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High-voltage measurement techniques Halim, Armand Gregoire 1980

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H I G H - V O L T A G E MEASUREMENT  TECHNIQUES  by  Armand B.E.E.,  Seattle  Gregoire |Halim  University,  Washington,  1978  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  SCIENCE  in THE F A C U L T Y OF GRADUATE S T U D I E S (Department  of  We a c c e p t  this  to  the  Electrical  thesis  required  as  Engineering)  conforming  standard  T H E 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 June, (c)  1980  Armand G r e g o i r e  Halim,  1980  In  presenting  this  thesis  an advanced degree at the I  Library shall  f u r t h e r agree  for  scholarly  by h i s of  this  written  make i t  freely available  t h a t permission  for  I agree  reference and this  It  i s understood that copying or  for f i n a n c i a l gain shall  permission.  U n i v e r s i t y of B r i t i s h  Columbia  for  that  study. thesis  purposes may be granted by the Head of my Department  2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  r.  the requirements  f o r e x t e n s i v e copying o f  Depa rtment The  fulfilment of  the U n i v e r s i t y of B r i t i s h Columbia,  representatives. thesis  in p a r t i a l  or  publication  not be allowed without my  -11  ABSTRACT  The Department of E l e c t r i c a l Engineering at the University of B r i t i s h Columbia acquired a high-voltage test set i n 1979 f o r teaching and r e search purposes. dergraduate  To make t h i s test set useful f o r experiments which un-  students can do themselves, various additions and modifications  had to be made. This thesis describes these additions and modifications.  First, a  Faraday cage had to be constructed with interlocking safety c i r c u i t s . periments were then developed  Ex-  to show basic high-voltage phenomena with  AC voltage, with DC voltage, and with impulse voltages.  Considerable  modifications were required to eliminate noise i n the impulse measuring system.  iii  T A B L E OF CONTENTS  ABSTRACT.  1  T A B L E OF CONTENTS  »  LIST  OF T A B L E S  LIST  OF I L L U S T R A T I O N S  1  2.  3.  1  ^  i  v  i  INTRODUCTION  1  1.1  Significance  1  1.2  Test  2  1.3  Scope of  equipment this  Thesis  2.1  Introduction  2.2  Alternating  2.3  Direct  2.4  Impulse  3  3 Voltage  3  Voltage  6  Voltage  10  MEASUREMENTS  1  3.1  Introduction.  3.2  AC v o l t a g e  3.4  •  Objective  3.2.2  Measuring  3  I  measurements  3.2.1  DC v o l t a g e  i  2  GENERATION OF H I G H VOLTAGES  3.3  1  l  v  ACKNOWLEDGEMENTS  1.  1  14 •  Devices  measurements  3  14 •  .  .  14 23  3.3.1  Objective  23  3.3.2  Measuring Devices  23  Impulse  voltage  measurements  29  3.4.1  Objective  29  3.4.2  Setup  of  Measuring  System  30  3.4.3  Noise  in  Measuring  Systems  42  l  iv  4.  EXPERIMENT  EXERCISES  4.1  Introduction  4.2  AC t e s t  .  48  . . . . . . . . . .  48 49  4.2.1  Breakdown v o l t a g e  of  4.2.2  Corona voltage  a  of  sphere gaps single  .  .  .  conductor  .  .  .  and a  .  .  .  49  bundle  conductor A•3  4.4  5.  LIST  DC t e s t  50  • • > » * • > •  •  •  •  •  >  «  «  o  .  .  •  a P o i n t - P l a n e gap  >  •  «  »  «  «  •  •  .  51 51  .  .  .  .  .  .  .  53 54  4.4.1  Preliminary  4.4.2  Noise Reductions  OF R E F E R E N C E S  .  '  Polarity  CONCLUSIONS  .  *  4.3.2  test  .  «  .  Impulse  .  »  R i p p l e measurement in  .  «  4.3.1  effect  .  >  Preparations  54 57  60  61  APPENDIX  I  62  APPENDIX  II  66  V  LIST OF TABLES  Table 1.  2. 3. 4.  Page F l a s h o v e r 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 o f e i t h e r p o l a r i t y , and f o r f u l l n e g a t i v e s t a n d a r d impulses and i m p u l s e s w i t h l o n g e r t a i l s . . .  16  Breakdown v o l t a g e s o f a sphere gap o f 10 cm f o r d i f f e r e n t gap s p a c i n g s . . .  49  Corona onset v o l t a g e s o f a s i n g l e conductor bundle conductor.  diameter and a 51  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 . ? . . • • 52 .  LIST  OF  ILLUSTRATIONS  Figure  Page  1.  Effect  2.  Single-stage test  3.  Three-stage  4.  of  Series  on w i t h s t a n d  test  resonant  reactor 5.  time  voltage  transformer transformer  circuit  for  2  circuits  4  cascade single  5 transformer/  unit  Half-period  6 rectification  with  ideal  circuit  elements  7  6.  Villard  circuit  7.  Greinacher doubler-circuit  8  8.  Zimmermann-Wittka  9  9.  Greinacher cascade  circuit  10.  Example of  rectifier  11.  Basic  12.  Multiplier  8  cascade  circuit  impulse-voltage  circuit  circuit  lib  circuits  10  circuits  after  connection  Marx  11 for  3 stages  in  •>  voltage  12  13.  Sphere gaps  14.  B r e a k d o w n v o l t a g e U^Q of sphere gaps as a f u n c t i o n o f gap 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. • P e a k v o l t a g e measurement a c c o r d i n g to Chubb and Fortescue  15.  for  9  measurement  16.  Peak voltage  17.  Basic  18.  M e a s u r e m e n t o f DC v o l t a g e voltage resistor  19.  measurement  circuits  of  voltage  with  Electrostatic  21.  Voltmeter  with  configuration  voltmeters the  capacitive  divider-  transformers by means o f  •  •  17 18  •  20 22  a  high24  M e a s u r e m e n t o f a DC v o l t a g e resistive divider  20.  17  for  by means o f  a 25  high  sphere-plate  voltages  26  electrode 27  vii  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 i m p u l s e g e n e r a t o r  24.  B l o c k diagram of i m p u l s e 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 i m p u l s e v o l t a g e  36  26.  Impulse waveshapes o b t a i n e d 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 l o w e r c a p a c i t a n c e v a l u e  system . . . .  .37  27.  Impulse v o l t a g e measuring system w i t h divider  28.  C o n n e c t i o n 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 t o a cathode-ray o s c i l l o s c o p e  40  Compensation o f s i g n a l c a b l e c a p a c i t a n c e by a complex c a b l e t e r m i n a t i o n  41  Impedance matching f o r damped c a p a c i t i v e v o l t a g e dividers  41  29. 30.  resistive  31  39  31.  Impulse v o l t a g e g e n e r a t i n g and measuring systems. . . 42  32.  C u r r e n t s i n d u c e d i n the c a b l e 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  C o r r e c t measurement c i r c u i t l a y o u t , a v o i d i n g b r a i d and 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  46  33. 34.  cable  O v e r a l l c i r c u i t o f 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 p o i n t - p l a n e gap  53  36.  Output of a compensated a t t e n u a t o r 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 o b t a i n e d by u s i n g EMTP . . .  56  38.  a. b.  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 ground l o o p s and an o r d i n a r y c o a x i a l c a b l e  58  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 l o o p s and a s h i e l d e d c a b l e  58  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 l o o p s and a s h i e l d e d c a b l e . O s c i l l o s c o p e i s i n s i d e a m e t a l box  59  vi'ii  ACKNOWLEDGEMENTS  I for  his  tions a  would help  his  I Council  to  e x p r e s s my  throughout  he made.  visiting  for  like  Also,  professor  of  very  Canada  this  work and  wish  to  to for  my  supervisor,  the  timely  c o n v e y my g r a t i t u d e  f r o m The K a t h o l i e k e  considerable  am a l s o  I  thanks  Dr.  H.W.  suggestions to  Universiteit  Dr.  D.  Van  Dommel, and  correc-  Dommelen,  Te L e u v e n  (Belgium),  Engineering  Research  help.  grateful  for  their  to  Natural  financial  Sciences support.  and  1  1.  A withstand period  of  normal  service  be o f  time  A C , DC  having  a  by  of  value  the  to  (having  half  value.  1-. 1  Significance The w i t h s t a n d  ful  a  completion  present  is  in  of  the  insulation  time 1.2  specified,  is  and  the  For the  ysec  voltage  specified  test  is  over-voltage test  insulation absolutely  gives  below  cause the  temperature  the  reduces  overall  failure  to  half  and  test  ground),  DC t e s t  the  A  standard  insulation  for  length  However,  defects.  For  insulation  no  of  time  time.  gross  does not  this  reason the  to  can Success-  defect  this  is  mean t h a t  characteristics  the  determined  that  specified  pulse  desired  a demonstration  an  a  voltages,  after  value.  may  or  virtual  a  time  to  waveshape i s  some a s s u r a n c e t h a t  of  a withstand  1 minute  the  under  50 y s e c  structure. free  Dielectric  a voltage  the  rise  for  respect  typically  restricted  encountered  F o r AC o r  time  a  test  the  is  often  (Practical  Strength).  Practical  further  with  an impulse  virtual  for  that  specified  virtual  supplemented w i t h measurements of Dielectric  than  and w a v e - s h a p e .  has b e e n ^ r e a c h e d . ^  has  insulation  greater  The v o l t a g e  polarity  rise  an  specified polarity  application  pulse  withstand  a  subjects  stress  conditions.  virtual  lightning  test  a voltage  specified  duration test  voltage  INTRODUCTION  the  value to  tests  required  to  rise  in  dielectric  dielectric  without  general  the  Strength  further  behaviour  of  increase an  cause  local  of in  the  of  immediate  these  material,  the  insulator  done w i t h  weak r e g i o n s .  strength  strength  are  in  applied terms  continued breakdown. The  This  temperature  regions,  and  a n d may  result  voltage. of  application will rise  consequently  Figure  withstand  of  in 1  voltage  eventual illustrates versus  2  time  of  voltage  application.  -Withstand voltage, peak value  0 8 Time, Figure  1.2  Test  Equipment  Test  equipment  system. be  sources be  w i l l  with  Scope of  First, cussed test  in  set.  the  in  a  time  consists of is  a voltage  either  methods. thesis.  on w i t h s t a n d  of  source and a  AC, DC, or  A review  of  voltage.  Impulse  these various  Various measuring  measuring type  can  voltage  apparatus w i l l  also  and t h e i r  measurements are  dis-  relate  the  thesis.  in  An e x t e n s i v e test  be u s e d t o  of  Thesis  g e n e r a l and  Finally,  this  generation  UBC h i g h - v o l t a g e had to  different  this  this  Effect  source which  be done  discussed in  1.3  typically  The v o l t a g e  constructed  1:  seconds  high  voltages  particular  as  investigation  set  obtain  series of  w h i c h was d e v e l o p e d w i t h  of  is  then  they of  the  described.  reasonably accurate  exercises for the  help  of  Dr.  to  UBC  impulse measuring Various  high-voltage system of  techniques  of  the  shielding  oscillograms.  undergraduate Van Dommelen.  students  is  presented  3  2.  2.1.  G E N E R A T I O N OF H I G H VOLTAGES  Introduction High-voltage  verify  its  (a)  AC  voltage  (b)  DC  voltage  (c)  Impulse  formers,  equipment  performance.  Generation  With  power  tested  with  three  types  of  voltages  to  are:  voltage  of  high  therefore,  additional  These  is  voltages  the  first  circuits,  impulse voltages.  in  type  the  laboratories of  high  AC v o l t a g e  DC v o l t a g e  can also  is  voltage  can  then  usually  done u s i n g  produced be  is  of  transformed  be produced d i r e c t l y  by  AC  trans-  type.  into  DC a n d  electrostatic  generators. The UBC-High V o l t a g e AC v o l t a g e to  up  to  75 K V r m s ,  Set  can produce  DC v o l t a g e  up  to  all  three  200 KV, and  forms,  namely  60 Hz  impulse voltage  up  200 K V .  2.2  Alternating  Voltage  Transformers generally turn by  Test  have  ratios  is  than  Figure  power  the  voltage  arrows  between  the  windings  two  indicates  high  fed  voltage  basic the  rating  for  of  test  magnitude  of  the  the  in  laboratories  frequently current  is  much  to  larger  usually  One end o f  transformers  be c o m p l e t e l y  H and  voltages  supply.  circuits  winding  and  The p r i m a r y  from mains  except  must  alternating  power  transformers.  grounded,  2 shows  high  lower  transformer  usually  cascade where  generating  considerably  a regulating  winding  for  the  supplied  high-voltage  be connected  in  isolated.  transformers. stress  excitation  on t h e winding  The l e n g t h  of  insulation E or  iron  core  4  F.  The f u i l y  the  two  isolated winding  terminals  or  at  the  may b e g r o u n d e d  center  tap,  as  if  n e c e s s a r y at  according reasons of  2:  Single  E  -  - High-voltage  F  -  to  one  (b)  H  Excitation Iron  To g e n e r a t e  employs  stage  test  transformer  winding winding  circuits  (a)  Single pole  (b)  Fully  isolation  isolated  core  voltages  Figure  of  shown.  (a)  Figure  either  2 are  above a few now r a r e l y  instead  several transformers  hundred used;  KV,  for  e c o n o m i c a l and  a series connection  (introduced  in  single-stage  of  1 9 1 5 b y W.  the  high  transformers technical  voltage  P e t e r s e n F.  windings  Dessauer  and  o E.. W e l t e r ) .  The c i r c u i t  windings  the  the  E of  stages  consist  of  configuration  upperstages  immediately  below.  three-binding  is  shown  are  supplied  The  individual  transformers.  from  in  Figure  the  stages,  3.  coupling except  The  excitation  windings for  the  K  of  uppermost,  5  K  E  3 U -  •  3 P  3 P  I  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 c i r c u i t i s usually used to generate the high voltage. c i r c u i t i s shown i n Figure 4 .  The basic  I t comprises the load, which i s almost purely  capacitive, i n series with a continuously variable inductance.  The  inductance  i s varied to produce series resonance with the capacitive load at the supply frequency.  High voltages are then obtained by i n j e c t i n g current into the"  series c i r c u i t .  Control of the high voltage i s obtained by regulation of the  supply current. Some of the advantages of series resonant c i r c u i t s are as follows: 1.  Harmonics, which are caused by saturation i n the transformers, are attenuated.  2.  I f f a i l u r e of the test object occurs, a power arc does not develop. Instead, the voltage collapses immediately after the load capacitance i s short-circuited.  This i s of great importance to the cable industry  where a power arc can sometimes lead to dangerous explosions.  6  Cable under test  Reactor  AC  L  l  r  Supply  L  l  r  r  1 J  r  (b)  Figure  4:  Series  resonant  circuit  transformer/reactor (a) The s e r i e s other  resonant  laboratories  circuit have  actual  circuit  (b)  used  test  set  the  circuit  uses  single  equivalent  h a s now b e c o m e a c c e p t e d  also  T h e UBC h i g h - v o l t a g e  for  unit.  for  a single  for  circuit  cable  general  testing.  Many  applications.  transformer  with  one  end  grounded.  2.3  Direct  The period tor  Voltage  simplest  rectifier,  C will  smoothed  give  direct  circuit  for  shown i n  Figure  a pulsating voltage  the  with  direct  generation 5.  a...high  The c i r c u i t  voltage,  residual  of  ripple  without  and w i t h is  DC v o l t a g e the  smoothing  obtained.  is  the  smoothing capacitor  halfcapaciC a  7  4  F i g u r e 5:  Half-period rectification a) b) c)  with ideal circuit-elements.  Circuit Output v o l t a g e curve w i t h o u t smoothing c a p a c i t o r C Output v o l t a g e curve w i t h smoothing c a p a c i t o r C  To o b t a i n h i g h e r d i r e c t v o l t a g e s , v o l t a g e m u l t i p l i e r c i r c u i t s Some of t h e s e v o l t a g e m u l t i p l i e r c i r c u i t s Villard  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  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 .  circuit.  cascade c i r c u i t .  circuit:  doubling c i r c u i t . and  are:  1.  Villard  a r e used.  T h i s c i r c u i t , shown i n F i g u r e 6,  i s the s i m p l e s t  The b l o c k i n g c a p a c i t o r C i s charged to t h e peak v a l u e  thus i n c r e a s e s t h e p o t e n t i a l of the h i g h - v o l t a g e o u t p u t t e r m i n a l w i t h  r e s p e c t t o t h e t r a n s f o r m e r v o l t a g e by t h i s amount. output v o l t a g e u ( t ) i s i m p o s s i b l e .  However, smoothing of  the  8  C  Figure 6:  Villard a) b)  Greinacher Doubler-circuit:  circuit  C i r c u i t diagram Voltage curve  Extension of the V i l l a r d c i r c u i t 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 V i l l a r d c i r c u i t to be smoothed. Figure 7  The complete c i r c u i t i s shown i n  $  (a) Figure 7:  "  (b)  Greinacher doubler-circuit a) b)  Zimmermann-Wittka c i r c u i t :  C i r c u i t diagram Voltage curve I f two V i l l a r d c i r c u i t s are connected i n  opposition as i n Figure 8 , an unsmoothed direct voltage i s produced between  9  the o u t p u t t e r m i n a l s , w i t h a, peak v a l u e t h r e e times t h a t of t h e vo  transformer  l t a g e a n d , under no l o a d c o n d i t i o n s , a mean o u t p u t v o l t a g e U = 2. Uj,,  • (a). Figure 8:  (no-load  condition)  C i r c u i t diagram Voltage curve  G r e i n a c h e r cascade c i r c u i t : circuit.^  (b)  Zimmermann-Wittka c i r c u i t a) b)  t  A three-stage c i r c u i t  T h i s i s an e x t e n s i o n of G r e i n a c h e r D o u b l e r i s shown i n F i g u r e 9 as an example; many p r a c -  t i c a l c i r c u i t s c o m p r i s e o n l y the p a r t s shown i n b o l d l i n e s .  U = 6U>  F i g u r e 9:  G r e i n a c h e r cascade c i r c u i t  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 :  (no-load  This c i r c u i t ,  condition). shown i n F i g u r e 10,  g i v e s low r i p p l e and v o l t a g e drops even when o u t p u t c u r r e n t s a r e h i g h .  10  Figure  DC v o l t a g e electrostatic used very  can also  Impulse  Figure of  the  for  11  switch  value  U,  its  DC v o l t a g e s  circuit kV  200  gap  the  two  voltages.  F.  low  power  rating,  by  this  using  method  is  not  for  in  the  the  UBC l a b o r a t o r y kV l e v e l  100  and  is  the  done  with  Greinacher  level.  to  most  The  important  impulse  a DC v o l t a g e  basic  capacitor and  UQ  The d e s i r e d  impulse  the  elements  then  voltage  circuits C  s  is  charged  discharged u(t)  used  appears  by  for via  the a  high-ohmic  ignition  across  genera-  the  of load  Ctc  The v a l u e s impulse  high  the  shows  resistance  capacitor  of  namely,  Voltage  impulse  charging  of  rectifier  doubler-circuit  tion  Because  electrostatically,  often.  half-period  2.4  be generated  generators.  The g e n e r a t i o n the  Example of cascade rectifier circuits (no-load condition)  10:  of  voltage. and  long  circuit  A short decay  rise  times  time  determine  requires  require  slow  rapid  the  wave  charging  discharging.  shape of of  This  C^ t o is  the the  achieved  peak by  •11  uo R*  I  u(t)  u(t)  I  (t=0) circuit  (t=0) circuit  a  h  (a)  Lightning impulse T = 1.2 ys T = 50 y s  Switching impulse T r = 250 Th = 2500  voltage  voltage ys ys  C  s  r  (b) •Figure  11:  Basic a)  R  e  C  s  >>  R^.  To  >>  C^.  The  whereas C R S  the  £  for  charging Marx  parallel voltage  As All  circuit  voltage,  then  which  impulse  on the b.  rise  tail  are  one  commonly Several  corresponds  a  capacitors  to  s  '  the  wave  front  a  time  are  curves  with the  series, number  of  has  time  e  the  to  choose  constant  CgCR^ + R )  a peak v a l u e multiplier impulse giving of  to  a  one has  for  lightning  R^C^  circuit  impulse  a, and  lib.  higher  than  circuit  capacitors  the  DC  proposed  by  are  a multiplied  charged  total  in  charging  stages.  multiplier  charged  curves  possible  constant  Figure  identical  three-stage C  as  uses  the  Voltage  high  in  in  circuits.  U as  voltage  voltages  discharged  example,  has  shown  impulse  b)  on  The o u t p u t  1923.2>3  and  an  a peak v a l u e  impulse  generate  in  Circuits  exponential  decay  switching  To  E.  the  obtain  impulse-voltage  the  circuit stage  is  shown  in  Figure  charging-voltage  12.  UQ',  12  Figure  via  the  the  capacitors  series  high  reduced  C '  a  resistors  will  g  again  to  M u l t i p l i e r c i r c u i t a f t e r Marx for stages in c i r c u i t l i b connection.  charging  connection  discharge  ships  12:  of  via  single  be  a l l  R^'.  connected  damping  the  in  R ' £  equivalent  the  series  resistors  resistors  stage  When a l l  so  R(j';  switch that  gaps is  finally,  and R ^ ' . circuit  3  all  The n - s t a g e  where  the  F break  down,  charged  via  the  C '  C^  will  s  and  circuit  following  can  be  relation-  hold: U  0  C s  = n U = n  0  '  C  '  impulse  both  voltage.  the  R  s  T h e UBC h i g h - v o l t a g e can produce  R  standard  set  = n R  d  = n R e  test  d  uses  lightning  ' '  e theccircuit' impulse  shown  in- Figure  voltagec and  the  lib  and  switching  13  3.  3.1  Introduction  It  is  generally  directly. to  a  or  or  measure h i g h convert  the  voltages  quantity  can be measured w i t h  A high-voltage  transformer,  a high-voltage  The l e a d s  (c)  A measuring  (d)  The  the  AC and is  required  for  for  cable,  or  or  to  currents  be  measured  conventional  high-current  or  UBC l a b o r a t o r y divider  is  of  the  measuring  instru-  system  for  the  instrument,  the  advantage  the  distortion  AC/DC  small  of  the  waveform  They  and  are  and  into  connects is  capacitive  the  test  circuit.  terminating,  of  and  dividers  the  are  capacitive  impulse measurements  generator  impulse  usually  transient  can be a n a l y z e d more  etc.  attenuating,  DC m e a s u r e m e n t s ,  and  the  used. divider  capacitive  circuit.  the  coaxial  self-inductance  an o s c i l l o s c o p e i s  digital  voltage  and a  low  voltage  type.  side  Coaxial  shielding  of  the  cables  effect  divider  have  which  minimizes  signal.  voltmeters  instruments.  uses  of  device  a  instrument.  For  impulse  cable, which  impedance,  this any  divider,  networks.  both r e s i s t i v e  The m e a s u r i n g recording  with  recording  used  a voltage  measuring  together  impulse measurements. a part  example,  connecting  impedances or  indicating  The r e s i s t i v e  often  which  device;  adapting  with  to  A converting  (b)  divider  is  to  comprises:  (a)  In  practical  current  oscilloscopes.  generally  for  not  The u s u a l : p r o c e d u r e  low v o l t a g e  ments  the  MEASUREMENTS  easily.  peak-voltmeters  provided  with  generally  recorders,  the  used.  are  very  HV-test  set.  However,  with which  common  impulse  newer  To  indicating observe  equipment  waveforms  14  In r e g a r d to d i r e c t measurements of h i g h v o l t a g e s , v o l t a g e gaps such as sphere gaps a r e commonly u s e d ; peak v o l t a g e s a r e then o b t a i n e d . measurement o f DC v o l t a g e s can a l s o be done by an e l e c t r o s t a t i c  3.2  Direct  voltmeter.  AC V o l t a g e 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  v a l u e 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 t h a n 3%.^ T h i s e r r o r requirement w i l l be met i f d i v i d e r or voltage transformer than 1%.4 ders, it  the v o l t a g e r a t i o of the  voltage  i s s t a b l e and known w i t h an e r r o r of  i n the case of high-impedance s y s t e m s , such as a v o l t a g e  less divi-  may not be p o s s i b l e t o comply w i t h t h i s e r r o r r e q u i r e m e n t .  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 t h a n 3% may have t o be a c c e p t e d . The secondary o b j e c t i v e i s t o measure the a m p l i t u d e of h a r m o n i c s , 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 or not more than 1% of the f u n d a m e n t a l , w h i c h e v e r i s l a r g e r . ^  amplitude Harmonic  measurements r e q u i r e a wave a n a l y s e r i n a d d i t i o n t o the e x i s t i n g  equipment.  A measuring e r r o r of not more t h a n 5% f o r harmonics up to the s e v e n t h and not more than 10% f o r those up to the twenty s e v e n t h , i s r e q u i r e d the wave a n a l y s e r . ^  3.2.2  Measuring Devices The f o u r most common A C - v o l t a g e measuring d e v i c e s a r e : 1.  Sphere gaps  2.  M e a s u r i n g c a p a c i t o r s (Chubb & F o r t e s c u e )  3.  Capacitive voltage  4.  Voltage  dividers  transformers  for  15  Sphere  gaps:  Sphere value  of  gaps  high  calibration length data  for  are  voltages,  tables  with  in  voltage  exceeds  a  period  voltages  with  voltage  Figure sphere  frequencies  13  shows  is  The r a t i o  because  with  increasing  geneous  and  at  the  demonstrated  in  up  of to  on  same t i m e Figure  the  for  a  of The  gap  calibration  Measurement  ysec  once  discharge voltage". frequency  peak of  the  of  1.  few  500 KHz c a n be  peak  investigations,  a function  Table  voltage  low  frequency  for  voltage  the  applied  Over  considered  or to  such  of be  constant.  AC v o l t a g e s  arrangement  S/D the the  field  must  the  be  too  curves  begin  become to  with  large,  becomes i n c r e a s i n g l y  breakdown v o l t a g e s  14 w h e r e  not  measurement  inhomo-  random.  level  off  This  as  increases.  Humidity of the  sphere  by  gaps,  relative  density  h a s no  air  d may b e  applying  the  significant  however, density found  following  influence  the  breakdown  d.  The a c t u a l  from  the  if  slowly.  (Spacing/Diameter)  ratio  of  been o b t a i n e d .  in  a power  the  basic S/D  as  occurs within  raised  the  extensive  Standard Rules  breakdown  occur  amplitude  measurement  of  included  gap  peak v a l u e  always  the  spheres have  "British  "static  gaps.  is  of  a sphere  the  Breakdown w i l l the  sizes the  the  for  breakdown v o l t a g e s  Sphere gaps"-^ a r e  Breakdown of  short  used  and as a r e s u l t  giving  different  recommended  Voltage  commonly  the  voltage  value  breakdown is  breakdown  tabulated  formula:^*^  on  U^Q  voltage  proportional  voltage (standard  at  to air  value)  S/D  Kilovolts p.  B o h  .'  6 0  u  peak at 20°C ; 1013 v n i l l i b a r s Sphere diameter, cm  1  -a  O. ft. CO CO  0.05 0.10 0.15 0.2.0. 0.25 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0 1.2 1.4 1.5 1.6 ] .8 2.0 2.2 2.4 2.6 2.8 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 9.0 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28  2  5  2.8 4.7 6.4 .8.0 9.6 11.2 14.4 17.4 20.4 23.2 25.8 28.3 30.7 (35.1) (38.5) (40.0)  8 0 9 6 11 2 14 3 17 4 20 4 23 4 26 3 29 2 32 0 37 6 42 9 45 5 48.1 53 0 57 5 61 5 65 5 (69 0) (72 5) (75.5) (82 5) (88 5)  6.25  14.2 17.2 20.2 23.2 26.2 29.1 31.9 37.5 42.9 45.5 48.1 53.5 58.5 63.0 67.5 72.0 76.0 79.5 (87.5) (95.0) (101) (107)  10  16.8 19.9 23.0 26.0 28.9 31.7 37.4 42.9 45.5 48.1 53.5 59.0 64.5 69.5 74.5 79.5 84.0 95.0 105 115 123 (131) (138) (144) (150) (155)  12.5  15  16.8 19.9 23.0 26.0 28.9 31.7 37.4 42.9 45.5 48.1 53.5 59.0 64.5 70.0 75.0 79.5 85.0 97.0 108 119 129 138 146 (154) (161) (168) (174) (185) (195)  •. 16.8 19.9 23.0 26.0 28.9 31.7 37.4 42.9 45.5 48.1 53.5 59.0 64.5 70.0 75.5 80.0 3.5.5 98.0 110 122 133 143 152 161 169 177 (185) (198) (209) (219) (229)  25  31.7 37.4 42.9 45.5 48.1 53.5 59.0 64.5 70.0 75.5 81.0 86.0 99.0 112 125 137 . 149 161 173 184 195 206 ' 226 244 261 275 (289) (302) (314) (326) (337) (347) (357) (356)  j  . 50  75  59.0 64.5 70.0 75.5 81.0 86.0 99.0 112 125 138 151 164 177 189 202 214 239 263 286 309 331 353 373 392 411 429 445 460 489 515 (540) (565)  59.0 64.5 70.0 75.5 81.0 86.0 99.0 112 125 138 151 164 177 190 203 215 240 265 290 315 339 363 387 410 432 453 473 492 530 565 600 635-  100  86.0 99.0 112 125 138 151 164 177 190 203 215 241 266 292 318 342 366 390 414 438 462 486 510 555 595 635 675  150  200  138 151 164 177 190 203 215 241. 266 292 318 342 366 390 414 438 462 486 510 560 610 655 700  266 292 318 342 366 390 414 438 462 486 510 560 610 660 705  T h i s t a b l e i s not v a l i d f o r the measurement o f impulse v o l t a g e s below 10 kV. The f i g u r e s i n the b r a c k e t s , which are f o r spacings o f more than 0.5D are o f d o u b t f u l accuracy.  -Table 1 :  F l a s h o v e r 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 n e g a t i v e s t a n d a r d impulses and impulses w i t h l o n g e r t a i l s : One sphere earthed.^  17  '////////<  1000  kV  /  800  D=10C) c m  600 0  \  50crn  1,00  200  / /  25 c m  i  10 err 1 10  20  30 s  d *  d  U  do  1013 = 0.289  where-:  273 + 20 273 + t b 273 + t  b:  p r e s s u r e i n mbar  t:  temperature i n  Udo  :  cm  50  F i g u r e 1 4 : Breakdown v o l t a g e of sphere gaps as f u n c t i o n of gap s p a c i n g s , f o r v a r i o u s sphere d i a m e t e r s D.  F i g u r e 1 3 : Sphere gaps f o r v o l t a g e measurement  U  UO  »•  u  do (1)  Udo  °C  breakdown v o l t a g e at p r e s s u r e 1013 mbar and  temperature  20°C. Even under a p p a r e n t l y i d e a l c o n d i t i o n s , h a v i n g made a l l o w a n c e s 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 e l e c t r o d e s u r f a c e and p r o p e r adjustment uncertainty  of 3% r e m a i n s .  for  spherical  of the s p a c i n g , a measuring  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 e x c e s s i v e space and a r e e x p e n s i v e , Continuous v o l t a g e measurements a r e o b v i o u s l y i m p o s s i b l e w i t h sphere g a p s , s i n c e the v o l t a g e s o u r c e 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  Inspite  of  their  devices  in  high—voltage  they  can a l s o  disadvantages,  be  used  sphere  laboratories.  as v o l t a g e  gaps  can be  Apart  limiters,  useful  and  from voltage  versatile  measurements,  as voltage-dependent  switches, 2  as  pulse  sharpening  gaps  The UBC H i g h - v o l t a g e against  Measuring  As  test  over-voltages.  measurements  as  part  and  of  as v a r i a b l e  set  uses  high-voltage  sphere  They  have  also  this  thesis  gaps  been  for  adapted  capacitors,  transformer for  AC  etc.  protection  voltage  project.  Capacitors:  opposed  to  sphere  gaps,  the  circuit  suggested  by  Chubb  and  2 Fortescue  in  AC v o l t a g e with  its  1913  is  capable  continuously  current  Figure  and  and v o l t a g e  15:  of  measuring  accurately.  the  Figure  15  shows  of the  curves.  Peak v o l t a g e measurement Chubb a n d F o r t e s c u e . a) b)  peak value  Circuit Current  and v o l t a g e  according  curves  to  a  high circuit  19  A charging voltage  u(t),  through  two  flows  of  moving-coil  peak v a l u e  are  fulfilled. the  U of  _  1  I  = -  ±  If  the  voltage  and w i t h  6  In is  -  of  one  symmetrical  is  current that  applied is  The  passed arithmetic  measured w i t h is  the  = i-  proportional  certain  rectifiers  or  conditions  assumed i d e a l ,  then  for  with  [u(T/2)  reference  -  to  u(0)]  the  (2)  zero  line:  (3)  U  4  of  when  period  rectifiers)  allows  maximum p e r  half-period.  to  the  r  ^Cdu = £  this  can o c c u r .  have only  measurement  are  (oscillating of  done  by  crossover  each  used,  the  only  than  high-voltage  current  half-period.  one  rotating  w i t h more  of  u(t)  mechanical  contacts,  AC v o l t a g e s  observing in  assumed that  synchronous  Oscillographic monitoring  usually one  was n o t  rectifiers  The u s e o f  rectifiers  correct  is  expression, it  semiconductor  controllable  n e c e s s a r y and  to  obtains  derivation  half  a  <>  a s i n u s o i d , but  allowed  C and  ground.  branch  this  the  = \ lie  maximum p e r  is  to  provided  UCT/2)  is  one  capacitor  left-hand  is  of  t = 0 t o T/2  dt  T = -jr,  the  change  has:  f o r  = 2  of  a n d V2  rectifiers  i i  u(0)  rate  high-voltage  voltage  the  i /  in  high  T  u(T/2)  i-^  of  ±1 = 1=0-4^ dt  the  As shown b e l o w ,  the  behaviour  the  by  rectifiers  current  period  given  through  instrument.  the  conducting  i,  antiparallel  mean v a l u e  If  current  i-]_,  which  one shape is  20  As the frequency f, the measuring capacitor C, and the current 1^ can be determined precisely, measurement of symmetrical AC voltages using the technique of Chubb & Fortescue with the appropriate layout i s very accurate, and i s suitable for the c a l i b r a t i o n of other peakvoltage 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 c i r c u i t s have been developed which permit the measurement of peak values of high AC-voltages with the aid of capacitive dividers.  Compared with the c i r c u i t of Chubb and Fortescue, most of these  methods have the advantage that the reading i s p r a c t i c a l l y  independent  of frequency, and multiple extrema per half-period of the voltage to be measured can be permitted.^  Cl u(t)  . u2  Cb)  (a) 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 1 6 .  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 v a l u e U2 of the l o w e r arm v o l t a g e U£(t)  of the c a p a c i t i v e d i v i d e r .  charges the c a p a c i t o r C voltage.  M  The r e s i s t o r R  M  which d i s -  i s meant t o f o l l o w r e d u c t i o n s of the a p p l i e d  The c h o i c e of time c o n s t a n t f o r t h i s d i s c h a r g e p r o c e s s i s  determined by t h e d e s i r e d response o f the measuring system.  In general  one c h o o s e s , Rm Cm < 1 s e c o n d ,' and R  m m » C  (5)  J  <6>  The r e s i s t o r R2 i s n e c e s s a r y t o m i n i m i z e c h a r g i n g of current f l o w i n g through the r e c t i f i e r  V .  by the  The v a l u e of R2 must be  chosen i n such a way t h a t t h e DC v o l t a g e drop a c r o s s R2 w h i c h causes DC c h a r g i n g of C2 remains as s m a l l as p o s s i b l e . have R2 << RJJJ.  In t h i s case one must  On t h e o t h e r hand, t h e c a p a c i t i v e d i v i d e r r a t i o  not be a f f e c t e d much by R 2 , w h i c h r e q u i r e s R2 >> ^  should  .  W i t h a l l t h e s e c o n d i t i o n s , the r e l a t i o n between the peak v a l u e of the h i g h v o l t a g e and the i n d i c a t e d v o l t a g e U C,  + C  i s g i v e n by:  ,  2  =  U  M  U  m  The w o r k i n g p r i n c i p l e of the " I m p u l s e Peak V o l t m e t e r " of the  (7)  UBC  high-voltage test  s e t i s based on t h i s t e c h n i q u e , even though a more  elaborate c i r c u i t  i s employed.  I n the c o n t r o l b o x , t h e r e i s a l s o an AC  v o l t m e t e r w h i c h o p e r a t e s on the same p r i n c i p l e but i n d i c a t e s peak v a l u e d i v i d e d by J2 (r^^)  i n s t e a d of peak v a l u e .  Voltage Transformers: High AC v o l t a g e s can be measured v e r y a c c u r a t e l y w i t h v o l t a g e  trans-  22  formers.  The b a s i c  capacitive  voltage  Inductive expensive  to  extensively  since they  work,  mainly  voltage  source.  are  The t y p e  of is  because i t  pole  shown  for  require  supply networks  testing  single  transformers  winding. in  of  transformers  voltage  build  high—voltage  circuits  isolated  in  Figure  very  very  high  large  inductive  17.  voltages number  capacitive voltage often  u(t)  of  are  very  turns  of  transformer  considered unsuitable  imposes a high  and  capacitive  used  for  normal  l o a d upon  TuoCt).  2  2  (a)  Figure  17:  Basic  (b)  circuits  a)  Inductive  1 2 3  Primary winding Secondary winding Iron core  voltage  of  voltage  transformers  transformers b) C^, L W  Capacitive voltage transformer C Divider capacitors Resonance i n d u c t o r Matching transformer 2  (marking  Inductive  is  and c a p a c i t i v e v o l t a g e  measurements o n l y  voltages w i l l  the  u(t) u (t)  tory  the  are  required.  reproduce  not  low.  possible shape.  to  the  when p a r t i c u l a r l y The  shape of  D e p e n d i n g on measure the  transformers  the  primary  type  peak v a l u e ,  of  are  of  used i n  voltage,  a voltage if  the  measuring device  the  a)  labora-  p r e c i s e measurements of  secondary voltage the  as under  rms v a l u e  or  to  moderate  transformer  load  resistance  connected, display  it  the  is wave  23  3.3  DC V o l t a g e  3.3.1  Objective  The -  general  to  -  to  an e r r o r  To  than  the  satisfy (a)  the  (c)  The  the  actual  error  ratio  of  the  are:^.  voltage,  typically  3%. typically  ripple of  with  amplitude  the  or  an e r r o r  of  not  than  more  DC v o l t a g e , w h i c h e v e r  requirements,  of  of  the  not  to  be  the  is  not 1% larger.  measuring  system has  than  frequency is  than  it  divider  is  and  1%.  may n o t  an o v e r a l l  In  the  stable case  be p o s s i b l e  error  slightly  of to  known  highcomply  with  e x c e e d i n g 3%  accepted.  drawn  less  voltage  more  systems where  current  voltage  than  amplitude,  specification,  not  mean v a l u e  mean v a l u e  above  an e r r o r  may h a v e  is  the  measurements  specifications:^  impedance this  DC v o l t a g e  more  ripple  The v o l t a g e  The  not  10% o f  certain  with  (b)  of  arithmetic  f u l f i l l  of  arithmetic  measure the  more of  objective  measure the  with  to  Measurements  from 0.05  the  fundamental  of  the  system used  and known w i t h i n the  source  at  full  voltage  mA.  response of  adequate  high-voltage  ripple  for  10% f o r  frequency  up  to  measuring  ripple  frequencies  from  five  times  this  frequency.  3.3.2  Measuring Devices  Measurement be  done w i t h  the  of  the  arithmetic  mean v a l u e  of  a high  following:  (a)  High-voltage  (b)  Electrostatic  resistors  and v o l t a g e  voltmeters  dividers.  DC v o l t a g e  can  24  (c)  F i e l d strength  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 a r e o t h e r methods f o r DC v o l t a g e measurements. are s u i t a b l e for  the d e t e r m i n a t i o n  In p h y s i c s l a b o r a t o r i e s  of the peak v a l u e U of h i g h DC v o l t a g e s .  the n u c l e a r resonance method i s o f t e n a p p l i e d  to measure DC v o l t a g e s . which i s p r o p o r t i o n a l  Sphere gaps  P r o t o n s a r e a c c e l e r a t e d i n an e l e c t r i c  to the v o l t a g e to be measured.  At c e r t a i n  field kinetic  e n e r g i e s t h e s e p r o t o n s c o l l i d e w i t h l i g h t atomic n u c l e i , p r o d u c i n g sonant n u c l e a r t r a n s f o r m a t i o n s  which permit very accurate  re-  determination  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 V o l t a g e The c u r r e n t  flowing  dividers:  through a r e s i s t o r connected to a DC s o u r c e 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  c a t i o n s the c u r r e n t must be v e r y s m a l l , of the o r d e r of 1 mA f o r  appliexample,  because o t h e r w i s e e x c e s s i v e l o a d i n g of the v o l t a g e s o u r c e and e x c e s s i v e h e a t i n g of the measuring r e s i s t o r w i l l o c c u r . ^ small current  On the o t h e r h a n d , a  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 ;  form of l e a k a g e c u r r e n t s  i n i n s u l a t i n g m a t e r i a l s and on  s u r f a c e s , and a l s o a s a r e s u l t of corona d i s c h a r g e s . problems, a s p e c i a l design for h i g h - v o l t a g e The s i m p l e D C - v o l t a g e measuring c i r c u i t  •  rh  these occur i n  the  insulating  To a v o i d t h e s e  r e s i s t o r s i s needed. i s shown i n F i g u r e 1 8 .  Rl  u(t) F i g u r e 18: Ammeter  Measurement of DC v o l t a g e by means of a high-voltage r e s i s t o r .  The ammeter instrument  is is  assumed at usually  mean v a l u e U o f  the  Replacing a resistor which  is  the  R ,  earth  chosen,  DC  shown  in  the  A sensitive  indication  of  moving-coil  which  is  the  arithmetic  connection  of  a voltmeter  voltage.  ammeter  with  one o b t a i n s  2  potential.  Figure  a parallel  a voltage  divider  for  measuring  DC  and  voltages  19.  Ri  Figure  T h e UBC h i g h - v o l t a g e DC v o l t a g e s . the  The  "Control  Impulse  The u(t)  is  voltmeters  and v e r y  of  low  applied,  reduce  the  be  calculated  small  energy  schematic  to  to  measure  this  (IPV) the  M e a s u r e m e n t o f a DC v o l t a g e by means o f a resistive divider  divider  method  can be u s e d ,  peak value  of  to  measure  instead  a DC  of  voltage.  Voltmeters:  Electrostatic  surement  system uses  Peak Voltmeter  Box V o l t m e t e r " ,  Electrostatic  resistance  test  19:  of  the  have  capacitance,  high the  voltages.  device  electric  spacing from the  the  s of  the  change  W(t)  is  field  advantage which  = \  very  high  makes them u s e f u l  internal for  mea-  2  shown  in  produces  electrodes. of  of  energy  C u (t) 2  of  Figure a force This  the  20. F(t)  When a which  attractive  electric  voltage tends  force  can  field:  (8)  26  u(t)  •Fit)  b)  Figure  The of  20:  Electrostatic a) b)  Using Using  1. 2. 3.  Movable Axis of Mirror  capacitance energy  one  C depends  voltmeters  spherical a movable  segment  spacing  dW + F d s = 0 a n d a s s u m i n g  voltages.  s.  4, 5.  Using  disconnection  Hueter) (after Starke and S c h r o d e r )  Light Scale  the of  source  law of  conservation  the voltage  source  obtains:  F ( t )  ,_<L1<JLL= i 2  =  ds  Taking  the  arithmetic  = F  This  high  electrodes (after e l e c t r o d e segment  electrode rotation  on the  for  force  defined reading.  is  value  mean v a l u e  1 dC 1 =  2  d7 T  / ^  counter-balanced of  spring  F of  (  t  t  )  )  t  "  2  d7 U  by a s p r i n g .  extension  which  (9)  force,  1 dC d  dj; ds  the  2 ^ s U  (  2  2  (10)  r m s  At  equilibrium  c a n be t r a n s l a t e d  there  into  a  is  some  voltage  Field-Strength Meters: Variable capacitance  2 i s the basic p r i n c i p l e of this device.  The schematic of the device i s shown i n Figure 21. electrodes 1 and 1  The two measuring  are alternately passed under the semi-circular  opening 2 of the grounded plate 3; this produces a variable between each electrode and the high—voltage  electrode 4.  H  1,1' 2 3 4 5 6  Revolving semicircular discs Semicircular opening Earthed covering plate High-yoltage electrode Commutator Ammeter  capacitance  28  At constant  r a t e of r e v o l u t i o n , a p e r i o d i c a l t e r n a t i n g c u r r e n t  i ( t ) flows between the measuring e l e c t r o d e s , which i s r e c i t i f i e d by commutator 5.  The  by a m o v i n g - c o i l  a r i t h m e t i c mean v a l u e I a f t e r r e c t i f i c a t i o n  ammeter b .  i s read  Since the c u r r e n t I i s p r o p o r t i o n a l to  measured v o l t a g e , the r e a d i n g o f the ammeter can be converted voltage  a  into a  reading.  R i p p l e - v o l t a g e measurement Ripple voltages  are AC  circuits: components superimposed on the DC  For smoothed DC v o l t a g e s , the peak v a l u e s  voltage.  9U of the r i p p l e v o l t a g e s  always much s m a l l e r than the mean v a l u e U, which i s why  an  measurement, performed w i t h a r e s i s t i v e d i v i d e r , i s too  insensitive.  To  separate  F i g u r e 22.  The  a c a p a c i t o r i s used.  The  circuit  i s shown i n  d i v i d e r r a t i o ,of t h i s  C i r c u i t f o r measuring r i p p l e voltages .  by:  I f the f u l l magnitude of the r i p p l e  i s to appear on the lower arm  the d i v i d e r , the d i v i d e r r a t i o must be as c l o s e to one frequencies  oscilloscopic  a  F i g u r e 22:  i s given  are  the r i p p l e from the DC v o l t a g e , a v o l t a g e d i v i d e r made  up of a r e s i s t o r and  circuit  the  of  as p o s s i b l e f o r a l l  i n the r i p p l e spectrum, which r e q u i r e s  uRC  »  1  (12)  29  In  the  instead  of  project.  UBC h i g h - v o l t a g e a single  The is,  A surge  arrestor  to  protect  the  previously, to  3.4  the  voltage  which  is  also  drop  will  appear  u(t)  on  appears can be  installed in  of  a practical  and  oscilloscope  the  a resistive  in  case  development  on  the  of  of  installed,  this  thesis the  oscilloscope. lower  arm  collapses  voltage,  the  is  arm of  an  the  u(t)  whole  part  on  with  voltage  cause the  resistive  lower  displayed  parallel  the  divider  resistor  to  zero.  applied  divider.  This  can  oscilloscope.  Impulse  3.4.1  as  therefore, reduced  Sudden v o l t a g e  destroy  resistor,  ripple  divider  laboratory,  Voltage  Measurements  Obj e c t i v e  The -  general  To m e a s u r e in  the  error -  objectives  not  chopping  To m e a s u r e  The  above  measurement  the  the  £  T  if  0.5  with  impulses  on  the  and  tail,  are:^  impulses  typically  chopped  with  an  of  impulses  A which  is  chopped  dependent  on on  the the  front, time  to  follows:  if  the  full  measurements  3%.  an e r r o r  as  of  peak or  peak value  with T  typically  of  exceeding  To m e a s u r e  impulse-voltage  peak value  vicinity  typically  -  the  of  c  > 2  us,  ys  < T  time an  c  < 2  parameters  error  requirements  qualifications  A < 3%  not  will :^  ys,  A < 5%  which  define  exceeding  be met  if  the  impulse  shape,  10%.  the  system meets  the  following  30  (a)  The v o l t a g e r a t i o  of t h e d i v i d e r s h o u l d be s t a b l e and known  w i t h an e r r o r not exceeding (b)  1%.  The s c a l e f a c t o r of t h e o s c i l l o s c o p e o r peak v o l t m e t e r ( i n c l u d i n g a t t e n u a t o r or c o u p l i n g d e v i c e s ) s h o u l d be and known w i t h an e r r o r not e x c e e d i n g  (c)  2%.  The time s c a l e of the o s c i l l o s c o p e s h o u l d be s t a b l e and known w i t h an e r r o r not e x c e e d i n g  (d)  stable  2%.  The response time r e q u i r e m e n t s f o r measuring  systems depend  on the i m p u l s e 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 i m p u l s e and l i g h t n i n g i m p u l s e s chopped  on the peak o r t a i l - Switching impulses where  |T| < 0.2 | T | < 0.03 T  c  T  c r  ys. T  Q  and  | T | < 0.03  T  c r  i s chopping time i s time t o c r e s t  | T | i s r e s p o n s e time  3.4.2  Setup of M e a s u r i n g A measuring  System  system f o r i m p u l s e v o l t a g e s g e n e r a l l y c o n s i s t o f :  (a)  a Faraday Cage  (b)  a W i r i n g System  (c)  a Voltage Divider  (d)  a M e a s u r i n g Instrument and i t s c o n n e c t i o n t o t h e d i v i d e r  Faraday Cage: In p r a c t i c e , a h i g h - v o l t a g e c i r c u i t behaves as an antenna r e c e i v e s e x t e r n a l e l e c t r o m a g n e t i c waves.  which  E l e c t r o m a g n e t i c waves a r e a l s o  produced d u r i n g breakdown d i s c h a r g e p r o c e s s e s i n t h e h i g h - v o l t a g e c i r c u i t s t h e m s e l v e s , and t h e s e can i n t u r n d i s t u r b t h e s u r r o u n d i n g s .  However, the  31  •disturbing  effect  generally  worse  than  surroundings. conductive  ground which a  To  metal  Strong voltages  the  surroundings  that  eliminate shield  and  currents,  produce  Figure  these  in  the  Z  23:  K  circuit  G s  I  c  t  r  stray  of  ground  one u s e s  associated with  by  these  of  an  Figure  impulse  >  a  rapidly  shows  changing  type.  strong  generator  ground  the  highly  special  23  on  is  Stray  fields  schematically G and a  test  impedance.  impulse generator system. F i g u r e 23a f l u x in normal setup. F i g u r e 23b f l u x w i t h test setup in Faraday cage.  generator,  P test,  capacitances,  current  a  high  and d i s c h a r g e d rises.  circuit  circuit  a Faraday cage.  unavoidable  impulse  charging  high-voltage  a  Jumping p o t e n t i a l i n shows l i n e s of s t r a y shows l i n e s of s t r a y  C  the  high-voltage  of  consisting the  the  interference  potential  represents  on  interferences  form  cause  charged  transient  by  fields,  also  capacitances are  P;  exerted  electromagnetic  high voltage  object  of  for  stray  object,  Zg g r o u n d ground  impedance,  capacitances.  32  Electric  field  grounded  surroundings.  tances  C  Because  lines  which are of  the  high  have values  as high  generator's  ground  ground  cage w a l l . the  high-voltage  voltage  electrodes  as  stray  rate  voltage  of  change,  some k i l o a m p e r e s ,  through  Z  the  Figure  , will  entire  23b,  a l l  in  field  w i l l  the  charging  w h i c h when  result  stray  raise  the  lines  then  flow  potential  on  of  the  may  to  the  surge  transient located  terminate  the  capaci-  currents  is  w i l l  the  transients.  returning  circuit  and  ground  considerable  high-voltage  currents  and can not  inner  ground  inside on  the  surface  of  system of  the  circuit.  conductive metal highly  high  charged and d i s c h a r g e d d u r i n g  If  As mentioned  this  the  rapidly  The c h a r g i n g  cage w a l l  between  These can be r e p r e s e n t e d  as  potentials.  a Faraday cage,  exist  previously, in  order  to  Faraday.cages are get  conductive metal  rid  of  usually  background  enclosure acts  made o f  highly  interferences.  as a huge  cavity  However,  resonator -I r j  Q  when  excited  from  S e v e r a l modes of determined  by  inside  by  the  oscillations  the  fast  occur with  C  (aj ' )  lower the  large  resonant  pass  integers  a,b,c,  dimensions  Q  =  300  a very  an  high  impulse  generator.  Q-factor  which  '  are  dimensions  of  damped o s c i l l a t i o n s  the last  + '(b £' ) + 2  b  identifying of  the  ~c' c  the  /  n  , (See  / c  ,. „>. a p p e n d i x 2)  (13)  r e s o n a n c e mode.  shield.  m/us.'  frequencies  bandwith  a  m,n,p,  C  2  x  V  Due t o  of  formula:^  f" m , n , p = ^ 2\ V/  where:  discharge  of  are  some h i g h - v o l t a g e in  the  order  impulse-voltage for  tens  of  of  laboratories,  the  o n e MHz a n d a r e w e l l  measuring  system.  microseconds and  These  therefore  within lightly  cause  33  )  distortions. A p r a c t i c a l remedy for t h i s interference i s a reduction of the Qfactor of the electromagnetic  shield.  By covering the inner wall of the  shield with a special r e s i s t i v e coating the cavity resonance can be damped out a f t e r a few o s c i l l a t i o n s . The r e s i s t i v e coating does not affect the laboratory shielding since the currents induced i n the s h i e l d by external interference sources c i r c u l a t e in the outer layer of the metal wall. In order to keep the currents induced by the cavity resonance within the r e s i s t i v e coating layer i t s thickness has to be not smaller than the current penetration depth.  An analysis of the t o t a l resistance required  for an e f f e c t i v e damping, as well as of the available r e s i s t i v e coating indicate that a special material should be composed on a basis of magn e t i c powders and r e s i s t i v e paints having both high r e s i s t i v i t y and high Q  magnetic permeability. In the UBC High—voltage laboratory the Faraday cage i s made of aluminum sheets which are joined together by folding them.  Since aluminum  i s always oxidized i n a i r , these folding connections have a high resistance at high frequency and therefore the shielding behaviour i s lessened. However, with r e l a t i v e l y low surrounding interference and low operating voltage  (200 KV),  this shielding i s s u f f i c i e n t for our purposes.  Wiring System: The presence of electromagnetic  f i e l d s around the impulse generator  and the measuring system tends to induce noise i n the system, e s p e c i a l l y when loops are present  i n the system.  Therefore,  i t i s desirable to  minimize the area of the loops by arranging the wiring system i n such a way  that a l l cables extend from a cable tree to provide branch wiring  34  rather ments  than of  loops  a wiring  arrangement  used  Figure system. in  the  24  shows t h e  wrong  and  The  schematic  shown  in  UBC h i g h - v o l t a g e  Peak voltmeter  test  Control  center  Control  center  the  correct  Figure  24b  is  arrangethe  system.  Spark 9<V>  Test object  j / '  Peak voltmeter t  L  o«,v rectifier  1  Voltage divider  Figure  24:  B l o c k diagram of a)  wrong  b)  correct  impulse  arrangement wiring  of  test  Impulse generator  facility.5  of  c o n t r o l and s i g n a l c a b l e s (existence of loops) ; c o n t r o l and s i g n a l c a b l e s (branch  wiring)  35  Voltage  Divider:  A divider resistors should known  or  for  recording  capacitors  reproduce reduction  The main  the  or  wave  high  transient  combinations shape of  the  voltages,  of  both.  voltage  sources  of  error  common t o  Residual inductance  in  2.  Stray  (a)  capacitance:  any  all  3.  Impedance  4.  Oscillations divider  divider This  resistive  from any  is  in  in  the  a  (c)  Between  divider  an M^r)  normally  or  divider a  acceptable  1 usee  a resistive  divider  the  when may  response time  response  time  curve,  for  to  the  divider  to  ground.  sections  of  the  divider.  leads.  caused by  ground  capacitance  and l e a d  residual  superimposed upon  measuring  the  standard  duration  be  can be e v a l u a t e d rising  A  the  surge  errors  due  to  by  of  the  the  IR  drop.  resistive  impulse  of  large.  from  inductance.  inductance  divider.  large  element.  divider  the  is  are:^>4  the  the  give  linearly  of  of  the  to  capacitive  of  behaviour for  dividers  lead.  the  which  of  section  to  divider,  voltage  However,  voltage-time  of  of  be measured w i t h  section  circuit  terminal  frequency-dependent  causes  to  interconnecting  resistive  usee wave.  The  from any  the  1.2/50  which  (b)  high-voltage  generates  divider  drop  case„of  causes  Each type  types  high-voltage  the  consist  ratio.  1.  In  may  is  of  less  stray  a than  capacitance,  3  comparing  the  impulse voltages  "measured" of  constant  rate  2 S, the  with  the  '-'true"  response of  steepness from the  S is  a  voltage-time system showing  accurately  voltage  error  ST.  known,  curve  of  the  same w a v e .  Figure  RC b e h a v i o u r  and RLC b e h a v i o u r .  the  time  response  The r e s p o n s e o f  the  T can be  divider  can  25 If  shows the  determined be  36  improved earth of  by  choosing  a low  c a p a c i t a n c e by  the  divider  surface  of  to  the  Figure  placing  give  Display  divider  theoretically  the  existence  residual  imposed.  it  can be  mize  the  of  of  seen that loading  is  of  electrode  a wedge-shaped  constructed on  internal  From the  the  high-voltage  distribution  end  along  the  fast  from pure  as w e l l  as  slow  and  its  leads,  transfer  function,  R(C^ +  C ) 2  has  the  transients;  divider  product  voltage, .  capacitors,  measuring  divider  the  impulse  RC b e h a v i o u r RLC b e h a v i o u r  a  certain  be  however,  instrument  which  to  response  is  quite  with  and  limitation  given  below,  large  to  mini-  effect.  s  Qi C  x  +  C  2  ' s +  1  (  R(C  the  the  the  the  V-^s)  transients  at  of  2  a  compensating  impedance  V (s)  Otherwise,  or  stray-capacitance  System showing System showing  perfect  inductance  is  resistance  a special  a uniform  a) b)  is  of  divider.3.4,5  25:  When t h e  value  large  error  natural  will  occur  frequency  of  L  during the  +  1 4  )  C ) 2  slow  divider  transients. is  a major  For  fast  concern.  The  37  c a p a c i t a n c e and  r e s i d u a l i n d u c t a n c e of the d i v i d e r determine t h i s n a t u r a l  frequency which i s u s u a l l y around 200 MHz.  However, i f one  uses l a r g e  v a l u e s of c a p a c i t a n c e s , the n a t u r a l frequency w i l l be lowered f a l l w i t h i n the bandwidth of the measuring instrument the r e c o r d e d waveform would be d i s t o r t e d . e x p e r i m e n t a l l y i n the UBC the manufacturer,  laboratory.  may  and as a r e s u l t ,  T h i s behaviour  was  observed  With the c a p a c i t o r s s u p p l i e d by  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  w i t h a l a r g e c a p a c i t a n c e v a l u e on the lower arm l a t i o n s do appear. d i v i d e r of 4.14  and  The  yF lower  of the d i v i d e r ,  oscil-  impulse waveshapes o b t a i n e d w i t h the c a p a c i t i v e c a p a c i t a n c e v a l u e have been produced both numer14  ically  ( u s i n g the UBC  Electromagnetic  m e n t a l l y (shown i n F i g u r e 26). O s c i l l a t i o n s can a l s o occur due The r e s i d u a l inductance and v o l t a g e arm  and  T r a n s i e n t s Program)  and e x p e r i -  to t r a v e l l i n g wave r e f l e c t i o n s .  the s t r a y c a p a c i t a n c e to ground of the h i g h -  l e a d cause the d i v i d e r to behave as a t r a n s m i s s i o n l i n e .  IMPULSE VOLTAGE  UJ  o 0~) —I  x:  TIME (MICROSECONDS:  (a)  13  38  Time s c a l e : 2 usec/div. Voltage scale: 5 V/div.  (b) F i g u r e 26:  Impulse waveshapes o b t a i n e d w i t h t h e c a p a c i t i v e d i v i d e r o f 4.14 yF lower c a p a c i t a n c e v a l u e . (a)  numerically  (b)  experimentally  R e f l e c t i o n s o c c u r because t h e r e i s no impedance m a t c h i n g a t b o t h ends of t h e l i n e .  One end i s s h o r t - c i r c u i t e d by t h e c a p a c i t o r o f t h e l o w e r  arm and t h e o t h e r end i s u s u a l l y b a d l y matched.  These o s c i l l a t i o n s a r e  a t t e n u a t e d v e r y l i t t l e s i n c e t h e c a p a c i t o r s and t h e l e a d have low l o s s e s . To o b t a i n h i g h a t t e n u a t i o n continuously-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 have been developed which a r e composed of s e r i e s c o n n e c t i o n s and  of r e s i s t o r s  capacitors. '  M e a s u r i n g Instrument and i t s c o n n e c t i o n  to t h e d i v i d e r :  Depending on t h e measurement q u a l i t y , t h e r e q u i r e d measuring  instru-  ment c o u l d be an impulse peak v o l t m e t e r , an o s c i l l o s c o p e o r a d i g i t a l transient recorder.  Impulse peak v o l t m e t e r s can o n l y measure t h e peak  v a l u e o f the impulse wave and t h e r e f o r e do n o t s u p p l y enough i n f o r m a t i o n about t h e shape o f t h e i m p u l s e .  W i t h an o s c i l l o s c o p e o r d i g i t a l t r a n s i e n t  r e c o r d e r , f u l l i n f o r m a t i o n o f the impulse wave can be o b t a i n e d .  39  The  measuring instrument  d i v i d e r by a c o a x i a l c a b l e .  i s u s u a l l y connected to the  Depending upon the amplitude l e v e l and  type of o s c i l l o s c o p e , the s i g n a l may f l e c t i o n p l a t e s or i t may  e i t h e r be  be connected to 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 .  f e d d i r e c t l y to the input t e r m i n a l s of  A d d i t i o n a l attenuators  o f t e n needed to reduce the amplitude of the s i g n a l . v o l t a g e l a b o r a t o r y an e l e c t r o n i c o s c i l l o s c o p e and attenuator  circuit  diagram and  are high-  travelling^wave  end w i t h i t s surge impedance.  i t s equivalent c i r c u i t  are shown i n F i g u r e  C i r c u i t diagram  b)  Equivalent c i r c u i t with earth capacitance.  In measuring systems w i t h c a p a c i t i v e d i v i d e r s , as i n F i g u r e termination test  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 a)  UBC  the  For a r e s i s t i v e v o l t a g e d i v i d e r , the s i g n a l c a b l e i s  at the measuring instrument  F i g u r e 27:  The  de-  have been used.  oscillations.  The  In the UBC  the  a hundred—to-one  Impedance matching i s always r e q u i r e d to a v o i d  terminated  voltage  i s u s u a l l y done w i t h a s e r i e s matching at the i n p u t s e t .uses t h i s type of matching.  T h i s matching has  28, end. the  effect  40  t h a t o n l y h a l f the v o l t a g e at the d i v i d e r tap e n t e r s the c a b l e , however, t h i s i s doubled a g a i n a t the open end, measured at the measuring i n s t r u m e n t  so t h a t f u l l v o l t a g e w i l l  again.  be  For f a s t t r a n s i e n t s the  Osc.  F i g u r e 28:  C o n n e c t i o n 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 c a t h o d e - r a y 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 cable, C = signal cable capacitance. Q  v o l t a g e r a t i o o f t h i s system i s  V]_(t)  C-L +  Vo(t)  C1  C  2  (15)  but f o r slow t r a n s i e n t s the c a b l e c a p a c i t a n c e  C  c  i n c r e a s e s the  ratio  as i n d i c a t e d below: Ci a = _i  T h i s e r r o r may F i g u r e 29. C^ + C  2  + Co + C_  i  £_  ( 1 6 )  be reduced by a complex t e r m i n a t i o n proposed by  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,  = C3 + C  c  Burch,^  so t h a t the  equation  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 z  0 ' c c  9TC  I F i g u r e 29:  Osc,  |«2(.t:  Compensation o f s i g n a l c a b l e c a p a c i t a n c e by a complex c a b l e t e r m i n a t i o n , characteristic =•0 impedance o f t h e s i g n a l c a b l e , Cc = s i g n a l c a b l e c a p a c i t a n c e , C3 = a u x i l i a r y c a p a c i t a n c e .  In the case o f a damped c a p a c i t i v e divider.;- s e r i e s matching i s a l s o a p p l i e d ; however, t h e t e r m i n a t i o n r e s i s t o r a t t h e c a b l e i n p u t must be reduced by r e s i s t a n c e IL, c o n t a i n e d i n t h e l o w - v o l t a g e arm,"* F i g u r e 30,  Ri  1  I —= C lL =— T  Ro  F i g u r e 30:  ^ 0" 2 2 Z _ iRX  0  Z  Q  > c c  'u (t) 2  Impedance matching f o r damped capacitive voltage dividers .  m  Osc,  42  3.4.3  N o i s e i n M e a s u r i n g Systems Different  s o u r c e s of n o i s e may be d e s c r i b e d w i t h r e f e r e n c e to  the  t y p i c a l i m p u l s e v o l t a g e measuring system shown i n F i g u r e 3 1 .  F i g u r e 31:  Impulse v o l t a g e g e n e r a t i n g and measuring s y s t e m s . G C D I  -  impulse generator front capacitor voltage divider recording instrument  The n o i s e t a k e s the form of c u r r e n t  0 - test object CA - measuring c a b l e T - i s o l a t i n g transformer  (or v o l t a g e s )  injected into various  components of the system w h i c h g i v e r i s e t o measuring e r r o r s i n form of p o t e n t i a l following a)  the  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 .  types of n o i s e can be i d e n t i f l e d :  The  »^»^ »^  C u r r e n t s induced i n the s h i e l d of the measuring c a b l e 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 n s t r u m e n t ' s  ground d u r i n g t r a n s i e n t s .  To  e l i m i n a t e t h e s e c u r r e n t s , b o t h the d i v i d e r and the measuring i n s t r u m e n t have to be grounded o n l y a t one p o i n t , w h i c h i s  43  usually at the divider side.  In the UBC laboratory, the  oscilloscope i s not grounded d i r e c t l y , but only i n d i r e c t l y through the shield of the measuring cable. b)  Currents induced i n 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 i s represented by a dotted l i n e i n Figure 31. induced currents may  The  be due to quasi-stationary (magnetic and  e l e c t r i c ) f i e l d s as well as to radiation f i e l d s .  Radiation  f i e l d s are generally b u i l t up by very high frequency phenomena such as triggering of sphere gaps of the impulse generator, or discharges i n the test c i r c u i t . may  The quasi-stationary f i e l d s  be generated by current flowing i n the high-voltage  Currents may  also be induced due to capacitive coupling between  the cable shield and the high—voltage c)  circuit.  circuit.  Signals penetrating d i r e c t l y 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 f i e l d s as well as to radiation f i e l d s .  These currents may  penetrate into the measuring instrument,  or may  not  depending on the e f f e c t i v e -  ness of the i s o l a t i n g transformer and the high frequency  blocking  devices (low-pass f i l t e r s ) . There are two techniques currents.  One way  to suppress the high-frequency  shield  i s to increase the shield impedance, which can be  achieved by winding the measuring cable (of coaxial type) on a f e r r i t e  44  core the  or  by  sliding  cable.  cables along  The  a number  disadvantage  or  very  rapid  the  line  is  no  particular  frequency  other  braid  eliminate both  the  i  and  the  and  over is  current  waves)  wide-band  attenuation,  of  the  the  that  (standing  the  voltage  places  is is  loop.  core  and  may  length for  of  long  signal  distribution  a lumped  dissipative  because at  coincide  the  originally cabinet, drops.  cable  inducing induced  a  with  a  (in  practice,  bypass  its  length.  zero-  flowing  flowing  in  the  of  32  to  grounded compares shield.  high-voltage  secondary  between  capacitance  is  a double  the  signal  and hence  Figure  in  This  the  shield  a cable with  capacitance  the  both  outermost  and  shields.  through  The  current  the  cable  flowing  to  current  represents  2  additional  throughout  coaxial  the  C  ground,  the  currents,  a simple  isolating  For  many  13)  applying  oscilloscope  3 2 , i-^  (or  2  the  at  of  tertiary)  case of  or  Figure  circuit;  cable  is  interfering  cases  In  the and  the  ends  two  (or  technique  voltage  location  alternative  permits  cable's  at  the  provides the  this  toroids  location."'  The method  pulses,  longer  ferrite  of  non-uniform  inductance  current  of  the  winding  instrument to  screen  by  the  transformer).  simple  coaxial  cable  the  induced  current  is  given  expression:^  L12 C2  s2 Io(s)  =  where of  L  the  If  1  2  is  the  primary  the  is  maximum.  be  avoided.  S = Laplace operator  IT (S) 1 +  s2  2  mutual  and  C  (17)  2  inductance,  secondary  instrument This  L  case  condition  loops  is  and  L  2  are  the  self  inductances  respectively.  grounded,  leads  Lj, and  to  C  2  = °°,  the  maximum n o i s e ,  induced and  should  current therefore  45  ~1  k  l  x  L  1 2 J 12 L2.  x  System  2  diagram  Equivalent  circuit  (a)  1  !1  1.  C2  J  23  ' L l ^ •L  77777m77777Z7777777^777777777777m7/7m System  diagram  Equivalent  3  circuit  (b) Figure  For shield  32:  Currents  induced  in the cable  stationary  magnetic  a)  coaxial  Simple  the double-shield  i s grounded  at both  coaxial ends,  shields  by quasi-  fields.  b)  cable,  Double  provided  the current  coaxial  that  the  i n the inner  outer  shield  is  given by: s (Li2  -  2  Li3).C  2  I Cs) = 1 + s (L 2  and  the current  (18)  .Il(s)  2  i n the outer  2  -  shield  L  2  3  ) . C  2  i s given  by t h e  equation:'  ^13 I3<s)  Ii(s)  (19)  46  Since the  ~ ^13  induced  shield  0>  a  current  takes  most  in  of  To h a v e b e t t e r the  outermost  as w e l l  Direct instrument metal  the  is  avoided  thus  effect,  is  shield  the  In  addition,  same  while  area), the  a good p r o t e c t i v e  iron  will  the  negligible,  giving  an  have  conduit  is  measuring  the  self  often  cable  effect.  used  from  inductance  outer-  of  electric the  signals  putting  into  the  the  active  measuring  parts  of  the  measuring  instrument  inside  a  measuring  system  is  enclosure.  in  Figure  layout 33.  of  This  the  UBC h i g h - v o l t a g e  are  not  the  shielding  layout  laboratory  also with  of  the  describes the  the  exception  shielding that  system  ferrite  cores  used.  enclosure  Figure  33:  Finally,  to  isolating power  as  increased.  of  by  3 almost  shield  current,  fields.  penetration is  inner  This  shield  The o v e r a l l shown  the  shield.  cable  2 and loop  shielding  as magnetic  measuring  (loop  C o r r e c t measurement c i r c u i t l a y o u t , avoiding c a b l e b r a i d and c a b i n e t c u r r e n t interference.  block  transformer  input  of  the  the  currents  and a low  measuring  pass  induced filter  instrument.  It  into are is  the  mains w i r e ,  installed often  before  sufficient  an the to  in  wind t h e power c o r d on a f e r r i t e c o r e , which was a l s o done i n t h e UBC high voltage laboratory.  4.  4.1  EXPERIMENT EXERCISES  Introduction All  t e s t s are done on the "HAEFELY MULTI TEST SET" which i s a  v e r s a t i l e system capable o f p r o d u c i n g  a l l major v o l t a g e  types:  - AC v o l t a g e s 50/60 Hz, up to 75 KV rms. - DC v o l t a g e s up to 200 KV. - Impulse v o l t a g e s up t o 200 KV. This f l e x i b i l i t y  a l l o w s the system to be used i n many areas  such  as the f o l l o w i n g : Industrial applications:  F a c t o r y t e s t s on i n s u l a t o r s , capacitors, formers,  switchgear,  bushings,  instrument  c a b l e s and d i s t r i b u t i o n  trans trans-  formers . U t i l i t y applications.:  Field  t e s t i n g o f l a i d - i n c a b l e s and  p l e t e l y assembled Teaching  and r e s e a r c h  comrr  switchgear.  applications: Demonstrates w i t h AC, DC and  impulse  voltages. Generation  and measurement of h i g h t e s t  voltages . Laboratory  t r a i n i n g i n high-voltage  tech  nology . Experiments w i t h i n s u l a t o r and e l e c t r o d e configurations. Teaching  and r e s e a r c h a p p l i c a t i o n w i l l be d i s c u s s e d i n t h i s  chapter  49  4.2  AC  4.2.1  test  Breakdown v o l t a g e  A minor A  resistor,  circuit A  of  during unit  which has  breakdown  five  less  starting  to  value,  limit  installed than  the  so  the  to  has  b e made to  primary  that  the  operating  the  experiment,  s e v e r a l breakdown  readings  rithmetic  s h o u l d be  mean v a l u e  can be  The b r e a k d o w n v o l t a g e s 22.8°C Using  system has  be  for  this  inserted  current  in  of  the  during  the  primary  breakdown.  maximum p r i m a r y  current  experiment.  current  protection  (37A).  p o l i s h e d and  Then  the  gaps  enough r a t e d  was  is  sphere  to  transformer  resistor  Before be  modification  the  five-ohm  of  and the  990 m b a r , correction  for  taken  of  are  standard  breakdown v o l t a g e s  in  Gap (mm)  d (KV) U  a  made t o  of  the  spheres  remove any  each spacing,  s p h e r e gap gap  formula  breakdown v o l t a g e s  2:  for  surfaces  should  dust  particles.  from which  the  a-  determined.^>3  standard  Table  tests  different  factor  the  10 cm d i a m e t e r ,  spacings are  of  equation  calculated Table  of  and  (1),  shown the  in  Table  compared w i t h  the  DO  Accepted (KV)  U^Q  2.  accepted  2.  U  at  corresponding  Breakdown v o l t a g e s o f a s p h e r e gap o f d i a m e t e r f o r d i f f e r e n t gap s p a c i n g s . .Corresponding (KV)  taken  10  %  cm  error  10  31.25  32.3  31.6  2 .2  20  57.23  59.0  59.1  0.2  30  82.00  84.7  84.1  0.7  It  can be  of  3%;  seen that  therefore,  4.2.2  the  the  result  Corona voltage  Either shields point  start  the  on  A simple  connected  experiment.  light  to  appear  is  the  calculated  18  corona onset value  C  e  V  c o  the  measuring  which  and a bundle  for  conductor  in  the the  uncertainty  on  voltage  the  obtained  avoid  IT  s  ,  n  Corona sharp  from aluminum  source,  one  voltage The  voltage  from the  2r(n-l)  r  nr  to  conductor. This  conductor  experiment.  laboratory,  voltage.  is  this  can be b u i l t  with  no  state  the  shield  With  at  used  of  conductor  corona begins the  conductor  ends  corona  the  below  acceptable.  can be  both  until  with  is  s t i l l  a single  creased this  is  DC s o u r c e  be p l a c e d  effects.  Having  of  an AC o r  must  error  can is  i n -  voltage  can be  formula:  f o i l .  11  compared '  12  KV cm  where:  Eo =  ,„ . 3 0 m6  C :  self  e  V : C Q  . 0.426, (1 H ; )  capacitance  Corona onset of  KV —  (^ /km) F  voltage  n:  number  r:  subconductor  s:  spacing between  m:  Surface  6:  Relative  (21)  (KV)  subconductors  or  radius  adjacent  roughness  air  (cm)  density  subconductors  factor  (  0  < m < 1  (cm) )  51  For bundle) the  a  single  of  39.5  calculated  Table  conductor  cm h e i g h t and  the  from the  conductor  ground  experimental  (2  platform  corona  onset  conductors  and  0.35  voltages  cm  are  per  radius, shown  in  3.  Table  3:  Corona onset v o l t a g e s of a s i n g l e conductor and a bundle c o n d u c t o r .  h  =  39.5  r  =  .35  Single  Value  cm  Conductor  Since  the  differences  conclude  DC  4.3.1  that  the  The h i g h from high  (KV)  85.88  84.85  1.20  126.59  123.04  2.81  between  experiment  the is  two  values  consistent  are  with  fairly the  small,  one  theoretical  can  formula.  complete  measurement  DC v o l t a g e s ,  AC v o l t a g e s .  Greinacher  doubler  circuit  as  of  T h e DC v o l t a g e and the  ponent  Value  (KV)  difference  test  Ripple  meter  %  Experimental  Calculated  cm  Bundled Conductor (2 C o n d u c t o r s ) s = 2 cm  4.3  and a bundle  ripple  or  by  explained  An a r r e s t o r  has  only  the  be put  The  can be  generator  a  be m e a s u r e d ,  Figure  and  its  resistive divider  capacitor  is  appears  parallel  either  2.  resistive  ripple in  to  chapter  measured w i t h  a capacitive  to  in  a DC v o l t a g e  is  is  The r e c t i f i c a t i o n  an o s c i l l o s c o p e .  such that  whose r i p p l e  with  the  half  and to  lower  and  either block  or  the  devices.  a DC a peak  the  resistive  measuring  produced  wave  shows  measuring  divider  meant  on the  34  are  device  DC  voltmeter, voltcom-  divider. as  a  52  -  Grounding Resistive  switch divider  -  C o n t r o l box voltmeter  -  Capacitor's Capacitor  DC resistor  Arrestor - P e a k voltmeter - Oscilloscope  Figure  34:  protection blocked if  the  the  Overall  against  DC v o l t a g e voltage  measuring  table  Table  of  overvoltages, w i l l  suddenly device  The p e r c e n t in  circuit  if  appear drops no  the  on the to  for  U  (KV)  measurement  because a considerable terminal  zero.  arrestor  ripples  ripple  This  is  different  of  experiment.  amount  of  the measuring  fault  4:  Percent  C  values  %  of  DC v o l t a g e s  are  ripple  0.12  24.90  0.11  37.50  0.12  50.00  0.13  62.50  0.14  74.80  0.14  87.50  0.15  for  to  used.  12.25  ripples  device  c a n c a u s e damage  4:  D  the  different  values  of  DC  voltages.  shown  53  4.3.2  Polarity  Positive effect  of  this  effect  gap.  capacitor  addition,  the  of  The iment,  are  positive point  the  C  against  s  voltage  may n o t  rectifiers  of  and  the  corresponding  shown  point  DC v o l t a g e s  A protective  arrangement  and  spacing  the  a P o i n t - P l a n e gap  and n e g a t i v e  smoothing  loading  In  in  Figure  electrode  electrode.  For,  has  are  applied  resistor  (6000  sudden short be  to  fi)  is  circuits  i n c r e a s e d beyond  observe used  to  during  70 KV t o  the  polarity  protect  the  breakdown.  In  avoid  over-  capacitors.  point-plane  gap,  relationship 35.  w h i c h was used  between  ' One c a n s e e t h a t  lower  a positive  breakdown for  breakdown v o l t a g e s point  electrode  for  the  the  voltage  experand  larger  spacings,  than  negative  a  electrons  a  move  KV Breakdown voltage (magnitude)  80  4  10  20  30  40  50  60  (a)  Figure  35:  Polarity (a) (b)  effect  in  a point-plane  gap.  Electrodes configuration Breakdown v o l t a g e v e r s u s s p a c i n g  towards  it,  producing  excess  plates,  and  therefore  the  positive  growth of  charges  discharge  in  the  channel  curve  direction is  of  the  stimulated.  G  ap  54  4.4  Impulse Test  4.4.1  Preliminary Preparations A.  O s c i l l o s c o p e and i t s a t t e n u a t o r  To determine t h e r e q u i r e d bandwidth of the o s c i l l o s c o p e the h i g h e s t frequency,  f  m  a  x  ,  has t o be c o n s i d e r e d , which i s a f u n c t i o n o f the s i z e  of the g e n e r a t i n g  system and can be determined by the f o r m u l a : ^  -max  where:  4(  H  g  +  MHz  )  H c  C = v e l o c i t y of l i g h t ,  300 / y s m  Hg = the h e i g h t of g e n e r a t o r H The  c  (22)  in m  = the h e i g h t o f f r o n t c a p a c i t o r i n m  approximate bandwidth o f the o s c i l l o s c o p e i s then g i v e n by the  formula:^  f  l  where:  i  m  (-3dB) = — 2^ T(osc)  T( c)  1 :  = :  O S  (23)  4 TT fmax  For t h e "HAEFELY" t e s t system, the generator are both of 1 m h e i g h t and consequently  and t h e f r o n t c a p a c i t o r  the upper l i m i t o f o s c i l l o s c o p e  bandwidth i s :  3  ™  flim  a x  0  0  4(1+1)  = 37.5 MHz  <-3dB) = —  = 75 MHz  4.TT The  ,  (24)  (25)  f max  TEKTRONIX 475 o s c i l l o s c o p e has a bandwidth o f 200 MHz which  clearly  s a t i s f i e s the r e q u i r e m e n t . The a t t e n u a t o r has t o be a d j u s t e d c o r r e c t l y so t h a t n e i t h e r o v e r compensation n o r undercompensation o c c u r .  The b e h a v i o u r o f a compen-  s a t e d a t t e n u a t o r e x c i t e d by a square wave i s shown i n F i g u r e 36.  F i g u r e 36:  Output of a compensated a t t e n u a t o r f o r d i f f e r e n t degrees of compensation. (a) (b) (c)  C o r r e c t compensation Overcompensated Undercompensated  56  B.  Circuit  The  impulse waveform  Transients  Analysis  Program  can be p r e d i c t e d  (EMTP)^  The  the  circuit.  Theoretically,  and  resistors  only,  unavoidable  inherent  was m e a s u r e d w i t h 1  uH w a s  the  one  (shown  a  since  simple  Figure  circuit  exists  resonant  that  of  impulse  the  Including  finds in  the  inductance  obtained.  circuit,  waveform  but  input  this  there  in  with  the  program  circuit  UBC E l e c t r o m a g n e t i c is  the  model  of  consists  of  capacitors  interconnection  is  quite  the  circuit  circuit.  and  inherent is  the  This  inductance  an a p p r o x i m a t e  inductance  a curvature  at  the  in  long  the  value model  beginning  of  of of the  37).  IMPULSE VOLTAGE  Ti Mc IMICR03EC0NGS)  Figure  Thus, line  to  the  Impulse  determine  through  The of  37:  the  30% a n d  inherent  impulse  voltage  origin  of  90% p o i n t s  inductance  circuit  on  the  waveform  the has  can be ground  obtained  waveform, the to  be  by  using  customary  EMTP.  straight  drawn.  r e d u c e d by platform,  putting thus,  all  the  components  eliminating  the  57  s u p p l i e d metal base. to  T h i s procedure was used i n the l a b o r a t o r y n o t o n l y  reduce the inductance  but a l s o t o e l i m i n a t e o r minimize t h e ground  loops .  4.4.2  N o i s e Reductions A.  Ground loop e l i m i n a t i o n  Due  to t h e e x i s t e n c e of r a d i a t i o n f i e l d s  and q u a s i - s t a t i o n a r y  fields,  ground l o o p s have t o be e l i m i n a t e d o r minimized t o reduce common mode interference.  T h i s can be achieved  by p u t t i n g the whole impulse  circuit  on the ground p l a t f o r m and l a y i n g the measuring c a b l e as c l o s e as p o s s i b l e to  t h e ground B.  platform.  Further noise  reduction  In a d d i t i o n t o ground loop e l i m i n a t i o n , common mode i n t e r f e r e n c e can f u r t h e r be reduced by u s i n g a m u l t i s h i e l d c a b l e i n s t e a d o f a simple coaxial cable.  T h i s w i l l a l l o w t h e ground c u r r e n t , which f o r m e r l y  i n t h e i n n e r c a b l e s h i e l d , t o flow i n t h e o u t e r a t r i a x i a l cable l a i d  shields.  In t h e l a b o r a t o r y ,  i n a grounded copper tube i s used.  As a comparison, t h e impulse o s c i l l o g r a m of t h e c i r c u i t w i t h loops and a simple  c o a x i a l c a b l e and t h a t o f t h e c i r c u i t w i t h  ground l o o p s and a s h i e l d e d c a b l e a r e shown i n F i g u r e 38. that t h e n o i s e has been reduced  reduced  I t can be seen  be seen i n F i g u r e 38b.  i n t e r f e r e n c e s a r e due :to r a d i a t i o n f i e l d s  line.  ground  considerably.  Some minor i n t e r f e r e n c e s can s t i l l  which p e n e t r a t e  flowed  and q u a s i - s t a t i o n a r y  These fields  i n t o t h e o s c i l l o s c o p e d i r e c t l y and/or through t h e power  58  (a)  5S555SSSBB Time s c a l e : 2 y s e c / d i v . F i g u r e 38a:  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 loops and a simple c o a x i a l c a b l e .  ground  (b)  Time s c a l e : 0.5 "Figure 38b:  ysec/div.  Impulse o s c i l l o g r a m o f the c i r c u i t w i t h reduced ground loops and s h i e l d e d c a b l e .  To e l i m i n a t e them, t h e 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 m e t a l box and a low-pass f i l t e r i s i n s e r t e d i n t h e incoming power l i n e . a r e s u l t , a c o n t i n u o u s and c l e a n o s c i l l o g r a m was o b t a i n e d  (shown i n  F i g u r e 39).  Time s c a l e : 0.5 F i g u r e 39:  usec/div.  Impulse o s c i l l o g r a m of t h e c i r c u i t w i t h reduced ground loops and a s h i e l d e d c a b l e . Oscilloscope i s i n s i d e a m e t a l box.  As  5.  CONCLUSIONS  The UBC high-voltage test set, which has been s l i g h t l y modified and expanded, can now be used f o r various experiments f o r undergraduate students.  AC and DC tests have been performed repeatedly with repro-  ducible r e s u l t s . For impulse tests various techniques of shielding have been applied in the UBC high-voltage laboratory to obtain reasonably accurate oscillograms.  impulse  61  LIST  OF R E F E R E N C E S  1.  Power System I n s t r u m e n t a t i o n and Measurement Committee of the IEEE Power E n g i n e e r i n g S o c i e t y , " I E E E Guide f o r F i e l d T e s t i n g Power 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 , 1978.  2.  D.  Kind,  "An  Technique",  Introduction (Book),  To H i g h - V o l t a g e  Braunschweig,  Vieweg,  Experimental 1978.  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 Engineering", (Book), Pergamon P r e s s L t d . , O x f o r d , 1970.  4.  IEC 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 " , Bureau C e n t r a l de 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 , Part  5.  3:  Measuring  A . J . Schwab, The M . I . T .  6.  7.  Devices.  "High-Voltage  Press,  Measurement  Massachusetts,  Techniques",  A . J . Schwab, " 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 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 , 1973, P a p e r No: T73 0 6 2 - 7 . Aa.  Pedersen, J .  Voltage  Stavness,  Measurements  Electra.No:  59,  L.  Thione,  pp.  Impulse Measuring B . C . , Canada,  "Instruments  O s c i l l o s c o p e s and  1978,  (Book),  1972.  Crest  for  Impulse  Voltmeters",  41-90.  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 Shield", 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.  Malewski  EHV No: 10.  V.  3,  A.  IRR-IMS  No:  Inoue,  Bundled Paper  G.R.  IEEE  Nourse,  Trans,  "Transient  Measurement  on Power A p p a r .  and  Techniques  Syst.,  Vol.  35,  Group 1976,  (1), pp.  "High-Voltage  Conductors",  No:  A78  " F a c i n g UHV M e a s u r i n g  Problems",  155-256.  Travelling  Waves w i t h  IEEE PES Winter  Meeting,  Corona Discharge New Y o r k ,  " 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 Book - 345 KV and A b o v e " , Power 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 , CA, 1975.  13.  N.  "Electromagnetic  Systems",  14.  IEEE  No:  4,  H.W.  Dommel,  Trans,  Phenomena  in  on Power A p p a r .  Electric  Impulse Voltage  Measuring  and  PAS-96,  Syst.,  Vol.  1977.  Engineering, Canada.  on  1978,  170-3.  12.  Ari,  in  PAS-97,  1978.  Palva,  Electra 11.  and  Systems",  V6T  "Transients  Program  The U n i v e r s i t y 1W5.  of  User's Manual",  British  Columbia,  Dept.  of  Vancouver,  Electrical B.C.,  APPENDIX I SAFETY REGULATIONS FOR  HIGH-VOLTAGE EXPERIMENTS  Experiments w i t h h i g h v o l t a g e s c o u l d become p a r t i c u l a r l y dous f o r the p a r t i c i p a n t s should  the s a f e t y p r e c a u t i o n s be  hazar-  inadequate.  To g i v e an i d e a of the r e q u i r e d s a f e t y measures, as an example the s a f e t y r e g u l a t i o n s of the High-Voltage  I n s t i t u t e of The  Technical  2 U n i v e r s i t y o f Braunschweig s h a l l be d e s c r i b e d below. the a p p r o p r i a t e s a f e t y r e g u l a t i o n s and to p e r s o n s .  Strict  Fundamental Rule:  as f a r as p o s s i b l e prevent  risk  observance i s t h e r e f o r e the duty of everyone  working i n the l a b o r a t o r y . e a r t h i s understood  These supplement  Here any v o l t a g e g r e a t e r than 250 V a g a i n s t  to be a:.high v o l t a g e . Before e n t e r i n g a high-voltage convince  h i m s e l f by p e r s o n a l o b s e r v a t i o n t h a t a l l  the conductors lie  setup everyone must  which can assume h i g h p o t e n t i a l  i n c o n t a c t zone a r e e a r t h e d , and  and  that a l l  the main l e a d s a r e i n t e r r u p t e d .  Fencing A l l high-voltage  setups must be p r o t e c t e d a g a i n s t u n i n t e n t i o n a l  e n t r y of the danger zone. m e t a l l i c fences.  T h i s i s a p p r o p r i a t e l y done w i t h the a i d of  When s e t t i n g up  the fences  f o r v o l t a g e s up  the f o l l o w i n g minimum c l e a r a n c e s to the components at should not be  high-voltage  reduced:  f o r a l t e r n a t i n g and  direct voltages  f o r impulse v o l t a g e s However, f o r v o l t a g e s l e s s than 100 50 cm has  to 1  to be m a i n t a i n e d ,  KV  50 cm  f o r every 100  KV  20 cm  f o r every  KV  100  a minimum c l e a r a n c e of  independent o f the type o f v o l t a g e .  MV  63  For voltages over 1 MV, i n p a r t i c u l a r f o r switching impulse voltages, the values quoted could be inadequate;  special protective measures must  then be introduced. The fences should be r e l i a b l y connected with one another conduct i v e l y , earthed and provided with warning boards inscribed: "High-voltage!  Caution!  Highly dangerous!"  I t i s forbidden to introduce conduc-  tive objects through the fence whilst the setup i s i n 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 c i r c u i t breaker, which, on opening the door, interrupts a l l the main leads to the setup.  These power c i r c u i t  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 c i t y network), the main leads must be interrupted v i s i b l y before entry to the setup by an additional open i s o l a t i n g switch; The switched condition of a setup must be indicated by a red lamp "Setup switched on" and by a green lamp "Setup switched o f f " .  Earthing A high-voltage setup may be entered only when a l l the parts which can assume high-voltage i n the contact zone are earthed. only be effected by a conductor earthed inside the fence.  Earthing may Fixing the  .64  e a r t h i n g l e a d s onto t h e p a r t s t o be e a r t h e d s h o u l d be done w i t h t h e a i d of i n s u l a t i n g r o d s .  Earthing switches w i t h a c l e a r l y v i s i b l e operating  position, are also permissible.  I n high-power setups w i t h d i r e c t  supply  from t h e h i g h - v o l t a g e network, e a r t h i n g i s a c h i e v e d 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 o n l y f o l l o w a f t e r s w i t c h i n g t h e c u r r e n t s o u r c e o f f , and may be removed o n l y when t h e r e i s no l o n g e r anyone p r e s e n t w i t h i n t h e fence o r i f t h e setup i s v a c a t e d a f t e r removal o f e a r t h .  A l l metallic parts  of t h e setup w h i c h do n o t c a r r y p o t e n t i a l d u r i n g normal s e r v i c e must be o  e a r t h e d r e l i a b l y and w i t h an adequate c r o s s s e c t i o n o f a t l e a s t 1.5 mm .  C i r c u i t and Test Setup Inasmuch as t h e setup i s not s u p p l i e d from ready w i r e d d e s k s ,  clearly  marked i s o l a t i n g s w i t c h e s must be p r o v i d e d i n a l l l e a d s t o t h e l o w - v o l t a g e c i r c u i t s o f h i g h - v o l t a g e t r a n s f o r m e r s and a r r a n g e d a t an e a s i l y f i a b l e p o s i t i o n outsider.the fence.  identi-  These must be opened b e f o r e e a r t h i n g  and b e f o r e e n t e r i n g t h e s e t u p . A l l l e a d s must be l a i d so t h a t t h e r e a r e no l o o s e l y hanging  ends.  Low v o l t a g e l e a d s which can assume h i g h p o t e n t i a l s d u r i n g breakdown o r f l a s h o v e r s and l e a d o u t o f t h e fenced a r e a , e.g. measuring c a b l e , ^ c o n t r o l c a b l e , s u p p l y c a b l e , must be l a i d i n s i d e t h e setup i n e a r t h e d s l e e v i n g . A l l components o f the..setup must be e i t h e r r i g i d l y f i x e d o r suspended so t h a t they cannot t o p p l e d u r i n g o p e r a t i o n o r be p u l l e d down by t h e l e a d s . F o r a l l setups i n t e n d e d f o r r e s e a r c h p u r p o s e s ,  a circuit  s h a l l be f i x e d o u t s i d e t h e f e n c e i n c l e a r l y v i s i b l y  position.  diagram  A t e s t setup may be put i n t o o p e r a t i o n o n l y a f t e r t h e c i r c u i t has been checked and p e r m i s s i o n t o b e g i n  work g i v e n  by an a u t h o r i z e d  65  person.  Conducting the Experiments Everyone carrying out experiments i n the laboratory i s personally responsible for the setup placed at h i s disposal and for the experiments performed with i t .  For experiments during working hours one  should t r y , i n the interest of personal safety, to make sure that a second person i s present i n the testing room.  I f 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 i n the same room.  Explosion and Fire,..Risk, Radiation Protection In experiments with o i l and other e a s i l y inflammable materials, special care i s necessary owing to the danger of explosion and f i r e . In each room where work i s 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 d i s posed of immediately i n metal cans.  Special regulations must be  observed when radioactive sources are used.  66  APPENDIX I I FORMULA OF MODE OSCILLATIONS  The  f o r m u l a o f mode o s c i l l a t i o n s  i na rectangular  resonator  can be d e r i v e d from MAXWELL's e q u a t i o n s :  ,  x  H  =  E  | I  V x E . - w f A f t e r an e x t e n s i v e m a n i p u l a t i o n  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 o f TM modes and TE modes a r e o b t a i n e d f o r t h e boundary c o n d i t i o n s x = 0, x = a and y = 0, y = b: TM modes: n E  n E  r \ ™ r -i 3mir „ _ .mirx. „. ,mry. i (wt-gz) " (x,y) = Re { - f h — C C o s ( ) SinC-r -) e }a h a mn]_ a b x 2  ox-^ m  oyi  E  O Z i  J  t  ( x  '  y )  \  =  R  T, e  r - j 3mr _ „. ,mT7x _ /nTry. j (wt-gz) -, * < h^b" Cmn-L S i n C ^ ) Cos(-^-) e }a x  o y i  ( x , y ) = Re { C ^  Sin(^) Sin(^) e ^ " ^ } z a  ( x , y ) = Re ( ^ f f  where:  C  m n  J  y  C  H  J  z  S i n ( ^ ) C o s ( ^ ) «J  m n i  C  m n i  Cos(=?)  S i n (52*)  c o r r e s p o n d s t o the p a r t i c u l a r  g i v e n c h o i c e o f m and n.  B  z  = yew  h  2  = ( -a )  -  2  ( a— r - (-;b-)  + ( b^ )  2  e ^ " ^  } a  x  >a  mode d e f i n e d by a  (m, n a r e i n t e g e r s )  y  The e l e c t r i c f i e l d s t r a v e l i n g n  E  O X 2  r \ rt (x,y) = R  -f ~j Bmn „ i —jC  e  i n the o p p o s i t e d i r e c t i o n a r e :  n m n 2  T? / \ T> -iBnir Eoy (x,y) = R { 2 Cmn J  2  e  h  b  S  /HITTX. „ . /niry. j (cot+Bz) C o s ( — ) Sin(-^-) e J  l  n  2  /imrx. „ /niry. (—) C o s e  J  j (cot+Bz)  \ i ax  } ay  A p p l y i n g 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  is  obtained: z=0:  E  O X l  (x,y)  (Mi + M ) Cos ( 2 ^ ) a 2  where:  Therefore,  K  l =  C  h^a  mni  M-^ = - M  z  =  C ;  + E  O X 2  (x,y)  SinC ^) b  = 0  S i n cot = 0  5  x  2  E  ( 'y) x  o x l  + ox ( .y) E  x  2  =  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  where:  BC =  p i s an i n t e g e r  C  PTT  T>  But  rP-  ^  g  2  =  yeco  -  ,mi7.2 (—)  -  a  ,1117.2 (—)  b  Therefore,  ,  = U  I  (—)  V  /u7  a  2  (SE)  + (£1) +  2  2  b  c  or  f = —  —  2i7/ye"  \ /  c ^ ) + <ir 2  + c^-)  2  y  The same e x p r e s s i o n can d e r i v e d from E TE modes.  ) 2  ( x , y ) and E  ( x , y ) and from  

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