UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

High frequency method of locating power cable faults Nalos, Ervin Joseph 1947-12-31

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
831-UBC_1947_A7 N6 H5.pdf [ 10.59MB ]
Metadata
JSON: 831-1.0105076.json
JSON-LD: 831-1.0105076-ld.json
RDF/XML (Pretty): 831-1.0105076-rdf.xml
RDF/JSON: 831-1.0105076-rdf.json
Turtle: 831-1.0105076-turtle.txt
N-Triples: 831-1.0105076-rdf-ntriples.txt
Original Record: 831-1.0105076-source.json
Full Text
831-1.0105076-fulltext.txt
Citation
831-1.0105076.ris

Full Text

I  £3  h«-j  High Frequency Method of Locating Power Gable  #7  fly  Faults  E r v i n Joseph Nalos  A Thesis submitted i n P a r t i a l Fulfilment of the Requirements f o r the Degree of Master of Applied Scince i n the Department of E l e c t r i c a l Engineering  The U n i v e r s i t y of B r i t i s h August  ,1947  Columbia  1  Table of Contents Page I.  Introduction  3  I I . Mathematical Analysis A.  Symbols used  6  B.  Analysis of Transmission  C.  Analysis of Faulted Line, end O.C.  .  .  .  8  D.  Analysis of Faulted Line, end S.C.  .  .  .  9  E.  Analysis of Faulted Line, end char.imp.  F.  Analysis of Double Faults  11  G-.  E f f e c t of Long Instrument Leads . . . .  12  H.  Alternate Approach,far end char. imp.  Lines  . . . .  7  . 10  .  . 13  . . . .  15  I I I . Discussion of Experiments A.  C i r c u i t Diagram and Apparatus  B.  Calculations  C.  1.  C h a r a c t e r i s t i c Termination  .  .  .21  2.  Far End Open-circuited  .  .  .22  3.  Far End S h o r t - c i r c u i t e d  . . . .  23  4.  Double Faults  5.  E f f e c t of Long Lead-in Cable  .  . 25  6.  Alternate Method,Charact.Termin.  . 26  .  24  Dicussion of Results 1.  E f f e c t of Harmonics .  2.  A d d i t i o n a l Errors  3. 4.  Accuracy,Limitations,and Bibliography  5.  Acknowledgement  .  .  .  .  .30 31  .  .  Conclusion .  .  . . .  33 35 36  2 L i s t of I l l u s t r a t i o n s /  Page  Pig.l  Transmission Line  Pig.2  Faulted L i n e , f a r end O.C.  .  . . .  9  Fig.3  Equivalent C i r c u i t of Faulted Line  . . .  9  Fig.  7 .' .  4 Line with Double Fault c o r r e c t l y terminated  Fig.5  11  Equivalent C i r c u i t of Line with Double Fault 11  Fig.6a Line with Lead-in Cable..  .  .12  Fig.6b C i r c l e s of constant Attenuation,Frequency  . 14  Fig.7  Video-frequency  .  .  .  Amplifier  Fig.7a Layout of Apparatus . ...  16  .  .  Fig.7b Schematic Diagram of Layout Fig.8  .  .  .  . . .  .  .  .  17  .  .17  S-function Method of Measuring Attenuation  Fig.9a,9b Fig.10  Reflected voltage and' current wave .  Connection  to A m p l i f i e r  Fig.10a  A r t i f i c i a l Fault .  Fig.10b  C h a r a c t e r i s t i c Termination  Fig. 11a,lib,lie  .  . .  .  . .  . .  .19  .  .20  .  .20  . . . . .  E f f e c t of Harmonics  F i g . l i d High-pass F i l t e r C i r c u i t Fig.12  .  .  .  .  .  .  .  .  20 .  30 .32  Tuned C i r c u i t to,eliminate Harmonics  L i s t of Tests  18  .  33  f a c i n g pages shown  Test 1,2,3  s  Input Impedance,line c o r r e c t l y  terminated ... 21  Test 4,5  :  Input Impedance,Line O.C.  Test 6,7  : 'Effect of Harmonics  Test 8  :  Double Fault . . .  Test 9  :  E f f e c t of Mismatch at Far End  .  .  24  Test 10  :  E f f e c t of Long Input Cable  .  .  26  Test 11  :  Alternate Method with Char.Term. .  28  and S.C.  22  . . . . . .  30  . . .  24  3 HIGH FREQUENCY METHOD OF LOCATING POWER CABLE FAULTS I. Introduction The l o c a t i o n of a f a u l t i n power cable i s by no means a simple task and the techniques used at the present warrant f u r t h e r improvement.In practise,power  cables are  burried in'dry or wet-ground,placed i n conduit,or l a i d i n troughs,separately or i n groups; t h e i r path may cross an open f i e l d or a busy i n t e r s e c t i o n . Frequently,they are adjacent to non current-carrying e l e c t r i c a l may  conductors.Cables  be terminated i n potheads, i n manholes,or near the top of  a l i n e pole.Occasionally,one end of a cable may be i n a c c e s s i ble as f o r example i n c e r t a i n types of ring-buss switch boxes.Due to the various conditions under which cables are used,methods of f a u l t l o c a t i o n successful under one set of conditions w i l l not n e c e s s a r i l y work on others. Many methods of f a u l t l o c a t i o n have been devised but each of them has i t s p a r t i c u l a r limitations.The simple D.C. bridge techniques-'  have been superseded to some extent by 17  e l e c t r i c a l pick-up methods. '  These,however, are of l i t t l e  use i n l o c a t i n g f a u l t s i n armored c a b l e , i n lead-sheath cable located amongst a number of other cables,or i n cables adjacent to n o n - e l e c t r i c a l current-carrying structures because the audio s i g n a l employed does not always leave the cable at the point of the f a u l t but rather passes along the cable armor or other conductors i n a devious path. The echo-ranging technique ^ i s at present l i m i t e d to telephone work because the lengths of power cable used are r e l a t i v e l y short.For power cables,where the v e l o c i t y of electro-magnetic waves i s approximately  500 ft/microsecond,the  pulse returns too r a p i d -  l y to be detected unless the cable i s longer than 100 f t or so. Moreover,the echo-ranging  method requires elaborate trans-  mitting and r e c e i v i n g equipment which at present makes i t impractical. A l l numbered references are given i n bibliography.  4 The l i m i t a t i o n s and i m p r a c t i c a b i l i t y of these various techniques l e d to the development of a supplementary method 5  employing high frequencies.  The method,utilizing frequen-  cies from 0.1 Mc to 32 Mc,is based on the p r i n c i p l e that standing waves may  be established on e l e c t r i c a l l y long l i n e s  and that reflections are produced at d i s c o n t i n u i t i e s such as open and short c i r c u i t s where the f a u l t resistance does not equal the c h a r a c t e r i s t i c impedance of the cable.Since the cable input impedance i s a f u n c t i o n of the frequency.it i s possible to a s c e r t a i n the frequencies where maximum impedances occur by recording the frequencies corresponding  to  maximum input voltages. By proper i n t e r p r e t a t i o n of these frequency differences between adjacent impedance peaks,the distance to the f a u l t may  e a s i l y be c a l c u l a t e d .  This method i s l i m i t e d to f a u l t s whose r e s i s t a n c e i s l e s s than a t h i r d of the c h a r a c t e r i s t i c impedance.The most accurate determinations are obtained when the f a u l t  resis-  tance i s zero;however,such cases are r a r e l y found i n p r a c t i se and i t i s thus necessary to burn f a u l t s down u n t i l  they  can be detected.This requires time as well as s p e c i a l  equip-  ment. Frequently, the resistance of a burnt down f a u l t  will  r i s e during the t e s t to a value which makes the method i n applicable without f u r t h e r carbonization of the f a u l t . The object of t h i s research has been twofold: F i r s t l y , t o review the high frequency method i n an endeavor to develop a method of l o c a t i n g high-resistance f a u l t s ; secondly, to develop expressions permiting the use of t h i s method i n instances where cable potheads are r e l a t i v e l y i n accessible, such as on top of poles.In e f f e c t , t h i s means t a king into account long instrument leads* The f i r s t of these objectives has been achieved  by  the development of a simple method of measuring the cable input impedance.Briefly,the  method consists of terminating  the cable at the remote end i n i t s c h a r a c t e r i s t i c impedance and measuring simultaneously the voltage drops across  a  5  standard r e s i s t o r and across the cable. The r a t i o of these drops i s an i n d i c a t i o n of the cable input impedance at that frequency.Observations  are taken on a band of frequencies on  a f a u l t e d cable and on a good cable,both terminated i n the c h a r a c t e r i s t i c impedance.The d i f f e r e n c e of these two important e f f e c t s i s a t t r i b u t e d to r e f l e c t i o n s from the f a u l t . Prom a p l o t of impedance as a f u n c t i o n of frequency,by  a  short graphical computation,the distance to the f a u l t may e a s i l y be obtained.To f u l f i l l the secondary objective n e c e s sary expressions permiting the use of long instrument have been developed  leads  and are presented i n the main body of  the t h e s i s . F a u l t s as high as twenty times the c h a r a c t e r i s t i c impedance have been s u c c e s s f u l l y located on r e l a t i v e l y short lengths of cable.The  distance to the f a u l t has been estimated  well within 5 $ and higher accuracy i s to be expected cables.  on longer  6  II.  MATHEMATICAL ANALYSIS  A. Symbols used In Mathematical Analysis. x E I z y c a b k E E 1^I ZZ1 3  r  3  K =  distance from sending end rms voltage a t distance x from sending end rms current at distance x from sending end series impedance of cable per unit length shunt impedance of cable per u n i t length propagation constant* attenuation constantc « ( a * jb) / z y phase constant constants s a t i s f y i n g boundary conditions sending end voltage receiving end voltage sending end current receiving end current input impedance equivalent receiving end impedance t o t a l length of given cable 88  1  VR  R -  Fault resistance ( /cos2 b l ) d = (R/R*Z ) = ( l / l o k ) 2 ^/Rg+Zj 3  =  al  Q  d  =  u = V  ( lV lV 2 oV R  R  R  Z  Z (R Z ) (R,R~*R~z * Z ) , _ _ _ x 1 2 2 o oV R_Z (R +Z ) ' 1 o 2 o Characteristic Impedance of Lead-in Cable  =  R l  0  2 t  0  2  v  rt  Z " Q  Z =  Sending end Impedance appearing a t Sending End of Lead-in Cable  3  Z  0  "  3  Z o l a x~ r V r  =  r  =  r  • = =  c  -  b  V r  =  Rc+JXc, 3  3  Z  I.(r• j x ) 3  3  o 1/2 itanh {al+fal^+coth Dal-»(al}y = coth 2 Qal+Cal)^ 1/2 ^coth [ a l * ( a l ) l - t a n h [ a l + ( a l ) ^ = csch 2 ^.l+Cal)^ 1/2 Jtan [bl+(bl)g-cot tbl+(hl)lf= -cot 2 fcl+(bl) -] 1/2 jtan [blt(bl)g«cot [bl+(bl) ij= esc 2 [bl*(bl) -} Voltage drop across f i x e d standard r e s i s t o r r which i s a measure of the r f current through the cable Voltage drop across cable which, when divided by r f current gives the cable impedance Standard r e s i s t o r used i n measuring r f current through cable  * Notation used here i s not standard.  0  0  0  7.  B. Analysis of Transmission Lines, - Iz —dE dx  dE d x  d l = Ey dx  d2l_ dx2  z dl dx  2  T  2  -  =  I  v dE  z  —o  X  y  Izy fist  Solving these two d i f f e r e n t i a l equations, we obtain: E = I  =  k-^cosh cx + kgSinh cx  (1)  k_cosh cx * k^sinh cx  (2)  The constants k are obtained by boundary conditions, as follows: At Sending end, where x = 0, E = E I * I  =  r  p  k  x  = k  3  Also, -  ck^sinh cx  «*• ckgcosh cx  iSH • dx  cE^sinh cx r  +  ckocosh cx  = I z cosh cx  +  k^z sinh cx  p  Hence, ckk c cE  s 2  r  r  E  s  I  s  z 3  I z « kij.z  "  But Z  I cosh c l + r  E  r  g a Is «  kg = k  p  =  d  from which  E cosh c l  =  B  E  r/Z  c  r  I^cosh c l + thus  sin*  1  c l  I Z sinhc l r  I Z r  E  Q  r/z,  (3)  0  E cosh c l  Er/1.  V  I Z sinh c l r  Iz  5  0  E* / z sinh c l 0  (4)  8.  .  z  z  Z cosh c l * r  Z cosh c l  Z sinh c l 0  (5)  Z sinh c l  Q  r  For Open-circuited end, Z i s i n f i n i t e , f o r Short-circuited end, i t i s zero. r  Hence,  Z  o c  - Z coth c l  (6)  0  Z sc „ = Z^tanh cl o n  C. Analysis of Faulted Line with f a r end open-circuited. The c i r c u i t i s shown i n F i g . 2 and the equivalent c i r c u i t i s shown i n F i g . 3; from t h i s , we obtain, Z  s RZ coth clg  r  Q  R + Z c o t h clg 0  Rcoth cl2Cosh c l i R+Z coth c l g  sinh c l -  0  cosh c l i  Rcoth c l g s i n h c l !  +  R + Z coth clg Q  1 + tanh c l ^ (k + tanh clg)  (7)  K + tanh cl.,+ tanh c l ~ 1. I f attenuation i s n e g l i g i b l e , c and i n the above expression, "~ tanh c l = tanh j b l • j t a n b l Hence, Z  3  a  a + jb i s appr. jb  j ( l - t a n hl]^tan big) + jktan h i ! '  (8)  K + j (tan b l ^ t a n big) If b l ! S multiple of big, the above r a t i o equals l / 2 f o r b l g 0,^2113... , this being a pure resistance, i s  a  n  l n t e  r a l  a  2.  I f attenuation i s small but not n e g l i g i b l e , a l i s small  sinhg2al = 2al  cosh  al- 1  tanh c l  sinh 2al+jsin 2bl _ a l 2 (cosh al-sin bl) 2  2  + jtan b l  cos hl 2  9.  X, R o—  Fig. 2  Fig. 3 al.  al.  <  1 +  (k+  k  cos2  +  3  i  b  * jtan b l ) (  2  2  al.  al-  c o s bl-  cos^ bl-  2  ^  c o s 2  * Jtan b l ^  -) * j (tan bl}+ tan b l ) 2  Jl-vs (k««-s )-tan b l ^ tan b l l + j £(k+s ) tanbl^+s^tanbLgl 1  2  2  (K + s^ + s )  +  2  2  j (tan b l i +tan b l ) 2  ....(9)  D. Analysis of Faulted Line with f a r end s h o r t - c i r c u i t e d . The only difference between this and the previous case i s In the value of the equivalent impedance which now becomes RZ tanh c l Z  a  -O  0  d.  R + Z tanh c l Q  2  ' Rtanh clocosh c l - i * - + sinh c l ! Ri-Z tanh c l 0  2  cosh c l - i *  Rtanh c l o s i n h c l - i £ i R*Z  Z  s  tanh c l  0  2  s  Z 2.  s  0  2  (10)  2  I f attenuation i s n e g l i g i b l e , again substituting tanh c l Z  i J  (tanh c l + tanh cl]_(l+ktanh c l ) 1 «• ktanh c l + tanh cl^tanh c l 2  1.  v  2  jtan b l , then  (-ktan b l ^ t a n b l ) + j ( t a n bl^+tan b l ) 2  2  ( l - t a n b l ^ t a n b l ) 4 jktan b l 2  2  I f attenuation i s small but not n e g l i g i b l e  (11)  10.  (s-j + s (1+ks ]_) -k tanbl-L tanblgl+jfcanblg (1+ksj) + tanbl^ (l+ksg)] 2  \ . l * k s * s i s - tanblitanbl ]+ j[(k+ s])tanbl * s tan bl-jl 2  2  2  2  2  (12) E. Analysis of Faulted Line with f a r end terminated In 3urge impedance. The receiving end impedance of the equivalent c i r c u i t becomes, Z  Z  r  Z  Q  0  0  — •—  m  d *• tanh c l ^  83 I I I •  Z tanh c l ^  ..(13)  i • • —i .^^.mmmm.m •  1 + d tanh c l ^  r  I f the attenuation i s n e g l i g i b l e , then tanh c l t a n h j b l jtan b l s  Z _  d+jtan bin  s  _  Z  d(l+tan bl ) + j ( l - d ) t a n b ^ 2  C  8S  Z  s  When b l  > s/  B  • (X^f)  (resistive)  d  0  =  Z  a  • • e e  a  1 + d^ tan^ bin  1+jdtan b l i  D  2  1  When bl-j_ = 0,T,2.n;.. , / Z  2.  = dZ,  R+Z  =  + Z tanh c l ^  • • - i - n i P . i»  1.  r  Zo  Vd(  "  )  I f the attenuation i s small but not n e g l i g i b l e , [(d*3j) (l^s^)  + dtan2bl£l + j (l-d2) tan b ^  (l*dsi)  2  +  d  2  When b l j » 0,%*!} When bin = f *T -1  *•) 2.) —  2  ( d < 3  , Z / s  a  (15)  t a n bl-  i>  (i*a.,)  l / d which can e a s i l y be v e r i -  f i e d by substituting and taking the l i m i t as b l ^ approaches  "72.  11.  F. Analysis of Double Faults F i g . 4 shows the c i r c u i t diagram f o r the case of charact e r i s t i c termination which i s the only case considered. The equivalent c i r c u i t i s shown i n Fig.. 5 . In most cases a t tenuation i s small and f o r s i m p l i f i c a t i o n I t Is neglected i n this consideration. I f not small, attenuation may be accounted f o r i n a manner described previously. i Z +Z tanh c l ^ Again, J Z *Z tanh c l i Z  Z  s  z  S  r  0  r  0  r  o 2/ Z .R+J o Z  R  o  0 o 2/Z 4R  +  z  R  d +jtan b l 2  o  2  t a n b l  t a n  Fig. 4  2  b  l  2  2  l+jdgtan b l  2  Hence,  Fig. 5  -  Z  Z  _  R  2  2  I T —  Z  ^s Zo  R-L (d +jtan b l )  s l s l  ^ 2  R  d  + R  l/z  ^  ^  +  dg+jtan b l  2  u+jvtan b l  2  1  +  d  2  l / z  R  )  t  a  n  b l  2  (16)  (d -vZ tan b l ^ t a n b l ) + j (tan bl *-uZ tan h l ^ ) . . . ( 1 7 ) (uZ -tan b l j t a n b l ) - j ( v Z t a n bl +-d tan D I 2 ) 2  Q  D  2  2  2  0  2  0  2  As an example, i f R-|_« 100 ; R = 50 ; Z = 50 2  Q  l = 200 f t . ; 1 = 75 f t x  2  the above expression becomes ( . 5 - t a n 2 f t a n . 7 5 f ) + j (tan.75f+1.25tan2f) (l.25-tan2f  tan.75f) + j (tan.75f+ - 5 t a n 2 f )  which i s plotted i n Test 8. This analysis i s merely of academic value and the occurence of this case In a power cable i s extremely u n l i k e l y . I t i s included merely to complete the study and might be used to advantage i n telephone work.  12.  G. E f f e c t of Long Lead-In Cable on Impedance of Cable under Test Often f a u l t e d cables are overhead or not d i r e c t l y accessible and an a u x i l i a r y lead i s brought out to the apparatus from the end of the•faulted cable. This cable i s not usually short e l e c t r i c a l l y a t frequencies of 2-3 Mc and hence i t s e f f e c t has to be calculated. From F i g . 6awe obtain by a process analogous to previous d e r i vations, Z cosh c l + z l s i n h c l s o z'coshcl * Z sinh c l o s J  s  _  Z  s/Zp  ¥  JL  A  F i g . 6a  tanh c l  1 + Zs/Z  (18a)  tanh c l  0  With n e g l i g i b l e attenuation, this reduces t o : Z  - •  s/Z  4 0  J  t a n  1 + O'Zs/z  1  t  b  a  l  n  (18b) D  l  Alternately, from (l8a) and ( l 8 b ) , z ; ( s / Z -Iten WL) Z  Q  - «  Z  0  (l-jZa/ « ^ z  (19)  bl)„  The p l o t of expression (l8b) f o r 25 f t . of Cable RG8/U i s given i n Test 10 together with the curves  obtained  by a test on a cable with a 100 Ohm f a u l t a f i x e d distance from the sending end.  13  H. An Alternate Approach of Analysis of Cable Faults with f a r End Terminated i n Characteristic Impedance, This method may be used to advantage i f apparatus i s available f o r measuring reactive component of cable impedance with reasonable accuracy.  The tedious calculations  encountered i n Eq. 14 and 15 are avoided by the use of this method.  Since the f a r end of the cable i s c o r r e c t l y termi-  nated, no r e f l e c t i o n s return to the sending end.  The input  Impedance of the cable behaves as though i t were terminated at the f a u l t with an impedance  Z  = R  R  which i s f i x e d .  /R Z  Z  +  0  If Z  .— ~  ,=  cosh ( c l )  and  0  s  o  V o- r'  4 i- l Z  sinh ( c l )  Z r  Z  Z  z  then Z  Z cosh c l + Z s i n h c l  g  r  Z ^o  c  Z cosh c l + Z sinh c l o r coshcl sinh ( c l )  cosh c l cosh ( c l ) z  s  Z  u  Q  + sinh c l sinh  Q  r ~i s ' s tanh|cl4(cl)J = — ; „ ^o R  -  4 sinh c l cosh ( c l )  Q  + J  )  Q  (cl) i 0  X  * r 4jx  ( o) 2  s  J  As before, i f c = a*jb, tanh c l = ] (  s l n n &  1  c  o  s  n  a  l ) * 3* ( s i n b l cos b l )  c o s h a l cos bl+sixth a l s i n b l If i n the above equation a value of c l 4- ( c l ) = [al+(al)^J + 2  2  2  2  Q  j£bl+(bl)J], i s substituted f o r c l , keeping [al-»-(al)"] 0  constant (rg-r,)  2  t x  2  = r | which i s a c i r c l e i n the ( r x j Tlane. s  14.  Similarly, i f [bl * ( b l ) l c o n s t a n t , 0  r  s  +  ( s" l) x  x  In Eq. (21) and  2  (21,  • *f  22)  (22)  *1 - eoth ^ [ a l + f a l j j s coth 2 ( a l ) i f attenuation i s n e g l i g i b l e Q  r x r  a  x  b  = csch 2 [al+(al) ~J= csch 2 ( a l ) 0  "  Q  "  = cot 2 p x L 4 ( b l ) " ] 0  = esc 2 [ b l 4 ( b l j " ] 0  F i g . 6b shown below gives a c l e a r e r idea of the symbols enumerated above.  Further plots of s i m i l a r figures with neg-  l i g i b l e attenuation are shown i n connection with Test 11 a Lead covered Cable* with a 100 Ohm  Fault and terminated  on In  i t s Surge Impedance.  Es»2l -  tV  Note:  - const I  Coogfcmt Atentdhbri  CM const 4f«K circles pass+VircooV) 0,o). ^ ^ ^  I f attenuation Is small, a l « 0, and Eq. (21), i . e .  c i r c l e of constant "attenuation" depends only on ( a l ) which Q  i s a constant f o r a given l i n e and f a u l t .  Hence the radius  vector from o r i g i n to a point on the circumference c i r c l e represented by Eq. (21) * 2 - No. 8 conductor,  of the  i s the sending end Impedance  paper-insulated, lead-covered,  HKv Cable  15.  with i t s appropriate angle.  To determine what impedance  corresponds to a given frequency i t i s noted that ( h l ) i s c  a constant and that (hi) i s a l i n e a r function of frequency, the constant depending on the type of cable under t e s t .  Know-  ing this constant, any c i r c l e of constant (bl) also represents a c i r c l e of constant frequency, cutting the other c i r c l e at 2 points (usually), and giving the expected impedance at that frequency. Ill A.  DISCUSSION OF EXPERIMENTS  C i r c u i t Diagram and 1.  Apparatus.  The general method of locating f a u l t s was  des-  cribed i n the l a t t e r part of the introduction and the c i r c u i t diagram i s given below i n F i g . 7a s-nd 7b.  The  ap-  paratus consists of a Signal Generator with variable Frequency up to 5 Mc, an amplifier covering the videofrequency ranges, a power-pack giving 300 v o l t s D.C.,  a  filament transformer with, 6.3AC v o l t s output, a standard dropping r e s i s t o r , and 2 vacuum-tube voltmeters.  A Sig-  nalyst or T r i p l e t Signal Generator are s a t i s f a c t o r y f o r this method.  The c i r c u i t diagram of the Video-frequency  f i e r i s shown i n F i g . T  Ampli-  and the arrangement of measuring  the drop across the standard r e s i s t o r and the cable are shown enlarged i n F i g . 10.  A Cathode-ray Oscilloscope i s  also required i f the waveshape i s to be examined.  The  Cossor  double beam oscilloscope enables the examination of waves up to 3 Mc.  The output of the generator was amplified to about  3 volts at an intermediate frequency thus making i t possible  16.  to measure accurately the drop across the cable.  -SDK  • B o o  .OI  .01  \<ao  • oi  5K AO  60K  8"  Pig. 7 Video-frequency 2.  Amplifier  Tests were made on 2 types of cables.  Tests 1 to  10 were made on cable FT&R AN Type RG8/U and test 11 was made on a 2-conductor,  oil-impregnated, lead-covered cable,  loaned especially f o r this test by the B r i t i s h Columbia E l e c t r i c Railway Co. Ltd.  Por the purposes of comparing  calculated and experimental results, attenuation was neglected i n the mathematical expressions derived before.  This  i s well j u s t i f i e d as the calculations below show. The atp  tenuation was calculated by the S-function method and checked by measurements of a shorted quarterwave section. Cable: Type RG8/U, surge impedance=52 ohms, velocity=60$ app. Apparatus: Bontoon Q Meter • • Frequency of test: O.935 Mc determined by cable length of 100 f t . Cable length = l44vel/freq.in Mc  17.  Fig.Ta Layout of Apparatus  Sample oable Under T e s t See  "Fig. 10  Fig.7b S c h e m a t i c Diagram of L a y o u t  18.  Q .- 200  With c o i l only,  C  1  = 281.5 uuf  L]_ = 100  uh  With c o i l and cable i n series, Q  2  = 78  C  2  = 255 uuf  C = Capacity to resonate cable inductance of 11 uh at O.935 Mc i s 10 12 1 2635 uuf Lw [(2)(3.14)(.935)] (11)10 o  2  since C 1  6  1*9  - = —=- = 1.11 and hence 1^ = 111 uh and cable i n 2 l ductance i s (111-100)'= 11 uh C o i l resistance = X / Q = l / C ^ Q ^ = 3.02 ohms C  L  C 1  C o i l and cable resistance i n series = l/CgWQg Cable resistance = (8.55-3.02) Q of cable =  c2~ cl R -R X  X  2  ^  I  m  6  3  e  8.55 ohms  r 5.53 ohms _  n  ^  5.53  From Graph shown i n F i g . :8-., at f Z C Q  0  :  (-935)(52)(2635)10  6  = .128,  Ito.  S = 275 and attenuation a = S/Ql = 2 7 5 / H 4 0 = .24 d b /  1 0 0  f  t  #  Fig. Q When a sample of quarter-wave section was tested with f a r end short-circuited, the impedance was found to be 2000 ohms  19.  From F i g . (;S.a) and (b) below s  F i g . :9^a I? = 2000 ki  F i g . :9b  and -X = . Hence k = 1/20 l . o  Thus the r e f l e c t e d current wave i s 1/20 less than the input current wave due to attenuation. db = 201og ±i/±  s 2  .44 db per 200 f t = .22 db/100 f t .  Since the attenuation varies approximately root of the frequency,  as the square  even at 10 Mc this value i s small  compared to the phase-shift constant and hence the omission of attenuation i s j u s t i f i e d i n our tests provided the cable i s not unreasonably long.  The attenuation of the  lead-covered cable of the BCER Co. Ltd. i s of the same order, i n fact somewhat smaller, and can therefore be neglected. 3.  The a r t i f i c i a l f a u l t and the c h a r a c t e r i s t i c  Termination are shown i n F i g . 10.  The size of the r e s i s t o r s  must be kept small p h y s i c a l l y and a l l connecting leads must be as short as i s p r a c t i c a l l y possible i n order to minimize stay capacities to ground.  To prevent leakage e f f e c t s , a  shield i s put over the entire r e s i s t o r as i s indicated i n F i g . 10. B.  Calculations  1. Far end terminated i n c h a r a c t e r i s t i c termination In test l , a 1000 ohm f a u l t was i n j e c t e d at a  20.  Fig.  \o  C o n n e c t i o n o f Cable t o A m p l i f i e r F o r a c c u r a t e measurements t h i s c o n n e c t i o n may be i n s t a l l e d i n case where i t i s s h i e l d e d . The c a b l e i s t h e n connected t o the a m p l i f i e r by a s t a n d a r d c o n n e c t o r . The l e a d s go t o the Vacuum Tube V o l t m e t e r .  F i g . \oa  F i g . lob  Pig • '  o a  T h i s f i g u r e shows the a r t i f i c i a l f a u l t between conductor and ground. A l s o shown I s a s h i e l d w h i c h i s normall y p l a c e d o v e r the c a b l e t o a s s i m i l a t e a f a u l t i n a power cable. F i g . iob C h a r a c t e r i s t i c T e r m i n a t i o n on Cable FT & R AN Type RG8/U. The sheath i s t e r m i n a t e d by 4 p i g t a i l s whose ends a r e s o l d e r e d t o t h e ground end o f t h e r e s i s t o r . A s h i e l d f i t s over the e n t i r e t e r m i n a t i o n . R e s i s t o r s s h o u l d n o t be wire-wound i f p o s s i b l e , t o m i n i m i z e the c a p a c i t i v e r e a c t a n c e at h i g h f r e q u e n c i e s . Small carbon r e s i s t o r s g i v e best results.  TESTS ON CABLE Otcud  FT4 R  A N TYPE- RG8/U  diagram o— Zoo  MOTE. Oi\cu\a\ei :  Qvtves do not account  5OJQ.  Tomce%2\.  1=  ^of a^eooahon  (2) (?e{th  wliicli i s negligible at \o\tt<{tt<\oenc\e$.  impend'VBIIJ.  © Calculated W t  feftttiofl  Characteristic- lamination ®  Fao^ £ Imprf-fcct-termination  Te»r2  «• :  7 f fi--i H ' f f f t m t u  r:t  © Calculated ' © Faoft^  IllilllillllllH P R I N T E D  Ifsf  U.S.A. • 1 1  111111111  @  -Vefmination  llllllllllllllllllllllllift 3  • 11111111  fPCO. IN  Wm' '  Cef tetibn  Reflation -\fom  © Calculated faoHrPe^Ktpn  ImfrtfftH+ef initiation  mtttttmttttttt 3  xm  iENE DIETZ6EN CO^NO. 3 ^ 6  pee*?. IM  MC.  2 3m «  distance of 100 f t . and i t was observed that the difference between any two minimum values of Impedance i s 3.2 Mc. Since the cable v e l o c i t y i s approximately 60$ that of l i g h t , i . e . 5.9«10^ ft/sec, the phase-shift constant, b = w/v « (.01 f ) appr., where f i s the frequency i n Mc. Hence, corresponding to h a l f wavelength, b l = (.01)(3.2) and distance to f a u l t  3«l4  1 = '  _  (.01) (3.2)  "  g  Q  _  f  t  (  _  c  f  1  0  Q  f  1 t  )  «  _  To estimate the size of the f a u l t , which can also be done by other methods,' i t i s found that peak of curve occurs when Z  s/Z  - 1.045 =  a t maximum j hence R = 5 2 / . 0 4 5 •  R  = 1158 ohms ( c f 1000 ohms) In test 2, the peak to peak separation s t i l l corresponds  to h a l f wavelength and equals 3.15 Mc and hence the  distance to the f a u l t , 1 =  3.14  _ 99.8 f t . (cf 100 f t )  (.01) (3.15) Also maximum observed value of Zs/Z of f a u l t i s  0  i s 1.17 and hence si'ze  5 2 / .17 = 306 ohms (cf 340 ohms.)  In test 3 , peak to peak i s 3.20 Mc, giving distance to f a u l t as  3*14  98 f t  =  (cf 100 f t )  (.01)(3.20) Also size of f a u l t i s 5 2 / . 4 9 = since maximum value of Z /z 3  0  106 ohms (cf 100 ohms)  i s 1.49  In tests where faulted l i n e i s terminated i n surge impedance i t i s often d i f f i c u l t to estimate the correct value of Z . Q  In tests 1, 2 and 3,- a value of resistance  O  RINTCDI(J.U  2  3  Fff&p.  IN M C  4  O  |  2  J E U G E N E DIETZGEN C * N O . 3 4 6  FREM <N MC-  BX  22.  close to Z  i s put on the f a r end of a good conductor which  q  i s often available i n the same sheath and a curve of frequency against Z / s  Z  i s run.  on the graphs.  These are shown as black dotted curves  Then a similar curve i s run with the same  r e s i s t o r on the f a r end of the faulted cable.  These two  curves are then subtracted and the r e s u l t Is due to the f a u l t r e f l e c t i o n only, provided the mismatch at the f a r end i s not too great.  I t i s r e a d i l y seen that f a u l t s  twenty  times the surge impedance can be detected by this method. The reason why this i s possible i s due to the f a c t that the observed r e f l e c t i o n i s from the f a u l t alone and not, as i n the following tests, due to a combination of r e f l e c t i o n s from the f a u l t as well as the end of the cable.  In the above c a l -  culations, use was made of Eq. 14 whose maximum value i s R/R+Zj. 2.  Far end open-circuited In test 4 i t i s to be noted that as frequency ap-  proaches zero, Z / 2  approaches l / k and when the second  s  minimum i s reached at 1.57 Mc, Z ^ g  2-fjk tan bl-j^ k+j (tan bl-j-1/tan b l ) 1  )  -z  (  Z  i n Eq. 8 becomes  z  s  °  From graph i n test 4, k - .5 s / Z = .60  4+k tan bl- /.36 2  = k »(tan b l - l / t a n b l )  2  2  L  1  2  1  •  Z  0  f = 1.57 Mc.) Thus bl'2  Thus tan b l 1  n  r (12.86 + V164' „ 5 5 i\ .61  1.42 radians, and since second minimum occurs at  3/4 wavelength i . e . 3 T / 2 , b l  = ( 3 / 2 - M ^ ) = 3.29 radians. T  2  23  Thus 1 1  ±  2  - 1.42/(.01)(1*57) « 90.5 f t ( c f 100 f t ) = 3.29/(.0l)(l.57)  s i n c e h = .0l(f)/Mc/  - 209  f t ( c f 200 f t )  f o r this cable.  Size o f f a u l t i s d e t e r m i n e d from k * Z / ; thus Q  R  R r (52) (2) = 104 ohmsCpf 100 ohms) The f i r s t minimum of the graph could have been used as well had the second harmonic signal not been so large. of the open-circuited end,  In case  i t i s preferable to use the f i r s t  maximum or the second minimum point of the curve but not the f i r s t minimum, since the harmonic d i s t o r t i o n a t that point i s most pronounced.  Attenuation of higher harmonics at the  increased frequency of the second minimum increases the accuracy of r e s u l t s . 3»  Far end s h o r t - c i r c u i t e d In t e s t 5, when the f i r s t  k = .5 from 0C Test Z  s/Z  c  maximum i s rea,ched a t .53 Mc,  " 2.55  Eq. (12) becomes:  f = .53 Mc" fs_ ; s  1  / 2 x (1 + cot b l ) *• j cot b l 2  2  Zo k From experimental data above and from above equation i n ( c o t b l ) , we obtain, 2  2  cot^bLg + 2.25 c o t b l - .630 = 0 2  2  cot b l  2  from which we get,  = ,502 and big .« 1.103 radians  Wow a t the f i r s t maximum (bl +bl^ ) = ~^/2 since the entire length of the cable i s a quarter-wave length at this f r e quency.  Thus,  FREC? IN M C  24-  bl  2  = 1.103  =  radians  .47  "  Hence, since.b = .01 f  /Mc/,  .47/ 001) (.53)  1-L -  =  89 f t ( c f 100 f t ) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^  and 1  2  *  = 1.103/(.01)(.53)= 208 f t ( c f 200 f t )  Size of Fault Is estimated i n the same manner as f o r the open c i r c u i t test.  In this case "k" may also be obtained  from a reading of the f a u l t resistance and impedance. mum  characteristic  For this test i t i s best to use the f i r s t maxi-  or f i r s t minimum / not counting zero frequency/.  The  undesirable second harmonic e f f e c t does not seem to be as pronounced since i t does not occur at low-impedance peaks. The explanation f o r this i s given i n a l a t e r 4.  paragraph.  Double Faults In test 8 calculated and obtained curves are drawn  f o r a 100 ohm f a u l t 200 f t from sending end and a 50 f a u l t 275 f t from sending end.  ohm  The true r e f l e c t i o n from  these two f a u l t s Is again obtained by putting the surge impedance / resistance i n this case/ at the f a r end of the cable and subtracting any small discrepancies due to mismatch. sheath. £s _ Zo ~  For t h i s , a good conductor i s required i n the same Curve 1 i s a graph of a special case of Eq. (.5-  17:  tan 2f tan .75 f ) + 3 (tan.75f+1.25 tan 2f)  (1.25-tan 2f tan.75f) «* j (tan.75f*.5 tan 2f)  An expression of this type i s not easy to p l o t but fortunately such f a u l t s are not met In power cables.  26,  The experimental  curve i s rather d i f f i c u l t to analyze  without having a f a i r l y d e f i n i t e idea where the f a u l t s are beforehand.  The curve i s p l o t t e d merely as an i l l u s t r a t i o n  of the workability of the method f o r any number of f a u l t s . I t should be noted that above 3 Mc.,  the peaks of the  observed curves are diminished due to attenuation which has not been taken into account i n the calculated curves. the v a r i a t i o n of attenuation with frequency and the  If  decreased  gain of the a m p l i f i e r at these frequencies had been accounted f o r , the peaks of the calculated curve would have diminished as w e l l .  I t i s well to keep i n mind that at this  stage the accuracy of the method i s impaired due to stray capacities. 5»  E f f e c t of long l e a d - i n cable In p r a c t i s e , a cable pothead may be located on a pole;  i n this case the leads to the cable under test cannot be made short unless the test apparatus Is brought up on top of the pole.  This i s c l e a r l y impractical and i t Is neces-  sary to develop an expression such as Eqs. (18) and  (19)  which take into account a f i x e d length of input cable.  A  low-loss cable with n e g l i g i b l e attenuation i s obviously the most advantageous.  I f a cable whose c h a r a c t e r i s t i c imped-  ance Is approximately  the same as that of the cable under  test i s used, one need only subtract the length of the Input cable from the t o t a l length to the f a u l t to get the actual length to the f a u l t .  This i s the s i t u a t i o n which un-  i n t e n t i o n a l l y arose i n Test 10, i n which the values of the  e&r\o  Zvrzcr Oris Ft o  F  lapo-rC/vetE Rse/u ON  Iwgpflhfcg  OF^OLTEP  Cable-  CmcotT'  \QOJl FAUrr  : 2^56^2.  184.5'  2 * '  \ \  IK.  m  © Calcolated Exult* Iwput Cable (3) ^efkctvon^om fault, W^-f^t'l^mma-br^ ^-\«^uTCflbW Impcf-fectTermmtrtt'on ^ In^ut Cable (No^oH)  > P R I N T E D  ftt U.S.A.  E U G E N E DIETZSEN CO.NO. 3 4 6 B X  26,  c h a r a c t e r i s t i c impedances are close together.  I f this vere  not the case, i t would he necessary to investigate further the expressions In Eq. 18 and 19.  I t i s noted from the  calculated curve i n test 10 that as long as the characterist i c impedances are within 10$ of one another, we may assume the cable to be merely lengthened.  From curve (2) i n test  10, the observed difference between adjacent peaks Is 1.32 Mc.  The approximate distance to the f a u l t i s hence  ( '?7)(2) 1  (.oil)(1.32)  . 216.5 f t .  since f o r the lead-covered 2-conductor cable,  b « (.011) f /Mc/ Thus actual distance to f a u l t i s  (216.5 - 25) = 191.5 f t (cf 184.5 f t . ) Again, i f one wishes to investigate the size of the f a u l t , the f i r s t maximum of the curve i s desirable, since attenuation errors are l e a s t there; thus, 1.53 =(R+Z)^ and R R  6.  (56/.53) = 106 ohms (cf 100 Ohms)  Alternate method with c h a r a c t e r i s t i c termination a t far end. A close study of expressions developed i n Eq. (21) and  (22) open up a d i f f e r e n t approach to this problem by incorporating the e f f e c t of a sending end impedance Into the propagation constant as a f i x e d additional value.  Circles  of constant frequency 'can then be drawn and checked against the frequencies obtained f o r various input impedances. alternate tests are proposed here.  Two  In both, one f i r s t draws  the c i r c l e of zero attenuation / true f o r power cables / which gives the input Impedance with i t s angle at a l l frequencies.  This c i r c l e can be drawn by knowing the  c h a r a c t e r i s t i c impedance of cable and the f a u l t resistance, since the minimum and maximum input impedances are Ry{R+Z\ 0  andfR+Z^/R respectively.  I f apparatus measuring the re-  actance component of the impedance Is available, one method would be to determine the point of maximum reactance recording the corresponding  frequencies.  Test (11) by c i r c l e s (2-2) and ( 2 - 2 ) . ,  tance to the f a u l t may  This i s shown i n Prom this the d i s -  t  be determined.  and  Another p o s s i b i l i t y  would be to use a dropping r e s i s t o r " r " i n F i g . 7b whose value Is Z  Q  f o r the cable.  In t h i s case one records the  frequencies when the voltmeters V,, and V. read the same values i . e . when Z  s  = Z.  C i r c l e (.1-1.) corresponds to these  0  values of the input impedance and by knowing at what f r e quency the meters read the same values, the distance to the f a u l t may  be determined.  This method i s only of value when  accurate readings of reactance are to be taken.  Preliminary  tests indicated the p l a u s i b i l i t y of this method but not very accurate results are obtainable without additional r e f i n e ments.  This method i s unfortunately rather complex when  applied to shorted and open l i n e s .  In these cases one  ob-  tains s p i r a l s instead of c i r c l e s and t h e i r analysis i s too complicated  to be of p r a c t i c a l value.  For the lead-covered cable, with c i r c u i t as shown i n test 11,  ^  +  =  t a  Z  ^|"j  b l  /(  a l  ) ] o  tanh ( j . O l l ' f l «- .76)  with n e g l i g i b l e attenuation and 100 ohm f a u l t at a distance o f " l " f t from sending end.  These values automatically check  with the c i r c l e of constant attenuation. of maximum reactance was about 1.12 mc.  The observed point The c i r c l e  (2-2),  passing through this point and the point (1,0) having i t s centre on the x„ axis Is thus uniquely determined.  Hence,  from Eq. (21) and (22) -  - c o t 2 [ ( b l + ( b l ) ) ] = -.48 0  When dealing with resistances only, ( c l ) i s r e a l and hence 0  bl  0  Thus cot 2 b l = .48  i s zero.  b l - .56 radians or ( T / 2 + . 5 6 ) rad.  -  2.13 rad.  The l a t t e r value i s chosen since c i r c l e ( 2 - 2 ) crosses the point of maximum reactance f o r the second time / c a p a c i t i v e / i . e . h a l f wavelength from f i r s t point of maximum reactance. For this cable,  b "  (.011) f  Hence distance to the f a u l t i s  1 = —2.1g _ (.011) (1.12)  1 7 3  f  t  (  c f  l 8 2 t  f t  )  Alternately, when a dropping r e s i s t o r was used whose value was  the c h a r a c t e r i s t i c impedance of the cable / 5 6 Ohms/  and frequencies were recorded consecutively a t which the two drops across the r e s i s t o r and across the cable were equal / Z = Z /, the values should correspond to c i r c l e ( l - l ) s  Q  From experiment, these frequencies are: ?, 1.11, I . 8 7 , 2.65,....Mc.  For a l l these values cot 2 b l = 0 since the  centre of the c i r c l e ( l - l ) l i e s on the o r i g i n . A,  bl = quencies  f =  5*/*,  7" A ,  ? , 1.11,  .... corresponding  1.87,  Thus to fre-  2.65,efe  Hence distance to the f a u l t i s :  22C  195 f t (cf 184.5 f t )  =  4(.Oil)(1.11)  SI  '  191 f t ( f 184.5 f t ) — — —  s  C  4(.011)(1.&7) Z_ _ 4(.Oil) (2.65)  188 f t (cf 184.5 f t ) •  •—-—.  The size of the f a u l t , which i s r e l a t i v e l y unimportant, can be found by similar means as i n previous t e s t s . The accuracy of these results i s w e l l within 10$ and can be r e l i e d on f o r similar t e s t s .  I f desired, any p a r t i c u l a r  point on the zero attenuation c i r c l e can be checked by drawing c i r c l e s such as (3-3) f o r a given frequency  and  the actual input impedance at this frequency should equal the radius vector from the o r i g i n to the point where the c i r c l e (3-3) cuts the zero attenuation c i r c l e . also checked In test  (11).  This was  ft  N T E D i p L .  2  g  4  Fee~> In MC .  0  I  JL  J U 6 E N E DIETZ6EN  Ffc6S>. IN We  C4  N(  3o  C. D i s c u s s i o n o f R e s u l t s 1. E f f e c t o f Harmonics The o u t p u t v o l t a g e o f t h e s i g n a l g e n e r a t o r i s "by no means s i n u s o i d a l and c o n t a i n s second harmonic v o l t a g e t o a c o n s i d e r a b l e d e g r e e . W i t h t h i s i n mind, i t i s d e s i r a b l e t o i n v e s t i g a t e which of the d i s c u s s e d t e s t s i s l e a s t to  critical  t h i s predominant second harmonic. F i g . 11 a , l i b , a n d 11c  show t h e e f f e c t o f t h i s second harmonic on t h e i n p u t  imped-  ance as t h e f r e q u e n c y i s v a r i e d .  Par  end:open-circuited In  at  Short-circuited  Fig.11a,maximum impedance  t h e p o i n t where t h e impedance  Terminated i n Z  Q  t o second harmonic o c c u r s  t o the fundamental i s a m i n i -  mum; hence a t t h i s f r e q u e n c y a bump i s o b s e r v e d . T h i s bump i s c l e a r l y seen i n t e s t (6) and i n t e s t (4j . I t i s e s p e c i a l l y prominent a t t h e f i r s t  q u a r t e r - w a v e l e n g h t because t h e a t t e -  n u a t i o n i s n e g l i g i b l e a t t h i s l o w f r e q u e n c y . T h e bump a t t h e n e x t minimum i s a l m o s t n e g l i g i b l e compared t o t h e f i r s t bump. I n F i g . l i b t h e s i t u a t i o n i s more f o r t u n a t e b e c a u s e , f o r the  t e s t w i t h t h e f a r end s h o r t - c i r c u i t e d t h e minimum ;  impedan-  ce t o t h e f u n d a m e n t a l does n o t o c c u r a t a p o i n t o f maximum i m pedance t o t h e second harmonic.By a d d i n g t h e impedances due to  t h e f i r s t and second harmonic i t i s noted t h a t t h e bumps  o c c u r h a l f way between f r e q u e n c i e s o f maximum and minimum i n p u t impedance.Thus i n t h i s t e s t , t h e p e r c e n t a g e o f second harmonic i s n o t so c r i t i c a l .  T h i s bump c a n be e a s i l y o b s e r -  ved i n t e s t ( 5 ) a n d [ l \ i n d i c a t i n g a l a r g e second harmonic c o n t e n t .  31.  Pig. l i e shows the e f f e c t of s l i g h t mismatch at termination of cable.  I f the terminating r e s i s t o r i s too  high, the deviation from perfect termination /curve 1/ has the properties of a small "open c i r c u i t " i . e . maximum impedance occurs at same points as f o r open c i r c u i t . Alternately, i f the terminating r e s i s t o r i s too small, the curve of impedance tends towards that of s h o r t - c i r c u i t e d f a r end.  This follows from the fact that a small resistance  approaches zero / s h o r t - c i r c u i t / i n the l i m i t .  In this case,  the e f f e c t of the second harmonic i s almost n e g l i g i b l e at a l l times since the variations of impedance are small at a l l frequencies.  This leaves the curve of input impedance  versus frequency almost s i n u s o i d a l . I t i s concluded  that  i f the signal contains considerable d i s t o r t i o n , this test i s by f a r the most advantageous from a l l points of view. The elimination of harmonics Is discussed i n a l a t e r section. 2.  Additional errors Aside from errors due to d i s t o r t e d waveshape, the  s i m p l i c i t y of the method does not lend i t s e l f to many errors except at high frequencies when stray capacities between various parts of the c i r c u i t and ground reach sizable values.  To prevent the large capacities, short leads are  used throughout the c i r c u i t i n addition to carbon, not wire-wound r e s i s t o r s .  I t i s thus important  to keep the  value of the dropping r e s i s t o r low, i n order to minimize the e f f e c t of the capacitive reactance across i t s terminals. Another source of error i s 60-cycle hum .coming from  32. the amplifier.  The small amount which came through was  e a s i l y removed by a high-pass f i l t e r c i r c u i t shown i n Pig.  ll . d  (  Amplifier  -dj—-  )  Calk uooerTisi  Vr  -pass  Pig.  11  d.  High f i l t e r c i r c u i t to eliminate 60-cycles This f i l t e r c i r c u i t i s not required f o r tests with f a r end s h o r t - c i r c u i t e d or c o r r e c t l y terminated since i n those cases the cable i t s e l f provides an e f f e c t i v e short f o r the 60cycle. An e f f o r t was also made to eliminate the higher harmonics from the generator.  By beating the signal gener-  ator against the c a r r i e r of a radio s t a t i o n i t was found • that harmonics as high as the 5th were detected, the second being by f a r the worse.  When a tuned c i r c u i t i s interposed  between the signal generator and the amplifier, higher harmonics are eliminated because the impedance of the tuned c i r c u i t i s high when not a t resonance. to the fundamental harmonics.  Thus the impedance  i s much lower than the Impedance to a l l  When the tuned c i r c u i t shown i n F i g . 12 was i n -  cluded i n the c i r c u i t , a considerable difference was obtained between the impedances. this c i r c u i t  To be of p r a c t i c a l value  would have to be designed to remain at  resonance as the frequency setting on the signal generator.  33.  i s varied. •o o  oPig. 12 Tuned c i r c u i t to eliminate harmonics Some improvement In waveshapewas also obtained by adjusting the bias i n the o s c i l l a t o r so that the output would be decreased but more sinusoidal. With short leads and carbon r e s i s t o r s , the only considerable error remaining i s due to capacity of the v o l t meter to ground.  This probably accounts f o r the larger  discrepancies i n the calculations.  I t i s also important  to connect the voltmeters i n such a fashion that they both measure the same part of the wave.  Por a sine wave, both  p o s i t i v e swings and negative swings are equal but f o r a distorted wave a good measure of impedance i s s t i l l obtained i f both meters measure the same part of the wave. 3.  Accuracy, l i m i t a t i o n s and conclusions In a l l the tests carried out, an accuracy of better than  10$ was obtained i n estimating the distance to the f a u l t . An accuracy of better than 5$ was obtained f o r tests with f a r end terminated In surge impedance, indicating that this i s the best method to be used.  Faults as high as twenty  times the c h a r a c t e r i s t i c impedance are e a s i l y detected by this method.  With the present amplifier and size of  r e s i s t o r s , the upper l i m i t - of frequency i s about 5 Mc hence tests f o r l i n e s shorter than 25 f t . do not y i e l d accurate r e s u l t s .  I t i s to be noted here that  improved  accuracy i s obtained when f a u l t s farther away are being tested.  The tests with long "instrument leads" gave  results well within experimental errors and t h e i r a p p l i cation to measurements where cable potheads are located on poles i s very u s e f u l . The procedure f o r tests with f a r end c o r r e c t l y terminated i s as follows: a.  Set up c i r c u i t shown i n Pig. 7b  b.  Connect Z  c.  Record readings of V f o r f a u l t e d cable.  d.  Record readings of V f o r a good cable.  e.  Plot curves of cable input impedance against frequency.  f.  Subtract curve f o r good cable from curve f o r faulted cable, getting net r e s u l t due to f a u l t alone.  g.  Difference i n frequency between adjacent peaks of resultant curve represents a wavelenght.  1.  From propagation constant of cable, f i n d distance to f a u l t .  Q  across f a r end of cable as i n F i g . 10b. r  and V  c  as frequency i s varied  r  and V  c  as frequency i s varied  Repeated tests on same cable y i e l d the same r e s u l t i n dicating the r e l i a b i l i t y of the method.  The range of  frequency used with the present type of equipment i s 100 Kc to 4 Mc approximately.  35  Bibliography 1.  Blankmayer,W.H.  Power l i n e F a u l t Locator, p.166  Electronics.Vol.17 No.l 2.  Chandler, Steward,Jr.  January 1944.  The"S"-function Method of  Measuring Attenuation of Coaxial R.f. Cable, pp.616-19*Electrical Engineering.Yol.64 Ho.9 September 1945. 3.  Golding, E.W.  E l e c t r i c a l Measurements and Measuring  Instruments, Pitman & Sons,ltd., 4.  Honnel, M.A.  Location of Line F a u l t s . E l e c t r o n i c s .  Vol.17 No.11 5.  Noakes.F.  November 1944.  High Frequency Method of Location of Faults  on Power Cables, pp.46-7 No.13 6.  S l a t e r , J . C.  Vahey,J. A.  E l e c t r i c a l News.Vol.53  July 1 1944.  1  "  Microwave Transmission. McG-raw-Hill  Book Co.,Inc. 7.  1944.  1942.  Eecent Developments i n Cable F a u l t Locating.  p.96. Edison E l e c t r i c I n s t i t u t e B u l l e t i n . Vol.7 March 1939. 8.  Woodruff, L. F.  P r i n c i p l e s of E l e c t r i c Power Transmis-  sion. John Wiley & Sons,Inc. p.97.  1938.  36  ACKN OWLEDG-EMENT The author wishes to express h i s appreciation to Dr. P. Noakes i n suggesting  the topic and f o r h i s  h e l p f u l assistance during the course of the research.  An  Abstract of the  High Frequency Method of Locating Power Cable Faults By E r v i n Joseph Nalos  A Thesis submitted i n P a r t i a l Fulfilment of the Requirements ments f o r the Degree of Master of Applied Science i n the Depart0ment of E l e c t r i c a l Engineering  The University of B r i t i s h August  1947  Culumbia  The Location of a f a u l t i n a power cable i s by no means a simple task and the techniques used at present warrant further improvement.Many methods of f a u l t l o c a t i o n have been devised but each has i t s p a r t i c u l a r limitations.Some of these methods include D.C.  and A.C. bridge  methods,echo-ran-  ging methods,and high-frequency methods.The l i m i t a t i o n s and i m p r a c t i c a b i l i t y of these various techniques has been the main reason for this research. In this thesis,a review of the high-frequency method has been made,resulting  i n the development of a method of l o -  cating high-resistance faults.Expressions,permiting the use of this improved method i n instances where cable potheads are rel a t i v e l y inaccessible have also been developed and checked experimentally .Brief l y , the method consists of determining input impedance of the cable with i t s remote end  the  terminated  i n i t s surge impedance.This i s done by simultaneously measuring the voltage drops across a standard r e s i s t o r and across the cable.The r a t i o of these drops Is an i n d i c a t i o n of the cable impedance at that frequency.Obao'vations are taken on a band of frequencies on a faulted cable and on a good cable,both terminated i n the c h a r a c t e r i s t i c impedance.The difference of these two effects i s attributed to the r e f l e c t i o n s from the f a u l t . From the p l o t of the impedance as a function of the  frequency,  by a short graphical computation,the distance to the f a u l t  may  be obtained.Faults as high as twenty times the surge impedance have been successfully located on r e l a t i v e l y short lenghts of cable.The distance to the f a u l t has been estimated well within  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0105076/manifest

Comment

Related Items