UBC Theses and Dissertations

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UBC Theses and Dissertations

High-voltage measurement techniques 1980

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H I G H - V O L T A G E MEASUREMENT T E C H N I Q U E S b y A r m a n d G r e g o i r e | H a l i m B . E . E . , S e a t t l e U n i v e r s i t y , W a s h i n g t o n , 1 9 7 8 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T OF THE R E Q U I R E M E N T S FOR THE D E G R E E OF M A S T E R OF A P P L I E D S C I E N C E i n THE F A C U L T Y OF G R A D U A T E S T U D I E S ( D e p a r t m e n t o f E l e c t r i c a l E n g i n e e r i n g ) We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE U N I V E R S I T Y OF B R I T I S H C O L U M B I A J u n e , 1 9 8 0 ( c ) A r m a n d G r e g o i r e H a l i m , 1 9 8 0 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i lab le for reference and study. I further agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thesis fo r f inanc ia l gain sha l l not be allowed without my written permission. The Univers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Depa rtment r. -11 ABSTRACT The Department of Electrical Engineering at the University of British Columbia acquired a high-voltage test set in 1979 for teaching and re- search purposes. To make this test set useful for experiments which un- dergraduate students can do themselves, various additions and modifications had to be made. This thesis describes these additions and modifications. F i r s t , a Faraday cage had to be constructed with interlocking safety ci r c u i t s . Ex- periments were then developed to show basic high-voltage phenomena with AC voltage, with DC voltage, and with impulse voltages. Considerable modifications were required to eliminate noise in the impulse measuring system. i i i T A B L E OF CONTENTS A B S T R A C T . 1 1 T A B L E OF CONTENTS » 1 1 1 L I S T OF T A B L E S ^ l L I S T OF I L L U S T R A T I O N S v i ACKNOWLEDGEMENTS v i i l 1 . I N T R O D U C T I O N 1 1 . 1 S i g n i f i c a n c e 1 1 . 2 T e s t e q u i p m e n t 2 1 . 3 S c o p e o f t h i s T h e s i s 2 2 . G E N E R A T I O N OF H I G H V O L T A G E S 3 2 . 1 I n t r o d u c t i o n 3 2 . 2 A l t e r n a t i n g V o l t a g e 3 2 . 3 D i r e c t V o l t a g e 6 2 . 4 I m p u l s e V o l t a g e 1 0 3 . M E A S U R E M E N T S 1 3 3 . 1 I n t r o d u c t i o n . • I 3 3 . 2 A C v o l t a g e m e a s u r e m e n t s 14 3 . 2 . 1 O b j e c t i v e • 14 3 . 2 . 2 M e a s u r i n g D e v i c e s • 14 3 . 3 DC v o l t a g e m e a s u r e m e n t s . . 23 3 . 3 . 1 O b j e c t i v e 23 3 . 3 . 2 M e a s u r i n g D e v i c e s 23 3 . 4 I m p u l s e v o l t a g e m e a s u r e m e n t s 29 3 . 4 . 1 O b j e c t i v e 2 9 3 . 4 . 2 S e t u p o f M e a s u r i n g S y s t e m 3 0 3 . 4 . 3 N o i s e i n M e a s u r i n g S y s t e m s 42 i v 4 . E X P E R I M E N T E X E R C I S E S . 4 8 4 . 1 I n t r o d u c t i o n . . . . . . . . . . 48 4 . 2 A C t e s t 4 9 4 . 2 . 1 B r e a k d o w n v o l t a g e o f s p h e r e g a p s . . . . . . . . . 4 9 4 . 2 . 2 C o r o n a v o l t a g e o f a s i n g l e c o n d u c t o r a n d a b u n d l e c o n d u c t o r 5 0 A • 3 DC t e s t • • > » * • > • • • • • > « « > o « » « * ' • > • « » « « • • 5 1 4 . 3 . 1 R i p p l e m e a s u r e m e n t . . . . . . . . . . 5 1 4 . 3 . 2 P o l a r i t y e f f e c t i n a P o i n t - P l a n e g a p . . . . . . . 53 4 . 4 I m p u l s e t e s t 54 4 . 4 . 1 P r e l i m i n a r y P r e p a r a t i o n s 54 4 . 4 . 2 N o i s e R e d u c t i o n s 57 5 . C O N C L U S I O N S 60 L I S T OF R E F E R E N C E S 61 A P P E N D I X I 62 A P P E N D I X I I 66 V LIST OF TABLES Table Page 1. Flashover v o l t a g e s f o r AC v o l t a g e s , f o r DC v o l t a g e s of e i t h e r p o l a r i t y , and f o r f u l l negative standard impulses and impulses w i t h longer t a i l s . . . 16 2. Breakdown v o l t a g e s of a sphere gap of 10 cm diameter f o r d i f f e r e n t gap spacings. . . 49 3. Corona onset v o l t a g e s of a s i n g l e conductor and a bundle conductor. 51 4. Percent r i p p l e s f o r d i f f e r e n t values of DC v o l t a g e s . ? . . • • 52 . L I S T OF I L L U S T R A T I O N S F i g u r e P a g e 1. E f f e c t o f t i m e o n w i t h s t a n d v o l t a g e 2 2. S i n g l e - s t a g e t e s t t r a n s f o r m e r c i r c u i t s 4 3. T h r e e - s t a g e t e s t t r a n s f o r m e r c a s c a d e 5 4. S e r i e s r e s o n a n t c i r c u i t f o r s i n g l e t r a n s f o r m e r / r e a c t o r u n i t 6 5. H a l f - p e r i o d r e c t i f i c a t i o n w i t h i d e a l c i r c u i t e l e m e n t s 7 6. V i l l a r d c i r c u i t 8 7. G r e i n a c h e r d o u b l e r - c i r c u i t 8 8. Z i m m e r m a n n - W i t t k a c i r c u i t 9 9. G r e i n a c h e r c a s c a d e c i r c u i t 9 10. E x a m p l e o f c a s c a d e r e c t i f i e r c i r c u i t s 10 11. B a s i c i m p u l s e - v o l t a g e c i r c u i t s 11 12. M u l t i p l i e r c i r c u i t a f t e r M a r x f o r 3 s t a g e s i n c i r c u i t l i b c o n n e c t i o n •> 12 13. S p h e r e g a p s f o r v o l t a g e m e a s u r e m e n t 17 14. B r e a k d o w n v o l t a g e ÛQ o f s p h e r e g a p s a s a f u n c t i o n o f g a p s p a c i n g s , f o r v a r i o u s s p h e r e d i a m e t e r s D . • • 17 15. P e a k v o l t a g e m e a s u r e m e n t a c c o r d i n g t o C h u b b a n d F o r t e s c u e 18 16. P e a k v o l t a g e m e a s u r e m e n t w i t h c a p a c i t i v e d i v i d e r - • • 20 17. B a s i c c i r c u i t s o f v o l t a g e t r a n s f o r m e r s 22 18. M e a s u r e m e n t o f DC v o l t a g e b y m e a n s o f a h i g h - v o l t a g e r e s i s t o r 24 19. M e a s u r e m e n t o f a DC v o l t a g e b y m e a n s o f a r e s i s t i v e d i v i d e r 25 20. E l e c t r o s t a t i c v o l t m e t e r s f o r h i g h v o l t a g e s 26 21. V o l t m e t e r w i t h t h e s p h e r e - p l a t e e l e c t r o d e c o n f i g u r a t i o n 27 v i i 22. C i r c u i t f o r measuring r i p p l e v o l t a g e s . . 28 23. Jumping p o t e n t i a l i n impulse generator system . . . . 31 24. Block diagram of impulse t e s t f a c i l i t y 34 25. D i s p l a y of a wedge-shaped impulse voltage 36 26. Impulse waveshapes obtained w i t h the c a p a c i t i v e d i v i d e r of 4.14 yF lower capacitance value .37 27. Impulse v o l t a g e measuring system w i t h r e s i s t i v e d i v i d e r 39 28. Connection of the c a p a c i t i v e v o l t a g e d i v i d e r to a cathode-ray o s c i l l o s c o p e 40 29. Compensation of s i g n a l cable capacitance by a complex cable t e r m i n a t i o n 41 30. Impedance matching f o r damped c a p a c i t i v e v o l t a g e d i v i d e r s 41 31. Impulse voltage generating and measuring systems. . . 42 32. Currents induced i n the cable s h i e l d s by q u a s i - s t a t i o n a r y magnetic f i e l d s 45 33. Correct measurement c i r c u i t l a y o u t , a v o i d i n g cable b r a i d and cabinet current i n t e r f e r e n c e 46 34. O v e r a l l c i r c u i t of the r i p p l e measurement experiment. . 52 35. P o l a r i t y e f f e c t i n a point-plane gap 53 36. Output of a compensated attenuator f o r d i f f e r e n t degrees of compensation 55 37. Impulse v o l t a g e waveform obtained by using EMTP . . . 56 38. a. Impulse o s c i l l o g r a m of the c i r c u i t w i t h ground loops and an or d i n a r y c o a x i a l cable 58 b. Impulse o s c i l l o g r a m of the c i r c u i t w i t h reduced ground loops and a s h i e l d e d cable 58 39. Impulse o s c i l l o g r a m of the c i r c u i t w i t h reduced ground loops and a s h i e l d e d cable. O s c i l l o s c o p e i s i n s i d e a metal box 59 v i ' i i ACKNOWLEDGEMENTS I w o u l d l i k e t o e x p r e s s my t h a n k s t o my s u p e r v i s o r , D r . H . W . D o m m e l , f o r h i s h e l p t h r o u g h o u t t h i s w o r k a n d f o r t h e t i m e l y s u g g e s t i o n s a n d c o r r e c - t i o n s h e m a d e . A l s o , I w i s h t o c o n v e y my g r a t i t u d e t o D r . D . V a n D o m m e l e n , a v i s i t i n g p r o f e s s o r f r o m T h e K a t h o l i e k e U n i v e r s i t e i t T e L e u v e n ( B e l g i u m ) , f o r h i s c o n s i d e r a b l e h e l p . I am a l s o v e r y g r a t e f u l t o N a t u r a l S c i e n c e s a n d E n g i n e e r i n g R e s e a r c h C o u n c i l o f C a n a d a f o r t h e i r f i n a n c i a l s u p p o r t . 1 1 . I N T R O D U C T I O N A w i t h s t a n d v o l t a g e t e s t s u b j e c t s a n i n s u l a t i o n f o r a r e s t r i c t e d p e r i o d o f t i m e t o a v o l t a g e s t r e s s g r e a t e r t h a n t h a t e n c o u n t e r e d u n d e r n o r m a l s e r v i c e c o n d i t i o n s . T h e v o l t a g e s p e c i f i e d f o r a w i t h s t a n d t e s t may b e o f A C , DC ( h a v i n g a s p e c i f i e d p o l a r i t y w i t h r e s p e c t t o g r o u n d ) , o r a p u l s e h a v i n g a s p e c i f i e d p o l a r i t y a n d w a v e - s h a p e . F o r A C o r DC t e s t v o l t a g e s , t h e d u r a t i o n o f a p p l i c a t i o n i s s p e c i f i e d , t y p i c a l l y 1 m i n u t e a f t e r t h e d e s i r e d t e s t v a l u e h a s b e e n ^ r e a c h e d . ^ F o r a n i m p u l s e t h e w a v e s h a p e i s d e t e r m i n e d b y t h e v i r t u a l r i s e t i m e a n d t h e v i r t u a l t i m e t o h a l f v a l u e . A s t a n d a r d l i g h t n i n g p u l s e h a s 1 . 2 y s e c v i r t u a l r i s e t i m e a n d 5 0 y s e c v i r t u a l t i m e t o h a l f v a l u e . 1-. 1 S i g n i f i c a n c e T h e w i t h s t a n d v o l t a g e t e s t i s a d e m o n s t r a t i o n t h a t a n i n s u l a t i o n c a n w i t h s t a n d a s p e c i f i e d o v e r - v o l t a g e f o r a s p e c i f i e d l e n g t h o f t i m e . S u c c e s s - f u l c o m p l e t i o n o f t h e t e s t g i v e s some a s s u r a n c e t h a t n o g r o s s d e f e c t i s p r e s e n t i n t h e i n s u l a t i o n s t r u c t u r e . H o w e v e r , t h i s d o e s n o t m e a n t h a t t h e i n s u l a t i o n i s a b s o l u t e l y f r e e o f d e f e c t s . F o r t h i s r e a s o n t h e t e s t i s o f t e n s u p p l e m e n t e d w i t h m e a s u r e m e n t s o f i n s u l a t i o n c h a r a c t e r i s t i c s ( P r a c t i c a l D i e l e c t r i c S t r e n g t h ) . P r a c t i c a l D i e l e c t r i c S t r e n g t h t e s t s a r e d o n e w i t h c o n t i n u e d a p p l i c a t i o n o f a v o l t a g e b e l o w t h e v a l u e r e q u i r e d t o c a u s e i m m e d i a t e b r e a k d o w n . T h i s w i l l c a u s e t h e t e m p e r a t u r e t o r i s e i n l o c a l w e a k r e g i o n s . T h e t e m p e r a t u r e r i s e f u r t h e r r e d u c e s t h e d i e l e c t r i c s t r e n g t h o f t h e s e r e g i o n s , a n d c o n s e q u e n t l y t h e o v e r a l l d i e l e c t r i c s t r e n g t h o f t h e m a t e r i a l , a n d may r e s u l t i n e v e n t u a l f a i l u r e w i t h o u t f u r t h e r i n c r e a s e i n t h e a p p l i e d v o l t a g e . F i g u r e 1 i l l u s t r a t e s t h e g e n e r a l b e h a v i o u r o f a n i n s u l a t o r i n t e r m s o f w i t h s t a n d v o l t a g e v e r s u s 2 t i m e o f v o l t a g e a p p l i c a t i o n . - W i t h s t a n d v o l t a g e , p e a k v a l u e 0 8 T i m e , s e c o n d s F i g u r e 1 : E f f e c t o f t i m e o n w i t h s t a n d v o l t a g e . 1 . 2 T e s t E q u i p m e n t T e s t e q u i p m e n t t y p i c a l l y c o n s i s t s o f a v o l t a g e s o u r c e a n d a m e a s u r i n g s y s t e m . T h e v o l t a g e s o u r c e w h i c h i s e i t h e r o f A C , D C , o r I m p u l s e t y p e c a n b e c o n s t r u c t e d w i t h d i f f e r e n t m e t h o d s . A r e v i e w o f t h e s e v a r i o u s v o l t a g e s o u r c e s w i l l b e d o n e i n t h i s t h e s i s . V a r i o u s m e a s u r i n g a p p a r a t u s w i l l a l s o b e d i s c u s s e d i n t h i s t h e s i s . 1 . 3 S c o p e o f t h i s T h e s i s F i r s t , t h e g e n e r a t i o n o f h i g h v o l t a g e s a n d t h e i r m e a s u r e m e n t s a r e d i s - c u s s e d i n g e n e r a l a n d i n p a r t i c u l a r a s t h e y r e l a t e t o t h e UBC h i g h - v o l t a g e t e s t s e t . A n e x t e n s i v e i n v e s t i g a t i o n o f t h e i m p u l s e m e a s u r i n g s y s t e m o f t h e UBC h i g h - v o l t a g e t e s t s e t i s t h e n d e s c r i b e d . V a r i o u s t e c h n i q u e s o f s h i e l d i n g h a d t o b e u s e d t o o b t a i n r e a s o n a b l y a c c u r a t e o s c i l l o g r a m s . F i n a l l y , a s e r i e s o f e x e r c i s e s f o r u n d e r g r a d u a t e s t u d e n t s i s p r e s e n t e d w h i c h w a s d e v e l o p e d w i t h t h e h e l p o f D r . V a n D o m m e l e n . 3 2 . G E N E R A T I O N OF H I G H V O L T A G E S 2 . 1 . I n t r o d u c t i o n H i g h - v o l t a g e p o w e r e q u i p m e n t i s t e s t e d w i t h t h r e e t y p e s o f v o l t a g e s t o v e r i f y i t s p e r f o r m a n c e . T h e s e a r e : ( a ) A C v o l t a g e ( b ) DC v o l t a g e ( c ) I m p u l s e v o l t a g e G e n e r a t i o n o f h i g h v o l t a g e s i n l a b o r a t o r i e s i s u s u a l l y d o n e u s i n g t r a n s - f o r m e r s , t h e r e f o r e , t h e f i r s t t y p e o f h i g h v o l t a g e p r o d u c e d i s o f A C t y p e . W i t h a d d i t i o n a l c i r c u i t s , t h e A C v o l t a g e c a n t h e n b e t r a n s f o r m e d i n t o DC a n d i m p u l s e v o l t a g e s . DC v o l t a g e c a n a l s o b e p r o d u c e d d i r e c t l y b y e l e c t r o s t a t i c g e n e r a t o r s . T h e U B C - H i g h V o l t a g e T e s t S e t c a n p r o d u c e a l l t h r e e f o r m s , n a m e l y 6 0 H z A C v o l t a g e u p t o 7 5 K V r m s , DC v o l t a g e u p t o 2 0 0 K V , a n d i m p u l s e v o l t a g e u p t o 2 0 0 K V . 2 . 2 A l t e r n a t i n g V o l t a g e T r a n s f o r m e r s f o r g e n e r a t i n g h i g h a l t e r n a t i n g v o l t a g e s i n l a b o r a t o r i e s g e n e r a l l y h a v e c o n s i d e r a b l y l o w e r p o w e r r a t i n g a n d f r e q u e n t l y m u c h l a r g e r t u r n r a t i o s t h a n p o w e r t r a n s f o r m e r s . T h e p r i m a r y c u r r e n t i s u s u a l l y s u p p l i e d b y a r e g u l a t i n g t r a n s f o r m e r f e d f r o m m a i n s s u p p l y . O n e e n d o f t h e h i g h - v o l t a g e w i n d i n g i s u s u a l l y g r o u n d e d , e x c e p t f o r t r a n s f o r m e r s t o b e c o n n e c t e d i n c a s c a d e w h e r e t h e w i n d i n g s m u s t b e c o m p l e t e l y i s o l a t e d . F i g u r e 2 s h o w s t w o b a s i c c i r c u i t s o f t e s t t r a n s f o r m e r s . T h e l e n g t h o f v o l t a g e a r r o w s i n d i c a t e s t h e m a g n i t u d e o f t h e s t r e s s o n t h e i n s u l a t i o n b e t w e e n t h e h i g h v o l t a g e w i n d i n g H a n d t h e e x c i t a t i o n w i n d i n g E o r i r o n c o r e 4 F . T h e f u i l y i s o l a t e d w i n d i n g may b e g r o u n d e d i f n e c e s s a r y a t e i t h e r o f t h e t w o t e r m i n a l s o r a t t h e c e n t e r t a p , a s s h o w n . ( a ) ( b ) F i g u r e 2 : S i n g l e s t a g e t e s t t r a n s f o r m e r c i r c u i t s E - E x c i t a t i o n w i n d i n g ( a ) S i n g l e p o l e i s o l a t i o n H - H i g h - v o l t a g e w i n d i n g ( b ) F u l l y i s o l a t e d F - I r o n c o r e To g e n e r a t e v o l t a g e s a b o v e a f e w h u n d r e d K V , s i n g l e - s t a g e t r a n s f o r m e r s a c c o r d i n g t o F i g u r e 2 a r e n o w r a r e l y u s e d ; f o r e c o n o m i c a l a n d t e c h n i c a l r e a s o n s o n e e m p l o y s i n s t e a d a s e r i e s c o n n e c t i o n o f t h e h i g h v o l t a g e w i n d i n g s o f s e v e r a l t r a n s f o r m e r s ( i n t r o d u c e d i n 1 9 1 5 b y W. P e t e r s e n F . D e s s a u e r a n d o E.. W e l t e r ) . T h e c i r c u i t c o n f i g u r a t i o n i s s h o w n i n F i g u r e 3 . T h e e x c i t a t i o n w i n d i n g s E o f t h e u p p e r s t a g e s a r e s u p p l i e d f r o m t h e c o u p l i n g w i n d i n g s K o f t h e s t a g e s i m m e d i a t e l y b e l o w . T h e i n d i v i d u a l s t a g e s , e x c e p t f o r t h e u p p e r m o s t , c o n s i s t o f t h r e e - b i n d i n g t r a n s f o r m e r s . 5 K E 3 P I 3 U - • 3 P H Figure 3: Three-stage test transformer cascade E - Excitation winding H - High-voltage winding K - Coupling winding For test objects with large capacitance, for example cables, a series resonant circuit is usually used to generate the high voltage. The basic circuit is shown in Figure 4 . It comprises the load, which is almost purely capacitive, in series with a continuously variable inductance. The inductance is varied to produce series resonance with the capacitive load at the supply frequency. High voltages are then obtained by injecting current into the" series ci r c u i t . Control of the high voltage is obtained by regulation of the supply current. Some of the advantages of series resonant circuits are as follows: 1. Harmonics, which are caused by saturation in the transformers, are attenuated. 2 . If failure of the test object occurs, a power arc does not develop. Instead, the voltage collapses immediately after the load capacitance is short-circuited. This is of great importance to the cable industry where a power arc can sometimes lead to dangerous explosions. 6 R e a c t o r C a b l e u n d e r t e s t A C S u p p l y L l r l L r r r 1 J ( b ) F i g u r e 4 : S e r i e s r e s o n a n t c i r c u i t f o r s i n g l e t r a n s f o r m e r / r e a c t o r u n i t . ( a ) a c t u a l c i r c u i t ( b ) e q u i v a l e n t c i r c u i t T h e s e r i e s r e s o n a n t c i r c u i t h a s now b e c o m e a c c e p t e d f o r c a b l e t e s t i n g . M a n y o t h e r l a b o r a t o r i e s h a v e a l s o u s e d t h e c i r c u i t f o r g e n e r a l a p p l i c a t i o n s . T h e UBC h i g h - v o l t a g e t e s t s e t u s e s a s i n g l e t r a n s f o r m e r w i t h o n e e n d g r o u n d e d . 2 . 3 D i r e c t V o l t a g e T h e s i m p l e s t c i r c u i t f o r t h e g e n e r a t i o n o f a . . . h i g h DC v o l t a g e i s t h e h a l f - p e r i o d r e c t i f i e r , s h o w n i n F i g u r e 5 . T h e c i r c u i t w i t h o u t t h e s m o o t h i n g c a p a c i - t o r C w i l l g i v e a p u l s a t i n g d i r e c t v o l t a g e , a n d w i t h s m o o t h i n g c a p a c i t o r C a s m o o t h e d d i r e c t v o l t a g e w i t h r e s i d u a l r i p p l e i s o b t a i n e d . 7 4 Figure 5 : H a l f - p e r i o d r e c t i f i c a t i o n w i t h i d e a l c i r c u i t - e l e m e n t s . a) C i r c u i t b) Output voltage curve without smoothing c a p a c i t o r C c) Output voltage curve w i t h smoothing c a p a c i t o r C To o b t a i n higher d i r e c t v o l t a g e s , voltage m u l t i p l i e r c i r c u i t s are used. Some of these voltage m u l t i p l i e r c i r c u i t s are: 1. V i l l a r d c i r c u i t . 2 . Greinacher D o u b l e r - c i r c u i t . 3. Zimmermann-Wittka c i r c u i t . 4. Greinacher cascade c i r c u i t . 5. S e p a r a t e - r e c t i f i e r cascade c i r c u i t . V i l l a r d c i r c u i t : This c i r c u i t , shown i n Figure 6, i s the simplest doubling c i r c u i t . The b l o c k i n g c a p a c i t o r C i s charged to the peak value and thus increases the p o t e n t i a l of the high-voltage output t e r m i n a l w i t h respect to the transformer v o l t a g e by t h i s amount. However, smoothing of the output voltage u ( t ) i s impossible. 8 C Figure 6: Villard circuit a) Circuit diagram b) Voltage curve Greinacher Doubler-circuit: Extension of the Villard circuit by a r e c t i f i e r V2 and a smoothing capacitor C2 enables the no-load output voltage of the Villard circuit to be smoothed. The complete circuit i s shown in Figure 7 $ (a) " (b) Figure 7: Greinacher doubler-circuit a) Circuit diagram b) Voltage curve Zimmermann-Wittka ci r c u i t : If two Villard circuits are connected in opposition as in Figure 8, an unsmoothed direct voltage is produced between 9 the output t e r m i n a l s , w i t h a, peak va lue th ree t imes tha t of the t ransformer vo l t a g e and, under no l oad c o n d i t i o n s , a mean output v o l t a g e U = 2. Uj,, • t (a). (b) F igu re 8: Zimmermann-Wittka c i r c u i t (no- load c o n d i t i o n ) a) C i r c u i t d iagram b) Vo l tage curve Gre inacher cascade c i r c u i t : Th is i s an ex tens ion of Gre inacher Doub le r - c i r c u i t . ^ A t h r e e - s t a g e c i r c u i t i s shown i n F i gu re 9 as an example; many p r a c - t i c a l c i r c u i t s compr ise on ly the pa r t s shown i n b o l d l i n e s . U = 6U> F igu re 9: Gre inacher cascade c i r c u i t (no - load c o n d i t i o n ) . S e p a r a t e - r e c t i f i e r cascade c i r c u i t : Th is c i r c u i t , shown i n F igu re 10, g i ves low r i p p l e and vo l t age drops even when output cu r ren t s are h i g h . 10 F i g u r e 10: E x a m p l e o f c a s c a d e r e c t i f i e r c i r c u i t s ( n o - l o a d c o n d i t i o n ) DC v o l t a g e c a n a l s o b e g e n e r a t e d e l e c t r o s t a t i c a l l y , n a m e l y , b y u s i n g e l e c t r o s t a t i c g e n e r a t o r s . B e c a u s e o f i t s l o w p o w e r r a t i n g , t h i s m e t h o d i s n o t u s e d v e r y o f t e n . T h e g e n e r a t i o n o f h i g h DC v o l t a g e s i n t h e UBC l a b o r a t o r y i s d o n e w i t h t h e h a l f - p e r i o d r e c t i f i e r c i r c u i t f o r t h e 100 k V l e v e l a n d t h e G r e i n a c h e r d o u b l e r - c i r c u i t f o r t h e 200 k V l e v e l . 2.4 I m p u l s e V o l t a g e F i g u r e 11 s h o w s t h e t w o m o s t i m p o r t a n t b a s i c c i r c u i t s u s e d f o r t h e g e n e r a - t i o n o f i m p u l s e v o l t a g e s . T h e i m p u l s e c a p a c i t o r C s i s c h a r g e d v i a a h i g h - o h m i c c h a r g i n g r e s i s t a n c e t o a DC v o l t a g e UQ a n d t h e n d i s c h a r g e d b y i g n i t i o n o f t h e s w i t c h g a p F . T h e d e s i r e d i m p u l s e v o l t a g e u ( t ) a p p e a r s a c r o s s t h e l o a d c a p a c i t o r C t c T h e v a l u e s o f t h e c i r c u i t e l e m e n t s d e t e r m i n e t h e w a v e s h a p e o f t h e i m p u l s e v o l t a g e . A s h o r t r i s e t i m e r e q u i r e s r a p i d c h a r g i n g o f C ^ t o t h e p e a k v a l u e U, a n d l o n g d e c a y t i m e s r e q u i r e s l o w d i s c h a r g i n g . T h i s i s a c h i e v e d b y •11 uo ( t = 0 ) R* I I c i r c u i t a u ( t ) ( t = 0 ) ( a ) c i r c u i t h u ( t ) L i g h t n i n g i m p u l s e v o l t a g e T s = 1 . 2 y s T r = 50 y s S w i t c h i n g i m p u l s e v o l t a g e T C r = 2 5 0 y s T h = 2 5 0 0 y s ( b ) • F i g u r e 1 1 : B a s i c i m p u l s e - v o l t a g e c i r c u i t s . a ) C i r c u i t s b ) V o l t a g e c u r v e s R e >> R ^ . To o b t a i n a p e a k v a l u e U a s h i g h a s p o s s i b l e o n e h a s t o c h o o s e C s >> C ^ . T h e e x p o n e n t i a l r i s e o n t h e w a v e f r o n t h a s a t i m e c o n s t a n t R ^ C ^ w h e r e a s t h e d e c a y o n t h e t a i l h a s a t i m e c o n s t a n t C g C R ^ + R e ) f o r c i r c u i t a , C S R £ f o r c i r c u i t b . T h e o u t p u t v o l t a g e c u r v e s o f t h e l i g h t n i n g i m p u l s e a n d t h e s w i t c h i n g i m p u l s e a r e s h o w n i n F i g u r e l i b . To g e n e r a t e i m p u l s e v o l t a g e s w i t h a p e a k v a l u e h i g h e r t h a n t h e DC c h a r g i n g v o l t a g e , o n e c o m m o n l y u s e s t h e m u l t i p l i e r c i r c u i t p r o p o s e d b y E . M a r x i n 1 9 2 3 . 2 > 3 S e v e r a l i d e n t i c a l i m p u l s e c a p a c i t o r s a r e c h a r g e d i n p a r a l l e l a n d t h e n d i s c h a r g e d i n s e r i e s , g i v i n g a m u l t i p l i e d t o t a l c h a r g i n g v o l t a g e w h i c h c o r r e s p o n d s t o t h e n u m b e r o f s t a g e s . A s a n e x a m p l e , a t h r e e - s t a g e m u l t i p l i e r c i r c u i t i s s h o w n i n F i g u r e 1 2 . A l l i m p u l s e c a p a c i t o r s C s ' a r e c h a r g e d t o t h e s t a g e c h a r g i n g - v o l t a g e UQ', 12 F i g u r e 1 2 : M u l t i p l i e r c i r c u i t a f t e r M a r x f o r 3 s t a g e s i n c i r c u i t l i b c o n n e c t i o n . v i a t h e h i g h c h a r g i n g r e s i s t o r s R ^ ' . When a l l t h e s w i t c h g a p s F b r e a k d o w n , t h e c a p a c i t o r s C g ' w i l l b e c o n n e c t e d i n s e r i e s s o t h a t i s c h a r g e d v i a t h e s e r i e s c o n n e c t i o n o f a l l d a m p i n g r e s i s t o r s R ( j ' ; f i n a l l y , a l l C s ' a n d C ^ w i l l d i s c h a r g e a g a i n v i a t h e r e s i s t o r s R £ ' a n d R ^ ' . T h e n - s t a g e c i r c u i t c a n b e r e d u c e d t o a s i n g l e s t a g e e q u i v a l e n t c i r c u i t w h e r e t h e f o l l o w i n g r e l a t i o n - s h i p s h o l d : U 0 = n U 0 ' R d = n R d ' C = - C ' R = n R ' s n s e e T h e UBC h i g h - v o l t a g e t e s t s e t u s e s t h e c c i r c u i t ' s h o w n i n - F i g u r e l i b a n d c a n p r o d u c e b o t h t h e s t a n d a r d l i g h t n i n g i m p u l s e v o l t a g e c a n d t h e s w i t c h i n g i m p u l s e v o l t a g e . 1 3 3 . MEASUREMENTS 3 . 1 I n t r o d u c t i o n I t i s g e n e r a l l y n o t p r a c t i c a l t o m e a s u r e h i g h v o l t a g e s o r c u r r e n t s d i r e c t l y . T h e u s u a l : p r o c e d u r e i s t o c o n v e r t t h e q u a n t i t y t o b e m e a s u r e d t o a l o w v o l t a g e o r c u r r e n t w h i c h c a n b e m e a s u r e d w i t h c o n v e n t i o n a l i n s t r u - m e n t s o r o s c i l l o s c o p e s . A h i g h - v o l t a g e o r h i g h - c u r r e n t m e a s u r i n g s y s t e m g e n e r a l l y c o m p r i s e s : ( a ) A c o n v e r t i n g d e v i c e ; f o r e x a m p l e , a v o l t a g e d i v i d e r , a v o l t a g e t r a n s f o r m e r , a h i g h - v o l t a g e m e a s u r i n g i m p e d a n c e , e t c . ( b ) T h e l e a d s r e q u i r e d f o r c o n n e c t i n g t h i s d e v i c e i n t o t h e t e s t c i r c u i t . ( c ) A m e a s u r i n g c a b l e , t o g e t h e r w i t h a n y a t t e n u a t i n g , t e r m i n a t i n g , a n d a d a p t i n g i m p e d a n c e s o r n e t w o r k s . ( d ) T h e i n d i c a t i n g o r r e c o r d i n g i n s t r u m e n t . I n t h e UBC l a b o r a t o r y b o t h r e s i s t i v e a n d c a p a c i t i v e d i v i d e r s a r e u s e d . T h e r e s i s t i v e d i v i d e r i s u s e d f o r DC m e a s u r e m e n t s , a n d t h e c a p a c i t i v e d i v i d e r f o r A C a n d i m p u l s e m e a s u r e m e n t s . F o r i m p u l s e m e a s u r e m e n t s t h e c a p a c i t i v e d i v i d e r i s a p a r t o f t h e i m p u l s e g e n e r a t o r c i r c u i t . T h e m e a s u r i n g c a b l e , w h i c h c o n n e c t s t h e l o w v o l t a g e s i d e o f t h e d i v i d e r w i t h t h e r e c o r d i n g i n s t r u m e n t , i s o f c o a x i a l t y p e . C o a x i a l c a b l e s h a v e t h e a d v a n t a g e o f s m a l l s e l f - i n d u c t a n c e a n d a s h i e l d i n g e f f e c t w h i c h m i n i m i z e s t h e d i s t o r t i o n o f t h e s i g n a l . A C / D C v o l t m e t e r s a n d i m p u l s e p e a k - v o l t m e t e r s a r e v e r y common i n d i c a t i n g i n s t r u m e n t s . T h e y a r e u s u a l l y p r o v i d e d w i t h t h e H V - t e s t set. T o o b s e r v e t h e w a v e f o r m a n o s c i l l o s c o p e i s g e n e r a l l y u s e d . H o w e v e r , n e w e r e q u i p m e n t o f t e n u s e s d i g i t a l t r a n s i e n t r e c o r d e r s , w i t h w h i c h i m p u l s e w a v e f o r m s c a n b e a n a l y z e d m o r e e a s i l y . 14 In regard to d i r e c t measurements of h i gh v o l t a g e s , v o l t a g e gaps such as sphere gaps are commonly used; peak v o l t a g e s are then ob ta i ned . D i r e c t measurement o f DC vo l t ages can a l s o be done by an e l e c t r o s t a t i c vo l tme te r . 3.2 AC Vo l tage Measurements 3 .2 .1 Obj e c t i v e The main o b j e c t i v e of AC measurements i s to measure the peak or rms va lue of the v o l t a g e , t y p i c a l l y w i t h an e r r o r of not more than 3%.^ Th is e r r o r requirement w i l l be met i f the v o l t a g e r a t i o of the v o l t a g e d i v i d e r or v o l t a g e t rans former i s s t a b l e and known w i t h an e r r o r of l e s s than 1%.4 i n the case of high- impedance systems, such as a vo l t age d i v i - d e r s , i t may not be p o s s i b l e to comply w i t h t h i s e r r o r requ i rement . In such cases an o v e r a l l e r r o r of s l i g h t l y more than 3% may have to be accep ted . The secondary o b j e c t i v e i s to measure the ampl i tude of harmonics , t y p i c a l l y w i t h an e r r o r of not more than 10% of the harmonic ampl i tude or not more than 1% of the fundamenta l , whichever i s l a r g e r . ^ Harmonic measurements r e q u i r e a wave ana l yse r i n a d d i t i o n to the e x i s t i n g equipment. A measur ing e r r o r of not more than 5% f o r harmonics up to the seventh and not more than 10% f o r those up to the twenty seven th , i s r e q u i r e d f o r the wave a n a l y s e r . ^ 3 .2 .2 Measur ing Dev ices The four most common AC-vo l tage measuring dev ices a r e : 1. Sphere gaps 2 . Measur ing c a p a c i t o r s (Chubb & For tescue) 3 . C a p a c i t i v e v o l t a g e d i v i d e r s 4 . Vo l tage t rans fo rmers 1 5 S p h e r e g a p s : S p h e r e g a p s a r e c o m m o n l y u s e d f o r t h e m e a s u r e m e n t o f t h e p e a k v a l u e o f h i g h v o l t a g e s , a n d a s a r e s u l t o f e x t e n s i v e i n v e s t i g a t i o n s , c a l i b r a t i o n t a b l e s g i v i n g b r e a k d o w n v o l t a g e s a s a f u n c t i o n o f t h e g a p l e n g t h f o r d i f f e r e n t s i z e s o f s p h e r e s h a v e b e e n o b t a i n e d . T h e c a l i b r a t i o n d a t a r e c o m m e n d e d i n t h e " B r i t i s h S t a n d a r d R u l e s f o r M e a s u r e m e n t o f V o l t a g e w i t h S p h e r e g a p s " - ^ a r e i n c l u d e d i n T a b l e 1 . B r e a k d o w n o f a s p h e r e g a p o c c u r s w i t h i n a f e w y s e c o n c e t h e a p p l i e d v o l t a g e e x c e e d s t h e " s t a t i c b r e a k d o w n d i s c h a r g e v o l t a g e " . O v e r s u c h a s h o r t p e r i o d t h e p e a k v a l u e o f a p o w e r f r e q u e n c y v o l t a g e o r o f v o l t a g e s w i t h f r e q u e n c i e s up t o 5 0 0 K H z c a n b e c o n s i d e r e d t o b e c o n s t a n t . B r e a k d o w n w i l l a l w a y s o c c u r o n t h e p e a k o f l o w f r e q u e n c y AC v o l t a g e s i f t h e v o l t a g e a m p l i t u d e i s r a i s e d s l o w l y . F i g u r e 1 3 s h o w s t h e b a s i c a r r a n g e m e n t f o r v o l t a g e m e a s u r e m e n t w i t h s p h e r e g a p s . T h e r a t i o S / D ( S p a c i n g / D i a m e t e r ) m u s t n o t b e t o o l a r g e , b e c a u s e w i t h i n c r e a s i n g r a t i o S / D t h e f i e l d b e c o m e s i n c r e a s i n g l y i n h o m o - g e n e o u s a n d a t t h e s a m e t i m e t h e b r e a k d o w n v o l t a g e s b e c o m e r a n d o m . T h i s i s d e m o n s t r a t e d i n F i g u r e 1 4 w h e r e t h e c u r v e s b e g i n t o l e v e l o f f a s S / D i n c r e a s e s . H u m i d i t y h a s n o s i g n i f i c a n t i n f l u e n c e o n t h e b r e a k d o w n v o l t a g e o f s p h e r e g a p s , h o w e v e r , t h e b r e a k d o w n v o l t a g e i s p r o p o r t i o n a l t o t h e r e l a t i v e a i r d e n s i t y d . T h e a c t u a l b r e a k d o w n v o l t a g e a t a i r d e n s i t y d may b e f o u n d f r o m t h e t a b u l a t e d v a l u e Û Q ( s t a n d a r d v a l u e ) b y a p p l y i n g t h e f o l l o w i n g f o r m u l a : ^ * ^ K i l o v o l t s peak at 20°C ; 1013 vni l l ibars B p. o h 6 0 .' Sphere diameter, cm u -a O. ft. CO CO 2 5 6.25 10 12.5 15 25 . 50 1 75 100 150 200 0.05 2.8 0.10 4.7 0.15 6.4 0.2.0. .8.0 8 0 0.25 9.6 9 6 0.30 11.2 11 2 0.40 14.4 14 3 14.2 0.50 17.4 17 4 17.2 16.8 16.8 •. 16.8 0.60 20.4 20 4 20.2 19.9 19.9 19.9 0.70 23.2 23 4 23.2 23.0 23.0 23.0 0.80 25.8 26 3 26.2 26.0 26.0 26.0 0.90 28.3 29 2 29.1 28.9 28.9 28.9 1.0 30.7 32 0 31.9 31.7 31.7 31.7 31.7 1.2 (35.1) 37 6 37.5 37.4 37.4 37.4 37.4 1.4 (38.5) 42 9 42.9 42.9 42.9 42.9 42.9 1.5 (40.0) 45 5 45.5 45.5 45.5 45.5 45.5 1.6 48.1 48.1 48.1 48.1 48.1 48.1 ] .8 53 0 53.5 53.5 53.5 53.5 53.5 2.0 57 5 58.5 59.0 59.0 59.0 59.0 59.0 59.0 2.2 61 5 63.0 64.5 64.5 64.5 64.5 64.5 64.5 2.4 65 5 67.5 69.5 70.0 70.0 70.0 70.0 70.0 2.6 (69 0) 72.0 74.5 75.0 75.5 75.5 75.5 75.5 2.8 (72 5) 76.0 79.5 79.5 80.0 81.0 81.0 81.0 3.0 (75.5) 79.5 84.0 85.0 3.5.5 86.0 86.0 86.0 86.0 3.5 (82 5) (87.5) 95.0 97.0 98.0 99.0 99.0 99.0 99.0 4.0 (88 5) (95.0) 105 108 110 112 112 112 112 4.5 (101) 115 119 122 125 125 125 125 5.0 (107) 123 129 133 137 138 138 138 138 5.5 (131) 138 143 . 149 151 151 151 151 6.0 (138) 146 152 161 164 164 164 164 6.5 (144) (154) 161 173 177 177 177 177 7.0 (150) (161) 169 184 189 190 190 190 7.5 (155) (168) 177 195 202 203 203 203 8.0 (174) (185) 206 214 215 215 215 9.0 (185) (198) ' 226 239 240 241 241. 10 (195) (209) 244 263 265 266 266 266 11 (219) 261 286 290 292 292 292 12 (229) 275 309 315 318 318 318 13 (289) 331 339 342 342 342 14 (302) 353 363 366 366 366 15 (314) 373 387 390 390 390 16 (326) 392 410 414 414 414 17 (337) 411 432 438 438 438 18 (347) 429 453 462 462 462 19 (357) 445 473 486 486 486 20 (356) 460 492 510 510 510 22 489 530 555 560 560 24 515 565 595 610 610 26 (540) 600 635 655 660 28 j (565) 635- 675 700 705 This tab le i s not v a l i d for the measurement of impulse voltages below 10 kV. The f igures i n the brackets, which are for spacings of more than 0.5D are of doubtful accuracy. -Table 1 : Flashover voltages f o r AC v o l t a g e s , f o r DC volta g e s of e i t h e r p o l a r i t y , and f o r f u l l negative standard impulses and impulses w i t h longer t a i l s : One sphere earthed.^ 17 '////////< \ 1000 kV 800 600 0 1,00 200 / D=10C ) c m 50crn 25 cm / / 10 err i 1 10 20 30 UO cm 50 s »• F igu re 13 : Sphere gaps f o r vo l t age measurement F igu re 14: Breakdown vo l tage of sphere gaps as f u n c t i o n of gap spac ing s , f o r v a r i o u s sphere d iameters D. U d * d U do 273 + 20 1013 273 + t b = 0.289 273 + t u d o Udo (1) where-: b: t: Udo : pressure i n mbar temperature i n °C breakdown vo l tage at p ressure 1013 mbar and temperature 20°C. Even under apparen t l y i d e a l c o n d i t i o n s , hav ing made a l lowances f o r such f a c t o r s as a i r d e n s i t y , minimum c l e a r a n c e s , smooth e x a c t l y s p h e r i c a l e l e c t r o d e su r face and proper adjustment of the s p a c i n g , a measuring u n c e r t a i n t y of 3% remains . Sphere gaps are now r a r e l y used f o r measuring v o l t a g e s above 1MV, because they r e q u i r e excess i ve space and are expens ive , Cont inuous vo l t age measurements are obv ious l y imposs ib le w i t h sphere gaps , s i nce the vo l t age source i s s h o r t - c i r c u i t e d at the i n s t a n t of measurement. 18 I n s p i t e o f t h e i r d i s a d v a n t a g e s , s p h e r e g a p s c a n b e u s e f u l a n d v e r s a t i l e d e v i c e s i n h i g h — v o l t a g e l a b o r a t o r i e s . A p a r t f r o m v o l t a g e m e a s u r e m e n t s , t h e y c a n a l s o b e u s e d a s v o l t a g e l i m i t e r s , a s v o l t a g e - d e p e n d e n t s w i t c h e s , 2 a s p u l s e s h a r p e n i n g g a p s a n d a s v a r i a b l e h i g h - v o l t a g e c a p a c i t o r s , e t c . T h e UBC H i g h - v o l t a g e t e s t s e t u s e s s p h e r e g a p s f o r t r a n s f o r m e r p r o t e c t i o n a g a i n s t o v e r - v o l t a g e s . T h e y h a v e a l s o b e e n a d a p t e d f o r AC v o l t a g e m e a s u r e m e n t s a s p a r t o f t h i s t h e s i s p r o j e c t . M e a s u r i n g C a p a c i t o r s : A s o p p o s e d t o s p h e r e g a p s , t h e c i r c u i t s u g g e s t e d b y C h u b b a n d 2 F o r t e s c u e i n 1 9 1 3 i s c a p a b l e o f m e a s u r i n g t h e p e a k v a l u e o f a h i g h AC v o l t a g e c o n t i n u o u s l y a n d a c c u r a t e l y . F i g u r e 15 s h o w s t h e c i r c u i t w i t h i t s c u r r e n t a n d v o l t a g e c u r v e s . F i g u r e 1 5 : P e a k v o l t a g e m e a s u r e m e n t a c c o r d i n g t o C h u b b a n d F o r t e s c u e . a ) C i r c u i t b ) C u r r e n t a n d v o l t a g e c u r v e s 19 A c h a r g i n g c u r r e n t i , g i v e n b y t h e r a t e o f c h a n g e o f t h e a p p l i e d v o l t a g e u ( t ) , f l o w s t h r o u g h t h e h i g h - v o l t a g e c a p a c i t o r C a n d i s p a s s e d t h r o u g h t w o a n t i p a r a l l e l r e c t i f i e r s a n d V2 t o g r o u n d . T h e a r i t h m e t i c m e a n v a l u e o f c u r r e n t i-^ i n t h e l e f t - h a n d b r a n c h i s m e a s u r e d w i t h a m o v i n g - c o i l i n s t r u m e n t . A s s h o w n b e l o w , t h i s c u r r e n t i s p r o p o r t i o n a l t o t h e p e a k v a l u e U o f t h e h i g h v o l t a g e p r o v i d e d t h a t c e r t a i n c o n d i t i o n s a r e f u l f i l l e d . I f t h e b e h a v i o u r o f t h e r e c t i f i e r s i s a s s u m e d i d e a l , t h e n f o r t h e c o n d u c t i n g p e r i o d o f o n e h a s : ± 1 = 1=0-4^ f o r t = 0 t o T / 2 d t _ 1 T i UCT/2) r I± = - / i i d t = i - ^ C d u = £ [ u ( T / 2 ) - u ( 0 ) ] ( 2 ) I f t h e v o l t a g e i s s y m m e t r i c a l w i t h r e f e r e n c e t o t h e z e r o l i n e : u ( T / 2 ) - u ( 0 ) = 2 U ( 3 ) a n d w i t h T = -jr, o n e o b t a i n s 6 = \ lie <4> I n t h e d e r i v a t i o n o f t h i s e x p r e s s i o n , i t w a s n o t a s s u m e d t h a t u ( t ) i s a s i n u s o i d , b u t w h e n s e m i c o n d u c t o r r e c t i f i e r s a r e u s e d , o n l y o n e max imum p e r h a l f p e r i o d c a n o c c u r . T h e u s e o f s y n c h r o n o u s m e c h a n i c a l r e c t i f i e r s o r c o n t r o l l a b l e r e c t i f i e r s ( o s c i l l a t i n g c o n t a c t s , r o t a t i n g r e c t i f i e r s ) a l l o w s c o r r e c t m e a s u r e m e n t o f AC v o l t a g e s w i t h m o r e t h a n o n e m a x i m u m p e r h a l f - p e r i o d . O s c i l l o g r a p h i c m o n i t o r i n g o f h i g h - v o l t a g e s h a p e i s n e c e s s a r y a n d i s u s u a l l y d o n e b y o b s e r v i n g t h e c u r r e n t i-]_, w h i c h i s a l l o w e d t o h a v e o n l y o n e c r o s s o v e r i n e a c h h a l f - p e r i o d . 20 As the frequency f, the measuring capacitor C, and the current 1̂ can be determined precisely, measurement of symmetrical AC voltages using the technique of Chubb & Fortescue with the appropriate layout is very accurate, and is suitable for the calibration of other peak- voltage measuring devices. The disadvantages of this technique are the dependence of the reading upon the frequency and the need to monitor the wave. Capacitive Voltage Dividers: Several r e c t i f i e r circuits have been developed which permit the measurement of peak values of high AC-voltages with the aid of capacitive dividers. Compared with the circuit of Chubb and Fortescue, most of these methods have the advantage that the reading is practically independent of frequency, and multiple extrema per half-period of the voltage to be measured can be permitted.^ Cl u(t) . u 2 (a) Cb) Figure 16: Peak voltage measurement with a capacitive divider a) Circuit b) General form of the voltage •21 The h a l f - p e r i o d c i r c u i t i s shown i n f i g u r e 16. In t h i s c i r c u i t the measuring c a p a c i t o r CJJJ i s charged to the peak va lue U2 of the lower arm vo l t age U£(t) of the c a p a c i t i v e d i v i d e r . The r e s i s t o r RM which d i s - charges the c a p a c i t o r CM i s meant to f o l l o w reduc t i ons of the a p p l i e d v o l t a g e . The cho i ce of t ime constant f o r t h i s d ischarge process i s determined by the d e s i r e d response of the measuring system. In genera l one chooses, R C < 1 second, and (5) m m ' R m Cm » J <6> The r e s i s t o r R2 i s necessary to min imize charg ing of by the cu r ren t f l o w i n g through the r e c t i f i e r V . The va lue of R2 must be chosen i n such a way tha t the DC v o l t a g e drop ac ross R2 which causes DC charg ing of C2 remains as sma l l as p o s s i b l e . In t h i s case one must have R2 << RJJJ. On the o ther hand, the c a p a c i t i v e d i v i d e r r a t i o shou ld not be a f f e c t e d much by R2 , which r e q u i r e s R2 >> ^ . With a l l these c o n d i t i o n s , the r e l a t i o n between the peak va lue of the h igh vo l t age and the i n d i c a t e d vo l t age UM i s g iven by: C, + C2 , U = U m (7) The working p r i n c i p l e of the " Impulse Peak Vo l tme te r " of the UBC h i g h - v o l t a g e t e s t set i s based on t h i s t echn ique , even though a more e labo ra te c i r c u i t i s employed. In the c o n t r o l box , there i s a l s o an AC vo l tme te r which operates on the same p r i n c i p l e but i n d i c a t e s peak va lue d i v i d e d by J2 (r^^) i n s tead of peak v a l u e . Vo l tage Transformers : High AC vo l t ages can be measured very a c c u r a t e l y w i t h vo l t age t r a n s - 22 f o r m e r s . T h e b a s i c c i r c u i t s o f s i n g l e p o l e i s o l a t e d i n d u c t i v e a n d c a p a c i t i v e v o l t a g e t r a n s f o r m e r s a r e s h o w n i n F i g u r e 1 7 . I n d u c t i v e v o l t a g e t r a n s f o r m e r s f o r v e r y h i g h v o l t a g e s a r e v e r y e x p e n s i v e t o b u i l d s i n c e t h e y r e q u i r e v e r y l a r g e n u m b e r o f t u r n s o f t h e h i g h — v o l t a g e w i n d i n g . T h e t y p e o f c a p a c i t i v e v o l t a g e t r a n s f o r m e r u s e d e x t e n s i v e l y i n s u p p l y n e t w o r k s i s o f t e n c o n s i d e r e d u n s u i t a b l e f o r n o r m a l t e s t i n g w o r k , m a i n l y b e c a u s e i t i m p o s e s a h i g h c a p a c i t i v e l o a d u p o n t h e v o l t a g e s o u r c e . u ( t ) u ( t ) u 2 ( t ) ( a ) ( b ) 2 TuoCt). F i g u r e 1 7 : B a s i c c i r c u i t s o f v o l t a g e t r a n s f o r m e r s a ) I n d u c t i v e v o l t a g e t r a n s f o r m e r s b ) C a p a c i t i v e v o l t a g e t r a n s f o r m e r 1 P r i m a r y w i n d i n g 2 S e c o n d a r y w i n d i n g 3 I r o n c o r e C ^ , C 2 D i v i d e r c a p a c i t o r s L R e s o n a n c e i n d u c t o r W M a t c h i n g t r a n s f o r m e r ( m a r k i n g a s u n d e r a ) I n d u c t i v e a n d c a p a c i t i v e v o l t a g e t r a n s f o r m e r s a r e u s e d i n l a b o r a - t o r y m e a s u r e m e n t s o n l y w h e n p a r t i c u l a r l y p r e c i s e m e a s u r e m e n t s o f m o d e r a t e v o l t a g e s a r e r e q u i r e d . T h e s e c o n d a r y v o l t a g e o f a v o l t a g e t r a n s f o r m e r w i l l r e p r o d u c e t h e s h a p e o f t h e p r i m a r y v o l t a g e , i f t h e l o a d r e s i s t a n c e i s n o t l o w . D e p e n d i n g o n t h e t y p e o f m e a s u r i n g d e v i c e c o n n e c t e d , i t i s p o s s i b l e t o m e a s u r e t h e p e a k v a l u e , t h e r m s v a l u e o r t o d i s p l a y t h e w a v e s h a p e . 23 3 . 3 DC V o l t a g e M e a s u r e m e n t s 3 . 3 . 1 O b j e c t i v e T h e g e n e r a l o b j e c t i v e o f DC v o l t a g e m e a s u r e m e n t s a r e : ^ . - t o m e a s u r e t h e a r i t h m e t i c mean v a l u e o f t h e v o l t a g e , t y p i c a l l y w i t h a n e r r o r o f n o t m o r e t h a n 3 % . - t o m e a s u r e t h e r i p p l e a m p l i t u d e , t y p i c a l l y w i t h a n e r r o r o f n o t m o r e t h a n 10% o f t h e a c t u a l r i p p l e a m p l i t u d e o r n o t m o r e t h a n 1% o f t h e a r i t h m e t i c m e a n v a l u e o f t h e DC v o l t a g e , w h i c h e v e r i s l a r g e r . To f u l f i l l t h e a b o v e e r r o r r e q u i r e m e n t s , t h e m e a s u r i n g s y s t e m h a s t o s a t i s f y c e r t a i n s p e c i f i c a t i o n s : ^ ( a ) T h e v o l t a g e r a t i o o f t h e v o l t a g e d i v i d e r i s s t a b l e a n d k n o w n w i t h a n e r r o r o f n o t m o r e t h a n 1%. I n t h e c a s e o f h i g h - i m p e d a n c e s y s t e m s w h e r e i t may n o t b e p o s s i b l e t o c o m p l y w i t h t h i s s p e c i f i c a t i o n , a n o v e r a l l e r r o r s l i g h t l y e x c e e d i n g 3% may h a v e t o b e a c c e p t e d . ( b ) T h e c u r r e n t d r a w n f r o m t h e h i g h - v o l t a g e s o u r c e a t f u l l v o l t a g e i s n o t l e s s t h a n 0 . 0 5 m A . ( c ) T h e f r e q u e n c y r e s p o n s e o f t h e s y s t e m u s e d f o r m e a s u r i n g r i p p l e v o l t a g e i s a d e q u a t e a n d k n o w n w i t h i n 10% f o r f r e q u e n c i e s f r o m t h e f u n d a m e n t a l o f t h e r i p p l e f r e q u e n c y up t o f i v e t i m e s t h i s f r e q u e n c y . 3 . 3 . 2 M e a s u r i n g D e v i c e s M e a s u r e m e n t o f t h e a r i t h m e t i c m e a n v a l u e o f a h i g h DC v o l t a g e c a n b e d o n e w i t h t h e f o l l o w i n g : ( a ) H i g h - v o l t a g e r e s i s t o r s a n d v o l t a g e d i v i d e r s . ( b ) E l e c t r o s t a t i c v o l t m e t e r s 24 (c) F i e l d s t reng th meter . For the r i p p l e v o l t a g e measurement, a v o l t a g e d i v i d e r made up of a c a p a c i t o r and a r e s i s t o r i s used . There are o ther methods f o r DC v o l t a g e measurements. Sphere gaps are s u i t a b l e f o r the de te rm ina t i on of the peak v a l u e U of h i g h DC v o l t a g e s . In p h y s i c s l a b o r a t o r i e s the nuc lea r resonance method i s o f t en a p p l i e d to measure DC v o l t a g e s . Pro tons are a c c e l e r a t e d i n an e l e c t r i c f i e l d which i s p r o p o r t i o n a l to the v o l t a g e to be measured. At c e r t a i n k i n e t i c energ ies these protons c o l l i d e w i t h l i g h t atomic n u c l e i , p roduc ing r e - sonant n u c l e a r t rans fo rmat ions which permi t ve ry accura te de te rm ina t i on of the DC v o l t a g e . H i g h - v o l t a g e R e s i s t o r s and Vo l t age d i v i d e r s : The cu r ren t f l ow ing through a r e s i s t o r connected to a DC source can i n d i c a t e the v o l t a g e to be measured. However, f o r h i g h - v o l t a g e a p p l i - c a t i o n s the cu r ren t must be ve ry s m a l l , of the order of 1 mA f o r example, because o therw ise excess i ve l oad ing of the v o l t a g e source and excess i ve hea t ing of the measuring r e s i s t o r w i l l o c c u r . ^ On the o ther hand, a sma l l cu r ren t i s e a s i l y f a l s i f i e d by e r r o r c u r r e n t s ; these occur i n the form of leakage cu r ren ts i n i n s u l a t i n g m a t e r i a l s and on i n s u l a t i n g s u r f a c e s , and a l s o as a r e s u l t of corona d i s c h a r g e s . To avo id these problems, a s p e c i a l des ign f o r h i g h - v o l t a g e r e s i s t o r s i s needed. The s imple DC-vo l tage measur ing c i r c u i t i s shown i n F i g u r e 18. Measurement of DC vo l t age by means of a h i g h - v o l t a g e r e s i s t o r . • rh u ( t ) R l Ammeter F i gu re 18: T h e a m m e t e r i s a s s u m e d a t e a r t h p o t e n t i a l . A s e n s i t i v e m o v i n g - c o i l i n s t r u m e n t i s u s u a l l y c h o s e n , t h e i n d i c a t i o n o f w h i c h i s t h e a r i t h m e t i c m e a n v a l u e U o f t h e DC v o l t a g e . R e p l a c i n g t h e a m m e t e r w i t h a p a r a l l e l c o n n e c t i o n o f a v o l t m e t e r a n d a r e s i s t o r R 2 , o n e o b t a i n s a v o l t a g e d i v i d e r f o r m e a s u r i n g DC v o l t a g e s w h i c h i s s h o w n i n F i g u r e 1 9 . R i F i g u r e 1 9 : M e a s u r e m e n t o f a DC v o l t a g e b y m e a n s o f a r e s i s t i v e d i v i d e r T h e UBC h i g h - v o l t a g e t e s t s y s t e m u s e s t h i s d i v i d e r m e t h o d t o m e a s u r e DC v o l t a g e s . T h e I m p u l s e P e a k V o l t m e t e r ( I P V ) c a n b e u s e d , i n s t e a d o f t h e " C o n t r o l B o x V o l t m e t e r " , t o m e a s u r e t h e p e a k v a l u e o f a DC v o l t a g e . E l e c t r o s t a t i c V o l t m e t e r s : E l e c t r o s t a t i c v o l t m e t e r s h a v e t h e a d v a n t a g e o f v e r y h i g h i n t e r n a l r e s i s t a n c e a n d v e r y s m a l l c a p a c i t a n c e , w h i c h m a k e s t h e m u s e f u l f o r m e a - 2 s u r e m e n t o f l o w e n e r g y h i g h v o l t a g e s . T h e s c h e m a t i c o f t h e d e v i c e i s s h o w n i n F i g u r e 2 0 . W h e n a v o l t a g e u ( t ) i s a p p l i e d , t h e e l e c t r i c f i e l d p r o d u c e s a f o r c e F ( t ) w h i c h t e n d s t o r e d u c e t h e s p a c i n g s o f t h e e l e c t r o d e s . T h i s a t t r a c t i v e f o r c e c a n b e c a l c u l a t e d f r o m t h e c h a n g e o f e n e r g y o f t h e e l e c t r i c f i e l d : W ( t ) = \ C u 2 ( t ) ( 8 ) 2 6 u(t) b) •Fit) F i g u r e 2 0 : E l e c t r o s t a t i c v o l t m e t e r s f o r h i g h v o l t a g e s . a ) U s i n g s p h e r i c a l e l e c t r o d e s ( a f t e r H u e t e r ) b ) U s i n g a m o v a b l e e l e c t r o d e s e g m e n t ( a f t e r S t a r k e a n d S c h r o d e r ) 1 . M o v a b l e e l e c t r o d e s e g m e n t 4 , 2 . A x i s o f r o t a t i o n 5 . 3 . M i r r o r L i g h t s o u r c e S c a l e T h e c a p a c i t a n c e C d e p e n d s o n t h e s p a c i n g s . U s i n g t h e l a w o f c o n s e r v a t i o n o f e n e r g y dW + F d s = 0 a n d a s s u m i n g d i s c o n n e c t i o n o f t h e v o l t a g e s o u r c e o n e o b t a i n s : F ( t ) =,_<L1<JLL= i 2 ( t ) dj; d s 2 d s (9) T a k i n g t h e a r i t h m e t i c m e a n v a l u e F o f t h e f o r c e , = 1 d C 1 / 2 ^ s 1 d C 2 F = 2 d7 T ^ U ( t ) d t " 2 d7 U r m s ( 1 0 ) T h i s f o r c e i s c o u n t e r - b a l a n c e d b y a s p r i n g . A t e q u i l i b r i u m t h e r e i s some d e f i n e d v a l u e o f s p r i n g e x t e n s i o n w h i c h c a n b e t r a n s l a t e d i n t o a v o l t a g e r e a d i n g . Field-Strength Meters: 2 Variable capacitance is the basic principle of this device. The schematic of the device is shown in Figure 21. The two measuring electrodes 1 and 1 are alternately passed under the semi-circular opening 2 of the grounded plate 3; this produces a variable capacitance between each electrode and the high—voltage electrode 4. H 1,1' Revolving semicircular discs 2 Semicircular opening 3 Earthed covering plate 4 High-yoltage electrode 5 Commutator 6 Ammeter 28 At constant rate of revolution, a p e r i o d i c a l t e r n a t i n g current i ( t ) flows between the measuring electrodes, which i s r e c i t i f i e d by a commutator 5. The arithmetic mean value I a f t e r r e c t i f i c a t i o n i s read by a moving-coil ammeter b. Since the current I i s proportional to the measured voltage, the reading of the ammeter can be converted into a voltage reading. Ripple-voltage measurement c i r c u i t s : Ripple voltages are AC components superimposed on the DC voltage. For smoothed DC voltages, the peak values 9U of the r i p p l e voltages are always much smaller than the mean value U, which i s why an o s c i l l o s c o p i c measurement, performed with a r e s i s t i v e d i v i d e r , i s too i n s e n s i t i v e . To separate the r i p p l e from the DC v o l t a g e , a a voltage d i v i d e r made up of a r e s i s t o r and a capacitor i s used. The c i r c u i t i s shown in Figure 22. The d i v i d e r r a t i o ,of t h i s c i r c u i t i s given by: If the f u l l magnitude of the r i p p l e i s to appear on the lower arm of the d i v i d e r , the d i v i d e r r a t i o must be as close to one as possible for a l l frequencies i n the r i p p l e spectrum, which requires Figure 22: C i r c u i t for measur- ing r i p p l e voltages . uRC » 1 (12) 2 9 I n t h e UBC h i g h - v o l t a g e l a b o r a t o r y , a r e s i s t i v e d i v i d e r i s i n s t a l l e d , i n s t e a d o f a s i n g l e r e s i s t o r , a s a p r a c t i c a l d e v e l o p m e n t o f t h i s t h e s i s p r o j e c t . T h e r i p p l e v o l t a g e w h i c h a p p e a r s o n t h e l o w e r a r m o f t h e d i v i d e r i s , t h e r e f o r e , r e d u c e d a n d c a n b e d i s p l a y e d o n a n o s c i l l o s c o p e . A s u r g e a r r e s t o r i s a l s o i n s t a l l e d i n p a r a l l e l w i t h t h e l o w e r a r m r e s i s t o r t o p r o t e c t t h e o s c i l l o s c o p e i n c a s e t h e v o l t a g e u ( t ) c o l l a p s e s t o z e r o . S u d d e n v o l t a g e d r o p o f u ( t ) w i l l c a u s e t h e w h o l e v o l t a g e , a p p l i e d p r e v i o u s l y , t o a p p e a r o n t h e r e s i s t i v e p a r t o f t h e d i v i d e r . T h i s c a n d e s t r o y t h e o s c i l l o s c o p e . 3 . 4 I m p u l s e V o l t a g e M e a s u r e m e n t s 3 . 4 . 1 O b j e c t i v e T h e g e n e r a l o b j e c t i v e s o f i m p u l s e - v o l t a g e m e a s u r e m e n t s a r e : ^ - To m e a s u r e t h e p e a k v a l u e o f f u l l i m p u l s e s a n d i m p u l s e s c h o p p e d i n t h e v i c i n i t y o f t h e p e a k o r o n t h e t a i l , t y p i c a l l y w i t h a n e r r o r n o t e x c e e d i n g 3%. - To m e a s u r e t h e p e a k v a l u e o f i m p u l s e s c h o p p e d o n t h e f r o n t , t y p i c a l l y w i t h a n e r r o r A w h i c h i s d e p e n d e n t o n t h e t i m e t o c h o p p i n g T £ a s f o l l o w s : i f T c > 2 u s , A < 3% i f 0 . 5 y s < T c < 2 y s , A < 5% - To m e a s u r e t h e t i m e p a r a m e t e r s w h i c h d e f i n e t h e i m p u l s e s h a p e , t y p i c a l l y w i t h a n e r r o r n o t e x c e e d i n g 1 0 % . T h e a b o v e r e q u i r e m e n t s w i l l b e m e t i f t h e s y s t e m m e e t s t h e f o l l o w i n g m e a s u r e m e n t q u a l i f i c a t i o n s : ^ 30 (a) The v o l t a g e r a t i o of the d i v i d e r should be s t a b l e and known wi t h an e r r o r not exceeding 1%. (b) The s c a l e f a c t o r of the o s c i l l o s c o p e or peak voltmeter ( i n c l u d i n g attenuator or c o u p l i n g devices) should be s t a b l e and known w i t h an e r r o r not exceeding 2%. (c) The time s c a l e of the o s c i l l o s c o p e should be s t a b l e and known wi t h an e r r o r not exceeding 2%. (d) The response time requirements f o r measuring systems depend on the impulse shapes, such as the f o l l o w i n g : - F u l l 1.2 ys l i g h t n i n g impulse and l i g h t n i n g impulses chopped on the peak or t a i l |T| < 0.2 ys. - Switching impulses |T| < 0.03 T Q and |T| < 0.03 T c r where T c i s chopping time T c r i s time to c r e s t | T| i s response time 3.4.2 Setup of Measuring System A measuring system f o r impulse v o l t a g e s g e n e r a l l y c o n s i s t of: (a) a Faraday Cage (b) a Wiring System (c) a Voltage D i v i d e r (d) a Measuring Instrument and i t s connection to the d i v i d e r Faraday Cage: In p r a c t i c e , a high-voltage c i r c u i t behaves as an antenna which r e c e i v e s e x t e r n a l electromagnetic waves. Electromagnetic waves are a l s o produced during breakdown discharge processes i n the high-voltage c i r c u i t s themselves, and these can i n turn d i s t u r b the surroundings. However, the 3 1 • d i s t u r b i n g e f f e c t o f t h e s u r r o u n d i n g s o n t h e h i g h - v o l t a g e c i r c u i t i s g e n e r a l l y w o r s e t h a n t h a t e x e r t e d b y t h e h i g h - v o l t a g e c i r c u i t o n t h e s u r r o u n d i n g s . To e l i m i n a t e t h e s e i n t e r f e r e n c e s o n e u s e s a h i g h l y c o n d u c t i v e m e t a l s h i e l d i n t h e f o r m o f a F a r a d a y c a g e . > a S t r o n g e l e c t r o m a g n e t i c f i e l d s , a s s o c i a t e d w i t h h i g h r a p i d l y c h a n g i n g v o l t a g e s a n d c u r r e n t s , a l s o c a u s e i n t e r f e r e n c e o f a s p e c i a l t y p e . S t r a y g r o u n d c a p a c i t a n c e s a r e c h a r g e d a n d d i s c h a r g e d b y t h e s e s t r o n g f i e l d s w h i c h p r o d u c e t r a n s i e n t p o t e n t i a l r i s e s . F i g u r e 23 s h o w s s c h e m a t i c a l l y a h i g h v o l t a g e c i r c u i t c o n s i s t i n g o f a n i m p u l s e g e n e r a t o r G a n d a t e s t o b j e c t P ; Z K r e p r e s e n t s t h e u n a v o i d a b l e g r o u n d i m p e d a n c e . F i g u r e 2 3 : J u m p i n g p o t e n t i a l i n i m p u l s e g e n e r a t o r s y s t e m . F i g u r e 2 3 a s h o w s l i n e s o f s t r a y f l u x i n n o r m a l s e t u p . F i g u r e 2 3 b s h o w s l i n e s o f s t r a y f l u x w i t h t e s t s e t u p i n F a r a d a y c a g e . G i m p u l s e g e n e r a t o r , P t e s t , o b j e c t , C s t r s t r a y g r o u n d c a p a c i t a n c e s , Zg g r o u n d i m p e d a n c e , I c c h a r g i n g c u r r e n t f o r s t r a y g r o u n d c a p a c i t a n c e s . 32 E l e c t r i c f i e l d l i n e s e x i s t b e t w e e n t h e h i g h v o l t a g e e l e c t r o d e s a n d t h e g r o u n d e d s u r r o u n d i n g s . T h e s e c a n b e r e p r e s e n t e d a s s t r a y g r o u n d c a p a c i - t a n c e s C w h i c h a r e r a p i d l y c h a r g e d a n d d i s c h a r g e d d u r i n g t r a n s i e n t s . B e c a u s e o f t h e h i g h r a t e o f v o l t a g e c h a n g e , t h e c h a r g i n g c u r r e n t s may h a v e v a l u e s a s h i g h a s some k i l o a m p e r e s , w h i c h w h e n r e t u r n i n g t o t h e s u r g e g e n e r a t o r ' s g r o u n d t h r o u g h Z , w i l l r e s u l t i n c o n s i d e r a b l e t r a n s i e n t g r o u n d p o t e n t i a l s . I f t h e e n t i r e h i g h - v o l t a g e c i r c u i t i s l o c a t e d i n s i d e a F a r a d a y c a g e , F i g u r e 2 3 b , a l l s t r a y f i e l d l i n e s w i l l t e r m i n a t e o n t h e c a g e w a l l . T h e c h a r g i n g c u r r e n t s w i l l t h e n f l o w o n t h e i n n e r s u r f a c e o f t h e c a g e w a l l a n d c a n n o t r a i s e t h e p o t e n t i a l o f t h e g r o u n d s y s t e m o f t h e h i g h - v o l t a g e c i r c u i t . A s m e n t i o n e d p r e v i o u s l y , F a r a d a y . c a g e s a r e u s u a l l y m a d e o f h i g h l y c o n d u c t i v e m e t a l i n o r d e r t o g e t r i d o f b a c k g r o u n d i n t e r f e r e n c e s . H o w e v e r , t h i s h i g h l y c o n d u c t i v e m e t a l e n c l o s u r e a c t s a s a h u g e c a v i t y r e s o n a t o r Q -I r j w h e n e x c i t e d f r o m i n s i d e b y t h e f a s t d i s c h a r g e o f a n i m p u l s e g e n e r a t o r . ' S e v e r a l m o d e s o f o s c i l l a t i o n s o c c u r w i t h a v e r y h i g h Q - f a c t o r w h i c h a r e d e t e r m i n e d b y t h e f o r m u l a : ^ f = ̂ \ / ( j ) 2 + (£) 2 + (13) V a b c / c , C " m , n , p 2 V x a ' ' b ' ~c ' / n , . „>. ( S e e a p p e n d i x 2 ) w h e r e : m , n , p , i n t e g e r s i d e n t i f y i n g t h e r e s o n a n c e m o d e . a , b , c , d i m e n s i o n s o f t h e s h i e l d . C Q = 3 0 0 m / u s . ' D u e t o l a r g e d i m e n s i o n s o f some h i g h - v o l t a g e l a b o r a t o r i e s , t h e l o w e r r e s o n a n t f r e q u e n c i e s a r e i n t h e o r d e r o f o n e MHz a n d a r e w e l l w i t h i n t h e p a s s b a n d w i t h o f t h e i m p u l s e - v o l t a g e m e a s u r i n g s y s t e m . T h e s e l i g h t l y d a m p e d o s c i l l a t i o n s l a s t f o r t e n s o f m i c r o s e c o n d s a n d t h e r e f o r e c a u s e ) 33 distortions. A practical remedy for this interference is a reduction of the Q- factor of the electromagnetic shield. By covering the inner wall of the shield with a special resistive coating the cavity resonance can be damped out after a few oscillations . The resistive coating does not affect the laboratory shielding since the currents induced in the shield by external interference sources circulate in the outer layer of the metal wall. In order to keep the currents induced by the cavity resonance within the resistive coating layer i t s thickness has to be not smaller than the current penetration depth. An analysis of the total resistance required for an effective damping, as well as of the available resistive coating indicate that a special material should be composed on a basis of mag- netic powders and resistive paints having both high re s i s t i v i t y and high Q magnetic permeability. In the UBC High—voltage laboratory the Faraday cage is made of aluminum sheets which are joined together by folding them. Since aluminum is always oxidized in air, these folding connections have a high resistance at high frequency and therefore the shielding behaviour is lessened. However, with relatively low surrounding interference and low operating voltage (200 KV), this shielding is sufficient for our purposes. Wiring System: The presence of electromagnetic fields around the impulse generator and the measuring system tends to induce noise in the system, especially when loops are present in the system. Therefore, i t is desirable to minimize the area of the loops by arranging the wiring system in such a way that a l l cables extend from a cable tree to provide branch wiring 34 r a t h e r t h a n l o o p s F i g u r e 2 4 s h o w s t h e w r o n g a n d t h e c o r r e c t a r r a n g e - m e n t s o f a w i r i n g s y s t e m . T h e s c h e m a t i c s h o w n i n F i g u r e 2 4 b i s t h e a r r a n g e m e n t u s e d i n t h e UBC h i g h - v o l t a g e t e s t s y s t e m . Peak voltmeter Spark 9<V> Control center Test j / ' object Peak voltmeter Control center t L o«,v rectifier Voltage divider 1 Impulse generator F i g u r e 2 4 : B l o c k d i a g r a m o f i m p u l s e t e s t f a c i l i t y . 5 a ) w r o n g a r r a n g e m e n t o f c o n t r o l a n d s i g n a l c a b l e s ( e x i s t e n c e o f l o o p s ) ; b ) c o r r e c t w i r i n g o f c o n t r o l a n d s i g n a l c a b l e s ( b r a n c h w i r i n g ) 3 5 V o l t a g e D i v i d e r : A d i v i d e r f o r r e c o r d i n g h i g h t r a n s i e n t v o l t a g e s , may c o n s i s t o f r e s i s t o r s o r c a p a c i t o r s o r c o m b i n a t i o n s o f b o t h . E a c h t y p e o f d i v i d e r s h o u l d r e p r o d u c e t h e w a v e s h a p e o f t h e v o l t a g e t o b e m e a s u r e d w i t h a k n o w n r e d u c t i o n r a t i o . T h e m a i n s o u r c e s o f e r r o r common t o a l l t y p e s o f d i v i d e r s a r e : ^ > 4 1 . R e s i d u a l i n d u c t a n c e i n a n y r e s i s t i v e o r c a p a c i t i v e e l e m e n t . 2 . S t r a y c a p a c i t a n c e : ( a ) f r o m a n y s e c t i o n o f t h e d i v i d e r t o t h e h i g h - v o l t a g e l e a d . ( b ) f r o m a n y s e c t i o n o f t h e d i v i d e r t o g r o u n d . ( c ) B e t w e e n s e c t i o n s o f t h e d i v i d e r . 3 . I m p e d a n c e d r o p i n t h e i n t e r c o n n e c t i n g l e a d s . 4 . O s c i l l a t i o n s i n t h e d i v i d e r c i r c u i t c a u s e d b y c a p a c i t a n c e f r o m d i v i d e r h i g h - v o l t a g e t e r m i n a l t o g r o u n d a n d l e a d i n d u c t a n c e . I n t h e c a s e „ o f a r e s i s t i v e d i v i d e r , t h e r e s i d u a l i n d u c t a n c e o f t h e d i v i d e r g e n e r a t e s a n M ^ r ) v o l t a g e w h i c h i s s u p e r i m p o s e d u p o n t h e I R d r o p . T h i s c a u s e s f r e q u e n c y - d e p e n d e n t b e h a v i o u r o f t h e d i v i d e r . A r e s i s t i v e d i v i d e r i s n o r m a l l y a c c e p t a b l e f o r m e a s u r i n g t h e s t a n d a r d i m p u l s e o f a 1 . 2 / 5 0 u s e e w a v e . H o w e v e r , w h e n t h e d u r a t i o n o f t h e s u r g e i s l e s s t h a n 1 u s e e a r e s i s t i v e d i v i d e r may g i v e l a r g e e r r o r s d u e t o s t r a y c a p a c i t a n c e , 3 w h i c h c a u s e s t h e r e s p o n s e t i m e t o b e l a r g e . T h e r e s p o n s e t i m e c a n b e e v a l u a t e d b y c o m p a r i n g t h e " m e a s u r e d " v o l t a g e - t i m e c u r v e , f o r l i n e a r l y r i s i n g i m p u l s e v o l t a g e s o f c o n s t a n t r a t e 2 S , w i t h t h e ' - ' t r u e " v o l t a g e - t i m e c u r v e o f t h e s a m e w a v e . F i g u r e 2 5 s h o w s t h e r e s p o n s e o f a s y s t e m s h o w i n g RC b e h a v i o u r a n d R L C b e h a v i o u r . I f t h e s t e e p n e s s S i s a c c u r a t e l y k n o w n , t h e r e s p o n s e t i m e T c a n b e d e t e r m i n e d f r o m t h e v o l t a g e e r r o r S T . T h e r e s p o n s e o f t h e d i v i d e r c a n b e 36 i m p r o v e d b y c h o o s i n g a l o w v a l u e o f r e s i s t a n c e o r c o m p e n s a t i n g t h e e a r t h c a p a c i t a n c e b y p l a c i n g a s p e c i a l e l e c t r o d e a t t h e h i g h - v o l t a g e e n d o f t h e d i v i d e r t o g i v e a u n i f o r m s t r a y - c a p a c i t a n c e d i s t r i b u t i o n a l o n g t h e s u r f a c e o f t h e d i v i d e r . 3 . 4 , 5 F i g u r e 2 5 : D i s p l a y o f a w e d g e - s h a p e d i m p u l s e v o l t a g e , . a ) S y s t e m s h o w i n g RC b e h a v i o u r b ) S y s t e m s h o w i n g R L C b e h a v i o u r When t h e d i v i d e r i s c o n s t r u c t e d f r o m p u r e c a p a c i t o r s , t h e r e s p o n s e i s t h e o r e t i c a l l y p e r f e c t o n f a s t a s w e l l a s s l o w t r a n s i e n t s ; h o w e v e r , w i t h t h e e x i s t e n c e o f i n t e r n a l i m p e d a n c e o f t h e m e a s u r i n g i n s t r u m e n t a n d r e s i d u a l i n d u c t a n c e o f t h e d i v i d e r a n d i t s l e a d s , a c e r t a i n l i m i t a t i o n i s i m p o s e d . F r o m t h e d i v i d e r t r a n s f e r f u n c t i o n , w h i c h i s g i v e n b e l o w , i t c a n b e s e e n t h a t t h e p r o d u c t R ( C ^ + C 2 ) h a s t o b e q u i t e l a r g e t o m i n i - m i z e t h e l o a d i n g e f f e c t . V 2 ( s ) Qi s V - ^ s ) C x + C 2 ' s + 1 ( 1 4 ) R ( C L + C 2 ) O t h e r w i s e , a l a r g e e r r o r w i l l o c c u r d u r i n g s l o w t r a n s i e n t s . F o r f a s t t r a n s i e n t s t h e n a t u r a l f r e q u e n c y o f t h e d i v i d e r i s a m a j o r c o n c e r n . T h e 37 capacitance and r e s i d u a l inductance of the d i v i d e r determine t h i s natural frequency which i s usually around 200 MHz. However, i f one uses large values of capacitances, the natural frequency w i l l be lowered and may f a l l within the bandwidth of the measuring instrument and as a r e s u l t , the recorded waveform would be d i s t o r t e d . This behaviour was observed experimentally i n the UBC laboratory. With the capacitors supplied by the manufacturer, o s c i l l a t i o n s do not appear on the o s c i l l o s c o p e , whereas with a large capacitance value on the lower arm of the d i v i d e r , o s c i l - l a t i o n s do appear. The impulse waveshapes obtained with the capacitive d i v i d e r of 4.14 yF lower capacitance value have been produced both numer- 14 i c a l l y (using the UBC Electromagnetic Transients Program) and experi- mentally (shown i n Figure 26). O s c i l l a t i o n s can also occur due to t r a v e l l i n g wave r e f l e c t i o n s . The r e s i d u a l inductance and the stray capacitance to ground of the high- voltage arm and lead cause the d i v i d e r to behave as a transmission l i n e . 13 UJ o 0~) —I x: IMPULSE VOLTAGE TIME (MICROSECONDS: (a) 38 Time s c a l e : 2 usec/div. Voltage s c a l e : 5 V/div. (b) F i g u r e 26: Impulse waveshapes obtained w i t h the c a p a c i t i v e d i v i d e r of 4.14 yF lower capacitance v a l u e . (a) n u m e r i c a l l y (b) experimentally R e f l e c t i o n s occur because there i s no impedance matching at both ends of the l i n e . One end i s s h o r t - c i r c u i t e d by the c a p a c i t o r of the lower arm and the other end i s u s u a l l y badly matched. These o s c i l l a t i o n s are attenuated very l i t t l e s ince the c a p a c i t o r s and the lead have low l o s s e s . To o b t a i n high a t t e n u a t i o n continuously-damped c a p a c i t i v e voltage d i v i d e r s have been developed which are composed of s e r i e s connections of r e s i s t o r s and c a p a c i t o r s . ' Measuring Instrument and i t s connection to the d i v i d e r : Depending on the measurement q u a l i t y , the r e q u i r e d measuring i n s t r u - ment could be an impulse peak voltmeter, an o s c i l l o s c o p e or a d i g i t a l t r a n s i e n t recorder. Impulse peak voltmeters can only measure the peak value of the impulse wave and therefore do not supply enough in f o r m a t i o n about the shape of the impulse. With an o s c i l l o s c o p e or d i g i t a l t r a n s i e n t recorder, f u l l i n f o r m a t i o n of the impulse wave can be obtained. 39 The measuring instrument i s usually connected to the voltage d i v i d e r by a coaxial cable. Depending upon the amplitude l e v e l and the type of o s c i l l o s c o p e , the s i g n a l may e i t h e r be fed d i r e c t l y to the de- f l e c t i o n plates or i t may be connected to the input terminals of the v e r t i c a l a m p l i f i e r of the o s c i l l o s c o p e . Additional attenuators are often needed to reduce the amplitude of the s i g n a l . In the UBC high- voltage laboratory an e l e c t r o n i c o s c i l l o s c o p e and a hundred—to-one attenuator have been used. Impedance matching i s always required to avoid travelling^wave o s c i l l a t i o n s . For a r e s i s t i v e voltage d i v i d e r , the s i g n a l cable i s terminated at the measuring instrument end with i t s surge impedance. The c i r c u i t diagram and i t s equivalent c i r c u i t are shown in Figure 27. Figure 27: Impulse voltage measuring system with r e s i s t i v e d i v i d e r a) C i r c u i t diagram b) Equivalent c i r c u i t with earth capacitance. In measuring systems with capacitive d i v i d e r s , as in Figure 28, termination i s usually done with a series matching at the input end. The UBC test set .uses t h i s type of matching. This matching has the e f f e c t 40 that only h a l f the voltage at the d i v i d e r tap enters the c a b l e , however, t h i s i s doubled again at the open end, so that f u l l v o l t a g e w i l l be measured at the measuring instrument a g a i n . For f a s t t r a n s i e n t s the Osc. Figure 28: Connection of the c a p a c i t i v e voltage d i v i d e r to a cathode-ray o s c i l l o s c o p e . ZQ = c h a r a c t e r i s t i c impedance of the s i g n a l c a b l e , C Q = s i g n a l cable capacitance. voltage r a t i o of t h i s system i s V]_(t) C-L + C2 Vo(t) C 1 (15) but f o r slow t r a n s i e n t s the cable capacitance C c increases the r a t i o as i n d i c a t e d below: Ci + Co + C_ a = _i i £_ ( 1 6 ) This e r r o r may be reduced by a complex te r m i n a t i o n proposed by Burch,^ Figure 29. By a d j u s t i n g the a d d i t i o n a l c a p a c i t o r C3, so that the equation C^ + C 2 = C3 + C c i s s a t i s f i e d , the r a t i o w i l l be independent of f r e - 41 quency as a f i r s t approximation, 1 I |«2(.t: z 0 ' c c 9TC Osc, Figure 29: Compensation of s i g n a l cable capacitance by a complex cable t e r m i n a t i o n , =•0 c h a r a c t e r i s t i c impedance of the s i g n a l c a b l e , Cc = s i g n a l cable capacitance, C3 = a u x i l i a r y capacitance. In the case of a damped c a p a c i t i v e divider.;- s e r i e s matching i s al s o a p p l i e d ; however, the te r m i n a t i o n r e s i s t o r at the cable input must be reduced by r e s i s t a n c e IL, contained i n the low-voltage arm,"* Figure 30, 1 Ri Cl=T= Z 0" R2 L — I — ^ _ i X R o ' u 2 ( t ) ZQ > c c m Osc, Figure 30: Impedance matching f o r damped c a p a c i t i v e voltage d i v i d e r s . 42 3 .4 .3 No i se i n Measur ing Systems D i f f e r e n t sources of n o i s e may be desc r i bed w i t h re fe rence to the t y p i c a l impulse v o l t a g e measuring system shown i n F i g u r e 31. F i g u r e 31: Impulse v o l t a g e genera t ing and measuring systems. G - impulse generator 0 - t e s t ob jec t C - f r o n t c a p a c i t o r CA - measuring cab le D - v o l t a g e d i v i d e r T - i s o l a t i n g t rans former I - r eco rd i ng inst rument The n o i s e takes the form of cu r ren t (or v o l t a g e s ) i n j e c t e d i n t o v a r i o u s components of the system which g i ve r i s e to measuring e r r o r s i n the form of p o t e n t i a l d i f f e r e n c e s superimposed upon the a c t u a l s i g n a l . The f o l l o w i n g types of n o i s e can be i d e n t i f l e d : »^»^ »^ a) Cur ren ts induced i n the s h i e l d of the measuring cab le due to ground p o t e n t i a l d i f f e r e n c e s between the d i v i d e r ' s ground and the measuring i ns t r umen t ' s ground dur ing t r a n s i e n t s . To e l i m i n a t e these c u r r e n t s , both the d i v i d e r and the measuring inst rument have to be grounded on ly at one p o i n t , which i s 43 usually at the divider side. In the UBC laboratory, the oscilloscope is not grounded directly, but only indirectly through the shield of the measuring cable. b) Currents induced in the shield of the measuring cable i f i t forms part of a loop made up of the divider ground connection, the cable shield, the instrument case, and the ground return; such a loop is represented by a dotted line in Figure 31. The induced currents may be due to quasi-stationary (magnetic and electric) fields as well as to radiation f i e l d s . Radiation fields are generally built up by very high frequency phenomena such as triggering of sphere gaps of the impulse generator, or discharges in the test c i r c u i t . The quasi-stationary fields may be generated by current flowing in the high-voltage c i r c u i t . Currents may also be induced due to capacitive coupling between the cable shield and the high—voltage c i r c u i t . c) Signals penetrating directly into the active parts of the measuring instrument due to lack of screening. They are mainly due to radiation f i e l d s . d) Currents induced into the mains wire due to stationary fields as well as to radiation f i e l d s . These currents may or may not penetrate into the measuring instrument, depending on the effective- ness of the isolating transformer and the high frequency blocking devices (low-pass f i l t e r s ) . There are two techniques to suppress the high-frequency shield currents. One way is to increase the shield impedance, which can be achieved by winding the measuring cable (of coaxial type) on a ferrite 44 c o r e o r b y s l i d i n g a n u m b e r o f f e r r i t e t o r o i d s o v e r t h e l e n g t h o f t h e c a b l e . T h e d i s a d v a n t a g e o f t h i s t e c h n i q u e i s t h a t f o r l o n g s i g n a l c a b l e s o r v e r y r a p i d p u l s e s , t h e v o l t a g e a n d c u r r e n t d i s t r i b u t i o n a l o n g t h e l i n e i s n o n - u n i f o r m ( s t a n d i n g w a v e s ) a n d a l u m p e d d i s s i p a t i v e i n d u c t a n c e n o l o n g e r p r o v i d e s w i d e - b a n d a t t e n u a t i o n , b e c a u s e a t a p a r t i c u l a r f r e q u e n c y t h e l o c a t i o n o f t h e c o r e may c o i n c i d e w i t h a z e r o - c u r r e n t l o c a t i o n . " ' T h e o t h e r a l t e r n a t i v e i s a p p l y i n g a d d i t i o n a l c a b l e s h i e l d s . T h i s m e t h o d p e r m i t s t h e c a b l e c u r r e n t s , o r i g i n a l l y f l o w i n g t h r o u g h t h e s i g n a l c a b l e ' s b r a i d a n d t h e o s c i l l o s c o p e c a b i n e t , t o b y p a s s b o t h a n d h e n c e t o e l i m i n a t e t h e i n t e r f e r i n g v o l t a g e d r o p s . T h e o u t e r m o s t s h i e l d i s g r o u n d e d a t b o t h e n d s o r a t many p l a c e s t h r o u g h o u t i t s l e n g t h . F i g u r e 32 c o m p a r e s t h e t w o c a s e s o f a s i m p l e c o a x i a l c a b l e a n d a c a b l e w i t h a d o u b l e s h i e l d . I n F i g u r e 3 2 , i-^ i s t h e i n d u c i n g c u r r e n t f l o w i n g i n t h e h i g h - v o l t a g e c i r c u i t ; i 2 ( o r 13) i s t h e i n d u c e d c u r r e n t f l o w i n g i n t h e s e c o n d a r y ( o r t e r t i a r y ) l o o p . C 2 r e p r e s e n t s t h e c a p a c i t a n c e b e t w e e n t h e i n s t r u m e n t c a s e a n d t h e g r o u n d , ( i n p r a c t i c e , t h e c a p a c i t a n c e o f w i n d i n g t o s c r e e n o f t h e i s o l a t i n g t r a n s f o r m e r ) . F o r t h e s i m p l e c o a x i a l c a b l e t h e i n d u c e d c u r r e n t i s g i v e n b y t h e e x p r e s s i o n : ^ s 2 L12 C2 I o ( s ) = IT (S) S = L a p l a c e o p e r a t o r ( 1 7 ) 1 + s 2 L 2 C 2 w h e r e L 1 2 i s t h e m u t u a l i n d u c t a n c e , a n d L j , a n d L 2 a r e t h e s e l f i n d u c t a n c e s o f t h e p r i m a r y a n d s e c o n d a r y l o o p s r e s p e c t i v e l y . I f t h e i n s t r u m e n t c a s e i s g r o u n d e d , C 2 = ° ° , t h e i n d u c e d c u r r e n t i s m a x i m u m . T h i s c o n d i t i o n l e a d s t o m a x i m u m n o i s e , a n d s h o u l d t h e r e f o r e be a v o i d e d . 45 ~1 x 2 S y s t e m d i a g r a m ( a ) x l k L 1 2 J 12 L2. E q u i v a l e n t c i r c u i t 1 ! 1 1. 77777m77777Z7777777^777777777777m7/7m S y s t e m d i a g r a m (b) J 2 3 ' L l ^ • L 3 E q u i v a l e n t c i r c u i t C2 F i g u r e 3 2 : C u r r e n t s i n d u c e d i n t h e c a b l e s h i e l d s b y q u a s i - s t a t i o n a r y m a g n e t i c f i e l d s . a ) S i m p l e c o a x i a l b ) D o u b l e c o a x i a l F o r t h e d o u b l e - s h i e l d c o a x i a l c a b l e , p r o v i d e d t h a t t h e o u t e r s h i e l d i s g r o u n d e d a t b o t h e n d s , t h e c u r r e n t i n t h e i n n e r s h i e l d i s g i v e n b y : I 2 Cs) = s 2 ( L i 2 - L i 3 ) . C 2 1 + s 2 ( L 2 - L 2 3 ) . C 2 . I l ( s ) ( 1 8 ) a n d t h e c u r r e n t i n t h e o u t e r s h i e l d i s g i v e n b y t h e e q u a t i o n : ' ^ 1 3 I 3 < s ) I i ( s ) ( 1 9 ) 46 S i n c e ~ ^ 1 3 a 0> ( l o o p 2 a n d l o o p 3 a l m o s t h a v e t h e s a m e a r e a ) , t h e i n d u c e d c u r r e n t i n t h e i n n e r s h i e l d i s n e g l i g i b l e , w h i l e t h e o u t e r - s h i e l d t a k e s m o s t o f t h e c u r r e n t , t h u s g i v i n g a g o o d p r o t e c t i v e e f f e c t . To h a v e b e t t e r s h i e l d i n g e f f e c t , a n i r o n c o n d u i t i s o f t e n u s e d a s t h e o u t e r m o s t s h i e l d . T h i s w i l l s h i e l d t h e m e a s u r i n g c a b l e f r o m e l e c t r i c a s w e l l a s m a g n e t i c f i e l d s . I n a d d i t i o n , t h e s e l f i n d u c t a n c e o f t h e m e a s u r i n g c a b l e s h i e l d i s i n c r e a s e d . D i r e c t p e n e t r a t i o n o f s i g n a l s i n t o t h e a c t i v e p a r t s o f t h e m e a s u r i n g i n s t r u m e n t i s a v o i d e d b y p u t t i n g t h e m e a s u r i n g i n s t r u m e n t i n s i d e a m e t a l e n c l o s u r e . T h e o v e r a l l l a y o u t o f t h e s h i e l d i n g o f t h e m e a s u r i n g s y s t e m i s s h o w n i n F i g u r e 3 3 . T h i s l a y o u t a l s o d e s c r i b e s t h e s h i e l d i n g s y s t e m i n t h e UBC h i g h - v o l t a g e l a b o r a t o r y w i t h t h e e x c e p t i o n t h a t f e r r i t e c o r e s a r e n o t u s e d . e n c l o s u r e F i g u r e 3 3 : C o r r e c t m e a s u r e m e n t c i r c u i t l a y o u t , a v o i d i n g c a b l e b r a i d a n d c a b i n e t c u r r e n t i n t e r f e r e n c e . F i n a l l y , t o b l o c k t h e c u r r e n t s i n d u c e d i n t o t h e m a i n s w i r e , a n i s o l a t i n g t r a n s f o r m e r a n d a l o w p a s s f i l t e r a r e i n s t a l l e d b e f o r e t h e p o w e r i n p u t o f t h e m e a s u r i n g i n s t r u m e n t . I t i s o f t e n s u f f i c i e n t t o wind the power cord on a f e r r i t e core, which was a l s o done i n the UBC high voltage l a b o r a t o r y . 4. EXPERIMENT EXERCISES 4.1 Introduction A l l tests are done on the "HAEFELY MULTI TEST SET" which i s a v e r s a t i l e system capable of producing a l l major voltage types: - AC voltages 50/60 Hz, up to 75 KV rms. - DC voltages up to 200 KV. - Impulse voltages up to 200 KV. This f l e x i b i l i t y allows the system to be used i n many areas such as the following: I n d u s t r i a l a p p l i c a t i o n s : Factory tests on i n s u l a t o r s , bushings, capacitors, switchgear, instrument trans formers, cables and d i s t r i b u t i o n trans- formers . U t i l i t y applications.: F i e l d t e s t i n g of l a i d - i n cables and comrr p l e t e l y assembled switchgear. Teaching and research applications: Demonstrates with AC, DC and impulse voltages. Generation and measurement of high test voltages . Laboratory t r a i n i n g i n high-voltage tech nology . Experiments with i n s u l a t o r and electrode configurations. Teaching and research a p p l i c a t i o n w i l l be discussed i n t h i s chapter 4 9 4 . 2 A C t e s t 4 . 2 . 1 B r e a k d o w n v o l t a g e o f s p h e r e g a p s A m i n o r m o d i f i c a t i o n t o t h e s y s t e m h a s t o b e m a d e f o r t h i s e x p e r i m e n t . A r e s i s t o r , w h i c h h a s e n o u g h r a t e d v a l u e , h a s t o b e i n s e r t e d i n t h e p r i m a r y c i r c u i t o f t h e t r a n s f o r m e r t o l i m i t t h e p r i m a r y c u r r e n t d u r i n g b r e a k d o w n . A f i v e - o h m r e s i s t o r w a s i n s t a l l e d s o t h a t t h e m a x i m u m p r i m a r y c u r r e n t d u r i n g b r e a k d o w n i s l e s s t h a n t h e o p e r a t i n g c u r r e n t o f t h e p r o t e c t i o n u n i t ( 3 7 A ) . B e f o r e s t a r t i n g t h e e x p e r i m e n t , t h e s u r f a c e s o f t h e s p h e r e s s h o u l d b e p o l i s h e d a n d s e v e r a l b r e a k d o w n t e s t s m a d e t o r e m o v e a n y d u s t p a r t i c l e s . T h e n f i v e r e a d i n g s s h o u l d b e t a k e n f o r e a c h s p a c i n g , f r o m w h i c h t h e a - r i t h m e t i c m e a n v a l u e c a n b e d e t e r m i n e d . ^ > 3 T h e b r e a k d o w n v o l t a g e s o f a s p h e r e g a p o f 10 cm d i a m e t e r , t a k e n a t 2 2 . 8 ° C a n d 9 9 0 m b a r , f o r d i f f e r e n t g a p s p a c i n g s a r e s h o w n i n T a b l e 2 . U s i n g t h e c o r r e c t i o n f a c t o r f o r m u l a o f e q u a t i o n ( 1 ) , t h e c o r r e s p o n d i n g s t a n d a r d b r e a k d o w n v o l t a g e s a r e c a l c u l a t e d a n d c o m p a r e d w i t h t h e a c c e p t e d s t a n d a r d b r e a k d o w n v o l t a g e s i n T a b l e 2 . T a b l e 2 : B r e a k d o w n v o l t a g e s o f a s p h e r e g a p o f 1 0 cm d i a m e t e r f o r d i f f e r e n t g a p s p a c i n g s . G a p (mm) U d ( K V ) . C o r r e s p o n d i n g UDO ( K V ) A c c e p t e d Û Q ( K V ) % e r r o r 1 0 3 1 . 2 5 3 2 . 3 3 1 . 6 2 . 2 2 0 5 7 . 2 3 5 9 . 0 5 9 . 1 0 . 2 3 0 8 2 . 0 0 8 4 . 7 8 4 . 1 0 . 7 I t c a n b e s e e n t h a t t h e e r r o r i s s t i l l b e l o w t h e m e a s u r i n g u n c e r t a i n t y o f 3%; t h e r e f o r e , t h e r e s u l t i s a c c e p t a b l e . 4 . 2 . 2 C o r o n a v o l t a g e o f a s i n g l e c o n d u c t o r a n d a b u n d l e c o n d u c t o r E i t h e r a n A C o r DC s o u r c e c a n b e u s e d f o r t h i s e x p e r i m e n t . C o r o n a s h i e l d s m u s t b e p l a c e d o n b o t h e n d s o f t h e c o n d u c t o r t o a v o i d s h a r p p o i n t e f f e c t s . A s i m p l e c o r o n a s h i e l d c a n b e b u i l t f r o m a l u m i n u m f o i l . H a v i n g c o n n e c t e d t h e c o n d u c t o r w i t h t h e v o l t a g e s o u r c e , o n e c a n s t a r t t h e e x p e r i m e n t . W i t h n o l i g h t i n t h e l a b o r a t o r y , v o l t a g e i s i n - c r e a s e d u n t i l c o r o n a b e g i n s t o a p p e a r o n t h e c o n d u c t o r . T h e v o l t a g e a t t h i s s t a t e i s t h e c o r o n a o n s e t v o l t a g e . T h i s v o l t a g e c a n b e c o m p a r e d 11 12 w i t h t h e c a l c u l a t e d v a l u e w h i c h i s o b t a i n e d f r o m t h e f o r m u l a : ' 18 C e V c o r 2 r ( n - l ) IT , KV n r s n cm w h e r e : , „ . . 0 . 4 2 6 , KV E o = 30 m6 ( 1 H ; ) — ( 2 1 ) C e : s e l f c a p a c i t a n c e ( ^ F / k m ) V C Q : C o r o n a o n s e t v o l t a g e (KV) n : n u m b e r o f s u b c o n d u c t o r s r : s u b c o n d u c t o r r a d i u s (cm) s : s p a c i n g b e t w e e n a d j a c e n t s u b c o n d u c t o r s (cm) m: S u r f a c e o r r o u g h n e s s f a c t o r ( 0 < m < 1 ) 6: R e l a t i v e a i r d e n s i t y 5 1 F o r a s i n g l e c o n d u c t o r a n d a b u n d l e c o n d u c t o r (2 c o n d u c t o r s p e r b u n d l e ) o f 3 9 . 5 cm h e i g h t f r o m t h e g r o u n d p l a t f o r m a n d 0 . 3 5 cm r a d i u s , t h e c a l c u l a t e d a n d t h e e x p e r i m e n t a l c o r o n a o n s e t v o l t a g e s a r e s h o w n i n T a b l e 3 . T a b l e 3 : C o r o n a o n s e t v o l t a g e s o f a s i n g l e c o n d u c t o r a n d a b u n d l e c o n d u c t o r . - h = 3 9 . 5 cm r = . 3 5 cm C a l c u l a t e d V a l u e ( K V ) E x p e r i m e n t a l V a l u e ( K V ) % d i f f e r e n c e S i n g l e C o n d u c t o r 8 5 . 8 8 8 4 . 8 5 1 . 2 0 B u n d l e d C o n d u c t o r (2 C o n d u c t o r s ) s = 2 cm 1 2 6 . 5 9 1 2 3 . 0 4 2 . 8 1 S i n c e t h e d i f f e r e n c e s b e t w e e n t h e t w o v a l u e s a r e f a i r l y s m a l l , o n e c a n c o n c l u d e t h a t t h e e x p e r i m e n t i s c o n s i s t e n t w i t h t h e t h e o r e t i c a l f o r m u l a . 4 . 3 DC t e s t 4 . 3 . 1 R i p p l e m e a s u r e m e n t T h e h i g h DC v o l t a g e s , w h o s e r i p p l e i s t o b e m e a s u r e d , a r e p r o d u c e d f r o m h i g h A C v o l t a g e s . T h e r e c t i f i c a t i o n c a n b e e i t h e r h a l f w a v e o r G r e i n a c h e r d o u b l e r a s e x p l a i n e d i n c h a p t e r 2 . F i g u r e 3 4 s h o w s t h e c o m p l e t e c i r c u i t o f a DC v o l t a g e g e n e r a t o r a n d i t s m e a s u r i n g d e v i c e s . T h e DC v o l t a g e i s m e a s u r e d w i t h a r e s i s t i v e d i v i d e r a n d a DC v o l t m e t e r , a n d t h e r i p p l e b y a c a p a c i t i v e r e s i s t i v e d i v i d e r a n d e i t h e r a p e a k v o l t - m e t e r o r a n o s c i l l o s c o p e . T h e c a p a c i t o r i s m e a n t t o b l o c k t h e DC c o m - p o n e n t s u c h t h a t o n l y t h e r i p p l e a p p e a r s o n t h e l o w e r r e s i s t i v e d i v i d e r . A n a r r e s t o r h a s t o b e p u t i n p a r a l l e l w i t h t h e m e a s u r i n g d e v i c e a s a 52 - G r o u n d i n g s w i t c h - R e s i s t i v e d i v i d e r - C o n t r o l b o x DC v o l t m e t e r - C a p a c i t o r ' s r e s i s t o r - C a p a c i t o r - A r r e s t o r - P e a k v o l t m e t e r - O s c i l l o s c o p e F i g u r e 3 4 : O v e r a l l c i r c u i t o f t h e r i p p l e m e a s u r e m e n t e x p e r i m e n t . p r o t e c t i o n a g a i n s t o v e r v o l t a g e s , b e c a u s e a c o n s i d e r a b l e a m o u n t o f t h e b l o c k e d DC v o l t a g e w i l l a p p e a r o n t h e t e r m i n a l o f t h e m e a s u r i n g d e v i c e i f t h e v o l t a g e s u d d e n l y d r o p s t o z e r o . T h i s f a u l t c a n c a u s e d a m a g e t o t h e m e a s u r i n g d e v i c e i f n o a r r e s t o r i s u s e d . T h e p e r c e n t r i p p l e s f o r d i f f e r e n t v a l u e s o f DC v o l t a g e s a r e s h o w n i n t a b l e 4 : U D C ( K V ) % r i p p l e 1 2 . 2 5 0 . 1 2 2 4 . 9 0 0 . 1 1 3 7 . 5 0 0 . 1 2 5 0 . 0 0 0 . 1 3 6 2 . 5 0 0 . 1 4 7 4 . 8 0 0 . 1 4 8 7 . 5 0 0 . 1 5 T a b l e 4 : P e r c e n t r i p p l e s f o r d i f f e r e n t v a l u e s o f DC v o l t a g e s . 5 3 4 . 3 . 2 P o l a r i t y e f f e c t I n a P o i n t - P l a n e g a p P o s i t i v e a n d n e g a t i v e DC v o l t a g e s a r e a p p l i e d t o o b s e r v e t h e p o l a r i t y e f f e c t o f t h i s g a p . A p r o t e c t i v e r e s i s t o r ( 6 0 0 0 fi) i s u s e d t o p r o t e c t t h e s m o o t h i n g c a p a c i t o r C s a g a i n s t s u d d e n s h o r t c i r c u i t s d u r i n g b r e a k d o w n . I n a d d i t i o n , t h e v o l t a g e may n o t b e i n c r e a s e d b e y o n d 7 0 K V t o a v o i d o v e r - l o a d i n g o f t h e r e c t i f i e r s a n d c a p a c i t o r s . T h e a r r a n g e m e n t o f t h e p o i n t - p l a n e g a p , w h i c h w a s u s e d f o r t h e e x p e r - i m e n t , a n d t h e c o r r e s p o n d i n g r e l a t i o n s h i p b e t w e e n b r e a k d o w n v o l t a g e a n d s p a c i n g a r e s h o w n i n F i g u r e 3 5 . ' One c a n s e e t h a t f o r l a r g e r s p a c i n g s , a p o s i t i v e p o i n t e l e c t r o d e h a s l o w e r b r e a k d o w n v o l t a g e s t h a n a n e g a t i v e p o i n t e l e c t r o d e . F o r , a p o s i t i v e p o i n t e l e c t r o d e t h e e l e c t r o n s m o v e KV B r e a k d o w n v o l t a g e ( m a g n i t u d e ) 80 4 1 0 2 0 30 4 0 5 0 60 G a p ( a ) F i g u r e 3 5 : P o l a r i t y e f f e c t i n a p o i n t - p l a n e g a p . ( a ) E l e c t r o d e s c o n f i g u r a t i o n ( b ) B r e a k d o w n v o l t a g e v e r s u s s p a c i n g c u r v e t o w a r d s i t , p r o d u c i n g e x c e s s p o s i t i v e c h a r g e s i n t h e d i r e c t i o n o f t h e p l a t e s , a n d t h e r e f o r e t h e g r o w t h o f d i s c h a r g e c h a n n e l i s s t i m u l a t e d . 54 4.4 Impulse Test 4.4.1 Preliminary Preparations A. Oscilloscope and i t s attenuator To determine the required bandwidth of the o s c i l l o s c o p e the highest frequency, f m a x , has to be considered, which i s a function of the size of the generating system and can be determined by the formula:^ MHz (22) -max 4 ( H g + H c ) where: C = v e l o c i t y of l i g h t , 300 m / y s Hg = the height of generator i n m H c = the height of front capacitor i n m The approximate bandwidth of the os c i l l o s c o p e i s then given by the formula:^ f l i m (-3dB) = — (23) 2^ T(osc) 1 where: T ( O S c ) = : : 4 T fmax For the "HAEFELY" test system, the generator and the front capacitor are both of 1 m height and consequently the upper l i m i t of os c i l l o s c o p e bandwidth i s : 3 0 0 = 37.5 MHz , (24) ™ a x 4 ( 1 + 1 ) f l i m <-3dB) = — = 75 MHz (25) 4.TT f max The TEKTRONIX 475 o s c i l l o s c o p e has a bandwidth of 200 MHz which c l e a r l y s a t i s f i e s the requirement. The attenuator has to be adjusted c o r r e c t l y so that n e i t h e r over- compensation nor undercompensation occur. The behaviour of a compen- sated attenuator e x c i t e d by a square wave i s shown i n Figure 36. Figure 36: Output of a compensated attenuator f o r d i f f e r e n t degrees of compensation. (a) Correct compensation (b) Overcompensated (c) Undercompensated 56 B . C i r c u i t A n a l y s i s T h e i m p u l s e w a v e f o r m c a n b e p r e d i c t e d w i t h t h e UBC E l e c t r o m a g n e t i c T r a n s i e n t s P r o g r a m ( E M T P ) ^ T h e i n p u t o f t h e p r o g r a m i s t h e m o d e l o f t h e c i r c u i t . T h e o r e t i c a l l y , t h e i m p u l s e c i r c u i t c o n s i s t s o f c a p a c i t o r s a n d r e s i s t o r s o n l y , b u t s i n c e t h e c i r c u i t i n t e r c o n n e c t i o n i s q u i t e l o n g u n a v o i d a b l e i n h e r e n t i n d u c t a n c e e x i s t s i n t h e c i r c u i t . T h i s i n d u c t a n c e w a s m e a s u r e d w i t h a s i m p l e r e s o n a n t c i r c u i t a n d a n a p p r o x i m a t e v a l u e o f 1 uH w a s o b t a i n e d . I n c l u d i n g t h i s i n h e r e n t i n d u c t a n c e i n t h e m o d e l o f t h e c i r c u i t , o n e f i n d s t h a t t h e r e i s a c u r v a t u r e a t t h e b e g i n n i n g o f t h e w a v e f o r m ( s h o w n i n F i g u r e 3 7 ) . IMPULSE VOLTAGE Ti Mc IMICR03EC0NGS) F i g u r e 3 7 : I m p u l s e v o l t a g e w a v e f o r m o b t a i n e d b y u s i n g E M T P . T h u s , t o d e t e r m i n e t h e o r i g i n o f t h e w a v e f o r m , t h e c u s t o m a r y s t r a i g h t l i n e t h r o u g h 30% a n d 90% p o i n t s h a s t o b e d r a w n . T h e i n h e r e n t i n d u c t a n c e c a n b e r e d u c e d b y p u t t i n g a l l t h e c o m p o n e n t s o f t h e i m p u l s e c i r c u i t o n t h e g r o u n d p l a t f o r m , t h u s , e l i m i n a t i n g t h e 57 supplied metal base. This procedure was used i n the laboratory not only to reduce the inductance but also to eliminate or minimize the ground loops . 4.4.2 Noise Reductions A. Ground loop elimination Due to the existence of r a d i a t i o n f i e l d s and quasi-stationary f i e l d s , ground loops have to be eliminated or minimized to reduce common mode interference. This can be achieved by putting the whole impulse c i r c u i t on the ground platform and l a y i n g the measuring cable as close as possible to the ground platform. B. Further noise reduction In addition to ground loop elimination, common mode interference can further be reduced by using a m u l t i s h i e l d cable instead of a simple coaxial cable. This w i l l allow the ground current, which formerly flowed in the inner cable s h i e l d , to flow i n the outer s h i e l d s . In the laboratory, a t r i a x i a l cable l a i d i n a grounded copper tube i s used. As a comparison, the impulse oscillogram of the c i r c u i t with ground loops and a simple coaxial cable and that of the c i r c u i t with reduced ground loops and a shielded cable are shown i n Figure 38. I t can be seen that the noise has been reduced considerably. Some minor interferences can s t i l l be seen i n Figure 38b. These interferences are due :to r a d i a t i o n f i e l d s and quasi-stationary f i e l d s which penetrate into the os c i l l o s c o p e d i r e c t l y and/or through the power l i n e . 58 (a) 5S555SSSBB Time scale: 2 ysec/div. Impulse oscillogram of the c i r c u i t with ground loops and a simple coaxial cable. Figure 38a: (b) Time scale: 0.5 ysec/div. "Figure 38b: Impulse oscillogram of the c i r c u i t with reduced ground loops and shielded cable. To e l i m i n a t e them, the o s c i l l o s c o p e i s s h i e l d e d w i t h a metal box and a low-pass f i l t e r i s i n s e r t e d i n the incoming power l i n e . As a r e s u l t , a continuous and clean o s c i l l o g r a m was obtained (shown i n Figure 39). Time s c a l e : 0.5 usec/div. Figure 39: Impulse o s c i l l o g r a m of the c i r c u i t w i t h reduced ground loops and a shi e l d e d cable. O s c i l l o s c o p e i s i n s i d e a metal box. 5. CONCLUSIONS The UBC high-voltage test set, which has been slightly modified and expanded, can now be used for various experiments for undergraduate students. AC and DC tests have been performed repeatedly with repro- ducible results. For impulse tests various techniques of shielding have been applied in the UBC high-voltage laboratory to obtain reasonably accurate impulse oscillograms. 6 1 L I S T OF R E F E R E N C E S 1. P o w e r S y s t e m I n s t r u m e n t a t i o n a n d M e a s u r e m e n t C o m m i t t e e o f t h e I E E E P o w e r E n g i n e e r i n g S o c i e t y , " I E E E G u i d e f o r F i e l d T e s t i n g P o w e r A p p a r a t u s I n s u l a t i o n " , I E E E I n c . , New Y o r k , 1 9 7 8 . 2 . D . K i n d , " A n I n t r o d u c t i o n T o H i g h - V o l t a g e E x p e r i m e n t a l T e c h n i q u e " , ( B o o k ) , B r a u n s c h w e i g , V i e w e g , 1 9 7 8 . 3 . E. K u f f e l a n d M. A b d u l l a h , " H i g h - V o l t a g e E n g i n e e r i n g " , ( B o o k ) , P e r g a m o n P r e s s L t d . , O x f o r d , 1 9 7 0 . 4 . I E C S t a n d a r d , " H i g h - V o l t a g e T e s t T e c h n i q u e s " , B u r e a u C e n t r a l d e l a C o m m i s s i o n E l e c t r o t e c h n i q u e I n t e r n a t i o n a l e , G e n e v e , 1 9 7 6 , P a r t 3 : M e a s u r i n g D e v i c e s . 5 . A . J . S c h w a b , " H i g h - V o l t a g e M e a s u r e m e n t T e c h n i q u e s " , ( B o o k ) , T h e M . I . T . P r e s s , M a s s a c h u s e t t s , 1 9 7 2 . 6 . A . J . S c h w a b , " E l e c t r o m a g n e t i c I n t e r f e r e n c e i n I m p u l s e M e a s u r i n g S y s t e m s " , I E E E P E S Summer M e e t i n g , V a n c o u v e r , B . C . , C a n a d a , 1 9 7 3 , P a p e r N o : T 7 3 0 6 2 - 7 . 7 . A a . P e d e r s e n , J . S t a v n e s s , L . T h i o n e , " I n s t r u m e n t s f o r I m p u l s e V o l t a g e M e a s u r e m e n t s O s c i l l o s c o p e s a n d C r e s t V o l t m e t e r s " , E l e c t r a . N o : 5 9 , 1 9 7 8 , p p . 4 1 - 9 0 . 8 . R . M a l e w s k i , D . t r a i n , A . D e c h a m p l a i n , " C a v i t y R e s o n a n c e E f f e c t i n L a r g e HV L a b o r a t o r i e s E q u i p p e d w i t h E l e c t r o m a g n e t i c S h i e l d " , IEEE P E S W i n t e r M e e t i n g , New Y o r k , 1 9 7 7 . 9 . R . M a l e w s k i a n d G . R . N o u r s e , " T r a n s i e n t M e a s u r e m e n t T e c h n i q u e s i n EHV S y s t e m s " , I E E E T r a n s , o n P o w e r A p p a r . a n d S y s t . , V o l . P A S - 9 7 , N o : 3 , 1 9 7 8 . 1 0 . V . P a l v a , I R R - I M S G r o u p ( 1 ) , " F a c i n g UHV M e a s u r i n g P r o b l e m s " , E l e c t r a N o : 3 5 , 1 9 7 6 , p p . 1 5 5 - 2 5 6 . 1 1 . A . I n o u e , " H i g h - V o l t a g e T r a v e l l i n g W a v e s w i t h C o r o n a D i s c h a r g e o n B u n d l e d C o n d u c t o r s " , I E E E P E S W i n t e r M e e t i n g , New Y o r k , 1 9 7 8 , P a p e r N o : A 7 8 1 7 0 - 3 . 1 2 . " T r a n s m i s s i o n L i n e R e f e r e n c e B o o k - 3 4 5 K V a n d A b o v e " , E l e c t r i c P o w e r R e s e a r c h I n s t i t u t e , P a l o A l t o , C A , 1 9 7 5 . 1 3 . N . A r i , " E l e c t r o m a g n e t i c P h e n o m e n a i n I m p u l s e V o l t a g e M e a s u r i n g S y s t e m s " , I E E E T r a n s , o n P o w e r A p p a r . a n d S y s t . , V o l . P A S - 9 6 , N o : 4 , 1 9 7 7 . 1 4 . H . W . D o m m e l , " T r a n s i e n t s P r o g r a m U s e r ' s M a n u a l " , D e p t . o f E l e c t r i c a l E n g i n e e r i n g , T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r , B . C . , C a n a d a . V 6 T 1 W 5 . APPENDIX I SAFETY REGULATIONS FOR HIGH-VOLTAGE EXPERIMENTS Experiments with high voltages could become p a r t i c u l a r l y hazar- dous for the p a r t i c i p a n t s should the safety precautions be inadequate. To give an idea of the required safety measures, as an example the safety regulations of the High-Voltage I n s t i t u t e of The Technical 2 Un i v e r s i t y of Braunschweig s h a l l be described below. These supplement the appropriate safety regulations and as f a r as possible prevent r i s k to persons. S t r i c t observance i s therefore the duty of everyone working i n the laboratory. Here any voltage greater than 250 V against earth i s understood to be a:.high voltage. Fundamental Rule: Before entering a high-voltage setup everyone must convince himself by personal observation that a l l the conductors which can assume high p o t e n t i a l and l i e i n contact zone are earthed, and that a l l the main leads are interrupted. Fencing A l l high-voltage setups must be protected against unintentional entry of the danger zone. This i s appropriately done with the aid of m e t a l l i c fences. When set t i n g up the fences f o r voltages up to 1 MV the following minimum clearances to the components at high-voltage should not be reduced: for a l t e r n a t i n g and d i r e c t voltages 50 cm for every 100 KV for impulse voltages 20 cm for every 100 KV However, for voltages le s s than 100 KV a minimum clearance of 50 cm has to be maintained, independent of the type of voltage. 63 For voltages over 1 MV, in particular for switching impulse voltages, the values quoted could be inadequate; special protective measures must then be introduced. The fences should be reliably connected with one another conduc- tively, earthed and provided with warning boards inscribed: "High-volt- age! Caution! Highly dangerous!" It is forbidden to introduce conduc- tive objects through the fence whilst the setup is in use. Safety-Locking In high-voltage setups each door must be provided with safety switches; these allow the door to be opened only when a l l the main leads to test setup are interrupted. Instead of direct interruption, the safety switches may also operate the no-voltage relay of a power circuit breaker, which, on opening the door, interrupts a l l the main leads to the setup. These power circuit breakers may only be switched on again when the door i s closed. For direct supply from a high-voltage network (e.g. 10 KV city network), the main leads must be interrupted visi b l y before entry to the setup by an additional open isolating switch; The switched condition of a setup must be indicated by a red lamp "Setup switched on" and by a green lamp "Setup switched off". Earthing A high-voltage setup may be entered only when a l l the parts which can assume high-voltage in the contact zone are earthed. Earthing may only be effected by a conductor earthed inside the fence. Fixing the . 64 earthing leads onto the parts to be earthed should be done w i t h the a i d of i n s u l a t i n g rods. E a r t h i n g switches w i t h a c l e a r l y v i s i b l e operating p o s i t i o n , are a l s o p e r m i s s i b l e . In high-power setups w i t h d i r e c t supply from the high-voltage network, e a r t h i n g i s achieved by e a r t h i n g i s o l a t o r . E a r t h i n g may only f o l l o w a f t e r s witching the current source o f f , and may be removed only when there i s no longer anyone present w i t h i n the fence or i f the setup i s vacated a f t e r removal of e a r t h . A l l m e t a l l i c p a r ts of the setup which do not ca r r y p o t e n t i a l during normal s e r v i c e must be o earthed r e l i a b l y and w i t h an adequate cross s e c t i o n of at l e a s t 1.5 mm . C i r c u i t and Test Setup Inasmuch as the setup i s not s u p p l i e d from ready wired desks, c l e a r l y marked i s o l a t i n g switches must be provided i n a l l leads to the low-voltage c i r c u i t s of high-voltage transformers and arranged at an e a s i l y i d e n t i - f i a b l e p o s i t i o n outsider.the fence. These must be opened before e a r t h i n g and before e n t e r i n g the setup. A l l leads must be l a i d so that there are no l o o s e l y hanging ends. Low voltage leads which can assume high p o t e n t i a l s during breakdown or fl a s h o v e r s and lead out of the fenced area, e.g. measuring c a b l e , ^ c o n t r o l c a b l e , supply c a b l e , must be l a i d i n s i d e the setup i n earthed s l e e v i n g . A l l components of the..setup must be e i t h e r r i g i d l y f i x e d or suspended so that they cannot topple during operation or be p u l l e d down by the lead s . For a l l setups intended f o r research purposes, a c i r c u i t diagram s h a l l be f i x e d o u t s ide the fence i n c l e a r l y v i s i b l y p o s i t i o n . A t e s t setup may be put i n t o operation only a f t e r the c i r c u i t has been checked and permission to begin work given by an authorized 65 person. Conducting the Experiments Everyone carrying out experiments in the laboratory i s personally responsible for the setup placed at his disposal and for the experi- ments performed with i t . For experiments during working hours one should try, in the interest of personal safety, to make sure that a second person is present in the testing room. If this i s not possible, then at least the times of the beginning and end of an experiment should be communicated to a second person. When working with high-voltages outside working hours, a second person familiar with the experimental setups must be present in the same room. Explosion and Fire,..Risk, Radiation Protection In experiments with o i l and other easily inflammable materials, special care is necessary owing to the danger of explosion and f i r e . In each room where work is carried out with these materials, suitable f i r e extinguishers must be to hand, ready for use. Easily inflammable waste products, e.g. paper or used cotton waste, should always be dis- posed of immediately in metal cans. Special regulations must be observed when radioactive sources are used. 66 APPENDIX I I FORMULA OF MODE OSCILLATIONS The formula of mode o s c i l l a t i o n s i n a rec t a n g u l a r resonator can be derived from MAXWELL's equations: , x H = E | I V x E . - w f A f t e r an extensive manipulation of these d i f f e r e n t i a l equations, the e l e c t r i c and the magnetic f i e l d s of TM modes and TE modes are obtained f o r the boundary c o n d i t i o n s x = 0, x = a and y = 0, y = b: TM modes: n r \ ™ r -i 3mir „ _ .mirx. „. ,mry. i (wt-gz) " E m (x,y) = Re { - f h — C Cos( ) SinC-r 2-) e J } a ox-^ J h z a mn]_ a b x n t \ T , r - j 3mr _ „ . ,mT7x x _ /nTry. j (wt-gz) -, * E o y i ( x ' y ) = R e < h^b" Cmn-L S i n C ^ ) Cos(-^-) e J } a y a z E O Z i ( x , y ) = Re { C ^ S i n ( ^ ) S i n ( ^ ) e ^ " ^ } C m n i S i n ( ^ ) C o s ( ^ ) «J } a x H o y i ( x , y ) = Re ( ^ f f C m n i Cos(=?) S i n (52*) e ^ " ^ > a y where: C m n corresponds to the p a r t i c u l a r mode defined by a given choice of m and n. (m, n are i n t e g e r s ) B z = yew - ( — r - (-;-) a b h 2 = ( - ) 2 + ( ^ ) 2 a b The e l e c t r i c f i e l d s t r a v e l i n g i n the oppos i te d i r e c t i o n a r e : n r \ rt -f ~j Bmn „ n / H I T T X . „ . /niry. j (cot+Bz) \ -E O X 2 ( x , y ) = R e i —j- C m n 2 C o s ( — ) S i n ( - ^ - ) e J i ax T? / \ T> - iBnir /imrx. „ /niry. j (cot+Bz) E o y 2 ( x , y ) = R e { J h 2 b Cmn2 S l n ( — ) C o s e J } ay App l y i ng boundary c o n d i t i o n z = 0 and z = C, the f o l l o w i n g i s ob ta i ned : z = 0 : E O X l ( x , y ) + E O X 2 ( x , y ) = 0 (Mi + M 2 ) Cos ( 2 ^ ) S i n C 5 ^ ) S i n cot = 0 a b where: Kl = C m n i h^a x The re fo re , M-̂  = - M 2 z = C ; E o x l ( x ' y ) + E o x 2 ( x . y ) = 0 M.. C o s ( — ) S±n(~^-) { S i n (tot - BC) - S i n (cot + BC) } = 0 1 a b -2 Cos cot S i n BC S i n BC = 0 BC = PTT where: p i s an i n t e g e r C T> ^ rP- 2 ,mi7.2 ,1117.2 But g = yeco - ( — ) - ( — ) a b Therefore, , = U I ( — ) 2 + ( £ 1 ) 2 + (SE)2 /u7 V a b c or f = — — \ / c ^ ) 2 + < i r ) 2 + c^-) 2 2i7/ye" y The same expression can derived from E (x ,y ) and E (x ,y ) and from TE modes.

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