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Determination of conductor clearances-to-ground for EHV AC and DC transmission lines Stremlaw, Arthur John 1968

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THE DETERMINATION OF CONDUCTOR CLEARANCES-TO-C-ROUND FOR EHV AC AND DC TRANSMISSION LINES  by ARTHUR JOHN STREMLAW B.A.Sc., U n i v e r s i t y of W a t e r l o o , 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  i n t h e Department o f Electrical  Engineering  We accept t h i s t h e s i s as conforming required  to the  standard  Research Supervisor' Members of t h e Committee  Head o f t h e Department Members o f t h e Department of E l e c t r i c a l E n g i n e e r i n g THE UNIVERSITY OF BRITISH COLUMBIA May, 1968  In presenting this thesis  in p a r t i a l fulfilment of the requirements  for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make it freely available for reference and Study.  I further agree that permission for extensive  copying of this  thesis for scholarly purposes may be granted by the Head of my Department or by hits representatives.  It is understood that copying  or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of tnW^Aj^t-tA The University of B r i t i s h Columbia Vancouver 8, Canada Date (Y\O^A  ^ \^  Wg>  ABSTRACT Th? a n a l y s e s p r e s e n t e d i n t h i s t h e s i s a r e based on a c o n s i d e r a t i o n of i n d u c t i o n e f f e c t s below t r a n s m i s s i o n l i n e s and t h e h a z a r d s j a s p r e s e n t e d t o the p u b l i c .  The r a p i d i n c r e a s e  •of t r a n s m i s s i o n v o l t a g e s has caused a g r e a t d e a l of concern among u t i l i t i e s about these h a z a r d s .  The i n d u c t i o n e f f e c t s  are a f u n c t i o n o f l i n e h e i g h t and a t p r e s e n t t h e r e i s c o n f l i c t concerning-these  dimensions.  P r i m a r i l y , t h i s t h e s i s i s concerned  with the establishment  of t h e minimum l i n e - t o - g r o u n d c l e a r a n c e s of EHV ac and dc transmission l i n e s .  These c l e a r a n c e s a r e e s t a b l i s h e d i n terms  of t h e e l e c t r i c f i e l d under t h e l i n e based on t h e " e l e c t r i c f i e l d recognition level". "Equations a r e d e r i v e d f o r t h e e l e c t r i c f i e l d , and potent i a l a t any p o i n t below t h e l i n e i n Chapter are then used i n Chapter  2.  These e q u a t i o n s  3 t o show t h e e f f e c t of conductor  s p a c i n g , h e i g h t and s i z e on t h e f i e l d .  A l s o , the e f f e c t of  sky w i r e s and bundle conductors i s noted.  Chapter 4 d e r i v e s  an a l l o w a b l e v a l u e of e l e c t r i c f i e l d which i s used i n Chapter 5 to derive the required heights.  Chapter  6 considers a reduc-  t i o n of these c l e a r a n c e s or i n d u c t i o n e f f e c t s u s i n g ground w i r e s below t h e l i n e conductors  for shielding  purposes.  ."" _.' E x p e r i m e n t a l r e a d i n g s a r e o b t a i n e d i n Chapter 7 t o v e r i f y the e q u a t i o n s d e r i v e d i n Chapter and bundle conductors  2 and t h e e f f e c t s of sky w i r e s  on t h e e l e c t r i c f i e l d below t h e l i n e .  Chapter 8 e s t a b l i s h e s r i g h t - o f - w a y w i d t h s based on i n d u c t i o n effects.  (ii)  TABLE OF CONTENTS Page • ABSTRACT  .  ..  (ii)  TABLE OF CONTENTS .  (iii)  LIST OF ILLUSTRATIONS  '  (v)  LIST OF TABLES  (viii)  LIST OF SYMBOLS  '  ACKNOWLEDGEMENT 1.  (ix). .  ' (xi)  INTRODUCTION .  . 1  1.1 Development of EHV and E f f e c t s on Line Design 1.2 P r e s e n t a t i o n of the Problem  1 2  1.3 O b j e c t i v e s of the Thesis  6  2. DERIVATION OP EQUATIONS FOR THE ELECTRIC FIELD AND POTENTIAL DUE TO AN n-CONDUCTOR SYSTEM  8  2.1 General D e s c r i p t i o n of the System 2.2 Assumptions 2.3 D e r i v a t i o n ... ........ 3. THE EFFECT OF PHYSICAL PARAMETERS, BUNDLE CONDUCTORS AND SKY WIRES ON THE ELECTRIC FIELD BELOW THE . LINE 3.1 The E f f e c t of Conductor Spacing, Height and S i z e on the E l e c t r i c F i e l d 3.2 The E f f e c t of Bundle Conductors on the Electric Field 3.3 The E f f e c t of Sky Wires on the E l e c t r i c Field 4. AN ANALYSIS OF A MODEL OF A HUMAN BEING 4.1 4.2 4.3 4.4 4.5  Method of Approach Assumptions Co-Ordinate System Mathematical A n a l y s i s Dependance of the Surface Value of E l e c t r i c F i e l d on the R a t i o of a/b 4.6 A P r a c t i c a l Approach to the Determination of the Value of a/b; f o r Human Beings .... 4.7 E v a l u a t i o n of a L i m i t i n g Value of Eox  (iii)  8 8 10 •  . 13 13 16 20 22 22 22 . 24 25 29 30 32  Page 5. DETERMINATION OP MINIMUM HEIGHTS FOR AC AND DC SYSTEMS 5.1 Method o f Approach 5.2 AC Cases 5.3 DC Cases  36 .  6. SHIELDING EFFECTS OF GROUND WIRES BENEATH THE LINE CONDUCTORS . 6.1 S h i e l d i n g E f f e c t s of Ground Wires 6.2 R e d u c t i o n I n L i n e H e i g h t s 7. MEASUREMENT OF THE POTENTIAL OF AN OBJECT BELOW A TRANSMISSION LINE 7.1 7.2 7.3 7.4  Method o f Measurement . Instrument D e s i g n C a l c u l a t e d Values v s E x p e r i m e n t a l Values E x p e r i m e n t a l V e r i f i c a t i o n of the E f f e c t of Sky Wires 7.5 E x p e r i m e n t a l V e r i f i c a t i o n o f t h e E f f e c t of Bundle Conductors  8. ESTABLISHMENT OF THE WIDTH OF RIGHT-OF-WAYS. 8.1 Right-of—Way C l e a r a n c e s 8.2 Width Requirements Based on E l e c t r o s t a t i c Induction Effects APPENDIX I  D i s c u s s i o n of t h e M i l l e r G r a d i e n t Meter  REFERENCES  36 37 43 47 47 49 54 54 57 60 62 63 66 66 66 73 77  (iv)  LIST OF ILLUSTRATIONS Figure 1.1 2.1  Page C.S.A. and N.E.S.C. Standards f o r L i n e - t o Ground Clearances D e r i v a t i o n of the E l e c t r i c  5  F i e l d and P o t e n t i a l  f o r an n-Conductor System  '-9"  3.1  Electric  3.2  V a r i a t i o n i n F i e l d P r o f i l e s with Conductor Height Spacing and S i z e E f f e c t of Conductor Spacing, Height and S i z e  15  on Emax  17  3.3  Field Profiles  f o r ac and dc Cases  3.4  Effect  of Bundle Conductors on the F i e l d  3.5  Effect  of Sky Wires on the F i e l d  4.1  P r o l a t e Spheroid  4.2  Conducting P r o l a t e Spheroid i n a Uniform  ....  .......  14  19 19 24  Electric Field  •  26  4.3  Plot..of a/b vs Age f o r .Males and-Females .......  33  5.1  230KV ac Cases - 1 Conductor Bundle  38  5.2  345KV ac Cases - 1 Conductor Bundle  38  5.3  345KV ac Cases - 2 Conductor Bundle  39  5.4  500KV ac Cases - 1 Conductor Bundle  39  •5.5  500KV ac Cases - 2 Conductor Bundle  40  5.6  500KV ac Cases - 4 Conductor Bundle  40  5.7  735KV ac Cases - 4 Conductor Bundle ......  5.8  345KV dc Cases - 1 Conductor Bundle  5.9  345KV dc Cases - 2 Conductor Bundle  •5.I.O  500KV dc Cases - 2 Conductor Bundle  5-11  500KV dc Cases - 4 Conductor Bundle  (v)  ..  41 45  . •  45 46 46  Figure 6.1 6.2 6.3 6.4 6.5 6.6  Per Cent Decrease i n Emax/V Using 1 t o 5 Ground Wires i n t h e i r Optimum . P o s i t i o n  48  345KV ac Cases with S h i e l d i n g - 1 Conductor Bundle  50  345KV ac Cases with S h i e l d i n g - 2 Conductor Bundle  50  500KV ac Cases with S h i e l d i n g - 1 Conductor Bundle  51  500KV ac Cases with S h i e l d i n g - 2 Conductor Bundle ..  51  500KV ac Cases with S h i e l d i n g - 4 Conductor Bundle ....  52  .6.7 • 735KV ac Cases with S h i e l d i n g - 4 Conductor Bundle  52  7.1  Coupling Capacitances I n s u l a t e d Object  between the Line and an  7.2  Schematic Diagram of UBC Instrument  7.3  Test Arrangment to C a l i b r a t e the Meters .....  59  7.4  C a l i b r a t i o n Curves  59  7.5  Test R e s u l t s f o r 230KV L i n e  61  7.6  Test R e s u l t s f o r 360KV Line  61  7.7  360KV Test L i n e f o r Sky Wire E f f e c t  62  7.8  230KV Test L i n e f o r Bundle Conductor E f f e c t . .  64  8.1 .  230KV Cases - 1 Conductor Bundle . Right-of-Way Widths  8.2  345KV Cases - 1 Conductor Bundle Right-of-Way Widths  8.3 8.4  54 ,  58  68 .  69'  345KV Cases - 2 Conductor Bundle Right-of-Way Widths  69  500KV Cases - 1 Conductor Bundle Right-of-Way Widths  70  (vi)  Figure 8.5 8.6 8.7 1.1  Page 500KV C a s e s - .2 C o n d u c t o r B u n d l e Right-of-Way Widths  70  500KV C a s e s - 4 C o n d u c t o r B u n d l e Right-of-Way Widths  71  735KV C a s e s - 4 C o n d u c t o r Right-of-Way Widths  71  M i l l e r Gradient Meter  (vii)  Bundle 73  LIST OF TABLES TABLE 4.1  PAGE - L i m i t i n g V a l u e s of Eox  34  5.1  Data Summary f o r ac Systems  37  5.2  Comparison of L i n e - t o - G r o u n d C l e a r a n c e s  42  5.3  Data Summary f o r dc Systems  44  6.1  L i n e - t o - G r o u n d C l e a r a n c e s w i t h and w i t h o u t 49  Ground Wires 7.1  ..Measurement o f Sky Wire E f f e c t  7.2  Measurement of Bundle Conductor E f f e c t  1.1  M i l l e r Measurements  f o r 345KV S u b s t a t i o n Bus  (viii)  63 65 75  LIST OF SYMBOLS a  = semi-major a x i s of a s p h e r o i d  a ,a,,a £  6  .  = u n i t v e c t o r s i n the s p h e r o i d a l c o - o r d i n a t e system  A  = a r e a of the probe  b  = semi-minor a x i s of a s p h e r o i d  b..: s  = semi-minor a x i s as determined by s u r f a c e a r e a  by  = semi-minor a x i s as d e t e r m i n e d by volume  c  = f o c u s of a s p h e r o i d  C  =  capacitance  C-^Cg  =  constants  d  = conductor  D  = conductor  e  = eccentricity  o  G  J  phase s p a c i n g  = p e r m i t t i v i t y of f r e e space  0  e  diameter  .  = p e r m i t t i v i t y of the .person  t,X,e  = prolate spheroidal co-ordinates  E  - electric  f  = dimensionless f a c t o r  h^jhgjh^  = metric  H  field  coefficients  • = conductor h e i g h t above ground  Hi  = h e i g h t of the i t h conductor plane  H!  - h e i g h t of the i t h image conductor ground plane  1  J-Q  = displacement  I  = conduction  above the ground  current density . . current  (ix)  below the  n  = number of conductors  p  = r e s i s t i v i t y of a man  +q^  = charge per u n i t length on the i t h conductor  -q..  . = charge per u n i t length on the i t h image conductor  r.  = distance between the i t h conductor and the point P  r!  •• = distance between the i t h image conductor and the point P  1  1  R  = conductor radius  S  . surface area  t  = time  T  = r e l a x a t i o n time = permeability of free space  UjjU^  = d i r e c t i o n vectors  V  = line-to-ground  Vm Vs  - - volume of a *person = volume of a spheroid *  to  = angular frequency ;•.  V  = weight of a person  x,y,z  = Cartesian  0  = potential function  0  : primary p o t e n t i a l f u n c t i o n  0-^  = induced p o t e n t i a l f u n c t i o n  a  = angle  q  (x)  voltage  co-ordinates  ACKNOWLEDGEMENT I would l i k e t o express  thanks t o my s u p e r v i s o r  Dr. E. Noakes f o r h i s guidance and encouragement d u r i n g the course o f my r e s e a r c h and f o r t h e o p p o r t u n i t y t o work w i t h him on t h i s p r o j e c t . My s i n c e r e thanks t o M.M.Z. K h a r a d l y  f o r his valuable  c o u n s e l and p a t i e n c e i n r e a d i n g t h e p r e l i m i n a r y d r a f t . I would l i k e t o thank Eugene Lewis and Graham Dawson f o r r e a d i n g the f i n a l d r a f t .  A l s o , I would l i k e t o thank  Mr. A. MacKenzie f o r h i s a s s i s t a n c e , and i n p a r t i c u l a r , my w i f e f o r t y p i n g both d r a f t s . Acknowledgement i s g i v e n t o the N a t i o n a l Research C o u n c i l f o r f i n a n c i a l support  (xi)  of t h e r e s e a r c h .  1 1. 1.1.  INTRODUCTION Development of EHV  and E f f e c t s on L i n e Design  In o r d e r to meet the i n c r e a s i n g demand f o r e l e c t r i c a l energy, power u t i l i t i e s are t u r n i n g more and more t o transmission.  EHV  The need t o t r a n s m i t l a r g e r q u a n t i t i e s of  power and the i n c r e a s i n g remoteness of sources this decision.  underlie  Recent s u r v e y s h a v e i n d i c a t e d t h a t w i t h i n  the next decade n e a r l y 30,000 c i r c u i t m i l e s of EHV  lines  w i l l be o p e r a t i n g i n comparison w i t h a p p r o x i m a t e l y (2)  8,000  now  i n existence.  A study  by the U.S.  Surveys on power r e q u i r e m e n t s up t o 1980  N a t i o n a l Power i n d i c a t e s t h a t the  • a b i l i t y t o s u p p l y more power at a cheaper r a t e i s t i e d d i r e c t l y t o EHV  development.  The b a s i c t r a n s m i s s i o n v o l t a g e , even as l a t e as I960, was  230KV.'^Since  then»development of l i n e s  a t 345KV ac or dc and above has become prominent. ent a 735KV l i n e i s  o p e r a t i o n a l i n Canada w h i l e  operating At  pres-  research  i s b e i n g conducted a t t h i s v o l t a g e l e v e l i n s e v e r a l o t h e r countries. ^ ) , ( 6 ) ^  g  nQQ  ^  f  o r  kigh  e r  v o l t a g e s has  already  been r e a l i z e d and the next s t e p i s f e l t t o be 1,000KV. ( 7 ) , ( 8 ) The advent of e x t r a - h i g h - v o l t a g e t r a n s m i s s i o n has been w i t h o u t  i t s complications.  l i n e d e s i g n has been a f f e c t e d .  not  Every f a c e t of t r a n s m i s s i o n Radio i n t e r f e r e n c e and  corona  l o s s e s i n c r e a s e d t o the p o i n t whereby phase c l e a r a n c e and tor  s i z e are now  conduc-  determined by t a k i n g these e f f e c t s i n t o a c c o u n t ,  as w e l l as l o a d requirements.  The need f o r h i g h e r  insulation  l e v e l s has r e s u l t e d i n i n c r e a s e d i n s u l a t o r s t r i n g s and to-structure clearances.  As a consequence of the  c l e a r a n c e s , i n t r i c a t e conductor c o n f i g u r a t i o n s and  line-  increased loading  requirements of t r a n s m i s s i o n l i n e s , the towers themselves have become more complex i n d e s i g n and t a l l e r .  Because of  the. h i g h cost of towers and i n s t a l l a t i o n , span l e n g t h s have been i n c r e a s e d to h e l p d e f e r t o t a l l i n e c o s t . 1.2 •Presentation of the Problem Due  t o the c o m p l i c a t i o n s of a n a l y s i s of the many f a c t o r s  t h a t a f f e c t EHV  l i n e d e s i g n most r e s e a r c h at a new  i s done e x p e r i m e n t a l l y . ^ ^ '  As more l i n e s become o p e r a t i o n a l  every e f f o r t i s made t o present d a t a - ^ ' ' ^ 1  11  (  12  on every . f a c t o r  of. l i n e d e s i g n as a r e f e r e n c e f o r f u t u r e d e s i g n s . approach p l u s r e i n f o r c e m e n t  voltage l e v e l  This p r a c t i c a l  by mathematical a n a l y s i s where p o s s i b l e  are r e s p o n s i b l e f o r e s t a b l i s h i n g g u i d e - l i n e s t h a t h e l p determine the p h y s i c a l makeup and geometry of the l i n e .  The  final  design  i s of course s u b j e c t t o economic c o n s i d e r a t i o n s . To date, however, i n s u f f i c i e n t a t t e n t i o n has been p a i d t c a c c u r a t e l y s p e c i f y i n g the.minimum c l e a r a n c e s of conductors ground.  This f a c t o r becomes r a t h e r c r i t i c a l a t h i g h e r  f o r two reasons.  The  f i r s t and more important  from  voltages  reason a r i s e s  from c o n s i d e r a t i o n of p u b l i c s a f e t y w i t h r e s p e c t t o the e f f e c t s of e l e c t r o s t a t i c i n d u c t i o n i n o b j e c t s below the l i n e .  The  second  i s f o r reasons of economy. Several s t u d i e s > ( 1 4 )  h  a v e  been c a r r i e d out i n the past  concerning  e l e c t r o s t a t i c i n d u c t i o n .but these were u s u a l l y  c o n f i n e d to induced v o l t a g e s i n communication networks. problems of p u b l i c s a f e t y i n the v i c i n i t y of EHV l i n e s was  f i r s t put forward by E r i t h  the v o l t a g e induced  • who  v  p o i n t e d out t h a t may  F u r t h e r s t u d i e s of e l e c t r o s t a t i c  i n d u c t i o n i n o b j e c t s , based on t h e i r c o u p l i n g t o the l i n e and the hazards presented 1  transmission  i n i n s u l a t e d o b j e c t s below the l i n e s  reach a l e t h a l v a l u e .  taken by R o s s . ^ ^  The  capacitance  t o humans, was  under-  B u c h a n ^ ^ used the above approach i n 1  s t u d y i n g the e f f e c t s of e l e c t r o s t a t i c i n d u c t i o n as r e l a t e d t o the hazards of h a n d l i n g g a s o l i n e .  His r e s u l t s , however,;^  were obtained p r i m a r i l y through the use of models i n an e l e c t r o l y t i c tank.  I t has been standard p r a c t i c e to date to  analyze complicated  s i t u a t i o n s u s i n g models i n e l e c t r o l y t i c  tanks or t e l e d e l t o s paper-.  A s i m p l e r • method has r e c e n t l y  been d e v i s e d by Comsa.^ ^ In t h i s case a dry a i r model i s 2<  used o p e r a t i n g at a h i g h frequency.'  I t s c h i e f advantages  are i t s s i m p l i c i t y and i t s a b i l i t y to a l l o w use of l a r g e r models. An a p p r e c i a t i o n of the magnitudes of p o t e n t i a l induced i n the v i c i n i t y of EHV presented  l i n e s up t o and i n c l u d i n g 735KV was  by Berg and Noakes.^ '' Equations 19  were d e r i v e d  f o r the p o t e n t i a l at any p o i n t below the l i n e u s i n g an e l e c t r o s t a t i c approach.  A computer was  then used to p l o t (21)  the p o t e n t i a l p r o f i l e s .  More r e c e n t s t u d i e s by M i l l e r  (22) ' and Ko.uvenhover have been concerned w i t h c u r r e n t s  ' induced  4  i n men d o i n g l i v e l i n e maintenance.  E v a l u a t i o n of t h e  s t r e n g t n o f t h e c u r r e n t s p a s s i n g through t h e man and the e f f e c t on h i s h e a l t h has' been t h e i r main  concern.  The u n d e r l y i n g motive o f each o f t h e above s t u d i e s i s p u b l i c s a f e t y and s a f e t y t o p e r s o n n e l  o p e r a t i n g i n and around  EHV  i n objects i s a function  lines.  S i n c e t h e v o l t a g e induced  of t h e d i s t a n c e t h e o b j e c t i s from t h e source  i t becomes  obvious, t h a t t h e minimum h e i g h t of a t r a n s m i s s i o n l i n e i s a c r i t i c a l dimension. At p r e s e n t  these l i n e - t o - g r o u n d , c l e a r a n c e s a r e d i c t a t e d (23) by t h e Canadian Standards A s s o c i a t i o n i n Canada and t h e (24) N a t i o n a l E l e c t r i c a l S a f e t y Code i n the U n i t e d S t a t e s .  However,  i t should be noted t h a t t h e r e i s c o n s i d e r a b l e disagreement between these codes as F i g u r e 1.1 i n d i c a t e s .  The d i s c r e p a n c i e s  i n c r e a s e s i g n i f i c a n t l y as t h e v o l t a g e i n c r e a s e s .  Each Canadian  p r o v i n c e and American s t a t e l o o s e l y i n t e r p r e t s t h e a p p r o p r i a t e code and t h e n , based on t h e i r own r e s e a r c h o r r e g i o n a l needs, .specify t h e i r own r e q u i r e m e n t s .  This f u r t h e r complicates  the problem.. The  -  codes a r e b a s e d . p r i m a r i l y on t h e m e c h a n i c a l  r e q u i r e d below t h e l i n e . however, t h i s allowance  Some allowance  clearances  i s made f o r v o l t a g e ,  v a r i e s from r e g i o n t o r e g i o n .  A  (18) study by M c M u r t r i e  t r i e d t o combine t h e m e c h a n i c a l arguments  w i t h a s a f e l i m i t o f approach. t o v o l t a g e s below 460KV.  The s t u d y , however, i s l i m i t e d  With the r a p i d r i s e i n transmission  l i n e v o l t a g e s i t has become obvious t h a t t h e c l e a r a n c e s must  LEGEND 55 i  • : Accessible  To Pedestrians Only  •Accessible To Vehicles Only  /  /  N.ES.C.  N£.S.C.  50A  Uj  ^  45  Q  o  C.S.A. Proposed '"' Revision '/N.E.S.C. Proposed Revision  oc 40 H 10  UJ O  C.S.A.  Proposed Revision 'N.E.S.C. Proposed Revision  35 H Uj  o  C.S.A.  5 30 p=  C.S.A.  20 A  100 200 UNE-TO-GROUND Figure  1.1  300 400 VOLTAGE IN KV  500  C.S.A. and N.E.S.C. Standards f o r L i n e - t o Ground C l e a r a n c e s • • •  be i n c r e a s e d but no one i s c e r t a i n as t o how much. The r e c e n t use o f EHV dc f o r t r a n s m i s s i o n has f u r t h e r c o m p l i c a t e d t h e problem.  No one i s c e r t a i n what h e i g h t s  •should be used f o r dc l i n e s and f o r t h e moment the p r a c t i c e i s t o a p p l y t h e e x i s t i n g ac s t a n d a r d s f o r the c o r r e s p o n d i n g voltage l e v e l .  T h i s f a c t i l l u s t r a t e s the need f o r r e s e a r c h  w i t h r e s p e c t t o l i n e - t o - g r o u n d c l e a r a n c e s f o r dc systems as w e l l as ac systems. 1.3  Objectives of the Thesis I t i s the main o b j e c t i v e o f t h i s t h e s i s t o determine  the minimum h e i g h t requirements  '  o f EHV t r a n s m i s s i o n . l i n e s ,  e i t h e r ac o r dc, based on a c o n s i d e r a t i o n o f the e l e c t r i c f i e l d s t r e n g t h below t h e l i n e . is  The purpose o f such a study  fourfold; 1)  To p r e s e n t a new approach t o the problem.  2) To determine  these h e i g h t s w i t h a view o f e s t a b l i s h i n  an i n t e r n a t i o n a l code. 3) To a l l o w more a c c u r a t e economic s t u d i e s . 4)  To reduce t h e hazards  to public safety.  A g e n e r a l d e s c r i p t i o n o f t h e system, the assumptions used and t h e d e r i v a t i o n of e q u a t i o n s f o r t h e e l e c t r i c  field  and p o t e n t i a l a t an a r b i t r a r y p o i n t due t o an "n" conductor system a r e p r e s e n t e d i n Chapter  2.  The e f f e c t s o f conductor  s p a c i n g , h e i g h t and s i z e on t h e e l e c t r i c f i e l d i s c o n s i d e r e d i n Chapter  3»  The use o f bundle conductors and t h e e f f e c t  of sky w i r e s a r e a l s o noted.  The d e r i v a t i o n o f an a l l o w a b l e  v a l u e o f t h e e l e c t r i c f i e l d due t o the l i n e w i t h r e s p e c t t o  7  a human b e i n g model i s presented i n Chapter 4. i s used i n Chapter  This v a l u e  5 t o p l o t a set of curves t h a t would' .enable  an e n g i n e e r t o s e l e c t t h e proper minimum h e i g h t based on conductor s p a c i n g and s i z e .  The p l o t s o b t a i n e d w i l l  most p r a c t i c a l ranges o f conductor  cover  s p a c i n g and s i z e and they  w i l l be o b t a i n e d f o r both t h e ac and dc c a s e s .  The use  and m e r i t s o f p l a c i n g ground w i r e s below the l i n e f o r s h i e l d i n g purposes a r e i n v e s t i g a t e d i n ' C h a p t e r 6.  The e f f e c t  of u s i n g from 1 t o 5 ground w i r e s f o r s h i e l d i n g i s noted and i n d i c a t e s t h e reduced hazards  t o the g e n e r a l p u b l i c  when t h i s t e c h n i q u e i s employed.  A l s o a comparison i s made  of t h e r e q u i r e d h e i g h t s as i n d i c a t e d i n Chapter o b t a i n e d u s i n g t h e ground w i r e t e c h n i q u e .  5 w i t h those  A general d e s c r i p t i o n  o f t h e i n s t r u m e n t s used and t h e measurements made of t h e induced p o t e n t i a l o b t a i n e d f o r two t y p i c a l systems a r e p r e s e n t e d i n Chapter 7.  The r e a d i n g s o b t a i n e d and p o t e n t i a l p r o f i l e s  p l o t t e d a r e compared w i t h t h e c a l c u l a t e d v a l u e s expected as a measure o f t h e a c c u r a c y of t h e a n a l y s i s used.  In addition,  measurements a r e made t o e x p e r i m e n t a l l y v e r i f y t h e e f f e c t o f bundle conductors and s k y w i r e s on t h e e l e c t r i c f i e l d  below  the l i n e .  A method i s proposed i n Chapter 8 t h a t i s used t o  determine  t h e w i d t h o f t r a n s m i s s i o n l i n e r i g h t - o f - w a y s based  -on i n d u c t i o n e f f e c t s . used throughout  The r a t i o n a l i z e d FPS system o f u n i t s i s  the t h e s i s .  2  DERIVATION OP EQUATIONS FOR THE ELECTRIC FIELD AND AND POTENTIAL DUE TO AN n-CONDUCTOR SYSTEM  2.1 General D e s c r i p t i o n of the System The system under study c o n s i s t s of 'n' s e p a r a t e conductors a r b i t r a r i l y arranged over a. p e r f e c t l y / c o n d u c t i n g ground  plane  The s i t u a t i o n i s i l l u s t r a t e d i n P i g u r e 2.1 where the conductors are  c o n s i d e r e d t o be p a r a l l e l t o the ground.  The e l e c t r i c  f i e l d or the v o l t a g e induced a t any p o i n t i n space may be found i n terms of the known v o l t a g e s of t h e conductors and t h e i r d i s t a n c e s from t h i s p o i n t . 2.2  Assumptions .The a n a l y s i s t o be c a r r i e d out w i l l be a p p l i c a b l e to.  e i t h e r balanced 3 phase ac cases or dc cases.  F o r ac cases  the e l e c t r i c f i e l d a t any p o i n t i n space i s the phasor comb i n a t i o n •• of the f i e l d s induced by each l i n e .  The r e s u l t a n t  phasor a t any p o i n t i n space i s f i x e d i n magnitude and r o t a t e s at' s i x t y H e r t z .  As such the ac. .case can "be  a n a l y z e d as a s e t of phasors 120 e l e c t r i c a l degrees a p a r t • and f i x e d i n time.  The v a l u e s d e r i v e d i n t h i s t h e s i s i n d i c a t e  the maximum v a l u e t h a t the r e s u l t a n t phasor can a c h i e v e . The rector: cos ( Qt). • i s ' o m i t t e d . ".In  order t o s i m p l i f y the d e r i v a t i o n s e v e r a l  assumptions  w i l l be made. 1) The e a r t h i s taken t o be homogeneous and p e r f e c t l y conducting. 2) The conductors a r e assumed t o be u n i f o r m and i n f i n i t e i n length.  ':  9  A*  F i g u r e 2.1  D e r i v a t i o n of the E l e c t r i c F i e l d and P o t e n t i a l f o r an h-Condu'ctor System  10 3) The charge on the conductors i s assumed t o be u n i f o r m l y d i s t r i b u t e d a l o n g and around the  conductor.  4) Because of the r e l a t i v e dimensions i n v o l v e d the. charge-, on the conductor--,  can be c o n s i d e r e d ' as a l i n e source  l o c a t e d on t h e a x i s a t the c e n t e r of the conductor.;; . 5) The ground p o t e n t i a l plane i s taken a t the s u r f a c e of the e a r t h t o r e p r e s e n t a worst case s i t u a t i o n . The s o l u t i o n can be f u r t h e r s i m p l i f i e d b y u s i n g the method, of images t o c o n s i d e r the e f f e c t of the e a r t h and.by u s i n g the p r i n c i p l e of s u p e r p o s i t i o n t o o b t a i n the t o t a l  field.  2• 3 D e r i v a t i o n C o n s i d e r P i g u r e 2.1.  The t o t a l e l e c t r i c f i e l d E t .  due t o conductor ' i ' and i t s image a t the p o i n t P can be w r i t t e n as: Et  ±  where (25)  Er.  and  Er! 1  = Er  ±  + Er^  2.1  2itr. e  1 o  2jcr! e 1 o  The t o t a l x component of the e l e c t r i c f i e l d a t the p o i n t P i s : Ex.  2xe  Since. 1  Since! 1 r !1  2.2  But since, = - (H. - X) / r . and since! = (H! + X) /V. and H. =H! 1 '1 ' 1 X 1 ' 1 1 1 In g e n e r a l then f o r an n-conductor system the t o t a l e l e c t r i c v  f i e l d a t an a r b i t r a r y p o i n t P can be -written as: n Ex  H.-X i  2ite  r.  o  +  H.+X l  ,,2  2.3  1  i=l  S i n c e E = - grad V i t i s a l s o p o s s i b l e t o w r i t e an e x p r e s s i o n for  the p o t e n t i a l a t p o i n t P r e l a t i v e t o the ground p l a n e where  V=0  as:  f Vp = V(X) Vp  2ite  = \ g r a d V dX n  q ln  2.4  i  i=l I f the charges on the conductors are known, the e l e c t r i c f i e l d and p o t e n t i a l a t any p o i n t about the l i n e can be found. -Normally, however, the charges on the conductors are unknown. They can be found by a p p l y i n g the boundary c o n d i t i o n s of the system;namely the l i n e t o ground v o l t a g e t h a t appears on each conductor. kth  The e x p r e s s i o n f o r the v o l t a g e a p p e a r i n g on the  element due t o the charges on the o t h e r conductors i s : n Vk  A similar  1  2ite.  q ln ±  ik  2.5  ik  e x p r e s s i o n can be w r i t t e n f o r each l i n e .  Solution  of the problem i n v o l v e s n s i m u l t a n e o u s e q u a t i o n s and i s best  12  handled  i n m a t r i x form.  -  11  In  1  1 1  V n  1 ~ 2ace  In  11  1  1 1 1  W r i t i n g the e q u a t i o n s t h i s way g i v e s :  'In 2.6  0  nl  In  In  r ' nn  r  'nl  x  nn  n  or i n a b b r e v i a t e d form: i=l,n  j=l,n  2.7  The m a t r i x PC i s known as the p o t e n t i a l c o e f f i c i e n t m a t r i x and t h e e n t r i e s a r e known as Maxwell's P o t e n t i a l The i n v e r s e of t h e PC m a t r i x a l l o w s d e r i v a t i o n on each  Coefficients.  (26)  of the charge  conductor. ~~  -1  2.8  "Equation 2 . 3 or 2 . 4 can then be used t o s o l v e f o r t h e f i e l d or t h e p o t e n t i a l .  Thus i f t h e l i n e - t o - g r o u n d v o l t a g e s of a  system a r e known t h e p o t e n t i a l or e l e c t r i c f i e l d a t any p o i n t can be s p e c i f i e d by d e t e r m i n i n g t h e PC M a t r i x which i s based s o l e l y on the geometry of t h e system.  13  3. THE AND 3.1  EFFECT OF PHYSICAL PARAMETERS, BUNDLE CONDUCTORS SKY WIRES ON THE ELECTRIC FIELD BELOW THE LINE  The E f f e c t of Conductor S p a c i n g , Height the E l e c t r i c F i e l d  and S i z e on  U s u a l l y , a t r a n s m i s s i o n l i n e assumes a d e f i n i t e symmetry about an a x i s .  Only h o r i z o n t a l c o n f i g u r a t i o n s are d e a l t  w i t h i n t h i s t h e s i s as most EHV t h i s type.  Due  l i n e s i n e x i s t e n c e today are of  t o the p h y s i c a l symmetry,only the  coefficients  on and above the d i a g o n a l of the PC m a t r i x need be c a l c u l a t e d . Many l i n e s l i e i n h i g h i s o k e r a n i c areas and as such sky w i r e s are added f o r p r o t e c t i o n .  I n the a n a l y s i s presented  Chapter 2 these l i n e s are handled as l i n e conductors  in  whose  -voltage i s z e r o . The for  shape of the p r o f i l e f o r the e l e c t r i c f i e l d at  a s i n g l e p o l e and double p o l e dc case and a t h r e e phase  ac case i s shown i n F i g u r e 3.1. for  X=0  a l i n e h e i g h t of 20'0"  i n each case.  The  and  The p r o f i l e s were computed conductor s i z e of 1024MCM  electric field  "to l i n e - t o - g r o u n d v o l t a g e .  i s normalized with respect  I n s p e c t i o n of e q u a t i o n  2.3  i n d i c a t e s t h a t these p r o f i l e s can be a l t e r e d by e i t h e r v a r y i n g the l i n e v o l t a g e or conductor p o s i t i o n .  The p o s i t i o n can  be  v a r i e d by a l t e r i n g e i t h e r the conductors  s p a c i n g or i t s h e i g h t .  The  f i e l d can a l s o be a l t e r e d by u s i n g a d i f f e r e n t s i z e d  conductor.  The  e f f e c t of each of these f a c t o r s on the e l e c t r i c f i e l d a t  for  an ac case i s i l l u s t r a t e d i n F i g u r e 3.2.  X=0  The range of p a r a -  meters s e l e c t e d i s i n d i c a t i v e of those i n use today.  The h e i g h t  s p a c i n g both have a s i g n i f i c a n t e f f e c t on the shape of the  and  profile.  E/V IN %  -1-0  14  >v  •0>S ,. •  -3r.O  -2-0  -PO (I)  0  DC  CASE  1-0 SINGLE  . i  .  .  2-0  DC  CASE  DOUBLE ^E/V  ;  ka  -2-0  -7-0  (3) AC  P i g u r e 3-1  CASE  Y/D  3-0  Y/D  POLE IN%  E» -03--  I 0*25-0"  -3-0  3-0  POLE  -3-0  (2)  i  <6  0  THREE  VO  2-0  PHASE  E l e c t r i c F i e l d P r o f i l e s f o r ac and dc Cases  3-0 Y/D  R=0-05 H1=20 ~0" H2 = 30'0" 40''-0' ,  1-0 1-5 RATIO OF Y/D  R=0-05 D1= 40-0" D2=30'-0" D3 = 2a-0"  1-0 1-5 RATIO OF Y/D  D = 20'- 0 R = 0-15 R> 0*10 R=0-05  1-0 RATIO OF gure 3.2  PS Y/D  2-0  V a r i a t i o n i n F i e l d P r o f i l e s w i t h Conductor H e i g h t , S p a c i n g and S i z e  2-5  16 w h i l e t h e r a d i u s does n o t .  I n a l l cases the maximum  e l e c t r i c f i e l d l i e s i n a r e g i o n near the outer  conductor.  The p o i n t a t which i t a c t u a l l y occurs i s dependent upon t h e ratio,  o f t h e conductor s p a c i n g t o height,, but n o r m a l l y i t  l i e s a t a d i s t a n c e between 1.0 and 1.5 times t h e conductor spacing.  Only i f t h e ratio;.: o f D/H<l/2 w i l l Emax occur  beyond 1.5. The  curves c o n t a i n e d i n F i g u r e 3-3 were d e r i v e d f o r t h e  range of parameters used above.  The v a l u e of t h e E - f i e l d  p l o t t e d r e p r e s e n t s the maximum o b t a i n e d a t ground l e v e l f o r the p a r t i c u l a r c o n f i g u r a t i o n . used throughout  (The e x p r e s s i o n Emax w i l l be  t h i s t h e s i s t o r e p r e s e n t the maximum f i e l d  i n t e n s i t y c a l c u l a t e d f o r any f i e l d p r o f i l e below t h e l i n e unless otherwise stated.)  A d i r e c t comparison of t h e r e l a t i v e  per cent change i n Emax f o r a 100$ change i n any one parameter can be made w h i l e t h e o t h e r s a r e h e l d c o n s t a n t .  The r e s u l t s  of such a change i n each parameter on Emax a r e i n t h e order of magnitudes t a b u l a t e d below. Voltage  +100/$  Height  - 65$  Spacing  + 30 $  Radius  + 10 $  The most important parameter a s i d e from system voltage^, i s conductor h e i g h t and i t s importance above.  i s clearly established  T h i s f a c t h e l p s demonstrate t h e need f o r a c c u r a t e  d e t e r m i n a t i o n ' o f conductor h e i g h t i n view of p u b l i c s a f e t y . 3.2 The E f f e c t of Bundle Conductors on the E l e c t r i c  Field  I t was s t a t e d p r e v i o u s l y t h a t t h e t r e n d o f conductor  , /-Sr  1-5r  < 1-0  ^P0\-  >0-5  0-5  UJ  H=40'-0'  D  8  0  20 HEIGHT IN  0  40 FEET  H=20'-0'  20 SPACING  IN  40 FEET  1'5r  1-0  >0-5 o  >0-5  UJ  0  20 SPACING  Q  JL  20  40 IN  HEIGHT  FEET  1'5r  /•5r  1-0  1-0  .40 IN  FEET  * 0-5  o  Ui 0-02  0-04 RADIUS  F i g u r e 3-3  0-06 IN  0-0$  0'10  FEET  0 0  002  0-04  : RADIUS  0-06  0-08  IN  FEET  E f f e c t o f Conductor Spacing, Height and S i z e on Emax  0-Ji  18  d e s i g n f o r EHV l i n e s has been towards the use of bundle conductors f o r reasons f o r economy, r a d i o i n t e r f e r e n c e and corona.  The use of bundle conductors i n p l a c e of l a r g e  s i n g l e c o n d u c t o r s g r e a t l y a l t e r s the v a l u e o f the e l e c t r i c field.  T h i s f a c t i s i l l u s t r a t e d i n F i g u r e 3.4 where the v a l u e  of E has been n o r m a l i z e d w i t h r e s p e c t to V.  A l t h o u g h each  sytem i s c a p a b l e of t r a n s m i t t i n g the same power., the-use of bundle conductors r e s u l t s i n a h i g h e r maximum e l e c t r i c near the s u r f a c e of the e a r t h .  field  The i n c r e a s e i n the f i e l d  c o u l d be as h i g h as 40$ f o r the bundle conductor case vs the s i n g l e conductor case.  The minimum h e i g h t s , w h i c h at p r e s e n t  do not d i f f e r e n t i a t e between conductor c o n f i g u r a t i o n s , but are based s o l e l y on system v o l t a g e and m e c h a n i c a l c l e a r a n c e , w o u l d s p e c i f y the same c l e a r a n c e f o r each of t h e s e l i n e s . of  I n view  e l e c t r o s t a t i c i n d u c t i o n t h i s would seem i n c o r r e c t . In t h i s t h e s i s , b u n d l e conductor c o n f i g u r a t i o n s a r e .  handled by u s i n g a Geometric Mean R a d i u s ^ ^ ' ( G M R ) t e c h n i q u e . 2  T h i s t e c h n i q u e can be used t o reduce a v e r t i c a l , h o r i z o n t a l or t r i a n g u l a r c o n f i g u r a t i o n of ,'n' conductors' t o a s i m p l e 3 conductor h o r i z o n t a l c o n f i g u r a t i o n e q u i v a l e n t . T h i s method, a l l o w s a s u b s t a n t i a l s a v i n g s i n time and c a l c u l a t i o n s w i t h no l o s s i n a c c u r a c y . An exact s o l u t i o n ' w o u l d ' h a v e r e q u i r e d ' c a l c u l a t i n g the c e n t e r of charge d i s p l a c e m e n t s t h a t r e s u l t from the p r o x i m i t y e f f e c t s of bundle conductors and then employing-the s t a n d a r d s o l u t i o n u s i n g a PC m a t r i x f a r i n excess of a 3x3.  Even i f the p r o x i m i t y e f f e c t s are i g n o r e d ,  19  D = 36'~0"  7-5  4-583 MCM AT 18" BUNDLE SPACING 2-1780 MCM AT 18" BUNDLE SPACING 1-3120 MCM  1-0  ^  H=35~0"  0-5  0 0-5  F i g u r e 3.4 :  ' Effect  1-0 RATIO OF  1>5 Y/D  o f Bundle Conductors on t h e F i e l d  Uj  Q:  +1'0 •0  Is1  -2-0h  C•^T J_ i -3>0 ^  Uj  •4-0 -5-0 L  F i g u r e 3-5 :  Effect  20  o f Sky'Wires on t h e F i e l d  2-5  c o n s i d e r a t i o n of the charge on each conductor r e s u l t s i n a l a r g e PC matrix and i n c r e a s e s s o l u t i o n time.  The GMR  technique i s s u f f i c i e n t l y accurate i n comparison other methods f o r the range  of conductor, s i z e s and con-  f i g u r a t i o n s under study i n t h i s 3.3  The E f f e c t  with the  thesis.  of Sky Wires on the E l e c t r i c  Field  Sky wires a r e used on t r a n s m i s s i o n l i n e s as a p r o t e c t i o n a g a i n s t d i r e c t s t r i k e s by l i g h t n i n g .  They are  p o s i t i o n e d above the l i n e conductors and attached d i r e c t l y to ground.  U s u a l l y only two wires are used and t h e i r exact  l o c a t i o n i s dependent upon the i s o k e r a n i c l e v e l of the region.  In the past these wires were normally p o s i t i o n e d (28)  u s i n g d i r e c t s t r o k e theory  at a p r o t e c t i v e angle of  30° midway between the two l i n e conductors.  Present  p r a c t i c e has been t o move the sky wires c l o s e r t o the outer conductors.  An i n v e s t i g a t i o n of the e f f e c t ' of these  wires on the f i e l d below the l i n e conductors shows i t t o he n e g l i g i b l e .  T h i s f a c t i s i l l u s t r a t e d i n F i g u r e 3'5.  These r e s u l t s were obtained independent  of conductor spacing,  h e i g h t or s i z e . The s p a c i n g of the sky wires was v a r i e d from' 1/4 t o 5/4 that of the l i n e conductors s p a c i n g . i n the range  They were l o c a t e d  20 t o 40 degrees above the conductors.  The  shape of the p r o f i l e s i s a l t e r e d n e g l i g i b l y and the g r e a t e s t v a r i a t i o n i n Emax was l e s s than 5$ f o r the range of p o s i t i o n s tried.  I t should be noted that the change i n the e l e c t r i c  f i e l d as-compared to the case w i t h o u t ground w i r e s was  at  worst-an increase  4%.  of l e s s than 0.5%  and  a decrease of  These f a c t s i n d i c a t e t h a t the sky w i r e s have a n e g l i g i b l e e f f e c t on the f i e l d below the l i n e .  S i n c e the e f f e c t i s  u s u a l l y a s l i g h t decrease i n the f i e l d  thus•favouring  g r e a t e r s a f e t y , a n a l y s i s can be f u r t h e r s i m p l i f i e d by t a k i n g sky w i r e s i n t o account.  not  4. AN ANALYSIS OF A MODEL OF A HUMAN BEING The  corona l o s s e s and r a d i o i n t e r f e r e n c e presented  by a t r a n s m i s s i o n l i n e a r e due t o t h e e l e c t r i c f i e l d s e t up about t h e l i n e c o n d u c t o r s .  I t i s f e l t therefore, that  d e r i v a t i o n ' o f minimum h e i g h t s h o u l d be determined i n r e l a t i o n ' to t h i s  field.  4.1 Method o f Approach (29) I t has been found e x p e r i m e n t a l l y i s a b l e t o sense an induced s t r e n g t h i s 6KV/in.  t h a t a human b e i n g  e l e c t r i c f i e l d when the  This corresponds t o a s u r f a c e c u r r e n t  d e n s i t y o f 0.5uA/sq. i n .  The s e n s a t i o n p r o d u c e d a t t h i s :  i s l i k e a " c o o l i n g breeze b l o w i n g a c r o s s t h e s k i n " . intensity  field  increases the sensation increases.  level  As t h e  I t i s t o be  noted t h a t t h i s e f f e c t does n o t p r e s e n t an immediate shock hazard  o r h e a l t h hazard  on a s h o r t term b a s i s .  The e f f e c t  of l o n g range exposure t o such a f i e l d i s a t p r e s e n t unknown. I t i s f e l t t h a t i n d i v i d u a l s p a s s i n g near or w o r k i n g i n the u n i f o r m f i e l d - o f a t r a n s m i s s i o n l i n e should n o t have t o experience  this sensation.  By assuming a p r o l a t e s p h e r o i d a l  model f o r a human, an e x p r e s s i o n f o r t h e e l e c t r i c f i e l d a t i t s s u r f a c e can be d e r i v e d .  I f the value of t h i s f i e l d i s  to be l i m i t e d  t o 6KV/in.- then t h i s f a c t can be used t o d e t e r -  mine t h e l i n e  height.  4.2  Assumptions I n order t o s i m p l i f y a n a l y s i s t h e f o l l o w i n g assumptions  are made r e g a r d i n g the p r o l a t e s p h e r o i d model:  23  J  1) The c u r r e n t s i n d u c e d i n i t a r e assumed t o have no e f f e c t on t h e s o u r c e . 2) I t i s assumed t o be h o m o g e n i o u s , i s o t r o p i c , and (•57)  has t h e f o l l o w i n g c o n s t a n t s . p = lfl-m ( i n t e r i o r ) \  e = 80€ .1  .  Q  p = 10 A-m 4  u  = p  (exterior)  o  •  3) The r e l a x a t i o n t i m e f o r c h a r g e  i n d u c e d on t h e s p h e r o i d i s :  T = ep T = 7.1 x 1 0 ~ ^ s e c s  (on s u r f a c e )  T^ = 7 . 1 x l O  ( i n s i d e t h e man)  -  1  ^ sec  S i n c e t h e l i n e f r e q u e n c y i s 60 H e r t z t h e r e d i s t r i b u t i o n ) of  charge  instantly. 4) I n v i e w  o v e r t h e s p h e r o i d c a n be assumed  t o take place  T h u s , a q u a s i s t a t i c s i t u a t i o n i s assumed  to exist  o f t h e above c o n s t a n t s t h e s p h e r o i d c a n be t r e a t e d  as a good c o n d u c t o r a t l i n e f r e q u e n c y and h e n c e t h e c o n d u c t i o n c u r r e n t c a n be assumed much l a r g e r t h a n t h e displacement current. 5) The f i e l d to  i n the v i c i n i t y  o f t h e s p h e r o i d i s assumed  be u n i f o r m , d i r e c t e d i n t h e n e g a t i v e X - d i r e c t i o n ,  and due t o s o u r c e s l o c a t e d a t i n f i n i t y . i s taken equal t o the l a r g e s t f i e l d  I t s magnitude  value occurring •  o v e r t h e mans h e i g h t when he i s n o t p r e s e n t .  The  a n a l y s i s i s c a r r i e d o u t f o r t h a t i n s t a n t •of t i m e a t . w h i c h B i s a maximum. A n a l y s i s c a n be f u r t h e r s i m p l i f i e d c o - o r d i n a t e system i s used.  i f a prolate spheroidal  24  4.3 Co-Ordinate System A p r o l a t e s p h e r o i d as shown i n F i g u r e 4.1 i s obtained by r o t a t i n g an e l l i p s e about i t s major a x i s . be the'new c o - o r d i n a t e s . co-ordinate  L e t e,\,9  When the e l l i p s e i s r o t a t e d the  e d e f i n e s p r o l a t e s p h e r o i d a l s u r f a c e s , whose  orthogonal surfaces are confocal hyperboloids (30) d e f i n e d by X.  of two s h e e t s  The measure.of r o t a t i o n from the Y a x i s i n  the Y-Z plane i s d e f i n e d as 9.  The p e r p e n d i c u l a r  distance  from the. X a x i s t o t h e p o i n t i n q u e s t i o n i s d e f i n e d as r .  y = r cos 0 z=r  sin  6  F i g u r e 4.1  Prolate  Spheroid  25 The r e l a t i o n s between c a r t e s i a n . c o - o r d i n a t e s and  prolate  spheroidal co-ordinates are: x =  CA.E  y = cj(e -l) (l-\ )  cos 9  z = cvj(e -l)  sin 9  2  2  (l-\ )  2  2  4.1  The m e t r i c c o e f f i c i e n t s a r e :  h  ( 2 ,2N l =- c (e -X ) \ (e -l ) 2  = c (e -X ) ) \ (l-X 2  2  4.2  2  h_ = c (£ -l) ( l - X ) 2  4.4  2  Mathematical. A n a l y s i s The a n a l y s i s of a c o n d u c t i n g s p h e r o i d i n a u n i f o r m  e l e c t r i c f i e l d i s a s i m p l e inhomogeneous boundary v a l u e ' problem.  I f a u n i f o r m p a r a l l e l f i e l d Eox i s a p p l i e d  the' X a x i s as shown i n F i g u r e 4.2  along  the p o t e n t i a l of the  a p p l i e d f i e l d a t X-I's: -  "  0 • =' - EoxX o - - EoxcXe  4.3  T h i s p r i m a r y p o t e n t i a l 0 , i s a s o l u t i o n of L a p l a c e s O  e q u a t i o n i n the form of a product of two f u n c t i o n s . 0  O  = C F 1  1  (e)  F  2  (X)  That i s  A.A  26 where C-^ = - Eoxc, F ( \ ) = \, and F-^e) = e. 2  I t i s not  regular at i n f i n i t y . VLO  V L-l20  VL + 120  ©  ©  •ox  V  •V=o  Figure  4.2  Conducting P r o l a t e Spheroid i n a Uniform E l e c t r i c Field  I f the boundary c o n d i t i o n s a r e t o be met then the p o t e n t i a l 0^ due t o the induced d i s t r i b u t i o n of charge on the s p h e r o i d must v a r y f u n c t i o n a l l y over every s u r f a c e of the f a m i l y E = c o n s t a n t i n e x a c t l y t h e same manner as 0 . I t d i f f e r s from 0  i n t h a t i t must be r e g u l a r a t i n f i n i t y .  q  A s o l u t i o n f o r 0^ can assume the form: 0  - C G (e):F (\)  X  2  1  where F ( \ ) = X. as b e f o r e . 2  equation.  4.5  2  But 0^ must s a t i s f y L a p l a c e ' s  S u b s t i t u t i n g f o r 0-j. from e q u a t i o n 4.5 i n t o L a p l a c e ' s  e q u a t i o n and n o t i n g t h a t A0^/^9=0  £2 a,  2  +  2e  / 2 -, \ (e -1)  de  one o b t a i n s :  2G  U -D 2  0  4.6  27  E q u a t i o n 4.6 i s a second  o r d e r d i f f e r e n t i a l e q u a t i o n and  possesses two s o l u t i o n s .  One i s a l r e a d y known from 4.4.  U s i n g t h i s known s o l u t i o n and n o t i n g t h e form of 4.6 i t i s (31) possible to write  de  By s u b s t i t u t i n g 4.7 and F  4.7  (\) from 4.4 i n t o 4-5 t h e  2  f o l l o w i n g r e s u l t i s obtained: oo 0  1  =  0  de  O  £  '1 The c o n s t a n t  2  4.8  (e -D 2  may be determined  the p o t e n t i a l a t any s u r f a c e e  Q  from the c o n d i t i o n t h a t  i s a constant.  That i s :  0 s = 0-,1 + 0 o oo  -  0o +  0o  de  of  2  (e -D 2  de  1+ '1  e  2  (e -D 2  e=e  therefore: 4.9  de ffe2/(e 2-1) , ,  28 The p o t e n t e n t i a l a t any p o i n t i n space can he w r i t t e n as 0 = 0  O  0  +  n  fie^o)  (  de  4.10  de  2/ 2 v e (e -1) n  A knowledge o f t h e p o t e n t i a l o f t h e s p h e r o i d and e v a l u a t i o n of the i n t e g r a l s i n t h e above e x p r e s s i o n c o m p l e t e l y  defines  In t h i s case 0 =0  the p o t e n t i a l a t any p o i n t i n space. because t h e s p h e r o i d i s on the ground.  The i n t e g r a l s can  (32) be e v a l u a t e d and w r i t t e n i n t h e f o r m : ' ' w  de  2/ 2 v e ( e -1) n  1  £  1  2  +  In/e-l\ \E+l/  4.11  S u b s t i t u t i o n of the l i m i t s o f the i n t e g r a l s i n t o 4.11  a l l o w s e q u a t i o n 4.10 t o be r e w r i t t e n a s :  0 = 0  But 0  o  - 0  1 £  1 2  +  1  EO  +  ln/e-l\ \e+ll  1 ln/£_-l 2  - EoxcX.£ t h u s :  0 = - EOXC\E + E o x c \ e o [ j . + |  l n  (f^)  equation  29 The s o l u t i o n f o r t h e e l e c t r i c f i e l d a t t h e s u r f a c e e i s found from t h e r e l a t i o n : £=£  S u b s t i t u t i n g 4.12 the  *£=£  v  O  4.13  O  i n t o 4.13  v a l u e of the e l e c t r i c f i e l d  i s found t o be:  " £  I T  -O  ~ i  E  <  = 0.  and n o t i n g t h a t  +  5  l  n  £ -1" O  ^  4.14  o  l-£  1 + ~  ln  The above e x p r e s s i o n d e f i n e s the e l e c t r i c f i e l d a t t h e . s u r f a c e of t h e s p h e r o i d i n terms of the o r i g i n a l 4.5  field.  Dependence of the S u r f a c e Value of E l e c t r i c F i e l d . R a t i o of a/b I t was noted i n s e c t i o n 4.1  t h a t the e l e c t r i c  r e c o g n i t i o n l e v e l o c c u r s a t 6KV/in.  on t h e  field  I f e q u a t i o n 4.14 i s  r e a r r a n g e d i t i s p o s s i b l e t o determine an a l l o w a b l e v a l u e of Eox based on E  = 6KV/in.  That i s :  o E o  Eox .=  4.15  X  M  o £  £0 2  where f  £  0  1  0  -1  +  +  1 l n £0 -1£ +1 2 0  £  0  2  ln  £  0  £  0  -1 +1  30 I n t h e above e q u a t i o n E-. i s known and i f X i s taken to.be. o u n i t y then d e t e r m i n a t i o n of Eox i s dependent on the v a l u e of f .  Since £  = l / e , where e i s the e c c e n t r i c i t y , i t s  q  v a l u e i s g i v e n by:  ;.l  £0 =  2  VJ  The v a l u e of E of a/b.  4.16  -(b /a ) 2  q  and hence o f f i s dependent upon the r a t i o  I n the l o w e r l i m i t when a/b = 1 the s p h e r o i d  t o a sphere and the v a l u e of f i s u n i t y . would be 6KV/in.  i n t h i s case.  reduces  The l i m i t on Eox  However, i n t h e upper l i m i t  as the v a l u e of a/b approaches i n f i n i t y , the v a l u e of f approaches i n f i n i t y .  I n t h i s case the a l l o w a b l e e l e c t r i c f i e l d  Eox approaches z e r o . 4.6 A P r a c t i c a l Approach t o the D e t e r m i n a t i o n of the Value of • a/b f o r Human Beings The v a l u e of 'a' corresponds easily obtainable.  t o a persons h e i g h t and i s  On the o t h e r hand 'b' must be  determined.  I t can be e v a l u a t e d through a c o n s i d e r a t i o n of the volume and s u r f a c e a r e a of the person,.' I f the s p e c i f i c g r a v i t y f o r humans i s taken as 1.0  then  the volume occupied by a person can be found a s : Vm = 27.7 W  cu. i n  where W r e p r e s e n t s the weight  4.17 of the i n d i v i d u a l .  The volume  of a s p h e r o i d i s g i v e n by: 2  Vs  = |  3  reab  .  . 4.18  Equating Vs/2 t o equation 4.17 a s o l u t i o n f o r b f o l l o w s i f a persons h e i g h t and weight are known.  . b = 3• 64 J^W/aJ / 1  case:  in.  2  y  where b  In t h i s  4.19  i s the value of b based  on the volume.consideration.  I t i s a l s o p o s s i b l e t o determine  the s u r f a c e area of a person  v  from b i o l o g i c a l c o n s i d e r a t i o n s : ^ ' w  Sm =(71.84W * 0  425  a * 0  7 2 5  0.155) sq. i n .  4.20  The s u r f a c e area of a spheroid i s g i v e n by: S = 2Kb  2  +  e  I f S/2 i s equated  sin^e  t o equation 4.20 another s o l u t i o n f o r b  r e s u l t s which can be denoted • of b  g  4.21  as 'b •.  In g e n e r a l the value  I s l a r g e r than the value of b ". v  the average of b  andb  I f 'b' i s taken as  both c o n d i t i o n s are reasonably  s a t i s f i e d . ' Therefore: b + b s b = -s2  . 4.22  The above equations demonstrate q u i t e c l e a r l y that the value of 'b' I s p r i m a r i l y dependent upon the weight of an i n d i v i d u a l .  At any f i x e d h e i g h t t h e r e f o r e , a t h i n  person  i s f a r more a f f e c t e d by the f i e l d than a heavy person. determination of the worst  A  case c o n d i t i o n f o r Eox reduces  t o f i n d i n g the minimum weight a person, achieves a t some  32  a r b i t r a r y h e i g h t and then comparing the r a t i o s of a/b f o r the v a r i o u s h e i g h t s . 4.7  E v a l u a t i o n of a L i m i t i n g Value of Eox The d e r i v a t i o n of a meaningful 1imit  on Eox i s dependent  upon the r e l a t i o n between people's h e i g h t s and w e i g h t s . S t a t i s t i c a l d a t a on t h i s r e l a t i o n are a v a i l a b l e i n many b i o l o g i c a l handbooks.  '  In t h i s t h e s i s two cases are  c o n s i d e r e d on the b a s i s of these d a t a .  F i r s t the worst p o s s i b l e  case i s assumed by combining maximum h e i g h t s w i t h minimum w e i g h t s a t any age l e v e l .  The second case i s based on com-  b i n i n g average h e i g h t s w i t h average w e i g h t s .  The r e s u l t s are  i l l u s t r a t e d i n F i g u r e 4.3. The c u r v e s of the worst case i n d i c a t e t h a t a/b i s a ~ maximum f o r a 13 y e a r o l d male or a 12 y e a r o l d female.  The  v a l u e s of Eox f o r these cases a r e c o n s i d e r a b l y l o w e r than f o r the case of a man  over 25 y e a r s of age.  The r e s u l t s  based  on averages i n d i c a t e l o w e r v a l u e s of a/b i n a l l cases but s t i l l p o i n t s out t h a t people i n t h e i r teens a r e most susceptible.  The v a l u e of Eox c o r r e s p o n d i n g t o each of the  above cases i s t a b u l a t e d i n Table 4.1.  The case of a  man  25 y e a r s and over i s i n c l u d e d f o r a comparison. A c c o r d i n g t o Table 4.1 the l i m i t i n g v a l u e of Eox s h o u l d be t a k e n as 0.8KV/ft.  However, use of t h i s v a l u e may  prove  more s t r i n g e n t t h a n r e q u i r e d , s i n c e the p r o b a b i l i t y of a c h i e v i n g maximum h e i g h t and minimum weight s i m u l t a n e o u s l y i s deemed small.  A more m e a n i n g f u l v a l u e may  be found by c o n s i d e r i n g  4  150  Worst Case  12-5  10-0  7-5  5-0  2-5  0  10 AGE  F i g u r e 4.3  15 (YEARS)  20  P l o t of a/b vs Age f o r Males and Females  -I—_—c  25  the c l e a r a n c e s s p e c i f i e d by t h e v a l u e s of ^ahle  4.1 f o r  a given voltage l e v e l . Table 4.1 Case  L i m i t i n g Values of Eox  MALE. Age (Yrs)  Eox (KV/ft) •  FEMALE Height (Ihs)  Aver a^5e 15  1.383  65.6  25  1.528  68.3  13  0.809  66.8  25  1.081  73.1  Worst  The  Age (Yrs)  Eox (KV/ft)  Height (Ins)  12  1.365  59.0  12'  0.800  .64.7  s e n s a t i o n produced by e x c e s s i v e e l e c t r i c  i s unrecorded  f o r 230KV l i n e s now i n e x i s t e n c e .  fields I n an  a r e a a c c e s s i b l e t o p e d e s t r i a n s o n l y , most codes i n Canada s p e c i f y a l i n e c l e a r a n c e o f 22'0" t o 24'0".  The l i n e h e i g h t s  r e q u i r e d f o r t h e v a l u e s o f Eox i n Table 4.1 can be computed f o r a range of. 230KV cases and compared a g a i n s t t h e accepted values.  The r e s u l t s l i s t e d below a r e o b t a i n e d u s i n g  conductor  s p a c i n g s and s i z e s o f 22'0" t o 32'0" and 606MCM t o 1277MCM respectively. Eox  X  Height  0.800  64.7  31:0"  0.809  66.8  30.8' - 34.8'  1.091  73.1  26.1'  - 29.1'  1.365  59.0  22.4'  - 24.8'  1.383  65.6  22.4'  - 24.8'  1.528  68.3  21.3'  - 23.3'  - 35.0"  35 In c o n s i d e r a t i o n of accepted p r a c t i c e and the number of cases c o v e r e d , the a l l o w a b l e v a l u e of Eox i s t a k e n t o be: Emax = 1.365KV/ft.  at  4'11"  U s i n g t h i s v a l u e i t i s now p o s s i b l e t o compute t h e r e q u i r e d l i n e c l e a r a n c e s f o r systems a t any v o l t a g e l e v e l .  4.23  36  5. DETERMINATION OF MINIMUM CONDUCTOR HEIGHTS FOR AC AND DC SYSTEMS 5.1 Method o f Approach I t was p o i n t e d out i n Chapter 3 t h a t the e l e c t r i c i s a f f e c t e d by system v o l t a g e , conductor separation.  field  s i z e , h e i g h t and  A g e n e r a l e x p r e s s i o n can. be w r i t t e n f o r t h e  e l e c t r i c f i e l d as: n  .  E =Y^_ i=l The  q P(Hi,Xi,di)  '  ±  charge, as determined  5  .  1  from 2.8 can be w r i t t e n a s :  ri q  ±  = ^T^ G ( H i , D i , d i ) V i  5-2  i=l S u b s t i t u t i n g 5.2 i n t o 5.1: n ' E ^)  V i F ( H i , X i , d i ) G(Hi,Di,di)  5.3  i=l where Xi=Di+x.  A t any v o l t a g e l e v e l V i i s known. I f E  i s f i x e d a t 1.365KV/ft. i t i s then p o s s i b l e t o use e q u a t i o n 5-3 t o s o l v e f o r any one parameter h o l d i n g t h e o t h e r two f i x e d by an i t e r a t i v e t e c h n i q u e .  Since height i s d e s i r e d  i t must be s o l v e d f o r any c o m b i n a t i o n  of conductor  or s i z e t h a t may occur f o r any v o l t a g e l e v e l .  spacing  -^t s h o u l d  be p o i n t e d out t h a t t h e i t e r a t i v e process l e n d s i t s e l f q u i t e r e a d i l y t o use of a d i g i t a l computer.  The r e s u l t s  listed  below were o b t a i n e d u s i n g an IBM 7044 computer w i t h an  IBFTC C o m p i l e r i n F o r t r a n IV  language.  5.2 AC Cases In o r d e r t o make the r e s u l t s o b t a i n e d as u s e f u l and as g e n e r a l as. p o s s i b l e a s u r v e y of e x i s t i n g EHV  systems  was undertaken.  conductor  A number of phase s p a c i n g s and  s i z e s are p o s s i b l e f o r any one v o l t a g e l e v e l .  The  results  o b t a i n e d below cover most p o s s i b l e combinations t h a t are i n e x i s t e n c e today.  The range-  :  of v a l u e s used is. shown i n  Table 5.1.  ••• Table 5.1  ">-'.  :  ' ".•  :;  Data Summary f o r ac Systems  Voltage KV  Spacing Ft •  Conductor MCM  Bundle Spacing  GMR Ft.  -230  22 - 32  605 -  1 .  -  -  5345  22 - 34  1351- 2355  1  -  -  345  22 - 36  795 Min. 1277 Max.  2 2  12" 18"  0.215 0.290  500  32 - 42  . 2800-3120  1  -  500  ' 26 - 42  1780-2493  2  18"  0.3-0.4  500  38 - 54  520 - 795  4  18"  0.5-0.7  735  44 - 60  795 Min. 1277 Max.  4 4  18" 20"  0.7 0.9  The curves of F i g u r e s constraint and  Conductors Per Phase  1034  5.1 to 5.7  a l l meet the r e q u i r e d  on Emax .s p e c i f i e d by e q u a t i o n  r a d i i indicated  The  -  4-23 f o r  the s p a c i n g s  r a d i i a p p e a r i n g on the curves  cover the most common conductor s i z e s i n use today f o r the system i n d i c a t e d and are expressed i n f e e t .  Any v a l u e of  Rj= 0-055 ~ , = 0-050 R = 0'045 Rj=0-040 2  20  24 SPACING  28 IN  FEET  32  F i g u r e 5.1 230KV ac Cases - 1  36 Conductor Bundle  R = 0-075 4  R =0-070 3  V? -0-065 2  ' Rj= 0-055 s  26 SPACING F i g u r e 5.2  30 IN FEET  345KV a:c Cases - 1  Conductor Bundle  42  SPACING P i g u r e 5.3  4Q\ 30  1  IN  FEE  345KV a c c a s e s - 2 c o n d u c t o r  —i  1—i—;  bundle  —i  34 38 42 46 SPACING • IN FEET P i g u r e 5.4 500KV a c c a s e s - 1 c o n d u c t o r b u n d l e  R = 0. 40 3  R = 0-35 2  ,0-30  30 SPACING  34 IN  FEET  F i g u r e 5-5 .500KV ac Cases - 2  38  42  Conductor Bundl  R = 0>7 3  42 SPACING  46 IN FEET  F i g u r e 5.6 500KV a:c Cases - 4  50  54  Conductor Bundle  r a d i u s n o t i n d i c a t e d d i r e c t l y i s o b t a i n a b l e through i n t e r polation with negligible error.  As an example o f this., c o n s i d e r  the use o f a 1024MCM-24/13 s t r a n d ACSR c a b l e w i t h an O.D. of 1.165  i n c h e s , on t h e 230KV system a t 3 0 ' 0 " s p a c i n g .  By  i n t e r p o l a t i o n t h e expected h e i g h t of t h i s l i n e would be 24 f e e t . feet.  A c t u a l c a l c u l a t i o n s p e c i f i e s - a h e i g h t of 24.1  The e r r o r i s l e s s than 0.5%. The  curves c o n t a i n e d i n P i g u r e 5.7 a r e based on estimated  v a l u e s t h a t may be used a t t h i s l e v e l .  To d a t e . o n l y one  system i n t h e w o r l d i s o p e r a t i n g at t h i s v o l t a g e l e v e l , however, t h e p r i n c i p l e - of bundle conductors  will  continue  to be employed a t t h i s v o l t a g e l e v e l and a t any immediate higher l e v e l s .  Bundle s p a c i n g and conductor  s i z e i s expected,  to i n c r e a s e i f a l t e r e d a t a l l .  7  ;  I  ,  44 Figure  5.7  J  1  48 52 SPACING IN FEET 735KV a;c Cases - 4  _!  56  1  60  Conductor Bundle-  The  conductor  c l e a r a n c e s d e r i v e d above are based on  a v o l t a g e c o n s i d e r a t i o n and are completely independent •mechanical  requirements.  The v a l u e s i n F i g u r e s  5.1 t o 5.7 are i n excess of any mechanical s p e c i f i e d t o date. on mechanical  of  clearance as  Since e x i s t i n g codes are based  primarily  c l e a r a n c e s t h i s would seem i n c o r r e c t i n view  of i n d u c t i o n e f f e c t s .  Table 5.2 l i s t s the h e i g h t s r e q u i r e d at  present by the C.S.A. and N.E.S.C. e l e c t r i c a l codes f o r each voltage l e v e l , above.  i n a d d i t i o n t o the range of values d e r i v e d  Land a c c e s s i b l e to p e d e s t r i a n s i n d i c a t e s the minimum  r e q u i r e d clearance while l a n d a c c e s s i b l e to v e h i c l e s the maximum clearance r e q u i r e d . compared. all  indicates  Only present standards are  The v o l t a g e s l i s t e d below are l i n e - t o - l i n e and  c l e a r a n c e s are i n f e e t . Table 5.2  Voltage KV  Comparison of Line<-to-Ground Clearances  Conductors Per Phase  Minimum Clearance to Ground Derived C.S.A. N.E.S.C.  230  1  22.4-24.8  21.7-27.7  29.0-34.0  345  1 2  29.4-34.4 33-8-40.0  22.3-28.3  33-8-38.8  500  1 2 4  41.5-46.0 45.4-52.9 54.0-61.1  23.0-29.0  40.4-45.4  735  4  73.8-81.9  24.0-30.00  50.0-55.0  The v a l u e s of acceptable clearance as s t a t e d by C.S.A. are extremely low i n comparison with the d e r i v e d v a l u e s . L i n e s being b u i l t at present u s i n g these values can be  43  termed hazardous i n view of p u b l i c s a f e t y . P i g u r e 1.1  As shown i n  these v a l u e s are b e i n g upgraded t o  correspond  more t o i n d u s t r i e s view of h i g h e r c l e a r a n c e s .  However, the  p r e s e n t proposed r e v i s i o n s do not appear to be  sufficient  when compared .with the d e r i v e d v a l u e s .  other  hand., the p r e s e n t N.E.S.C. standards for  On the  appear t o be adequate  most l i n e s up t o 500KV" and 2 conductor bundles.  t h i s v o l t a g e l e v e l and f o r 4 conductor bundles the appear low.-  Above values  The p r o p o s a l t o reduce these v a l u e s seems  u n d e s i r a b l e and w i l l o n l y i n c r e a s e the i n d u c t i o n hazards t o the p u b l i c . In both cases the need t o s p e c i f y c l e a r a n c e s based on a c c e s s i b i l i t y seems i r r e l e v a n t i n view of the d e r i v e d h e i g h t s . .Since most l a n d i n and around t r a n s m i s s i o n l i n e s w i l l e v e n t u a l l y become a c c e s s i b l e t o vehicle1T the".present -  system of  d e f i n i t i o n i s o n l y : r e l a t i v e and hence meaningless..  It is  t h e r e f o r e recommended t h a t l i n e c l e a r a n c e s be d e r i v e d from e l e c t r i c a l c o n s i d e r a t i o n s , as was  done i n t h i s t h e s i s .  In  view of the c l e a r a n c e s s p e c i f i e d above i t i s suggested t h a t these h e i g h t s be accepted 5.3  as a guide f o r f u t u r e d e s i g n s .  DC Cases Use  o f . h i g h v o l t a g e dc t r a n s m i s s i o n has had. o n l y l i m i t e d  a p p l i c a t i o n i n . N o r t h America.  Because of t h i s f a c t > o n l y  few l i n e s have been b u i l t or proposed t o d a t e . survey as was  a  A broad  c a r r i e d out f o r the ac cases i s d i f f i c u l t .  As  such,some of the parameter ranges used are based on e x i s t i n g '  dc t e s t c o n f i g u r a t i o n s  and the author's own judgement  as t o p o s s i b l e v a l u e s t h a t may be used.  Only double  pole  l i n e s weie c o n s i d e r e d i n t h i s t h e s i s as most s i n g l e p o l e l i n e s a r e used f o r c r o s s i n g l a r g e b o d i e s of water.  As  such, the s h o r t distance-..: they a r e above ground i s n e g l i g i b l e . The parameter ranges f o r double p o l e systems a r e l i s t e d below i n Table 5.3' Table 5.3  Data Summary f o r dc Systems  Voltage KV  Spacing Ft.  . Conductor MCM  Conductors P e r Phase  Bundle Spacing  345  30 - 46  345  GMR Ft.  1780-2300  1  -  30 - 46  2156 M i n . 2574 Max.  2 2  16" 18"  500  40 - 56  2300 M i n . 3120 Max.  2 2  16" 18"  O.'l:, 0.3  500 .  40-56  954-1780  4  18"  0.3-0.7  0.2 '0.3  U s i n g t h e t e c h n i q u e l i s t e d i n s e c t i o n 5.1 r e s u l t s f o r t h e dc cases a r e o b t a i n e d and shown i n F i g u r e s 5.8 t o 5.11.  Only  two v o l t a g e l e v e l s were c o n s i d e r e d as most cases a t p r e s e n t are e i t h e r o p e r a t i n g a t these l e v e l s o r w i t h i n 10$ o f these values. Comparison o f ac systems w i t h dc systems a t any v o l t a g e l e v e l shows t h a t t h e l a t t e r r e q u i r e s as much as 15$ l e s s c l e a r a n c e . ' T h i s i s another f a c t o r i n f a v o u r of u s i n g dc a t h i g h e r v o l t a g e l e v e l s and i t a l s o p o i n t s out the p o s s i b l e e r r o r i n a p p l y i n g ac c l e a r a n c e s t o dc l i n e s as i s now t h e case.  R =0-08 4  R = 0-07 3  R = 0-06 2  R^O-05  30  34 SPACIN6  38 IN  FEET  42  F i g u r e 5.8 345KV dc Gases - 1 ' Conductor Bundle  R = 0>30 3  34 SPACING  38 42 IN FEET  F i g u r e 5.9 345KV dc Cases - 2  Conductor Bundle  40  44 SPACING  48 IN FEET  F i g u r e 5.10 500KV dc Cases - 2  40  44 SPACING  46 IN  52  56  Conductor Bundle  52  56  FEET  F i g u r e 5.11 500KV dc Cases - 4 Conductor Bundle  47 6. SHIELDING EFFECTS OF GROUND WIRES BENEATH THE LINE CONDUCTORS " 6.1 S h i e l d i n g E f f e c t s o f Ground Wires I t i s suggested may be reduced conductors.  t h a t t h e e l e c t r i c f i e l d a t ground l e v e l  b y - p l a c i n g ground w i r e s underneath the l i n e  I f the f i e l d  intensity  i s reduced by a s i g n i f i c a n t  amount i t might r e s u l t i n a r e d u c t i o n i n t h e h e i g h t s as d e r i v e d i n Chapter  5.  T h i s c o u l d r e s u l t i n l a r g e economic s a v i n g s i f  the r e d u c t i o n i n h e i g h t i s s i g n i f i c a n t .  Alternatively, i f  s h i e l d i n g i s employed a t t h e same h e i g h t , i n d u c t i o n hazards might be reduced. In o r d e r . t o speed a n a l y s i s o f t h e e f f e c t o f ground w i r e s on t h e f i e l d , a t e s t case was computed w i t h 1,2,3 and 5 ground w i r e s p l a c e d beneath t h e l i n e .  The t e s t l i n e was assumed t o  have a 50'0" s p a c i n g , a 40'0" h e i g h t and an e f f e c t i v e r a d i u s of 0.3 f e e t . voltage.  The r e s u l t s a r e n o r m a l i z e d w i t h r e s p e c t t o  A survey o f e x i s t i n g systems i n d i c a t e s t h a t t h e  minimum l i n e t o s t r u c t u r e c l e a r a n c e a t any v o l t a g e l e v e l i s 7'0".  Thus t h e ground -wires cannot l i e c l o s e r than t h i s  tance  t o a l i n e conductor.  dis-  A l s o , because of mechanical  c o n s i d e r a t i o n s t h e minimum h e i g h t o f ground w i r e s was taken as 20'0".  To l o c a t e t h e optimum p o s i t i o n of t h e ground w i r e s  t h e i r s p a c i n g was v a r i e d from D/4 t o 5D/4 w h i l e t h e i r h e i g h t was v a r i e d from 20'0" t o 33'0" a t each s p a c i n g  increment.  The f o l l o w i n g p o i n t s were noted: l ) The maximum v a r i a t i o n i n Emax/V was l e s s than 4% for  t h e range o f h e i g h t s t r i e d a t each s p a c i n g and f o r each  case.  T h i s would teid t o i n d i c a t e t h a t t h e ground w i r e s a r e  independent o f h e i g h t above ground f o r t h e r e g i o n t r i e d . 2)  The s h i e l d i n g e f f e c t o f t h e ground w i r e s was reduced  as they were moved h o r i z o n t a l l y c l o s e r t o t h e c e n t e r of t h e configuration.  The optimum p o s i t i o n w i t h r e s p e c t t o s p a c i n g  o c c u r r e d i n a l l cases when .the ground w i r e s were d i r e c t l y below t h e l i n e  conductors.  3) The e l e c t r i c f i e l d p r o f i l e s a r e a l t e r e d n e g l i g i b l y over t h e range o f p o s i t i o n s The p e r cent decrease  tried. i n Emax/V a t ground l e v e l w i t h  the ground w i r e s ' i n t h e i r optimum p o s i t i o n f o r 1 t o 5 ground w i r e s i s shown i n F i g u r e 6.1.  30  > g  OF  Uj  20  Uj (o Uj  Cfc o Uj  10  0 0  1  2 NUMBER  F i g u r e 6.1  OF  3 GROUND  4 WIRES  5  P e r Cent Decrease i n Emax/V U s i n g 1 t o 5 Ground Wires i n T h e i r Optimum"'Position  49  The d e c r e a s e i n Emax o b t a i n e d u s i n g g r o u n d w i r e s s h o u l d be investigated with respect height.  However, b e f o r e  be n o t e d t h a t  to the effect i n reducing  line  s u c h a n a t t e m p t i s made i t s h o u l d  t h e e f f e c t o f a s i n g l e ground w i r e i s almost  n e g l i g i b l e . , w h i l e u s i n g 5 • i s i m p r a c t i c a l because o f expense. I t would appear t h a t t h e use o f 3 ground w i r e s i n t h e i r p o s i t i o n i s worth consideration.  optimum  O n l y a c c a s e s w i l l be  investigated. 6.2  Reduction The c u r v e s  i n Line  Heights  shown i n . F i g u r e 6.2 t o 6.7 a r e o b t a i n e d b y  meeting the required allowable ; value  on Emax g i v e n i n  s e c t i o n 4.7 w i t h 3 g r o u n d w i r e s p r e s e n t configuration.  as p a r t o f t h e l i n e  A d i r e c t comparison of the heights  f o r i d e n t i c a l c a s e s w i t h and w i t h o u t  derived  g r o u n d w i r e s , b a s e d on  t h e p a r a m e t e r r a n g e s o f T a b l e 5.1, i s shown i n T a b l e 6.1 where a l l d i m e n s i o n s a r e i n f e e t . T a b l e 6.1 L i n e - t o - G r o u n d C l e a r a n c e s Voltage KV  !  w i t h and w i t h o u t  Ground W i r e s  Conductors C l e a r . T o Height Minus Height w i t h P e r Cent P e r Phase S t r u c t u r e Shielding S h i e l d i n g Decrease  345-  1 2  9  500  1 2 4  •11  735  4  18  -. 24.1-27.5 28.6-32.9  18-20 15-18  41 -.5-46.0' . 45.4-52.9 ' 54.0-61.1  34.6-37.9 39.0-44.9 45.5-51.4  17-17' 14-16 16-16  73.8-81.9  63.1.-70.2  14-14  29.4-34.4 33.8-40.0  Since. the l i n e t o s t r u c t u r e c l e a r a n c e  i s of- t h e o r d e r  o f 9'0" f o r 345KV s y s t e m s i t w o u l d seem h i g h l y u n l i k e l y  that  24' 22  26 30 34 38 SPACING IN FEET F i g u r e 6.2 345KV ac cases w i t h s h i e l d i n g 1 conductor bundle  51  34 i 30  1  34 SPACING  F i g u r e 6.4  1  38 IN  i  FEET  42  '  i  46  500KV ac cases w i t h . s h i e l d i n g " 1 conductor bundle  R = 0-70 3  R =0>60 2  R =0-50 f  42 SPACING  46 IN  FEET  50  P i g u r e 6.6 500KV ac. cases w i t h 4 conductor bundle  54 shielding  R = 0-90 3  R =0-80 2  -.0-70  48 52 56 SPACING IN FEET P i g u r e 6.7 • 735-KV 'ac cases w i t h 4 conductor bundle  60 shielding  ground w i r e s would be used a t t h i s v o l t a g e l e v e l because of the r e q u i r e d m e c h a n i c a l  clearances.  However, at a l l  h i g h e r v o l t a g e l e v e l s i t would appear t h a t a u s e f u l r e d u c t i o n i n l i n e h e i g h t can be a c h i e v e d through the use of 3 ground w i r e s p l a c e d below the l i n e c o n d u c t o r s .  This r e d u c t i o n  i n h e i g h t on the average i s i n the o r d e r of 17%.  Since  conductor v i b r a t i o n problems i n c r e a s e w i t h tower h e i g h t i t i s d e s i r a b l e t o keep the l i n e s as c l o s e t o the ground as possible. w i r e s may  In view of t h i s the s a v i n g s i n h e i g h t u s i n g ground prove u s e f u l .  The s a v i n g s i n tower c o s t s v e r s u s the i n s t a l l a t i o n c o s t of the ground w i r e s would, of c o u r s e , be the d e c i d i n g f a c t o r i n i n c o r p o r a t i n g t h i s technique.  I n any case, i t i s f e l t  t h a t t h i s s h i e l d i n g technique c o u l d s t i l l be a p p l i e d i n popu l o u s areas t o reduce e l e c t r o s t a t i c i n d u c t i o n e f f e c t s where t h i s i s important.  I t i s noted t h a t use of 3 ground w i r e s  below the l i n e conductors reduces i m a t e l y .; 30%.  the e l e c t r i c f i e l d by approx-  T h i s means t h a t i n d u c t i o n e f f e c t s would  a l s o be d i r e c t l y reduced  by a s i m i l a r amount.  •factor cannot be o v e r l o o k e d .  Such a s a f e t y  I n c o r p o r a t i o n of t h i s i d e a  might a l l o w g r e a t e r u t i l i z a t i o n of a r e a laying i n the r i g h t of-way of the t r a n s m i s s i o n l i n e s .  7. MEASUREMENT OP THE TRANSMISSION LINE  POTENTIAL OP AN OBJECT BELOW A  7.1 Method of Measurement In t h i s c h a p t e r a method to-measure t h e p o t e n t i a l below a transmission l i n e i s presented.  U s i n g t h i s method e x p e r i -  mental r e s u l t s a r e o b t a i n e d f o r s e v e r a l l i n e s and compared a g a i n s t t h e t h e o r e t i c a l v a l u e s p r e d i c t e d by t h e equations o f Chapter 2.  I n a d d i t i o n , r e a d i n g s a r e taken t o v e r i f y the e f f e c  of bundle conductors  and sky w i r e s .  In F i g u r e 7.1 t h e p o t e n t i a l induced  i n an o b j e c t l o c a t e d  a t t h e p o i n t P(x,y) due t o any one l i n e can be w r i t t e n a s : V C.  10  V(x,y) •  (C  V. og  7.1  + C. ^  10/  where C. : the l i n e t o o b j e c t 10  capacitance  C g= t h e o b j e c t t o ground c a p a c i t a n c e Q  V =V/-120 f  Insulated Object  *9  '3g  Metering • Circuit  F i g u r e 7.1  Coupling Capacitances  between t h e L i n e and  55  The c h a r g i n g c u r r e n t f l o w i n g through C\  t o the o b j e c t can  q  be w r i t t e n as: V. w C  C. Og  I =  ,C.  7.2  10  +-c  og I f a measurement of V(x,y) i s t a k e n t h i s i s analogous *  10  c l o s i n g s w i t c h S^ through a m e t e r i n g c i r c u i t .  In t h i s  V. co C. ( l + jcoRC \ 1.'. io\ og)  to  case:  J  1 + jcoR(c. 0  + C  io  v  os'  7.3  )  and V(x,y)  V. co C.  R 10  1  7.4  1 + iioRfc. + C \ io J  E q u a t i o n 7.4  \  ogl  i n d i c a t e s t h a t the p o t e n t i a l at P w i l l be g r e a t l y  a f f e c t e d by the r e s i s t a n c e of the m e t e r i n g c i r c u i t .  Since  C. and C - are of the o r d e r of a few p i c o f a r a d s , R would have t o io og 12 approach  10  ohms or b e t t e r i n o r d e r t h a t V(x,y) i s i n d e p -  endent of the c i r c u i t . 7.1.  In t h i s case e q u a t i o n 7.4  A l t h o u g h the v a l u e of  and C^  Q  reduces  to  w i l l d i f f e r f o r each  l i n e , the e f f e c t of the m e t e r i n g c i r c u i t i s the same i n each case.  An i n d i r e c t .method has been d e v i s e d t o measure V(x,y)•  s i n c e a h i g h impedance meter capable of r e a d i n g up t o 20KV was not r e a d i l y o b t a i n a b l e . I f the o b j e c t i s grounded^'then the net charge .on i t w i l l g i v e r i s e t o a secondary  field.  appearing  The p o t e n t i a l at  the s u r f a c e of the o b j e c t due f i e l d must be z e r o .  t o the l i n e and t h i s secondary  By c h o o s i n g  the o b j e c t to be a sphere  whose r a d i u s i s 'a', i t i s p o s s i b l e t o w r i t e :  • V(x,y)  °- f + i _ \ 4rt£ la 2x 1  , 0  '  7.5  Q  or upon r e a r r a n g i n g : V(x,y) 4Jt£ CL' = 1 _ -;-+  a  1  2x  I n the case of an ac system the c u r r e n t f l o w i n g t o the sphere to m a i n t a i n i t at z e r o p o t e n t i a l would  be:  V ( x , y ) 4rcoo£  I =  .  i  a  +  _°  7.6  i  2x  The v a l u e of I w i l l be of the o r d e r of microamperes f o r V(x,y) of the order of KV.  Therefore,  by c o n n e c t i n g a microammeter  i n s e r i e s between the sphere and ground t h i s c h a r g i n g can be measured..  S i n c e to, x, a and  can be computed and i s important  £  q  current  are known then V(x,y)  compared a g a i n s t the expected v a l u e .  t h a t the spheres dimensions s h o u l d be  small  w i t h respect, t o the d i s t a n c e of the- sphere from the source so t h a t the d i s t o r t i o n i t i n t r o d u c e s w i l l not e f f e c t source. -  the  It  7.2 Instrument Design An i n s t rurn en t i s r e q u i r e d t o read t h e c h a r g i n g t h a t f l o w s through t h e probe t o t h e ground.  current  An ac micr'o-  -.-ammeter w i t h a c a p a b i l i t y of r e a d i n g 1.0 t o 20uA would be d e s i r a b l e but such movements a r e extremely  expensive and  were n o t r e a d i l y a v a i l a b l e . I n s t e a d an o p e r a t i o n a l a m p l i f i e r was used t o a l l o w measurements i n a range more s u i t e d t o a l r e a d y  existing  — m e t e r s . --Because-it-was-necessary t o measure t h e c h a r g i n g c u r r e n t under a c t u a l l i n e s , t h e i n s t r u m e n t p o r t a b l e , f l e x i b l e and b a t t e r y  designed  had t o be  operated.  A schematic o f the c i r c u i t i s shown i n F i g u r e 7.2. The i n p u t r e s i s t a n c e v a r i e s from 200 ohms i n t h e 50K range t o 1 i n t h e 10 megohms range.  Some o f t h e d e s i g n  features  of t h e i n s t r u m e n t a r e : 1) I t has a f u l l s c a l e d e f l e c t i o n o f 0.1 t o 20uA by u s i n g the proper s c a l e s e t t i n g . ..2) I t can be b i a s e d t o compensate f o r c u r r e n t  offset  i n the operational a m p l i f i e r . 3) I t uses mercury c e l l b a t t e r i e s f o r l o n g e r l i f e and stable  output.  4) An i n e x p e n s i v e p a n e l type ac v o l t m e t e r w i t h a 0-1V f u l l - s c a l e I s used as an i n d i c a t o r . . The i n s t r u m e n t i n F i g u r e 7.3.  was c a l i b r a t e d u s i n g t h e set-up  shown  The r e s u l t s o f t h e t e s t s a r e shown i n  5-WAY  SWITCH  F i g u r e 7.2. Schematic Diagram Of UBC Ins'truinerit :  WMg  59  F i g u r e 7.3. ''Last Arrangement 'To .Calibrate Meters  20r  fl!  0 UBC  .  .  2-5  5-0  INSTRUMENT-  —  10  :  —  __  ,  7-5  u_  10-0  SCALE  i  1  i  i  i  0  5.  10  15  20  UBC  INSTRUMENT-20  SCALE  AND  MILLER  F i g u r e 7.4. C a l i b r a t i o n Curves'  METER  60 Figure 7.4 "X second method f o r r e a d i n g 'the'charging c u r r e n t (21) proposed by M i l l e r  was  i n the d e s i g n of h i s g r a d i e n t meter,  "This i n v o l v e d r e c t i f y i n g the ac s i g n a l by means of a diode b r i d g e and u s i n g . a 0-15uA f u l l s c a l e dc mlcroammeter. M i l l e r meter was  a l s o b u i l t and was  ment shown i n F i g u r e 7 . 3 shown i n F i g u r e 7 . 4 .  t e s t e d u s i n g the  The arrange-  The r e s u l t s of these t e s t s are  I t s h o u l d be noted t h a t the  Miller  -meter- -accurately- measures-charging -current- but - h i s — t e c h n i q u e of r e a d i n g the v o l t a g e g r a d i e n t under t r a n s m i s s i o n l i n e s i s incorrect.  A d i s c u s s i o n of t h i s t e c h n i q u e and  meter i s p r e s e n t e d  the-gradient  i n Appendix I .  7 . 3 C a l c u l a t e d Values vs E x p e r i m e n t a l  Values  A measure of the induced p o t e n t i a l was made by r e a d i n g the c h a r g i n g c u r r e n t through a grounded l'O" diameter sphere.  The p o s i t i o n of the sphere was  aluminum  moved h o r i z o n t a l l y  from y=-2.5D t o y=+2.5D i n 10 f o o t increments  from the  centre  — o f the c o n f i g u r a t i o n , -while v e r t i c a l l y s i t u a t e d a t a f i x e d l e v e l above ground.  Measurements were taken under  two  d i f f e r e n t l i n e s operating at d i f f e r e n t voltage l e v e l s .  The  parameters of these l i n e s are g i v e n below. Voltage -----KV  Spacing Ft.  Height - -Ft.  Conductor MCM  No. Per Phase  235  18  39.3  795  1  360  35  54.0  795  2  Bundle "Spacing  12"  4-000  3-000  MEASURED ^  VALUES  2-000  Ui £  "a.  7-000  •000  J L  0  72-5  '"Figure 7, b .  25 DISTANCE  IN  Test''Results  37 FEET  SO  For o O X v Lj.no  4-000r  CALCULATED  VALUES  3'000Y  $  2-000  o  1-000  •ooo  0  25  50 DISTANCE  IN  75 FEET  100  F i g u r e 7.6.. Test R e s u l t s F o r 360KV. L i n e  62  A comparison  of the c a l c u l a t e d and measured v a l u e s f o r  ,-each.-of--these l i n e s i s shown i n F i g u r e 7.5  and 7.6.  measured v a l u e s are an average of the M i l l e r and Instrument  readings.  The  UBC  The r e s u l t i n g d i s c r e p a n c i e s were  l e s s than 5$ in. most .-cases.  The r e a d i n g s were h i g h e r than  expected f o r the 230KV case and lower than expected f o r the 360KV case. - - unbalance  These e f f e c t s c o u l d r e s u l t i f a s l i g h t v o l t a g e occurred', between the c o n d u c t o r s .  The good agreement  between c a l c u l a t e d v a l u e s and measured v a l u e s v e r i f i e s the v a l i d i t y of the e q u a t i o n s i n Chapter 2.  The induced  a t any l e v e l can be found by employing the t e c h n i q u e  potential outlined  above and u s i n g e i t h e r the M i l l e r meter or the UBC  instrument.  7.4  Wires  E x p e r i m e n t a l V e r i f i c a t i o n of the E f f e c t of Sky I t ""was'" p o i n t e d out i n s e c t i o n 3.6  t h a t the presence  of  sky w i r e s above the l i n e conductors has v i r t u a l l y no effect, on the e l e c t r i c f i e l d and hence the p o t e n t i a l below the l i n e . As a check o n . t h i s , an a c t u a l 360KV l i n e was the c o n f i g u r a t i o n shown i n F i g u r e  selected having  7-7.  © o  o  61  AIR EARTH  F i g u r e 7.7.  360KV Test L i n e For Sky Wire E f f e c t  63 U s i n g t h e t e c h n i q u e p r e s e n t e d above,a measure o f the induced p o t e n t i a l - a t t h e 4'0" l e v e l was made.  A comparison  of the  measurec v a l u e s and those t h a t would be expected i f no sky1  w i r e s wer? p r e s e n t i s shown i n Table 7.1.  Table 7.1  Measurement o f Sky Wire E f f e c t  Feet  Miller Meter KV  UBC Instrument KV '  Computed Values KV  0  1.043  1.051  0.960  +9.0  10  1.295  1.320  1.204  +8.6  20  1.766  1.733  1.705  +2.6  30  2.153  2.136  2.175  -1.4  40  2.447  2.405  2.451  -1.0  50  2.473  2.462 •  2.487  -0.8  60  2.220  2.187  2.329  -5.4  70  2.018  1.985  2.063  -3-1  80  1.749  1.733  1.765  -1.4  90  1.413  1.413  1.481  -4.6  Average Error In P e r Cent  The d i f f e r e n c e on the average was w i t h i n 4$,which i s w i t h i n experimental error.  I t i s thus j u s t i f i a b l e t o i g n o r e the e f f e c t  of sky w i r e s . 7.5 E x p e r i m e n t a l V e r i f i c a t i o n o f t h e E f f e c t s of Bundle  Conductors  I n s e c t i o n 3-5 i t was p o i n t e d out t h a t u s i n g bundle  conductors i n p l a c e o f s i n g l e conductors g r e a t l y i n c r e a s e s •4;he -fi-?ld- i n t e n s i t y and hence the p o t e n t i a l near t h e e a r t h ' s surface.  As a check on t h i s an e x i s t i n g 230KV" l i n e was s e l e c t e d  t h a t used a bundle conductor c o n f i g u r a t i o n a l o n g one p o r t i o n of i t s l e n g t h and a l a r g e s i n g l e ccnductor. a l o n g the  remainder.  .The c o n f i g u r a t i o n s of the l i n e are shown i n F i g u r e 7.8  EARTH  - F i g u r e 7.8  EARTH  ._230KV -Test-Line For Bundle-Conductor  A comparison  Effect  i s made i n Table 7.2 between the p o t e n t i a l - measure-,  ments o b t a i n e d a t X = 4'0" and the v a l u e s expected u s i n g t h e • bundle c o n f i g u r a t i o n as w e l l as- the s i n g l e conductor. d i r e c t comparison  by measuring  p o t e n t i a l v a l u e s f o r the  and s i n g l e conductors was n o t p o s s i b l e . )  (A. bundle  The r e a d i n g s i n Table  7.2 a r e an average o f the M i l l e r meter and the UBC i n s t r u m e n t "measurement's;  The" measufed""values a r e ' i n good agreement w i t h  -the v a l u e s expected f o r -the bundle conductor case.  The  d i f f e r e n c e between the expected bundle v a l u e s and t h e expected s i n g l e c c n d u c t o r v a l u e s i s much l a r g e r than p o s s i b l e e x p e r i m e n t a l error.  T h e r e f o r e , the r e a d i n g s can be assumed t o r e p r e s e n t t h e  bundle conductor v a l u e s .  As such the a n t i c i p a t e d e f f e c t o f  'bundle conductors v e r s u s s i n g l e conductors i s t r u e .  65  -—Table 7.2~ Measurement "of"Bundle"Conductor E f f e c t Eeet  Measured. KV  Computed P o t e n t i a l i n KV Bundle Single  P e r Cent E r r o r For Bundle  0  1.396  1.453  1.068  -4.0  10  1.539  1.503  1.111  +2.4  20  1.875  1.739  1.293  +8.1  30  2.355  2.144  1.591  +9.8  "40  "2.759  2.488  ~1.839  +10.9  50  2.800  2.593  1.912  +8.0  60  2.559  2.449  1.802  +4.4 "  70  -2.321  2.153  1.'583  +1.8  80  1.825  1.810  1.330  +0.8  90  1.551  1.486  1.091  +4.5  100  1.195  1.207  0.886  -1.4  8. ESTABLISHMENT OP THE WIDTH OF RIGHT-OF-WAYS 8.1  Right-of-Way  Clearances  The r i g h t - o f - w a y o f a t r a n s m i s s i o n l i n e i s t h a t s t r i p of l a n d t h e l i n e occupies and t h e c l e a r i n g t o e i t h e r s i d e o f the l i n e .  A t p r e s e n t t h e w i d t h of t h e r i g h t - o f - w a y i s d e t e r - . .  mined m o s t l y hy mechanical  requirements.  S i n c e , i n most  cases  a l i n e must c r o s s f o r e s t e d l a n d t h e ' w i d t h of t h e r i g h t - o f way  i s u s u a l l y f i x e d t o a l l o w ample room f o r c o n s t r u c t i o n ,  s a f e t y from f a l l i n g t r e e s , and p r o t e c t i o n i n case of f i r e . In d e n s e l y p o p u l a t e d  a r e a s , l a n d i s a t a premium and e x c e s s i v e  right-of-way widths i s undesirable.  The u t i l i t i e s a r e a t  p r e s e n t r e l u c t a n t t o reduce l a r g e r i g h t - o f - w a y w i d t h s because . of p o s s i b l e i n d u c t i o n e f f e c t s t h a t would prove hazardous t o public.  I t i s d e s i r a b l e t h e r e f o r e t o t r y and s p e c i f y t h i s  width i n r e l a t i o n t o induction e f f e c t s . 8.2 Width Requirement Based on E l e c t r o s t a t i c I n d u c t i o n E f f e c t s Danger from e l e c t r o s t a t i c i n d u c t i o n r e s u l t s o n l y when the i n s u l a t e d  o b j e c t i s grounded and c u r r e n t f l o w s .  Iti s  .  (38)  accepted  that the threshold of perception  occurs a t 1  m i l l i a m p e r e and t h a t c u r r e n t s up t o 9 m i l l i a m p e r e s f o r men and 6 m i l l i a m p e r e s f o r women c o n s t i t u t e no hazard a l t h o u g h may  prove e x c e e d i n g l y annoying.  they  A person coming i n c o n t a c t  w i t h an i n s u l a t e d o b j e c t can be viewed e l e c t r i c a l l y as shown i n F i g u r e 7.1. I n t h i s case R can be taken t o be t h e person's resistance.  I t was shown p r e v i o u s l y t h a t t h e v o l t a g e  i n an i n s u l a t e d o b j e c t due t o each l i n e i s :  induced  67  V. C.  V(x,y) =  Tc v  7.1  1 0  1  + c. )  Og  1 0  When S^ i s c l o s e d t h e c u r r e n t f l o w i n g through t h e r e s i s t o r is:  I =  (l 3o)R0 )  Y^C.  o g  +  1+juR ( C .  0+  7.3  C ) Qg  But f o r R s m a l l t h i s reduces t o :  I  V.-wC.  1  1  1  8.1  0  For a grounded o b j e c t t h e c u r r e n t f l o w i n g from ground t o m a i n t a i n i t a t zero p o t e n t i a l can be w r i t t e n a s : toC  V(x,y) og  8.2  I  S u b s t i t u t i n g f o r V(x,y) from 7.1 g i v e s coV.C  Tc  1  og  C. Og  8.3  1 0  + c. ) io'  I f C >> C. then t h e above e x p r e s s i o n reduces t o e q u a t i o n og io r  8.1.  I n t h e case.of an o b j e c t c l o s e t o t h e ground w i t h  r e s p e c t t o i t s d i s t a n c e from t h e l i n e t h e above assumption i s true. I t i s shown i n e q u a t i o n 8.2 t h a t t h e c h a r g i n g c u r r e n t t o ground i s dependent upon t h e o b j e c t s c a p a c i t a n c e the p o t e n t i a l o f t h e p o i n t i n space i t o c c u p i e s . complicated  conducting  t o ground and I n t h e case o f  o b j e c t s t h i s p o t e n t i a l may be c o n s i d e r e d  equal t o t h e v a l u e t h a t would occur a t t h e object's-center o f gravity.  A c c o r d i n g t o t h i s i f a ' S p h e r e i s c o n s i d e r e d a t X=6'0",  i t s p o t e n t i a l w i l l always be V(6,y), independent of i t s r a d i u s .  68 The r a d i u s would t h e n a f f e c t o n l y t h e sphere's c a p a c i t a n c e ~~ahd"Tncreas'es or d e c r e a s e s "the c u r r e n t f l o w t o ground" w i t h an i n c r e a s e or decrease of r a d i u s r e s p e c t i v e l y . U s i n g t h i s approach i t i s p o s s i b l e t o f i n d a t o l e r a b l e V g'  l e v e l of i n d u c e d p o t e n t i a l by s p e c i f y i n g a worst case  Q  From p r e v i o u s s t u d i e s i t i s f e l t t h a t C a t worst might * og r e a c h 5000 p f . ^ ^ I f t h e c u r r e n t i s t o be l i m i t e d i n t h e . r e g i o n from 1 t o 5 m i l l i a m p e r e s t h i s would r e s u l t i n an "acceptable range of V(x,y) of from 0.5 to- -2 .~5KV. - In-vlew of t h e above and. of the reduced p r o b a b i l i t y of flammable o b j e c t s t o i g n i t e as t h e v o l t a g e i s reduced below 1KV i t i s f e l t t h a t a t o l e r a b l e l i m i t on V(x,y) s h o u l d be taken as 1KV. The above c r i t e r i o n can be used t o s p e c i f y t h e w i d t h of a r i g h t - o f - w a y f o r any l i n e o p e r a t i n g a t any v o l t a g e .  If  a v e r t i c a l h e i g h t of r e a c h of 6'0" i s assumed then the w i d t h can be s p e c i f i e d by f i n d i n g t h e h o r i z o n t a l l o c a t i o n from the •center of t h e c o n f i g u r a t i o n a t which the induced p o t e n t i a l i s 1KV.  160  Uj  5: Ql  700  -1  1  :  725  WIDTH  '  750  OF  775  ~ >  200  RIGHT-OF-WAYS  Figure--8.4 500KV Cases-1 Conductor Bundle Right-of-Way Width  20Or  200 WIDTH F i g u r e 8. 5 JiQQXjZJCIaaa^^  OF  RIGHT-OF-WAYS  200  r  46  £0  54=D  J.  40L150  JL  175 WIDTH OF  200 225 RIGHT-OF-WAYS  250  F i g u r e 8.6 500KV Cases-4 Conductor Bundle Right-of-Way Widths  220r  D=  44  48  225 WIDTH  52  OF  V  56~  250 275 RIGHT-OF-WAYS  F i g u r e 8.7 735KV Cases-4 Conductor Bundle Right-of-Way Widths  72  The curves of F i g u r e s - 8 . 1 t o 8.7  i n d i c a t e the r e q u i r e d  w i d t h of the r i g h t - o f - w a y s , as measured from the c e n t e r of the c o n f i g u r a t i o n f o r the s p a c i n g s and l i n e h e i g h t s i n d i c a t e d . At each v o l t a g e l e v e l the maximum e f f e c t i v e r a d i u s as i n Table 5.1 was Mechanical  used. c l e a r a n c e s u s u a l l y r e q u i r e a 150 f o o t c l e a r a n c e  from the c e n t e r of the c o n f i g u r a t i o n . /excess and  presented  This clearance i s i n  of the v a l u e r e q u i r e d f o r most l i n e s o p e r a t i n g a t  345KV.  230  This i n d i c a t e s t h a t i n populous areas once the  l i n e i s c o n s t r u c t e d more l a n d near l i n e s a t v o l t a g e s up t o 345KV c o u l d be u t i l i z e d .  Above t h i s v o l t a g e l e v e l the  r e q u i r e d based on i n d u c t i o n e f f e c t s exceed the requirement.  widths  mechanical  In view of p u b l i c s a f e t y the w i d t h s as d e r i v e d  i n t h i s t h e s i s would appear more d e s i r a b l e . I t s h o u l d be noted t h a t a peak occurs i n each r i g h t o f way  curve.  T h i s p o i n t r e p r e s e n t s the worst case f o r the  c o n f i g u r a t i o n under s t u d y .  Maximum s a f e t y f o r the p u b l i c  r e s u l t s i f these v a l u e s are used f o r a l l l i n e s a t t h a t v o l t a g e and  spacing.  operating  73  APPENDIX I :  DISCUSSION OF THE MILLER GRADIENT METER  A f i e l d i n t e n s i t y , o r g r a d i e n t meter, as i l l u s t r a t e d (29) i n F i g u r e 1.1, was developed for. s t u d i e s by M i l l e r  x  ;  c o n c e r n i n g l i v e l i n e maintenance. UARD ELECTRODE ENTRAL ELECTRODE  METAL  CASE  A  > L_1I TEFLON SPACERS  /  t f ~  I  =  J  D  J  D-^dT  J  1  )MICROAMME TER  HANDLE Cog COAXIAL  CABLE' A  -  A  F i g u r e 1.1. M i l l e r G r a d i e n t Meter The meter c o n s i s t s o f a main c i r c u l a r e l e c t r o d e surrounded by a guard r i n g .to e l i m i n a t e f r i n g i n g .  The main e l e c t r o d e  i s connected t o a microammeter through a s h i e l d e d l e a d and then t o t h e s h i e l d o f t h e c i r c u i t .  The a r e a o f t h e main  e l e c t r o d e i s so dimensioned as' t o a l l o w a f i e l d i n t e n s i t y o f 100 o r 1000 v o l t s / i n . t o d r i v e l u A through t h e c i r c u i t .  74  The g r a d i e n t meter was used t o read t h e e l e c t r i c  flux  'impinging on t h e s u r f a c e of a workman by p l a c i n g t h e probe i n f r o n t o f the a r e a b e i n g i n v e s t i g a t e d .  I n a d d i t i o n , the meter  i t s e l f minus t h e probe was coupled between a lineman and a s u i t a b l e r e f e r e n c e ' p o t e n t i a l t o measure t h e t o t a l c u r r e n t f l o w i n g through t h e man.  induced  I t was a l s o proposed  that  the g r a d i e n t meter c o u l d be used t o measure t h e low i n t e n s i t y f i e l d s t h a t e x i s t a few f e e t above ground under a HV power l i n e . In t h i s case a l a r g e probe was b u i l t and supported on a t r i p o d at  an a r b i t r a r y h e i g h t above ground and t h e t r i p o d was moved  from y=-2D t o y=+2D.  The r e s u l t s o f these a p p l i c a t i o n s a r e (29) (38)  p r e s e n t e d i n M i l l e r ' s papers.  '  w  '  The t e c h n i q u e t o measure e l e c t r i c f i e l d i n t e n s i t y and t o t a l i n d u c e d c u r r e n t o f a workman w h i l e bounded t o a bucket, or w h i l e s t a n d i n g on the tower i s c o r r e c t as l o n g as t h e l i n e man i s a t t h e r e f e r e n c e p o t e n t i a l .  I n t h i s case t h e meter-  measures the e l e c t r i c f i e l d emanating (connected t o t h e l i n e ) or i m p i n g i n g (connected t o t h e ground) due t o t h e n e t charge a p p e a r i n g on t h e workman a t any i n s t a n t . induced c u r r e n t can be measured.  S i m i l a r i l y the t o t a l  I f t h e workman i s i s o l a t e d  i n space no n e t charge would appear and no e l e c t r i c f i e l d would impinge  on h i m . ^ 9 ) j  n  t h i s case no measure can be made of t h e  induced c u r r e n t o r e l e c t r i c  field.  In view of t h i s i t s h o u l d be p o i n t e d out t h a t t h e t e c h n i q u e t o read low i n t e n s i t y f i e l d s under t r a n s m i s s i o n l i n e s w i t h the M i l l e r meter i s i n c o r r e c t .  T h i s can be seen d i r e c t l y from (38) the r e s u l t s p r e s e n t e d i n M i l l e r ' s paper concerning a set  75  of measurements of t h e v o l t a g e g r a d i e n t made under a 345KV . s u b s t a t i o n bus.  These measurements which  are i n K V / i n . ,  are l i s t e d below i n Table 1.1. Table 1.1  M i l l e r Measurements, for 345KV S u b s t a t i o n Bus Feet  M i l l e r Readings at X=6» A t X=0'  Computed V a l u e s A t X=6 At X=0 1  1  0  650  90  102  83  10  650  100 •  117  107  20  950  150  168  152  30  780  110  146  141  40  500  9  0  -  9  8  99  I n s p e c t i o n o f e q u a t i o n 2.3 i n d i c a t e s t h a t , i n t h e r e g i o n near the ground, t h e e l e c t r i c f i e l d  i s n e a r l y constant.  In  the l i n e under study Emax a t t h e s i x f o o t l e v e l was o n l y 9% g r e a t e r than a t ground l e v e l .  The r e s u l t s i n Table 1.1 i n d i c a t e  t h a t Emax a t t h e s i x f o o t l e v e l i s more than s i x times l a r g e r i t s c o r r e s p o n d i n g v a l u e a t ground l e v e l . The above r e a d i n g s a t t h e s i x f o o t l e v e l do n o t r e f l e c t the f i e l d v a l u e s a t t h i s p o i n t but i n s t e a d a r e a measure of the c h a r g i n g c u r r e n t through t h e l i n e - t o - p r o b e c a p a c i t a n c e . As i t was p o i n t e d out p r e v i o u s l y , t h e probe i s o l a t e d i n space has no n e t charge and hence no e l e c t r i c f i e l d i m p i n g i n g on i t s surface.  However, at. any p o i n t i n space, t h e probe i s  c a p a c i t i v e l y coupled t o t h e l i n e and ground as F i g u r e 7.1 illustrates.  I n t h e case near t h e ground, t h e c u r r e n t f l o w i n g  through the meter i s determined  p r i m a r i l y by t h e probe's  c o u p l i n g c a p a c i t a n c e t o t h e l i n e and i s g i v e n by e q u a t i o n 8.1.  than  Even i f t h e probe i s grounded t h e c u r r e n t f l o w i s s t i l l determined  by t h i s c a p a c i t a n c e .  i n c r e a s e d or decreased  As t h e probe's h e i g h t i s  a c o r r e s p o n d i n g i n c r e a s e or decrease  i n c h a r g i n g c u r r e n t w i l l occur s i n c e t h e probe's c o u p l i n g c a p a c i t a n c e t o t h e l i n e i s dependant upon h e i g h t . The above argument can be s u b s t a n t i a t e d from M i l l e r ' s readings.  I t was p o i n t e d out t h a t a s e t o f r e a d i n g s were  t a k e n a t ground l e v e l by l a y i n g t h e probe on t h e ground and v a r y i n g i t from y=-2D t o y=:+2D.  I n t h i s case t h e probe i s  at a r e f e r e n c e p o t e n t i a l and i s n o t c a p a c i t i v e l y coupled t o the ground.  T h e r e f o r e , an a c c u r a t e measure of t h e e l e c t r i c  f i e l d i s expected.  The r e a d i n g s o b t a i n e d a t ground l e v e l a r e  i n good agreement w i t h t h e c o r r e s p o n d i n g c a l c u l a t e d v a l u e s as shown i n Table I.1-. would decrease  The ground c a p a c i t a n c e of t h e probe  s i g n i f i c a n t l y at the s i x foot l e v e l .  case r e a d i n g s a r e expected at ground.  In this  t h a t a r e p r o p o r t i n a t e l y h i g h e r than  T h i s i s indeed t h e case f o r t h e r e a d i n g s a t the  six. f o o t l e v e l , as shown i n Table I . I . .  I t can be concluded  t h a t t h e M i l l e r probe can be used t o measure t h e e l e c t r i c  field  or induced c u r r e n t i n o b j e c t s t h a t a r e l o c a t e d a t the r e f e r e n c e p o t e n t i a l and form p a r t o f t h e r e f e r e n c e boundary. the probe cannot be used t o measure low i n t e n s i t y t r a n s m i s s i o n l i n e s as was s t a t e d . was  However, f i e l d s under  The probe can be used as  done i n s e c t i o n 7.1, t o measure t h e induced c u r r e n t o r  v o l t a g e g r a d i e n t i f i t s ground c a p a c i t a n c e can. be determined.  77 REFERENCES 1.  L.M. Olmstad - Design Survey Reveals P a t t e r n s of EHV E l e c t r i c a l World - Nov. 15, 1965, p. 99-118.  2.  Ph. Sporn - The U.S. National.Power Survey C i g r e - V o l . 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