REASONS FOR THE DISPERSION OF BREAKDOWN VOLTAGES IN SF6

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REASONS FOR THE DISPERSION OF BREAKDOWN VOLTAGES IN SF6

W. Hauschild, W. Mosch

To cite this version:

W. Hauschild, W. Mosch. REASONS FOR THE DISPERSION OF BREAKDOWN VOLTAGES IN SF6. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-251-C7-252. �10.1051/jphyscol:19797123�.

�jpa-00219095�

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JOURNAL DE PHYSIQUE CoZZoipe 67, suppZ6ment au n07, Tome 40, JuiZZet 1979, page C7- 251

REASONS FOR THE DISPERSION OF BREAKDOWN VOLTAGES IN SF6

W. Hauschild and W. Mosch.

Dresden TechnicaZ University, Department for EZectricaZ Engineering Dresden, G.D.R.

Abstract: The breakdown in SF6 is a stochastic process, on the one hand because of the random development of elec- tron avalanches ]I[ [2] [3], on the other hand because of random influences on the electrostatic field by micro-particles, micro-protrusions, or micro-discharges fl]

[u

^]⁴^[

01.

It is investigated which of the random influences causes the dispersion of the breakdown voltage at dif- ferent kinds of the stressing voltage, Semi-empirical calculation of the breakdown voltage: The breakdown voltage Ud can be calculated ]I[ [2] according to

Ud= E d i * e h * d - ~ *kt*ef = Udi*ktsef, (1) Edi

-

intrinsic electrical strength of

-

SF6, measured with a stress time in the order of 1 min:

Edi/k~cm'l = 890.~~~/MPa; ( 2 )

-

curvature factor, describing the macroscopic curvature of the electrode and calculated from the streamer theory [

I

] L6] (Edh- maximum breakdown strength) eh = Edh/Edi ( 3 ) d

-

gap distance;

-

9

., -

uniformity factor according to

-

Schwaiger (Eo

-

mean and Eh maximum field strength) ;

2

= Eo/Eh (4)

k+

-

time factor, describing the changes

-

or the electrical strength caused by very short (impulse voltages) or very long (operation voltages) stress time;

a random variable, Random changes of the micro-field affect the roughness factor ef, which is also a random variable. The distribution functions of kt and ef can be estimated from measured breakdown voltages. Under ideal conditions (very smooth electrodes, absolutely clean sys- tem) and d.c. or a.c. voltage (t=l min),.

ef= 1 and kt= 1 are valid and eq.(l) de- liveres the maximum possible breakdown voltage Ud = Udi. Under technical'conditions the ,expression

Ed = ef kt * Edi (5) can be understood as the applicable electrical strength [ 2 ] .

Time factor and avalanche statistics:

Under the assumption ef = 1, according to eq,(5) the time factor kt is a field strength related to Edi. For a uniform field the avalanche statistics give the breakdown probability depending on %he field strength and the number of starting electrons [I] [3], This is the distribution function of kt (fig, 1).

ef

-

roughness factor, describing the

-

^Fig,^1: Distribution function of the time

influences of roughness, micro-protru- factor kt depending on the number sions and micro-particles. of starting electrons (theoreti-

cally for a uniform field) Random influences due to avalanche sta- For one or a few starting electrons kt tistics can affect the time factor kt, has a large dispersion. If the number of which therefore has to be considered as starting electrons is high, the random

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797123

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character of kt can be neglected (see also [.)]7 At switching impulses (s,i,), a.c,, and doc, voltage kt is independent of pressure and equal to one (kt = kt63 =

1, fig. 2) or slightly smaller than one for very long stress times

. ] I [

At lightning impulses the stress time is so short that the number of starting electrons is very limited. Now kt is random and has to be described by its distribution function.

Fig. 2: Modal value of the time factor ktG3 and of the roughness factor ef 63 (experimentally)

I I I I I

01 02 Q3 Htb 45

SF, gas pressure p~

Fig, 3: Rate of dispersion

st

^{for the}

time factor kt and

rf

^{for the}

roughness factor ef (experimentally )

Starting from a measured double exponential distribution for the impulse breakdown voltage

[u m,

the parameters of the double exponential distribution for the time factor kt, the modal value k t63 (fig. 2, lei.) and the rate of dispersion t t (fig- 3;

rt

^1.i. ⁾were calculated,

~ 0 t h kt63, and

rt

decrease with increasing gas pressure, For impulse voltages Ud

>

UdlOO (breakdown probability p = 1) the p,arameters kt63 and

rt

depend not only on the gas pressure, but also on the stress time

,

Roughness factor and random changes of the micro-field: At lightning impulses the motion of micro-particles and the formation of micro-discharges cannot occur: and the roughness factor has a fixed value ef = ef63 L = 1 (fig, 2). At a.c, voltage but also at switching impulses the micro-field near the electrode is randomly changed by moved particles, emission processes, micro-discharges at protrusions etc. from place to place and time to time, The roughness factor ef is random now and is described by its distribution function, Because of the double-exponentially distributed breakdown voltage (sic, and s.i,

) ] I [

the roughness factor possesses the same distribution with the modal value e

f 63 (fig, 2) and the rate of dispersion

rf

(fig, 3). C h the other hand, ef63 does not depend on the kind of voltage, b u t r f for a. c, is higher than for s ,i, The di,f

-

ferent reasons for the dispersions

i)ct

and

)Lf

were shown by the differents dependen- ces of f t and

aCf

on pressure (fig, 3) : At lightning impulses the dispersion of the time factor is caused by the avalanche statistics and ft decreases with increasing pressure. At a.c, or s.i. voltage the dispersion of the roughness factor is caused by the micro-field the influence of which on the breakdown process is larger at higher pressures andgf in- creases with increasing pressure,

Acknowledgement: The authors are grateful to the VEB 'Pransformatorenwerk "Kaxl Liebknechtw Berlin/GDR for the support given in carrying out the investigations and to the Research Co-operation ELTRA,

References: [ I ] Mosch, W,; Hauschild, W,:

Hochsp~ungsisolierungen mit Schwefel- hexafluorid, VEB Verlag Technik Berlin

1979.

fU

Hauschild, W.: ELEKTRIE 33 (1979) 4. f31 Mosch, W,; Hauschild, W,:

ICPIG 13, Berlin (19771, paper 0418.

f i Bortnik, I.M. : ICPIG 13, ~erlin(1977), paper 0428,

01

Baumgartner, R. G. : Thesis Em Ziirich 1977.

fi]

Pedersen, A,;

Bregnsbo, E,: 2,ISH Ziirich (19751, PPO 432-436,

] 7 [

Blair, D.T,A. ; Crichton,B.H. ; Sommerville, I.C, : ISGD Knoxville (1 9781, PPO 360-3650