HIGHT VOLTAGE ENGINEERING

ELECTRICAL BREAKDOWN IN GASES, SOLIDS, AND LIQUIDS

INTRODUCTION

With the ever-increasing demand for electrical energy, the power system is growing both in size and complexities. The generating capacities of power plants and transmission voltage are on the increase because of their inherent advantages. If the transmission voltage is doubled, the power transfer capability of the system becomes four times and the line losses are also relatively reduced. As a result, it becomes a stronger and economic system. In India, we already have 400 kV lines in operation and 800 kV lines are being planned. In big cities, the conventional transmission voltages (110 kV–220 kV, etc.) are being used as distribution voltages because of increased demand.

A system (transmission, switchgear, etc.) designed for 400 kV and above using conventional insulating materials is both bulky and expensive and, therefore, newer and newer insulating materials are being investigated to bring down both the cost and space requirements. The electrically live conductors are supported on insulating materials and sufficient air clearances are provided to avoid flashover or short circuits between the live parts of the system and the grounded structures. Sometimes, a live conductor is to be immersed in an insulating liquid to bring down the size of the container and at the same time provide sufficient insulation between the live conductor and the grounded container. In electrical engineering all the three media, viz. the gas, the liquid and the solid are being used and, therefore, we study here the mechanism of breakdown of these media.

CORONA DISCHARGES

In the uniform field and quasi-uniform field gaps, the onset of measurable ionization usually leads to a complete breakdown of the gap. In non-uniform fields, various manifestations of luminous and audible discharges are observed long before the complete breakdown occurs.

These discharges may be the transient or steady state and are known as ‘coronas’. An excellent review of the subject may be found in a book by Loeb.

The phenomenon is of particular importance in h.v. engineering where non-uniform fields are unavoidable. It is responsible for considerable power losses from h.v. transmission lines and often leads to deterioration of insulation by the combined action of the discharge ions bombarding the surface and the action of chemical compounds that are formed by the discharge.

It may give rise to interference in communication systems. On the other hand, it has various industrial applications such as high-speed printing devices, electrostatic precipitators, paint sprayers, Geiger counters, etc. The voltage gradient at the surface of the conductor in the air required to produce a visual a.c. Corona in the air is given approximately by the Peek’s expression.

There is a distinct difference in the visual appearance of a corona at wires under different polarity of the applied voltage. Under positive voltage, a corona appears in the form of a uniform bluish-white sheath over the entire surface of the wire.

On negative wires, the corona appears as reddish glowing spots distributed along the wire. The number of spots increases with the current. Stroboscopic studies show that with alternating voltages a corona has about the same appearance as with direct voltages. Because of the distinctly different properties of coronas under the different voltage polarities, it is convenient to discuss separately positive and negative coronas. In this section, a brief review of the main features of corona discharges and their effect on breakdown characteristics will be included. For a detailed treatment of the basic fundamentals of this subject, the reader is referred to other literature sources.

1. Positive or anode coronas

The most convenient electrode configurations for the study of the physical mechanism of coronas are hemispherically capped rod-plane or point-plane gaps. In the former arrangement, by varying the radius of the electrode tip, different degrees of field non-uniformity can be readily achieved. The point plane arrangement is particularly suitable for obtaining high localized stress and for localization of dense space charge. In discussing the corona characteristics and their relation to the breakdown characteristics it is convenient to distinguish between the phenomena that occur under pulsed voltage of short duration (impulse corona), where no space charge is permitted to drift and accumulate, and under long-lasting (d.c.) voltages (static field corona).

Under impulse voltages at a level just above the ionization threshold, because of the transient development of ionization, the growth of discharge is difficult to monitor precisely. However, with the use of ‘Lichtenberg figures’ techniques, and more recently with high-speed photographic techniques, it has been possible to achieve some understanding of the various discharge stages preceding breakdown under impulse voltages.

The observations have shown that when a positive voltage pulse is applied to a point electrode, the first detectable ionization is of a filamentary branch nature, as shown diagrammatically in Fig. 2.1(a). This discharge is called a streamer and is analogous to the case of uniform field gaps at higher PD values. As the impulse voltage level is increased, the streamers grow both in length and their number of branches as indicated in Figs 2.1(b) and (c). One of the interesting characteristics is their large number of branches which never cross each other. The velocity of the streamers decreases rapidly as they penetrate the low field region.

2. Negative or cathode corona

With a negative polarity point-plane gap under static conditions above the onset voltage, the current flows in very regular pulses as shown in Fig. 2.2 (b), which indicates the nature of a single pulse and the regularity with which the pulses are repeated. The pulses were studied in detail by Trichel and are named after their discoverer as ‘Trichel pulses’.

The onset voltage is practically independent of the gap length and in value is close to the onset of streamers under positive voltage for the same arrangement.

The pulse frequency increases with the voltage and depends upon the radius of the cathode, the gap length, and the pressure. The relationship between the pulse frequency and the gap voltage for different gap lengths and a cathode point of 0.75mm radius in atmospheric air is shown in Fig. 2.2. A decrease in pressure decreases the frequency of the Trichel pulses.

CLASSICAL GAS LAWS

In the absence of electric or magnetic fields charged particles in weakly ionized gases participate in molecular collisions. Their motions follow closely the classical kinetic gas theory.

The oldest gas law established experimentally by Boyle and Mariotte states that for a given amount of enclosed gas at a constant temperature the product of pressure (p) and volume (V) is constant or

PV = C = const.   2.1

In the same system, if the pressure is kept constant, then the volumes V and V0 are related to their absolute temperatures T and T0 (in K) by Gay–Lussac’s law:

When temperatures are expressed in degrees Celsius, eqn (2.2) becomes;

Equation (2.3) suggests that as we approach Ɵ = -273°C the volume of the gas shrinks to zero. In reality, all gases liquefy before reaching this value.

According to eqn (2.2) the constant C in eqn (2.1) is related to a given temperature T0 for the volume V0:

The ratio C0/T0_ is called the universal gas constant and is denoted by R. Equation (2.5) then becomes

pV = RT = C        2.6

Numerically R is equal to 8.314 joules/°Kmol. If we take n as the number of moles, i.e. the mass m of the gas divided by it’s mol-mass, then for the general case eqn (2.1) takes the form

pV = nC = nRT,   2.7

Equation (2.7) then describes the state of an ideal gas, since we assumed that R is a

constant independent of the nature of the gas. Equation (2.7) may be written in terms of gas density N in volume V containing N1 molecules.

Putting N = NA where NA = 6.02 * 1023 molecules/mole, NA is known as the Avogadro’s number. Then eqn (2.7) becomes

The constant k = R/NA is the universal Boltzmann’s constant (=1.3804 *1023 joules/°K) and N is the number of molecules in the gas.

The fundamental equation for the kinetic theory of gas is derived with the following assumed conditions:

·        Gas consists of molecules of the same mass which are assumed spheres.

·        Molecules are in continuous random motion.

·        Collisions are elastic – simple mechanical.

·        Mean distance between molecules is much greater than their diameter.

IONIZATION AND DECAY PROCESSES

At normal temperature and pressure, gases are excellent insulators. The conduction in the air at the low field is in the region 10-16 – 10-17 A/cm2. These current results from cosmic radiations and radioactive substances present in the earth and the atmosphere. At higher fields, charged particles may gain sufficient energy between collisions to cause ionization on impact with neutral molecules.

It was shown in the previous section that electrons on average lose little energy in elastic collisions and readily build up their kinetic energy which may be supplied by an external source, e.g. an applied field. On the other hand, during inelastic collisions a large fraction of their kinetic energy is transferred into potential energy, causing, for example, ionization of the struck molecule. Ionization by electron impact is for higher field strength the most important process leading to the breakdown of gases. The effectiveness of ionization by electron impact depends upon the energy that an electron can gain along the mean free path in the direction of the field.

This simple model is not applicable for quantitative calculations, because ionization by collision, as are all other processes in gas discharges, is a probability phenomenon, and is generally expressed in terms of cross-section for ionization defined as the product Piσ = σi where Pi is the probability of ionization on impact and σ is the molecular or atomic cross-sectional area for interception defined earlier. The cross-section &i is measured using monoenergetic electron

beams of different energy. The variation of ionization cross-sections for H2, O2, and N2 with electron energy.

It is seen that the cross-section is strongly dependent upon the electron energy. At energies below ionization potential, the collision may lead to excitation of the struck atom or molecule which on collision with another slow moving electron may become ionized. This process becomes significant only when densities of electrons are high. Very fast moving electrons may pass near an atom without ejecting an electron from it. For every gas, there exists an optimum electron energy range which gives a maximum ionization probability.

STREAMER OR KANAL MECHANISM OF SPARK

 

We know that the charges in between the electrodes separated by a distance d increase by a factor eαd when field between electrodes is uniform. This is valid only if we assume that the field E0 = V/d is not affected by the space charges of electrons and positive ions. Raether has observed that if the charge concentration is higher than 106 but lower than 108 the growth of an avalanche is weakened i.e., dn/dx < eαd.

Whenever the concentration exceeds 108, the avalanche current is followed by a steep rise in current and breakdown of the gap takes place. The weakening of the avalanche at lower concentration and rapid growth of avalanche at higher concentration have been attributed to the modification of the electric field E0 due to the space charge field. Fig. 2.6 shows the electric field around an avalanche as it progresses along the gap and the resultant field i.e., the superposition of the space charge field and the original field E0. Since the electrons have higher mobility, the space charge at the head of the avalanche is considered to be negative and is assumed to be concentrated within a spherical volume. It can be seen from Fig. 2.6 that the filed at the head of the avalanche is strengthened.

 

The field between the two assumed charge centers i.e., the electrons and positive ions is decreased as the field due to the charge centers opposes the main field E0 and again the field between the positive space charge center and the cathode is strengthened as the space charge field aids the main field E0 in this region. It has been observed that if the charge carrier number exceeds 106, the field distortion becomes noticeable. If the distortion of field is of 1%, it would lead to a doubling of the avalanche but as the field distortion is only near the head of the avalanche, it does not have significance on the discharge phenomenon. However, if the charge carrier exceeds 108, the space charge field becomes almost of the same magnitude as the main field E0 and hence it may lead to the initiation of a streamer. The space charge field, therefore, plays a very important role in the mechanism of electric discharge in a non-uniform gap.

Townsend suggested that the electric spark discharge is due to the ionization of gas molecule by the electron impact and release of electrons from cathode due to positive ion bombardment at the cathode. According to this theory, the formative time lag of the spark should be at best equal to the electron transit time tr. At pressures around atmospheric and above p.d. > 103 Torr-cm, the experimentally determined time lags have been found to be much shorter than tr. Study of the photographs of the avalanche development has also shown that under certain conditions, the space charge developed in an avalanche is capable of transforming the avalanche into channels of ionization known as streamers that lead to the rapid development of breakdown. It has also been observed through measurement that the transformation from avalanche to streamer generally takes place when the charge within the avalanche head reaches a critical value of

n0eαx ≈ 108 or αXc ≈ 18 to 20

where Xc is the length of the avalanche path in field direction when it reaches the critical size. If the gap length d < Xc, the initiation of the streamer is unlikely.

The short-time lags associated with the discharge development led Raether and independently Meek and Meek and Loeb to the advancement of the theory of streamer of Kanal mechanism for spark formation, in which the secondary mechanism results from photoionization of gas molecules and is independent of the electrodes.

Raether and Meek have proposed that when the avalanche in the gap reaches a certain critical size the combined space charge field and externally applied field E0 lead to intense ionization and excitation of the gas particles in front of the avalanche head. There is a recombination of electrons and positive ion resulting in the generation of photons and these photons, in turn, generate secondary electrons by the photoionization process. These electrons under the influence of the electric field develop into secondary avalanches as shown in Fig. 2.9. Since photons travel with the velocity of light, the process leads to rapid development of conduction channel across the gap.

Raether after thorough experimental investigation developed an empirical relation for the streamer spark criterion of the form

where Er is the radial field due to space charge and E0 is the externally applied field. Now for the transformation of avalanche into a streamer Er ≈ E

Therefore, αxc = 17.7 + ln xc

For a uniform field gap, breakdown voltage through the streamer mechanism is obtained on the assumption that the transition from avalanche to streamer occurs when the avalanche has just crossed the gap. The equation above, therefore, becomes

αd = 17.7 + ln d

When the critical length Xc ≥ d minimum breakdown by streamer mechanism is brought about.

The condition Xc = d gives the smallest value of α to produce streamer breakdown.

Meek suggested that the transition from avalanche to streamer takes place when the radial field about the positive space charge in an electron avalanche attains a value of the order of the externally applied field. He showed that the value of the radial field can be obtained by using the expression.

where x is the distance in cm which the avalanche has progressed, p the gas pressure in Torr and  α   the Townsend coefficient of ionization by electrons corresponding to the applied field E. The minimum breakdown voltage is assumed to correspond to the condition when the avalanche has crossed the gap of length d and the space charge field Er approaches the externally applied field i.e., at x = d, Er = E. Substituting these values in the above equation, we have

The experimentally determined values of α/p and the corresponding E/p are used to solve the above equation using trial and error method. Values of α/p corresponding to E/p at a given pressure are chosen until the equation is satisfied.

BREAKDOWN IN NON-UNIFORM FIELDS

where d is the gap length. The integration must be taken along the line of the highest field strength.

 The expression is valid also for higher pressures if the field is only slightly non-uniform.

In strongly divergent fields there will be at first a region of high values of E/p over which α/p > 0. When the field falls below a given strength Ec  the integral

ceases to exist. 

Townsend mechanism then loses its validity when the criterion relies solely on the γ effect, especially when the field strength at the cathode is low.

In reality breakdown (or inception of discharge) is still possible if one takes into account photoionization processes. The criterion condition for breakdown (or inception of discharge) for the general case may be represented to take into account the non-uniform distribution of

where Ncr is the critical electron concentration in an avalanche giving rise to the initiation of a streamer (it was shown to be approx. 108), xc is the path of avalanche to reach this size and d the gap length.

Figure 2.9 illustrates the case of a strongly divergent field in a positive point plane gap. Equation (2.15) is applicable to the calculation of breakdown or discharge inception voltage, depending on whether direct breakdown occurs or the only corona.

BREAKDOWN IN LIQUID DIELECTRICS

Liquid dielectrics are used for filling transformers, circuit breakers and as impregnates in high voltage cables and capacitors. For transformer, the liquid dielectric is used both for providing insulation between the live parts of the transformer and the grounded parts besides carrying out the heat from the transformer to the atmosphere thus providing a cooling effect. For a circuit breaker, again besides providing insulation between the live parts and the grounded parts, the liquid dielectric is used to quench the arc developed between the breaker contacts. The liquid dielectrics mostly used are petroleum oils. Other oils used are synthetic hydrocarbons and halogenated hydrocarbons and for very high-temperature applications silicone oils and fluorinated hydrocarbons are also used.

The three most important properties of liquid dielectric are (i) The dielectric strength (ii) The dielectric constant and (iii) The electrical conductivity. Other important properties are viscosity, thermal stability, specific gravity, flash point, etc. The most important factors which affect the dielectric strength of oil are the presence of fine water droplets and the fibrous impurities. The presence of even 0.01% water in oil brings down the dielectric strength to 20% of the dry oil value and the presence of fibrous impurities brings down the dielectric strength much sharply. Therefore, whenever these oils are used for providing electrical insulation, these should be free from moisture, products of oxidation and other contaminants.

The main consideration in the selection of a liquid dielectric is its chemical stability. The other considerations are the cost, the saving in space, susceptibility to environmental influences, etc. The use of liquid dielectric has brought down the size of equipment tremendously. In fact, it is practically impossible to construct a 765 kV transformer with air as the insulating medium. Table 2.1. Shows the properties of some dielectrics commonly used in electrical equipment.

Liquids which are chemically pure, structurally simple and do not contain any impurity even in traces of 1 in 109, are known as pure liquids. In contrast, commercial liquids used as insulating liquids are chemically impure and contain mixtures of complex organic molecules. In fact, their behavior is quite erratic. No two samples of oil taken out from the same container will behave identically. The theory of liquid insulation breakdown is less understood as of today as compared to the gas or even solids. Many aspects of liquid breakdown have been investigated over the last decades but no general theory has been evolved so far to explain the breakdown in liquids. Investigations carried out so far, however, can be classified into two schools of thought.

The first one tries to explain the breakdown in liquids on a model which is an extension of gaseous breakdown, based on the avalanche ionization of the atoms caused by an electon collision in the applied field. The electrons are assumed to be ejected from the cathode into the liquid by either a field emission or by the field enhanced thermionic effect (Shottky’s effect).

This breakdown mechanism explains breakdown only of highly pure liquid and does not apply to explain the breakdown mechanism in commercially available liquids.

It has been observed that conduction in pure liquids at the low electric field (1 kV/cm) is largely ionic due to dissociation of impurities and increases linearly with the field strength. At moderately high fields the conduction saturates but at high field (electric), 100 kV/cm the conduction increases more rapidly and thus breakdown takes place. Fig. 2.10 (a) shows the variation of current as a function of the electric field for hexane. This is the condition nearer to breakdown. However, if the figure is redrawn starting with low fields, a current-electric field characteristic as shown in Fig. 2.10 (b) will be obtained.

The second school of thought recognizes that the presence of foreign particles in liquid insulations has a marked effect on the dielectric strength of liquid dielectrics. It has been suggested that the suspended particles are polarizable and are of higher permittivity than the liquid. These particles experience an electrical force directed towards the place of maximum stress. With uniform field electrodes, the movement of particles is presumed to be initiated by surface irregularities on the electrodes, which give rise to local field gradients. The particles thus get accumulated and tend to form a bridge across the gap which leads finally to initiation of breakdown. The impurities could also be in the form of gaseous bubbles which obviously have lower dielectric strength than the liquid itself and hence on the breakdown of the bubble the total breakdown of liquid may be triggered.

1. Electronic Breakdown

Once an electron is injected into the liquid, it gains energy from the electric field applied between the electrodes. It is presumed that some electrons will gain more energy due to the field than they would lose during a collision. These electrons are accelerated under the electric field and would gain sufficient energy to knock out an electron and thus initiate the process of an avalanche. The threshold condition for the beginning of avalanche is achieved when the energy gained by the electron equals the energy lost during ionization (electron emission) and is given by

e λ E = Chv

where λ is the mean free path, he is the energy of ionization and C is a constant. Table

2.2 gives typical values of dielectric strengths of some of the highly purified liquids.

The electronic theory whereas predicts the relative values of dielectric strength satisfactorily, the formative time lags observed are much longer as compared to the ones predicted by the electronic theory.

Table: 2.2. Dielectric strengths of pure liquids

 BREAKDOWN IN SOLID DIELECTRICS

Solid insulating materials are used almost in all electrical equipment, be it an electric heater or a 500 MW generator or a circuit breaker, solid insulation forms an integral part of all electrical equipment especially when the operating voltages are high. The solid insulation not only provides insulation to the live parts of the equipment from the grounded structures, it sometimes provides mechanical support to the equipment. In general, of course, a suitable combination of solid, liquid and gaseous insulations are used.

The processes responsible for the breakdown of gaseous dielectrics are governed by the rapid growth of current due to the emission of electrons from the cathode, ionization of the gas particles and fast development of the avalanche process. When a breakdown occurs the gases regain their dielectric strength very fast, the liquids regain partially and solid dielectrics lose their strength completely.

The breakdown of solid dielectrics not only depends upon the magnitude of the voltage applied but also it is a function of time for which the voltage is applied. Roughly speaking, the product of the breakdown voltage and the log of the time required for breakdown is almost a constant i.e,

Vb = 1n tb = constant

The characteristics is shown in Fig. 2.11

The dielectric strength of solid materials is affected by many factors viz. ambient temperature, humidity, duration of the test, impurities or structural defects whether a.c., d.c. or impulse voltages are being used, the pressure applied to these electrodes, etc. The mechanism of a breakdown in solids is again less understood. However, as is said earlier the time of application plays an important role in breakdown process, for discussion purposes, it is convenient to divide the time scale of voltage application into regions in which different mechanisms operate. The various mechanisms are:

·        Intrinsic Breakdown

·        Electromechanical Breakdown

·        Breakdown Due to Treeing and Tracking

·        Thermal Breakdown

·        Electrochemical Breakdown

1. Intrinsic breakdown in solids

If the dielectric material is pure and homogeneous, the temperature and environmental conditions suitably controlled and if the voltage is applied for a very short time of the order of 10–8 second, the dielectric strength of the specimen increases rapidly to an upper limit known as intrinsic dielectric strength. The intrinsic strength, therefore, depends mainly upon the structural design of the material i.e., the material itself and is affected by the ambient temperature as the structure itself might change slightly by temperature condition.

In order to obtain the intrinsic dielectric strength of a material, the samples are so prepared that there is high stress in the center of the specimen and much low stress at the corners

as shown in Fig. 2.12. The intrinsic breakdown is obtained in times of the order of 10–8 sec. and, therefore, has been considered to be electronic in nature.

The stresses required are of the order of one million volt/cm. The intrinsic strength is generally assumed to have been reached when electrons in the valance band gain sufficient energy from the electric field to cross the forbidden energy band to the conduction band. In pure and homogenous materials, the valence and the conduction bands are separated by a large energy gap at room temperature, no electron can jump from valance band to the conduction band.

The conductivity of pure dielectrics at room temperature is, therefore, zero. However, in practice, no insulating material is pure and, therefore, has some impurities and/or imperfections in their structural designs. The impurity atoms may act as traps for free electrons in energy levels that lie just below the conduction band is small. An amorphous crystal will, therefore, always have some free electrons in the conduction band. At room temperature, some of the trapped electrons will be excited thermally into the conduction band as the energy gap between the trapping band and the conduction band is small.

An amorphous crystal will, therefore, always have some free electrons in the conduction band. As an electric field is applied, the electrons gain energy and due to collisions between them, the energy is shared by all electrons. In an amorphous dielectric, the energy gained by electrons from the electric field is much more than they can transfer it to the lattice. Therefore, the temperature of electrons will exceed the lattice temperature and this will result in an increase in the number of trapped electrons reaching the conduction band and finally leading to complete breakdown. When an electrode embedded in a solid specimen is subjected to a uniform electric field, the breakdown may occur.

An electron entering the conduction band of the dielectric at the cathode will move towards the anode under the effect of the electric field. During its movement, it gains energy and on collision, it loses a part of the energy. If the mean free path is long, the energy gained due to motion is more than lost during collision. The process continues and finally may lead to the formation of an electron avalanche similar to gases and will lead finally to breakdown if the avalanche exceeds a certain critical size.

ELECTROMECHANICAL BREAKDOWN

When a dielectric material is subjected to an electric field, charges of opposite nature are induced on the two opposite surfaces of the material and hence a force of attraction is developed and the specimen is subjected to electrostatic compressive forces and when these forces exceed the mechanical withstand the strength of the material, the material collapses. If the initial thickness of the material is d0 and is compressed to a thickness d under the applied voltage V then the compressive stress developed due to electric field is

where εr is the relative permittivity of the specimen. If γ is Young’s modulus, the mechanical compressive strength is

Equating the two under equilibrium condition, we have

For any real value of voltage V, the reduction in thickness of the specimen cannot be more than 40%. If the ratio V/d at this value of V is less than the intrinsic strength of the specimen, a further increase in V shall make the thickness unstable and the specimen collapses.

The highest apparent strength is then obtained by substituting d = 0.6 d0 in the above expressions.

The above equation is approximate only as γ depends upon the mechanical stress. The possibility of instability occurring for the lower average field is ignored i.e., the effect of stress concentration at irregularities is not taken into account.

THERMAL BREAKDOWN

When an insulating material is subjected to an electric field, the material gets heated up due to conduction current and dielectric losses due to polarization. The conductivity of the material increases with an increase in temperature and a condition of instability is reached when the heat generated exceeds the heat dissipated by the material and the material breaks down.

Fig. 2.13 shows various heating curves corresponding to different electric stresses as a function of specimen temperature. Assuming that the temperature difference between the ambient and the specimen temperature is small, Newton’s law of cooling is represented by a straight line.

The test specimen is at thermal equilibrium corresponding to field E1 at temperature T1 as beyond that heat generated is less than heat loss. Unstable equilibrium exists for field E2 at T2,

and for field E3 the state of equilibrium is never reached and hence the specimen breaks down thermally.

In order to obtain a basic equation for studying thermal breakdown, let us consider a small cube (Fig. 2.14) within the dielectric specimen with side Δx and temperature difference across its faces in the direction of heat flow (assume here the flow is along x-direction) is ΔT. Therefore, the temperature gradient is

Here the second term indicates the heat input to the differential specimen. Therefore, the heat absorbed by the differential cube volume

The heat input to the block will be partly dissipated into the surrounding and partly it will raise the temperature of the block. Let CV be the thermal capacity of the dielectric, σ the electrical conductivity, E the electric field intensity. The heat generated by the electric field = σE2 watts, and suppose the rise in temperature of the block is ΔT, in time dt, the power required to raise the temperature of the block by ΔT is

The solution of the above equation will give us the time required to reach the critical

temperature Tc for which thermal instability will reach and the dielectric will lose its insulating properties.

However, unfortunately, the equation can be solved in its present from CV, K and σ are all functions of temperature and in fact, σ may also depend on the intensity of the electrical field.

Therefore, to obtain a solution of the equation, we make certain practical assumptions and we consider two extreme situations for its solution

Table: 2.3 Thermal breakdown voltage

Table 2.3 gives for thick specimen, thermal breakdown values for some dielectric under a.c. and d.c. voltages at 20°C.

BREAKDOWN IN COMPOSITE DIELECTRICS

A vacuum system is one in which the pressure maintained is at a value below the atmospheric pressure and is measured in terms of mm of mercury. One standard atmospheric pressure at 0°C is equal to 760 mm of mercury. One mm of Hg pressure is also known as one torr after the name of Torricelli who was the first to obtain pressures below the atmosphere, with the help of mercury barometer. Sometimes 10–3 tours are known as one micron. It is now possible to obtain pressures as low as 10–8 Torr.

In a Townsend type of discharge, in a gas, the mean free path of the particles is small and electrons get multiplied due to various ionization processes and an electron avalanche is formed. In a vacuum of the order of 10–5 Torr, the mean free path is of the order of few meters and thus when the electrodes are separated by a few mm an electron crosses the gap without any collision. Therefore, in a vacuum, the current growth prior to breakdown cannot take place due to the formation of electron avalanches.

However, if it could be possible to liberate gas in the vacuum by some means, the discharge could take place according to the Townsend process. Thus, a vacuum arc is different from the general class of low and high-pressure arcs. In the vacuum arc, the neutral atoms, ions, and electrons do not come from the medium in which the arc is drawn but they are obtained from the electrodes themselves by evaporating its surface material. Because of the large mean free path for the electrons, the dielectric strength of the vacuum is a thousand times more than when the gas is used as the interrupting medium.

In this range of vacuum, the breakdown strength is independent of the gas density and depends only on the gap length and upon the condition of the electrode surface. Highly polished and thoroughly degassed electrodes show higher breakdown strength. Electrodes get roughened after use and thus the dielectric strength or breakdown strength decreases which can be improved by applying successive high voltage impulses which of course does not change the roughened surface but removes the loosely adhering metal particles from the electrodes which were deposited during arcing. It has been observed that for a vacuum of 10–6 torrs, some of the metals like silver, bismuth-copper, etc. attain their maximum breakdown strength when the gap is slightly less than 3 mm. This property of vacuum switches permits the use of short gaps for fast operation.