"Applied Science, Faculty of"@en . "Electrical and Computer Engineering, Department of"@en . "DSpace"@en . "UBCV"@en . "Nalos, Ervin Joseph"@en . "2012-03-26T18:50:35Z"@en . "1947"@en . "Master of Applied Science - MASc"@en . "University of British Columbia"@en . "The Location of a fault in a power cable is by no means a simple task and the techniques used at present warrant further improvement. Many methods of fault location have been devised but each has its particular limitations. Some of these methods include D.C. and A.C. bridge methods, echo-ranging methods, and high-frequency methods. The limitations and impracticability of these various techniques has been the main reason for this research.\r\nIn this thesis, a review of the high-frequency method has been made, resulting in the development of a method of locating high-resistance faults. Expressions, permiting the use of this improved method in instances where cable potheads are relatively inaccessible have also been developed and checked experimentally. Briefly, the method consists of determining the input impedance of the cable with its remote end terminated in its surge impedance. This is done by simultaneously measuring the voltage drops across a standard resistor and across the cable. The ratio of these drops is an indication of the cable impedance at that frequency. Observations are taken on a band of frequencies on a faulted cable and on a good cable, both terminated in the characteristic impedance. The difference of these two effects is attributed to the reflections from the fault. From the plot of the impedance as a function of the frequency, by a short graphical computation, the distance to the fault may be obtained. Faults as high as twenty times the surge impedance have been successfully located on relatively short lengths of cable. The distance to the fault has been estimated well within [page missing]"@en . "https://circle.library.ubc.ca/rest/handle/2429/41763?expand=metadata"@en . "I \u00C2\u00A33 #7 h\u00C2\u00AB-j fly High Frequency Method of Locating Power Gable Faults Ervin Joseph Nalos A Thesis submitted i n Par t i a l Fulfilment of the Require-ments for the Degree of Master of Applied Scince i n the Department of E l e c t r i c a l Engineering The University of B r i t i s h Columbia August ,1947 1 Table of Contents Page I. Introduction 3 II. Mathematical Analysis A. Symbols used 6 B. Analysis of Transmission Lines . . . . 7 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. . 10 F. Analysis of Double Faults 11 G-. Effect of Long Instrument Leads . . . . 12 H. Alternate Approach,far end char. imp. . . 13 III. Discussion of Experiments A. Circuit Diagram and Apparatus . . . . 15 B. Calculations 1. Characteristic Termination . . .21 2. Far End Open-circuited . . . .22 3. Far End Short-circuited . . . . 23 4. Double Faults 24 5. Effect of Long Lead-in Cable . . 25 6. Alternate Method,Charact.Termin. . 26 C. Dicussion of Results 1. Effect of Harmonics . . . . . .30 2. Additional Errors 31 3. Accuracy,Limitations,and Conclusion 33 4. Bibliography 35 5. Acknowledgement . . . . . . . 36 2 L i s t of Illustrations / Page Pig.l Transmission Line 7 Pig.2 Faulted Line,far end O.C. . ' . . . . . 9 Fig.3 Equivalent Circuit of Faulted Line . . . 9 Fig. 4 Line with Double Fault correctly terminated 11 Fig.5 Equivalent Circuit of Line with Double Fault 11 Fig.6a Line with Lead-in Cable.. . . . . . .12 Fig.6b Circles of constant Attenuation,Frequency . 14 Fig.7 Video-frequency Amplifier 16 Fig.7a Layout of Apparatus . ... . . . . . . . 17 Fig.7b Schematic Diagram of Layout . . . . .17 Fig.8 S-function Method of Measuring Attenuation 18 Fig.9a,9b Reflected voltage and' current wave . .19 Fig.10 Connection to Amplifier . . . . . .20 Fig.10a A r t i f i c i a l Fault . . . . . . . .20 Fig.10b Characteristic Termination . . . . . 20 Fig. 11a,lib,lie Effect of Harmonics . . . . 30 Fig. l i d High-pass F i l t e r Circuit . . . . . 3 2 Fig.12 Tuned Circuit to,eliminate Harmonics . 33 Li s t of Tests facing pages shown Test 1,2,3 s Input Impedance,line correctly terminated . . . 21 Test 4,5 : Input Impedance,Line O.C. and S.C. 22 Test 6,7 : 'Effect of Harmonics . . . . . 30 Test 8 : Double Fault . . . . . . . 24 Test 9 : Effect of Mismatch at Far End . . 24 Test 10 : Effect of Long Input Cable . . 26 Test 11 : Alternate Method with Char.Term. . 28 3 HIGH FREQUENCY METHOD OF LOCATING POWER CABLE FAULTS I. Introduction The location of a fault i n power cable i s by no means a simple task and the techniques used at the present warrant further 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; their path may cross an open f i e l d or a busy intersection. Frequently,they are ad-jacent to non current-carrying e l e c t r i c a l conductors.Cables may be terminated i n potheads, i n manholes,or near the top of a line pole.Occasionally,one end of a cable may be inaccessi-ble as for example i n certain types of ring-buss switch bo-xes.Due to the various conditions under which cables are used,methods of fault location successful under one set of conditions w i l l not necessarily work on others. Many methods of fault location have been devised but each of them has i t s particular limitations.The simple D.C. bridge techniques-' have been superseded to some extent by 1 7 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 locating faults i n armored cable,in lead-sheath cable located amongst a number of other cables,or i n cables adja-cent to non-electrical current-carrying structures because the audio signal employed does not always leave the cable at the point of the fault but rather passes along the cable armor or other conductors i n a devious path. The echo-ranging technique ^ i s at present limited to telephone work because the lengths of power cable used are rel a t i v e l y short.For po-wer cables,where the velocity of electro-magnetic waves i s approximately 500 ft/microsecond,the pulse returns too rapid-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 receiving equipment which at present makes i t impractical. A l l numbered references are given i n bibliography. 4 The limitations and impracticability of these various techniques led 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 principle that standing waves may be established on e l e c t r i c a l l y long lines and that reflections are produced at discontinuities such as open and short c i r c u i t s where the fault resistance does not equal the characteristic impedance of the cable.Since the cable input impedance i s a function of the frequency.it i s possible to ascertain the frequencies where maximum impe-dances occur by recording the frequencies corresponding to maximum input voltages. By proper interpretation of these frequency differences between adjacent impedance peaks,the distance to the fault may easily be calculated. This method i s limited to faults whose resistance i s less than a third of the characteristic impedance.The most accurate determinations are obtained when the fault r e s i s -tance i s zero;however,such cases are rarely found i n practi-se and i t i s thus necessary to burn faults down u n t i l they can be detected.This requires time as well as special equip-ment. Frequently, the resistance of a burnt down fault w i l l rise during the test to a value which makes the method i n -applicable without further carbonization of the fault. The object of this 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 locating high-resistance faults; secondly, to develop expressions permiting the use of this 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 effect,this means ta-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 characteristic impedance and measuring simultaneously the voltage drops across a 5 standard resistor and across the cable. The ratio of these drops i s an indication of the cable input impedance at that frequency.Observations are taken on a band of frequencies on a faulted cable and on a good cable,both terminated i n the characteristic impedance.The difference of these two impor-tant effects i s attributed to reflections from the fault. Prom a plot of impedance as a function of frequency,by a short graphical computation,the distance to the fault may easily be obtained.To f u l f i l l the secondary objective neces-sary expressions permiting the use of long instrument leads have been developed and are presented i n the main body of the thesis.Faults as high as twenty times the characteristic impedance have been successfully located on re l a t i v e l y short lengths of cable.The distance to the fault has been estimated well within 5$ and higher accuracy i s to be expected on longer cables. 6 I I . MATHEMATICAL ANALYSIS A. Symbols used In Mathematical Analysis. x - distance from sending end E - rms voltage at distance x from sending end I - rms current at distance x from sending end z - series impedance of cable per unit length y - shunt impedance of cable per unit length c - propagation constant* a - attenuation constant- c \u00C2\u00AB (a* jb) 88 /zy 1 b - phase constant k - constants satisfying boundary conditions E - sending end voltage E 3- receiving end voltage 1^- sending end current I - receiving end current Z r- input impedance Z 3- equivalent receiving end impedance 1 - total length of given cable K = VR R - Fault resistance 3 = ( a l/cos2 bl) d = (R/R*Z Q ) = (l/lok) d 2 = ^/Rg+Zj ( R l V R l V R 2 Z o V R l Z 0 ( R 2 t Z 0 ) (R,R~*R~z * Z 2 ) , _ _ _ x v 1 2 2 o o V R_Z (Rrt+Z ) ' 1 o 2 o u = V = Z Q\" Characteristic Impedance of Lead-in Cable Z = Sending end Impedance appearing at Sending End of 3 Lead-in Cable Z 0 Rc+JXc, 3 \" 3 3 I.(r \u00E2\u0080\u00A2 j x ) r l = r a = Z Z 3 3 o o 1/2 itanh {al+fal^+coth Dal-\u00C2\u00BB(al}y = coth 2 Qal+Cal)^ 1/2 ^coth [al*(al)l-tanh [al+(al)^= csch 2 ^.l+Cal)^ x~ \u00E2\u0080\u00A2 1/2 Jtan [bl+(bl)g-cot tbl+(hl)lf= -cot 2 fcl+(bl)0-] r b = 1/2 jtan [blt(bl)g\u00C2\u00ABcot [bl+(bl) 0ij= esc 2 [bl*(bl)0-} V r = Voltage drop across fixed standard resistor r which is a measure of the r f current through the cable V c - Voltage drop across cable which, when divided by r f current gives the cable impedance r = Standard resistor used i n measuring r f current through cable * Notation used here i s not standard. 7. B. Analysis of Transmission Lines, dE - T \u00E2\u0080\u0094 - Iz dx dl = Ey dx d 2E d x 2 d2l_ dx2 z d l = I z y dx - v dE Izy X \u00E2\u0080\u0094o fist Solving these two differential equations, we obtain: E = k-^cosh cx + kgSinh cx I = k_cosh cx * k^sinh cx (1) (2) The constants k are obtained by boundary conditions, as follows: At Sending end, where x = 0, E = E r = kx I * I p = k 3 Also, - ck^sinh cx \u00C2\u00AB*\u00E2\u0080\u00A2 ckgcosh cx 5 Iz iSH \u00E2\u0080\u00A2 cE^sinh cx + ckocosh cx dx r d = I pz cosh cx + k^z sinh cx Hence, ck cE r \u00C2\u00AB kij.z 2 s I rz from which kg = I r Z Q k V B E r / z , E s = E pcosh c l I rZ 0sinh c l I s = I rcosh c l + E r / Z c sin* 1 c l z - Eg a E rcosh c l I rZ 0sinh c l 3 \" Is I^cosh c l + E * / z 0 sinh c l (3) (4) But Z r \u00C2\u00AB E r/1. thus 8. z . z Z rcosh c l * Z 0sinh c l (5) Z Qcosh c l Z rsinh c l For Open-circuited end, Z r i s in f i n i t e , for Short-circuited end, i t is zero. Hence, Z o c - Z 0coth c l Z n\u00E2\u0080\u009E = Z^tanh c l sc o (6) C. Analysis of Faulted Line with far end open-circuited. The c i r c u i t i s shown i n Fig. 2 and the equivalent ci r c u i t i s shown i n Fig. 3; from this, we obtain, Z r s RZ Qcoth clg R + Z 0coth clg Rcoth cl2Cosh c l i R+Z0coth clg sinh cl-cosh c l i + Rcoth clgsinh c l ! R + Z Qcoth clg 1 + tanh c l ^ (k + tanh clg) K + tanh cl.,+ tanh c l ~ (7) 1. If attenuation is negligible, c and i n the above expression, \"~ tanh c l = tanh j b l \u00E2\u0080\u00A2 jtan b l Hence, Z 3 a j(l-tan hl]^tan big) + jktan h i ! ' K + j (tan b l ^ t a n big) a + jb i s appr. jb (8) If b l ! i s a n l n t e S r a l multiple of big, the above ratio equals l / 2 for b l g a 0,^2113... , this being a pure resistance, 2. If attenuation is small but not negligible, a l i s small sinhg2al = 2al cosh a l - 1 tanh c l sinh 2al+jsin 2bl _ a l 2 (cosh 2al-sin 2bl) cos 2hl + jtan b l 9. X, o\u00E2\u0080\u0094 R 3 Fig. 2 Fig. 3 a l . a l . 1 + Zs/Zo = Vd( \" ) 2. If the attenuation is small but not negligible, [(d*3j) (l^s^) + dtan2bl\u00C2\u00A3l + j (l-d2) tan b ^ (15) ( l * d s i ) 2 + d 2 tan 2 bl-When b l j \u00C2\u00BB 0,%*!} When bin =f *T -1- *\u00E2\u0080\u00A2) 2.) \u00E2\u0080\u0094 ( d < 3 i > ( i * a . , ) , Z s / a l/d which can easily be veri-fied by substituting and taking the limit as b l ^ approaches \"72. 11. F. Analysis of Double Faults Fig. 4 shows the ci r c u i t diagram for the case of charac-t e r i s t i c termination which i s the only case considered. The equivalent c i r c u i t is shown i n Fig.. 5 . In most cases at-tenuation i s small and for simplification It Is neglected i n this consideration. If not small, attenuation may be ac-counted for i n a manner described previously. Again, Z s i S Z r+Z 0tanh c l ^ J r Z 0*Z rtanh c l i Z o R 2 / Z . R + J Z o t a n b l 2 zo + 0 z o R 2 / Z o 4 R 2 t a n b l 2 d 2+jtan b l 2 l+jdgtan b l 2 Fig. 4 Hence, Z Fig. 5 - Z s R l I T \u00E2\u0080\u0094 Z s R l R-L (d 2+jtan b l 2 ) ^ d 2 + R l / z ^ + ^ 1 + d 2 R l / z ) t a n b l 2 dg+jtan b l 2 u+jvtan b l 2 (16) ^s _ Zo (d 2-vZ Qtan bl^tan b l 2 ) + j (tan bl 2*-uZ 0tan hl^) (uZ D-tan bljtan b l 2 ) - j(vZ 0tan bl2+-d2tan D I 2 ) . . . ( 1 7 ) As an example, i f R-|_\u00C2\u00AB 100 ; R2= 50 ; ZQ= 50 l x= 200 f t . ; 12= 75 f t -the above expression becomes ( . 5 -tan 2 f tan .75f) + j (tan.75f+1.25tan2f) (l . 2 5 - t a n 2 f tan .75f) + j (tan.75f+ -5tan2f) which i s plotted in Test 8. This analysis is merely of academic value and the occurence of this case In a power cable is extremely unlikely. It is included merely to complete the study and might be used to advantage i n telephone work. 12. G. Effect of Long Lead-In Cable on Impedance of Cable under Test Often faulted cables are overhead or not directly accessible and an auxiliary lead i s brought out to the apparatus from the end of the\u00E2\u0080\u00A2faulted cable. This cable is not usually short e l e c t r i c a l l y at frequencies of 2-3 Mc and hence i t s effect has to be calculated. From Fig. 6awe obtain by a process analogous to previous deri-vations, Js _ Z cosh cl+zlsinh c l s o z'coshcl * Z sinh c l o s Zs/Zp \u00C2\u00A5 tanh c l 1 + Z s/Z 0 tanh c l JL A Fig. 6a (18a) With negligible attenuation, this reduces to: - \u00E2\u0080\u00A2 Z s / Z 0 4 J t a n b l 1 + O'Zs/z1 t a n D l (18b) Alternately, from ( l8a) and ( l8b) , z ; ( Zs/Z Q -Iten WL) - \u00C2\u00AB Z 0 (l-jZa/z\u00C2\u00AB ^ bl)\u00E2\u0080\u009E (19) The plot of expression (l8b) for 25 f t . of Cable RG8/U is given i n Test 10 together with the curves obtained by a test on a cable with a 100 Ohm fault a fixed distance from the sending end. 13 H. An Alternate Approach of Analysis of Cable Faults with far End Terminated i n Characteristic Impedance, This method may be used to advantage i f apparatus is available for measuring reactive component of cable im-pedance with reasonable accuracy. The tedious calculations encountered i n Eq. 14 and 15 are avoided by the use of this method. Since the far end of the cable i s correctly termi-nated, no reflections return to the sending end. The input Impedance of the cable behaves as though i t were terminated at the fault with an impedance Z R = R Z 0 / R + Z which is fixed. If Z . \u00E2\u0080\u0094 ~ ,= cosh ( c l ) 0 and Z r s sinh (cl) 4 Z i - Z l V Zo- zr' o then Z g Z rcosh c l + Z csinh c l Z Z cosh c l + Z sinh c l ^o o r coshcl sinh ( c l ) Q 4 sinh c l cosh ( c l ) Q ) cosh c l cosh ( c l ) Q + sinh c l sinh ( c l ) 0 i z s r ~i R s + J ' X s - tanh|cl4(cl)J = \u00E2\u0080\u0094 ; * r 4jx s ( 2 o) Z Q u \u00E2\u0080\u009E J ^o As before, i f c = a*jb, tanh c l = ] ( s l n n &1 c o s n a l ) * 3* (sin b l cos bl) cosh 2al cos 2bl+sixth 2 a l s i n 2 b l If i n the above equation a value of c l 4- (cl) Q= [al+(al)^J + j\u00C2\u00A3bl+(bl)J], i s substituted for c l , keeping [al-\u00C2\u00BB-(al)0\"] constant (rg-r,) 2 t x 2 = r | which is a circ l e i n the (r sxj Tlane. 14. Similarly, i f [bl * (bl) 0 lconstant, r s + ( x s \" x l ) 2 \u00E2\u0080\u00A2 * f (21, 22) In Eq. (21) and (22) *1 - eoth ^ [ a l + f a l j j s coth 2 ( a l ) Q i f attenuation is negligible r a = csch 2 [al+(al)0~J= csch 2 ( a l ) Q \" \" x x = cot 2 p x L 4(bl) 0\"] r b = esc 2[bl4(blj 0\"] Fig. 6b shown below gives a clearer idea of the symbols enumerated above. Further plots of similar figures with neg-l i g i b l e attenuation are shown i n connection with Test 11 on a Lead covered Cable* with a 100 Ohm Fault and terminated In i t s Surge Impedance. tV - const I Es\u00C2\u00BB2l - Coogfcmt Atentdhbri CM const 4f\u00C2\u00ABK circles pass+VircooV) 0,o). ^ ^ ^ Note: If attenuation Is small, a l \u00C2\u00AB 0, and Eq. (21), i.e. circ l e of constant \"attenuation\" depends only on ( a l ) Q which is a constant for a given line and fault. Hence the radius vector from origin to a point on the circumference of the ci r c l e represented by Eq. (21) is the sending end Impedance * 2 - No. 8 conductor, paper-insulated, lead-covered, HKv Cable 15. with i t s appropriate angle. To determine what impedance corresponds to a given frequency i t is noted that ( h l ) c i s a constant and that (hi) is a linear function of frequency, the constant depending on the type of cable under test. Know-ing this constant, any circle 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. I l l DISCUSSION OF EXPERIMENTS A. Circuit Diagram and Apparatus. 1. The general method of locating faults was des-cribed in the latter part of the introduction and the ci r c u i t diagram i s given below i n Fig. 7a s-nd 7b. The ap-paratus consists of a Signal Generator with variable Frequency up to 5 Mc, an amplifier covering the video-frequency ranges, a power-pack giving 300 volts D.C., a filament transformer with, 6.3AC volts output, a standard dropping resistor, and 2 vacuum-tube voltmeters. A Sig-nalyst or Triplet Signal Generator are satisfactory for this method. The c i r c u i t diagram of the Video-frequency Ampli-f i e r is shown i n Fig. T and the arrangement of measuring the drop across the standard resistor and the cable are shown enlarged in Fig. 10. A Cathode-ray Oscilloscope i s also required i f the waveshape is 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. AO \u00E2\u0080\u00A2 B o o -SDK .OI 6 0 K .01 5K \ CmcotT' \ \QOJl FAUrr : 2^56^2. 2 * ' 184.5' \ IK. m \u00C2\u00A9 Calcolated Exult* Iwput Cable (3) ^efkctvon^om fault, W^-f^t'l^mma-br^ -^\\u00C2\u00AB^ uTCflbW Impcf-fectTermmtrtt'on ^ In^ut Cable (No^oH) P R I N T E D f t t U . S . A . E U G E N E D I E T Z S E N C O . N O . 3 4 6 B X 26, characteristic impedances are close together. If this vere not the case, i t would he necessary to investigate further the expressions In Eq. 18 and 19. It is noted from the calculated curve in test 10 that as long as the characteris-ti 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 fault i s hence ( 1 ' ? 7 ) ( 2 ) . 216.5 f t . (.oil)(1.32) since for the lead-covered 2-conductor cable, b \u00C2\u00AB (.011) f /Mc/ Thus actual distance to fault i s (216.5 - 25) = 191.5 f t (cf 184.5 ft.) Again, i f one wishes to investigate the size of the fault, the f i r s t maximum of the curve i s desirable, since at-tenuation errors are least there; thus, 1.53 =(R+Z)^R and R (56/.53) = 106 ohms (cf 100 Ohms) 6. Alternate method with characteristic termination at far end. A close study of expressions developed i n Eq. (21) and (22) open up a different approach to this problem by incor-porating the effect of a sending end impedance Into the propagation constant as a fixed additional value. Circles of constant frequency 'can then be drawn and checked against the frequencies obtained for various input impedances. Two alternate tests are proposed here. In both, one f i r s t draws the circle of zero attenuation / true for 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 characteristic impedance of cable and the fault resistance, since the minimum and maximum input impedances are Ry{R+Z0\ andfR+Z^/R respectively. If apparatus measuring the re-actance component of the impedance Is available, one method would be to determine the point of maximum reactance and recording the corresponding frequencies. This i s shown i n Test (11) by circles (2-2) and (2 ,-2 t). Prom this the dis-tance to the fault may be determined. Another pos s i b i l i t y would be to use a dropping resistor \" r \" i n Fig. 7b whose value Is ZQ for the cable. In this case one records the frequencies when the voltmeters V,, and V. read the same values i.e. when Z s = Z 0. Circle (.1-1.) corresponds to these values of the input impedance and by knowing at what fre-quency the meters read the same values, the distance to the fault may be determined. This method is 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 refine-ments. This method is unfortunately rather complex when applied to shorted and open lines. In these cases one ob-tains spirals instead of circles and their analysis is too complicated to be of practical value. For the lead-covered cable, with c i r c u i t as shown i n test 11, ^ + = t a ^ | \" j b l / ( a l ) o ] Z tanh ( j . O l l ' f l \u00C2\u00AB- .76) with negligible attenuation and 100 ohm fault at a distance o f \" l \" f t from sending end. These values automatically check with the circl e of constant attenuation. The observed point of maximum reactance was about 1.12 mc. The cir c l e (2-2) , passing through this point and the point (1,0) having i t s centre on the x\u00E2\u0080\u009E axis Is thus uniquely determined. Hence, from Eq. (21) and (22) - -cot2[(bl+(bl) 0)]= -.48 When dealing with resistances only, ( c l ) 0 is real and hence b l 0 is zero. Thus cot 2b l = .48 bl - .56 radians or (T /2+.56) rad. - 2.13 rad. The latter value is chosen since c i r c l e (2-2) crosses the point of maximum reactance for the second time /capacitive/ i.e. half wavelength from f i r s t point of maximum reactance. For this cable, b \" (.011) f Hence distance to the fault is 1 = \u00E2\u0080\u0094 2 . 1 g _ 1 7 3 f t ( c f l 8 2 t f t ) (.011) (1.12) Alternately, when a dropping resistor was used whose value was the characteristic impedance of the cable / 5 6 Ohms/ and frequencies were recorded consecutively at which the two drops across the resistor and across the cable were equal /Z s = ZQ/, the values should correspond to ci r c l e ( l - l ) From experiment, these frequencies are: ?, 1.11, I .87, 2.65,....Mc. For a l l these values cot 2b l = 0 since the centre of the cir c l e ( l - l ) l i e s on the origin. Thus bl = A , 5*/*, 7\" A , .... corresponding to fre-quencies f = ? , 1.11, 1.87, 2.65,efe Hence distance to the fault i s : 22C = 195 f t (cf 184.5 f t ) 4(.Oil)(1.11) ' SI s 191 f t ( C f 184.5 f t ) 4(.011)(1.&7) \u00E2\u0080\u0094 \u00E2\u0080\u0094 \u00E2\u0080\u0094 Z_ _ 188 f t (cf 184.5 f t ) 4(.Oil) (2.65) \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u0094 - \u00E2\u0080\u0094 . The size of the fault, which i s relatively unimportant, can be found by similar means as i n previous tests. The accuracy of these results is well within 10$ and can be relied on for similar tests. If desired, any particular point on the zero attenuation cir c l e can be checked by drawing circles such as (3-3) for a given frequency and the actual input impedance at this frequency should equal the radius vector from the origin to the point where the circ l e (3-3) cuts the zero attenuation c i r c l e . This was also checked In test (11). ft N T E D i p L . 2 g 4 0 I JL J U 6 E N E D I E T Z 6 E N C4 N ( Fee~> In MC . Ffc6S>. IN We 3o C. D i s c u s s i o n of R e s u l t s 1. E f f e c t of Harmonics The output v o l t a g e of the s i g n a l generator i s \"by no means s i n u s o i d a l and contains second harmonic v o l t a g e to a consi d e r a b l e degree.With t h i s i n mind, i t i s d e s i r a b l e to i n v e s t i g a t e which of the discussed t e s t s i s l e a s t c r i t i c a l to t h i s predominant second harmonic. F i g . 11 a , l i b , a n d 11c show the e f f e c t of t h i s second harmonic on the input imped-ance as the frequency i s v a r i e d . Par e n d :open-circuited S h o r t - c i r c u i t e d Terminated i n Z Q I n Fig.11a,maximum impedance to second harmonic occurs at the p o i n t where the impedance to the fundamental i s a m i n i -mum; hence at t h i s frequency a bump i s observed.This 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 at the f i r s t quarter-wavelenght because the a t t e -n u a t i o n i s n e g l i g i b l e at t h i s low frequency.The bump at the next minimum i s almost n e g l i g i b l e compared to the f i r s t bump. In F i g . l i b the s i t u a t i o n i s more f o r t u n a t e because,for the t e s t w i t h the f a r end s h o r t - c i r c u i t e d ; t h e minimum impedan-ce to the fundamental does not occur at a p o i n t of maximum im-pedance to the second harmonic.By adding the impedances due to the f i r s t and second harmonic i t i s noted t h a t the bumps occur h a l f way between f r e q u e n c i e s of maximum and minimum input impedance.Thus i n t h i s t e s t , t h e percentage of second harmonic i s not so c r i t i c a l . This bump can be e a s i l y obser-ved i n test ( 5 ) a n d [ l \ i n d i c a t i n g a l a r g e second harmonic content. 31. Pig. l i e shows the effect of slight mismatch at termination of cable. If the terminating resistor i s too high, the deviation from perfect termination /curve 1/ has the properties of a small \"open ci r c u i t \" i.e. maximum impedance occurs at same points as for open c i r c u i t . Alternately, i f the terminating resistor is too small, the curve of impedance tends towards that of short-circuited far end. This follows from the fact that a small resistance approaches zero /short-circuit/ in the l i m i t . In this case, the effect of the second harmonic is almost negligible 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 sinusoidal. It is concluded that i f the signal contains considerable distortion, this test is by far the most advantageous from a l l points of view. The elimination of harmonics Is discussed i n a later section. 2. Additional errors Aside from errors due to distorted waveshape, the simplicity 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 resistors. It is thus important to keep the value of the dropping resistor low, in order to minimize the effect of the capacitive reactance across i t s terminals. Another source of error is 60-cycle hum .coming from 32. the amplifier. The small amount which came through was easily removed by a high-pass f i l t e r c i r c u i t shown i n Pig. lld. Vr ( -dj\u00E2\u0080\u0094- ) Amplifier Calk uooerTisi Pig. 11 d. -pass 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 is not required for tests with far end short-circuited or correctly terminated since i n those cases the cable i t s e l f provides an effective short for the 60-cycle. An effort was also made to eliminate the higher harmonics from the generator. By beating the signal gener-ator against the carrier of a radio station i t was found \u00E2\u0080\u00A2 that harmonics as high as the 5th were detected, the second being by far 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 ci r c u i t is high when not at resonance. Thus the impedance to the fundamental is much lower than the Impedance to a l l harmonics. When the tuned c i r c u i t shown i n Fig. 12 was in-cluded i n the circuit, a considerable difference was obtained between the impedances. To be of practical value this c i r c u i t would have to be designed to remain at resonance as the frequency setting on the signal generator. 33. is varied. \u00E2\u0080\u00A2o o o-Pig. 12 Tuned ci r c u i t to eliminate harmonics Some improvement In waveshapewas also obtained by ad-justing the bias i n the oscillator so that the output would be decreased but more sinusoidal. With short leads and carbon resistors, the only con-siderable error remaining is due to capacity of the volt-meter to ground. This probably accounts for the larger discrepancies i n the calculations. It i s also important to connect the voltmeters in such a fashion that they both measure the same part of the wave. Por a sine wave, both positive swings and negative swings are equal but for a distorted wave a good measure of impedance is s t i l l obtained i f both meters measure the same part of the wave. 3. Accuracy, limitations 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 fault. An accuracy of better than 5$ was obtained for tests with far end terminated In surge impedance, indicating that this is the best method to be used. Faults as high as twenty times the characteristic impedance are easily detected by this method. With the present amplifier and size of resistors, the upper li m i t - of frequency i s about 5 Mc hence tests for lines shorter than 25 f t . do not yield ac-curate results. It is to be noted here that improved accuracy is obtained when faults farther away are being tested. The tests with long \"instrument leads\" gave results well within experimental errors and their appli-cation to measurements where cable potheads are located on poles i s very useful. The procedure for tests with far end correctly terminated is as follows: a. Set up ci r c u i t shown i n Pig. 7b b. Connect Z Q across far end of cable as in Fig. 10b. c. Record readings of V r and V c as frequency i s varied for faulted cable. d. Record readings of V r and V c as frequency is varied for a good cable. e. Plot curves of cable input impedance against frequency. f. Subtract curve for good cable from curve for faulted cable, getting net result due to fault alone. g. Difference i n frequency between adjacent peaks of resultant curve represents a wavelenght. 1. From propagation constant of cable, find distance to fault. Repeated tests on same cable yield the same result in-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 is 100 Kc to 4 Mc approximately. 35 Bibliography 1. Blankmayer,W.H. Power lin e Fault Locator, p.166 Electronics.Vol.17 No.l January 1944. 2. Chandler, Steward,Jr. 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., 1944. 4. Honnel, M.A. Location of Line Faults. Electronics. Vol.17 No.11 November 1944. 5. Noakes.F. High Frequency Method of Location of Faults on Power Cables, pp.46-7 Elect r i c a l News.Vol.53 No.13 July 1 1944. 1 \" 6. Slater, J. C. Microwave Transmission. McG-raw-Hill Book Co.,Inc. 1942. 7. Vahey,J. A. Eecent Developments i n Cable Fault Locating. p.96. Edison E l e c t r i c Institute Bulletin. Vol.7 March 1939. 8. Woodruff, L. F. Principles 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 his appreciation to Dr. P. Noakes i n suggesting the topic and for his helpful assistance during the course of the research. An Abstract of the High Frequency Method of Locating Power Cable Faults By Ervin Joseph Nalos A Thesis submitted i n Partial Fulfilment of the Requirements ments for 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 Bri t i s h Culumbia August 1947 The Location of a fault in a power cable is by no means a simple task and the techniques used at present war-rant further improvement.Many methods of fault location have been devised but each has i t s particular limitations.Some of these methods include D.C. and A.C. bridge methods,echo-ran-ging methods,and high-frequency methods.The limitations and impracticability 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 in the development of a method of lo-cating high-resistance faults.Expressions,permiting the use of this improved method i n instances where cable potheads are re-latively inaccessible have also been developed and checked ex-perimentally .Brief ly, the method consists of determining the input impedance of the cable with i t s remote end terminated in i t s surge impedance.This is done by simultaneously measuring the voltage drops across a standard resistor and across the cable.The ratio of these drops Is an indication 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 ter-minated in the characteristic impedance.The difference of these two effects is attributed to the reflections from the fault. From the plot of the impedance as a function of the frequency, by a short graphical computation,the distance to the fault may be obtained.Faults as high as twenty times the surge impedance have been successfully located on relatively short lenghts of cable.The distance to the fault has been estimated well within "@en . "Thesis/Dissertation"@en . "10.14288/1.0105076"@en . "eng"@en . "Electrical and Computer Engineering"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "High frequency method of locating power cable faults"@en . "Text"@en . "http://hdl.handle.net/2429/41763"@en .