The above formula is applicable to systems with ~ < 3. If the nature of defects and hence failures remains unchanged as the insulation volume of the system is changed, the distribution law of Ubr also remains unchanged. For example, if the distribution obeys the Weibulllaw, the exponent bin the equation

does not change when the volume of insulating material is changed. As demonstrated by many authors, in this case the electric strength of large samples can be calculated based on the value of E hr measured for small-scale samples. In this case, the relation U hr.2

::

U br. 1 ( V; /V2 )

"b

can be used for calculations, where Ubr.1 and Ubr.2 are median values of Ubr for a system of samples with volumes VI and V2 , respectively, and b is the parameter of the Weibull distribution for Uhr of the system of samples with smaller areas. Examples of calculations of the working field strength for insulation systems using the results of modeling can be found in [321] for high-power cables with paper-oil insulation and in [322] for high-voltage pulse cables with composite polymer insulation. It is much more difficult to use Eq. (11.31) when Pn(U) obeys normal or lognormal distribution laws, since in this case, analytic expressions for DF are unknown. It can be demonstrated experimentally that the parameters of position M and shape cr of distributions depend on the sample dimensions. Not knowing the form of this dependence, it is impossible to determine by extrapolation the total probability of the system failure

Pn (U):: 1- IT {l-Pt [U{k)J} ,

(11.51)

k=l

where PI[U(k)] is the distribution function of the damage probability of the kth component of the prototype for voltages U ~ U(k), U(k) depends on the number

11.4 Choice of the Working Field Strength

389

(location) of the kth component in the prototype, and n is the number of components of the prototype that are taken into account in calculations (the scaling factor). In this formulation, the problem was solved in [323] for transmission lines. The permissible field strength Ep for systems with self-healing insulation and electric strength described by a normal distribution is determined using experimental values of E 50% and cr. These parameters can be measured for this insulation using experimental models with electrode areas equal to those of the electrodes of actual insulation systems. In this case,

where m is a coefficient determined by the system reliability Q. For gas insulation including air insulation, m is usually set to 2-3. Considering actual values of cr, Ep of air gaps is 30% less than E 50 % for 1.2/50 I.ls pulses and m = 2. Equation (11.31) is applicable only when the prototype actually represents an n-component model and the same voltage is applied to each component. In practice, this requirement is seldom satisfied. In most cases, the voltage is changed when going from one component to another, and hence Eq. (11.51) must be used insteadofEq. (11.31). For insulation whose failures are caused predominantly by PD, Epow are chosen using the permissible PD rate for the given operating lifetime. Different PD rate characteristics are used for different insulation types. For organic solid and composite insulation undergoing irreversible changes under exposure to PD, the apparent charge is used (see Sec. 10.3). In these cases, Epow is chosen from the condition (11.52) where E in is the average field strength of PD initiation in the prototype with a specified apparent charge, and crin is the standard deviation for Ein. It is natural that Eq. (11.52) is applicable when the DF of Ein is close to a normal distribution and the variation coefficient crinlEin does not exceed 0.15. In most cases, both conditions are satisfied (usually crinlEin < 0.1) [324]. Equation (11.52) was derived for the probability of inadmissible PD initiation at Epow equal to _10-3 • If during PD evolution and insulation degradation the physical mechanism and the character of the processes remain unchanged before breakdown or a sharp decrease in the electric strength, the main PD characteristics are its power and current. In this case, Epow can be determined using experimental dependences of these characteristics on the electric field. Finding these dependences is a complicated problem, because Epow is primarily determined by PD with magnitudes at a level of 10-14_10- 15 C. The PD characteristics that can be measured reliably at a level of 10-12_10- 11 C (for example, E in) cannot describe the long-term electric strength [324]. They can only be used as a criterion for the insulation state as a whole indicating the absence of rough defects, excessive insulation wetting, etc. Permissible

390

Chapter II Calculation ofInsulation

Table 11.6. Working field voltages in high-voltage systems with solid and composite

insulation Electri c field type Inhomogeneous field (the maximum value)

In ulation y tem

High-power tran former High-power converter transformers with dry gla bonded mica insul ation Equipment with oil- barrier insulation Cables Electrical machi nes Gas-filled systems with epoxy compound insulation ystem with purely oil in ulation High ly Capacitor insulation (lead-out inhomogeneous and capacitive current electric field transformers) (the average High-power transformers field trength) with oi l- paper insulation Pulsed capacitors with [!a[!er-film insulation

Thickness of insulation or insu lation la~er 30-200

Ell' [kV/cm] , at afTequency of SO Hz 20-40 6-20

16-100

30-40

12- 26

80- 110 IS- 3S 30- S0

3~

10- 100

10-20 I- IS 3- S

30-40 20-30

0.OS-O.08

100- ISO

0.OS-O.08

800- 1200

working field strengths Ep.w for different insulation systems are summarized in Table 11.6. The choice of Ep and geometrical parameters in HES design is often determined by the HES characteristics rather than by its operating lifetime and reliability. In generators of pulses of superhigh power, capacitive energy storage devices should ensure a maximum stored energy density. The geometrical parameters and the dielectric medium of a forming line should satisfy three requirements, including the maximum energy accumulated per unit of length W, the maximum rate of voltage rise in the line A (which limits the minimum pulse rise time), and the maximum breakdown voltage Ubr• Figure 11.8 [325] shows the dependences of W, A, and Ub" normalized by their maximum values, on the parameter pJe , where p = 60 In ( R / r) / Je is the wave

impedance of the line, in n, and Rand r are radii of the outer and inner electrodes, respectively. It can be seen that the dependences have clearly defined noncoincident maxima. Thus, if the line is calculated for maximum values of W, A will be 68% of its maximum value, whereas for maximum A, the energy content will be equal only to 54% of its maximum. Thus, when choosing the wave impedance of the line, a compromise must be achieved considering the requirements for the voltage pulse parameters. The data shown in Fig. 11 .8 and the foregoing are referred to a single forming line.

11.4 Choice of the Working Field Strength

o

391

'HI 50 60

Fig. 11.8. Dependence of stored energy (1), Ubr (2), and the rate of voltage rise (3) normalized by their maximum values on the parameter pJi for a coaxial line

For a double fonning line (DFL), when the condition isfied (where

PI

= 60 In (RI 1r) 1-Ii. and

P2

PI

= P2 = Rload 12

is sat-

= 60 In (R2 1RI ) 1-Ii. specify the wave

impedance of the internal and external DFL lines, respectively, and RI and R2 are their radii), the pulse amplitude at the load is equal to the charging voltage of the line, reflections are absent, and the maximum power is transmitted to the load. The maximum possible voltage in DFL is detennined by the minimum Ubr of lines fonning it. For typical relationships between PI and P2, Ubr I < Ubr2 . Thus, Uo= Ubr I = Ebrr In (Rl/r). The rate of voltage rise in DFL exceeds A lmax of a single line only when the wave impedance satisfies PI> P2> 2 and the pulse reflection coefficient of the load is sufficiently high. Therefore, from the standpoint of obtaining the maximum rate of voltage pulse rise, DFL has virtually no advantages over a single line. However, it should be taken into account that the DFL charging voltage is halved for the same value of Uload .

References

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References

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Additional References I Vacuum Insulation 1.1. A. V. Batrakov, A. B. Markov, G. E. Ozur, et ai., The effect of pulsed electron-beam treatment of electrodes on vacuum breakdown, IEEE Trans. Disch. El. Insul., 2, No.2, 237-242 (1995). 1.2. A. V. Batrakov, D.S. Nazarov, G. E. Ozur, et aT., Increasing the electric strength of a vacuum insulation by treating the electrodes with a low-energy, high-current electron beam, in: Proc. 17th ISDEIV, Berkeley (1996), pp. 487--491. 1.3. M. E. Cuneo, The effect of electrode contamination, cleaning and conditioning on high-energy pulsed power device performance, IEEE Trans. Disch. El. Insul., 6, No.4, 469--485 (1999). 1.4. S. Kobayashi, Recent experiments on vacuum breakdown of oxygen-free copper electrodes, in: Proc. 17th ISDEIV, Berkeley (1996), pp. 9-16. 1.5. S. Kobayashi, K. Sekikawa, K. Asano, et aT., Surface conditions and electrical breakdown characteristics of ozonized water treated copper electrodes of a vacuum gap, in: Proc. 19th ISDEIV, Xian (2000), pp. 47-50. 1.6. X. Ma and T. S. Sudarshan, High field performance ofthin-wa11 spacers in a vacuum gap, IEEE Trans. Disch. El. Insul., 7, No.2 (2000), pp. 277-282. 1.7. G. A. Mesyats, Cathode Phenomena in a Vacuum Discharge: the Breakdown, the Spark and the Arc, Nauka, Moscow (2000).

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II Gas Insulation II.1. N. L. Allen, D. E. Georgoulis, C. A. Stassinopoulos, et aI., Effects of negative direct voltage prestressing on the breakdown of conductor-rod gaps under positive impulse voltage, lEE Proc. Sci., Meas. Technol., 145, No.3, 105-108 (1998).

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III Liquid Insulation IlL I. C. Brossean, Breakdown of a thin dielectric liquid layer, IEEE Trans. El. Insul., 27, No.6, 1217-1221 (1992). IIl.2. S. Chigusa, N. Hayakawa, and H. Okubo, Static and dynamic breakdown characteristics of liquid helium for insulation design of superconducting power equipment, IEEE Trans. Disch. El. Insul., 7, No.2, 290-295 (2000). III.3. E. O. Forster, M. Yamashita, C. Mazzetti, and L. Caroli, The effect of the electrode gap on breakdown in liquid dielectrics, IEEE Trans. Disch. El. Insul., 1, No.3, 440446 (1994). III.4. V. Gehman, R. J. Gripshover, T. L. Berger, S. P. Bowen and R. K. P. Zia, Effects of filtration on the impulse breakdown strength of high-purity water, in: Proc. 10th IEEE Pulsed Power Conf., W. Baker and G. Cooperstein, eds. (1995), pp. 550-555. III.5. J. Gerhold, Cryogenic liquids-a prospective insulation basis for future power equipment, in: Proc. 13th Int. Conf. on Dielectric Liquids (ICDL'99), Nara (1999), pp.365-37l. III.6. J. Gerhold, Liquid helium breakdown as function of temperature and electrode roughness, IEEE Trans. Disch. El. Insul., 1, No.3, 432--439 (1994). IIL7. J. Gerhold, M. Hubmann, E. Telser, About the size effect in LiHe-breakdown, in: Proc. 12th Int. Conf. on Conductivity and Breakdowns in Dielectric Liquids, Rome (1996), pp. 324-328.

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IV Solid Insulation IV.1. D. P. Agoris, C. G. Karagiannopoulos, P. D. Bourkas, and C. S. Psomopoulos, Aging effects on solid insulators considering the form of the stressing pulses, Int. J. Power Energy Syst., 20, No.2, 86-90 (2000).

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