Dr.Qais Alsafasfeh

Electrical Breakdown of Gases in Uniform Fields

Introduction

At normal temperature and pressure, gases are excellent insulators but background

currents of the order of micro-amps can be measured if an electric field of several

kV/mm is applied. This current results from the electron/ion pairs produced by high-

energy particles, either cosmic rays or derived from natural radioactivity, striking an

air molecule:

high-energy particle + M ==> M+ + e

If the voltage is increased sufficiently, the electron is accelerated by the electric field

towards the positive electrode (or anode) and further ionisation can occur. The electron will collide with gas molecules and most of these will be elastic collisions,

but, if it has gained enough kinetic energy (KE), it will ionise the gas molecule it hits: e + M ==> M

+ + e + e.

Enough energy means energy greater than the ionisation energy of the molecule.

The process of acceleration until a collision with a molecule occurs, with most of the

collisions elastic, and some inelastic (i.e., ionising) is illustrated in the AVAL-1.exe

program. The KE gained by the electron is (electric field)*(distance travelled before the next collision) see box below.

Now there are two electrons and the process can repeat, and repeat, and repeat,

causing an exponential increase in the number of electrons. The situation after 4 such

sets of ionisations by accelerated electrons is illustrated in the AVAL-2.exe program

from which the diagram below is taken. (The original high-energy particle ionisation

occurs at A subsequent ionisations are caused by the accelerated electrons).

There are 1+1+2+4+8 = 16 positive ions

and 16 electrons here

Note that while the electron is accelerated towards the anode, the positively-charged

ion is obviously accelerated towards the cathode. However the ion, being far

heavier, is accelerated more slowly: the average velocity of the electrons is about ten

times faster than that for the ions. This causes the situation seen above with the

electrons moving swiftly to the right in a group, leaving clumps of 1, 2, 4 and 8 ions

behind. This is seen more clearly in the AVAL-4.exe program in which 10 sets of

ionisations have occurred (so there are 210, or 1024, electrons and the same number of

positive ions).

1.1

Kinetic energy gained by the electron = work done on the electron

= (force on the electron) * (distance travelled by the electron)

= (e.E)*x i.e., proportional to both the electric field and the distance gone.

Dr.Qais Alsafasfeh

The electron will normally have many elastic (low-energy) collisions before the

ionising collision hence the crooked paths seen in the animations. Because of the

random nature of the number of collisions before the ionising collision, the distance

between ionisations is also variable again, as seen in the animations.

Avalanches

In the AVAL-4 diagram below there are 1024 electrons (and the same number of

positive ions), the electrons and ions being indistinguishable in black and white

reproduction. The distribution graphs for the two charged particles are shown, and

explain the comet-like shape of the avalanche, as this phenomenon is called.

Note the overlapping of the two graphs: this means that there will be a number of

electron/positive-ion collisions which may result in recombination:

e + M+ ==> M + energy

This recombination energy is usually released as a photon of light energy.

(a) (b)

Cloud chamber photography of single avalanches (a) in nitrogen (N2) at 0.37 bar

and (b) in carbon dioxide (C02), both in a 36-mm gap.

The voltage was a DC voltage pulse lasting 0.4 ms. [H. Raether, Electron Avalanches and Breakdown in Gases, 1964, p.5]

1.2

positive

ions

electrons

Dr.Qais Alsafasfeh

The ionisation coefficients

The ionisation coefficient, , is defined as the probability that an electron will make an ionising collision in travelling unit distance in the direction of the anode.

In addition there is a possibility (especially for slower-moving electrons) that an

attaching collision takes place:

e + M ==> M.

The attachment coefficient, , is defined as the probability, per unit distance travelled in the direction of the anode, that an electron will attach to a molecule to form a negative ion.

As mentioned earlier, the kinetic energy (KE) gained between collisions needs to

exceed the energy required to ionise the molecule. The distance between collisions is

inversely proportional to the density and hence to the pressure so it should not be

surprising (see box) that

/p = f(E/p).

For similar reasons it is found that

/p = g(E/p).

For simplicity, an effective ionisation coefficient, , is defined as

=

Many text books use the empirical equation

/p = 1100(exp{-27.4 E/p})

for air but it is very approximate. Better ones are available but are generally more troublesome to apply (see, for example, MacAlpine & Li, IEEE Trans.D&EI, Vol.7,

pp.752-757, 2000). Here, and in general in this course, the units are assumed to be

mm, kV and bar or their combinations.

Clearly, if attachment is more likely

than ionisation when a collision

occurs, or >, avalanches cannot develop.

In nitrogen the attachment

coefficient, , is negligible; in

oxygen it is very small. So, in this

graph of /p versus E/p for air it is only at low fields, below 2.3 kV/mm

bar, that > (i.e., is negative). Even then it is only just below zero.

The field at which = is called the Critical Field.

1.3

-5

0

5

10

15

20

25

0 1 2 3 4 5 6

E/p (kV/mm.bar)

alpha/p (1/mm.bar)

Li-MacA

Geballe & H

Prasad

Morruzzi & P

The energy gained between collisions = e.E. = eE/p

because (= mean free path between collisions) is proportional to 1/p (p = pressure)

The probability of a collision resulting in ionisation is a function of the energy gained between

collisions, that is, from the above, a function of E/p, say F(E/p).

The number of collisions (any kind) per unit distance = 1/ = Ap (A is a constant)

the number of ionising collisions, , is F(E/p)*Ap, or, /p = f(E/p)

Dr.Qais Alsafasfeh

Avalanche calculations

The average size of an avalanche may be

calculated for uniform-field conditions by

considering the number of electrons n passing through a plane at a distance x from the cathode in the direction of the electric field (towards the

anode) in a time t. Simple integration (see box) gives

n(x) = ex

How big is an avalanche? Consider an electron produced at x = 0 in a 10-mm gap (e.g. as an

electron-ion pair due to a cosmic ray, or by

emission from the electrode) in air at

atmospheric pressure.

If the applied voltage is 25 kV, E = 2.5 kV/mm,

and is found (from the graph on the previous

page) to be close to zero.

Now try 30 kV: = 1.3 mm-1 the number of electrons in the head of the avalanche when it strikes the anode will be

n(10mm) = exp(13) = 4.4x105

Now try 35 kV n(10mm) = exp(30) = 1.1x1013 . This is a huge increase!

Clearly if the current (the sum of all the electrons in all the avalanches which occur in

a second) increases at this rate, breakdown MUST occur near this voltage.

The reverse calculation: what is the voltage which gives, say, 108 electrons in the

head of the avalanche when it strikes the anode?

n(10mm) = exp(10.) = 108

Therefore = 1.84 mm-1,

So, V = 32 kV.

Avalanches in non-uniform fields

In a non-uniform field, the same approach as used above gives

n(x) = exp( (E).dx ) This is useful in for example, coaxial cable or busbar systems see next lecure.

Sulphur hexafluoride, SF6

This is a very important insulating gas and is widely used in equipment for electrical

power transmission and distribution. It is colourless, odourless and heavy.

For SF6 the critical field is at 8.85 kV/mm as shown in the graph overleaf and

the attachment coefficient is much larger than that for oxygen.

From the right-hand graph, an empirical expression for the effective ionisation

coefficient, or (-), may be obtained as /p = 26E - 230.

1.4

The average size of an avalanche

Consider the number of electrons n passing through a plane at a distance x from the cathode in the direction of the

electric field (towards the anode) in a

time t.

The number of electrons passing through

a plane at a distance x + dx may be written as n + dn (again in a time t) where,

dn = n.dx, using the definition of ,

so that, integrating between limits of x = 0 and x, and remembering that each avalanche is started by a single electron, n(x) x

dn/n = .dx, 1 0

or, n(x) = ex

Unless the field is non-uniform, varying

with x, which means varies with x,

so n(x) = exp( .dx).

Dr.Qais Alsafasfeh

60

70

80

90

100

110

120

130

140

8 9 10 11

E/p, kV/mm.bar

Ionisation coefficients, 1/mm.bar

-50

0

50

100

150

200

8 10 12 14 16

E/p kV/mm.bar

Effective alpha / p, 1/(mm.bar)

This formula gives the critical field as Ec = 230/26 = 8.85 kV/mm.

How big is an SF6 avalanche? Consider an electron produced at x=0 in a 10-mm gap, as previously, but in SF6 at atmospheric pressure. If the applied voltage is 88.5, 89.0

and 90.0 kV, then, from the formula, = 0, 1.4 and 4.0, respectively, and the number of electrons in the head of the avalanche is n(10mm) = 1, 1.2 x 106 and 2.35 x 1017!

Clearly the size of an SF6 avalanche increases hugely within 1 to 2% above the

critical field. But what is the criterion for breakdown?

The Streamer Theory of electrical breakdown in gases

The electrons in the head of the avalanche increase the field ahead of it. Similarly, the

positive ions, particularly those in the high concentration zone just behind the head,

increase the field in the tail. When the avalanche is small, this is an insignificant

effect, but as the avalanche grows there must be a critical size when it is the

concentration of charge is great enough for the field to be increased to twice the

original gap field.

Both Raether (in Germany) and Meek (in England) came to the conclusion that when

there were about 108 electrons in the avalanche head, the field due to the avalanche

itself could equal the main field, and that this would lead to the development of a

channel of ionised conducting gas. Meek called this a streamer (Raether called it a

kanal, the German word for channel).

The mechanism they proposed was that in the region where the electrons and positive

ions overlap (see diagram on page 1.2), recombination would take place:

e + M+ ==> M + photon

This region will therefore be a source of photons which would speed off (at the

velocity of light) in all directions. When they strike molecules, photo-ionisation - the

ionisation of molecules by photon impact can occur:

photon + M ==> M+ + e

These photo-electrons initiate new avalanches: those in the higher-field zones ahead

and behind the mother avalanche, will grow even faster than the mother avalanche

did because the value of increases very quickly above the critical field. Between 4

and 8 kV/mm in air increases by a factor of 10; in SF6 the situation is even more

spectacular as breakdown tends to be close (within 1 or 2% - see above) to the critical

field.

1.5

-

Dr.Qais AlsafasfehThey would produce further avalanches ahead and behind, thus producing a column

of conducting ionisation. Consider electrons produced by photo-ionisation at A B C,

D and E in the figure below. At A the field is perhaps 5 times in the gap remote from

the avalanche a baby avalanche will develop far faster than the original or

mother avalanche owards the anode. Even at B the field is perhaps twice the gap

field so the baby avalanche will still develop much faster than the mother

avalanche. At C the field is zero nothing will happen. At D the field is again about

twice the gap field so the baby avalanche will still develop much faster than the

mother avalanche, and again in the anode direction (or, more precisely, towards the

maximum density of positive ions). At E the field is again about twice the gap field,

but in the opposite direction, so the baby avalanche will still develop much faster

than the mother avalanche, but in the cathode direction.

All this development of avalanches of similar size in electron numbers, though

occupying a smaller space, occurs immediately ahead of the head of the avalanche,

behind it in the tail region, and close besides the dipole area (in the mother

avalanche near E) thus extremely quickly, almost explosively, forming a column of

avalanches bridging of the gap between the electrodes (see the STREAMER

program). This column of free charges (positive ions and electrons) is conductive so current flows. Positive feedback occurs as, while the field is maintained, more and

more avalanches occur, the number of charged particles increases, the current

increases until the source impedance limits the current to the short-circuit current,

thus dropping the voltage across the gap to near zero. This defines electrical

breakdown.

The electric field

around a large

avalanche

The critical size for an avalanche to transform into a streamer for air is usually taken

as 108, which is therefore the breakdown criterion for uniform-filed gaps. It is easy to

demonstrate that taking the critical size as 108 or, say, 2x10

8 makes a change to the

calculated breakdown voltage which is usually negligible in practical terms.

For SF6, many workers have suggested that 107 gives better agreement with

experiment.

Taking N = 108 = ex = eK, gives K = 18.4, an alternative criterion.

For N = 107, K = 16.1.

1.6

B A

C

D

E

Dr.Qais AlsafasfehPaschen's Law Vbdn is a function of pd

This was discovered experimentally by a German scientist, F. Paschen, who published

it in 1889. It may be derived as follows: breakdown occurs when

exp(d) = 108, or d = K

/p = f(E/p) = K/pd

Hence, Vbdn = F(pd) or Paschen's Law.

A log/log graph of the

breakdown voltage of

nitrogen against pd.

Gallagher & Piermain, page 49

Note: 1 atm.cm = 1.013 bar.cm = 10.13 bar.mm = 1013 kPa.mm

The graph shown is for nitrogen, but similar shapes are found for all gases.

Note that for pd > 100 bar.mm (= 10 atm.cm in the figure) Paschens Law fails. This

is because of the field distortions around small imperfections, and dust particles, on

the electrode surface. This will be covered in Unit 2 on breakdown in compressed

gases.

Similarly, for a near vacuum, pd < 10-3 bar.mm (= 10

-4 atm.cm in the figure),

Paschens Law also fails. This is because the number of mean free paths in the

distance from cathode to anode becomes too low for it to be possible for avalanches to

develop. This will also be covered in Unit 2.

The so-called Paschen minimum can be of importance for electrical circuits on, for

example, printed circuit boards in space or near-space conditions. For power

engineering it is seldom of direct interest. Vacuum circuit-breakers operate on the

left-hand part of the curve. Atmospheric-pressure air as insulation involves

dimensions of the order of metres (e.g., overhead lines). SF6 is normally used at a

pressure of 4 to 5 bar and dimensions in the region of 10s of mm. Do the

calculations yourself.

The breakdown voltages at the

Paschen minima for various gases

Gallagher & Piermain, page 49

1.7

Dr.Qais Alsafasfeh

1. Electrical Breakdown of Gases in Quasi-Uniform Fields

Quasi-Uniform Fields

By this meant an electrode gap where the ratio of the maximum and minimum fields is less than about 10. Common examples are electrode systems where one electrode is a rod and the other is a tube and both are coaxial.

The avalanche size is given by

n(x) = exp( (E).dx )

(See page 1.4). If is known as a function of E ,and E is known as a function of x, the avalanche size can be determined. If analytical expressions are not known for these functions, or cannot be integrated, numerical integration can be used.

See Example quasi-uniform fields.pdf.

2. Electrical Breakdown of Compressed Gases in Uniform Fields

Introduction

The electrical breakdown strength of gases increases with pressure, as may be seen from the Paschen's Law graph (page 1.6). Why? As the pressure increases the mfp decreases and so a higher electric field is required in order that the electrons may gain sufficient kinetic energy (k.e.) between collisions to cause ionisation. However, it is found that Paschen's Law no longer applies for pressures above about 5 bar, unless great care is taken

to limit the emission current from the cathode and

to avoid the presence of dust, particularly conducting particles.

The higher the pressure the harder it becomes to avoid the effects of cathode emission currents and dust.

Electron Emission Currents

The graph at the right shows the very high currents caused by field-enhanced electron emission. The 3 graphs refer to plane-parallel electrodes: the electrodes just after being

manufactured and polished (top graph),

the same after several breakdowns (middle graph), and

the same with a thin (0.1mm) layer of polythene stuck to the surfaces (lowest graph).

2.1

Dr.Qais AlsafasfehThere are two mechanisms by which such emission can occur: (a) Schottky and (b) Fowler-Nordheim emission.

Simply explained, Schottky emission is the effect of a high field in reducing the work function, that is, the energy which electrons need in order to leave the metal; and Fowler-Nordheim emission is a quantum mechanical effect by which electrons can tunnel through a thin potential wall.

The latter requires virtually perfectly clean surfaces and is therefore only possible in near vacuum conditions. In all practical cases, therefore, only Schottky emission or field-enhanced thermal emission occurs.

Current density, J = AT2. exp(-BE/T) where E is the electric field at the surface, T is the temperature in degrees Kelvin and A & B are constants. It requires relatively high electric fields at the surface, before significant emission occurs, and so does not greatly affect breakdown at atmospheric pressure.

The breakdown of nitrogen at 15 bar and a 2mm

electrode separation 0

1

2

3

4

28 29 30 31 32 33 34 35 36 37 38 39 40

Impulse breakdown field, kV/mm

Number of breakdowns

Clean

Dusty

The two histogram figures demonstrate the effect of dust on the impulse strength of nitrogen (above) and SF6 (next page) at 15 atm - a lowering of the breakdown strength by some 30 to 50%, even with polythene-covered electrodes stopping electron emission.

Clearly imperfections such as emission currents and dust are the cause of the breakdown voltages for high pressure gases being lower than expected from Paschens Law.

Why does dust cause problems, and increasingly so as the pressure increases? Why do emission currents cause problems, and what causes them?

The breakdown of SF6 at 15 bar and a 2mm electrode separation

0

0.5

1

1.5

2

2.5

3

3.5

70 75 80 85 90 95 100105110115120125130135140

Impulse breakdown field, kV/mm

Number of breakdowns

Clean

Dusty

2.2

Dr.Qais Alsafasfeh

Why does dust cause a problem?

This illustration is merely for interest and for those of a mathematical bent.

The answer lies in the exponential relationship between and E, as the following example will show.

Consider a conducting particle of 10-m size attached to one electrode: suppose, for simplicity, it enhances the field by a factor of 5 for the first 5 m, 3 for the next 5 m and 2 for a further 5 m. First, the breakdown field for the case without a particle is calculated, using simple equations for (E) and assuming breakdown occurs for d=18.4 since this is the criteria for streamer formation across the gap.

Then, for 4 different pressures and some value of E, the values of .x for these 3 regions and the rest of the gap are calculated. By trial and error the value of E is found which makes (.x) = 18.4 (I used Excel).

The results are tabulated below. The value of E with a particle present is compared with the value for a clean gap without any particles present and it is seen that the effect of particles is very small at atmospheric pressure but rapidly becomes very significant.

Air pressure (in bar) 1 5 10 15

/p = 18.4/(p*10*1100) = 1.84 0.368 0.184 0.1227 ln(/p1100) = -27.4*p/E = -6.393 -8.003 -8.696 -9.101

without particle, E (in kV/mm) = 4.29 17.12 31.51 45.16 By trial and error: main gap field, with

particle =

4.20

16.15

28.61

39.54 First 5 m: .x = 1.49 5.04 8.100 10.32

Second 5 m: .x = 0.62 1.63 2.26 2.58 Third 5 m: .x = 0.21 0.40 0.46 0.46 Rest of gap, .10 = 16.07 11.37 7.61 5.04

Sum across gap of all these .x = 18.40 18.43 18.43 18.40

E(with particle)/E(without) = 0.980 0.943 0.908 0.876 Percentage strength reduction = 2.1 5.7 9.2 12.4

In case this is not clear, the full calculation is given overleaf for the 5 bar case. (N.B., as usual, all quantities are in units of kV, mm, bar and their combinations.

For the uniform-field case (no particle), at 5 bar,

exp(d) = 108, i.e., d = 18.4, so = 1.84 /mm

But /p = 1100 exp(-27.4 p/E)

So 1.84/5 = 1100 exp(-27.4 * 5/E)

E = 17.12 kV/mm

For the uniform-field case with a particle, at 5 bar, using E = 16.15 kV/mm,

exp(.dx) = 108, i.e., d = 18.4 .x

Since = 5*1100*exp(-27.4 p/E)

1.x = 5*1100*exp(-27.4 p/5E) *5*10-3 = 5.04

2.x = 5*1100*exp(-27.4 p/3E) *5*10-3 = 1.63

3.x = 5*1100*exp(-27.4 p/2E) *5*10-3 = 0.40

4.x = 5*1100*exp(-27.4 p/E) *9.975 = 11.37

Sum, .x = 18.4

2.3

Dr.Qais Alsafasfeh

Repeat calculation but for SF6

Consider the same conducting particle of 10-m size attached to one electrode and again enhancing the field by a factor of 5 for the first 5 m, 3 for the next 5 m and 2 for a further 5 m. The breakdown field for the cases with and without a particle are calculated in the same way, but assuming breakdown occurs for d=16.1, this being the criteria for streamer formation across the gap for SF6.

Again it is seen that the effect of particles is very small at atmospheric pressure but rapidly becomes very significant, indeed disastrous, for SF6.

SF6 pressure (in bar) 1 5 10 15

without particle, E (in kV/mm) = (230*p +1.61) / 26 =

8.91

44.29

88.52

132.75

By trial and error: main gap field, with particle =

8.88

25.66

37.60

48.65

First 5 m: .x = 4.62 10.93 12.94 14.37 Second 5 m: .x = 2.31 4.26 3.16 1.72 Third 5 m: .x = 1.16 0.92 (-1.72) (-4.60)

Rest of gap, .10 = 8.01 (-4821) (-13204) (-21818) Sum of positive .x values = 16.10 16.11 16.10 16.10

E(with particle) / E(without) = 0.996 0.579363 0.425 0.366 Percentage strength reduction = 0.4 42.1 57.5 63.4

Note: for most cases in SF6 the value of is negative for the main gap, so K is determined for the enhanced area only.

The Jumping Particle Mechanism

Another possible breakdown mechanism involving dust particles is the jumping particle mechanism: dust particles on the electrodes will become charged to the same potential and therefore be attracted to the opposite electrode. If light enough, they will accelerate towards the other electrode and, it is suspected, discharge by a minute spark when a few micrometres away, just before contact is made. It has been shown that at high pressures electrical breakdown can easily be triggered by small injections of plasma ionised gas into the gap.

Electron Emission

When the bare-electrode graphs of the emission figure on page 2.1 are re-plotted for the Shottky relationship, as log(emission current) versus (electric field), a good straight line was obtained as seen on the right. This shows that the emission was indeed the Shottky field-enhanced thermal emission process and not the Fowler-Nordheim quantum-mechanical barrier-tunnelling one.

2.4

Dr.Qais Alsafasfeh

As stated above, in a good vacuum it is likely that the mechanism for electron emission is the Fowler-Nordheim one, but for compressed gases the necessary thin energy barrier could not exist as the surfaces of metals are covered in thin layers of tarnish such as moisture, oxides and surface-adhering gas molecules there is no such thing as a clean surface at sub-microscopic levels. Consequently Schottky emission has to be assumed.

Virtually all the electron emission takes places at tiny protuberances little hills of micron dimensions on the surface of conductors where the field there may be magnified several times.

These can cause the electron emission to increase by several orders of magnitude. Typically 90% of the emission from a surface will come from a few of these hot spots. The figure shows the field enhancement caused at the tip of a hill shaped as half an ellipsoid of revolution.

Note that even a hemispherical hill has a field enhancement by a factor of 3 at its top.

The very high number of electrons emitted from the top of the hill are more likely to form avalanches which can transform into streamers in the high-field area near the emission point.

In addition, the avalanches do not need to become so large, in order to transform into streamers, as there are many developing in parallel, all adding to the field distortion which is what causes streamer development.

Conditioning of Electrodes

The lowering of breakdown strengths by the very high electron emission currents from bare electrodes at the high electric fields which can be reached at high pressures also need explaining. The electron emission tends to be from very small areas where a pointed protuberance (=a microscopic hill) enhances the field. However the very high current densities further distort the field locally leading to streamer-type breakdown mechanisms. Consequently gas gaps between bare electrodes will break down at very low voltages initially.

After several breakdowns the breakdown voltage will stabilise at a higher level: it is believed that this reflects the burning off, of areas of high emission and of particles of dust on the electrodes. The energy released by the spark burns, vaporises or melts the surface protuberances and dust particles. The electrodes are then said to be conditioned.

2.5

Dr.Qais Alsafasfeh

This agrees well with the graphs on page 2.1 and 2.4 where it is seen that the emission from the unconditioned electrodes greatly exceeds that of the conditioned electrodes. Also near the top of the conditioned-electrodes graph there seem to be a break where the emission decreases by what at first sight may appear a small amount, but is in fact a decrease by a factor of two. A reasonable explanation would be that the emitter of the highest current was melted by the current and ceased emitting.

Consequences and cautions

The effect of dust and electron emission in reducing the breakdown strength of gases from the values calculated using the streamer criterion has been demonstrated, but we cannot estimate the actual breakdown voltage. The field above the irregularity (dust or micro-hill) IS increased, so avalanches can form there easily. Electrons ARE emitted, so multiple avalanches can form simultaneously presumably 100 avalanches of 106 electrons distort the field much as an avalanche of 108 electrons would. But we obviously cannot know what irregularities are present their sizes and numbers.

Furthermore, even if we could know that the conditions are such as to cause a streamer to form in the enhanced-field region above a particular irregularity this does not mean breakdown will occur.

For example, in SF6, the field away from the enhanced-field region will probably be below the critical field and therefore the streamer will only develop in the high-field region. This localised streamer will act as a conducting extension of the irregularity - causing a new enhanced-field region at the streamers tip. But whether this will be sufficient to cause a further streamer, and thus be a self-propagating phenomena, leading to complete bridging of the gap and complete breakdown, is obviously unknown.

In general, practical applications of compressed gases are in general restricted to a maximum of about 5 bar, as a result of the many uncertainties and problems with the use of highly compressed gases, that is, the difficulties in achieving both a dust-free system and low electron emission rates.

2.6

Dr.Qais Alsafasfeh

3. Electrical Breakdown in Vacuum

Surprisingly, vacuum breakdown is a topic which has much in common with breakdown in compressed gases in that it is largely controlled by the imperfections. These are of two kinds: small areas of very high electron emission from small protuberances (very small pointed hills) on the electrode surfaces; and the presence of free particles.

In a vacuum of 1 bar (=10-3 torr) the average distance between collisions is about 50 mm so no avalanche or streamer breakdown can take place.

Small conducting particles will increase the field at their own surface and there may then be high levels of electron emission from their surface.

However, high-field emission of electrons from small sites (hills or conducting particles) on the cathode surface causes local heating of the anode surface opposite, where the jet of electrons impacts. This impact area will be very small since there is no spreading out of the beam of electrons since there are no collisions with gas molecules. Furthermore the current density at the emission source may be sufficient to cause melting or even explosion of the cathode protuberances, if it is pointed enough.

The extra scale shows the number of mean free paths in the gap width,

i.e., the number of times an electron will on average collide (elastically or inelastically) with molecules in crossing the gap

The heating at the point where the electrons impact causes the release of metal vapour and absorbed gases from the metal surface. It is this resulting vapour which breaks down.

Thus, in a vacuum of better than 1 bar, the breakdown strength is related to the electric field and to the condition and material of the electrodes, and not to the actual level of vacuum. There is therefore no difference between a l-bar, or a 0.0l-bar, vacuum as far as breakdown strength is concerned.

The small protuberances causing the high-density electron emission can be removed by medium-energy conditioning of the electrodes, again, as is the case with compressed gases.

2.7

Dr.Qais Alsafasfeh

Corona and Stepped Breakdown

Corona Introduction

The field is very high close to a metallic point or a knife-edge, if they are at a high

voltage. It decreases very quickly, most of it being gone within a distance equal to

the radius of the point or edge.

The graph shows the field between a 1-mm radius hemispherical point (at the end of a

1-mm radius rod) 30 mm from an earthed cup electrode, when 10kV is applied

between the two electrodes.

0

2

4

6

8

10

12

14

0 1 2 3 4 5

Distance from the surface, mm

E-field and (overall alpha)/10

E-field, kV/mm

(Overall alpha)/10, per mm

1 mm from the surface, the field has dropped by some 75%, 2 mm from the surface,

the field has dropped by some 90%.

Given the fast rise of with E (see the graphs on pages 1.3 and 1.4), it should not be

surprising that has dropped to zero by 1mm (and then goes negative), so that

nothing much happens outside the first 1 mm of gas. This is generally true provided

the radius of the pointed electrode is small compared with the gap size.

If the field is strong enough streamers will occur in the high-field area, this is called

corona.

Each streamer is a pulse of current and therefore can be measured in the circuit

supplying the high voltage. Since they last for a time of the order of a microsecond

and occur at intervals of 10 to 100 s, they cause radio interference and can also be

detected audibly (a sizzling noise). This can be a nuisance but can also be used to

detect incipient trouble in, for example, high-voltage machines.

All points or sharp edges when at a high voltage can exhibit corona. The point/cup

electrode system shown above is merely to make explanation and calculation easier.

Negative corona - calculations

The electric field at any point in the space between a point electrode and a plane may

be determined by a combination of computer field plotting and calculation. In the

case of the hemispherically-tipped point and cup system described above, the field

near the tip is given by E = 1.0345 V/r2.

3.1

Dr.Qais Alsafasfeh

The effective ionisation coefficient for air, = -, was shown in a graph on page 1.3. The best-fit polynomial for the data shown is found to be

/p = 0.0726(E/p)3 + 0.6551(E/p)2 2.972(E/p) + 2.2805 Using this equation, the value of /p was also plotted on the graph.

Now, the size of an avalanche starting from one electron at the surface of the

electrode is

n(x) = exp( (E).dx ) = exp(K) (see page 1.4) K is the area under the graph and can be found analytically by integration or, using

Excel, by adding up the very small areas between (e.g.) two radial distances 0.01 mm

apart. The area under the curve is K=23, so it would transform into a streamer well

before reaching the boundary of the ionisation area.

Why? The critical size of an avalanche to transform into a streamer is 108 electrons,

or e18.4

electrons. Another way of writing this is that the criterion for transformation

to a streamer is K = 18.4.

In fact careful calculation shows that an avalanche starting from one electron at 0.045

mm from the surface of the electrode will reach a size of 108, or e

18.4, electrons at the

ionisation boundary. This is where E, has dropped to 2.3 kV/mm, and so has dropped to zero. Further out E is less than this critical value and will be negative, so the avalanche will not only cease to grow, but will decrease in size as the free

electrons have attaching collisions. (In this case the ionisation boundary is at 1.1 mm

from the surface).

Calculation shows that if the applied voltage is reduced to 9.4 kV, then the size of an

avalanche starting from one electron at the surface of the electrode is the critical size,

108, or e

18.4, electrons by the time it reaches the ionisation boundary and stops

increasing in size.

If the voltage is now increased to

12 kV, the value of K reaches 18.4

(integrating from the surface of the

point electrode) at 0.12 mm from

the surface i.e., the avalanche

reaches critical size within a

distance of 0.12 mm.

Furthermore, an avalanche starting

from one electron at 0.135 mm

from the surface of the electrode

will reach a size of 108, or e

18.4,

electrons at the ionisation

boundary.

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4 5

Dist from the surface, mm

E-field and (overall alpha)/10

E-field, kV/mm

(Overall alpha)/10, per mm

Summarising, as the voltage is increased, streamers will start to occur at 9.4 kV this

is called the Corona Onset Voltage. At 10 kV any electron starting between the

surface and 0.045 mm away from the surface will develop into an avalanche which

will transform into a streamer. (An electron starting say 0.05 mm away from the

surface will develop into an avalanche which will never get big enough to transform

into a streamer). And at 12 kV any electron starting between the surface and 0.135

mm away from the surface will develop into an avalanche which will transform into a

streamer.

Another worked example is downloadable for a case where the radius of the tip of the

point electrode is r = 1.5 mm.

3.2

Dr.Qais Alsafasfeh

Negative corona - qualitative

An electron produced at A (see diagram)

will cause a larger avalanche to develop

than an electron produced at B. So there is

a region 1 (see diagram) near the

electrode where electrons will develop into

large enough avalanches (about 108

electrons) to transform into streamers.

There must also be a region 2 outside of

region 1 where electrons will develop

into avalanches which never get large

enough to transform into streamers.

Streamers consist of the column of ionisation formed by many (30 to 100?) baby

avalanches developing ahead and behind a main avalanche. Outside of the high-field

regions (1 and 2) where > (or > 0) that is, in region 3 attachment

predominates, so avalanches cannot form. It follows that streamers can only form in

the high-field region where > .

Note:

In both regions 1 and 2, > .

In region 3, > .

The boundary between region 2 and region 3, is at =

Negative corona - measurements

By inserting a resistor in the earth lead and applying the voltage to an oscilloscope,

these streamers may be seen as pulses (see next page), whose frequency increases

with the applied voltage. They are called Trichel pulses after the first person to

observe them (or, at least, the first to publish his observations).

Generally speaking, no

streamer can occur until the

previous one has decayed and

disappeared because its

conductivity lowers the electric

field nearby. This happens (a)

because the electrons and

positive ions collide and

recombine (to form molecules)

and (b) because the electrons

and positive ions drift away

towards the electrodes. Then

there is the further delay,

waiting for a free electron to

appear in the volume near the

pointed electrode from which

avalanches can develop and transform into streamers (i.e., region 1 in the figure

above). At higher voltages, both these processes happen faster, so the streamers

occur more frequently.

3.3

= line

0

20

40

60

80

100

0 5 10 15 20 25Applied voltage, kV

Pulse frequency, kHz

0.2 bar 0.4 bar

0.6 bar 0.8 bar

1.0 bar

Dr.Qais Alsafasfeh

The following graphs from saved DSO screens are for concentric electrodes as in

the diagram on page 3.1 with the earthed electrode having a 30-mm internal diameter

and the pointed electrodes hemispherical tip having a radius of 1.5 mm, as in the

worked example (Example neg corona.pdf).

Positive Corona

It would be expected that the situation when a positive voltage is applied to the

pointed electrode would be similar. The calculations do give similar results except

that the avalanches are starting near the ionisation boundary and coming inwards

towards the pointed electrode. The onset voltage is the same for the same electrode

geometry. However, although streamers appear at the onset voltage, as soon as the

voltage is raised by about a kV they cease! See the graphs overleaf.

Why? The reason is that there are many more avalanches than in the negative case

coming in towards the pointed electrode (think about the increased volume for

initiatory electrons to appear) and as soon as they turn into streamers, they clog up

the area near the surface of the pointed electrode with positive ions. These lower the

field there until streamers can no longer appear negative feedback control!

3.4

Dr.Qais Alsafasfeh

The 13-kV graph shows a pulse, due to a

streamer, just above the onset voltage. The

graphs below it show a noisy DC current,

larger for 21 kV than for 15 kV. This DC

current is in fact the sum effect of many small

pulses due to the many avalanches arriving at

the pointed electrode.

The cloud of positive charges (called space

charge) around the tip shown in the figure on

the right lowers the field locally: graph with

and without space charge are shown.

3.5

Dr.Qais Alsafasfeh

AC Corona

As all these events take place on a microsecond scale, and AC voltage changes so

slowly on a millisecond scale the positive and negative half-cycles are almost

independent.

Thus, in the positive half-cycle, there may be one pulse as the voltage passes through

the onset voltage in the rising part of the half-cycle but not on the falling part, as the

cloud of positive ions has not yet dispersed.

In the negative half-cycle, there

are pulses from the moment the

voltage passes through the

onset voltage in the rising part

of the half-cycle until it passes

through the onset voltage in the

falling part of the half-cycle.

As the voltage increases, the

frequency increases, as

expected. And vice versa.

This may be seen on the

diagram on the right, where the

pulses due to streamers are

shown on the lower graph.

-1

0

1

0 90 180 270 360

0 90 180 270 360

An actual oscilloscope reading of the negative half-cycle is shown below, firstly the

full half cycle, and then below that an expansion of the part during which pulses are

occurring (270o + 45

o). The increased pulse frequency near a phase angle of 270

o is

clearly seen..

6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000

9400 9600 9800 10000 10200 10400 10600 10800 11000 11200 11400 11600 11800 12000 12200 12400 12600 12800 13000

3.6

Dr.Qais Alsafasfeh

The 3-dimensional graph above shows pulses counted during several complete

cycles, plotted against phase angle, and separated according to size.

Stepped Breakdown Long Sparks and Lightning

The breakdown of a point/plane gap is not as simple as for a parallel plane/plane gap: in the latter,

when the streamer bridged the gap, it continually increased in conductivity until it formed a short-

circuit a spark, a breakdown. As shown above, in a point/plane gap, the streamers only develop

within the ionisation boundary and their length is typically of the same order as the radius of the

pointed electrode.

The exact situation is argued over but the following is your lecturers opinion! It appears that if the

voltage is high enough much more than the onset voltage for corona the streamer becomes so

highly conducting that it becomes self-propagating for a much greater distance than out to the ionising

boundary, because it distorts the field it is then called a leader. It stops propagating, perhaps because

it decreases the charge and hence voltage of the electrode system (a capacitor). Once recharged to full

voltage from the external circuit, the leader can advance again, as soon as a new streamer forms and

increases in conductivity, width and length, to be a continuation of the leader. The direction of the

streamer depends on where, near the tip of the previous leader, the first initiatory electron occurs.

Hence the twisting and turning of a long spark and of lightning as every step of the spark sends the

leader in a slightly different direction.

3.7

Dr.Qais Alsafasfeh

Electrical Breakdown of Solids & Liquids and across Surfaces

1. Solids as Electrical Insulators

Introduction

Now for something completely different. The breakdown of perfect solids is almost

impossible, and in practice the breakdown process always starts at imperfections,

either within the solid or at the conductors bonded to the solid insulation. The

mechanism by which breakdown occurs is called treeing.

The imperfections at which breakdowns are initiated in solid insulation are (a)

protuberances (micro hills) on the electrodes, or (b) metallic inclusions, (c) water

droplets or (d) gas bubbles (or voids) within the insulator.

Treeing

The field at the tip of a pointed

protuberance on the surface of an

electrode will be very much higher than

the main field elsewhere and will lead to

localised high electron emission currents

as for the compressed gas case. Because

of the small emission area these currents

can have very high densities and cause

local overheating of the insulator: this can

cause damage by either melting or

decomposition (as appropriate) and result

in a small void around the tip of the

protuberance. This effectively extends the

point because the void will break down

and the discharge is of course a conducting

plasma - and the process then repeats itself.

Thus, a tubular channel (or micro tunnel)

is formed which extends away from the

electrode towards the other one.

Sometimes the channel splits and forms

two branches, so that the channels begin

to look like a bush or tree. Not

surprisingly, this process is called treeing.

The simulation shown on the right is from

the program treeing.exe.

4.1

Dr.Qais Alsafasfeh

The overheating mechanism described above is not the only method of tree-formation.

The branches may also grow, due to the electrostatic repulsion between high

concentrations of electrons on the inside surface at the tip of the channel: these are

deposited after discharges inside the channel. The strong forces of repulsion can

cause cracking or splitting of the material. These cracks will tend to open up where

there is a weakness or fault in the insulating material and account for the randomness

in the direction of channel growth.

A third possible mechanism is that of electrons being accelerated along the channel to

such high energies that, when they hit the end of the channel, they can break chemical

bonds in the solid there. In the case of the long-chain polymers (plastics) this results

in shorter molecules: these will probably be liquid or gases, especially when the

channel tip is likely to be hot due to the discharges.

Three possible mechanisms have been described. Probably all three occur

simultaneously.

The acceleration of electrons to the extent that molecular bonds may be broken.

The impact of high-energy electrons causing local over-heating and hence melting or decomposition.

The repulsive force between electrons causing splitting of the material.

Note: the structure of flexible plastics is a spaghetti-like mass of long molecules of

the form M M M M M M M M M M M

(In polythene the monomer indicated by M is CH2. In PTFE it is CF2. In

polystyrene M is much more complicated).

If the molecule is broken into shorter

lengths it may be liquid or even

gaseous. Thus in the case of the CH2

family, molecules with more than 17

CH2 units will be solids (waxes,

polythene), molecules of less than 17

CH2 units will be liquids (paraffin,

petrol, oil) at room temperature, less

than 5 CH2 units will be gases

(methane, ethane, propane, butane).

Water trees and electrical trees

It is found that water greatly increases

the rate of growth of trees, perhaps

because the polar nature of the water

molecule allows it to penetrate deeper

into small faults and cracks in the

material. Water trees may be found in

bow-tie formations inside the

insulation and vented tree formations

starting at the interface between the

insulation and the conducting screen.

Electrical trees grow in the absence of water, and, after the water is used up, may

grow from a tree which started as a water tree. Thus it may continue the damage

until eventually the insulation is bridged and complete breakdown occurs.

4.2

-200

-100

0

100

200

300

400

0 10 20 30 40

n, number of C-atoms per chain

Temperature, degrees C

Gases Liquids Solids

BP

MP

Dr.Qais Alsafasfeh

Dr.Qais Alsafasfeh

2. Liquids as Electrical Insulators

Introduction

Transformers, power capacitors and cablesare the main users of insulating liquids and

petroleum mineral oils are the most common and the cheapest of them.

Theoretically, in pure, clean liquids the mean free paths are too short for ionisation to

occur. How then do liquids break down electrically? The theoretical intrinsic

strength as with solids is seldom if ever achieved in practical engineering

situations, as illustrated by the table below.

Power-frequency design fields for insulation systems compared with breakdown fields

for highly purified liquids

Insulation systems

Design field (kV/mm)

Very pure liquids Breakdown field

(kV/mm)

Transformer 2-6 Transformer oil 100

Cables 12-20 n-hexane 130

Capacitors 10-25 Polybutene 110

As solids, the answer is not simple but certainly the following are factors affecting the

breakdown strength and reducing it below the intrinsic strength:

the electrode material and its condition

the presence of water droplets, gas/vapour bubbles and free particles (particularly if long rather than round).

Then trees will start to grow, in the locally enhanced field, but cannot remain once the

voltage is removed surface tension turns the branches into strings of small bubbles

which float off towards the surface.

Water droplets become elongated in a large enough field as shown in the sequence

of photographs shown overleaf. When very long the end becomes rather pointed and

breakdown channels develop until the gap is bridged and breakdown initially of the

water vapour occurs.

Breakdown of a liquid dielectric (a very viscous silicone fluid) due to the instability of

a water globule at a very high electric field. Tenfold enlargements from 16-mm film

(after Krasucki).

4.4

Dr.Qais Alsafasfeh

Solid particles in the oil will experience a force tending to move them into the region

of highest field if the particle's permittivity is greater than that of the oil. This can

cause the setting up of a bridge of particles across the gap if there are sufficient of

them, particularly if they are long particles, like fibres. If they are metallic this is a

short-circuit and will probably lead to breakdown; if they are of high permittivity this

can cause significant field distortion and assist breakdown.

The field at the surface of an individual particle will be greater than elsewhere (in the

case of a spherical metallic particle, 3 times the average field). This may cause local

breakdown leading to vapourisation and breakdown as described above (bubbles

mechanism).

Weak link effects: as shown in the graphs below, there is also a distinct volume

effect, probably due to an increase in the probability of finding a particle in the

volume or an asperity on the electrode.

The electric strength of transformer oil under uniform-field conditions at 90

oC

for (a) power-frequency alternating voltage and (b) impulse voltage

(from Palmer & Sharpley, Proc IEE, 116, p.2029 (1969)

2. Surface Breakdown across Solid Electrical Insulators

Introduction

Flashover is the breakdown of a gap between two conductors, one at high voltage, the

other earthed, where the gap is bridged by a solid (or liquid) insulator: the breakdown

occurs in the gas across the surface of the solid insulator, and much lower than if the

insulator was not there.

Tracking is a slow process, taking typically months or years in the field, by which

meandering and branching carbon tracks develop across the surface of a solid

insulator, eventually short-circuiting most of the gap, when flashover occurs.

[Note: tracking is completely different from treeing; treeing occurs inside the

insulator].

Tracking

This is a complex process which depends not only upon the insulation itself but on the

condition of the surface. By definition, tracking is the formation of a permanent

conducting path across a surface of the insulation, with the conduction due to contain

carbon. However, not all carbon-based materials can track: neither polythene nor

perspex do so, but epoxy resin does.

4.5

Dr.Qais Alsafasfeh

Tracking occurs when there is a conducting film of moisture across the surface of the

insulation, which has condensed from the atmosphere. This will usually contain

contamination such as salt in coastal areas, carbonaceous dust from burning fuel or

brush gear in industrial areas, or cellulose fibres in (for example) a textile mill. Salt is

particularly important because it increases the conductivity of the film of moisture.

The usual mechanism by which the leakage current through the film of water is

interrupted is by its drying out. This occurs because of (a) the normal evaporation

process, particularly if the ambient temperature rises, and (b) the heating effect of the

leakage current itself. This will eventually cause a break in the film which virtually

stops the current. All the voltage applied across the insulator is then across the dried-

out gap (often called a dry band in books), which will then probably exceed the

breakdown voltage of air: a spark occurs, bridging the dry band. After a period of

sparking the insulator surface will be damaged.

Degradation of the insulation by the sparks is the result of heat from the sparks, and

the consequent bombardment by high-energy electrons, which carbonises the

insulation. In some materials (like polythene or perspex) the surface is merely melted

or eroded, but in most organic materials and plastics, the long polymer chains are

repeatedly broken until they are reduced to carbon (with the other materials being

vaporised). It follows that only organic insulation which can be degraded to carbon

by heat, can track.

The carbonised area is now (permanently) conducting and so current again flows.

The current will assist other parts of the wetted area to dry out until another dry band

is formed, breaking the circuit and, again, causing a spark. The cycle repeats until the

carbon tracks begin to link up and eventually form a continuous line from electrode to

electrode when complete failure of the insulation occurs. Note that the carbon bridge

is narrow so that the current approaching it through the wet film will he of

increasingly high density, so that the evaporation will take place preferentially near

the ends of the track so that the tracks tend to grow rather than start forming in

isolation from each other.

In practice it is likely that, once a substantial proportion of the gap has been bridged

by carbon tracks, the voltage gradient across the unbridged parts will be high enough

to initiate flashover which is the next topic.

The rate of degradation of the surface may also be accelerated by other processes,

such as physical weathering, ultra-violet radiation and chemical attack. (For example,

ozone and oxides of nitrogen generated by discharges may further degrade the

insulation).

Methods of minimizing tracking

Tracking may be prevented by ensuring that all surfaces are clean, dry and

undamaged and the materials used are highly track-resistant. Cleaning is not often

practicable; but may be used in critical cses.

Using non-tracking or track-resistant materials such as porcelain and silicone rubbers

will avoid tracking but will not be suitable for all applications. Porcelain does not

contain carbon and so does not track. Silicone rubbers exude low-molecular-weight

silicones which are oily and break up the moisture into droplets, thus preventing a

continuous moisture layer from forming so no conduction.

4.6

Dr.Qais Alsafasfeh

Good design helps by (a) limiting the access of dirt, (b) avoiding its accumulation in

areas between conductors, (c) increasing creepage paths as much as is practical and (d)

for indoor installations, ensuring either good ventilation or using air-conditioning

when the humidity is high.

The tendency to track may be tested by various tests, two of which are now briefly

described. Both will be used in a simplified form in the laboratory sessions.

The Comparative Tracking Index Test (CTI Test) is a relatively simple test which

only uses 100 to 600 volts and a very small sample. Drops of a solution of 0.1%

ammonium chloride are allowed to fall on the surface of the insulator between two

electrodes 4mm apart, at 30-second intervals. This continues until failure (high

current). The higher the voltage, the fewer drops required. The voltage at which

failure occurs on average after 50 drops is called the CTI. This limits its accuracy

and usefulness. It provides

good resolution between

materials with relatively

poor tracking resistance,

but lacks resolution for

materials normally required

for outdoor use for which

the test method in IEC

Standard Publication 587 ...

should be used. It is

described in IEC Standard

Publication No.112.

Some results of a typical test

are shown in the graph on the

right. For the weaker sample

(i.e., the leftmost of the two),

below 200 volts, it does not

break down, for 250 volts less

than 50 drops are sufficient and

for 300 volts less than 10 drops.

4.7

Fine tube Droplet of NH4Cl solution

2 platinum electrodes

Dr.Qais Alsafasfeh

The High-Voltage or Inclined-plane Test (IEC 587 Test) uses test voltages up to 6

kV and a larger surface area of the sample. Two stainless-steel electrodes are

clamped to the specimen which is set up with its longer axis at 45o to the vertical, and

the electrodes attached to the underside. A solution of 0.1% ammonium chloride with

a little wetting agent is fed into a filter paper pad clamped under the top electrode and

flows down the under-surface to the lower electrode (see the diagram from the

IEC587 standard on page 7.3). The minimum voltage to cause uniform sparking over

the wetted surface is applied (this must be a multiple of 250 V). At the end of each

hour the voltage is increased 250 V until failure or flashover occurs. In this way

materials are graded in terms of the voltage at which they fail.

A material which has a CTI of 500 on the low voltage test will fail at about 2 kV on

the inclined plane test; thus a range of 4 to 5 kV is available in which to evaluation the

more tracking-resistant materials.

4.8

Dr.Qais Alsafasfeh

Surface flashover

While tracking may take hours, days or even years to develop to complete breakdown,

flashover is an instantaneous occurrence, being a breakdown via a streamer

travelling through the air close to the surface of the insulator. The breakdown is at a

lower voltage than would be expected from the apparent values of the electric fields

and the normal streamer breakdown theory.

Thus in the three gaps shown below, cases (a) and (c) will break down at similar

voltages (which may be calculated from the streamer criterion). However in case (b)

the breakdown will be across the surface of the insulating spacer and at a significantly

lower voltage than (a) or (c). Why? Note that the field should be uniform and should

be the same in cases (a) and (b) and for most of (c).

Surface effects: there will be impurities on the surface of the insulating rod and these

provide a source of secondary electrons which are produced by the impact of photons

and electrons from the avalanche head. The surface appears to produce these

secondary electrons more efficiently than the air molecules (which are very far apart).

Thus, the surface provides in effect a greatly increased value of , and this causes

flashover on the spacer surface, at a voltage well below the breakdown voltage of the

gap if without the spacer present.

Dirty surfaces appear to produce these secondary electrons (i.e., have a high effective

value of ) more efficiently than clean surfaces. So the breakdown strength of a gap

with a spacer will vary greatly with the cleanliness of the spacer.

3-material interface. In case (b)

it is inevitable that the machining of

the spacer will not give a perfect

right angle at the ends and so, in the

sketch shown below there will be an

irregular gas gap.

This will have a higher electric field

than the rest of the gap (about twice

the main field) and will therefore

break down locally at about a half

of the no-spacer breakdown field

for the gap.

As the voltage across the whole gap increases, the discharge will get more intense and

feed electrons and ions into the main gap. These electrons will be multiplied through

the normal ionisation process, and could cause breakdown at a lower-than-expected

voltage.

4.9

Dr.Qais Alsafasfeh

The Design of High-voltage Equipment

The previous units have indicated why and how gases, liquids and solids break down

electrically, and why and how breakdowns occur across surfaces. In this chapter, the

design of some items of HV equipment are examined to see how this knowledge is

applied.

1. Cables

XLPE Distribution Cables

Distribution cables (

Dr.Qais Alsafasfeh

Oil-paper Transmission Cables

At transmission voltages (>50 kV) the insulation must be much thicker and may be

either oil-paper or extruded XLPE. Oil-paper cables use many layers of thin paper

tapes as insulation. After adding the sheath, almost all the air trapped between the

layers of paper is sucked out under vacuum, and then the cable is impregnated with

a mineral oil under pressure. This double process almost completely eliminates voids.

However, the oil filling results in the inconvenience of having oil reservoirs at

intervals along the route and stop joints to avoid undue hydrostatic pressure where

the cable goes up a hill. Stop joints are joints where the flow of oil is blocked: oil

cannot move from one section to the other. The good aspect is that if a cable is

damaged, it will leak oil only slowly and may be run for a considerable time (if the

pressure is kept up and the oil reservoirs are kept full) until it is convenient to repair it.

1. Oil-filled AC transmission cable

2. Mass-impregnated DC transmission cable (no oil duct)

3. XLPE AC transmission cable

4. 3-core XLPE distribution cable

5+6. XLPE distribution cables for DC

In the photograph it will be seen that oil-paper cables also use slightly-conducting

layers between the conductors and main XLPE insulation, in this case carbon-loaded

paper.

XLPE Transmission Cables

Polyethylene cable does not have these troublesome and costly oil pressurising

stations but is not yet commonly used above 300 kV except for short lengths (e.g.

within hydro electric. The problem is the increasing difficulty of avoiding the

presence of voids in larger cables and the progressive deterioration of the cable due to

the growth of trees in them. Continuous research into manufacturing techniques has

hugely improved the situation in respect of voids and hence the long-term reliability

of polyethylene cables. For greater stiffness cross-linked polyethylene (XLPE) is

used rather than ordinary polyethylene.

5.2

Dr.Qais Alsafasfeh

The photograph shows a 500-kV XLPE cable as

used in a pumped storage station in China.

The permittivity of polyethylene is lower (2.3)

than that for oiled paper (4.5), and therefore the

capacitance and charging current are lower on

XLPE cables than on oil-paper cables. This

means less reactive compensation is necessary.

The loss factor is also less: this means less heat is

generated in the insulation and thus allows an

increased current rating; it also means lower

losses.

2. Bushings

The insulators used where an hv

conductor passes through an

earthed metal wall (or similar) are

known as bushings. In air the

highest field would be at the edge

of the hole in the wall: this can be

reduced by placing a collar of metal

there. This might be sufficient if

there were no requirement to

separate one side of the wall from

the other side by a solid barrier.

Given that surface flashover occurs

at much lower fields than

breakdown, the air/conductor surface must be several times longer than the

radius of the hole in the wall.

The field will still be greater on the surface near the edge of the hole in the

wall so foil grading is used to control the voltage distribution in the

bushing: cylindrical foils are included during the winding on of the

bushing insulation and these will form a number of capacitors in series,

which, if equal in value, will ensure the voltage between each adjacent pair of foils is

equal. Their relative size can also be adjusted to have a lower gradient near the wall

than elsewhere.

5.3

Dr.Qais Alsafasfeh

A porcelain covering may be added to the external half of the bushing with shedding

to increase the creepage distance and break up the flashover path. The word

shedding refers to the strangely-shaped stack of discs or cones around the bushing

Perhaps because it causes it to shed water easily, that is, to allow the rainwater to

run together and drip off it at the edge. If the bushing is vertical, the shedding will be

smooth and sloping on top for this reason, and ridged underneath, again to break up

flashover paths.

9.3 Circuit Breakers

Sulphur hexafluoride circuit breakers

SF6 circuit breakers are widely used at transmission voltages and increasingly at

distribution voltages, too. SF6s high attachment coefficient removes free electrons

from the arc and its high thermal capacity removes heat from the arc.

For transmission voltages, the circuit breaker is a single sealed tank containing the

contacts and insulated with SF6 at a pressure of about 5 bars. As the contacts start to

move, the design is such that a quantity of SF6 gas is compressed by the movement

and is released by the contacts separating which separation also causes an arc. The

blast of SF6 gas blows out the arc. This puffer mechanism is unnecessary at

distribution voltages. A simplified explanatory diagram is shown below (animation:

puffer.exe) and below that is the real thing.

5.4

Dr.Qais Alsafasfeh

A major advantage of SF6 circuit breakers over older types (oil-blast and air-blast) is

their lack of maintenance and smaller size. Almost all the transmission-voltage

switchgear in urban areas is SF6-insulated.

It is extremely important for manufacturers to ensure that neither contaminating

particles nor moisture (must be less than 500 ppm) are present in the gas. If

contaminating particles are present, lower-than-

expected breakdowns may occur see Lecture 2.

If moisture is present (more than 500 ppm) this

will react with the chemical dissociation products

produced in the arc, to form highly corrosive

chemicals which will etch and erode the surfaces

of the insulators.

Vacuum circuit breakers

Vacuum circuit breakers (VCBs) are the norm at

distribution voltages. They are small because of

the good insulation and the very small movement

of one contact the moving electrode of about

0.5mm. They have a long life with virtually

zero maintenance, a maximum arc duration of

only 1 or 1.5 cycles at all levels of current, cause

no additional fire risk and produce no noise or

gas emissions when operated. The construction

is completely sealed, gives very consistent arcing

times and allows very fast automatic reclosure.

5.5

Dr.Qais Alsafasfeh

One of the two contact discs A 5 m x 5 m sample of the surface

To obtain such long-lifetimes and consistent results, it is necessary to ensure

the metal contacts are not damaged by local heating at the arc root;

the metal contacts are outgassed before sealing the vacuum; and

the metal vapour from the arc does not condense on the insulating walls of the

breaker and eventually cause a short-circuit;

These are ensured by

causing the arc to move across the surface of the contacts by cutting slots in them

(see photograph above) such that magnetic fields are produced by the current

through the contact to the shaft (F=BiL);

careful heating of the contact material by

a high-frequency discharge, with a

vacuum pump running to remove the

absorbed gases before sealing

(outgassing);

removing electron emission points by

the same high-frequency discharge; and

placing a thin cylinder surrounding the

contacts so that any metal vapour will

condense there, thus shielding the

insulating walls from metal deposits.

It is common for enclosures around the VCB to be

filled with SF6 gas to avoid external flashover ( i.e.,

vacuum inside the bottle, SF6 outside).

9.4 Overhead Line Insulators

Post insulators support conductors and need to be rigid

(see the pin-type insulator on the right), but insulator

strings for overhead lines at voltages above 100 kV

need to be flexible to absorb the forces on the lines

from the wind. They are therefore made up of cap and

pin insulators (on right, lower picture) which are

connected together to form strings.

5.6

Dr.Qais Alsafasfeh

For 400 kV, a string of typically about 20

cap and pin insulators are used. The voltage

drop across each insulator tends to be uneven

due to their different surface resistances

because of the differing amounts of pollution

which they have collected, and to be much

higher near the HV conductor end and, to a

much lesser extent near the earthed arm of

the tower. This is due to the stray capacitance

between the metal of the cap (and the pin

which is plugged into it) and the tower. To

decrease this effect, a metal loop is attached to

the HV end, to produce stray capacitance

between the metal cap and this HV loop (see

the bottom left photo).

All insulator designs - whether of the pin-type,

for distribution voltages, cap-and-pin strings

for higher voltages, or post insulators for

outdoor switchgear have this in common:

they have long creepage paths between HV and earth. These are to make it more

difficult for surface flashover to occur but unfortunately also make it easier to trap

pollution. As always, designs must be a compromise.

When the pollution becomes moist it tends to conduct and then dry out to form dry

bands, with local arcing or flashover. Materials used for outdoor insulators are

usually chosen to resist tracking but surface erosion may occur and this encourages

the collection of moisture and pollution.

5.7

Strings of cap & pin insulators

on a 400-kV transmission tower

Dr.Qais Alsafasfeh

Composite insulators with a fibre-glass rod for tensile strength and a shedded cover

are becoming more common as a replacement for the cap-and-pin strings. This

shedded cover is commonly made from silicone rubber, a material which has the

advantage of eroding rather than tracking when a surface discharge occurs

The problem of contamination by pollution can be overcome by regular washing of

the insulators or by coating them with grease which breaks up the water film into

small separate droplets. The former can be done when the insulators are live but is

not usually cost-effective on high transmission towers unless they are situated in very

polluting conditions. Also the automatic washing equipment can be unreliable

because of corrosion and the multitude of valves and joints involved. Very wet

insulators, particularly the post-type, tend to flash over very easily, so live washing is

not always advantageous.

Greasing is effective but is labour-intensive and only practical in switchgear

enclosures not on transmission towers. Also, after a while, the grease tends to trap

dirt and is eventually no longer effective. Also in hot weather the grease tends to melt

and drip off. The removal of old and dirty coats of grease is very unpleasant work.

A power utility

helicopter

washing

insulators

5.8

Composite insulators

60 to 150 kV

Dr.Qais Alsafasfeh

Maintenance work on a 400-kV

transmission line the worker is sitting

in a seat suspended by poly-propylene

chains.

Remote-controlled jet-washing on the

190m-high towers of the 400-kV line

crossing the Thames River. Servo-

controlled nozzles are used.

5.9

Dr.Qais Alsafasfeh

High-voltage AC & DC generators

To check that the design is within the specification, the equipment must be tested, so

voltage sources at levels higher than the rated voltages must be available.

1 AC High-Voltage Sources

1.1 Cascaded Transformers

Alternating voltages above a few hundred kV are often achieved by cascading two or

more transformers: an example is shown in the diagram where two 240V/200kV

transformers are cascaded with the top 240 volts being tapped off from the first

transformers secondary winding (c1-e1) as input to the second transformers primary

winding (a2-b2).

The first transformer has its tank earthed, but

the second has its tank insulated from earth

and at a potential of 200kV above earth: the

lower ends of the second transformers

primary (b2) and secondary (d2) windings are

connected to the tank. The advantage of

this arrangement is that each transformer

only needs to have an insulation level of

200kV.

A Haefely cascaded 1800 kV ac supply is

shown below: three 600 kV transformers are

cascaded and have outputs from the high end

of their windings at 600, 1200 and 1800 kV

respectively.

6.1

Dr.Qais Alsafasfeh

1.2 Series Resonant Testers

These are employed to give high voltages at relatively low cost: a high-voltage

transformer feeds a series circuit comprising a variable reactor and the test object.

The variable reactor is achieved either by using a low-voltage variable reactor on the

LV side of a transformer, as shown in the diagram below; or by using an HV reactor

with a variable air gap. The test object (show as a cable in the diagram below) is

effectively a capacitance.

The reactor is tuned until the circuit is at resonance at the supply frequency. The

voltage across the test object is then the supply voltage multiplied by the circuit Q-

factor (typically 20 to 50).

If the test object capacitance is low, extra capacitors may be connected in parallel to

allow tuning to the resonant frequency.

Alternately, a higher frequency may be used by replacing the mains-frequency supply

(50 Hz) by a variable frequency supply from a solid-state converter.

There are many advantages to the Resonant Tester method:

The voltage waveshape is improved by removing harmonics from the power supply;

The power required from the source is much lower than the kVA in the series resonant circuit (typically around 5%) and is supplied at unity power factor;

If the test object fails, the energy available is small (just the stored energy in the capacitor) and the voltage immediately collapses (no longer in resonance), so less

damage occurs and there is less danger.

2 DC High-Voltage Sources

2.1 The Voltage Doubler

A simple way to achieve high direct voltages is of course by half or full-wave rectification, followed by a smoothing capacitor. A more efficient design, however, is the voltage doubler circuit.

In your figure, the voltage at X varies from +Vrms2 to - Vrms2 and the voltage at y between 0 and 2Vrms2, so the output capacitor will be charged to 2Vrms2.

6.2

Dr.Qais Alsafasfeh

In practice the leakage resistance (tan) of the capacitors, the finite reverse resistance of the rectifiers and other leakage paths will cause both capacitors to self-discharge slightly and so there will be some ripple.

2.2 The Multistage Rectifier

Multistage rectifier circuits are a further development of the doubler circuit and are

able to produce output of 1 MV or more. In the drawing of a 3-stage circuit below, the

left-hand column of capacitors remain charged to a potential difference of

approximately 2Vmax (= 2Vrms2) at steady state but the potentials at the nodes oscillate up and down by V. The capacitors in the right-hand column also are charged to a pd of approximately 2Vmax, but the node voltages remain constant.

The word, approximately is used above because there are ripple effects due to the

leakage currents as well as the load currents (if the generator is supplying a load).

The charging process from the initial state (all capacitors uncharged) is explained

below.

The use of a high-frequency supply will decrease the ripple and the voltage

regulation but may not be convenient.

Note that polarity reversal is readily possible by swapping the two diodes attached to

each left-hand node. The figure opposite a 4-stage rectifier shows how the design

may be adjusted to make this a simple operation.

6.3

Dr.Qais Alsafasfeh

2.3 Van der Graaff Generators are

HV DC electrostatic generators with an

output of up to (currently) 25 MV, although

relatively little current is available. The belt

is charged by a set of sharp points which are

typically set at 10kV and produce a corona

discharge.

The charged belt delivers charge to the

collector which is a set of sharp points where

corona will occur due to the charge on the belt:

these spray the opposite charge onto the belt

until it is discharged, which increases the

charge on the hv electrode. Further spray

points can be added to charge the belt in the

opposite polarity.

The voltage achieved will be limited by the

level at which a balance occurs between the

belt current and the sum of the output current,

leakage current and corona loss current. For

the higher voltages the whole unit may be

enclosed and pressurised with SF6.

3 High-Voltage Impulse Sources

3.1 Introduction

Impulse testing is done with a fast rise-time pulse which rises to its maximum in

about 2 s and falls asymptotically to zero much more slowly: it falls to 50% of its peak value in 50 s. Such pulses are produced by discharging a capacitor through an R-C circuit. There are two methods used, the single-stage impulse generator (which

will now be described) and the Marx impulse generator a multi-stage version of the

single-stage.

6.4

Dr.Qais Alsafasfeh

3.2 The IEC 60-2 (1973) Standard

The IEC 60-2 (1973) documents define the shape and tolerances as follows: a front

time T2, of 1.2 s (30%) and a time to half value T2 of 50 s (20%). The front time is defined as 1.67T, where T is the time to rise from 30% to 90% of the peak

value as shown in the figure on the previous page. The time to half value is defined

as the time from the 'virtual origin' at 01 to the point where the voltage has dropped to

half of its peak value. The 'virtual origin' is where BA produced intersects with the

time-axis.

3.3 Single-stage Impulse Generators comprise a wave-shaping circuit added

on to a direct-voltage generator: this circuit allows a charged capacitor to discharge

through an R-C circuit and the impulse voltage is the potential difference across one

of the capacitors as shown in the circuit overleaf.

In the circuit above, C1 >> C2, so the overall situation is that C1 discharges via R1+R2

with C2 charging up initially through R1 and then staying at the same voltage as R2.

By Laplace we find that the voltage across C1 is given by

vimp(t) = Vo [R2/(R1+R2) [exp(-t) - exp(-t)]

where = 1/C1(R1+R2) and = (R1+R2)/C2R1R2.

This may be explained more usefully by considering that, in the long term, C1 is just

discharging through R1 and R2 in series, so that the voltage across C1 may be written

after the peak as

vC1(t) = Vo exp(-t / C1(R1+R2)) = Vo exp(-t).

Therefore, bearing in mind the voltage-divider effect of R1 and R2, the voltage across

C2 after the maximum is given by

vC2(t) = Vo {R2/(R1+R2)} exp(-t) for t >> 1/

Initially C2 is uncharged, so vC2(0) = 0. It is charged very quickly from C1, but to

determine the charging rate we must consider the Thevenin equivalent of the rest of

the circuit: it is a source of magnitude VT = Vo R2/(R1+R2), with a series resistance

of RT = R1R2 / (R1+R2). It follows that, before the peak

vC2(t) = Vo {R2/(R1+R2)}{1 - exp(-t)} for t

Dr.Qais Alsafasfeh

The two graphs above illustrate the last two equations.

To comply with the international standard shown on the previous page, it is quite

simple to show that the characteristic times must be about 1/ = 70s and 1/=0.4s.

The switch in a single-stage impulse generator can be

the mechanical approach of two spheres (the spark breakdown will occur before mechanical contact occurs, so avoiding contact bounce);

by fixed-gap spheres (breakdown will occur at the appropriate voltage for the gap setting); or

by the use of a triggertron (a small ancilliary spark-gap on one of the spheres can be used to 'trigger' the main-gap breakdown).

3.4 The Marx impulse generator

This multi-stage impulse generator avoids

the difficulty in switching very high

voltages by connecting many capacitors in

parallel for charging and then connecting

them in series in order to discharge them

through an R-C circuit, as before.

Thus, if there are 20 capacitors all charged

to +10kV, in parallel, and they are then

connected in series, their total voltage will

be +200kV this can be discharged through

the usual impulse-generator R1-R2-C2

network to give an impulse of over 100

kV.

6.6

0

20

40

60

80

100

0 1 2 3 4

Time, microseconds

Voltage, kV

0

25

50

75

100

0 25 50 75 100 125 150

Time, microseconds

Voltage, kV

Dr.Qais Alsafasfeh

The actual circuit of a 4-stage

Marx generator is shown at

right.

The diagram on the right shows that

the effective circuit of a four-stage

impulse generator is in effect, a

parallel arrangeme