Dielectric Phenomena in High Voltage Engineering (1915) — part 9 of 12

Temperature 30 deg. C.

60 Cycles

High frequency (alternator), 90,000 cycles

Damped oscilla- tion, train f req. 120 sec. 200.000 cycles

Single impulse.

sine shape, cor- responding to half cycle of 200,000 cycle

Si

1

Inst.

1 min.

Inst.

1 min.

Inst.

1 min.

kv./mm. (max.)

kv./mm. (max.)

kv./mm.

(max.)

1

kv./mm. (max.)

Transil Oil between Flat Terminals — Square Edge. 2.5-cm. Diameter,

0.25-cm. Space

17

1 6.7

1

30

39

Oiled Pressboard.

lO-cm. Diameter

—Square-edge Discs in Oil

35.5 39.5

31.0 37.0

9.5 6.1 2.5

7.3 4.1 1.76

37.0 42.0

29.0 24.0

72.0

2.5

5.0

15.0

1 2

8

Varnished Cambric

53.0

46.5 31.0 31.0 27.5

19.5

' 13.5

10.0

17.6

10.0

7.3

108.0 78.0 70.0

60.0

1

0.6 1.5 2.5 3.6

2

42.0 42.0 33.0

55.0 49.0 41.0

56.0 41.0 30.5

5

8 12

1

SOLID INSULATIONS 185

Energy Loss in SoUd Insulation. — In general, enei^ loss in solid inBulation:

(1) Increases with increasing voltage.

(2) Increases with increasing temperature.

(3) Increases with increasing frequency.

(4) Increases with increasing moisture content.

(5) Increases with increasing impurities, as occluded air, etc.

EllonilltparmD.

—Insulation Iobb and power fttctor.

Fia. 158. — Insulation loss and power factor vs. temperature. (Data, Fig. 157,)

For good uniform insulation free from foreign material, mois- ture, etc., the loss at constant temperature and frequency varies approximately as the square of the applied voltage. The author has found that approximately for good insulations p = afe* = bfg* X 10~* watts/cu. cm.

186

DIELECTRIC PHENOMENA

where/ = frequency in cycles per sec.

J = gradient kv./mm.

b = constant varies with different insulations. It is 8 to 10 for varnished cambric in a uniform field, and thickness in order of 5 mm.

Compare calculated values with values given in Table LXXVII at both 60 cycles and high frequency (25 deg. C). With occluded air or water, where the /V loss becomes large in comparison with the ''hysteresis" lass, the rate of increase is greater. Due to combinations of resistance and capacity it may then take the form,^ p — bfg^+ {cPg^ + ag^). Fig. 157 shows characteristic curves between energy loss, power factor, and voltage of insula- tion in good condition.

The loss increases very rapidly with temperature. The tem- perature curves are shown in Fig. 158. The effect of exposing to the air is also shown. Loss in different insulations is given in Table LXXVII.

Table LXXVII. — Insulation Losses (Efifective Sine Wave 60 Cycles)

Total thickness.

Insulation

No. of layers

Temp., deg. C.

Volts per mm.

Watts per

mm.

t

CU. CDS.

4.0

Varnished cloth

15

25

4,000

6,000

8,000

10,000

12,000

0.005 0.015 0.035 0.060 0.090

4.0

Varnished cloth

15

90

4,000

0.025

«

6,000

8,000

10,000

12,000

0.075 0.150 0.240 0.350

2.5

Oil-treated paper

30

25

10,000 14,000

0.040 0.070

2.6

Oil-treated paper

30

60

10,000 14,000

0.043 0.080

2.6

Oil-treated paper

30

90

10,000 14,000

0.050 0.100

2.5

Oil* treated paper

30

120

10,000

0.050

14,000

0.100

These losses may be lower or very much higher, depending upon the con- dition of the insulation. 1 See Fig. 152.

SOLID INSULATIONS

187

High Frequency Loss in Different Insulations (Alexanderson, Proc. Inst. Radio Engrs., June, 1914)

Frequenc}' kilocycle

Material (thiclcDess 6 mm.)

Volta per mm.

Glass

Mioa

Vaniiahed cambric

Asbestos

Lobs watts, cu. cm.

P.P. avg.

Loss watts, cu. cm.

P.P. avg.

Loss watts, cu. cm.

P. F.

avg.

Loss watts, cu. cm.

P.F. avg.

500

20 40 60 80 20 40 60 80

0.02 0.05 0.08 0.11 0.08 0.20 0.32 0.40

02

0.7 1.3 2.0

500 500 500

1.4

1.4

0.04 0.05 0.08 0.07 0.12 0.24 0.35

1.8

0.08 0.12 0.18

8.3

32.0

1000

3.0 5.3 7.6

1000 1000 1000

1.8

0.28 0.45 0.65

3.3

32.0

1

The rate of increase of the loss with the frequency will vary greatly if the insulation contains moisture. If the moisture is arranged in such a way as to approximate a condenser and resist-

m "

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60 100

ElloroUi-Hlgh Toniioa

Fio. 159. — Dielectric loss »s. voltage in a 2750 kv-a, 120 kv, 60^ trans^rmer.

10 » o^ 90

Tempentttro Bite aboTe 21 0.

Fig. 160. — Dielectric loss »«. tem- perature in a 3750 kv-a, 120 kv. 60— transformer at 100 kv.

ance in series, as in Fig. 152, the loss may, over a limited range, increase approximately as the square of the frequency. If the insulation is in good condition the loss may increase approxi- mately directly as the frequency.

The best method of comparing different insulations is by meas- urement of losses.

Operating Temperatures of Insulations. — The maximum operating temperature of insulations is indefinite. For low- vol-

188

DIELECTRIC PHENOMENA

tage apparatus, temperatures not high enough to cause direct electrical failure may cause mechanical failure in short periods by drying out the insulation, cracking, etc. The maximum safe temperature, at which the life is not greatly shortened mechan- ically by cracking, drying out, etc., varies with different insula- tions, but is approximately as follows:

Fibrous materials, cloth, varnish, etc 100 deg. C.

Asbestos, mica and similar materials, in combination with binders'

varnish, etc 150 deg. C.

Mica, asbestos — alone very high.

These values are given without consideration of the electrical effects. Often the electrical properties will limit the tempera- tures below these values. Heat conductivity must be considered in design.

140 ISO

120

no

100

90

S 80

f TO

60 40 80 20 10

1 2

Total Arcing Dlitancc.

Fig. 161. — Surface arc-over in oil. (Hendricks.)

Surface Leakage. — Strictly speaking, on clean dielectric sur- faces, appreciable leakage does not occur. What is generally termed "surface leakage" is a rupture of one dielectric at the surface of another dielectric by overflux concentration due to differ- ence in permittivities, etc. For instance, on a porcelain insulator in air the flux may be suflBciently concentrated at portions of the surface to cause the air to rupture. The appearance is that of leakage over the porcelain surface. "Surface leakage" then is quite indefinite, and for a given leakage distance depends upon the position and shape of the electrodes, relative capacities of the materials, etc. (See Fig. 161.) The effects of actual leakage and

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SOLID INSULATIONS 189

apparent leakage in air may be seen in Table LXXVIII, page 190. In (1) the spark-over is given with the surface out. In (4) the decrease must be due to actual leakage as there is no flux concentration. In (2) and (3) flux concentration is balanced against increased surface.

Solid Insulation Barriers in Oil. — Properly placed barriers of solid insulation in oil greatly increase the strength of the oil spaces by limiting the thickness of the oil, preventing moisture chains lining up, etc. This should always be considered in design. In placing barriers, however, the arrangement should be such that the stress on the oil is not increased by the higher permit- tivity of the solid insulation. Data for a simple arrangement are given in Table LXXVIII. It will be noted that in most cases the strength is not greatly increased on account of difference of per- mittivity of oil and solid insulation. The reliability is much greater, however.

Table LXXVIII. — Pressboard Barriers in Oil

Kv. Gap 0.24 cm. effective

Oil only 23.0

1 — 0.08-cm. sheet of pressboard midway between electrodes 24 . 7

1 — 0.08-cm. sheet of pressboard against one electrode 22 . 7

Kv. Gap 0.40 cm. effective

Oil only 35.3

2 — 0.08-cm. sheets of pressboard against one electrode 36.5

Kv. Gap 0.56 cm. effective

Oil only 53 . 9

3 — 0.08-cm. sheets of pressboard against one electrode 44 .

Kv. Gap 1.16 cm. effective

Oil only 96.0

1 — 0.08-cm. sheet of pressboard 0.1 cm. from each terminal 95.3

1 — 0.08-cm. sheet of pressboard 0.33 cm. from each terminal 102.0

2 — 0.08-cm. sheet of pressboard at midpoint 88 . 5

1 — 0.08-cm. sheet of pressboard on each terminal 94 .5

Strength of pressboard — 0.08 cm., 15 kv.; 0.16 cm., 28 kv.

Terminals 6 cm. in diameter, rounded with a 3-cm. radius at the edges.

190

DIELECTRIC PHENOMENA

Surface Arc-oveb in Aib

^

C

"^ iX) 7.6 cm. Air only between parallel ^ plates. Rounded edges

Effective kv. kv./cm.

128.0 16.8

••- 6ciifa-*|

"If— (2) 7.6 cm. Over corrugated rubber cylin- der between above plates. Surface oiled Surface dry

94.0 87.0

(3) Corrugated rubber cylinder above plates. Surface oiled- Surface dry

between

109.0 89.0

12.4 11.4

14.3 11.7

(4) Smooth rubber cylinder between above

plates. Oiled surface 122.0 16.0

Surface dry 62.0 8.0

•^8.8 onu

Note. — Maximum possible kv. arc-over 128. Data shows that although corrugations increase stress, actual gain is made by their use by reduction of true leakage.

Impregnation. — Insulations, such as dry paper, with low dielec- tric strength and low permittivity, are impregnated with oils or compounds of high strength and permittivity. The result is a dielectric of greater strength and permittivity. If the impreg- nating is improperly done, for instance so as to leave oiled spots and unoiled spots, the dielectric strength may be less than the dry paper alone. This is due to the difference in permittivities of the dry and oiled spots, which causes a concentration of stress on the electrically weak dry spots.

Mechanical. — It is of great importance to arrange designs in such a way that local cracking, or tearing is not caused by high localized mechanical stresses. This is especially so with porce-

SOLID INSULATIONS 191

lain, as in the line insulators. Expansion of a metal pin, localized mechanical stress due to sharp corners, expansion of improper cement, etc., will cause gradual cracking of the porcelain. The so-called deterioration of line insulators is often caused in this way.

Direct Current. — As the breakdown depends upon the maxi- mum point of the voltage wave, the direct-current puncture vol- tage in air and oil is (a/2) or 1.41 times the sine wave alternating puncture voltage. In air and oil there is very little loss with alternating current until the puncture voltage is reached. With solid insulatioA losses occur with alternating current as soon as voltage is applied. In the time tests the insulation is thus considerably weakened by heating, especially thick insulation. This causes decreasing breakdown voltages in the time tests as the frequency is increased. In certain insulations the loss must be very small for direct current. The gain for direct current in solid insulation in the time tests is thus greater than the 41% given above.

CHAPTER VIII

THE ELECTRON THEORY

A brief review of the electron theory will be given in this chapter.

A gas is a very poor conductor of electricity. A condenser or electroscope may be left charged in air a great length of time with- out considerable loss or leakage. If, however, the surrounding air and the terminals of the condenser or electroscope are sub- jected to the action of X-rays, ultraviolet light, or radio-active substances, the leakage becomes quite rapid. All of these agents in some way act as carriers or change the nature of the gas so that the current passes from terminal to terminal. The gas is said to be ionized.

Fig. 162. — Cathode ray tube.

If terminals are placed in a vacuum tube and high voltage is applied between them, a visible discharge or beam of rays is shot out from the cathode. These cathode rays proceed in straight lines. A pin-hole diaphragm may be placed in their path and a narrow beam obtained (see Fig. 162). This beam may be de- flected by a magnetic or dielectric field. J. J. Thomson pointed out that it acts in every way as if it were made up of negatively charged particles traveling at very high velocities.^ Every test that has been made bears this out. Where the particles strike the glass it becomes luminescent. These particles of negative electricity or "charged" corpuscles are called electrons. The velocity, "charge," and mass of these electrons have been measured.

^ These ra3r8 have been made use of in an oscillograph. In this instrument the beam acts as a pointer and is made to trace a curve under influence of the fields produced by the current or voltage of the wave which is being

measured.

192

THE ELECTRON THEORY 193

A "charged" body in motion is deflected by the electric fields in the same way as a wire-carrying current. The deflection de- pends upon the ratio of the "charge" e and the mass m. By noting the deflection of the cathode rays in the electric field, J. J. Thomson found the value of the ratio e/m. The most accurate value of the ratio with e measured in electromagnetic units is 1.8 X 10^. Each ion in a gas acts as nuclei in the condensation of water vapor. The condensation in the presence of the ions may be made to occur by change of pressure. By observing the rate of fall of the cloud the number of drops or electrons can be calculated. If the total "charge" is measured, e can be at once obtained. This was done by C. T. R. Wilson, e' was also later determined by Millikan and found to be 4.77 X 10-^® electrostatic units or 1.6 X 10"^® electromagnetic units. The mass of the electron seems to be about 1/1800 of the hydrogen atom, or the same mass as the hydrogen ion in electrolytic conduction. This mass is about 8.9 X 10-' grams when the velocity is considerably below that of light, and apparently changes with velocity. It must be considered as that determined by force divided by acceleration. The velocity of the electron varies from 10' to 10 cm./sec.

The beta particle of radio-active substances is identical with the cathode particle or electron. The gamma rays are, probably, ether waves produced by the action of the beta particles in a way similar to that in which X-rays are produced by the im- pingement of cathode particles on solids. The alpha particle is a positively charged atom of helium.

The elemental positive particles corresponding to the electron have so far not been found. Ion is a general term used for positive or negative atoms or molecules, electrons, or positive particles.

Take two electrodes in air and apply some low potential between them. Direct ultraviolet light upon the negative electrode. If the voltage is gradually increased, the current in- creases almost directly up to (a). Fig. 163. There is then a con- siderable range between (a) and (6) where an increase in voltage does not greatly increase the current. At (6) the current sud- denly increases very rapidly with increasing voltage. It appears that negative "particles" or electrons are produced or set free at the negative conductor by the ultraviolet light. These "particles of electricity" are attracted to the positive conductor' and thus show as current in the galvanometer in the circuit. The number reaching the positive conductor increases with in-

194

DIELECTRIC PHENOMENA

creasing voltage. The current thus increases with increasing voltage. The potential at (a) is sufficient to cause practically all of the negative particles that are produced by the light to reach the positive conductor. An increase of the voltage above the value at (a) can thus cause very little increase in current unless a new source of ionization is applied or the number of ions is increased in some way. When the voltage is raised above the value at (6), the current increases very rapidly with increasing voltage. A new source of ionization has resulted.

The velocity at which ions travel increases with increasing voltage or field intensity. The new source of ionization results when the ions have reached a definite velocity in their mean free

path. Townsend has ex- plained this on the hypothesis that ions traveling at suffi- cient speed generate new ions on collision with neutral atoms or molecules. Thus after a sufficient voltage is applied, the velocity of the ions in their mean free path becomes great enough to pro- duce new ions by collision with atoms or molecules by separat- ing the positive and negative parts of the atoms or molecules. These in turn produce new ions so the ionic density increases very rapidly. The positive ions travel to the negative conductor; the negative ions to the positive conductor. It seems, however, that the electron plays the principal part in impact ionization.

It may be of interest to review in a brief way how the law of visual corona was derived, to show that it is a rational law, and to illustrate a practical application of the electron theory.

In 1910 an investigation was conducted in which the visual corona voltages of various sizes of polished parallel wires at various spacings were determined.^ For any given conductor the voltage gradient at rupture, g«, was found to be constant independent of the spacing (except at very small spacings), but increased very rapidly as the radius of the conductor was decreased. Thus air apparently had a greater strength for small conductors than large 1 F. W. Peek, Jr., Law of CJorona, A.I.E.E., June, 1911.

5/

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b

4*

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4S

f

a

8a

ura

ion

J

y

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L

Yoltt

Fig. 163. — Variation of current with voltage through ionized space between parallel plate electrodes.

THE ELECTRON THEORY 196

ones. This was formerly pointed out by Prof. Ryan. The curve of experimental data between g« and radius r was found to be regular and continuous. A number of equations could readily be written which would fit these data. It was desired, however, to establish or build up a rational equation. The old idea of air films at the surface of the conductors was abandoned after tests with very light (aluminum) and very heavy (tungsten) metals showed that the density of the metal of the conductor had no influence on Qv, which should be the case if the difference were caused by air films, as the air film should vary with the density of the conductor.

A rational law of visual corona was deduced from the data, as follows:

—^ of the energy of

the moving ions, or whatever form it may, is necessary to rupture insulation. This is borne out by experiments with transients, which show that finite time is necessary to rupture insulation; that if this time be limited the voltage must be increased to accomplish the same results in the limited time, also heating results at rupture, etc. These imply definite finite energy.

The gradient or stress to rupture air in bulk in a uniform field, (7o> should be constant for a given air density or molecular spacing. In a non-uniform field, as that around a wire, the breakdown strength of air, go, is first reached at the conductor surface; at an infinitely small distance from the conductor surface the stress is still below the rupturing gradient. Hence, in order to store the necessary finite rupturing energy the gradient at the conductor surface must be increased to (;«, so that at a finite distance away the gradient is Qo- This means that a finite thickness of the insulation must be under a stress of at least go- The ruptur- ing energy is in the zone between g^ and Qo* The thickness of the zone should be a function of the conductor radius. It was found that at

0.301/r cm.

from the conductor surface the gradient at rupture is always con- stant and 30 kv./cm. (at standard air density). The relation between g» and r may now be directly expressed by the simple law

/, , 0.301\ _-/, , 0.301\ , , , . gv = ff,( 1 + —7-) = 30n + -~r--\ kv./cm. (max.)

196 DIELECTRIC PHENOMENA

For parallel planes or for air in bulk r = <*>

Thus the strength of air is constant and equal to 30 kv./cm., but in non-uniform fields is apparently stronger, as explained above. If the air is made less dense, that is the molecular spac- ing is changed, the strength of air in a uniform field should de- crease directly with the air density.

However, for non-uniform fields, the energy distance should also change thus

0.301/r«{5)

The complete equation including air density factor was found to take the simple rational form

17. = M 1 +

a3qi\

This equation holds for values of 6 as low as 0.02. As the fur

density is decreased, a minimum g^ is reached in the order of

5 = 0.002, g^ then increases

very rapidly with decreasing S.

(See Fig. 164.) At very high

vacuum the separation of the

molecules may be of a fairly

high order compared to the

dimension of the tube. There

is, thus, very little ionization

by collision, and the apparent

Fio. 164.— Variation of strength of strength becomes high. At

air with density showing increase in .■,■, uj-Upr vapiiiim as luwri

strength at very low densities. "'■"' °W^^^ vacuum, as usea

in the best X-ray tubes, the

only source of ionization is from the conductors themselves.

In the latest tubes the cathode is hot and is the only source

of ions. The number can be controlled by the temperature of

the cathode. '

If the energy distance is limited to less than .301 Vti by placing the conductors close together, the apparent gradient should in- crease. This also is borne out by experiment. The visual tests ' CooUdge X-ray tube.

THE ELECTRON THEORY 197

on various forms of electrodes, as spheres, wires, planes, etc., as well as loss measurements, all point to an energy storage distance and a constant strength of air of 30 kv./cm.

For continuously applied high /re(|iienq/ where the rate of energy or power is great, frequency may enter into the energy thus,

0.301

n/^.*(/)

and spark-over take place at somewhat lower voltages. Where the time is limited, as by an impulse of steep wave front, a much higher voltage should be required to start arc-over. This is also borne out by experiment.

Thus far the form of this rupturing energy has not been con- sidered as it was unnecessary, in order to develop a rational working equation.

When low potential is applied between two conductors any free ions are set in motion. As the potential and, therefore, the field intensity or gradient is increased, the velocity of the ions increases.^ At the gradient of go = 30 kv./cm. (5 = 1) the velocity of the ions becomes sufficiently great over the mean free path to form other ions by collision. This gradient is constant and is called dielectric strength of air. When ionic saturation is reached at any point, the air becomes conducting and glows, or there is corona or spark.

Appl3ring this to parallel wires: when a gradient gv is reached at the wire surface, any free ions are accelerated and produce other ions by collision with molecules, which are in turn acceler- ated. The ionic density is thus gradually increased by successive collision until at 0.301 Vr cm. from the wire surface, where go = 30, ionic saturation is reached, or corona starts. The distance 0.301 Vr cm. is, of course, many times greater than the mean free path of the ion, and many collisions must take place in this distance. Thus, for the wire, corona cannot form when the gradient of go is reached at the surface, as at any distance from the surface the gradient is less than ^p.

The gradient at the surface must therefore be increased to g^ so that the gradient a finite distance away from the surface (0.301 Vr cm.) is go. That is to say, energy is necessary to start corona, as noted above, go the strength of air, should vary with

^ See also explanation given in Theory of Corona, Bergen Davis, A.I.E.E.,

AprU, 1914. 13

198 DIELECTRIC PHENOMENA

b\ Qvi however, cannot vary directly with 5, because, with the greater mean free path of the ion at lower air densities, a greater ''accelerating" or energy distance is necessary. In the equation, a =» 0.301 Vr/^; that is, a increases with decreasing 5.

When the conductors are placed so close together that the free accelerating or energy storage distance is interfered with, the gradient g« must be increased in order that ionic saturation may be reached in this limited distance.

Over a wide range, initial ionization of the air cannot affect the starting voltage of a steadily applied low-frequency e.m.f. since such ionization must necessarily be very small compared to the residual ionization after each cycle. If the ionization is very small when such a voltage is first applied an appreciable time is necessary before corona starts, but the starting voltage is not affected.

The initial ionization should, however, have a considerable effect upon transient voltages of short duration, steep wave-front voltages, etc. Thus, if for given electrodes, the time of applica- tion is less than that normally necessary to bring the initial ioniza- tion up to ionic .saturation, a higher voltage should be required to cause corona or spark-over in the limited time. Experiments show, however, that even with impulse voltages the initial ioniza- tion may be varied over a great range without appreciable change in the impulse spark-over voltage of a given pair of electrodes in open air. The effect of initial ionization may be observed to a greater extent at low air densities, where the number of free ions may be made an appreciable per cent, of ionic saturation. When the electrodes are of such a nature as to require considerable brush discharge in the path of the spark before spark-over, the steep wave-front voltage required to cause discharge over a given gap is much higher than the required steady voltage. If spheres and needles, set to spark-over at the same 60-cycle voltage, are placed in parallel and impulse voltage of steep wave front ap- plied, spark-over will take place across the spheres only.

CHAPTER IX PRACTICAL CORONA CALCX7LATIONS FOR TRANSMISSION LINES

Summary of Various Factors Affecting Corona. — If potential is applied between the conductors of a transmission line and gradu- ally increased, a point is reached when wattmeters placed in the circuit begin to read. The watt loss is low at first but increases with increasing voltages. At the point where the meters begin to read, a hissing noise is heard, and if it is quite dark, localized

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Fig. 166. — Characteristic corona loss, current, and power factor curves.

(Line A. Conductor length, 109,500 cm. (total). Spacing, 3 10 cm. Diameter, 1 . 18 cm. (3/0 cable). Temp., 12** C. Bar., 75.)

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FiQ. 167. — Loss near the critical voltage of new and old cables.

(Data Fig. 166. Line calcu- lated. X, new cable, o, weathered cable).

streamers and glow points can be noticed at spots on the con- ductors. These first streamers are caused by dirt and irregulari- ties. The watt increase is still gradual. Slowly raising the voltage, the true visual critical corona point is finally reached. The effect is striking; corona suddenly jumps out, as it were, all along the line. The line immediately becomes very noisy, and the loss increases very rapidly with increasing voltage. The intensity of the light also increases with increasing voltage. If

199

200 DIELECTRIC PHENOMENA

one is close to the conductors an odor of ozone and nitrous oxide, the result of chemical action on the air, is noticed. There is, thus, heat, chemical action, light, and sound in the process of corona formation. These naturally all mean energy loss.

It becomes of great importance in the design of high-voltage transmission lines to know the various factors which affect the corona formation, and to have simple working formulsB for pre- determining the corona characteristics, so that the corona loss will not be excessive.

Loss begins at some critical voltage, which depends upon the size and spacing of the line conductors, altitudes, etc., and in- creases very rapidly above this voltage. Figs. 166 and 167 show typical corona loss curves during fair weather.

An extensive investigation on an experimental transmission line (see Fig. 168) has shown that the corona loss in fair weather is expressed by the equation:

p = a(/+ c)(e - CoY

where p = loss in kilowatts per kilometer length of smgle-line

conductor.

e = effective value of the voltage between the line con- ductors and neutral in kilo volts. ^

/ s= frequency.

c = a constant = 25

and a is given by the equation

A

d where r = radius of conductor in centimeters.

8 = the distance between conductor and return con- ductor in centimeters. 8 = density of the air, referred to the density at 25

deg. C. and 76 cm. barometer as unity. A = a constant = 241.

Bo = the effective disruptive critical voltage to neutral, and is given by the equation

Co = moQo^r log« «/r kv. to neutral*

where Qo is the disruptive gradient of air in kilovoUs per centi- meter at 25 deg. C. and 76 cm. barometer, and is constant for all

^ Hence, in single-phase circuits, e is one-half the voltage between con- ductors. In three-phase circuits, e is 1/V^3 times the voltage between conductors.

a = -zy/r/s

Fig. 165. — Corona at 230 kv. LineA, 3/Ocable. 310cm. (122 iii.tHp&cmg.

IFacina pool 200.)

Flo. 108. — ExperimentAl transmiaaion line.

CORONA CALCULATIONS FOR TRANSMISSION LINES 201

practical transmission line sizes of conductor frequencies, etc. For very small conductors Qd is used. (See pages 136, 141, 142.)

go = 21.1 kv. per cm. (effective).

nio is a constant depending upon the surface condition of the conductions, and is

mo = 1 for perfectly smooth polished wire,

nio = 0.98 to 0.93 for roughened or weathered wires, and decreases to

mo = 0.87 to 0.83 for seven-strand cables (where the radius is taken as the outer radius of the cable). Luminosity of the air surrounding the line conductors does not begin at the disruptive critical voUage Co, but at a higher voltage e^, the visiud critical voUage. The mstud critical voUagCj e,, is much higher for small conductors than the disruptive critical voUa^je, €„; it is also higher for large conductors, but to a less extent. For very small conductors Cd replaces Co. (See page 141.)

While theoretically no appreciable loss of power should occm* below the visual voltage, Cv, some loss does occur, due to irregu- larities of the wire surface, dirt, etc., as indicated by brush dis- charges, and local corona streamers. (See page 143.)

As the loss between 6„ and Co depends upon dirt, roughened condition of the wire surface, etc., it is unstable and variable and changes as the surface of the conductors changes. For the larger sizes of stranded transmission conductors in practice the surface is generally such that the loss approximately follows the quadratic law, even between Co and e„. This is shown by the circles in Fig. 167, which are measured points on a weathered conductor. The crosses indicate how the points come on a new conductor. For a small conductor the difference between the calculated and measured losses on the section of the curve between Co and Ct, is still greater. Above 6„ the curves coincide and follow the quadratic law. In practice it is rarely admissible to operate above the e© voltage.^ Cases are known in which conductors have deteriorated by the action of nitric acid formed by exces- sive brush discharge.

It is interesting to note that the loss below e„ actually follows the probability curve

but this need not be considered in practice.

^ Operation at 6o voltage at high altitudes gives relatively greater margin and less loss than at sea level as there is greater difference between e^ and e«.

202

DIELECTRIC PHENOMENA

The corona loss is:

(a) A loss proportional to the frequency / plus a small constant loss,

(&) Proportional to the square of the excess voltage above the disruptive critical voltage, e„,

(c) Proportional to the conductor radius t and log, s/r. The critical voltage thus increases very rapidly with increasing r, spacing.

The disru'piive critical voltage, e^, is the voltage at which the disruptive volt^^ gradient of the air is reached at the conductor surface. Hence it is:

(a) Proportional to the conductor radius r and log, s/r. The critical voltage thus increases very rapidly with increasing r, and to a much less extent with increasing s.

(6) Proportional to the air density or becomes very low at high altitudes.

(c) Dependent somewhat on the conditions of the conductor surface, as represented by m.

The effects of various atmos- pheric conditions and storms on the critical voltage and loss will now be considered.

(a) Humidity has no effect on ^ the critical voltage.

(6) Smoke lowers the critical voltage and increases the loss. (c) Heavy winds have no eSect on the loss or critical voltage at ordinary commercial frequencies.

(d) Fog lowers the critical voltage and increases the loss.

(e) Sleet on the wires, or falling sleet, lowers the critical voltage and increases the loss. High voltages do not eliminate sleet formation.

(/) Rain storms lower the critical voltage and increase the loss.

(ff) Snow storms lower the critical voltage and increase the loss.

{h) At high altitudes the loss is very much greater on a given conductor, at a given voltage, than it is at sea level. For a given voltage larger conductors must be used at high altitudes.

CORONA CALdULATIONS FOR TRANSMISSION LINES 203

Fig. 169 shows a typical loss curve during storm and a corre- sponding fair weather curve.

Practical Corona Formule and Their Application. — The for- mulsB required for the determination of the corona characteristics of transmission lines are:

METRIC UNITS

Disruptive Critical Voltage

Co = 21.1mo rB log« s/r kv. to neutral (35)

Power Loss 244

P =

d

(f + 25)V^s(e - eo)nO- ^^^X'to^' ""^ ^""^^^ (^)

Where the conductors are small use formulae (34a), (35a), and (36), Chapter V.

Visual Critical Voltage

Cv = 21.1m,dr/ 1 + ' - \ log, s/r kv. to neutral (20)

a = ^-^2^

273 + <

where

e = effective kilovolts to neutral applied to the line* 5 = air density factor

= 1 at 25 deg. C, 76 cm. barometer b = barometric pressure in centimeters t = temperature in degrees Centigrade r = radius of conductor, centimeters s = spacing between conductor centers in centimeters / = frequency cycles per second.

For approximating storm loss consider Co = 0.8 of fair weather value in formula (2).

Irregularity Factors

mo = 1 for polished wires

= 0.98 — 0.93 for roughened or weathered wires

= 0.87 — 0.83 for seven-strand cables m» = TWo f or polished wire = 1 m» = 0.72 for local corona all along cable m, = 0.82 for decided corona all along cable.

'e — volte between line times l/y/S for three-phase lines and volts between line times H for single-phase or two-phase lines.

204 DIELECTRIC PHENOMENA

ENGLISH UNITS

Disruptive Critical Voltage

e, = 123m»r5 Ic^w «/r kv. to neutral (35')

Power Loss

P-f(/ + 25)v^(e - ..)nO-' S'ndSctor"^"' <"' ""'^ P^')

Where the conductors are small use formula (34a), (35a) and 36, Chapter V.

Visual Critical Voltage

c, = 123m,«r/l + -~r^) log,as/r kv. to neutral (20')

e = effective kilovolts to neutral applied to the line'

6 = wr density factor

= 1 at 77 deg. F. and 29.9 in. barometer b = barometric pressure in inches ( = temperature in degrees Fahrenheit r = radius of conductor, inches s = distance between conductor centers in inches / = frequency, cycles per second.

Fia. 170. Fm. 171.

'e '^ volts between line times l/'v/S (oi' three^haae lines and volte between line times ii for single-phase or two-phase lines.

CORONA CALCULATIONS FOR TRANSMISSION LINES 205

80

M

"324

3

•522

a *1 • 20

ol8

16 14

^■BM >— ^^ ai^H mm^~ m^^ i^^m ^^^ ^^— ^^— ■ ■ ■■ ^^— ■ ■ m«

-^ ■^— — ^— ^— -^ ^— ^— ^— '^— ^:- I

80

u

370

loo

s

55

Iso

a

n 40

16000

6000 10000

AltttDde-Teet

Fig. 172. — Approximate barometric readings at different altitudes.

1000 2000 8000

Altitii40-Met0rB

4000

In order to illustrate the use of the formulae, the following practical example is taken:

Given: three-phase line Length Spacing Conductor Max. temperature

Then

Elevation

Barometer (from Fig. 172) 28.85 in.

120

s/r =

EXAMPLE

60 cycles 100 miles 120 in.

1/0 cable — diam. 0.374 in. 100 deg. F. 1000 ft.

0.187

= 642

logio s/r = 2.81 (from Fig. 171 or tables)

Vr/s = 0.0394 (from Fig. 170 or calculated) 17.96 17.9 X 28.85

S =

459+100

= 0.925

459 + < nio = 0.87

eo = 123mora logio s/r = 123 X 0.87 X 0.187 X 0.925 X 2.81 (35')

= 52.0 kv. to neutral p = 390(/ + 25)VV7i{e - eo)nO-* (340

= 0.014(e — 52.0)* kw. per mile of single conductor. Since there are three conductors:

p = 0.042(e — 52.0)* kw. per mile of three-phase line.

The conductor (100 deg. F., 1000 ft. elevation) would glow at

e, = 123me5r ( 1 +

rorl

0.189

V^r

)

logio s/r = 62.6 kv. to neutral (20')

206

DIELECTRIC PHENOMENA

or 62.6 X 1.73 = 108.3 kv. between linea.

More decidedly at

71.3 X 1.73 = 123.4 kv. between lines.

The visual corona cannot be observed except on a very dark cloudy night.

To show the effect of altitude, the characteristics of the same line are calculated for 10,000 ft. elevation and tabulated in Table LXXIX. At this altitude

p = 0.0599(e — 36.8)^ kw. per mile of three-phase line Bo — 36.8 kv. to neutral.

(m„ = 0.72) 81.5 kv. local. Visual corona between lines

(m„ = 0.82) 92.7 kv. decided. Table LXXIX. — Corona Loss at Different Operatinq Voltages

Kv. to neutral e

Kw. per mile and total in 100 miles

1000 ft. elevation

10.000 ft. elevation

Kv. bet. lines

Fair weather

Storms

Fair weather

Storms

P per

mile,

3 oond.

100 miles

P per

mile,

3 cond.

100 miles

P per

mile*

3 cond.

100 miles

P per

mile,

3 oond.

100 miles

50

28.9 34.7 40.5 46.3

52.0 57.8 63.6 69.4

75.1 80.9 86.7

60

1.7

8.0

17.0

30.0 48.0 70.0 96.0

125.0 158.0 196.0

170

70

0.8

5.4

14.0 26.0 33.0 63.0

88.0 116.0 149.0

80 540

1,400 2,600 3,300 6,300

8,800 11,600 14,900

800

80

0.9

4.6 11.0 20.0 33.0

47.0 65.0 86.0

90

460 1,100 2,000 3,300

4,700 6,500 8,600

1,700

3,000 4,800 7,000 9,600

12,500 15,800 19,600

90 100 110 120

130 140 150

0.0

1.4

5.7

13.0

22.0 35.0 51.0

140

570