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Dielectric Phenomena in High Voltage Engineering (1915) — part 10 of 12

1 January 1915

1,300

2,200 3,500 6,100

For approximating the storm loss consider

6o » 0.80 per cent, of its value in fair weather. Then p = 0.042(e - 0.8 X 52.0) « = 0.042 (e - 41. 6) «

This will give an idea of the maximum storm loss; it assumes a storm over the whole line at the same time, a condition that is most unlikely to occur. The storm loss will also generally be less due to lower temperatures.

CORONA CALCULATIONS FOR TRANSMISSION LINES 207

The loss on a transmission line will vary from day to day de- pending upon the temperature and weather conditions. The above losses are calculated for summer temperature. For winter the losses would be much lower.

Safe and Economical Voltages. — It will generally be found that it is safe and economical to operate a line up to, but not above, the fair weather 60 voltage (determined for average barometer and 77 deg. F.). This gives a loss during storms of about 4.75 kw. per mile in the problem considered, but it is not likely that the storm will extend over the whole line at one time. Storm during cold weather will cause much less loss than the above. It thus is generally more economical to pay for the storm loss during small parts of the year rather than to try to eliminate it by an excessive conductor.

Thus for the above line a desirable operating voltage is in kilo- volts between lines (1000 ft. elevation) :

Co X 1.73 = 54.2 X 1.73 = 93.8

(10,000 ft. elevation)

Bo X 1.73 = 38.4 X 1.73 = 66.5

It is undesirable to operate the conductors above the glow point as there is likely to be considerable chemical action on the con- ductor surface.

Methods of Increasing Size of Conductors. — The corona start- ing voltage is increased by increasing the diameter of the con- ductor. Thus, with the same amount of copper a hollow tube would give a higher corona voltage.

A hemp center conductor is not reliable.

For the same resistance an aluminum conductor has about a 25 per cent, greater diameter than a copper conductor and thus, approximately, 25 per cent, higher corona voltage.

In order to still further increase the advantage of aluminum, a steel-core aluminum cable has been put into operation in Cali- fornia at 150 to 180 kv. The critical voltage may also be de- creased by grouping together conductors of the same potential.

Conductors not Spaced in Equilateral Triangle. — ^In three phase problems, it has been assumed that the conductors are arranged in an equilateral triangle. When the conductors are not spaced in equilateral triangle but, as is often the case in practice, symmet- rically in a plane, corona will start at a lower voltage on the center conductor, where the stress is greatest, than on the outside conductor.

208 DIELECTRIC PHENOMENA

The actual critical voltage for the center conductor will be approximately 4 per cent, lower, and for the two outer conductors 6 per cent, higher, than the value for the same «, in the equi- lateral triangle arrangement.

If a triangle is used where there is considerable difference between Sij 8% and 83, an exact calculation of the stress should be made. Such a calculation is quite complicated. (See Example Case 12, page 234.)

Voltage Change along Line. — For long lines the voltage, and therefore the corona loss, will vary at different parts of the line. This may be allowed for in a long line by calculating the loss per mile at a number of points. If a curve is plotted with these points as ordinates and length of line as abscissa the average ordi- nate may be taken as the loss per mile. The area of the curve is the total loss. A line operating very near the corona voltage may have no loss at load, but when the load is taken off there may be considerable loss due to the rise in voltage. This may sometimes be advantageous in preventing a very large rise in voltage when the load is lost. Grounding one conductor will also cause con- siderable loss on a line operating near the corona voltage by in- creasing the stress on the air at the conductor surface.

Agreement of Calculated Losses and Measured Losses on Commercial Transmission Lines. — It is generally difficult to make an exact comparison, as in most cases where losses have been measured on practical lines all of the necessary data, such as temperature along line, barometric pressure, voltage rise at the end of line, etc., has not been recorded. A range of voltage extending considerably above e^ is necessary to determine the curve. It is not generally possible to place such high voltages on practical lines.

The several examples given are ones in which it has been pos- sible to obtain sufficient data to make a comparison. In Fig.

173 the drawn curve is calculated from the formulaj for the tem- perature, barometric conditions, etc., under which measurements were made. The crosses represent the measured values. This agreement between measured and calculated losses is very inter- esting, as it is for a long three-phase line at very high altitude.^ (Note that the greater part of the curve is below e^.) In Fig.

174 are similar comparisons on a single-phase line at different

frequencies. These measurements were made before corona was

a factor in practical transmission. An exact agreement could not

^ Some of the first measurements on practical lines were made by Scott and Mershon, at high altitudes in Colorado. See A. I. E. E., 1898.

CORONA CALCULATIONS FOR TRANSMISSION LINES 209

be expected, as the wave shape was not known and was probably not a true sine wave. Another rather interesting comparison is made in a recent publication describing the system of the Au Sable Electric Co. ^ The line of No. copper cable is 125 miles long. With 140 kv. at the generating end, the voltage at the far end is 165 kv. Thus the .loss per mile is greater at the far end than at the generating end. The average calculated loss per mile is 15 kw. The article states that the actual average loss by prelimi- nary rough measurements was 15 to 20 kw. per mile. The above examples are given to illustrate how well the formula may be

iioor

90 100 110 120 180 XSoctivo KiIo*yoUa Between Linei

Fia. 173.

84 82 80 28 26

£24

•J

^22 ^20

?18

?16

Sio

8 6 4 2

•

»(

tyci

'•/

»-

:]ei

y ^

■- i

40 60 60 70 80 90100110120180140 ZBectlTe Kilo^Yolti

Fig. 174.

Comparison of calculated and measured losses.

Fig. 173. — ^Leadville. Three phase. (Test made by Faccioli.) 1/0 weathered cable. Spacing (flat) 124' (314 cm. ). Diameter, . 95 cm. Length of line, 63.5 miles (one conductor). Temp., 11** C. Bar., 60 cm. Frequency, 60—. Curve calculated, x measured.

Fig. 174.— Outdoor experimental line. (Tests by A. B. Hendricks, Pitts- field, 1906.) Wire conductor. Diameter, 0.064" (radius 0.081 cm.). Spacing, 48" (132 cm.). Length, about 800 ft. « =0.97.

applied in the predetermination of the corona loss of commercial transmission lines.* The Corona Limit of EQgh-voitage Transmission, with Tables.

— The question is often asked, what is the limiting distance im- posed on high-voltage transmission by the corona limit of vol-

1 N. E. L. A., June, 1912.

' Peek, F. W., Jr. Comparison of Calculated and Measured Corona Loss, A. I. E. E., Feb., 1915.

210

DIELECTRIC PHENOMENA

tage? In the first place it does not seem at present, except in very rare instances, that corona will be the limiting feature at all. The limiting feature will, in all probability, be an economic one; the energy concentrated naturally at any given point will be exceeded by the demand in the surrounding country before the transmission distance becomes so great that voltages above the corona limit are necessary. A quarter of a million volts may be used (except at high altitude) without an excessive conductor diameter or spacing (See Tables LXXX, LXXXI and LXXXII.) *

Table LXXX. — Corona Limft of Voltage * Kilovolts between Liue Three-phase Sea Level and 25 deg. C.

Sise B. ft S.

Diameter, inches

Spacing, feet

or cir. mils

0.230

0.261

0.290

0.330

0.374

• • ■

102

104

108

109

0.420

• • •

104

108

111

114

117

121

000

0.470

a • •

114

118

121

124

127

132

0000

0.530

• • ■

125

130

135

138

141

146

250,000

0.590

• • •

138

144

149

152

156

161

300,000

0.620

a • ■

151

156

161

165

171

350,000

0.679

a ^ •

161

166

170

175

180

400,000

0.728

• • «

171

176

180

185

192

450,000

0.770

• • •

178

184

190

194

200

500,000

0.818

• a •

188

194

199

205

210

800,000

1.034 1.152

234 256

241 264

244 270

256

1,000,000

281

^ These tables will give an approximate idea of the voltage limit imposed by corona. In general it will be found advisable to operate at or below the eo voltage. Above eo the storm loss becomes an important factor. Cal- culations should generally be made from formulae for each special case.

To find the voltage at any altitude multiply the voltage found above by the 5 corresponding to the altitude, as given in Table LXXXII.

' Kilovolts between lines corresponding to eo at 25 deg. C. and 76 cm. ba- rometer. Conductors arranged in an equilateral triangle.

CORONA CALCULATIONS FOR TRANSMISSION LINES 211

Table LXXXI. — Corona Limit op Voltage * Kilovolts between line Three-phase Sea Level and 25 deg. C.

Wires

SiseB. AS.

.DUmeter, inohes

Bpaeing, feet

•

or cm*

0.204

0.229

• • •

0.258

■ ■ •

• ■ ■

0.289

• • •

0.325

• • •

• B •

» • •

102

0.365

• • ■

B • «

• B •

102

105

107

110

113

000

0.410

• • •

• ■ ■

• • *

• ■ ■

109

113

116

119

121

124

0000

0.460

• ■ ■

B • •

• ■ •

• •

120

125

128

131

134

138

To find the voltage at any altitude multiply the voltage found above by the 5 corresponding to the altitude, as given in Table LXXXII.

For single phase or two phase find the three-phase volts above and multi- ply by 1.16.

Table LXXXII. — Altttudb Correction Factor at 25 deg. C.

Altitude, feet

1.00

5,000

0.82

500

0.98

6,000

0.79

1,000

0.96

7,000

0.77

1,500

0.94

8,000

0.74

2,000

0.92

9,000

0.71

2,500

0.91

10,000

0.68

3,000

0.89

12,000

0.63

4,000

0.86

14,000

0.58

Corona is generally thought of as affecting only very high voltage transmission lines and of little other practical importance. It may, however, exist at almost any voltage, as it depends not only upon voltage but also upon the configuration of the electrode and the spacing. It will exist in cables, on insulators, coils,

^ Kilovolts between lines corresponding to eo at 25 deg. C. and 76 cm. ba- rometer.

212 DIELECTRIC PHENOMENA

switches^ etc. ; in short wherever air is present, and where damage may be done by mechanical bombardment of small streamers, and by electrochemical action (ozone and nitrous oxide), unless means are taken to prevent it. In most cases its prevention is fairly simple. This is further treated in Chapter X.

CHAPTER X

PRACTICAL CONSIDERATION IN THE DESIGN OF APPARATUS WHERE SOLID, LIQUID AND GASEOUS INSULATIONS

ENTER IN COMBINATION

As important as the quality of the dielectric is the configuration of it and of the electrodes. It is also of importance in combining dielectrics of different permittivities to see that one does not weaken the other by causing unequal division of stress. It is possible to cause breakdown in apparatus by the addition of good insulation, dielectrically stronger than the original insulation.

Case 1. Breakdown Caused by the Addition of Stronger Insulation of EQgher Permittivity. — As an example take two

Air

Air Preoboard

Fia. 175. — Causing break-down by the addition of insulation.

parallel plates rounded at the edges and placed 2 cm. apart in air, as in Fig. 175(a).

(1) Apply 60 kv. (max.) between the plates. The gradient then is 60/2 = 30 kv./cm. max. (neglecting flux concentration at edges). As a gradient of 31 kv./cm. max. is required to rup- ture air there is no breakdown.

14 213

214 DIELECTRIC PHENOMENA

(2) Remove the voltage and insert between the plates a sheet of pressboard 0.2 cm. thick, as in Fig. 175(b). The constants of pressboard are

fc = 4 rupturing gradient = 175 kv./cm. max.

Ip = 0.2 cm. For air

fc = 1 rupturing gradient = 31 kv./cm.

Apply now the same voltage as before. The addition of the pressboard of higher permittivity has increased the capacity of the combination and, therefore, the total flux and the flux density in the air. The gradient has also been increased. The combina- tion may be considered as two condensers in series.

Where Ci = capacity of air condenser, c% = capacity of press- board condenser; e\ = voltage across the air condenser, 6% = voltage across the pressboard condenser; the total flux is

^ = CiCi = C262

therefore, -y ei = ~ ej

c = C2 + 61

ki ^2 / V

p ei = y (6 - 61)

(ki k2\ kffi

hie

^, ^ h^ ^ ^i^^ =^8 4

' ki/h + k^/U k,U + k^i ''''•*

6a = 60 - 58.4 = 1.6

_ ei _ kze

li kil2 ~r ^2*1

Then gi = ^ x 02 + 4 X 18 " ^^'^ kv./cm. max.

The air breaks down as gi is higher than the critical gradient, causing breakdown of air. As the broken down air is conducting, most of the applied voltage is placed on the pressboard. Thus, after the air ruptures, the gradient on the pressboard is:

g'i = -^-^ = 300 kv./cm. max.

CONSIDERATION IN THE DESIGN OF APPARATUS 215

This is much greater than the rupturing gradient of pressboard and causes it to break down. Therefore, the 2.(>-cm. space, which is safe with air alone, is broken down by the addition of stronger insulating material of higher permittivity. The stresses on this combination could have been calculated directly from (16a), Chapter II.

Another and convenient way of looking at this is as follows:

volts

Flux = re

flux resistance" or "elastance"

S ia termed the elastance and is the reciprocal of permittance. The reciprocal of the permittivity is termed the elastivity. For the given electrode arrangement, S is proportional to the elastivity and the length, as long as lines of force are practically straight lines. Let the relative elastivities be

Air =1.0

Pressboard = 0.25

Let the absolute elastivity of the air be o-a, and introduce for the sake of abbreviation a = tra/A, where A is the area.

Then the elastances for the different circuits in the test are:

(a) Air (2 cm.) Si = aX2 XI =2a

lb) Pressboard (0.2 cm.) Sp = a X 0.2 X 0.25 = 0.05a

(d) 1.8 cm. air + 0.2 cm. pressboard S =^ Sp + Sa = 1.85a

Thus when there is only air in the gap

60^ 30 *' 2a a

When 0.2 cm. of air is removed and the same thickness of press- board added, the total elastance is less and the flux increases or

** 1.85a a The "drop" across the air is

^2 X Sa = ^=^ X 1.85a = 58.4 kv. a

The "drop" across the pressboard is

^2 X Sp = ^^ X. 0.05a = 1.6 kv. a -'

216 DIELECTRIC PHENOMENA

58.4 kv. is sufficient to cause 1.8 cm. of air to break down. When the air breaks down the full 60 kv. appears across the pressboard which, in turn, breaks down.

The case discussed above is an exaggerated example of condi- tions often met in practice. In many power stations little bluish needle-like discharges, called "static," may be noticed around generator coils, bushings, etc. This "static" is simply over- stressed or broken down air, but unlike Case 1, the solid dielectric is sufficiently thick so that very little extra stress is put upon it by the broken down air. Damage may be caused in the course of time, however, by local beating, chemical bombardment, etc.

Case 2. Static or Ccmina on Gen- erator Coils. — Consider the terminal coil of a 13,200-volt generator, insu- lated by 0.25 cm. of built-up mica (A; = 4), and 0.45 cm. of varnished cambric {k - 5). In the slot is an annor of 0.1-cm. horn fiber (k = 2.5). In series with these is more or less air; assume 0.05 cm. for the purpose Fig. 176.— Corona on genera- °^ ^'^'^ calculation. A section of the tor coils. coil assembled in the machine isshown

in Fig. 176, The stress on the air may be approximately found by assuming the conductors as one flat plate of a condenser, and the frame as the other.

Then: Kilovolts between lines 13.20 eff.

Kilovolts to neutral 7.63 eff.

Kilovolts to neutral 10.7 max.

ff^r

''(li + l + li + g)

10.7

111

Since the disruptive strength of air is 31 kv./cm., it will break down, forming corona. Experience has shown that in time the

CONSIDERATION IN THE DESIGN OF APPARATUS 217

corona eats away the insulation by mechanical bombardment, local heating, and chemical action, and ultimately a short circuit results.

Assume that the machine is operated at 8000 volts. The air is then stressed to 26.7 kv./cm. and corona does not form. How- ever, should one phase become grounded, the voltage of the other two above ground would become 8.0 kilovolts instead of 4.62 kilovolts, the gradient on the air would rise to 46.3 kv./cm., and corona would result. Assume now that there are no grounds, but that the machine, which shows no corona at 8.0 kilovolts at sea level, is shipped to Denver. The altitude of Denver is ap- proximately 6000 ft. The corresponding barometer is 24.5 cm. (Fig. 172), and hence the relative air density at 25 deg. C. is 0.82. At this density the disruptive strength of air is 0.82 X 30 = 25.5 kv./cm. The air around the coils near the terminals having a gradient of 26.7 kv./cm. would glow.

The best method of preventing this corona on machine coils is to tightly cover the surface of the coil with a conductor, as tinfoil, and to connect the foil to the iron frame of the machine; this, in effect, short circuits the air space. Naturally, the foil should be slit in such a way as to prevent it from becoming a short-circuited turn by transformer action.

Case 3. Overstressed Air in Entrance Bustlings. — ^Assume that a ^-in. conductor, supplying power at 33 kv., enters a building through a 3-J^-in. porcelain bushing having a 1-in. hole (see diagram Fig. 177). The voltage between the rod and the ground ring is 19 kv. The stress on the air at the surface of the rod is:

ri = 0.375 in. fci = 1

Ti = 0.5 in. fca = 4

R = 1.75 in.

gair = 1 ^ (17)

/log*-^ loge-i

19 X 1.41

(0.375 X 1) (^-^ + ^)

«= 120 kv./in. or 47,5 kv./cm. max.

218

DIELECTRIC PHENOMENA

To cause corona on a rod of this size a gradient

..-3.(:.-)

= 3l/l+ , "^ \

\ V 0.375 X 2.54 /

= 40.5 kv./cm. max.

PorceUla

Ocpper

Fig. 177. — Corona in bushing.

is necessary. Hence, in the case considered, there will be corona, and chemical action on the rod which will become coated with a green surface of copper nitrate. The obvious cure for this is to coat the inside of the porcelain shell with a conductor and con- nect it to the rod.

Corona or "static" is often noticed where insulated cables come through a wall or bushing. For instance, three rubber covered cables may come through three bushings in a wall. If the voltage is high enough a glow will appear around the rubber in the air space inside the bushing. Ozone attacks rubber very rapidly. Such cables may soon be broken down by this simple cause. Such breakdowns are often ascribed to " high frequency." The remedy is to "short circuit the air space." In doing this by metal tubes slit lengthwise, to prevent eddy loss in the metal, care must be taken to bell the ends of the tube, otherwise the air will be stressed where the metal tube ends. The "belled" part may be filled with solid insulation.

Case 4. Graded Cable. — Assume that three insulations are available, all of exactly the same dielectric strength, but of per- mittivities as follows:

Insulation A^ k

Insulation B, k

Insulation C, k

Rupturing gradient, g

5.4 3.6 2.0 100 kv./cm.

Assume that it is desired to insulate a 1.0-cm. wire using 1.75 cm. of insulation with an outside lead cover. The best way of

CONSIDERATION IN THE DESIGN OF APPARATUS 219

applying the insulation is so that each part is stressed in propor- tion to its respective strength. This ideal cable is impossible, but the more nearly this condition is realized the higher the voltage that may be applied to the cable without rupture, (a) Using insulation A alone the breakdown voltage is

e ^ gr log. R/r = 75 kv.

This is the same for either BorC alone. '

(6) Using insulation A next to the wire, then B, then C, with

Mo*yc«

jpo*;^«m

^*%

Fig. 178. — Graded cable.

(a) Not graded. (6) Insulations properly arranged, (c) Insulations improperly arranged. Noted break-down voltage in each case.

thicknesses 0.25 cm., 0.6 cm., and 0.9 cm. respectively, as in Fig. 1786, the rupturing voltage is

e = 133 kv.

c = 63 kv.

Note that the area in Fig. 178a, b, and c represents the voltage, and therefore the rupturing voltage if the maximum g is the rup- turing gradient. This example is given to show how important it is to properly arrange insulations. In general the insulation of the highest permittivity should be placed where the field is densest. This applies not only to cables but all electrical apparatus. In spite of the fact that all of the above insulations had the same dielectric strength, and the same total thickness, the rupturing voltages with the difiFerent arrangement were 133 kv., 75 kv., and 63 kv. respectively. (Use equation (17).)

Case 6. Bushing. — Other cases where the principle of put- ting insulation of high permittivity at points of dense field is

220

DIELECTRIC PHENOMENA

Form of

Intulator

Cojnpaced

shown are illustrated in Figs. 18 and 179. The solid insulation of the lead in Fig. 18, because its contour follows the lines of force, does not increase the stress on the air near it. It is, for that reason, much better than an insulator which has the insulation arranged in such a way that the stress on the air is increased in the denser part of the field. However, by inserting the high

permittivity insulation in the dense fields at the rod, and cutting it away in the middle, a better ar- rangement is obtained (Fig. 179). In the zone between flux lines a and 6, there is now the insulation of high permittivity, and air of low per- mittivity, in series in the same way as in the graded cable, and with the same effect. In tests the insu- lation of the type of Fig. 179 arced over at 18 per cent, higher voltage than that of Fig. 18 (of same over- all dimensions), though its air path was 6.5 per cent, shorter.^

In practice it is generally neces- sary to add corrugations to increase the ^'leakage path'' on account of dirt settling on the surface, etc. The "ideal" design is not always the best in practice. Case 6. Transformer Leads or Bushings. — One of the most common bushings is the oil filled type. Ill the design of such a bushing two general problems present themselves: The internal stress on the oil, which determines the puncture voltage; the external stress on the air, which determines the arc-over voltage. In the design of a bushing, however, the whole dielectric circuit must be considered at the same time.

If the surface of the shell follows a line of force, the internal field does not cut the shell and cause flux concentration at points on the shell; the voltage per unit length of surface,

Fortescue, Paper, A.I.E.E., March, 1913. Weed, Discussion, A.I.E.E., March, 1913.
Figs. 18 and 179 cannot represent practical leads as the rod and torus field is changed hy the plane of the transformer case.

FiQ. 179. — Bushing. Rod and Torus.*

CONSIDERATION IN THE DESIGN OF APPARATUS 221

however, is not constant with this condition unless the lines of force are approximately straight parallel lines A bushing, when parallel planes are approximated, theoretically, need not be over 2 in. high for a 100-kv. arc-over. This imposes a large diameter compared to length, and large well-rounded metal caps, etc. Such a bushing would arc over with slightly dirty surfaces, mois- ture on surfaces, etc., at very low voltage. A practical lead must generally be fairly long and corrugated (See Table LXXVIII, page 190).

Where the surface follows a curved line of force, the internal field still does not cut the surface and cause the so-called ** leakage " by local flux concentration, but the gradient is not constant along this line of force. Local breakdowns precede spark-over.

If the lead does not follow a line of force, the lines from the outside pass through the shell to the inside. In this case the shell should be so shaped that the stress is divided parallel to the . surface and also perpendicular to the surface.

In an improperly designed bushing of this sort, breakdown might occur at places along the surface, and at other points out from the surface. For instance, as an extreme case, it might be imagined that the surface of a bushing followed an equipo- tential surface. There would then be no stress in the direction of the surface, but breakdown would occur by the stress per- pendicular to the surfaces, as corona. Conversely a condition might obtain which would cause greatest stress along the surface as when a line of force is followed. As the surface, due to dirt, etc., is generally weaker than the air, it is in most cases better not to have maximum stress along it. (See Table LXXVIII.) In any case the stress should be uniform measured in either di- rection. Where the shells follow a line of force the field is more readily approximated by experiment, or by calculation, than where the lines of form cut the shell, when flux refraction, etc., must be considered. The direction of the flux may be controlled by the arrangement of metal parts. The bushing problem is a space problem.

In practice it is generally necessary to add petticoats. These should be placed so as to produce the minimum disturbance in the field with minimum stress along their surfaces.

Another type of lead is the condenser lead, built with the object of stressing all of the solid insulating material approxi- mately equally. It consists of a number of cylindrical condensers

222

DIELECTRIC PHENOMENA

of equal thickness, but of unequal lengths, arranged in Buch a way as to make the several capacities equal (Fig. 180). If this were exactly the case, the voltages across the equal thicknesses of insulation and equal distances along with the surface would be equal. This condition is possible but not generally reached on account of the capacity of the condensers to ground, to the central rod, and to each other (Fig. 180) ; to secure equal division of voltage here (Fig. 180) it would be necessary to connect the condenser plates to proper sources of potential. The condition may be approached, however, to such a degree that a good prac- tical lead is the result when the insulating has been carefully done. A smaller diameter is obtained, but a greater length is re-

Fio. ISO. — Condenser bushing.

quired due to arcing distance in the (ur (».c., to avoid arcs of the nature of the heavy line. Fig. 180). The present practical form is a loi^ thin lead. (One disadvantage clwmed is shown in the small sketch accompanying Fig. 180.) Little flaws in various parts of the lead are lined up by the metal parts and put directly in series. The separation of the insulation by metal is, from ai>-

CONSIDERATION IN THE DESIGN OF APPARATUS 223

other standpoint, an advantage. A progressing corona streamer is stopped on reaching the metal surface at any layer. Concen- tration of flux at the edges of the metal cylinder must also be taken care of. The condenser lead is often arranged with a metal hat for flux control.

Fig. 181. — Diagramatic representation of flux, and capacities in condenser

bushing.

Case 7. Dielectric Field Control by Metal Guard Rings, Shields, Etc. — It is sometimes practical to accomplish more with metel than by added insulation. In a case where the field is not uniform, but very much more dense at one point than at another, the flux may be made more uniform by relieving the dense por- tion and distributing over the less dense portion by a proper ar- rangement of metal parts connected to a source of potential of the proper value. This is not always practical, as the necessary complicated potential connections often weaken the apparatus and make it much more liable to breakdown.

As a simple example : Fig. 182 represents two spheres of unequal size in air, one at potential e the other at potential — e, or a voltage 2e between them. All the flux from A ends on B. The flux den- sity at B is then much greater than at A and the air around B is very much more stressed than the air at the surface of A. The equipotential surface C may be covered with thin metal and no change takes place in the flux at A or B. If, however, C is con- nected by a wire to B the flux around B disappears and there is no

224

DIELECTRIC PHENOMENA

stress on the dielectric at the surface of B, The total flux in- creases because of the greater capacity between A and C The stress at A, due to increased flux density, increases, but it is still much less than the stress formerly at By and a greater potential is required for spark-over. In other words, the insulation is more uniformly stressed and therefore working at greater efficiency.

If instead of surrounding B or completely shielding it the sphere C be placed as in (c) and con- nected to B by a wire the stress is relieved at B and increased at A. The distribution at B is again more uniform.

An actual example where this principle was made use of in an emergency case several years ago by the author is illustrated in Figs. 183 and 184. In making some experiments 200 kv. were carried through the roof of ashed by porcelain bushings. During a heavy wind storm the roof was blown off and one bushing cracked as indicated by the jagged line. When the roof was replaced and an attempt made to put the bushing again into operation it was found that bad arcing took place to the damp wood at 130 kv. As no extra bushings were immediately ob- tainable, and it was necessary to finish the experiments, the ex- pedient of field control was made use of. By hanging a metal torus made of a coil of wire on the rod, the work of about fifteen minutes, the bushing was made operative up to 200 kv. This was not as good as a new bushing, not the best sort of bushing, but it was a means of making a defective bushing operative, and prevented a shut- down of a month or more.

The effect of this shield is shown diagrammatically in Fig. 184.

Fig. 182. — Simple illustration of flux control.

CONSIDERATION IN THE DESIGN OF APPARATUS 225

By moving the ring up and down the rod, a point of minimum flux density on the cracked surface of the porcelain ia found. It better distributed the flux and reduced the omximum flux density below the rupturing value.

Fig. 183. — Eatrance Fia. 184.— Making bushing shown in Fig. 183

bushing. operative by flux control Bilei lower part bad

broken oS.

Case 8. High Frequency. — Apparatus must be designed to meet not only normal but also, to a reasonable extent, abnormal conditions. Due to surges, lightning, arcing grounds, switching, etc., high frequency voltages travel over the line, say to a transformer. The voltage may not be increased at the trans^ former terminals, as the "high frequency" may exist only as a slight ripple on normal voltage wave. The lightning arrester therefore does not discharge, and a needle gap across the transformer terminals shows no voltage rise. A needle gap across a small section of the transformer may indicate a voltage several times normal line voltage. The points of greatest potential difference will depend upon the fre- quency and the transformer , constants. The fact that "high frequency" may enter an apparently high inductance and build up high local potentials is because the inductance also contains capacity. It is not possible to give a theoretical treatment of this here. It is simply mentioned to show that it is sometimes dangerous to thin insulation at one part and add it at another in order to get perfect flux distribution under normal conditions, because under abnormal conditions great potential differences may exist across the weak insulation. It ^so illus-

yi J.,.

2 \E n-

: %ii'^

^ ^»:.:i;;L

7 S

226 DIELECTRIC PHENOMENA

traies how '^ high frequency" generally is dangerous by building up high local potential differences. Where a large number of metal parts are used to distribute the flux under normal con- dition, the effect of the well-known multi-gap lightning arrester may come in and cause break-down at high frequencies.

It is, for somewhat similar reasons, not always best to follow ideal designs in line insulators, leads, etc. The ideal surface may be such as to make the surface time lag low or the rain arc-over low.

Case 9. Dielectric Field. — Draw the dielectric lines of force and equipotential surfaces between two parallel cylinders so that J-f 2 of the flux is included between any two adjacent lines of force, and ^^0 of the voltage is between any two adjacent equipotential circles.

Let S = 10 cm. between conductor centers r = 1 cm. = conductor radius.

From Chapter II, page 21,

S - V^2 _ 4^2 10 - v'lOO - 4 ^ -^

Z = ;r = ;r = U.IU

The distance between focal points of the lines of force is

S' = S - 2« = 10 - 0.20 = 9.80

It is desired to include one-twelfth of the total flux between lines of force. Draw radial lines from the flux centers K2 X 180 = 30 deg. apart. (See Chapter II, pages 14 and 19.) The point of intersection of a radial line with N. N. (Fig. 186a) is a point on the line of force. The line of force is hence a circle with center on N, N.y and passing through the point of intersection of th5 radial line N.N,, A, and A. The lines of force are therefore determined. The centers, etc., might have been calculated from equation (8), page 19. The line of force is also determined graphically by drawing the diagonal line through the intersec- tion of radial lines, as shown in Fig. 187.

The equipotential surfaces in this case may be found graphic- ally in a similar way by drawing diagonals through the inter- sections of the circles of the component fields. Other resultant fields may be drawn from corresponding plane diagrams if the

CONSIDERATION IN THE DESIGN OF APPARATUS 227

component fields are given for the same strength, or same poten- tial differences between the equipotential surfaces. Any number of fields may be so combined, two at a time. It is often possible to approximate for practical purposes the field of a complicated structure by so combining the simple fields of the component electrodes.

Fig. 186 (6) Fig. 186. — Method of drawing lines of force and equipotential surfaces.

The equipotential surfaces are circles with centers on the line

A'l, A't. See equation (7), page 18. The distance of the center

V ah

of the circles from A't is

■y and the radius is

where

a and h must be so chosen that the permittances between circles are equal.

228

DIELECTRIC PHENOMENA

For any point p on the line A'lA't (Fig. 1866), the potential to the neutral plane due to A't is

-4^ , 26

Due to A' I, it is

lA , 2a ^ , 2(S' - 6) 2,^ '°«* 5^ = 2;^ '°«* ^'—

Fig. 187. — Graphical method of drawing lines of force between two

cylinders.

The total voltage from any point p to the neutral is

6np — ^Inp I ^2np — n j^k

4' , jS' - 6) ""'■ = 2;^ '°8* ^6~

/, 2{S' - 6) , 26\ ^log« -5^-^7 — '- - log€ ^ j

It is desired to divide the field up into n equal voltages between the conductor surface and the neutral plane. The potential from the conductor to neutral is en and is known Due to A't :

-4> , 2(r - z)

2TKk

CONSIDERATION IN THE DESIGN OF APPARATUS 229

Due to A

eAin

2TKk

log*

2(5'

-(r -S'

— ;

e»

_ * 2irKk

log

5'-

(r- — z

.-. 4'

= 2rKk

log*

S' -

(r-

r — 2

Let |8 be the fraction of the voltage e« it is desired to place be- tween the neutral plane and any point p on the surface under consideration, then (Fig. 1866)

« 1 (S' - h)

P = — g^- (r-^) 'og« — 6—

log*^-^ = Pirn (,1^) = 0^

In this problem

loge ^^ = constant == F

r — z

„ , 9.8 - (1 - 0.1) , 8.92 ---- P = log* (1 - 0.1) = •««* 092 = 2-290

log«^=/SF

"" = anti-log /3F

6 =

(anti-log /3F + 1)

b is thus determined.

If it is desired to find h for the first circle from the conductor P = 0.9.

^' = 7JT1 " "8T = ^-^^ For the next circle

/S = 0.8

230

DIELECTRIC PHENOMENA

Other values are found and tabulated in Table LXXXIII. a and R are thus found. The circles may now be drawn with radii B, centers on A'iA'2j and intersecting A\A't b cm. from A^t.

Table LXXXIII. — Equipotential Surfaces

5' - 6

— 6

0-6

1.0

0.900

8.90

1.00

8.00

0.9

1.110

8.69

1.27

7.58

9.65

0.8

1.353

8.45

1.62

7.09

11.49

0.7

1.648

8.15

2.07

6.50

13.45

0.6

1.98

7.82

2.65

5.84

15.46

0.5

2.38

7.42

3.50

5.04

17.65

0.4

2.81

7.09

4.65

4.28

19.90

0.3

3.29

6.51

6.65

3.22

21.40

0.2

&•

3.80

6.00

10.35

2.20

22.80

0.1

4.34

5.46

21.15

1.12

23.67

0.0

&10

4.90

0.00

24.00

F - 2.290 = constant « = 0.1 5' =• 5 - 2.z = 9.8

The gradient at any point, and therefore the equigradient surfaces may be found as follows: The flux density at any point is

2jrXiXi

(Pages 21 and 23.) 2TkKen

D =

2S'irkKe.

2xXia;,log«|^ +

[i^W^

g -

XiXt

S'en

Hi^W^l

or for a given voltage, spacing and size of conductor, the term to the right is constant, and it follows:

XiXi

times a constant ^

XiXi

CONSIDBRATION IN THE DESIGN OF APPARATUS 231

18 the gradient at any point X\ cm. from ^'i and xi cm. from A't- Putting Xi in terms of xt and the angle a between si and the line A'tA't-

Xi/Xi

\ ^

^»-

Fio. 188. — Method of plotting equ^adient curves Table LXXXIV. — ESquiobadibnt Surpacbb

<■

0°

30"

80"

90°

lac

IHO"

ISO"

9 -21.4

Xt =

1.16

1.13

1.07

1.00

0.97

0.94

0.B3

9 - 16,1

X, =

1.64

1.60

1.44

1.32

1.27

1.23

1.20

d - 10.7

Xt -

2.91

2,85

2.25

2.00

1.85

1.75

1.74

g ~ 8.9

Xt -

4.90

3.40

2.71

2.37

2.10

2.06

2.02

g - 8.0

Xt —

4.0

3.08

2.69

2.38

2.26

2.20

t - fi.34

I, .

4.9±4v'-l'

8.20

4.70

3.81

3.27

3.17

3.10

g - 2.67

Xt -

Provenance

Shelf: Reference library
Book: Dielectric Phenomena in High Voltage Engineering (1915)

Author: F.W. Peek Jr.
Rights: Published in 1915, before 1929, and therefore in the public domain in the United States.
Collected By: StanBot reference library