book

Dielectric Phenomena in High Voltage Engineering (1915) — part 6 of 12

1 January 1915

At the start a number of tests were made to see if a spark-over in the cask had any effect upon the following spark-overs by ionization or otherwise. It was found that a number of spark- overs could be made in the cask with no appreciable effect. During the test, the air was always dry and the surfaces of the insulators were kept clean.

Table XXXVIII. — Suspension Insulator

Bar. cm.

Vac. cm.

Preasure

Temp, oent.

Kilovolta arc-over

75.4

37.4

38.0

22.0

0.50

121.0

75.4

34.3

41.1

22.0

0.54

131.0

75.4

30.0

45.4

22.0

0.60

144.0

75.4

26.4

49.0

22.0

0.65

158.5

75.4

23.0

52.4

22.0

0.70

165.0

75.4

19.3

56.0

22.0

0.74

177.5

75.4

17.5

57.9

22.0

0.87

183.2

75.4

15.0

60.4

22.0

0.80

195.0

Table XXXIX.— Leads Correction Factor for Leads Shown in Fig. 107

(a)

(6)

(c)

(d)

1.00

0.90

0.92

0.91

0.92

0.80

0.83

0.82

0.83

0.85

0.70

0.74

0.72

0.75

0.77

0.60

0.70

0.65

0.64

0.66

0.50

0.61

0.56

0.54

0.57

SPARK-OVER

Table XL. — Post and Pin Insulators Correction Factor for Insulators Shown in Fig. 108

113

(a)

(b)

(c)

Post

1.00

0.90

0.93

0.91

0.94

0.80

0.84

0.81

0.86

0.70

0.76

0.72

0.75

0.60

0.68

0.62

0.65 '^

0.50

0.60

0.52

0.53

Table XLI. — Suspension Insulatob

Fig. 109 Correction Factor for Units in String as Follows

Number of units

1.00 0.90

1.00 0.96 0.91

0.86 0.80 0.72

1.00 0.93 0.84 0.76 0.66 0.55

1.00 0.90 0.80 0.70 0.60 0.50

i:oo

1.00

0.80

0.70

0.60

0.50

Table XLII. — Suspension Insulator

Fig. 110 Correction Factor for Units in String as Follows

Number of units

1.00 0.90

1.00 0.94 0.87 0.81 0.72 0.62

1.00 0.92 0.84 0.73 0.63 0.52

1.00 0.90 0.80 0.70 0.60 0.50

1.00

0.80

0.70

0.60

0.50

Table XXXVIII is a typical data sheet. Tables XXXIX- XLI give even values of S and the corresponding measured cor- rection factors. If the spark-over voltage is known at sea level

114

DIELECTRIC PHENOMENA

.8 .9 1.01.1

20 10

Belaclw Density

Fig. 107. — ^Variation of spark- over voltage of transformer leads with air density.

(a) 15.2 cm. high by 17.8 cm. dia.

{h) 21 .6 cm. high by 17.8 cm. dia.

{d) 38. 1 cm. high by 17.8 cm. dia.

Height measured from case to metal cap on top.

.1 .2 .8 .4 .6 .6 .7 .8 .9 LOU BelatlYe Dentitlei

Fio. 108. — Variation of spark-over voltage insulators with air density.

(a) 30.2 cm. hiffh.

(6) 13 . 5 cm . high by 16 . 8 cm. dia.

210 200

190

180

170

160

140

180

«.120

|110

1 100

^80 3 70 60 GO 40 80 20 10

-/i

4SSS

;

)

_--«'

.^r

Aic Over VoltasM

Vartoos kit Densities

.2 .3 .4 .6 .6 .7 .8 .9 1.0 BalatLre Deoaity

FiQ. 109. — Suspension insulator. (Dia., 30 cm. Spacing 16.5 cm.)

210 200 190 180 170 160 160 140

ISO gl20 1 110 §100

I ^

S 70 60 60 40 SO

Arc Over Voltages

Various Air Densities

.1 Jl

.8 .4 .6 .6 .7 .8 .9 Belatlve Density

Fig. 110. — Suspension insulator. (Dia., 27 cm. Spacing 17 cm.)

SPARK-OVER

115

or 5 = 1(76 cm. bar., temperature 25 deg. C), the spark-over at any other value of d may be found by multiplying by the cor- responding correction factor. It will be noted that in most cases the correction factors are very nearly equal to 6. 6 would be the correction factor in a imiform field and should be, as already stated, taken as such in most cases, especially where dirt and moisture enter, as in practice. Furthermore, it should be taken

•

16000

14000

18000

12000

11000

10000

Isooo

•S 8000

».

^7000

6000

4000

8000

1000

•

.6 .6 .7 .8 9 1.0

8 RelatlTe Air Density

Fio. 111. — Approximate variation of air density with altitude.

as it is the actual correction factor for the starting point of local corona on insulators.

Fig. Ill is a curve giving different altitudes and corresponding S at 25 deg. C. If the spark-over voltage is known at sea level at 25 deg. C, the spark-over voltage at any other altitude may be estimated by multiplying by the corresponding 8, or more closely if the design is the same as any in the tables, by the cor- rection factor corresponding to 6. If the local corona starting

116 DIELECTRIC PHENOMENA

point is known at sea level, it may be found for any altitude by multiplying by the corresponding 6. If the barometric pressure and temperature are known, 6 may be calculated.

As an example of the method of making corrections: Assume a suspension insulator string of three units with a spark-over voltage of 205 kv. (at sea level 25 deg. C. temperature). 5 = 1. What is the spark-over voltage at 9000 ft. elevation and 25 deg. C?

From Fig. Ill, the b corresponding to 9000 ft.

6 = 0.71

Then the approximate spark-over voltage at 9000 ft., 25 deg. C. . is

ei = 0.71 X 205 = 145 kv.

If this happ>ens to be the insulator of Fig. 110, the correction factor corresponding to 6 = 0.71 is found in Table XLII, by inter- polation to be 0.71. The actual spark-over voltage for the special case happens to check exactly with that given by b. For prac- tical work a correction may generally be made directly by use of Fig. 111.

The spark-over voltage of an insulator is 100 kv. at 70 cm. barometer and 20 deg. C. What is the approximate spark-over voltage at 50 cm. barometer and 10 deg. C?

' 273 + 30 "•'*

3.92 X50 _ -, ^ = 273T10 = ^-^^

ci = 100 X ^-^ = 65 kv.

If the local corona starting point is known at sea level, it may be found very closely for any other altitude by multiplying by the correction i.

CHAPTER V

CORONA LOSS

In the present chapter the corona loss is discussed. It has been thought worth while to go into details in the description of the apparatus, methods of making loss tests, and reducing data^ as an example of an extremely large engineering investigation. Experimentally, the methods followed apply to any investigation; practically, many of the detailed observations have an important bearing; theoretically and experimentally the observed details are of importance and the methods of reducing data may be applied to other investigations.

Lines, Apparatus and Method of Test. — The Lines. The first investigation was made out of doors. The conductors used in

North

pS Dltclniclatota

South

Corona Losb Final Line Arransemonl

Line A Stendnrd Lhie .4B6"Diam. 7 Stci Gable

Line B Variable Line

■ni'n"-

-fflOV^-'

Fig. 112. — Experimental outdoor line.

this investigation were supported by metal towers arranged in two parallel lines of two spans each. The length of each span was approximately 0.150 km. These tower lines will be designated by A and B respectively. The conductors were strung in a hori- zontal plane with seven disk suspension insulators at each point ^Law of Corona, A. I. E. K, June, 1911. 8 "7

118

DIELECTRIC PHENOMENA

of support. For preliminary tests four No. 3/0 B. & S. (1.18 cm. diameter) seven-strand, hard-drawn copper cables were put in place on each line. A seven-strand steel ground cable was also strung. After a number of tests had been made the ground cables were removed from line A. The conductors on line A, however, were kept in place as a standard throughout all the investigations. The conductors were removed from S, and the first span of this line was used to support various sizes of conductors at various spaces. (See Fig. 112.)

These lines were erected in a large field. The prevailing winds were from the west over open country, that is, free from smoke from the city and the factory on the east.

Test Apparatus. — A railroad track was run directly under the line, and the testing apparatus was housed in three box cars.

120

100

»,^

•-^

t>.

(

■^

■^■^

C

?^s;

»>J

S=3

0-«

lii 2

»-4

1 • FandamenUl Yoltago Wave

2 - Origlnal Yoluco Ware 8 - Srd Harmonic Voltage 4* Fundamental Oarrent

:^'

'•^K'

5- 6-

Orif 3rd I

Inal larm

Can ionic

'ent Volt

40 60

80 100 120

Fig. 113. — ^Analysis of applied voltage and corona current wave.

This proved a very convenient arrangement, as the cars could be quickly run back to the factory when changes or repairs were necessary.

Power was supplied from an old Thomson-Houston machine with a smooth core, pan cake winding on the armature; it gave a very good wave, and was used in all tests. See oscillogram and analyzed wave. Fig. 113. It was rated at 35 kw., but this rating was quite conservative. This alternator was belted to a d.c. motor.

The high voltage transformer and the testing apparatus were placed in car No. 2. The portion of the car roof over the trans-

CORONA LOSS

119

former was made of heavy canvas. This could be quickly rolled back, and the leads from the line were dropped directly to the transformer terminal. By means of a framework and canvas cover the transformer could be protected from the weather, and investigations carried on during rain and snow storms. The power supply, speed and voltage, were all controlled from car No. 2. In fact all of the adjustments could be made from this car (see Fig. 114). The transformer was rated at 100 kw., 200,000 volts and 60 cycles. On the low side were four 500 volt coils. These coils could be connected in multiple or series for change of ratio. The high tension winding was opened at the neutral and taps were brought out for the ammeter, and current coil of the wattmeter. Three taps were also brought out here from the main winding for voltage measurement. (See Fig. 114.) The following tap ratios were thus obtained: 100/200,000; 200/200,000 and 200/200,000.

Botory Motor Alternator

Otf I

Freqaency M

Car U

Fig. 114. — Circuit connections in corona loss measurements.

Car No. 3 served as a dark room for making photographs and visual tests on short wires and cables.

Methods of Test — Accurate power measurements of corona are difficult to make, because of the nature of the load, low power factor and high voltage. It is not desirable to make the measure- ments on the low side because of the difficulty in separating the transformer iron and load losses, and these may be sometimes as large as the corona losses. In these tests the current coil of the wattmeter and the ammeter, were put in the high tension winding of the transformer at the neutral point, and the neutral was grounded. The voltage coil of the wattmeter was connected to a few turns of the high tension winding at the neutral.^ All of the loss measurements were also duplicated on the low side as a

^A. B. Hendricks, A. I. E. E. Transactions, Feb., 1911.

120

DIELECTRIC PHENOMENA

Weather

Cloudy-rain in morning. Barometer 75 cm. Temperature: wet 10 deg. C, dry 12 deg. C.

Line and connections

(1 and 3) (2 and 4) ground wires in place.

Total conductor length 109,600 cm.

Spacing 310 cm.

No. 3/0 seven-etrand cable diameter 1.18 cm.

Transformer ratio 1000/200,000

Frequency 60 cycles.

Table XLIII. — Experimental Line — A. Corona Lobs — 10-6-10. 4 p.m.

Low aide total readings

High side total readings

VoltB

Amperes

Kilowatto

Kilovolto

Amperes

Kilowatts

Line on

395

16.5

0.40

80.5

0.077

0.10

435

17.9

0.60

90.5

0.087

0.13

490

20.5

0.70

101.6

0.101

0.17

535

22.6

0.80

111.1

0.112

0.22

590

24.7

1.00

120.4

0.119

0.28

035

27.1

1.10

130.2

0.135

0.35

680

29.2

1.40

139.2

0.145

0.45

735

31.6

1.80

150.0

0.158

0.68

780

33.4

2.40

159.0

0.169

1.10

812

35.3

3.30

165.8

0.178

1.80

830

36.3

3.60

169.0

0.181

2.40

862

37.5

5.12

176.6

0.190

3.60

893

39.2

6.35

183.2

0.199

4.70

914

40.5

7.50

187.0

0.207

6.00

975

43.9

11.40

200.0

0.227

9.30

1020

47.8

14.50

209.0

0.243

12.60

1050

49.3

17.00

214.2

0.253

14.60

1080

52.7

19.50

220.2

0.267

17.60

1125

55.5

22.80

223.4

0.283

20.30

Line off

400

1.14

0.40

80.0

0.005

0.05

500

1.37

0.62

100.5

0.007

0.10

600

1.63

0.82

121.5

0.008

0.15

718

1.87

1.18

143.5

0.010

0.21

812

2.05

1.45

161.0

0.011

0.28

905

2.29

1.80

181.0

0.013

0.35

1015

2.69

2.20

202.2

0.015

0.44

1095

3.25

3.64

217.0

0.017

0.54

•

CORONA LOSS 121

check. Frequency was held at the test table by means of the motor field and a vibratmg reed type of frequency meter.

Voltage was controlled in two ways — ^by the potentiometer method and by rheostats in the alternator field. By the potenti- ometer method is meant a resistance in series with the supply on the low side of the transformer for voltage control and a multiple resistance across the transformer, taking about three times the exciting current) to prevent wave distortion. When the leading current was very high a reactance was arranged to shunt the generator and approximately unity power factor could be held. This prevented overloading the generator and reduced wave shape distortion. For a set of tests at a given frequency the ratio of the main transformer was kept the same. Where losses at several frequencies were to be compared the main transformer ratio also was changed to keep the flux on the generator as nearly constant as possible — for instance, at 45 cycles a ratio of 500/200,000 would be used, while at 90 cycles a ratio of 1000 to 200,000 would be used. Wattmeters especially adapted to the tests were con- structed. These were of the dynamometer type; each was pro- vided with a 75-volt and 150-volt tap. The voltmeter coil ratio on the transformer and the wattmeter tap were always changed to give the best reading. Four wattmeters were used in these tests. The meters were all carefully calibrated in the laboratory at unity power factor and at 0.10 leading power factor, at both 25 and 60 cycles.

Humidity, temperature and barometric pressures, as well as general weather observations, were taken during each test.

Indoor Line. — Later an extensive investigation was made in a large laboratory room, 17 meters wide by 21 meters long. The lines were strung diagonally between movable wooden towers.

_ m

Strips of treated wood 1.25 cm. square by 80 cm. long were used a9 insulators. The total length of conductor possible with four wires was 80 meters. By this arrangement it was possible to make a more complete study on the smaller sizes of conductors, and also to extend the investigation over a greater frequency range. The apparatus used was otherwise the same as in the outdoor tests.

The Quadratic Law. — Table XLIII is a typical data sheet for Line A. Fig. 115 and Fig. 118 show the characteristic corona curves. The corrected values for Table XLIII are recorded in Table XLIV.

122

DIELECTRIC PHENOMENA

Table XLIV. — Corona Loss, Obbebved Values Corrected from

Table XLIII

KilovolU

between

linee «i

Line ampere

Kilovolte to neutral e

Kilowatte line loss p

K.v.a.

Power factor

80.5

0.072 0.081 0.094 0.104 0.111

40.2 45.2 50.8 55.5 60.2

5.80

7.33

9.55

11.55

13.40

90.5

101.6

111.1

120.4

0.11

0.008

130.2

0.126

65.1

0.15

16.40

0.009

139.2

0.135

69.6

0.22

18.80

0.012

150.0

0.147

75.0

0.40

22.10

0.018

159.0

0.157

79.5

0.79

25.00

0.032

165.8

0.166

82.9

1.42

27.60

0.051

169.0

0.168

84.5

2.04

28.40

0.072

176.6

0.177

88.3

3.21

31.20

0.103

183.2

0.185

91.6

4.28

33.90

0.126

187.0

0.193

93.5

5.55

36.10

0.154

200.0

0.212

100.0

8.78

42.40

0.207

209.0

0.227

104.5

12.02

47.50

0.253

214.2

0.237

107.1

13.99

50.70

0.276

220.2

0.250

110.1

16.94

55.10

0.307

The shape of the curve between kilovolts and kilowatts sug- gests a parabola. After trial it was found that the losses above the knee of the curve follow a quadratic law. Below the knee it was found that the curve deviates from the quadratic law. This variation near the critical voltage is due to dirt spots, irregular- ities and other causes as discussed later. The main part of the curve may be expressed by^

p = c\e — Co)*

(32)

where

= the line loss.

= kilovolts to neutral.

is called the disruptive critical voltage, measured in

kilovolts to neutral.

The meaning of c© and c* will be considered later. The best mechanism of evaluation of constants for a given set of tests may now be considered. Equation (32) may be written

F. W. Peek, Jr., Law of Corona, A. I. E. E., June, 1911.

CORONA LOSS

123

then if. the quadratic law holds, the curve between Vp and e will be a straight line. Co will be the point where the line cuts the e axis, and c will be the slope of the line (see Fig. 116); eo and c may be evaluated graphically in this way. It is difficult to know how to draw the line accurately and give each point the proper weight. To do this the ZA method is used, as follows:^

17 16

14 18

12 11

■ " 8

^ 7

6 4

8 2 1

110 120180140160160170180190 200210

Betw«aa Ltnei

66 66 76 85 95 105

KUd-VoIuCmJ ToMeatral

Fio. 115. — Characteristic corona loss curve for large stranded

conductor. .

Line A conductors 1-2-3-4. 3/0, 7-8trand cable, diameter, 1.18 cm. Total conductor length, 109,500 cm. Spacing, 310 cm. Points^easured values. Curve calculated from p « 0.0115 (c— 72.1)*. Co = Disruptive critical voltage. e« » Visual critical voltage. Test table XLIV.

)

«o

The values of e and p for the set of readings to be investigated are first tabulated and a curve plotted (Fig. 116). All points that differ greatly from the straight line are eliminated as probably in error, or, as at the lower part of the curve, following a different law. The remaining readings are taken and formed into two groups, each of an equal number of readings.

Group 1. Sie SiVp Group 2. S2« 2)2/p

^ Steinmetz, Engineering Mathematics, page 232.

124

DIELECTRIC PHENOMENA

Then

A 2)6

Si6 - 2)26 ASVp = SiVp - S2V^

AS6

SSe -

SSVp

Co =

where n is the number of points used. Thus Bo and c are determined.

^i!

'*'

•

pr.

►*,/

—

ptl

,^^^S

no 120 190 14(qi50 leO 170 180 190 200 210 Bet.LInea 55 65 ^a76 85 96 105 To Iffeutral KlIoToltt BBecUre

Fia. 1 16. — Corona loss curve plotted between V^ and e. (Large conductor.

Data same as Fig. 115.)

Table XLV. — Corona Loss, Calculated Values for Fig. 115.

p = 0.0115 (c - 72.1)*

KUovolts be-

Kilovolts to

Kilowatts

Kilovolts be-

Kilovolts to

Kilowatto

tween lines e'

neutral e

P = c»(e-eo)«

tween lines e'

neutral e

P -€»(«-«•)■

144.2

71.2

0.0

183.2

91.6

4.17

150.0

75.0

0.10

187.0

93.5

5.08

159.0

79.5

0.63

200.0

100.0

9.03

165.8

82.9

1.34

209.0

104.5

12.10

169.0

84.5

1.77

214.2

107.1

14.10

176.6

88.3

3.02

220.2

110.1

16.70

CORONA LOSS

Table XLVI. — Corona Loss Method of Reducing (Data from Table XLIV)

125

Kilovolts between

Kilovolts to

Kw., p

lme«'

neutral e

120.4

60.2

0.11

0.332

130.2

66.1

0.15

0.388

139.2

69.6

0.22

0.470

150.0

75.0

0.40

0.632

159.0

79.5

0.79

0.889

165.8

82.9

1.42

1.192

169.0

84.5

2.04

1.428

176.6

88.3

3.21

1.792

183.2

91.6

4.28

2.069

187.0

93.5

5.55

2.356

200.0

100.0

8.78

2.963

209.0

104.5

12.02

3.467

214.2

107.1

13.99

3.740

220.2

110.1

16.94

4.116

Total conductor length 109,500 cm.

Spacing 310 cm.

No. 3/0 seven-strand cable diameter 1.18 cm.

ASc = 36.6 SSc = 606.8

ASVp

ssVp

= 3.935

91.6

2.069

= 18.711

93.5

2.356

100.0

2.963

c = ^ = 0.107

104.2

3.467

ASc

107.1 110.1

3.740 4.116

2tVp = 7.388

c* = 0.0115

= 285.1

22* ^^^

2,c

= 321.4

SiVp = 11.323 e, = 72.1

Bo —

Co' = 144.2

Table XLVI shows the method of reducing. The curve, Fig. 115, is drawn from the equation p = 0.0115 (e — 72.1)*. The circles show the experimental values, and indicate where the losses deviate from the quadratic law.

126

DIELECTRIC PHENOMENA

Table XL VII gives a similar set of data for a small wire, results are plotted in Figs. 117 and 118.

The

^^^M^

vi'

•

3«

■ 2

•

(

9 •

90 1C

5T3

oil

M) 1<

10 1

fiOS

etw«

e& L

25 86 45 66 66 76 To Neatrml

Kilo-YoTtt SlfectrTe

Fig. 117."— Characteristic corona loss curve for small wire.

No 8 copper wire. Diameter , 0.328 cm. Total length, 29,050 cm. Spacing, 0.328 cm. Table XLVII, Line B.

»S

■

»«^

■^

€ ^^

■^

100 120 140

160

180

200 Between Lines

60 60 70 Kllo-Yoltt XffectlTe

100

To Meutrel

Fia. 1 18. — Corona loss curve plotted between /oand «. (Small conductor.

Data same as Fig. 117.)

CORONA LOSS

127

Table XLVII. — Corona Loss ZA Method of Reducing

KUoTolts between

Kilovolts to

Kilowatt line

line tf

neutral e

loss p

70.0

35.0

0.02

0.14

80.0

40.0

0.07

0.26

91.2

45.6

0.26

0.51

101.3

50.6

0.85

0.92

110.0

55.0

1.42

1.19

120.0

60.0

2.02

1.42

130.0

65.0

2.71

1.65

141.5

70.7

3.51

1.87

70.0

35.0

0.06

0.24

80.0

40.0

0.10

0.32

90.5

45.2

0.26

0.51

101.3

50.6

0.96

0.98

109.9

54.9

1.43

1.20

152.0

76.0

4.45

2.11

160.4

80.2

5.17

2.27

170.0

85.0

6.06

2.46

180.6

90.3

7.04

2.65

190.6

95.3

8.26

2.87

200.0

100.0

9.52

3.08

193.6

96.8

8.60

2.93

176.0

88.0

6.65

2.58

155.0

77.5

4.66

2.16

136.0

68.0

3.01

1.73

Total conductor length 29,050 cm.

Spacing 183 cm.

No. 8 H. D. copper wire — diameter 0.328 cm.

Temperature 1.5

Barometer 76.6

2 2e = 841.1 2 sVp = 24.16

100.0

3.08

80.2

2.27

96.8

2.93

77.5

2.15

95.3

2.87

68.0

1.73

90.3

2.65

60.0

1.42

85.0

2.46

88.0

2.58

467.4

13.99

373.7

10.16

841.1 -

AZe = 93.7 A2/^ = 3.80

24.15

0.0406

Co —

c —

3.80

= 0.0408

93.7

0.00164 0.00164(e - 24.6)«

128

DIELECTRIC PHENOMENA

To further investigate the law it is now necessary to determine the various factors affecting e© and c*. These will be taken up

-^i

f J

'±

20 40 eO 80 100 120 140U018020D2V

Between Llnea 10 20804060 90 108090100110 KlIoVolli BSectlTO ^^ Neutral

Fig. 119. — Ck)rona loss plotted between /p and c to illustrate the

quadratic law.

Phosphor-bronze conductor. Diameter, 0. 051 cm. Spacing, 366 cm. Total length, 29,050 cm. Temp.,-6.5** C. Bar., 77.3 cm. Line B.

under separate headings. The loss near the critical point will then be discussed.

In Fig. 119, Vp and e are plotted. This is an especially inter- esting curve on account of its range. The measurements are

^ ^'

-,^^

1 'y^

e„ y/

„ J,^^

(

►^1

-:!

100

120

140 ICO 180 200 220 Between Linee

70 80 SO 100 UO Kilo- Volte XSectLTO To Neutral

20 40 60 80100120140ieOlB0200220

Between Lines 10 90 80 40 60 60 10 80 80 100 UO

Kllo-VoTti K«octiT«^°^"*"'

Fig. 120. Fig. 121.

Ck>rona loss plotted between y/v a^<^ ^ to illustrate the quadratic law.

Fig. 120. — No 8 copper wire. Diameter, 328 cm. Total length, 29,050 cm.

Spacing, 244 cm. Temp. 1.5. Bar., 76.6. Line B. Fig. 121. — 3 /o, 7-strand weathered cable. Diameter, 1.18 cm. Spacing, 310 cm. Total length, 109,600 cm. Temp., 16. Bar., 75 . 3. line A.

taken up to 20 times the disruptive critical voltage, and show how well the quadratic law holds. Figs. 120 and 121 are plotted in the same way to illustrate the quadratic law.

CORONA LOSS

129

Frequency. — To determine the way that frequency enters into the power equation

p = c*(e — Co)*

a series of loss curves were taken on line A at various frequencies.

These tests indicated that the loss varied almost directly with

the frequency over the range investigated. The data are given in

Tables XL VIII and XLIX. Thus when the frequency does not

Table XLVIII.—LijnB A. Conductob 2-3. Total Length 54,750 Cm.

KUovolto between lines

210

200 190

180

Kilowatts loss

4.9

3.2

2.0

1.3

5.1

. 3.7

2.6

1.6

6.1

4.3

2.8

1.7

6.9

5.0

3.4 3.6 3.8

1.9 2.1

7.5

5.6

2.6

100

8.0

5.6

3.7

2.4

115

9.3

7.1

5.0

3.4

Table XLIX. — ^Linb A. Conductors 1-2-3-4. Total Length 109,500 Cm.

Kilovolts between lines

210

200

190

180

Kilowatts loss

50 60 70 80

9.24 10.50 12.1 14.0

6.30

7.30

8.60

10.20

3.80 4.65 5.50 6.80 1

2.20 2.65 3.20 3.95

vary greatly from 60 cycles the equation may be written

p = a/(e — eo)*

It was then decided to make the investigation over a greater range of frequency, and on shorter lines to prevent wave distor- tion due to load, etc. These measurements were made on the indoor line. Table L gives data for a 0.333-cm. radius wire. Care was taken to keep the wave shape as nearly constant as possible. The results are plotted in Fig. 122. Co is the same for all fre-

130

DIELECTRIC PHENOMENA

Table L. — Corona Loss at Different Frequencies

New Galvanised Cable

Radius * 0.334 cm. Spacing — 61 om. Effective kv.

ToUl length - 0.0815 km. 2 - 1.00 Indoor line

Kilovolts to neutral «n

Kilowatts per km. (p)

'>"

Kilovolts to neutral tn

Kilowatts per km. (p)

1 a

Kilovolts to neutral en

Kilowatts per km. (p)

'-?

Kilovolts to neutral en

Kilowatts pet km. (p)

1 a

Test 60B, 40 cycles

Test blB, 60 cycles

Test 52B, 90 cycles

Test 53B. 120 cycles

50.5 53.5 56.2

59.2 64.0 66.8

71.5 73.7 70.7

67.5 65.0 60.2

1.10 2.57 4.16

5.84

9.10

11.66

15.95 18.44 16.23

12.30

10.20

6.64

6.28 0.80

1.05 1.69 2.04

2.42 3.02 3.40

3.99 4.30 3.95

3.60 3.36 2.58

2.29 0.89

64.0 62.5 68.0

72.0 78.0 87.3

91.5 82.0 72.8

62.7 56.0 61.6

67.2 70.2

3.31

9.15

14.56

20.10 28.46 40.20

49.70 34.60 21.10

6.23

5.65

10.20

15.76 19.30

1.82 3.02 3.88

4.48 6.20 6.32

7.02 5.83 4.67

2.90 2.32 3.20

3.90 4.38

89.5 85.8 87.0

82.8 77.5 74.0

66.0 60.4 50.3

54.3 58.4

61.5 64.0 56.0

48.2

37.50

31.60

18.90

12.75

4.90

6.02 9.45

7.84 7.35 7.48

6.93 6.13 5.64

4.35 3.75 1.40

2.24 3.08

45.0 50.7 63.7

56.2 60.2 69.0

72.7 71.0 76.5

81.0 87.5 95.0

80.0 75.5 70.6

66.6 69.5

0.67 2.88 6.73

10.30 15.60 30.00

37.40 32.00 41.30

53.50 60.80 90.00

51.20 41.50 29.70

25.60 13.66

0.82 1.69 2.59

3.21 3.04 5.46

6.10 5.65 6.42

7.30 8.35 9.60

68.2

7.15

46.7

6.42

5 42

5.06

3 69

i—

p^^

•a .•

I—

e _

10.2

^Y^

100

Iflectlre KilO'Volti to If eatral

Fig. 122. — Corona loss curves at different frequencies.

Table L.)

(Plotted from

quencies but the slope c varies with the frequency. Values of c* for various frequencies from 30 to 120 cycles and three different sizes of conductor are given in Table LI, and plotted in Fig. 123.

CORONA LOSS

Table LI. — Variation of c* with Fbbqubnct (Indoor Line)

f™.

Tnti 1-«B r - O.Oai em.

Length - 0.aS19 km.

T(M> 3T-t05 r - 0.10S cm.

heagtb - O.OgIS »- 1.00

r - 0.334 «bU lenaUi - 0.0816

e. per km.

c. p« km.

r. per km.

0,0052 O.OOSl 0.0078 0.0092 0,0107 0,0134

9.5 9.5 9.6 9.5 9.5 9.5

0.0071 0.0092 0.0119 0.0144 0.0167 0.0203

21.5 21.5 20,5 20.5 20.6 19.0

40 60

0.0139 0.0173

38.0 38.0

90 120

0.0240 0.0297

38.0 38.0

The points over this measured range lie on a straight line, and this line extended cuts the frequency axis at —25. This seems

Jim

•

IDM WM MXM 4000 tOOO 60007000

to mean for a given wire and spacing a constant loss plus a loss which varies directly as the frequency. The equation may be written

p ~ a(f + 25Ke - e,y

At zero frequency the equation reduces to

p = 25a(e — ft,)'

132

DIELECTRIC PHENOMENA

This is not necessarily the direct-current loss but is probably lower as the maximum voltage is applied for less time. Watson has made laboratory measurements of d.c. loss, using an influence machine as the source of power. ^ Some of these measurements are compared with the a.c. loss in Table LII, for the same maxi- mum voltages; the difference between the d.c. loss and the a.c. loss for the same effective voltages is much greater.

Table LII. — Comparison of D.C. Corona Loss wrm Loss at 60 Cycles

FOR SAME Maximum Voltaqe

Voltage

gradient

D.c. amps.

•

D.c. kilovolts

D.c. loss

P kw./km.

Corresponding

a.c. effective

kilovolts

Measured 60-cycle loss

Pi kw./km.

Ratio 60 cycles

d. c. loss

P? P

61 66 69 75

0.003 0.004 0.005 0.007

55 59 62 67

0.16 0.24 0.31 0.47

39.8 42.0 44.0 48.0

0.25 0.37 0.50 0.80

1.52 1.58 1.61 1.67

« = 100 cm. r = 0.0597 cm.

D.c. measurements from Watson, Institute of Electrical Engineers.

Relation between c* and s/r. — The powe^ equation may be written over the commercial range of frequency

p = c\e - BoY = a(/ + 25)(e - eoY

where the relation between c* and s/r has not to this point been investigated. The relation will first be determined for the prac- tical sizes of conductors at practical spacings of the outdoor line, and later over greater range from the indoor data. Only 60- cycle values will be used, as the data at this frequency are very complete. In Table LIII are values of c* for various sizes of wire and cable at various spacings. c* varies greatly with the radius of the conductor r and the spacing s. Plotting b/t and c* a curve is obtained that suggests a hyperbola. The curve between log c* and log s/r is a straight line. Therefore the follow- ing relation between c^ and s/r is established.

c» = A {s/rY

(33)

The fair weather value of c* for standard line A 1-2-3^-4 may now be examined in Table LIV.

' Watson, Journal Institution of Electrical Engineers, June, 1910.

CORONA LOSS

133

Table LIII. — Experimental Values — Lines A and B Relation between C' and s/r

Test No.

Diameter, cm.

a r

c» X 10* per km.

Style of conductor

Material

0.168

6550

1.07

280

Wire

Gal. iron

0.168

4880

1.07

256

Wire

Gal. iron

0.168

3700

1.08

326

Wire

Gal. iron

138

0.328

2980

1.10

331

Wire

Copper

0.168

2730

1.07

410

Wire

Gal. iron

137

0.328

2230

1.10

391

Wire

Copper

0.168

1820

1.07

506

Wire

Gal. iron

128

0.518

1530

1.05

412

Wire

Copper

136

0.328

1490

1.10

513

Wire

Copper

0.585

1480

1.07

513

Cable

Gal. iron

135

0.328

1120

1.10

570

Wire

Copper

94a

0.168

1090

1.07

633

Wire

Gal. iron

0.585

1060

1.07

543

Cable

Gal. iron

0.585

770

1.08

571

Cable

Gal. iron

134

0.328

740

1.10

772

Wire

Copper

126

0.518

700

1.11

687

Wire

Copper

1.181

525

1.02

950

Cable

Copper

0.585

520

1.07

784

Cable

Gal. iron

125

0.518

350

1.11

1070

Wire

Copper

0.585

310

1.07

1018

Cable

Gal. iron

100

0.953

193

1.08

1584

Cable

Gal. iron

Table LIV.

-Relation of c* to r for Main Experimental Lines

Line A 1-2-3-4

(Standard Line A)

Teet No.

c» X 10* per km.

1 i

Test No.

ca X 10» per km.

945

0.982

1.020

103

980

0.901

1.112

1050

0.966

1.037

104

892

0.878

1.138

945

0.959

1.043

105

890

0.866

1.158

945

0.933

1.074

109

869

0.928

1.078.

101

955

0.925

1.081

119

991

0.888

1.127

It is seen/ that these values are not exactly constant but appar- ently vary with the temperature and barometric pressure, c^ and 1/6 in curve, Fig. 125, suggest that c^ varies as 1/6. Multi- pl3ring by 8 then, reduces c^ to the standard temperature of 26

134

DIELECTRIC PHENOMENA

Table LV

(Corrected c* and s/r)

cno»

iog(cno»)

Test No.

Diam- eter, cm.

»/r

c» X 10*

read per km.

corrected

to 26'* C.

76 cm.

bar.

Corr. factor 6

corrected

to 26» C,

76 cm.

bar.

log*

Style of conductor

0.168

6550

280

300

1.07

5.704

8.787

Wire

0.168

4880

256

275

1.07

5.620

8.492

Wire

0.168

3700

326

347

1.08

5.852

8.215

Wire

138

0.328

2980

331

364

1.09

5.892

8.000

Wire

137

0.328

2230

391

429

1.09

6.062

7.709

Wire

0.585

1060

543

582

1.07

6.372

6.966

Cable

126

0.518

700

687

755

1.10

6.637

6.551

Wire

1.181

525

950

965

1.02

6.821

6.263

Cable

0.685

520

784

840

1.07

6.733

6.254

Cable

125

0.518

350

1070

1190

1.11

7.083

5.858

Wire

0.585

310

1018

1090

1.07

6.995

5.763

Cable

100

0.953

193

1584

1710

1.08

7.405

5.263

Cable

.015

.010

.006

.2 A .6 J yr JB 1.0

Fig. 125. — Relation between c* and 1/5.

Table LVI. — 2A Reduction op Relation of c' to

(c» i

Corrected to 25 deg. C— '

76 cm. Barometric PreHanre)

Test No.

loge (c>10»)

« logc ~

Teet No.

logt (e>10»)

log« -

5.704

8.787

126

6.637

6.551

•

5.620

8.492

6.871 .

6.263

5.852

8.215

6.733

6.254

138

5.892

8.000

125

7.083

5.858

137

6.062

7.709

6.995.

5.736

6.372

6.966

100

7.444

5.263

35.502

48.169

41.763

35.925

d =

CORONA LOSS

2i Iog6(cn0») « 36.50

2i log€ - = 48.17

22log€(cn0») = 41.76

2j log€ ^ = 35.02

AZ log€(c«10») = -6.26

A 2 log€ - = 12.25

22 log«(c»10*) « 77.26

22 log€ ^ = 84.09

A2log«c*XlO» -6.26

0.51 a - 0.60

135

A 2 logc -

12.25

log (cnO*) - d22 loge -

= 9.92

log (cnO») = -0.51og« - +9.92

c» = 20,500 -J-lO-s

deg. C. and 76 cm. barometric pressure. This particular correc- tion is not satisfactory as the range of 6 is small. It seems the best until more complete data are obtained. In Table LV all values of c are corrected to 25 deg. C. and 76 cm. barometer, and the constants calculated by the 2A method in Table LVI. This gives: c* = 20,50(K/r7s X 10"^ per km. of total conductor at 25 deg. C, 76 cm. barometer and 60 cycles.

Curve 124 is plotted from the points- calculated in Table LVII, while the circles show the actual experimental points.

Table LVII. — Calculation op Curve No. 124 from

(c« X 10» = 20,600-^^)

C3 X 10»

a r

c« X 10»

260

0.0633

129

2000

0.0224

460

600

0.0447

915

3000

0.0183

376

1000

0.0316

648

4000

0.0158

324

1600

0.0258

530

6000

0.0128

262

Curve 126 shows a straight-line relation between log s/r and log c*. The equation for the power loss at 25 deg. C. and 76 cm. barometric pressure and any frequency may now be written

p = 241(/ + 25)/r/s(e - eo)nO'^

(34)

136

DIELECTRIC PHENOMENA

where p = the energy loss per kilometer of conductor in kilo- watts.

e = kilovolts to neutral.

Co = disruptive critical kilovolts to neutral at 25 deg. C. and 76 cm. barometric pressure.

/ = the frequency in cycles per second.

r = the radius of the conductor in cm.

s = the distance between conductor centers in cm.

The value of Co varies with the radius of the conductor r, and the spacing s, and will be discussed later.

Relation between c^, and r and s for Small Conductors and Small Spacings. (Indoor Line). — The loss was investigated for very small conductors at large and small spacings, and for large conductors at small spacings, on the indoor line. The conductors ranged from 0.025 cm. to 0.46 cm. in radius, and the

•^

" A

Fig. 126. — Determination of equation between c* and s/r,

spacings from 12.5 to 275 cm. This investigation is, hence, an extension of the above investigation beyond the practical range. The quadratic law still holds — the relation between c*, r and «, however, becomes more complicated. This is also true of the disruptive critical voltage. Below a spacing of about 15 cm. it is difficult to express the loss in terms of a law, as the results are erratic, probably due to the great distortion of the field which is augmented when the corona starts, greatly increasing the loss above the quadratic.

For conductors 0.025 cm. in radius and above, and 15 cm. spacing and above, this data shows that

r + - + 0.04

^ 10"^ per km. of conductor (33a)

c^ = 20,500-

CORONA LOSS

137

The more complete equation is, therefore,

p = 241(/ + 25)-

r + - + 0.04

{e — CdY 10"* kw./km. /« . x of conductor^ ^ ^^

In Fig. 127 the points are measured corona loss values, while the curve is calculated from equation (34a) (r == 0.032, spacings 46 and 275 cm.). Data are given in the appendix.

It is interesting to note from (33a) that as r becomes very small the c^ term, at a given spacing, approaches a con- stant value — somewhat as if the corona diameter acts as the conductor diameter.

The Disruptive Critical Voltage. — The point of greatest stress around a cylin- drical conductor is at its sur- face. When s/r is large the gradient at the surface of the conductor may be expressed

de _ e dx r log* s/r

M20 I

•

X"^

}

kJ^

»)

40 60 80 e - K. Y. to Neutral

100 120

9 =

(12c)

Fia. 127. — Comparison of calculat- ed and measured corona loss for small conductors at small and large spacings.

ale

(Points measured. Curves calculated from equation (34o) Conductor radius, 0.032 cm. Spacings, 46 cm. and 275 cm. 5 = 1.01.)

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