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DETERMINATION OF LOW PROBABILITY FIRST BREAKDOWN VOLTAGES IN COMPRESSED SF6
S. Vibholm, A. Pedersen, P. Thyregod
To cite this version:
S. Vibholm, A. Pedersen, P. Thyregod. DETERMINATION OF LOW PROBABILITY FIRST
BREAKDOWN VOLTAGES IN COMPRESSED SF6. Journal de Physique Colloques, 1979, 40 (C7),
pp.C7-289-C7-290. �10.1051/jphyscol:19797142�. �jpa-00219116�
JOURNAL DE PHYSIQUE CoZZoque C7, suppl6ment au no?, Tome 40, JuiZZet 2979, page C7- 289
DETERMINATION OF LOW PROBABILITY FIRST BREAKDOWN VOLTAGES IN COMPRESSED SF6
S. Vibhoirn, A. Pedersen and P. ~ h y r e ~ o d * .
*The Technical University, Department of Physics, &liZding 309B, DX-2800 Lyngby, Dewnark.
Tlze TechnicaZ University, IMSOR, Building 349, DK-2800 Lyngby, Denmark.
1. I n t r o d u c t i o n . t i o n s , e . g . n o r m a l , W e i b u l l o r d o u b l e ex- A m e t h o d i s d e s c r i b e d w h i c h d e t e r m i n e s p o n e n t i a l / 2 / .
t h e p r o b a b i l i t y f o r t h e f i r s t b r e a k d o w n By c h o o s i n g t h e n o r m a l i z e d d o u b l e ex- n e a r o n s e t . The m e t h o d i s u s e d i n a n a n a - p o n e n t i a l minimum d i s t r i b u t i o n
l y s i s o f t h e e f f e c t o f s u r f a c e r o u g h n e s s on low p r o b a b i l i t y f i r s t b r e a k d o w n i n com-
p r e s s e d SF6 a t p o s i t i v e p o l a r i t y . we o b t a i n 2 . E x p e r i m e n t a l d e s i g n .
A v o l t a g e l e v e l Uo j u s t b e l o w t h e w i t h s t a n d v a l u e i s s e l e c t e d s u c h t h a t b r e a k d o w n w i l l n e v e r o c c u r . N v o l t a g e i m - p u l s e s a r e t h e n a p p l i e d a t t h i s l e v e l . An- o t h e r . v o l t a g e l e v e l U1
=
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i s s e l e c - t e d a n d f u r t h e r N i m p u l s e s a r e a p p l i e d . T h i s i s c o n t i n u e d u n t i l t h e f i r s t b r e a k - down o c c u r s a t s h o t number n a t a l e v e l Uk = Uo + kAU. The v o l t a g e l e v e l Uk r e p r e - s e n t s t h e b r e a k d o w n v o l t a g e f o r a low v a l - u e f r a c t i l e . The v a l u e o f t h i s f r a c t i l e d e p e n d s on t h e c h o s e n v a l u e o f A U a n d N . 3. S t a t i s t i c a l t h e o r y .L e t p k ( U o ,AU,N,6,8) d e n o t e t h e p r o b a - b i l i t y f o r t h e f i r s t b r e a k d o w n o c c u r r i n g a t s t e p number k ( k = 1 , 2
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) w i t h t h e o r i g i n a t U o . The p a r a m e t e r s 6 a n d 8 a r e , r e s p e c t - i v e l y , t h e p o s i t i o n p a r a m e t e r a n d t h e s c a l e p a r a m e t e r o f t h e a s s o c i a t e d b r e a k d o w n d i s - t r i b u t i o n . Changes i n p o s i t i o n a n d s c a l e p a r a m e t e r s c a n b e c o m p e n s a t e d b y c h a n g e s i n o r i g i n a n d s t e p v a l u e . T h i s means t h a tAs a c h a n g e i n N c a n b e c o u n t e r a c t e d b y s h i f t i n g t h e p o s i t i o n of t h e o r i g i n , it i s s u f f i c i e n t t o c o n s i d e r N = 1.
A s e q u e n c e o f e l e m e n t a r y c a l c u l a t i o n s l e a d s t o t h e f o l l o w i n g e x p r e s i o n s
i n w h i c h k = 2 , 3
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g i v e s p k i n t h e i n t e r - v a l s (1.4 +n
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The f o l l o w i n g a p p r o x j m a t i o n s a r e now i n t r o - d u c e d :
1. p1 i s r e p l a c e d b y F o ( u +
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-
F o ( ~ + n + ( k - l ) A u ) 1 . T h i s means t h a t t h e n o n - t r u n c a t e d d i s t r i b u - C o n s i d e r i n g e x t r e m e l y l o w v a l u e f r a c -t i o n i s r e p l a c i n g t h e t r u n c a t e d d i s t r i b u - t i l e s o n l y , i t c a n b e shown t h a t by a s u i -
t i o n . t a b l e c h o i c e o f o r i g i n a n d s c a l e t h e r e i s
The mean v a l u e a n d v a r i a n c e of t h e h a r d l y a n y n o t i c e a b l e d i f f e r e n c e b e t w e e n
d i s t r i b u t i o n a r e t h e n g i v e n b y , r e s p e c t - t h e v a r i o u s p o s s i b l e p r o b a b i l i t y d i s t r i b u -
i v e l y
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Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797142
d i v i d u a l b r e a k d o w n . The a p p l i e d v o l t a g e was a 1 1 2 5 0 0 u s i m p u l s e wave o f p o s i t i v e p o l a r i t y . E a c h o f t h e . 50 c y l i n d e r s was i n w h i c h y = 0 . 5 7 7 2
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i s E u l e r ' s c o n s t a n t .A s s u m i n g t h a t A U h a s a s u f f i c i e n t l y s m a l l v a l u e t h e b r e a k d o w n p r o b a b i l i t y c o r - r e s p o n d i n g t o t h e mean v a l u e o f k w i l l b e g i v e n b y
i n w h i c h a k i s t h e s t a n d a r d d e v i a t i o n o f t h e s t e p n u m b e r by r e p e a t e d t e s t i n g .
4 . D e t e r m i n a t i o n o f low p r o b a b i l i t y f i r s t b r e a k d o w n i n c o m p r e s s e d SF 6'
The b r e a k d o w n w i t h s t a n d v o l t a g e o f a n S F - i n s u l a t e d h i g h v o l t a g e a p p a r a t u s i s
6
l a r g e l y c o n t r o l l . e d b y t h e i n h e r e n t s u r f a c e r o u g h n e s s o f t h e e l e c t r o d e s . T h i s e f f e c t i s s o c o m p l e x t h a t i t c a n o n l y b e d e t e r - m i n e d e x p e r i m e n t a l l y .
T e s t s w e r e c a r r i e d o u t i n SF6 a t a p r e s s u r e o f 5 b a r s on a s y s t e m o f c o a x i a l c y l i n d e r s , o f w h i c h t h e i n n e r c y l i n d e r was made o f a l u m i n i u m a n d h a d a d i a m e t e r o f 2 2 . 0 mm. The o u t e r c y l i n d e r was made o f s t a i n l e s s s t e e l w i t h a d i a m e t e r o f 5 9 . 8 mm a n d h a d s u i t a b l y r o u n d e d e d g e s . The o v e r - a l l l e n g t h o f t h e c y l i n d r i c a l p a r t was 8 0 mm. The o u t e r c y l i n d e r was u s e d t h r o y g h o u t t h e e x p e r i m e n t s , b u t was c a r e f u l l y c l e a n e d a f t e r e a c h i n d i v i d u a l s p a r k , w h e r e a s t h e i n n e r c y l i n d e r s w e r e d i s c a r d e d . a s s o o n a s t h e y h a d b e e n s u b j e c t e d t o o n e s i n g l e s p a r k . R e p e a t e d u s e o f t h e o u t e r c y l i n d e r i s j u s t i f i e d by t h e f a c t t h a t t h e e l e c t r i c f i e l d n e a r i t s s u r f a c e i s s o low t h a t no i o n i z i n g p r o c e s s e s a r e p o s s i b l e . F i v e s e t s o f i n n e r c y l i n d e r s w e r e u s e d , e a c h s e t c o n - s i s t i n g o f t e n c y l i n ' d e r s w i t h a c o n s t a n t s u r f a c e r o u g h n e s s Ra. W i t h i n e a c h s e t Ra v a r i e d n o more t h a n 1 0 % . B e f o r e t e s t i n g e a c h c y l i n d e r was c a r e f u l l y c l e a n e d i n . a n u l t r a s o n i c b a t h w i t h a s u i t a b l e c l e a n i n g a g e n t . The g a s was r e n e w e d a f t e r e a c h i n -
t e s t e d a c c o r d i n g t o t h e e x p e r i m e n t a l d e - s i g n w i t h N = 1 0 0 a n d A U = 2 kV. I t i s e s s e n t i a l t h a t e a c h s a m p l e i s s u b j e c t e d t o o n e b r e a k d o w n o n l y , b e c a u s e o n e s i n g l e s p a r k w i l l i n e v i t a b l y c h a n g e t h e c o n d i t i o n s i n t h e s y s t e m .
E a c h v o l t a g e l e v e l m u s t b e r e p r o d u c e - a b l e w i t h a h i g h d e g r e e o f a c c u r a c y . T h e s e r e q u i r e m e n t s w e r e r e a d i l y met b y a n a u t o m a - t i c i m p u l s e g e n e r a t o r 1 3 1 .
F o r t h e s y s t e m u n d e r c o n s i d e r a t i o n t h e t h e o r e t i c a l b r e a k d o w n v o l t a g e U t h f o r i d e a - l i z e d e l e c t r o d e s i s 535 kV t a k i n g i n t o a c - c o u n t t h a t t h e c o m p r e s s i b i l i t y f a c t o r f o r SF6 a t 5 b a r i s 0 . 9 4 1 4 1 . The e x p e r i m e n t a l r e s u l t s a r e s u m m a r i z e d i n T a b l e 1. The v a l - u e s g i v e n f o r U f o r e a c h i n d i v i d u a l s u r - f a c e r o u g h n e s s a r e b a s e d on a p p r o x i m a t e l y 4 0 , 0 0 0 s h o t s .
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0 . 0 6 0 . 7 7 5 396 0 . 0 7 0 . 0 4 - 0 . 1 1 0 . 7 4 3 5 3 2 1 0 . 1 9 0 . 1 0-
0 . 2 8 0 . 6 0T a b l e 1.
I t i s s e e n t h a t e v e n t h e b e s t p o l - i s h e d e l e c t r o d e s u r f a c e i s s u b j e c t e d t o a c o n s i d e r a b l e l o w e r i n g o f t h e f i r s t b r e a k - down v o l t a g e d u e t o t h e e f f e c t o f s u r f a c e r o u g h n e s s .
3 .
R e f e r e n c e s ./1/ S . V i b h o l m , A . P e d e r s e n , P. T h y r e g o d : P r o c . X I 1 1 I C P I G , P a r t I , p . 4 3 1 - 4 3 2 , B e r l i n 1 9 7 7 .
/ 2 / W . H a u s c h i l d , W . B i i r g e r : Z . e l e k t r . I n - f o r m . - ~ . E n e r g i e t e c h n i k
2 ,
p . 2 8 3 - 2 9 5 , L e i p z i g 1 9 7 5 ./ 3 / J . M . C h r i s t e n s e n , G . C . C r i c h t o n , I . W . M c A l l i s t e r , A . P e d e r s e n , S. V i b h o l m : I S H - Z i i r i c h , p . 1 2 8 - 1 3 3 , 1 9 7 5 .
/ 4 / B . H . C r i c h t o n , D ' . J . T e d f o r d : J . P h y s . D :
~ p p l . p h y s .
