STATIC BREAKDOWN ANALYSIS OF COMPRESSED SF6 IN POSITIVE ROD-TO-PLANE GAPS

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STATIC BREAKDOWN ANALYSIS OF

COMPRESSED SF6 IN POSITIVE ROD-TO-PLANE GAPS

M. Abou-Seada, Kh. I. M. Ali

To cite this version:

M. Abou-Seada, Kh. I. M. Ali. STATIC BREAKDOWN ANALYSIS OF COMPRESSED SF6 IN

POSITIVE ROD-TO-PLANE GAPS. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-311-C7-

312. �10.1051/jphyscol:19797153�. �jpa-00219128�

JOURNAL DE PHYSIQUE CoZZoque C7, suppZdment au n07, Tome 40, JuilZet 1979, page C7- 311

STATIC BREAKDOWN ANALYSIS OF COMPRESSED SF6 IN WSaITIVE ROD-TO-PLANE GAPS

M.S. Abou-Seada and KH. I. M. ~ l i * .

xElectrical Engineering Dep., Faculty of Engineering, Cairo University, Cairo Egypt.

EZect~&al Mech. Res. Inst., Ministry of Irrigation, Cairo, Egypt.

A b s t r a c t

---

.- The p e c u l i a r v a r i f i t i o n o-.F brea- kdown v o l t a g e

V,

w i t h p r e s s u r e

P

i n cQm- p r e s s e d SF6 due t o corona-stab? l i e a t i o n of t h e a p p l i e d f i e l d i s

ell

p r o n o a ~ c e f i i?

rod-to-?lane Fiq. l ( a ). I n t h i s p2per a t h e o r e t i c a l a r q l y s i s of t h i s ~ t ~ i i l i z a - t i o n effect; i s con3ucted. AccorC!.n:ly a o r i t e r i o n

i s

developed f o ? c o r n ~ u t ~ . n g Vs of congress-d SF6

in

r o d - t o - ~ l s n e gans.

XETHOD OF _AWh1,YSIS

...

The e q u a t i o n s of u n i p o l a r corona

b,2]

are

s o l v e 8 a* e a c h p r e s s u r e a t d i f f e r e n t a p p l i e d v o l t a p h i g h e r t h a n t h e corona a- s e t v a l u e Vc computed a t P

[J].

S o l u t i o n i s c a r r i e d o u t u s i n g t h e s a t u r z t e d s o l u

-

t i o n conce>t a d v i s e d f o r gap c ~ - ~ i . g u r a t i o n p r o + u c i n g hi-ahly d i v e r y e n t npvlic2. f i e l d

1 Xccord ing t o th!-,. concept ,,k:?e snace charge i o n d e n s i t y

P i s

v e r y hiyll a t t h e e m i t t e r ( conductor i n c*)rons ) s v r f ace and d r o p s t'o

a

nf?gl i g i b l e value a t oil- i.nfini- t e s i ~ a l d i s t a n c e

6

from

it [ I ] .

T5e rr-s?rl- t a n t elec-kric f i e l d E

i s

assumed t o r i s e from a c r a c t i c a l l y z e r o value a t e m i t t e r

s u r f a c e

[I]

t o t h e c o r o m o n s e t value

Ec

a t 6 1 2 3

.

^E i s expressed a s 3

= T I ,

where

3 i s

a s c a l a r f u n c t i o n [ 1 , 2 J

.

^The

f o l l o m i n g e q u a t i o n s a r e d e r i - ~ e d f o r corn

-

p u t f n g t h e and E v s l u e s a t any f i n i t e d i s t a n c e

s

(>

8

) from e m i t t e r s11rfaceC1,

21*

^{1 1 l p d s}

p"FiZ ^go

⁶

³

⁽¹⁾

"

where

yi

i s t h e value of

P

a t

d .

Ass-u:ling an i n i t i a l a?proxi.nate v a l u e

?

i o f o r

Pi,

e q u a t i o n s ( 1 ) and ( 2 ) a r e so- 1-ved s i ~ u 1 " c n e o u s l y on t h e l i n e of maximum

f i e l d . I n b e g r a t i o n and d i t f e r e n t i a t i o n a r e rep!.aced by f i n i t 6 d i f f e r e n c e r e l q - t i o n s . i'he f i e l d l i n e

i s

di.vi:',ed i n t o n s t e 11s '0:: a r e g u l a r l y spaced e quipoten- t i ,xihis g i v e s u s .n r e f e r e n c e no5nts f o r congut,-ition o f d i f f e r e n c e s .

An

op- timum va!.ue of n is found t o be e q u a l t o

25.

i h c cii-stance

s

i s measured from smi- t t e r s7.w?qce a s

b

i s negli(z;.i3le with r e s - p e c t t o t h e l e n g t h of any s t e p . Usjnr ~ $ 5 - g i t a l c o x ? u t e r i t e r a t i v e technique t h e

9

ar.d I< r:i:;+;ributFons s a t i z f y i n g t h e boun- d a r y cofii i t i o n pertinent t o t h e at-cited p o t e n t i a l d i f f e r e n c e a c r o s s t h e pa? a m com?uted.

pi^,

^ie t a k e n a s

1 2 1

where

V

i- t h e a ? p l i e d v o l t . l s e and C @ i~

t h e s-;-:cr charge-f ref p o t e n t i a l .

p

v a l u e s s r e found t o increnc,e w i t h

V

a1 on? t h e vihcle f l e l $ - l i n e a t t h e sa:ne -re.:sure. Rencc t h e zean

j.on

char- ge

.:

^{no -:}

-'-

4y

P,,

d e f i n e <

a s

(

lH

p d - ) / Fi

,

0 -

:~!her2 !-I i.s t h e Gap Ien,$h, i n c r e a s e s :yitF!

V a t t h e same p r e s s n e . I t i s i n t e r e s t

-

i n g t o n o t i c e t h e t acoordfng t o t h e pro- s e n t s o l u t i o n concept,

P m

of a a t a c e r t a i n

P

and V),Vc c o m ~ r i s e s two v a l u e s . The f i r s t ,

Pml,

denends on

V , .

AccnrC.ing

A s

6

i s i n f i n i t e simnl

, E

can be a s s l ~ n e ? t o - e m i n c o n s t a n t i n s i d e

it

a t

i t s val-

ue a t -:he e m i t t e r s u r f z c e

c0.

Hence ;

'o '0, ,.f;ds, wheye

To= v -$

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797153

The seccnd va?ue,

Pm2

t7epenc?s 9n (V-Vc).

B a y e d on t h e above argument, me sug m st the ' o l l ~ ~ ~ ~ i n p bre akdntvn crr; ter:.r\r.

p,, = c

^{( 3}

2

where

9

^{m s}

i s

t h e value ~ f

?

^pi a t break- down vo%aSe and

C i s

a f ~ m c t i o n of gap parameters and gas p r e s s u r e .

A rrpriety of gaps >rodacing wide xa- nge of apnlied f i e l d divergence , f o r which a c c u r a t e breakclown voltage measurements were reyorted a t a wide p r e s s u r e range{4, 5 , 6 ]

,

were considered f o r t h e determ2

-

n a t i o n of t h e f u n c t i o n C.

Pas ^{i s}

^compu

-

t e d f o r each gap i n

i t s

corona-stabilized ph.?se of breakdown using t h e experimenta- l l y measured breakdown voltages. Accor

-

d i n g l y t h e fgllowing f 0rrn-e a r e deduced f o r C.

( i ) For p r e s s u r e s ur t o that; corre spon- ding t o t h e msximum break4ov:n v s l - t a g c , ??,

c = ~ = / r 1

-presents Vs, otherwise Vo i s incremen-ked an? a d i g5ta1 computer i t e r a t i v s process i s ner'orved 1:nti.l t h e condikior

i s

sa

-

t i s f i e d . 35-g.1 ( a ) i n d i c s t e s t h e c?ose a

: r e

ement observed between the e x p e r b e - n t a l l y measured v a l u e s of

Vs

and those com~uted according t o the sug-yestel c r i - t e r i o n . Fie. I.(b) d e p i c t s t h e f - d i s t - i

-

bution ~:.rl?Fle Fig. 1 ( c ) t o ( f ) d i ~ p l a y t h e E, : l i s t r i b u t i o n s p e y t i n e n t t o Vs tilt dS.ftenent pressllre values.

I n

t h e

E,

d i s t r i b ~ 1 f i o n s t h e a p g l i e d f e!.a eqhqnce- ment d ~ c t c c o r m ? ~ t a b i l l za"! on

i s

c k a r .

where A i s a c o n s t a n t whose value=

0.57

Y 10 C.P. bar-' and

Jr.

i s t h e r s t i o of t h e average t o

r.?xim7m

a ? n l i ~ d f i e l d s .

(iS.) For p r e s s u r e s P,\< P< pc, where Fc i s t h e miniram I r e s s u r e a t which co- rqna-f

res

b.renk5own occurs, reml- i n s c q a s t ? n t R+

i t s

~ 4 1 a t ~ 9

Qc.

4 se-9-empirical f o w u l a vrae pro- posed f

:r

comF,u+ini: Bc

C53 .

^Thi.;

^{i s}

^mo-

d i f teA

t?

f i t gaps hsvinq l a r g e r o t -radii.

The fo.-lruln. sugge sked has t h e form

-

P ^C

Tc e

/ r

0.85 x

lom2

:-:here PC i n h a r and

r

inat?.

P,,

i s

cmputed bp s r ~ b s % i t ~ ? t % n g t h e value o f

'k

obtsined a t PC i n e q u a t i o n ( 4 ) 2nd solv:n~ f o r P.

To comrute Vs ~ f a gap a t p r e s s l n e P,

an

a??roximate i n i t ' i a l value

Vo

equal t o

V

_C a t :? _C

i s

assumed f o r Vs.

9,

^corses-

pondins

t o Vo is

computed and ompared t o

~mscomputed from equation

(3).

I f t h e d i f f e w c o e i s within

2

0.05

PIS,

^{To re-}

Fig.1. Brcak?.own c h a r a c t e r i s t i c s of com- pressed SF6

i n

rod-to-plane gap.

REFErnCES

---

[I]

N.J. F e l i c i , D i r e c t C u r r e n t i P t . 11, (Cct. 1 % 3 ) 278

[2] ?,I.P. S'iarna an.? W. Janischawskyj,IEEE

~rans.Vol..PAS-88(l% 9)718

[3]

2l.S. kbou-Seada and I l h . A l . i , IEE23,IA.S paper, Toronto, Ontario, Canada, ( Oct

.

1978)193

141 C.N. Yorks and I.W. Dakin, AIEE 'Bans Pt. I , V01.72 (1%2)682

[5]

R.Haze?. and E.K~dfe1, IEEE Trans., Val. PLS-S (1976 )I78

[6] S.S~.ng!casaad, 1nter.H.V. Symp'osium, Zurich (1975 3379.