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The location of flashovers on Transmission lines Evans, Donald John 1949

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LB 4 ftf E 7 U Copt THE LOCATION OF FLASHOVERS ON TRANSMISSION LINES by Donald John Evans 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 SCIENCE In the Department of MECHANICAL AND ELECTRICAL ENGINEERING Approved: In charge of major work. S^ad of Department. THE UNIVERSITY OF BRITISH COLUMBIA 19^ 9 THE LOCATION OF FLASHOVERS ON TRANSMISSION LINES 3 U M M A R Y The object of t h i s thesis Is to f i n d a method for loc a t i n g transient as well as permanent f a u l t s on transmission l i n e s . Transient f a u l t s are those l a s t i n g f o r a f r a c t i o n of a second or so which do not cause serious enough damage to necessitate immediate repairs before the l i n e may be re-energized. However, transient f a u l t s such as i n s u l a t o r flashovers may cause enough damage to be a p o t e n t i a l permanent outage. I t i s thus desirable to be able to locate the po s i t i o n of the f a u l t , and to Inspect the l i n e and i n s u l a t o r s so that they may be repaired i f necessary when the l i n e can be conveniently removed from service. The method that seemed most desirable was based on the echo-ranging p r i n c i p l e such as i s used i n radar. This method has the advantages of accuracy and ease of i n t e r p r e t a -t i o n . A damped sine wave pulse Is generated at short i n t e r v a l s and fed onto the transmission l i n e by means of a coupling capacitor. This pulse t r a v e l s along the l i n e and i s p a r t i a l l y r e f l e c t e d from any disc o n t i n u i t y such as a flashbver to• ground. The transmitted pulse, and pulses r e f l e c t e d from the end of the l i n e and the f a u l t are shown on a viex^ing tubej the distance to the f a u l t being found by proportion. The l i n e i s pulsed only on the occurrence of a i v f a u l t ; thus any interference with radio i s eliminated. The pulse generator i s tripped by zero-sequence current or from the surge created by the f a u l t i t s e l f . The pulses were to be recorded on a skiatron or memory tube which holds the trace on the tube u n t i l i t i s erased at w i l l by the operator. This eliminates the necessity of photographic equipment and the disadvantages of delay and inconvenience of developing the f i l m . The work accomplished on the project included the theory of wave propagation along transmission l i n e s and the r e f l e c t i o n to be expected f o r arcing ground f a u l t s . A pulse generator was b u i l t to produce either a damped sine wave or a sharp-fronted wave with exponential decay. Experiments were -car r i e d out on coaxial cable with carbon and o i l arcs as the f a u l t , but no experiments were carried out on actual transmission l i n e s as no l i n e xiras available. The r e s u l t s of these experiments and the theory indicate that the method should be satisfactory on transmission l i n e s . Donald John Evans, University of B. C. i CONTENTS SUMMARY • Page 4i-t-I Introduction / I I Review of Lite r a t u r e 3 I I I Investigation 6 A. Choice of Method 6 B. Characteristics of Power Arcs 7 C. Theory of Wave Propagation 3 1. No-loss l i n e s 8 (a) Single-wire Lines a (b) Multiconductor Systems // 2. Attenuation and D i s t o r t i o n Z-5 - (a) S i n g l e - c i r c u i t Lines z5 (b) Multiconductor Systems zs 3. Reflection of Waves 30 (a) General Equations 3 0 (b) Reflections from Arcs 33 (c) Reflections from Terminations 3S (d) Reflections from Transpositions 39 (e) Successive Reflections *° (f ) Effect of Insulators * 2 D. The Equipment +3 1. General Description ^3 2, Pulse Generator is 3» Tripping C i r c u i t s • k. Recording the Information S3 5. Line Coupling Equipment ^ E. Experimental Results s«3 IV Discussion ^ V Conclusions 6 $ VI Literature Cited e a 11 Page VII Acknowledgments VIII Diagrams 1. System of conductors and their images tz 2. Ci rcui t constants for mutually coupled c i r cu i t s 3. General multiconductor system 3/ 4 . Configuration of the transmission l i n e , $ 5 5. Graph showing how the reflected voltage varies • with grounding resistance. 6. Lat t ice showing successive reflections % *o 7. Lat t ice showing successive reflections for the fault close to the sending end S. Block diagram 9. Wave shapes 10. Circui t diagram of the pulse generator 11. The thyratron tripping c i r cu i t 12. Two tube thyratron t r ip c i rcu i t 13. Line coupling apparatus 14-. Experiment with carbon arc 15. Experiment with an arc i n o i l 16. Pulse generator used for carbon arc experiment 1 THE LOCATION OF FLASHOVERS ON TRANSMISSION LINES 1 INTRODUCTION The purpose of t h i s i n v e s t i g a t i o n Is to develop a method f o r l o c a t i n g transient as well as permanent f a u l t s on transmission l i n e s . Methods now exist f o r find i n g permanent f a u l t s accurately. However, transient f a u l t s comprise approximately ninety percent of a l l f a u l t s , and are important because a damaged l i n e or i n s u l a t o r may result i n a permanent outage at some future time. I f the f a u l t y i n s u l a t o r ean be located accurately, i then the time and money spent p a t r o l l i n g the l i n e can be considerably reduced. Even a small reduction i n the amount of p a t r o l l i n g would J u s t i f y the i n i t i a l cost of the equipment. Thus i t would seem that problem i s economically worthwhile. The method developed uses the echo-ranging p r i n c i p l e . This p r i n c i p l e i s by no means new, and i s being used at present to locate non-transient f a u l t s on transmission l i n e s and cables. In the equipment developed, a pulse generator i s to be tripped from the i n i t i a l surge of the flashover i t s e l f , or from the zero-sequence current i n a transformer bank neutral. The pulses are r e f l e c t e d from the arc and returned to the sending end where they are shown aiong with the transmitted pulse on a viewing tube. The pulses are sent out f o r a time i n t e r v a l exceeding the arc duration i n order to ensure a clear r e f l e c t i o n from the end of the l i n e . The distance to the f a u l t can then be found by proportion. 3 11 REVIEW OF LITERATURE Several methods for lo c a t i n g transient f a u l t s are i n use, and have met with various degrees of success. Before these methods can he judged i t i s necessary to state the desirable q u a l i t i e s of a f a u l t locator. These are as follows! ( l ) accuracy; (2) ease of inte r p r e t a t i o n ; (3) simple recording; (40 low cost; (5) safety. There are various f a u l t - l o c a t i n g devices which do not depend on echo-ranging p r i n c i p l e s . One of these devices i s adapted to measure and record varia t i o n s i n current and po t e n t i a l at one or more points i n the length of the l i n e by 20 means of magnetic l i n k s . The f a u l t i s found approximately by calculations dependent on the degree of magnetism of the l i n k s . This method, however, lacks the q u a l i t i e s of accuracy and ease of interpretation. Another system uses an annunciator ammeter. Precision i s l i m i t e d here also because the current i s measured i n steps^ and because of v a r i a t i o n i n tower footing resistance. A method using automatic oscillographs has been developed to locate f a u l t s ^ . The distance i s found by analysis of the recorded currents and voltages. The accuracy of t h i s system i s of the order of ten per cent. Thus the main disadvantage of these and other such devices i s lack of accuracy. Fault-locating methods u t i l i z i n g t r a v e l l i n g waves come closest to f u l f i l l i n g the desirable q u a l i t i e s as l i s t e d previously. These systems can be c l a s s i f i e d under three main headings. 20 For references see Bibliography, (1) Fault-Generated surge method . This method has Just recently been developed^ and from i t two types of f a u l t l o c a t o r have been produced. In one of these the surge from the f a u l t t r a v e l s to the station end of the l i n e where i t s t a r t s a timing device. I t i s then r e f l e c t e d from the bus back to the f a u l t where i t i s returned once more to the end of the l i n e . The time i n t e r v a l between the two pulses i s proportional to the distance from the f a u l t . The accuracy of t h i s system depends to a large extent on the steepness of the wave front and the length of the time base employed. The investigators hope that with refinements a precision of plus or minus 0.1 mile w i l l be obtainable. The l i m i t a t i o n s of t h i s f a u l t locator are: operation on spurious pulses; the necessity of photography; and the t r a i n i n g required for i n t e r p r e t a t i o n of the r e s u l t s . The second method makes use of both of the surges which originate at the f a u l t and t r a v e l down the l i n e i n opposite directions. One arrives at the near end of the l i n e and t r i g g e r s a timing device. The other arrives at the f a r end and causes a radio transmitter to send out a pulse which stops the timing device. The time i n t e r v a l i s used to f i n d the distance to the f a u l t . An electronic time i n t e r v a l counter records the distance d i r e c t l y i n miles. This system h a s . a l l the advantages l i s t e d except low cost. I t i s thus economically p r a c t i c a l only where a radio l i n k i s already i n existence. (2) Frequency Modulation Method. A high frequency voltage with l i n e a r v a r i a t i o n of frequency i s Impressed on the end of the l i n e . The waves t r a v e l to the f a u l t and back, and the difference i n frequency at the sending end i s thus proportional to the distance to the f a u l t . This system has not the accuracy desirable. (3) Echo-Ranging Methods. The Hydro-Electric Power Commission of Ontario have a transient f a u l t locator under 21 • • development • A high frequency burst Is impressed through a coupling capacitor onto the transmission l i n e . The l i n e i s monitored t h i s way continuously, and the pulses are recorded by means of an automatic photographic attachment f i t t e d to the cathode-ray tube. This method i s accurate and, e a s i l y i n t e r -preted, but has the disadvantage of requiring photographic equipment. Also the pulses must not have a frequency that w i l l i n t e r f e r e with carrier-current devices or radio waves. Experiments performed by the Commission indicate that r a d i a t i o n from t h e i r pulses was i n the l i m i t s allowable. 6 111 INVESTIGATION A. Choice of Method A review of the e x i s t i n g methods indicates that one of the main disadvantages i s the necessity f o r photography which e n t a i l s a delay before any information i s ava i l a b l e . To eliminate t h i s disadvantage i t was decided to use a long memory tube which retains the trace u n t i l i t i s examined and erased by the operator. An echo-ranging method was chosen since i t i s suitable f o r t h i s type of recording^and has the additional q u a l i f i c a t i o n s of accuracy, ease of i n t e r p r e t a t i o n , and reasonable cost. To eliminate any interference with radio, since pulses of broadcast frequency may be used, the pulses are sent out only for a f r a c t i o n of a second when the f a u l t occurs. I t has been suggested that the high voltage pulses o r i g i n a t i n g from the f a u l t and t h e i r successive r e f l e c t i o n s may obscure the r e l a t i v e l y weak transmitted pulses. However, the r e f l e c t e d fault-generated pulses are soon attenuated, have a d i f f e r e n t shape from the a r t i f i c i a l pulse, and are not synchronized with the sweep. On the other hand, the transmitted pulses should show up c l e a r l y because of the many retraces. The r e s u l t s w i l l depend l a r g e l y on the tube c h a r a c t e r i s t i c s . I f the f a u l t surges give more trouble than anticipated, the a r t i -f i c i a l pulses may be delayed u n t i l these surges have attenuated greatly, but not u n t i l the power arc i s ex-tinguished. B. Characteristics of Power Arcs. o Something of the c h a r a c t e r i s t i c s of power arcs must be known before the type of r e f l e c t i o n to be expected from an arcing ground can be calculated. Interest i s thus mainly concentrated on the resistance of the arc path. An average voltage gradient at current peak for 6o-cycle arcs i n a i r with currents ranging from l e s s than 100 to over 20,000 amperes peak current i s JM- v o l t s per inch-' 0. Thus at peak current f o r say a 7-root arc, the voltage would be. 22>50 v o l t s . The corresponding current depends on the various impedances to the f a u l t , but would probably be over 5 0 0 rms amperes or 7°7 peak amperes. The r e s u l t i n g arc resistance i s H- ohms at peak current. For other points i n the h a l f cycle the resistance increases.SLightly,and becomes much higher near the zero current point. . The arc resistance would be the only consideration f o r a l i n e - t o - l i n e f a u l t . However, for arcing ground f a u l t s which comprise about 20 per cent of a l l f a u l t s , the resistance to ground depends also on the tower footing resistance. This resistance may vary from below an ohm to thousands of ohms, but i n general w i l l probably be below 25 ohms. C, Theory of Wave Propagation. I t i s desirable to be able to calculate the modifications that a pulse undergoes as i t tr a v e l s along the transmission l i n e , and to know, what magnitude and shape of r e f l e c t i o n i s to be expected from a given discontinuity. As an approximation, the losses are sometimes neglected as t h i s r e s u l t s i n great s i m p l i f i c a t i o n i n mathematics. 1. No-Loss Lines. (a) S i n g l e - c i r c u i t l i n e s . The fundamental d i f f e r e n t i a l equatio.ns f o r waves on s i n g l e - c i r c u i t l i n e s w i l l now be derived. The derivation follows that given i n reference 2, Chapter 6. For a short length of l i n e §x l e t /*- 5 resistance i n ohms per unit length j£ a Inductance i n henries per unit length c « capacitance between conductors i n farads per unit length g a leakage conductance between conductors i n mhos per unit length e. s voltage between l i n e s at the beginning of $"* A. m current i n l i n e s at the beginning of $-x | e ! j e+Se ! -i. i H f x The change i n voltage along - ^ = fx S"* The change i n current along £*- = - <zcf g-x. -c^S As Sic-— o the equations become where /o= -|-D i f f e r e n t i a t i n g © with respect to :* and sub-s t i t u t i n g , i n (f) D i f f e r e n t i a t i n g © with respect to % and sub-s t i t u t i n g i n (7) l e t ^ 7 C * . Then ^ / ^ J ^ y ^ - T T ^ y = Jr/(P^T-^ Prom and <g) Treating these as ordinary l i n e a r d i f f e r e n t i a l equations the solutions are ^ = £ C f € O where /?, 8> c, D a r e functions of £ only. Prom equations © , ® , and (§) 10 Since the equation must he true f o r a l l value's of 5C , i t must be an i d e n t i t y . Equating c o e f f i c i e n t s • J s * r A. r. * "/HIE 3 Let and l e t Z*/Z. .\ 3 = 2 /E±E±& Thus (§) and (f) become , r ./ex A X 7 _ <<- = € c +€ a = fS /?- j € B 3LL J For a l i n e extending to i n f i n i t y , B i n equations (2) and ® must be zero since « and ^  must be f i n i t e as -x—*- **> _ A x e = e /? 9 Thus — where 5 i s ca l l e d the surge Impedance operator. For very steep wave fronts the effect of the operator p Is predominant and 5 —• j? ~ . j? i s c a l l e d the surge Impedance, I f the applied voltage i s given as a function of *t Thus from (?) „ , For the loss-free l i n e /t = Thus h =• j£ and j = Z * s j* € ~£(*) But by Taylor 1s theorem This equation shows that f o r an i d e a l l i n e the wave trav e l s with no d i s t o r t i o n or attenuation at a v e l o c i t y / AT (b) Multi-conductor Systems. The previous section was concerned with a s i n g l e -phase l i n e with either a l i n e or p e r f e c t l y conducting earth return. When p r a c t i c a l power systems are con-sidered, the above theory must be modified because waves are induced i n the conductors not carrying the main waves. A knowledge of the magnitude of these induced waves i s necessary for the c a l c u l a t i o n of the r e f l e c t i o n expected from various types of f a u l t s . These induced waves also cause a modification i n the type and rate of attenuation and d i s t o r t i o n of the main waves. I f losses are neglected, i t can be shown that the currents and voltages on the l i n e s of the system are related by a set of l i n e a r equations. The follow-ing treatment follows that given i n reference 2, Chapter 6. F i g . 1 shows the system of m p a r a l l e l f i x e d conductors to be considered. The dimensions are P s? radius of conductor A. h =s height of 1 conductor /L above the zero p o t e n t i a l plane & s distance between/? and the image of s b a distance between A. and 5 F i g . 1. System of conductors and t h e i r images. From e l e c t r o s t a t i c s the following equations may be written: <Z, = P»<?, +• PziQz t- ' ' ' + p», Q~v \ <Z*. = yO/z Q, *• P*z <?**•••• <$>~*- \ <£n = Pin Q, +• Pa.n Cp z p»n <p/>t J where <Zk. i s the po t e n t i a l of conductor k. t QM. the charge per unit length, and p^ and /o^ are the reciprocal of capacities and can be calculated accordingly. The general equations are* 13 -1 QLA. 5 i A ~ x ? x / o " (farads) per cm /° -1 Pssi = = 2 x 9 w o " (farads) per cm D Equations (7s) may be written Q / n = /CVw/ »*- A A T J <Z 2. /-si-r-s f/minor- o-f D for which cofacf-or /'s prs 7 where /Cts = (-/) /G /7 and D = Pit. p\* • • • Pn, /9 I t can be seen that , P/ts , Av»/t are p o s i t i v e , and that A/ i s i s negative i f /*• 7* 5 . The f l u x l i n k i n g conductor /«- due to i t s own current i s « ^ / i,and the f l u x l i n k i n g i t due to the current i n eonductorSis L/ts ycs where L^A. « self-inductance c o e f f i c i e n t of conductor /*•, onof Z*,*mutual-Inductance c o e f f i c i e n t between si and s. Thus the t o t a l f l u x linkages f o r the conductors are <P, - *L,i -c. -t- L /* * -r ' -f~ Li/r% ) The inductances are given by .A. S to -9 hanry p<zr> cm ZO 2 / The general d i f f e r e n t i a l equations of the t r a v e l l -ing waves w i l l now be obtained. The e i r c u i t con-stants Involved are shown In f i g . 2 and designated as follows: / • A V V W V V V V V V V / I , o r r n n c r Y v y n f yvyyvvvvw^ ( rrrinrrrirrY J I I dx »f F i g . 2, C i r c u i t constants f o r mutually coupled c i r c u i t s . s self-eapacitanee c o e f f i c i e n t of conductor ^ /T/is « mutual-capacitance c o e f f i c i e n t between si and s series resistance of conductor / i leakage conductance to ground of conductor /z. s leakage conductance between and s also l e t 1 5 The leakage currents are ~ Cr/t <Z, -h G->z € 2 +• - • - -r Cri<n <2/r» = 9"*' (<Zm - <2i) r (- <Zz ) +... y. g„„ ^ The d i f f e r e n t i a l equations of the f i r s t conductor are Jot j /t - = y-^/ = Y, <z, v v;2 <Z2 + • - • + Ym<2~ D i f f e r e n t i a t i n g equation (fj) with respect to * and substituting equation (£4) there i s where +(2* Y""i + ?i* Y»z. Zl-n Y~s*) <2. JAS = Yis y £ 2 / 1 Yzs + 2s* Yss ¥•'•'+• z*-*« Yr" The complete set of d i f f e r e n t i a l equations f o r the m conductors are then 0= +• Jt2. <ZZ +• • - • + Jim <z<* O- Jzi<Z, r /?zz Gz + • • • Jxm <2<n where the J's are operators i n the time de r i v a t i v e p= , and the A's are operators i n both time and space derivatives. For any C to have a f i n i t e value the determinant of the c o e f f i c i e n t s must be zero. 25" 2 6 2 7 28 1* Thus An 7n ' • • J/<n A*z • • Jzrtn. e = o 29 J/ni J/lftZ • ' s^tn fi I t can he seen that equation(£|)will lead to a polynomial of degree sn i n -j^p- and degree /n i n p*= ^ 2 • This p a r t i a l d i f f e r e n t i a l equation w i l l give the most general solution to the problem. I f there are no losses the equations are simplified considerably since and . Z Y = P * L K Thus equation (z^ becomes and equation(gj) becomes A**. - (P2 Dsi* -I f 6 i s assumed to be a traveling wave e = f *~ SWJ& ) Thus Jks<Z= AT* D«s ft-K + su-Jr) A/to. <Z = (/v-*D*«. ~ f ) f Y'*+'tr*r) = SO-zf"(x+AsXr) Where f denotes the second derivative with respect to X. Equation now becomes AT* Pz, /V-1 Bzz On dividing by A r ^ / ^ ^ c +-/wjt^equation gives D>*. '• • Dz, Bzz • • Dm = O Dm/ &4*m 17 The v e l o c i t y /if must s a t i s f y t h i s equation of degree ^  i n Af . Thus there are 2m values f o r the v e l o c i t y of propagation ( m po s i t i v e and /n. negative). On each conductor there then can exist m p a i r s of waves of v e l o c i t i e s tv, , , • • • , eaeh pai r consisting of a forward and backward wave. Therefore * e , = fiiC*•*• P* (* +/U}*)+•••• 36 Integrating equation p a r t i a l l y with respect to "X and remembering that Y~ f o r no losses = ]T/VA. [K» (f/A. - P,A. )+/c,z (f^ - p2« /C^fa* -A"*,«)J 37 For high frequency waves there i s no i n t e r n a l magnetic f i e l d and equations (2J) become LyiA = 2-ln ~ x /a"9 - 3l£ henrys per cm 3a LAS - ZM ~ * /o~9 = henrys per cm 39 where c = 3x/ocm per* se.c From equation (30) D/tS = C " Z CpM/Tis r PZA. Kzs + f>m* A^s) By reference to equations (te) and (/9) i t can be shown that I/ts - (O *r~ /i*s ( C* *~ S Thus = (c-z-/v~z) = 3 42 and d e t e r m i n a t e ^ ) reduces to 3mm(c~*-/V~*)s ° 43 Therefore /V=±c and a l l waves have the v e l o c i t y of l i g h t . 40 4/ Equations (37) thus become +• Cfr9 (f* -Fx) +-••+ cf*^ (f„-F~) ^. /n= tfn.ff, - F,) *• <fm (fx - Fj) +• • • • -h cfnn (fn- ^ ) ^  where <JAA. - c / c u = s e l f surge admittance } cf^s = c /TAS - mutual surge admittance. - J I f the current I s defined by equations s i m i l a r to ($6) the following equations are obtained: =«?// (<3>-<Z.) *- 3*i fa-Cm) + • 3»> (9*- &») y d rJzz(9*-G*)+- •• • + 3"* C9» <Z» = ^,n((Jl-G,) + C$i-&*)•+ • 1 ' ^ nn (9n~ Gn) j where 3**. = = so/n ~£ a s e l f surge impedance J/is = Pis -g0/n~- = mutual surge Impedance c b 3 - J ('x-'V't) a forward current wave G - G (-XT-irjt) - reverse current wave The 3*9 and y's are related as follows: A. 1-3 • >. _(-/) Qninor* o f Q T~or~ which cofetc+oi- is 3sis) D ]I jnS _ (~0 (minor* of D for which co factor- is &*s) where D -/ D =-3ii, 3*, • • • j», 3 m gzn - • • 3.»r, y« y*/ - • • y»i tjm y«A7 • • • CJnn 19' For waves i n one d i r e c t i o n only x- » x,, y- . - . y-± 4,, a tf„ <£, 4- • • ' +• C/ni <Zn where the plus sign i s f o r waves t r a v e l i n g i n the forward d i r e c t i o n , and the minus sign f o r waves tr a v e l i n g i n the reverse d i r e c t i o n . These l i n e a r equations w i l l be used l a t e r to determine the behaviour of t r a v e l i n g waves at t r a n s i t i o n points. I t i s possible to resolve t r a v e l i n g waves into components, each having i t s own v e l o c i t y and surge impedance. The advantage of t h i s r e s o l u t i o n i s that I t may be used to simplify the ca l c u l a t i o n of the behaviour of waves at t r a n s i t i o n points"*", and i t may also be used to sim p l i f y the ca l c u l a t i o n of attenua-t i o n and di s t o r t i o n 3 * ^ . A f t e r the wave components have been found at the point of appli c a t i o n , each component may be treated separately as a wave tra v e l i n g according to i t s kind. Thus the shape of the main wave i s found by addition of the attenuated and d i s t o r t e d component waves. The following method f o r ca l c u l a t i n g the wave 10 components was developed by Bekkar . He showed that the waves may be resolved into two components f o r three-phase l i n e s ; one consisting of waves equal on 20/ a l l three l i n e s , and the other consisting of waves adding up to zero on the three l i n e s . Satoh extended the method to f i n d component waves f o r a 26 double-circuit three-phase system . The theory i s developed f o r a s i n g l e - c i r c u i t three-phase system with completely transposed l i n e s . Thus the inductances and capacitances are the same f o r a l l three l i n e s and losses are neglected. Let X and X, be the s e l f and mutual inductances per unit length. Then: &<Z-3 <?^- dx: £ xr X, 2 XT d X: Prom equation (7^ Q,= C<2, ' " C e * -f-C'tZ.3 where A",* = Ar/3 - /Cz3 - c ' and A " " = A » Z = A - 3 S = c since A°/z * /°«s - /=>st and p „ = = /=>33 i n equation @ . Since = - t~ equation @ becomes dx: s i m i l a r l y = c ci<2 , f C , — c. y - C * * * <>5C = e , dTt f c, •f-C dxr S5 SG S7 Now the waves are resolved i n t o components so that 21 e«.= <Z--f<Z£> <z3 - <z -h ec Equations <|S*) are now substituted into equations (££) and to give s i x new equations. These together with equations (£3) give is. £ -x J<2c = c, ) - r c - <=,) d<2-b ] These are the w e l l known wave equations, the solutions of which are two tr a v e l i n g waves prop-pagating In opposite di r e c t i o n s . Thus the equations f o r waves of the f i r s t kind such that the voltages and currents are the same on a l l l i n e s are -c = r+-<s <2= Z. F - 2, G •5"S> GO 6/ 6Z 63 €4-'22 where F i s an a r b i t r a r y function of (-x.-Ar,X:) and G i s an a r b i t r a r y function of (-x.+-str,x: ) The v e l o c i t y i s given by _ /  and the surge impedance by ^ _ f±Ji±^j r c + 2.c, Waves of the second kind such that the voltages and currents on the three l i n e s add up to zero are given by -<C«. = A / ' f t <2«. = i?* Z7/ - £?z G, where /> Is an a r b i t r a r y function of (x-/fz*) and C7, i s an a r b i t r a r y function of s^z . The v e l o c i t y and surge impedance are given by / S i m i l a r l y - O A = Fa. -t-G-a 6 ^ 6 6 57 6S S9 70 Now the main waves may be expressed i n terms of these a r b i t r a r y functions with the a i d of equations ^ ) and (g) <2z= <c\+CZb = Z , CF-Gr) + Z * ~Cr*) } Z, = <Z *• « i = Z, (F~&) + &z (/=i - G,) X . A ^ * = F-/-G- -f Fa. *• G* 7t s(_3 = f «*«c = F-t-C3r + F3 + &3 72 Also since ^ c = o and <z«. /- <2 « ^  <zc = o , then F/+• F* ^-/^j = o and *-G-*. *- G-3 -O . Equations @ , (g) and (73) permit the c a l -c u l ation of the magnitudes of the component waves and induced waves when any of the conductors are given a surge. For example, assume l i n e 1 i s given a surge <z, and consider only the p o s i t i v e l y t r a v e l i n g waves. Since there i s no current, i n l i n e s 3 and 2 F+Fz-O ^ 3 - F+F3 - O But F, f F* + F3 = o and thus F= - F* = - F3 = __' . *. <Z/ = 2. F + 2* F, - Z, F r 2 F2* F = -*± Ft •az 2F g 2, + 22* 2, +22* - - *' The voltage waves on l i n e s 2 and 3 are then <Z i = <Z3 = & F r 2* Fi = 2,F +2, F3 2, 1- £ 2z The component waves are _ 22* <Z, g*<2, K a . = ' - <Z(fc = 2, +22* 2, +22*. ^/ + 2 2 z 2. +22*. So f a r a l l the theory has been developed f o r a three-phase system with no ground wires. I f ground wires are present, the capacity and inductance c o e f f i c i e n t s C, c, , X , X, of equations (ss) and(£7) must be modified. One way to calculate the new values i s to start with equations (5$) • Suppose, f o r example, that c a l -culations are to be made on a three-phase l i n e with two ground wires. Then <Zz- 3 « ^ / y ( ? z * ^ 2 . ^ - J K / C J + 3*z <Z.3- 3,3<C, + 3z3 ' C a r 3.33^3 +-£+3-<'V. ^3 S3 ^-S O = 3/s ' +3*S><- a rgss r^jrs -*-S Lines 4 and 5 are grounded and thus e*=^*-=o . The currents >c+ and >is are now found from the l a s t two equations and substituted into the f i r s t three equations to give <2/ =• -4-i 9.H +- ^-2 3 - * - 3 3j< <2-z ~ -<"3i*. *- <*-*-2zz ^33az (2,3= ^'3/a *-*3z\ ^3^,3 where J„ = j„ - - — i -3iz-- % 12 ^SS-3r^ 3.*T) *• 3*-* (*3*v 3*s—3*¥ 3 3n.tf. 3-ss - 3+s-- R ' a 3*i C^3f. 3ss ~3sy.333-) +3si ("3^3ST -33* 3t-r) oi/3— £13 ~ ~ ' o ? V V o?Trf- — 3**-T 25 3zz - 3, 3^(3iv 3rsr-3f¥ 3*r) *-3*r (3MM3ZS- ~3** 3«« 3rr- 3% 3*9- - 3*3 3xv (3'»3r*-3*-*3sr) + 3ZT(3++ 3sr - 3*+ 1 3*>M 33-3- - 3**-3M3 (33+ Sav-- 3s* 3,f) l~33*/3*+ 3sr - 3a* ) These surge impedances may be found i n terms of the l i n e dimensions by means of equations (g7) , and the r e s u l t s used to obtain the modified capacitance and inductance c o e f f i c i e n t s - For example, The equations f o r the modified surge impedances simplify considerably I f the l i n e s are completely transpo sed. I t Is seen that the effect of the ground wires i s to decrease the ef f e c t i v e surge impedance of the ungrounded conductor. As a pulse t r a v e l s along a transmission l i n e i t s maximum amplitude w i l l be decreased, i t s i r r e g u l a r i t i e s w i l l be smoothed out, and the voltage and current waves w i l l cease to be s i m i l a r . The d i s t o r t i o n w i l l be eliminated i f the r e l a t i o n s h i p Rc= G-L holds. This equation never holds f o r transmission l i n e s , but Is approached f o r loaded telephone l i n e s . Attenuation i s always present as 2 . Attenuation and D i s t o r t i o n , (a) S i n g l e - c i r c u i t Lines. 26'. i t i s caused by conductor resistance as modified by skin e f f e c t , leakage to ground, and d i e l e c t r i c losses. The attenuation and d i s t o r t i o n may be found from the solution of equations (//) and (jz) . An accurate solution of these equations Is d i f f i c u l t , and thus an approximation i s made as follows. In equations @ and @ A. 9 / (3 V Z Here Z9 - ~ jf£ a n d *nus the expression ^ i s small f o r large values of p or high rates of change of voltage and current. Thus and ^ 2 3. = — ^ - 73 Equations (/£) and (72) now become 2£. rp-t-fM.) f£5 79 These equations show that the voltage wave Is propagated without d i s t o r t i o n and subject to at. attenuation of £ ~ " per unit length. The current wave t r a v e l s at the same v e l o c i t y , but i s d i s t o r t e d as can be seen from the i n t e g r a l term of equation • 27 I f a more accurate solution i s desired, i t i s necessary to solve equations (JT) and (7z) f o r the pulse used. Thus f o r a damped sine wave voltage applied, the equations become £ -/ex _-«*.£: • , , AS- , c?2. which give e.= £€ n J 6 s,r,c*j* <s>3 2 If ot-h/Q-f-jo The solution of these equations i s not attempted here. The foregoing theory i s worked out f o r values of si, jg, c, and q constant with regard to frequency. The t h e o r e t i c a l r e s u l t s f o r t h i s assumption do not agree e n t i r e l y with p r a c t i c a l r e s u l t s . Thus modifications are made. The resistance Increases with respect to frequency owing to skin effect and eddy current losses i n neighbour-ing conductors. For earth returns the resistance increases owing to the change i n d i s t r i b u t i o n of currents i n the earth. . For two f a i r l y widely spaced conductors, the inductance f a l l s s l i g h t l y as frequency increases owing to the concentration of current at the surface. The reduction occurs i n the constant term i n the ordinary formula. For earth return the Inductance varies due to 28". r e d i s t r i b u t i o n of currents In the earth as f r e -quency changes, and i s always greater than the Inductance calculated by the method of Images which assumes /L=o . Both capacitance and leakage may be considered independent of frequency. To ^ account f o r these new factors a modified d i f f e r e n t i a l equation Is derived. (See reference 2). I f J I s assumed to be zero, then from equation (3) where A and j£ are functions of p . The Inductance j£ may be wr i t t e n as JC- J£*+*£<Z where ^-i I s the part due to Internal linkages and i s the part due to f l u x outside the wire and thus i s Independent of frequency. Now i t may be shown that the r e l a t i o n between the e f f e c t i v e resistance /L , the e f f e c t i v e Internal inductance , and the d-c resistance /?„ may be expressed by the equation and CL = conductor radius. Thus from equation <^ £) .) « P s- <g.A* \ where AT = For a c i r c u i t with earth return the d i f f e r e n t i a l equation can be shown to be 29 where P' s s p e c i f i c earth resistance i n ohms per cu.cm. /ZQ s d-c resistance of the wire. Thus the equation to he solved i s Following the procedure used i n obtaining equation (j?), the voltage may be written Expanding the index by the binomial theorem and neglecting a l l but the f i r s t two terms, since the rate of change of voltage i s large, the equation becomes x e= € ^ € E(?) so where (b) Multiconductor Systems. The attenuation and d i s t o r t i o n on multiconductor systems may be found from the solution of equation , However, t h i s solution would be d i f f i c u l t , and i t i s only approximate since the v a r i a t i o n of resistance and inductance with frequency i s neglected. Another method i s to break up the t r a v e l i n g waves into two kinds as done on pages /9 to 22 , and then to apply d i f f e r e n t i a l equation (§^ > to each kind of wave. The value of <f must of course he calculated f o r each kind of wave. The attenuation and d i s t o r t i o n of each kind of wave i s then c a l -culated, and the r e s u l t s added i n the proper manner to obtain the actual wave shapes on the l i n e s . This method i s simpler, and also takes v a r i a t i o n of resistance and inductance into account. For the damped sine wave voltage applied, the equation to be solved would be e«£ £ I € 3,N J This equation i s not solved here. However, equation (£9> has been solved f o r a unit function applied 2 voltage , and a sharp fronted wave with an exponen-t i a l d e c a y 1 5 , 1 7 . I f the pulse i s applied to one l i n e , the attenuation may be found approximately by means of equation (79) . The attenuation f a c t o r i s thus £ where ^ " j y • The resistance Si i s increased by skin effect above i t s d-c value. For a frequency of 5 0 0 kc the e f f e c t i v e resistance i s about 4-0 times i t s d-e value. For a t y p i c a l 220 kv transmission l i n e t h i s r e s u l t s i n an attenuation to one-half the o r i g i n a l pulse i n about 130 miles. Reflection of Waves. (a) General equations. The general equations f o r the behaviour of t r a v e l i n g waves on a multi-conductor system at a t r a n s i t i o n point have been developed by L.V. Bewley\ The network used i s shown i n F i g . 3» F i g . 3, General Multi-conductor System. The symbols are defined below: Y11 j y*2 9 - • • %» z s e l f surge admittances of l i n e s on the l e f t . Yz, Ys, etc- s? mutual surge admittances of l i n e s on the l e f t . = s e l f surge admittances of l i n e s on the r i g h t . 5^ 2 j <fnj e/c. ~m mutual surge admittances of l i n e s on the r i g h t . U, , Ui } • • •(/» a series Impedance network on the l e f t . IV, , ; -Wn s series Impedance network on the r i g h t . N, , • • • a admittances to ground. Nitt N23, ntc. n admittances from junction to Junction. 32 €" 3 x s pot e n t i a l and current incident waves. e', <c ' a po t e n t i a l and current r e f l e c t e d waves. e", A." s p o t e n t i a l and current transmitted waves. The general equations are [ V/i, +• YA, UA. ( A//i -r- NIA +-•• f M»*A) - Y„ Nisi U, +• [ Y/t/n +• Yl/n Un (NH +• NlA + • • • + NmA. ) - Y,N N,A U, - • • • - y ^ , A A ™ c/« ] (eo -e„ ' ) + M I A C*. * eT ) . . . y / s / ^ (<Ln-h(z'r, ) - ( / V * y A///i y - - • -f AS*,* ) fez/i y <zX ) = f e," y • - - y e ^ ) 9 2 C e ^ y c ^ - ^ f ^ f c z - e ; ) y - • * - ^ r < 2 - - e - ; ] = <2^ ' I A / * f y,,, <s/V • - y <Zn) 93 For an n-wire system n equations of type and m equations of type (gj) can be writ t e n , and these equations solved f o r the 2n unknowns e, • - • • <2/7 9 <2, • • • • <Zn i I f the mutual connecting networks are removed then N^g, N,,^, etc., are a l l zero and equations (gz) and (93) reduce to (H-MA.UA) [YA., 02/-€,') Yin (<Zn-<L'N)\ - NA (*A. <-<Z\) = <Z.", y- • • • Cfjtr, <Z.n 94 (e/tf <zk)~ UL[YA, (<L,- <Z') y • • + YA„ (<Z"-<z~)] 33 Reflections from arcs* As under Heading 111 B the resistance of the arc varies throughout the h a l f cycle of the 60-cyele wave. The magnitude of the r e f l e c t i o n s to be ex-pected may be calculated from the general equations. Thus i f the f a u l t i s on l i n e 2 , equations @ ) and(g) give N, = /Vj = o 9 6 A / a . -Therefore Cf„ (<z,-<z') +• c/l2 - <zi.) f c/,3 C<Z3-<23) = C/g,, <z'r +. c/tt (Zz +• C/z3 <2-3 / " <Zaf <ZZ = <Zz <Z.3 + <Z'3 = <Z*3 The transmitted and r e f l e c t e d waves are found by substituting (9^ In @ and solving the r e s u l t i n g equations. 98 Thus p e2 = 99 _ g g 8 [ y > y « - y / « y ^ 3 where /OO As an approximation i t i s assumed that the l i n e s are completely transposed, and thus average surge Impedances are used i n c a l c u l a t i n g the surge admittances. Equationsvthus become I f the pulse i s applied to one l i n e only, i t w i l l be of i n t e r e s t to calculate the r e f l e c t i o n to be expected when the f a u l t i s on the pulsed l i n e , and when on one of the other l i n e s . From equations (100) i t i s seen that the r e f l e c t e d voltage depends only on the Incident voltage on the fa u l t e d l i n e . This i s known d i r e c t l y i f the pulse Is applied to that l i n e . I f the pulse i s applied to one of the other l i n e s the incident voltage on the fa u l t e d l i n e i s found by means of equations (53) where ^ 3 = o i f the pulse i s applied to l i n e 1. Thus e* = e, e 5 = , 0 7 c* '/ 3.11 For transposed l i n e s , To obtain an approximation of the magnitude of r e f l e c t i o n to be expected on an actual l i n e , an example problem i s worked out. According to a re-port on 220 kv transmission l i n e s i n the United 9 States and Canada as given by an A.I.E.E. Committee , about 67 percent of 220 kv l i n e s have two ground wires. Thus the modifications to be expected due to the presence of these ground wires should be calculated. •35 The dimensions of an average three-phase l i n e with two ground wires are given i n F i g . k, •k Diet. 5T9.9.I Grd. W/>CS RtstotiuS - . 0208 ZS' *~0 7?otooo C A ; ACSR. t-roa " Outsio/<z Dictnn<fher' Ractios = - of-62 ' Pig. ty. Configuration of the Transmission Line. The l i n e a r r e l a t i o n s h i p s between voltages and currents on the l i n e are given by equations where the modified surge impedances are defined by equations @) . The actual surge impedances as given by equations @ are 3u = CO In = 4&l 3zt = J34. = 79-3 «?/z = €0/n 'J^£ - /04-.4- 3*3" 3**= 23 3i3= £0 /n '-^3. = 6*3 3*+= / 0 9 S J ¥„ ~ ?4.f 3,+ = eo/n = + 3*s-= /09S 3«j-= tos From these impedances the modified surge Impedances are calculated from equations (76) • 3,'*= + 69-0 3*3 = = €90 3,3- 65-3- 30 3 - 34-S 3*3 36 6 I t w i l l be assumed that the l i n e s under con-sideration are completely transposed, and thus average surge impedances w i l l be used f o r c a l -c u lating the surge admittances. Let 3 a s e l f surge impedance - hkh # 2 3* n mutual surge Impedance 5 57»5 These two values are substituted Into equation @) to give y a s e l f surge admittance a 2.32 x lCT^ c/' m mutual surge admittance s -2 ,66 x IO*"1*" I f the f a u l t I s on the pulsed l i n e , equation (to^ gives the r e f l e c t e d voltage as e2'= T g z f ^  " 7* . D After substitution, the equation becomes e; = -I f the f a u l t i s not on the pulsed l i n e the r e f l e c t i o n i s given by equation (£05) as <z, = e.3 <° 7:72 7.7ZG+034-3 These equations give the maximum value of the r e f l e c t i o n to be expected f o r a resistance to ground of • A table i s given below to show how the magnitude of the r e f l e c t e d voltage varies with grounding resistance. Fig. 5 Is a graph of the r e s u l t s . Due to the varying arc resistance, the r e f l e c t e d wave w i l l he shaded i n as shown approximately i n Fig* 5* Tower 3-rounding Resistance Minimum Arc Resistance Total Resistance to Ground c R m 1/G Reflected voltage wave Fault on Pulsed l i n e Fault on other l i n e 1 2 3 *.0.987e «0.127ge 25 2 27 -0,c$92e -0.1155e 50 2 52 -O.Slle -0.1050e 75 2 77 -0.7^3® -0.0962e 100 2 102 -0.6£6e -O.O^ .gge I I I I 1 ° 3LO 40 eo so too Grounding Resistance, ft. F i g . 5. Graph Showing How the Reflected Voltage Varies with Grounding Resistance. I t would be expected where the pulse i s applied to one l i n e only, that the r e f l e c t i o n would not be affected by adjacent l i n e s as they are not carrying current. Thus from single l i n e theory the magnitude of the r e f l e c t i o n would be 3* This expression may be shown to be equivalent to equation by means of equation (gd) • (c) Reflections from Terminations. For the majority of l i n e s the termination consists of transformers. As an approximation, the transformer w i l l appear as a capacitance to a high-2 frequency pulse . The e f f e c t i v e capacitance O may be calculated from the expression cf ' /cZc9 (appro*) where C w = capacitance measured from end to end of the winding i n farads and Cy = capacitance to earth of the complete winding i n farads. To obtain some idea of these capacitances the values of Cf = farads and Cu,~ 9x /o~'z farads are taken. (See p. reference 2 ) . Thus O = /c«JCy • 9 x/o~"/bracts. Some idea of the effe c t of t h i s capacity on the applied pulse may be obtained by c a l c u l a t i o n of the impedance at pulse frequency. For frequencies of 300 kc and $00 kc the impedances are respect-i v e l y and 35^ -0-n. . This indicates that the r e f l e c t i o n w i l l be approximately that of an open c i r c u i t . According to Bewley 1 the'effective capacitance may vary from 0.0002 ;tcf to 0.001 /at f o r ordinary transformers. These values are con-siderably higher than that given above, and the approximation of an open c i r c u i t i s no longer v a l i d . The size and shape of the r e f l e c t i o n could be found by c a l c u l a t i o n . However, the r e f l e c t i o n magnitude w i l l be decreased from that f o r an open c i r c u i t . Reflections from Transpositions. A r e f l e c t i o n would be expected from a trans-p o s i t i o n i n a l i n e since I t represents a discon-t i n u i t y . I f the pulse i s applied between two l i n e s , a r e f l e c t i o n would be expected wherever the spacing between those two l i n e s Is varied at a transposition. However, i f the pulse i s applied between one l i n e and ground, a r e f l e c t i o n would be expected only when the s e l f surge impedance of that l i n e i s changed. From s i n g l e - l i n e theory the magnitude of the r e f l e c t i o n i s given by the expression e '- " '^ e For the example l i n e under consideration the s e l f surge impedances of the two outside l i n e s are equal. Thus a r e f l e c t i o n w i l l be produced i n only two of three transpositions. However, f o r these two trans-positions the r e f l e c t i o n w i l l be n e g l i g i b l e as i s seen by substituting the values of j?, and 3» . e = ± e,a o a o o s ez Thus one advantage i n applying the pulse from l i n e to ground i s that echos from transpositions w i l l not as l i k e l y be mistaken f o r f a u l t s , as i s possible i f the pulse were applied from l i n e to l i n e . However, echos from transpositions have some value i n f i x i n g points on the l i n e . Successive Reflections. When a pulse i s r e f l e c t e d from a discon-t i n u i t y i t w i l l be r e f l e c t e d again from the beginning of the l i n e , the magnitude of the r e f l e c t i o n depending on the terminal impedance. A convenient method f o r keeping track of these 1 r e f l e c t i o n s i s by means of a l a t t i c e diagram , Suppose, f o r example, that the pulse i s applied to the l i n e with the short c i r c u i t . The l a t t i c e diagram to be used f o r t h i s l i n e i s shown i n f i g . 6. As the f a u l t i s not a complete short c i r c u i t , waves w i l l propagate past the f a u l t as shown by the dotted l i n e s . The magnitudes of the r e f l e c t i o n s depend on the impedances at the points of discontinuity. The waves w i l l be d i s t o r t e d and attenuated as they t r a v e l along the l i n e , and i f the defining functions are known they may be i n -cluded i n the diagram. 77-c»ce D/'sfance. A/ong L/h<z F i g . 6. L a t t i c e Showing Successive Reflections. For the example shown the trace on the re-cording tube w i l l consist of a r e f l e c t i o n from the f a u l t and one from the f a r end of the l i n e . The many successive r e f l e c t i o n s reaching the tube a f t e r the end of the trace w i l l show up only very f a i n t l y on the tube as they are smaller and w i l l occur at a di f f e r e n t point on the screen f o r each pulse* I f the f a u l t i s close to the sending end, then successive r e f l e c t i o n s w i l l show up on the trace as shown by F i g . 7. These multiple echos can be re-, moved i f the output impedance of the pulse-sending apparatus i s made equal to the c h a r a c t e r i s t i c im-pedance of the l i n e . However, i t i s not necessary to remove these multiple echoes as they are easil y recognized as such. Fauf+ ' f i • 1 1 1 •— * 1 i 1 D i s t a n c e A/ong Lin^ —»-brtaf of Trace. F i g . 7, L a t t i c e Showing Successive Reflections f o r Fault Close to Sending End. Effect of Insulator Capacitance. As an ins u l a t o r may be represented by an impedance to ground, a r e f l e c t i o n would be ex-pected from each tower. However, the i n s u l a t o r capacity i s small, and as a re s u l t the r e f l e c t i o n I s very small f o r wave packets of the frequency being used. I f the capacity of an Insulator i s taken as lC r * A farads , then the reactance to ground f o r a frequency of 5 0 0 kc i s about 3OOOO/I, which i s large compared to the l i n e surge impedances of the order of 500ii. . Thus no v i s i b l e r e f l e c t i o n would be expected. D. The Equipment. General Description Before any equipment could be b u i l t i t was necessary to decide upon a suitable pulse shape. The pulse must be short enough to allow an echo to be recognized from a reasonably close f a u l t ; i t must not have any interference with radio waves or c a r r i e r equip-ment; and must be of such a character that i t can pass through a coupling capacitor onto a transmission l i n e with l i t t l e effect on i t s magnitude and shape. This l a t t e r consideration p r o h i b i t s the use of f a i r l y long duration u n i d i r e c t i o n a l pulses. For example, i f a O.OO^  uf coupling capacitor were used on a 60-kv l i n e with a surge impedance of 5 0 0 ohms, then the time constant would be 1.5 yU-eec. Thus I f a 1 0 ^ s e c . rectangular wave were impressed on the coupling capacitor, the l i n e voltage would consist of the i n i t i a l sharp r i s e of the pulse which would then die o f f exponentially. The t r a i l i n g edge of the rectangular pulse would produce a s i m i l a r pip i n the opposite d i r e c t i o n . On higher voltage l i n e s the coupling capacitor has a smaller capacity,and an even shorter time constant r e s u l t s . The only u n i d i r e c t i o n a l pulse that could be used would be a very narrow one which i s subject to comparatively high attenuation and d i s t o r t i o n . However, t h i s short pulse would have the advantage of accuracy, and i s a p o s s i b i l i t y f o r short l i n e s . The above considerations l e d to the choice of a high-frequency wave burst i n the form of a damped sine wave. Since the pulses are to be sent out for a short i n t e r v a l only, the interference with radio may be neglected. Interference with c a r r i e r equipment can e a s i l y be avoided by an appropriate choice of pulse frequency and the use of f i l t e r s to prevent mutual interference between the f a u l t locator and c a r r i e r equipment. The reactance drop i n the coupling capacitor may be tuned out with a suitable tuning c o i l . The pulse frequency i s not c r i t i c a l . I t i s l i m i t e d i n the upper d i r e c t i o n by increasing attenuation due to rad i a t i o n and skin e f f e c t , and i n the lower d i r e c t i o n by increased length of pulse and the r e s u l t i n g d i f f i c u l t y i n detecting near echos. F i g . S* i s a block diagram of the f a u l t locator. The f a u l t locator i s tripped by means of zero-sequence current or voltage i n i t i a t e d by the flashoover. A source of zero-sequence i s usually available f o r relaying, and may be used to f i r e a tri g g e r c i r c u i t which i n turn t r i p s a one-shot multivibrator. This multivibrator keys a tube i n the output of the pulse generator, and allows the pulses to be sent out on the l i n e f o r a period that Is somewhat longer than the inte r r u p t i n g time of the c i r c u i t breakers feeding the l i n e . Thus a f t e r the arc Is extinguished a clear echo w i l l be received from the end of the l i n e . The pulse generator starts.the sweep of the recording tube a few microseconds before the pulse BLOCK DIAGRAM FIG-- & Coupling = L — Capoc i to r Tnree - Phiasa. PovSG-r- Line frotec f i v e rube. Banc/ Pass F i l t e r A/lQster Mo/ti v/brator A-Delay C i r c u i t JL Cut- off 7o£<zs Shock O s c i l l a t o r 1_ One - Shot Mul ti vibrator T Triaoer C i r c u i t Start of FlybocK ^ J M r f Of W r W / E S H A P E S l From Master | Multivibrator-TO SYncft. P/at<z of */ I I From Master ' Mu/fi\ibrci.-for I i 7b Delay Circuit Pi a-re of"Z | Gr/at on pa lay Tube *3 Ou^puf of Ddlay Tube. *3 To Orioi of S^ock Output of J A o c A ' Tube. *f- I I I Output of Cuf-loff Tube 0 7 ana" Power Tube *3 Input to Cut-off rube. * T I Start- of Pulse 71 T, Is produced; thus allowing the transmitted pulse to he seen on the tube. Pulse, Generator The complete c i r c u i t /diagram of the pulse generator i s shown i n F i g . 1 0 . Tubes 1 and 2 comprise a m u l t i -v i b r a t o r which controls the time Inter v a l between pulses. The time i n t e r v a l should be a l i t t l e longer than the time necessary f o r a pulse to t r a v e l to the end of the l i n e and back which i s approximately equal to / O O Q ^n-sec, where X. i s the length of the l i n e i n feet. The frequency s t a b i l i t y of multivibrators i s poor. However, t h i s I s not a p a r t i c u l a r disadvantage since the sweep of the cathode ray tube i s synchronized with the outgoing pulse which thus appears at the same point on the trace each time. Pentode tubes are used In t h i s c i r c u i t , and coupling i s between the screen and control grids. Consequently, the plates have no extra loading as i n the triode type of multivibrator and steeper sides are obtained. The approximate wave shapes are shown i n f i g . 9 (a),(b). The negative rectangular wave from the p l a t e of tube 1 i s fed to the "synch", terminal of the £oss©r oscilloscope which i s b u i l t i n such a way that the negative-going side s t a r t s the flyback of the trace (time on Pig. 9 ) . A f t e r the flyback i s complete, the beam i s ready f o r the main trace. However, t h i s trace cannot begin u n t i l the "synch." terminal becomes p o s i t i v e CIRCUIT DIAGRAM OF PUL5E GENERATOR FIG. IO LIST OF P/*RTS R,- 2 1 0 0 0 -n. Ri • Sooao R,, =• 2ooou RiT • Sooo C, * 0 0 0 / c» * 0 00004 C,T = 0 oooov- ii. 9 /r>/7 Ri*. R„ = / n R,a ' - M O J O c*» 0 00/ 0 00007J c , „ - yo 1 r ^ J " m i R , . = R,i • • T n O - 00/ c „ . 0 OOO /<J7 s 0 - / L. t z 2S~ m h R+* y o o j R,z -. so<->oo Rao « jocoo - J V d O O C» = O-oo/ 0 O O O / i O Cx°* (J-O/ Rs, R,3 » / o o u o o /?.•/ - 20000 Rzt - #00 « O - O i " 0 o- 0/ Rt R,* , J o o o o = W O 0 000004- c „ = 0 OOOf Jo R> = (WOO R,, - » / M C , z 0 .0000/ 0 • 5 Ra- 5 J O O /?<» • <^J ri Ca - OOQOOZS c,* = 0 •S again at time T g. The width of t h i s negative pulse depends on the time taken f o r the completion of the flyback which i n turn increases as the speed of the main sweep decreases. Thus the width of t h i s negative wave i s determined by the slovrest sweep to be used, and i s found by experiment. The transmitted pulse must be delayed f o r a few microseconds a f t e r the st a r t of the sweep i n order that i t w i l l show on the trace. The f i r s t step i n producing the delay i s to apply the p o s i t i v e rectangular wave from tube 2 through condenser and r e s i s t o r Ry to a choke c o l l L 1 ? as shown i n F i g . 1 0 . The r e s u l t i n g wave form at the g r i d of delay tube 3 i s shown i n Fi g . 9 (e). The small r i s e i n g r i d voltage at time.T^ i s caused by potentiometer action of the r e s i s t o r i n series with the low ef f e c t i v e resistance of the g r i d to cathode of tube 3 . After the p o s i t i v e r i s e of the applied wave i s completed, the g r i d voltage returns exponentially to zero because of the inductance At time Tg the negative-going side of the wave from tube 2 suddenly cuts o f f tube 3 and causes shock o s c i l l a t i o n s i n the induct-ance L^. These o s c i l l a t i o n s are damped out a f t e r the f i r s t negative h a l f cyele owing to the g r i d drawing current on the following p o s i t i v e h a l f cycle. The r e -su l t i n g plate voltage i s a positive-going rectangular wave having a width which depends on the natural f r e -quency of the inductance (see F i g . 9 (d)). The accompanying i r r e g u l a r i t i e s do not af f e c t the next tube because of the large negative bias on i t s g r i d . This p o s i t i v e rectangular wave i s applied to the control g r i d of tube a. 6 A C 7 connected as a tri o d e . The g r i d i s biased past cut-off so that the tube con-ducts only f o r the period of the rectangular wave. The plate c i r c u i t consists of a variable damping r e s i s t o r , an air-core inductance, and a choice of various con-densers. When the g r i d i s driven p o s i t i v e , the tube draws a very high current as the plate i s connected to the power supply through the small resistance of the inductance. A f t e r about four ^ r-secs., the g r i d i s suddenly driven negative,, and the plate current stops very quickly and shocks the inductance into o s c i l l a t i o n . The frequency of o s c i l l a t i o n depends on whieh condenser i s placed i n p a r a l l e l with the inductance, and the number of o s c i l l a t i o n s i s c o n t r o l l e d by the variable damping r e s i s t o r shunting the L-C c i r c u i t . A triode connection i s used i n t h i s tube to obtain the low plate resistance necessary to damp out o s c i l l a t i o n s that tend to oeeur when the g r i d i s driven p o s i t i v e . A variable part of the output of the shock tube determined by the r e s i s t o r R2-j and potentiometer Rgij. i s fed into the g r i d of the cut-off tube. This tube i s connected as an ordinary amplifier except that f o r normal operation the switch 8^ i s on "automatic",and consequently the suppressor g r i d i s negative with respect to the cathode. Thus there i s no output from the plate. When i t i s desired to send pulses out on the l i n e , the suppressor i s temporarily connected to ground, and allows the pulses to be reproduced on the pjLate. I f the apparatus i s to be used to f i n d a permanent f a u l t where continuous pulsing i s desired, the suppressor g r i d may be connected d i r e c t l y to the cathode by changing switch S.^  over to "continuous". This modification allows a l i n e to be surveyed f o r f a u l t s before the breaker i s reclosed. The necessary power to feed the low-impedance transmission l i n e i s obtained from a 6L6 tube ( 3 ) connected as a triode cathode-follower fed from the plate of the cut-off tube. A choke-coupled cathode follower i s used to obtain high pulse output with low d i s t o r t i o n . A 4-00 ohm resistance i s placed i n series with the choke to bias the tube at the desired point. Thus when suitably tripped the pulse generator pro-duces pulses to be applied to the transmission l i n e and synchronizes them with the sweep of the recording tube. Tripping C i r c u i t s . As explained previously, the pulse generator i s to be tripped either from zero-sequence current, or from the i n i t i a l surge of the flashover. The l a t t e r method has the disadvantage of being susceptible to a greater number of f a l s e operations due to such things as switching surges and the sudden release of bound charges due to l i g h t n i n g . For eith e r method the pulses must be suddenly connected to the l i n e and then removed a f r a c t i o n of a second a f t e r the arc has been extinguished to obtain a r e f l e c t i o n from the f a r end of the l i n e . This i s accomplished with the a i d of the suppressor g r i d of the cut-off tube used i n conjunction with a long time-constant 7 one-shot electfcbn-coupled or pentode multivibrator. Pentodes are used i n preference to triodes to obtain a sharp front necessary f o r sudden application of the pulses. The r i s e time does not have to be as fast as that of the master multivibrator, however, and thus lower power tubes (6SJ7) are used. The action of t h i s c i r c u i t Is s i m i l a r to that of the master multivibrator except that one tube i s biased past cutoff to prevent continuous o s c i l l a t i o n . This i s accomplished f o r tube 6 by the voltage d i v i d e r consisting of r e s i s t o r s B.2l and Rg 2 which produce a bias of 33 v o l t s on the g r i d . Thus when the transmission l i n e i s operating normally, tube 5 I s conducting and the voltage drop across i t s plate r e s i s t o r (R^ j^ ) i s impressed on the suppressor g r i d of the cut-off tube. As the suppressor must be at least 120 v below the cathode, the plate supply f o r the one-shot multivibrator i s taken between ground and 200 v negative. The c i r c u i t can be tripped by a negative pulse applied to the control g r i d of tube 5 , or a p o s i t i v e pulse on the control g r i d of tube 6 . I f , f o r example, the g r i d of tube 5 were driven negative, the screen current would be reduced and the screen voltage would r i s e . Owing to the coupling between the screen of tube 5 & n d t n e control g r i d of tube 6, tube 6 s t a r t s to conduct, and consequently i t s screen voltage f a l l s because of the voltage drop i n r 1 7 # However, the screen i s connected through to the contfijol g r i d of tube 5 which i s thus driven more negative. The r e s u l t i n g cumulative action drives tube 5 t o cut-off and tube 6 Into conduction. The plate of tube 5 changes from a po t e n t i a l of nearly 200 v negative to ground pot-e n t i a l , and, being d i r e c t l y connected to the suppressor g r i d of the cut-off tube, allows the pulses to be sent out on the l i n e . i The period of conduction of tube 6* depends mostly on the resistances R-j^, R 1g ) and R ^ and the eondenser C^.. When tube 5 i s cut o f f , the g r i d of tube 6 i s connected to the power supply through R 1 5, R 1 9 > and Q^; and, being p o s i t i v e with respeet to the cathode, begins to draw current from the power supply to charge up Con-denser C-j^ w i l l also charge up through R-^ g but i t s resistance i s so large compared to R^©, that I t may be neglected. This charging process through R^ w i l l con-tinue u n t i l the g r i d on tube 6 i s s l i g h t l y below cathode p o t e n t i a l , when charging must continue more slowly through R^g. The screen current of tube 6 now begins to drop, and the screen voltage to r i s e . However, cumulative action cannot begin u n t i l the g r i d of tube 5 reaches cut-off. This depends to some degree on the time constant B^gC^ since i t determines the re s i d u a l charge l e f t on which must be removed by the increasing screen voltage of tube 6. As soon as the g r i d reaches cut-off, cumulative action begins and tube 5 I s driven to con-duction while tube 6 stops conducting. Now the plate voltage of tube 6 drops again, and the pulse generator i s disconnected from the l i n e . I t i s thus apparent that the pulse width of the multivibrator i s determined p r i n c i p a l l y by the resistance R^q which can be varied to give the desired length of signal. The small condenser C^y shunting t h i s r e s i s t o r increases the speed of action by allowing the inter-electrode capacities to be charged d i r e c t l y instead of through R^g. ' The one-shot multivibrator must be tripped on the occurrence of a f a u l t . I f zero-sequence current i s to be used to start the pulses, the thyratron t r i p c i r c u i t of F i g . 11 i s suitable. With no signal appliedjthe tube i s not conducting and the voltage across the tube and condenser i s equal to the supply voltage. On application of a large enough signal to the g r i d , the thyratron App/i<ZGf Zaro-Se<fue.r>c<z. Vo/-rs Bias Fig. 11. The Thyratron Tripping C i r c u i t . conducts suddenly, and the condenser Cg discharges, through the r e s i s t o r R^ u n t i l the plate voltage f a l l s below that necessary f o r conduction. The wave form at point "a" i s thus a sudden negative voltage which dries away exponentially as shown i n F i g . 11. This pulse Is applied to the control g r i d of tube 5 and t r i p s the one-shot multivibrator. The thyratron i s prevented from continued conduction by the four megohm r e s i s t o r i n series with the power supply. This r e s i s t o r i s large enough to reduce the current from the power supply below that necessary to keep the tube i n conduction. Reference to the c h a r a c t e r i s t i c s of the 2>gh thyratron tube show that with 300 v on the plate, the tube conducts f o r a d e f i n i t e g r i d voltage. The g r i d Is thus biased beyond t h i s point; the amount of additional bias depending on the minimum zero-sequence voltage desired to t r i p the equipment. This i s a valuable feature because zero-sequence current produced by switching may possibly be discounted with a large enough bias. A disadvantage of t h i s t r i p p i n g c i r c u i t i s that i t t r i p s only on the p o s i t i v e h a l f of the zero-sequence wave. Thus i f the f i r s t h a l f cycle were negative, t h i s time would be l o s t as f a r as the f a u l t - l o c a t i n g apparatus i s concerned. To overcome t h i s d i f f i c u l t y two thyratrons may be used, and the grids fed from a transformer with a center-tapped secondary as shown i n F i g . 12. 53-6 zte.ro- —a -JSOOv F i g . 12. Two Tube Thyratron Trip C i r c u i t . k-m Recording the Information. After a survey of d i f f e r e n t ways of recording the Information obtained during the flashover, i t was decided that a trace of the pulses transmitted and received would be most desirable. This method has the advantages of accuracy and ease of in t e r p r e t a t i o n of distance, as w e l l as giving information as to the type of f a u l t or multiple f a u l t s . I t also shows reference points such as trans-positions and Junctions which may help to locate the f a u l t . The accuracy of t h i s method depends l a r g e l y on the • length of sweep used to represent the transmission l i n e . For example, i f a 30-mile l i n e with say 10 supports per mile i s to be used; then with a l i n e a r sweep on a f i v e -inch tube, the flashover could probably be located w i t h i n two towers. For longer l i n e s the absolute accuracy would decrease proportionately. To offs e t t h i s , however, i t i s possible to use c i r c u l a r or s p i r a l sweeps and timing pips. The distance to the f a u l t i s e a s i l y obtained by proportion beeause the trace on the screen represents a map of the transmission l i n e . The disadvantage of any. non-linearity of the sweep i s e a s i l y overcome by a timing wave i n the form of pips or brightness modulation. Flashovers w i l l always give the c h a r a c t e r i s t i c echo of a short c i r c u i t . I f , hox^ever, the equipment were used to locate a permanent f a u l t , a d ditional information about the character of the f a u l t could be obtained from the size and shape of the echo. Although multiple f a u l t s seldom occur, t h i s method of recording w i l l detect them; the second f a u l t showing up as another echo on the trace. The "Skiatron" , a memory tube, was investigated as an a l t e r n a t i v e to the use of fluorescent tubes and photo-28* graphic equipment . This tube i s s i m i l a r to the ordinary cathode ray tube except that the fluorescent screen i s r e -placed by a screen consisting of a l k a l l - h a l i d e c r y s t a l s which become intensely coloured under electron bombard-ment. The length of time that the trace remains on the screen depends on the Intensity of electron bombardment. I t i s possible to obtain a trace which w i l l remain on the screen long enough f o r examination In d e t a i l at l e i s u r e . The trace may be inspected uflder ordinary l i g h t i n g , and af t e r the desired Information has been obtained i t may.be erased by the application of heat and l i g h t to the screen. ft Skiatron i s a trade name registered i n the United Kingdom i n the name of Scophony Ltd. under number 64OI79. These properties of the tube make i t suitable f o r the recording of the pulses. A record may be obtained by means of a tracing, or by photography with a simple camera. I t may even be s a t i s f a c t o r y to jiust note the required measurements from the tube. This method has the advantage of not requiring the complication and expense of a high-speed camera and f i l m * Also the r e s u l t s are immediately available since there i s no f i l m to be developed. A disadvantage of the Skia-tron tube i s that special equipment i s necessary to supply the heat and l i g h t f o r removal of the traee. Also during the time i n t e r v a l needed to obtain the i n -formation from the tube and to remove the trace, there i s a s l i g h t p o s s i b i l i t y of another transient f a u l t occurring. This d i f f i c u l t y could be overcome by the use of two tubes mounted such that one tube i s always i n operation. Further Information regarding the a v a i l a b i l i t y and cost of the tubes/was not obtainable from Scophony Ltd., and owing to lack of time, further i n v e s t i g a t i o n on these tubes had to be postponed. Line Coupling Equipment,. The l i n e coupling equipment consists p r i n c i p a l l y of a high-voltage coupling capacitor i n series with a power-frequency drain c o i l . The generated pulse i s applied between the capacitor and the c o i l . The c o l l must of course have enough Inductance to present a high impedance Pro-fccfive. Oojo F i g . 13. Line Coupling Apparatus. to the pulse frequency and carrier-current frequency, and yet be p r a c t i c a l l y a short c i r c u i t to power f r e -quency. Under steady-state conditions t h i s equipment would be adequate. However, i f the l i n e i s struck by l i g h t n i n g , a high voltage w i l l be incident on the drain c o i l with r e s u l t i n g danger to personnel and equipment. This d i f f i c u l t y i s overcome by means of a protective a i r gap placed i n p a r a l l e l with the drain c o l l . A t h y r i t e l i g h t n i n g arrester Is not necessary because the power arc i s extinguished by the high impedance of the coupling capacitor to power frequency. The gap may be set f o r a voltage s l i g h t l y higher than the maximum generated pulse voltage. The l i n e coupling equipment must present a high impedance to any carrier-current on the l i n e . This may be accomplished by the i n s e r t i o n of a wave trap i n series with the pulse output as shown i n F i g . 13. The wave trap consists of an inductance L^ i n p a r a l l e l with a condenser C^, the two forming a resonant c i r c u i t at the c a r r i e r frequency. The pulse frequency w i l l probably be higher than the c a r r i e r frequency, and w i l l thus pass through the condenser and the coupling condenser onto the transmission l i n e . The reactance drop i n these condensers w i l l decrease the pulse amplitude on the trans-mi ssion l i n e somewhat, but not too seriously f o r the sizes of coupling condensers used i n practice. This drop i n the condensers may be tuned out with a series i n -ductance. However, the inductance has the undesirable effect of slowing down the i n i t i a l amplitude of the damped sine wave. Because of lack of time, no experi-mental data was obtained on the effect that the tuning has on the pulse shape. E. Experimental Results, No experiments on transmission l i n e s could be ca r r i e d out as no l i n e s were av a i l a b l e . As a r e s u l t , a l l the equipment was tested out on coaxial cable. To obtain some information on the type of r e f l e c t i o n to be Currant- Limitina /?<zs/s/o/* Cos so/" Transmitted Pulse Return on o.c. at Arc Return on s. c. at Arc Return with Arc f r r r Pig. I*!-. Experiment with Carbon Arc. expected from arcs, experiments were performed with carbon arcs and arcs through a small gap i n o i l . The equipment used f o r the carbon arc i s shown i n f i g . ik with the r e s u l t i n g wave forms f o r a step wave input. I t i s seen that the resistance of the arc varies between that of an open c i r c u i t and a short c i r c u i t , but i s more often nearer that of a short e i r c u i t as indicated.by the darker r e f l e c t i o n shown on the negative pulse. The carbon arc sputtered considerably during i t s i n i t i a t i o n , and resulted i n appreciable back-ground disturbance. However, the r e f l e c t i o n from the arc was s t i l l e a s i l y v i s i b l e . After the sputtering had died •out, the background disturbance disappeared e n t i r e l y and the r e f l e c t i o n showed up c l e a r l y . I t i s noted that a somewhat weaker echo i s obtained from the end of the l i n e due to pulses s t r i k i n g the arc when i t s resistance i s high. The pulses are then r e f l e c t e d from the f a r end of the l i n e and pass again through the arc to the sending end. The apparatus used f o r the experiment with the arc i n o i l i s shown i n f i g . 15. The voltage was raised with the voltage regulator u n t i l the gap flashed over, and the echoes from the transmitted pulses were noted on the oscilloscope. The clearness of the r e f l e c t i o n varied greatly with the impedance of the current l l m i t e r and the power fed into the f a u l t . With a 1200-ohm cu r r e n t - l i m i t i n g r e s i s t o r the r e f l e c t i o n was not as clear as f o r a lower impedance reactor, and best r e s u l t s were obtained with no current l i m i t e r at a l l . This i s probably due to lowering of the arc resistance as wel l as Increased arcing time. The current fed to the f a u l t i n these experiments was l i m i t e d by the low kva r a t i n g ( l kva) Of the transformer used. A considerable amount of hlgh-frequeney high-voltage interference was noticed on the oscilloscope especially when cu r r e n t - l i m i t i n g impedances were used. I t was of high enough voltage to flashover the telephone-type GdrxzraJ-or' T Carbon Pro +<zc for^% 300 ' COOK Csaji) Ccrr<zr?-r L /mii~<z. r f Both 4JUUJUU 2 3 ° 4 ^ WAV£ SHAPES /?<z/~/<zcJ-/on as for Shorr Ci'rcui~r R<z.-P/<zc.-f-/bn as for Open C/z-cc//-/-|_ / ^K. S<ZC -(Apjor-ox.) F i g . 15 . Experiment With An Arc In O i l carbon protecting blocks, and i s caused by the low capacity of the transformer which i s unable to sustain the arc. From these r e s u l t s i t i s concluded that the more current fed into the f a u l t , the lower the resistance and the more nearly the r e f l e c t i o n approaches that of a short c i r c u i t . Thus i t seems probable that a good r e f l e c t i o n may be expected from the high-current power arcs on transmission l i n e s . The pulse used for the l a t t e r experiment was approximately one-tenth of a microsecond wide, and was obtained by means of the c i r c u i t shown i n F i g . l 6 . The po s i t i v e rectangular wave input pulse i s obtained from I ' ~ 3 S v 3/a 3 Fig. l 6 . Pulse Generator Used for Carbon Arc Experiment. the delay tube (No.3) and applied to the g r i d of tube 9. This i s a 6AG7 biased past cut-off to produce a negative rectangular wave with steep sides on the plate. The plate c i r c u i t contains a choke c o i l which tends to de-crease the steepness of the leading edge of the negative wave, but r e s u l t s i n a steeper t r a i l i n g edge. This i s a desirable effect because the t r a i l i n g edge only i s used by the next tube. The output of tube 9 i s d i f f e r e n t i a t e d by the capacitor 0^ and resistance R 1 with a r e s u l t i n g input to the g r i d of tube 10 (6L6) of a negative pulse followed by a p o s i t i v e pulse as shown i n F i g . l 6 . Tube 10 i s also biased past cut-off to produce an output of a negative-going rectangular pulse with a sharp leading edge and a somewhat slower t r a i l i n g edge. A very narrow pulse can be obtained i f the output i s d i f f e r e n t i a t e d to remove the low-frequency components. The two tubes used to obtain, t h i s pulse were b u i l t into the set f o r convenience. IV DISCUSSION Although the equipment has not been used on a trans-mission l i n e , i t i s expected from the t h e o r e t i c a l and p r a c t i c a l work done on the problem that the locator w i l l be successful. The example three-phase l i n e worked out i n the theory indicates that f o r a grounding resistance of 25_n,,a r e f l e c t e d voltage wave of approximately 90 percent of the incident wave i s obtained i f the pulse i s applied to the faulted l i n e . I f the pulse i s not applied to the faulted l i n e , the r e f l e c t e d voltage wave i s only about 1 1 percent of the incident wave. The pulse i s also attenuated i n i t s t r a v e l along the l i n e . The approximate attenuation formula shows that the pulse w i l l attenuate to about $8 percent of i t s o r i g i n a l value a f t e r t r a v e l i n g 100 miles. Thus for a f a u l t 100 miles away, the r e f l e c t e d pulse magnitude i s calculated to be 30 percent of the impressed pulse f o r the f a u l t on the pulsed l i n e , and 3 . 7 percent f o r the f a u l t on one of the other l i n e s . This l a t t e r f i g u r e shows that amplifiers w i l l be desirable. The equipment may be used to locate both transient and permanent f a u l t s . For transient f a u l t s the grounding resistance of the tower w i l l usually be low enough to give an e a s i l y detected r e f l e c t i o n . The brightness of the echo w i l l depend on the number of retraces made before the 63 breakers open and the arc i s extinguished. Even with the fastest breakers a few retraces w i l l occur before the l i n e i s opened. For permanent f a u l t s the l i m i t i n g f a c t o r i s the ground-ing resistance of the f a u l t . The smallest r e f l e c t i o n that can be recognized depends on the amount of background d i s -turbance, and must be obtained by experiment. The ground-ing resistance f o r a given magnitude of echo may be c a l -culated by means of equation o^^ » . For example, a r e -f l e c t i o n e f f i c i e n c y of 1 percent i s obtained f o r a grounding resistance of about 20000 Jfl f o r the l i n e considered. I t i s expected that the locator w i l l also indicate a conductor f a l l e n to the ground but not actually grounded. One disadvantage of the present method i s that the faulted l i n e i s not indicated by the locat o r . The size of the r e f l e c t i o n would probably t e l l whether the f a u l t was on the pulsed l i n e or one of the other two l i n e s , but i n general some other information would be necessary. One d i f f i c u l t y with the pulse now used i s that echoes from near f a u l t s w i l l be confused with the transmitted pulse. This drawback may be remedied somewhat on short l i n e s by an increase i n pulse frequency and a decrease i n pulse width, or by a change to a sharp-fronted pulse with an exponential decay. The accuracy of the method depends to a great extent on the length of sweep and the d i s t o r t i o n of the wave shape. The sweep length may be increased by the use of c i r c u l a r or s p i r a l sweeps. However, with a Skiatron tube the l i m i t a -t i o n may be i n sweep speed,as information from Scophony Limited gives the writing-speed of these tubes as approximately 200 meters per second. As time was not available to complete the project, certain th e o r e t i c a l and p r a c t i c a l problems had to be l e f t unsolved. One of the most i n t e r e s t i n g points i n the theory, the accurate c a l c u l a t i o n of d i s t o r t i o n and attenua-t i o n , had to be l e f t uncompleted. This solution would be of value i n deciding which points on the wave should be used to measure the distances accurately, and would also be useful i n determining the best wave shape to use. An accurate solution of the r e f l e c t i o n to.be expected from the end of the l i n e would also be useful. The shape w i l l be determined by the Euses and transformers. Some in t e r e s t i n g experimental work should also be carried out. The equipment should be t r i e d out on a trans-mission l i n e to check the calculations i n the theory. The pulse magnitude must be checked to see i f i t Is s a t i s f a c t o r y , and the frequency and width of the pulse should be varied to f i n d the one best f i t t i n g the requirements of narrow width low attenuation and d i s t o r t i o n , n e g l i g i b l e interference with c a r r i e r current, low modification from the coupling capacitor and a desirable shape for accuracy. The exponentially decaying wave should also be t r i e d out to see i f i t would be useful f o r short l i n e s . . A further investigation into the characteristics of the Skiatron tube or other memory tubes i s warranted. The tube must have a clearly defined image and a high enough writ ing speed to give the required accuracy. One d i f f i cu l t y * with these tubes i s that the trace has to be erased before another can be shown over it.- However, i t would not be de-sirable to have the tube inoperative during a storm since another fault may occur at any time. One solution to the problem would be to shift the bias on the tube s l igh t ly after an operation so that the next trace would be spaced from the previous one. Some work w i l l be necessary on l i ne coupling equipment. The effectiveness of the scheme suggested must be tested. I f the equipment i s to be ins ta l l ed inside a substation then a connecting l i ne of coax could be used. This introduces problems i n matching, since the characteristic Impedance of coaxial cable i s usually between 50 and 100-ft-'. Another unknown that can be found only by experiment i s the effect of the surge created by the flashpver i t s e l f on the pulse-sending apparatus. V CONCLUSIONS A fault locator has been developed for the location of transient as wjell as permanent faults . Theory and experiment indicate that the equipment should he capable of locating flashovers of Insulators since the arc resistance i s of the order'of two ohms, and the tower grounding resistance w i l l usually be small enough to give an easily detected ref lect ion. The distort ion of the applied wave i n i t s travel along the l ine has not been calculated. By an approximate method the attenuation has been found to decrease the pulse to one half of i t s i n i t i a l magnitude i n a distance of about 120 miles on a typical 220-kv l i n e . An echo may be received from the transpositions of a three-phase l i n e . For a typical three-phase l ine with two ground wires, however, the magnitude of this echo w i l l be of the order >of COS* percent of the Incident wave, and w i l l be theoretically zero for a three-phase l ine with f l a t spacing and no ground wires. I f the l ines were spaced ve r t i c a l l y , then definite echoes would be obtained from the transpositions. The echo from the terminal transformers and bus work can be used to mark the end of the l i n e . I f the fault Is less than half way to the far end of the l i n e , successive reflections w i l l occur on the trace unless precaution i s taken to match the output Impedance to the characteristic impedance of the l i n e . A pulse generator capable of producing a damped sine wave or sharp-fronted wave with exponential decay has been constructed. The generator has been used on coaxial cable with carbon arcs and arcs In o i l , and satisfactory reflections have been obtained. These experiments indicate a poss ib i l i t y of locating faults i n power cables by superposition of pulses on a high-voltage power-frequency or d-c voltage used to pro-duce an arc at the faul t . The pulse generator i s to be tripped by means of zero** sequence current i n a transformer bank neutral, or by means of the i n i t i a l surge of the faul t . The f i r s t method has the d is -advantage of indicating only llne-to-ground faul ts . Also false indications may be obtained from ordinary switching operations i f the breaker does not close the three phases simultaneously. The second method has the disadvantage of being subject to tripping from spurious surges such as .those caused by switching and the release of bound charges due to l ightning. IV LITERATURE CITED Books 1. Bewley, L.V., Traveling Waves on Transmission systems. New York, John Wiley and Sons, Inc., 1933» 2. B r i t i s h E l e c t r i c a l and A l l i e d Industries Research Association, "Surge Phenomena - Seven Years 1 Re-search f o r the Central E l e c t r i c i t y Board". Reference S/T 35, London, 19*1-1. 3. Bush, V., Operational C i r c u i t Analysis. New York, John Wiley and Sons, 1929. k-. Central Station Engineers of the Westinghouse E l e c t r i c and Manufacturing Company, " E l e c t r i c a l Transmission  and D i s t r i b u t i o n Reference Book"r Chicago, The Lakeside Press, R.R. Donnelley and Sons Company, 19*l4. 5. Coulthard, W.B., Transients In E l e c t r i c Circuits,. London, S i r Isaac Pitman and Sons Ltd., 19^-6.. 6. Fink, D.G-., Radar engineering. New York, McGraw** H i l l Book Company, Inc., 19^7. 7. Puckle, O.S., Time bases. New York, John Wiley and Sons, Inc., 19^3» P e r i o d i c a l s 'S, Abraham, L.G., Lebert, A.W., Magglo, J.B., Schott, J.T., "Pulse-echo measurements on telephone and t e l e v i s i o n f a c i l i t i e s " , A.I.E.E. Transactions. Vol. 66, pp. 54-1-8, January, I9H7. 9 . A.I.E.E. Committee Report, "Lighting Performance of 220 kv Transmission Lines - 11", A.I.E.E.  Transactions. Vol. 6 5 , p. 70 , February, 19-4-6. 1 0 . Bekku, S., I.E.E., Japan; J . , 1923 , No. lJ-15, p. 7 9 . 1 1 . Birklnshaw, R.J., "Transmission Line Surges", E l e c t r i c Review, v o l . 137 , pp. 2 7 - 3 0 , J u l y 6 , 1 9 ^ 5 . 1 2 . Dowell, J.C., "Attenuation and Successive Reflections of Traveling Waves", A.I.E.E. Transactions. Vol. 5 0 , p. 551 , 1 9 3 1 . 1 3 . Dupuls, H.P., Jacobs, W.E., "Fault Location and Relay Performance Analysis by Automatic Oscillographs", E l e c t r i c a l Engineering, v o l . 6 5 , pp". Ml -2-6, J u l y , 19^6. 11+. Eaton, J.R., Peck, J.K., Dunham, J.M., "Experimental Studies of Arcing Faults on a 75 &v Transmission System", A.I.E.E. Transactions, v o l . 5 0 , pp. 1*1-69-79 , December, 1 9 3 1 . 1 5 . Gates, B.G., "The Attenuation and D i s t o r t i o n of Traveling Waves on Overhead Power Transmission Systems at Voltages Below the Corona L i m i t " , Journal of the I n s t i t u t i o n of E l e c t r i c a l Engineers. Vol. gij-, p. 711 , 1939 . 16 . Haeff, A.V., "A Memory Tube", Electronics. September, 19"+7. 17 . Hawley, W.G., "Surge Characteristics of Single-C i r c u i t Three-phase Transmission Lines", I n s t i t u t i o n of E l e c t r i c a l Engineers, Vol. 9 2 , pt. 1 1 , pp. 3 9 - 4 6 , February, 19J+5. l o . Honnell, M.A., "Location of Line Faults", Electronics. V o l . 17, pp. 110-3, November, 19*14. 19. Kiebert, M.V., Ing l i s , A . F . , "Multivibrator Circuits"' , Proceedings of the Institute of Radio Engineers. Vol . 33, p. 53lj-, August, 19^5-20. Knapp, E.W., "Transmission Line Fault Locating System", Engineering Journal. Vo l . 2^, pp. 329~37> July, 19^1. 21. Les l i e , J .R . , Kidd; K . H . , "The Llnascope ~ an Echo-ranging Type Fault Locator for Hlgh-Vdltage Lines", A . I . E . E . Technical Paper "48-207. July, 19k$. 22. Margoulies, S., Fourmarier, P . , "The Localization of Faults on Overhead Lines by Means of Impulse Waves", Paper 307 of Conference Internationale des Grands Reseaux Electriques a Haute Tension, Paris , France, Gauthler-Vll lars , June 2k- to July 3, lSk&. 23. Mather, N.W., "Multivibrator Ci rcu i t s " . Electronics. p. I36, October, ISk-S, 2k, National Research Council of Canada, E l ec t r i c a l Engineering and Radio Branch, "Technical Manual for Merchant Marine Type 268 Radar with Circui t Diagrams", 19^7. 25. Roberts, F . F . , "New Methods for Locating Cable Faults Par t icular ly on High Frequency Cables", Journal of the Ins t i tu t ion of E l ec t r i c a l Engineers, Vol . 93, part 3, pp. 385-95, November, l$k6. 71 26. Satch, Y . , "Elect r ic Osci l lat ions in the Double-Circui t Three-phase Transmission Line", A . I . E . E . Transactions. Vo l . , September, 1927. 27. Savage, J . H . , "Localization of faults i n Low Voltage Cables, with Special References to Factory Techniques", Journal of the Inst i tut ion of  E l ec t r i c a l Engineers f Vol . 92, part 2, pp. 580-93, December, 19^5. 28. "Skiatron - a Dark Trace Tube", Electronics and Communications,, 19^7 Annual 29. Stevens, R .F . , St r ingf le ld , T .W. , "A Transmission Line Fault Locator Using Fault-generated Surges", A . I . E . E . Technical Paper 118-208. July, 19^8. 30. Strom, A . P . , "Long 60-cycle Arcs i n A i r " , E l ec t r i c a l Engineering. Vo l . 65, pp. 113-7, March, 19*^6. 31. Zarem, A . M . , "An Automatic Oscillograph with a Memory, " E l ec t r i c a l Engineering, March, 19^-6. 1 V l l ACKNOWLEDGEMENTS The author wishes to 'express his indebted-ness to thoae who have assisted i n the completion of this investigation; especially to Dr. F. Noakes for his guidance and encouragement. Acknowledgement i s also made to the B r i t i s h Columbia Telephone Company whose scholarship made the year's work possible. Donald J . Evans 

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