Dielectric Phenomena in High Voltage Engineering (1915) — part 11 of 12

'

■

8.63

6.73

5.83

5.40

5.29

1 Such a gradient does not e

iat on this line and hence Z] is imaginary.

(See plot F

g-8,f

«iiel6.)

Gradient at Equidistant Points on the Conductor Surface

Ancls iMt. horiHinUl a',A'>\ ud Un« throuch polot ud 0*

30"

eo*

BO"

120°

IW

180"

26.7

26.0

23.7

21.6

19.4

18.2

232 DIELECTRIC PHENOMENA

(1) Find the maximum gradient at the conductor surface for 100 kv. between conductors. This may be found directly from equation (12a), pages 24 and 29, and is 26.7 kv./cm.

(2) Find the gradient at six equidistant points on the con- ductor surface for 100 kv. between conductors. (See Table LXXXIV.)

(3) Calculate the equigradient curves for gradients of 21.4, 16.1, 10.7, 8.9, 8.0, 5.34, and 2.67 kv. per centimeter at 100 kv. between conductors. This may be done from the above equation by putting g equal to the required gradient, and finding Xs for given values of a. The results are tabulated in Table LXXXIV, and method of plotting is shown in Fig. 188.

A complete plot of Case 9 is shown in Fig. 8, page 16. Note that in such a diagram, the permittance or elastance of each of the small cells bounded by sections of lines of force and equipo- tential surfaces is equal.

Case 10. Dielectric Fields in Three Dimensions. — The field of a conductor arrangement which must be considered in three dimensions, as a rod and torus, rod through a plane, etc., is gen- erally represented on a plane figure in such a way that if the figure were revolved about its axis, the solid would be formed sur- rounded by its three-dimensional field. The small cells of the plane figure bounded by sections of lines of force and equipoten- tial surfaces would form cells in the solid of equal permittance.

In the case of figures, as those for parallel wires, a wire in a cylinder, and parallel planes, it is possible to represent the field by considering only two dimensions. The height and thickness of the cells on the plane give constant permittance, or average

^, . , - = constant. The third dimension is then the length

thickness

of the wire and need not be considered in drawing these ceUs.

In the case of the three-dimensional field, the cells on the plane must be of such a height and thickness that the solid cells have constant permittance, or where the cell is small

hr

— = constant.

z •

This can readily be seen from Figl 189.

It is a general law that the cells must be so arranged that the stored energy may be a maximum or the permittance a maximum. In cases where the field need only be considered in two dimensions.

CONSIDERATION IN THE DESIGN OF APPARATUS 233

ftl

M\

JUaf

Bod

\5

it is thus possible, without great difficulty, to draw a field by a series of approximations in which the cells have a constant

• or add up to maximum permittance. This is also possible for

a three-dimensional field, but extremely difficult because the cells must be drawn in such a way that the solid cells have constant permittance.

The best way in which to determine a field that cannot be read- ily calculated is experimentally. If the electrodes are immersed in an electrolyte in a large tank made of insulating material, and a small current passed between them, equi- potential surfaces may be measured at equal voltage intervals on a plane through the axis of revolution by means of a galvanometer.^ These surfaces correspond to the dielectric- equipotential surfaces. The lines of force may be drawn at right angles to these, so as to divide the field into solid cells of equal capacity (see above). It is difficult in practice to get results by this method when the problem includes several per- mittivities.

Theoretically it would be possible to use a solid material to represent, for instance, the porcelain shell of an insulator, and the electrolyte to rep- resent the air. The resistivities of the two materials should then have the same ratio as the elastivities of porcelain and air. It is difficult to find a solid material with a resistivity in the order of that of an electrolyte.

As a less exact experimental method, the lines of force may be obtained by mica filings and the problem then solved by approxi- mations. These methods may be developed into very useful ones for a study of flux control, etc.

Case 11. Effect of Ground on the Permittance and Gradient for Parallel Wires. — Such problems are solved by taking the "images" symmetrically below the ground.

^ Fortesque has described this method. See A.I.E.E., March, 1913. Much more exact results may be obtained than those shown in this paper.

Solid Gel Formed

by Botatlni Plane OeU «bo«««

Fia. 189.— Dielectric field three dimensions.

in

234 DIELECTRIC PHENOMENA

Voltages between AB due A, By Ai^ Bi are

*^ - + ^2^^ ^^8. f

«B

~ ^2wkK^ ^°^ S /S a S' where the wires \ _ ( ^ -) in„ ^ \ are far apart. /

e = ex +fiB + «A. + «B. = ;^ (logf + log. ^) - ;^ logf

The total voltage b

S . , 2A\ ^ , S2A

r a

^ = f = i^ (««*• "°^)

r a Where the wires are far apart the gradient is

e

^"o 1 S 2h

2 r log. — —

^ r a

The problem for a number of wires may be solved in the same way. The fluxes from the different wires may then not be the

same and the solution is more ^ ^ ' ^f difficult as a number of simul-

^ n taneous equations must be writ-

I \ / 1 ten and solved,

t \ / 1 Case 12. Three-phase Di-

I \ / electric Field with Symmetrical

^»^iM mM^M ^"^'^ andUnsymmetricalSpacings.—

The fluxes between conductors on a three-phase line vary sinu- soidally with the voltages. The instantaneous values of voltages may be added algebraically as

17,^ 1AA T?4r » f , above. The effective or maxi-

FiG. 190. — ^Effect of ground on ca- pacity between parallel wires. mum values are found by geo- metrical addition. To illustrate: find the fluxes for three three-phase conductors in an equilateral triangle, and also for flat spacing. In order to greatly simplify the problem, the effects of ground or "images" will be neglected, and the conductors considered far apart.

CONSIDERATION IN THE DESIGN OF APPARATUS 235

Then due to fluxes from

A \ B I C

1 AB r CB

(a) EjiB = 2^j^ (^^ ^^^ T" + ^^^^^BA + ^c log. ^) =e sin ^

6 sin (^ - 120)

Only two of the three equations which may be written as above are independent, since the sum of the voltages must be zero. The other independent equation is

(c) ^A + ^B + ^c =

A o

Conductors SpcLced in a Triangle o o (equilateral triangle).

B C Substituting spacing S in (a) and (6) and solving for ^^^ ^q, and ^^

2irkKe ^^ = o (1.5 sin e + 0.866 cos 6)

Slog.- r

Let c(1.5 sin 6 + 0.866 cos 6) = «« (sin ^ — a)

put ^ = 90 and ^ = and solve for €„ and a

2TrkKe . ,^ ,.^. 1.16(^fciiL)e . ,^ _.. ^fl = osm {$ - 150) = g ^ sin(^ — 150)

Vsiog*- log.-

2irAiiLe . ,^ ^^. 1.16(7rfcii:)e . ,^ ^^ ' ^^ = o sm {e — 30) = ^ g sm (^-30)

VSlog.- %.-

^(7 may be found in the same way, or for this particular case, ^A9 4^bj *^d }pc are equal by symmetry. For single phase:

2'KkKe

2hg.^

Therefore, when the wires are far apart, and with the same voltage between lines, the three-phase stress is —7= times the single-phase stress.

236 DIELECTRIC PHENOMENA

Flat Spacing A B C. — Putting S, 5, and 2S ia a and b and

o o o

solving as before,

^B = z sin ie - 150)

VS log. - - 0.58 log 2 r

^kKe . , _^,

= ^^ sin {$ - 150)

V3 log. ^ - 0.4

The flux, and therefore the stress, when the wires are far apart,

is greatest on the middle wire. For - = 500 it is 4 per cent.

greater than on the wires with the same S and triangular spacing as above. ^^, and ^c are 6 per cent, lower than for the triangular spacing. The gradients vary in the same way. Corona, therefore, starts on the center wire at a 4 per cent, lower voltage, and on the outer wires at a 6 per cent, higher volt- age than for triangular spacings.

Case 13. Occluded Air in Insulation. — It is interesting to estimate the effect of occluded air in solid insulation. Assume that in the process of manufacture air bubbles have formed in a sheet of rubber insulation. The sheet is 1 cm. thick. The " bub- bles" are thin compared to the rubber, and long in the direction of the length of the sheet. It is estimated that the largest ones are 0.01 cm. thick, and 0.1 cm. long and wide. The electrodes which the rubber insulates may be assumed as being practically paraUel planes. The working voltage is 40 kv., or the stress is 40 kv./cm. effective in the rubber. As the air bubbles are not thick enough to greatly disturb the field, the same flux passes through the air as through the rubber. The permittivity of the rubber is 3. The stress on the air is, therefore, 3 X 40 = 120 kv./cm. effective. Air breaks down at 21.2 kv./cm. effective at atmospheric pres- sure. It seems probable that these bubbles will break down, even after allowance is made for the extra strength of thin films, and a possible pressure higher than atmospheric. It is probable that the solid insulation would soon break down on account of heat and chemical action.

Case 14. General. — (a) Estimate the visual corona voltage when wires are wet. Compare with the visual corona voltage when wires are dry.

CONSIDERATION IN THE DESIGN OF APPARATUS 237

Calculate g^ from the formula on page 67, Chapter III. Insert the value in formula (20). Maximum e, to neutral is thus found. If the voltage used is a sine wave, reduce to effective kv. by dividing by y/2. For a three-phase line the voltage between wires may be found by multiplying by /3; for a single-phase line, by multiplying by 2. Compare with dry visual critical voltage calculated from equation (20) ; page 43.

(6) At what voltage will the above wires spark over wet and dry single phase; three phase?

Estimate dry spark-over voltage from equation given on page 83, Chapter IV. Estimate wet arc-over voltage by assuming needle gap spark-over.

(c) Calculate the dry arc-over curve for a 10-cm. sphere (grounded) at 5 « 0.90, and spacings from 1.5 to 10 cm.

Use equation (136), Chapter IV. Estimate a wet spark-over curve as outlined for spheres on page 105, Chapter IV.

(d) What is the voltage required to puncture 0.5 cm. of paper insulation when the time of application is limited to 1/120000 second? In 100 seconds?

Use equation on page 179, Chapter VII, of the form

9m = 1/(1 + T^) ^» "^ g» X thickness.

(e) Estimate the loss per cubic centimeter at 1000 cycles in a piece of varnished cambric, at 5.0 kv./mm., 25 deg. C. Use equation page 185, Chapter VII.

(/) What is the breakdown gradient of a piece of porcelain 2 cm. thick?

0.94,

, = 7.5(i+:^y)

where t = thickness in mm.

g = gradient in kv./mm. (eff.)

(See Chapter VII, page 174.)

DATA APPENDIX

MEASURED CORONA LOSS Indoor Line — 60-cycle

The current and watts given are measured values due to corona, divided by the total conductor length in kilometers. Corrections have been made for transformer and leads. The voltage is given to neutral. As these measurements were made on a single-phase line, the voltages between wires were twice the value given.

Corona Loss — Indoor Line — 60-cycle

Test lOB

Test IIB

Eff. kv. to neutral, e*

Amp. per km.

LOM

kw./km., p

Eff. kv. to neutral, tu

Amp. per km.

Loes kw./km., p

10.52

0.07 0.51 1.40 3.20

4.02

6.83

9.44

15.03

20.63

13.7 16.7 18.1 19.9

24.7 29.3 33.2 36.3

39.7 44.0 47.3 60.2

45.2 41.5 37.4 31.0

27.0 22.3

0.33

12.62

0.92

14.80

1.11

17.10

0.070

0.100 0.160 0.189 0.223

0.268 0.325 0.380

1.64

18.20

3.95

19.60

6.90

22.30 24.90

27.20 29.70

0.225 0.310

0.395

10.40 14.20

18.75 26.73

28.00 25.90

0.404 0.342

0.263

22.40 16.80

11.80 7.16 4.14 1.98

34.20

23.60 20.80

0.350 0.293 0.238 0.163

0.128 0.082

29.20 22.20

18.40

15.69

16.10

8.08

6.29 2.53

Spacing, 15.25 cm.

Radius, 0.032 cm.

Total cond. length, 0.0838 km.

6 - 1.02.

Spacing, 30.5 cm.

Radius, 0.032 cm.

Total cond. length, 0.0838 km.

8 - 1.02.

238

DATA APPENDIX

239

Tert 13B

•

Test 15B

Eff. ky. to neutnl. e*

Amp. per km.

kw./km., p

Eff. kv. to neutral, en

Amp. per km.

Lo« kw./km., p

19.5 24.3 29.6 34.0

38.0

0.051 0.071 0.099 0.133

0.146

0.96 1.78 3.23 4.95

6.49

9.13 12.51 16.35

21.00 26.25 34.40 40.60

1

50.50 59.50 72.00 83.10

93.40

17.3

23.7 30.2 36.1

42.2 49.8 56.7 62.5

66.5 71.4 78.6 84.4

89.4 95.4 99.3 91.0

81.6 67.9 52.1 39.1

27.0

0.059 0.078 0.109

0.35 1.17 2.34 3.92

5.76

43.0

0.166 0.200 0.223

0.246

9.26

46.7 62.4 .

57.5

0.196 0.224

13.21 16.70

20.00

62.5

0.285 0.327 0.359

0.385

24.35

68.3 73.1

79.1 84.0

0.310 0.322

0.345

30.95 37.20

41.90 50.50

90.0 93.6]

102.0

0.430 0.460

0.510

0.395 0.369

0.310

58.60 45.60

34.10 21.65

0.177 0.126

0.068

10.46 4.44

1.74

Spacing, 61 cm^

Radius, 0.032 cm.

Total cond. length, 0.0838 km.

9 -> 1.03.

Spacing, 91.5 cm.

Radius, 0.032 cm.

Total cond. length, 0.0838 km.

« - 1.012.

240

DIELECTRIC PHENOMENA

Spacing, 122 cm.

Radius, 0.032 cm.

Total cond. length, 0.0421 km.

5 -> 1.018.

Te8t20S

Test 21B

EflF. kv. to neutral, e*

Amp. per km.

Lon

kw./km., p

1

Eff. kv. to neutral, e%

Amp. per km.

Loaa

kw./km., p

17.8

0.21 1.29 2.17 3.71

5.16

6.94

9.80

14.60

19.23 21.12 26.70 33.10

42.70 61.70 35.60 25.00

15.95 7.44 4.55

19.8 24.5 27.2 30.7

34.8 39.8 44.8 50.4

55.1 60.6 64.6 70.0

77.9

87.6

94.3

101.6

1

0.81

24.6

1.15

30.1

. 2.02

36.2

0.110

0.128 0.159 0.190 0.233

0.258 0.273

2.19

42.0

3.42

47.0 63.2 62.0

67.6 73.4 78.1

0.129 0.156 0.177

0.212 0.234 0.246 0.266

0.310

3.86 6.04 6.47

8.45 10.80 12.40

85.2

93.2 100.2

0.346 0.385

15.10

19.30 26.60

87.0

0.350 0.298

0.250 0.178 0.114

32.60

76.1

41.00

66.2 49.4 40.1

k

Spacing, 183 cm.

Radius, 0.032 cm.

Total cond. length, 0.0342 km.

« = 1.012.

DATA APPENDIX

241

Test 22B

Te8t24B

Eff. kv. to neutral, en

Amp. per km.

Lon

kw./km., p

Eff. kv. to neutral, e*

Amp. per km.

Loas kw./km., p

20.7

0.72 1.01 1.21 1.98

2.34

3.57 ;

4.53 1 5.71

7.43

9.13 11.05 11.99

16.37 23.00 26.00 34.50

20.1 25.3 32.0 36.0

41.0 45.7 50.3 57.0

62.2 67.3 72.4 77.5

82.3 87.8 92.5 97.3

100.5 79.0 65.0 52.7

0.24

24.5

0.98

27.2

1.84

30.9

0.103

0.120 0.138

3.18

34.6 40.1 45.2

0.100 0.121 0.149 0.171

4.52 6.11 8.30

50.3 55.1

0.185

0.210 0.240 0.266 0.290

11.57 15.10

60.2 64.6 69.5

0.215 0.230

19.15 23.20 27.50

78.5

32.10

87.5

0.345 0.380 0.417

37.90

94.2

43.80

103.2

50.80

55.60

28.70

17.10

9.90

Spacing, 274.5 cm. Radius, 0.032 cm. Total cond. length, 0.0342 km. 2 = 1.012.

Spacing, 91.5 cm.

Radius, 0.057 cm.

Total cond. length, 0.0818 km.

8 » 1.0009.

242

DIELECTRIC PHENOMENA

Te8t26S

Teet28B

Eff. ky. to neutral, «»

Amp. per km.

LOM

kw./km., p

Eff. kv. to neutral, em

Amp. per km.

Loes kw./km., p

20.0

0.37 0.98 2.24 3.36

5.14

6.60

9.90

12.32

18.30 22.30 28.40 36.60

40.80 50.50 56.50 64.00

71.40

83.40

104.00

54.50

39.00 33.00 22.70

10.6

14.2 16.1 18.4

20.2 22.2 24.0 25.0

27.0 30.2 34.0 36.7

36.7 40.7 44.5 47.1

51.7 49.6 43.0

23 2

0.053

29

0.18

32.8

0.43

37.1

0.124 0.141 0.173 0.202

0.232 0.262 0.290 0.332

0.334

0.413 0.431

0.464 0.515 0.562 0.396

0.333

0.98

41.1 46.7 51.3

57.1 61.1 66.2 72.0

75.7 80.7 85.0

88.7

91.0

96.5

101.0

82.8

74.7 69.7

0.061 0.069 0.072

0.087 0.120 0.157 0.178

0.181 0.212 0.265 0.298

0.369 0.342 0.251

1.34 1.83 2.20

2.93

5.00

7.88

10.30

10.10 14.80 20.30 24.80

35.20 30.80 18.20

60.0

0.255

Spacing, 0.61 cm.

Radius, 0.057 cm.

Total cond. length, 0.08186 km.

8 - 1.002.

Spacing, 30.5 cm.

Radius, 0.057 cm.

Total cond. length, 0.0818 km.

a " 0.993.

DATA APPENDIX

243

Eff. kv. io neutral, ««

TestaOB

Amp. per km.

Teet 32B

kw./km., p

Eff. kv. to neutral, ««

Amp. per km.

Spacingi 61 cm.

Radius, 0.071 cm.

Total cond. length, 0.0815 km.

d - 0.98.

kw./km., p

21.7

0.18

0.92

. 2.45

22.5 27.2 32.5 37.2

41.1 45.6 50.3 55.0

60.0 65.7 72.0 77.2

82.5 89.2 92.2 85.2

70.0 61.7

0.21

25.6

0.049 0.062 0.086

0.100 0.123 0.146 0.178

0.194 0.222 0.257 0.278

0.298

0.31

31.5

1.41

36.2

4.30

5.80

8.60

11.70

15.30

19.50 24.60 29.70 36.30

45.20 54.00 63.00 76.00

81.20

92.00

114.30

60.20

45.30 38.60 26.20 13.40

2.70

40.5 45.7 49.7 54.2

59.5 64.0 68.2 73.0

78.5 83.5

0.138 0.156 0.180 0.204

0.238 0.269 0.290 0.322

0.352 0.384 0.441 0.486

0.500 0.530 0.600 0.459

0.356 0.319

3.68

5.03

7.35

10.18

13.50 17.40 23.20 27.60

31.40 40.00

88.2

44.00

95.0

35.80

96.5 100.0

20.80 . 14.32

103.0 90.2

79,5 75.2 65.5

•

r

51.7

Spacing, 91.5 cm.

Radius, 0.914 cm.

Total cond. length, 0.0815 km.

S - 1.002.

244

DIELECTRIC PHENOMENA

Teat 33S

Teit 4 IS

Eff. kv. to neutral, «•

Amp. per km.

Loss kw./km., p

Eff. kv. to neutral, en

Amp. per km.

Loes kw./km., p

24.7

0.31 1.53 2.45 3.50

4.96 6.37 9.67 12.9

15.5 20.8 34.8 29.6

15.3

28.3

35.5 41.0 48.6

53.7 59.0 63.8 69.4

73.6 71.9 60.1 54.2

69.9 67.0 47.0

29.8

0.071 0.108 0.184

0.208 0.234 0.265 0.306

0.353 0.325 0.244 0.210

0.250 0.224 0.161

2.72

32.6

4.90

35.6

10.40

39.3

13.25

43.7

17.50

47.6

23.40

51.5

30.02

66.3

35.70

60.2

34.10

65.5

19.86

67.0

13.66

54.4

19.35

16.30 8.87

Spacing, 61cm.

Radius, 0.0914 cm.

Total cond. length, 0.0815 km.

8 - 1.006.

Spacing, 61 cm.

Radius, 0.105 cm.

Total cond. length, 0.0423 km.

6 « 1.001.

DATA APPENDIX

245

Teet 45B

Test 47B

Eff. kv. to neutral, e»

Amp. per km.

1

LOSB

kw./km., p

Eff. kv. to neutral, e*

Amp. per km.

LOM

kw./km., p

22.3

0.06 ; 0.12 0.34 1.41 ,

1 1

2.70

4.78

8.10

10.70

14.70 19.50 1 24.80 1 30.10

1 1

37.20 ! 43.40 56.20 59.00

80.50 84.50 i 52.20 32.70 ;

45.0 50.0 54.5 60.5

65.7 70.5 75.5 79.0

87.0 91.7 96.5 93.5

90.0 82.0 75.8 58.0

42.6 40.0

0.080

0.100

' 0.104

0.37

25.8

0.74

29.7

1.90

35.7

5.76

39.5

0.152 0.174 0.205 0.230

9.13

44.2

12.60

50.2

16.30

54.0

18.75

59.5

26.80

64.5

31.40

69.0

38.20

74.0

0.321

34.10

m

79.7

29.80

82.7

21.70

88.7

16.20

98.0

4.22

99.7

0.49

103.0

0.24

86.7

75.5

Spacing, 61 cm.

Radius, 0.164 cm.

Total cond. length, 0.0185 km.

5 » 0.996.

Spacing, 91.5 cm.

Radius, 0.256 cm.

Total cond. length, 0.0815 km.

5 » 0.996.

16

246

DIELECTRIC PHENOMENA

Spacing, 61 cm.

Radius, 0.256 cm.

Total cond. length, 0.0815 km.

a - 1.00.

TeBt48fi

Teat 49B

Eff. kv. to neutral, tn

Amp. per km.

Loss kw./km., p

Eff. kv. to neutral, e.

Amp. per km.

Loss kw./km., t>

44.1

0.61 1.11 3.87 5.90

10.60 17.16 20.70 26.70

33.30 27.10 29.40 23.90

18.30

16.55

8.10

4.10

40.5 44.5 43.0

46.8

50.6 55.6 58.8 53.8

49.6 45.7 43.2 39.3

1.16

47.2

3.13

61.7

2.27

54.5

5.70

60.8

12.30

67.2

19.25

71.5

75.5

16.05

81.7

9.70

76.6

5.27

78.5

2.82

74.0

1.23

69.5

•

68.0

58.2

52.7

Spacing, 30.5 cm.

Radius, 0.256 cm.

Total cond. length, 0.0815 km.

a " 0.996.

DATA APPENDIX

247

Test 51B

Te8t54B

Eff. ky. to neutral, en

Amp. per km.

Loee

kw./km., p

1

Eff. kv. to neutral, e*

Amp. per km.

Loea

kw./km., p

62.5

0.159 0.190 0.220 0.261

0.318

9.15 14.55 20.10 28.45

40.20 49.70 34.60

22.10

5.65

10.20

15.75

19.30

25.5 31.8 37.7 42.7

47.1 57.0 63.2

69.7 76.5 78.7 84.5

89.3

95.0

99.1

102.2

97.2 92.0 87.0 76.7

82.0 72.1

0.051

68.0

72.0

0.06

78.0

0.30

87.3

0.30

91.5

0.49

82.0

1.03

72.8

1.81

56.0

0.152 0.164 0.184

0.210 0.238 0.263

5.08

61.5

6.48

67.2

12.22

70.2

17.20

23.90 28.40 31.90

26.00

20.90

16.50

5.82

9.10

2.67

Spacing, 61 cm. Spftcing, 91.5 cm.

Radius, 0.333 cm. Radius, 0.464 cm.

Total cond. length, 0.0817 km. Total cond. length, 0.0825 km.

6 » 0.999. 6 " 0.982.

AU of the above tests were taken at a temperature of about 25 deg. C.

MEASURED CORONA LOSS Outdoor Line — 60 cycle

Columns 1^ 2, and 3 are actual measured values and include transformer and lead losses. Column 4, the actual corona loss, for the length of line used in the test is obtained from Column 3 by subtracting transformer and lead losses.

These tests were made on comparatively long single-phase lines out of doors, and the conductor surfaces, etc., were not in as good condition as in the case of the indoor line. Transformer losses

248

DIELECTRIC PHENOMENA

for several temperatures are given. The voltage values are ef- fective between lines.

ToBt No. 146. Tiine A^

1 Test No. 18. Line A

L

Kv. bet. lines

Amp.

Kw.

Kw. line loss, p

Kv. bet. , lines

Amp.

Kw.

Kw. line loss, p

63.5

0.056

0.07

0.01

80.0

0.040

0.12

0.01

80.5

0.077

0.12

0.02

90.0

0.100

0.16

0.02

90.1

0.092

0.15

0.02

101.1

0.107

0.20

0.04

107.5

0.113

0.30

0.12

112.0

0.113

0.25

0.05

115.2

0.121

0.35

0.14

121.6

0.123

0.30

0.06

126.2

0.135

0.63

0.37

129.5

0.131

0.35

0.07

134.2

0.146

0.85

0.55

140.0

0.146

0.49

0.16

142.5

0.154

1.29

0.95

150.0

0.160

0.76

0.38

150.0

0.164

1.95

1.45

160.0

0.172

1.60

1.17

158.0

0.173

2.69

2.25

152.0

0.162

0.90

0.51

166.1

0.185

4.00

3.48

164.2

0.174

2.00

1.55

165.0

.0.183

3.51

3.02

172.0

0.187

3.40

2.90

173.7

0.196

5.00

4.45

183.2

0.205

5.60

5.02

163.4

0.184

2.70

2.23

188.2

0.210

6.92

6.30

170.4

0.193

4.20

3.67

196.4

0.223

9.02

8.42

181.0

0.198

6.06

5.42

202.2

0.237

11.06

10.36

203.0

0.251

12.84

12.04

206.0

0.242

12.90

12.09

199.2

0.243

11.50

10.73

187.2

0.211

6.95

6.34

193.4

0.227

9.10

8.49

196.4

0.225

9.60

8.90

176.4

0.197

4.74

4.17

•

Total conductor length, 10

(9,500 cm.

165.6

0.184

2.70

2.21

Spacing, 310 cm.

162.8

0.180

2.38

1.81

No. 3/0 7-strandhard-dra^

m copper-

154.4

0.169

1.28

0.85

weathered cable, diam. ]

L.18 cm.

166.0

0.176

2.94

2.45

Temperature, wet, 16 deg dry, 18.5.

. C.

184.4

0.198

6.49

5.87

Barometer, 75.5 cm.

172.0

0.193 0.177

3.85 2.03

3.31 1.57

Bright sun, wind.

160.0

Test No. 146. T.ine A

L

146.2

0.162

0.80

0.42

Total conductor length, 10 Spacing, 310 cm.

^,500 cm.

138.0

0.150

0.52

0.19

No. 3/0 7-strand cable, dia

. 1.18 cm.

127.6

0.137

0.40

0.12

Temperature, wet, 24 deg.

C.

122.5

0.129

0.33

0.08

dry, 30 deg.

C.

111.2

0.117

0.25

0.04

Barometer, 75.7 cm.

101.0

0.105

0.20

0.03

Hazy.

^Thia curve was taken after the line had been standing idle over a month in the summer. The "going up" points show an excess loss due to dust and dirt on the conductor. This disappears at high voltage and does not show in the "coming down" readings.

DATA APPENDIX

249

201.0 211.0 189.0 181.8

170.8 160.0 149.0 201.0

149.0 140.5 135.5 124.5

113.5 102.3

0.232

6.05

0.277

9.10

0.210

3.54

0.200

2.36

0.189

1.10

0.176

0.60

0.162

0.36

0.231

6.15

0.162

0.39

0.150

0.29

0.145

0.25

0.131

0.20

0.118

0.16

0.103

0.13

6.65 8.63 3.19 2.04

0.80 0.36 0.16 5.75

0.19 0.12 0.10 0.08

0.08 0.07

Total conductor length, 109,500 cm. Spacing, 310 cm.

No. 3/0 7H3trand H. D. copper- weathered cable, diam. 1.18 cm. Temperature, wet, 1

dry, 1 Barometer, 7.47 cm. Cloudy.

250

DIELECTRIC PHENOMENA

Test No. 84, Line A

Kv. bet. lines

Amp.

Kw.

Kw. line loas, p

Test No. 105, Line A

Kv. bet. lines

Amp.

Kw.

Kw. line loss, p

120.0

129.0 160.0 181.0

189.0 203.0 213.0 205.0

0.138 0.150 0.175 0.202

0.212 0.237 0.252 0.239

0.24 0.30 0.78 3.65

4.65

7.84

11.20

8.70

0.15 0.19 0.61 3.40

4.36

7.48

10.78

8.18

Total conductor length, 108,500cm. Spacing, 310 cm.

No. 3/0 7Hstrand cable (H. D. copper- weathered), 1.18 cm. Temperature, wet, 1 deg. C.

dry, 3 deg. C. Barometer, 75.2 cm. Cloudy.

79.8

90.7

101.5

109.5

120.5 130.0 141.5 147.0

153.6 159.0 169.8 174.0

181.0 186.2 192.6 200.6

208.6 216.0 221.0 227.0

234.0 189.0 195.0 203.8

212.0 219.0

0.080 0.093 0.106 0.114

0.127 0.139 0.154 0.165

0.168 0.178 0.199 0.190

0.198 0.204 0.212 0.221

0.237 0.247 0.259 0.271

0.288 0.210 0.217 0.229

0.242 0.257

0.03 0.04 0.06 0.08

0.10 0.14 0.19 0.21

0.25 0.30 0.51 0.70

1.20 1.74 2.70 4.00

5.60

7.40

9.00

11.00

13.60 2.30 3.10 4.96

6.70 8.60

0.01 0.01 0.02 0.03

0.04 0.06 0.09 0.08

0.12 0.16 0.35 0.53

1.02 1.55 2.49 3.77

5.34

7.13

8.70

10.66

13.25 2.10 2.88 4.72

6.44 8.31

Total conductor length, 109,500 cm. Spacing, 310 cm.

No. 3/0 7-8trand H. D. copper- weathered cable, diam. 1.18 cm. Temperature, wet, 13 deg. C. dry, 13 deg. C. Barometer, 76.2 cm. Bright sun, no wind, snow on ground.

DATA APPENDIX

251

Test No. 100. T.ine B

Test No.

73, Line B

Kv. bet. lines

Amp.

Kw.

Kw. line loss, p

Kv. bet. lines

Amp.

Kw.

Kw. line lose, p

67.0

0.025 0.028

0.02 0.03 0.05

0.02 0.02 0.02

43.0 60.0 69.7

0.016 0.022 0.026

77

88.0

0.08

0.06

98.9

0.035

0.07

0.03

80.6

0.030

.0.10

0.07

109.5

0.040

0.12

0.07

90.5

0.034

0.15

0.11

119.5

0.043

0.22

0.14

101.5

0.038

0.30

0.26

128.0

0.050

0.42

0.32

91.0

0.034

0.09

0.05

137.0

0.054

0.90

0.78

90.5

0.034

0.10

0.06

144.0

0.060

1.94

1.80

70.3

0.026

0.06

0.04

161.2

0.078

4.50

4.31

101.6

0.038

0.17

0.12

153.0

0.070

3.04

2.88

101.6

0.038

0.17

0.12

173.8

0.090

6.60

6.47

109.5

0.041

0.40

0.36

185.0

0.103

8.72

8.36

105.5

0.040

0.14

0.09

200.0

0.106

11.90

11.59

115.0

0.040

0.14

0.09

185.0

0.103

8.76

8.50

115.0

0.0425

0.88

0.82

159.0

0.078

4.10

3.92

121.5

0.048

0.16

0.09

139.0

0.058

1.22

1.10

126.5

0.053

2.00

1.93

161.2

0.080

4.70

4.51

130.5

0.055

2.48

2.40

211.8

0.135

14.80

14.46

140.5

0.064

3.70

3.61

144.5

073

4.26

4.16

Total condui Spacing, 91. 0.375-in. g

Btor leng 4 cm. Eilv. ste<

th, 29,05 3l cable,

cm. diam.

^ ^ ^ ■ %^

70.5

91.5

106.0

^0 • %# • 1^

0.030 0.038

0.03 0.06 0.18

0.00 0.02 0.13

0.953 cm. Temperatur

Barometer, ' Cloudy.

e wet, 1

dry, 1

74.7 cm.

deg. C. deg. C.

150.0

156.4 161.0 166.0

0.078

0.083 0.089 0.093

4.80

5.80 6.72 7.50

4.69

. 5.68 6.67 7.36

Total con Spacing, 0.23-in. 1

iductor 1 91.4 cm. galv. at

ength, 2< eel cab]

9,050 cm. e, diam.

0.585 c

m.

Temperal Baromete

iure wetj

dry,

r, 75.2 c

, 1 deg. { 3deg. (

Cloudy.

252

DIELECTRIC PHENOMENA

Test No. 79, Line B

Kv. bet. linee

Amp.

Kw.

Kw. line loefl, p

Test No. 80. Line B

Kv. bet. linee

Amp.

Kw.

Kw. line loM, p

213.0 205.0 202.0 186.0

181.0 168.4 159.6 150.0

138.0 120.0 120.0 110.0

99.0

0.105

8.64

0.010

7.68

0.094

7.40

0.088

6.00

0.081 0.072 0.063 0.058

0.048 0.043

5.00 3.96 3.00 2.24

1.14 0.20 0.26 0.19

0.13

8.38 7.40 7.13 5.80

4.80 3.81 2.88 2.13

1.06 0.14 0.20 0.14

0.09

Total conductor length, 29,050 cm.

Spacing, 244 cm.

0.23-in. galv. steel cable, diam. 0.585

cm. Temperature, wet, 1 deg. C.

dry, 3 deg. C. Barometer, 72.5 cm. Cloudy.

81.0

0.029

0.07

91.0

0.032

0.09

100.5

0.035

0.12

110.5

0.038

0.16

120.5

0.041

0.40

130.5

0.048

1.30

139.5

0.055

2.25

153.0

0.067

3.20

160.0

0.075

4.40

172.0

0.084

6.70

181.0

0.094

7.00

192.0

0.103

8.50

199.0

0.109

9.40

213.0

1

0.124

11.70

0.04 0.05 0.07 0.11

0.34 1.22 2.17 3.09

4.28 5.54 6.82 8.28

9.15 11.38

Total conductor length, 29,050 cm.

Spacing, 152 cm.

0.23-in. galv. steel cable, diam.

0.585 cm. Temperature, wet, 1 d^. C.

dry, 3 deg. C. Barometer, 72.5 cm. Cloudy.

DATA APPENDIX

253

Corona Loss — Outdoor Line — 60-ctclb

Test No. 125. Line B

Test No. 126. Line B

Kv. bet. lines

Amp.

Kw.

Kw. line loee,p

Kv. bet. lines

Amp.

Kw.

Kw. line loes, p

80.0

0.025

0.06

0.05

100.0

0.031

0.12

0.09

88.0

0.031

0.13

0.11

110.0

0.037

0.22

0.17

101.0

0.037

0.32

0.29

119.0

0.041

0.44

0.36

110.0

0.041

0.74

0.68

131.0

0.050

1.36

1.22

120.0

0.050

1.67

1.59

142.0

0.056

2.38

2.16

128.0

0.056

2.56

2.44

151.0

0.065

3.23

2.92

140.0

0.067

4.00

3.80

160.0

0.074

4.20

3.78

150.0

0.08

5.42

5.12

171.0

0.082

5.45

4.93

159.6

0.09

6.86

6.46

181.0

0.09

6.56

5.89

168.4

0.101

8.30

7.80

194.0

0.102

8.20

7.34

181.0

0.112

10.36

9.68

202.0

0.111

9.26

8.30

190.0

0.122

12.24

11.44

212.0

0.117

10.84

9.74

201.0

0.134

14.68

13.61

222.0

0.128

12.44

11.18

213.0

0.14a

17.28

16.14

231.0

0.135

13.80

12.38

206.0

0.144

15.76

14.72

225.0

0.129

12.88

11.58

196.6

0.128

13.60

12.70

217.0

0.124

11.64

10.45

186.2

0.117

11.44

10.69

205.0

0.112

9.70

8.70

175.0

0.103

9.20

8.59

196.6

0.104

8.56

7.68

165.6

0.096

7.76

7.27

186.6

0.096

7.32

6.56

153.4

0.083

5.92

5.57

176.0

0.086

6.12

5.51

143.0

0.074

4.56

4.33

165.0

0.078

4.96

4.49

134.0

0.064

3.34

3.18

156.4

0.069

3.96

3.59

123.0

0.053

2.00

1.90

142.4

0.056

2.46

2.24

114.0

0.044

1.00

0.94

134.0

0.051

1.60

1.45

104.0

0.038

0.38

0.34

125.0

0.044

0.82

0.71

Total condu

ctor leng

th, 29,06

cm.

Total conductor length, 2

!9,050 cm.

Spacing, 91.

4 cm.

Spacing, 183 cm.

No. 4 H. D

. copper

wire, dii

am. 0.518

No. 4 H. D. copper wi

ire, diam.

cm.

0.518 cm.

Tc^mperatuT

e, wet, i

5.0 deg. <

C.

Temperature, wet, 5.0 dq

5. C.

dry, ^

L6 deg. <

c.

dry, 4.5 dej

5. C.

Barometer,

75.9 cm.

Barometer, 75.9 cm.

Cloudy, 8lig

ht breez<

B.

Cloudy, slight breeze.

254

DIELECTRIC PHENOMENA

Test No. 137, Line B

Kv. bet. lines

Amp.

Kw.

Kw. line

lOM, p

Teet No. 138, Line B

Kv. bet. lines

Amp.

Kw.

Kw. line loM. V

80.0

go. 5

100.5 110.7

121.0 131.0 141.5 150.8

161.0 172.0 183.0 196.0

205.0 202.0 186.0 165.0

145.0 124.0 103.0

0.05

0.025

0.11

0.020

0.35

0.037

0.95

0.044

1.42

0.051

2.11

0.056

2.70

0.064

3.24

0.072

4.05

0.078

4.80

0.084

5.60

0.093

6.60

0.102

7.60

0.098

7.30

0.087

6.00

0.075

4.30

0.061

2.86

0.047

1.75

0.032

0.60

0.02 0.06 0.26 0.78

1.19 1.76 2.26 2.72

3.40 4.05 4.73 5.59

6.44 6.19 5.08 3.63

2.40 1.46 0.47

Total conductor lengthi 29,050 cm.

Spacing, 366 cm.

No. 8 new H. D. copper wire, diam.

0.328 cm. Temperature, wet, 1.5 deg. C.

dry, 1.5 deg. C. Barometer, 76.6 cm. Bright sun, slight breeze.

79.2

91.2

99.9

111.4

120.8 121.5 141.0 149.0

161.0 171.4 181.4 192.0

202.2 214.4 197.0 174.0

153.2 134.4

0.025 0.027 0.036

0.039 0.049 0.055 0.059

0.066 0.074 0.079 0.085

0.092 0.11 0.089 0.076

0.063 0.051

0.06 0.12 0.26 0.08

1.22 1.90 2.30 2.80

3.40 4.20 4.80 5.60

6.56 7.50 6.10 4.40

3.00 2.00

0.03 0.07 0.18 0.65

1.06 1.59 2.20 2.34

2.85 3.53 4.05 4.73

5.67 6.36 5.15 3.71

2.51 1.67

Total conductor length, 29,050 cm.

Spacing, 488 cm.

No. 8 new H. D. copper wire, diam.

0.328 cm. Temperature, wet, — 1.5 deg. C.

dry, + 1.5 deg. C, Barometer, 75.5 cm. Bright sun, slight breeze.

DATA APPENDIX

255

Test No. 92. Line B

Kv. bet. lines

51.0 56.5 61.6 66.5

71.0 76.0 83.0 90.5

101.0 110.5 120.5 131.5

144.5 158.0 170.0 181.0

190.0 204.0 215.0 222.0

Amp.

27.5

0.008

34.5

0.009

39.5

0.011

44.5

0.013

0.015 0.017 0.019 0.023

0.024 0.028 0.032 0.037

0.041 0.050 0.055 0.060

0.068 0.081 0.086 0.094

0.099 0.110 0.117 0.123

Kw.

0.02

0.05 0.10 0.22 0.37

0.49 0.60 0.81 1.07

1.43 1.80 2.30 2.80

3.50 4.40 5.30 6.18

6.70 8.00 9.00 9.64

Kw. line loas, V

0.01

0.04 0.09 0.20 0.31

0.40 0.49 0.66

0.88

1.17 1.46 1.88 2.28

2.84 3.57 4.33 5.15

5.43 6.50 7.30

7.84

Total conductor length, 29,050 cm.

Spacing, 410 cm.

0.066-in. galv. steel wire, diam. 168

cm. Temperature, wet, 0.5 deg. C.

dry, 2.0 deg. C. Barometer, 75.0 Cloudy, no wind.

Teat No. 95. Line B

Kv. bet. linee

Amp.

KV7.

Kw. line loaa, p

222.0 199.8 181.0 158.0

140.0

120.0

102.0

91.5

79.5 68.7 60.0 50.0

0.115

8.80

0.104

6.80

0.089

5.36

0.076

3.80

0.064

2.84

0.053

1.92

1.21

0.034

0.93

0.028

0.63

0.021

0.63

0.017

0.18

0.014

7.00 5.38 4.24 2.98

2.24 1.44 0.96 0.75

0.51 0.52 0.16

Total conductor length, 29,050 cm.

Spacing, 550 cm.

0.066 in. galv. steel wire, diam.

168 cm. Temperature, wet, 1.0 deg. C.

dry, 3.0 deg. C. Barometer, 75.0 cm. Cloudy, no wind.

256

DIELECTRIC PHENOMENA

Transformer Loss

Kv.

AmperoB

Kw.

Kv.

Amperes

Kw.

101.5

0.008

71.5

0.005

0.02

131.5

0.010

0.15

82.0

0.006

0.03

147.3

0.011

0.25

97.0

0.007

0.05

112.0

0.008

0.06

163.8

0.013

0.42

132.8

0.009

0.09

181.5

0.014

0.54

201.8

0.016

0.69

149.0

0.010

0.12

178.4

0.013

0.18

30*»C.

201.0

0.014

0.22

223.0

0.016 3'»C.

0.30

INDEX

A

Pagk

Air, at very low pressures 196

compressed 42

density 51

occluded in solid insulation 236

see Ck>rona. Altitude, effect of, on arc-over of bushings, leads and insulators. . Ill, 217

effect of I on corona 42, 50, 51

effect of, on corona loss 146

effect of, on sphere-gap spark-over ' . 96

variation of air density with 51

B

Barriers in oil 169, 189

Beta particle 193

Bushing, condenser type 220

effect of altitude on spark-over of Ill

oil-filled type 220

overstressed air in 217

rod and torus 220

transformer 220

C

Cable, graded 33, 218

Capacity, see Permittance.

Cathode rays 192

Compressed air 42

Corona, application of electron theory to 194

at very low air density 196

calculations for practical transmission lines 199

condition for spark or 27, 79, 84

in oil 155

Corona loss, a.c. and d.c 132

description of experimental lines 117

disruptive critical voltage 137

effect of frequency 129

effect of humidity, initial ionization, etc 147, 148

effect of moisture, frost, fog, sleet, rain and snow 145, 149

257

258 INDEX

Paob

Corona loss, effect of smoke and wind 149

effect of temperature and barometric pressure 146

for small conductors 136, 137, 140, 142

law of 134, 137, 140, 142

loss near the disruptive critical voltage 143

\ probability law 148, 162

quadratic law 121

Clorona, on generator coils 216

Corona on transmission lines, see Transmission lines.

Corona, visual, a.c. and d.c 38, 52, 75

application of electron theory to 41, 47, 194

calculation for concentric cylinder 48, 53, 57, 63

calculation of gradient 40, 42, 47, 53, 63, 67, 71

calculation of voltage 43, 54, 57

calculation of voltage wet 67, 237

derivation of law of 49, 58, 63

diameter of 74, 78

effect of air density 42, 51

effect of barometric pressure 50

effect of cables 43, 71

effect of conductor material 43, 44, 46, 48, 68

effect of conductor surface 43

effect of current in conductor 43, 68

effect of diameter of conductor 39, 44, 46, 48

effect of dirt 66

effect of humidity 43, 68

effect of initial ionization 43, 68

effect of oil 43, 66

effect of small spacing 42, 57

effect of spacing 39, 44, 45, 46

effect of temperature on 50, 51

effect of water on 43, 66, 67

influence of frequency on 65

on conductors close together 77

law of, for concentric cylinder 48, 53, 57, 63

law of, for parallel wires 40, 42, 43, 54, 57, 63

mechanical vibrations due to 78

photographic study of 73

positive and negative 75

stroboscopic study of 73

Cylinders, concentric, flux density 13

gradient 13, 29

permittance or capacity 13, 29

visual corona, see Visual corona 38 el seg.

spark-over and corona in oil 159

parallel, see Wires.

INDEX 269

D

Page

Dielectrici addition of fluxes 14

circuit 216

displacement 9

flux control 35, 223

flux density between concentric cylinders 13

flux density between parallel planes 11

flux density for parallel wires 14, 23

flux densities, sum of at a point 16, 20

flux refraction 30

formula for different electrodes 29

hysteresis 36, 37

spark lag in air 108

spark lag in oil 162

spark lag in solids 117

Dielectric field, analogy with Hooke's Law 4, 9

analogy with magnetic field 2

between concentric cylinders 12, 33

between parallel planes 10

between parallel wires 14

control 223

energy stored in 8, 9, 10

energy transfer in transmission 8, 9, 10

equation of equipotential surfaces between parallel wires. . . 16

equation of equipotential surfaces for spheres 26

equation of lines of force between parallel wires 20

equation of lines of force from spheres 26

experimental determination of 2, 232

image of 234

in three dimensions 232

methods of constructing 226

resultant 14

superposition of 14

three phase 238

Dielectrics, combination of dielectrics of different permittivities 30

combination of, in multiple 34

combination of, in series 31

gaseous 38, 79, 117

liquid 163

soUd 166

E

Elastance 11, 215

Elastivity 11, 216

260 INDEX

Page

Electron theory , application of, to visual corona 41y^7, 194

general discussion of 192

practical application of 194

Energy distance 41, 42, 48, 67, 156, 195

Equipotential surfaces, construction of 226

equation of, for parallel wires 16

equation of, for spheres 25

in three dimensions 232

Experimental study of, corona loss 117

dielectric fields 2, 232

solid insulations 166

spark-over. 79

strength of oil 163

visual corona 44

Flux, see Dielectric flux.

Frequency, effect on corona loss 129, 162

effect on visual corona 66

see High frequency.

G

Gamma rays 193

Gap, method of measuring high voltages 87

needle 87

sphere 88

Green's theorem 22

Gradient, at any pomt 230

at different points around a conductor 231