signature representation of underground cables

8/3/2019 Signature Representation of Underground Cables

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IEE 2nd International Conference on Advances in Power System Control, Operation and Managemen t, December 1993, Hong Kong

Signature Representation of Underground Cablesand its Applications to Cable Fault Diagnosis

C.M. Ho, W.K. Lee a n d Y.S. Hu n gUniversity of Hong Kong. Electrical and Electronic Engineering Department, Pokfulam Road, Hong Kong

AbstractThe pulse-echo method for cable fault location isstudied using transmission line theory. It is shownthat both the position and the magnitude of pulseechoes can be determined in terms of the cabledimensions and the fault conditions. For a healthycable, an algorithm for estimating the cable topologyand the cable dimensions from its pulse-echoresponse is obtained. This provides a justificalion for

taking the pulse-echo response as a signaturerepresentation of the cable.Keywords: pulse-echo method. cable fault location,signature representation.1. Introduction

The method of pulse-echo reflection is a commontechnique used for locating underground cable faults(e.g. see [ l , 41). In a fault diagnosis situation, thefield engineer would look for abnormalities in thepulse-echo response and try to deduce the locationand the nature of the fault from the position and theform of the echo suspected to be reflected from thefault. The technique however has its difficultiesparticularly for cables with tee joints which result i npulse-echoes that are hard to interpret. This is due toa lack of a comprehensive set of rules of an analyticalnature which tells the field engineer how the pulse-echo response is related to the cable dimensions andfault conditions.In this paper, we will first show how the position andthe magnitude of the pulses in a pulse-echo responseare related lo th e topology and the dimensions of thecable. (We use the terms topology and dimensions to

refer to the relative positions of tee joints in a cable,and the lengths of cable sections between joints andcable ends, respectively.) We then consider theinverse problem as to how one may deduce thetopology and the dimensions of th e cable from itspulse-echo response. It will be shown that an algo-rithm can be constructed to resolve this problem i nthe case of a healthy cable. As a result, the pulse-echo response of the cable can be taken as a time-domain signature representation uniquely character-izing the cable.2. Mathematical Model of a Cable

We will take a state-space approach to themodelling of a cable. A cable can be divided into Nsections each of 1,ength 6 1 , and the cable parameterswithin each section are lumped together as illustratedin Fig. 1 for the case of a straight cable. Let R , L, G ,C be the resistance, inductance, capacitance andconductance per unit length of the cable, and let

6 R = R61, 6 L = L.61, 6C = C61, 6 G = G61 (1)be the lumped parameters for one section of the cable.Taking the input voltage V , and the output currentI , of the kt h section as the state variables, a state-space model for the system is

. 1v, - U - v, G - , )6 C

Figure 186 1


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with the alphabet 'A ' and ending with 'a' having atotal distance, say, less than p . For this purpose, wefirst write down all possible return paths generated by'A' and 'a' only. This gives:

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'Aa'. ' A u A a ' , ' A d u A d , . . .

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Next, we insert the pair ' B b between an 'A' and an 'a'for th e paths generated above to obtain all possiblecombinations containing only one pair of ' B b . Thenwe consider inserting a second pair of 'Bb' eitherafter an 'A ' or a 'b ' in the paths that have beenobtained. This process is continued unt i l no furtherpairs of 'Bb' an be added with the total path lengthless than p. Then we proceed to add the pair 'Cr' tothe paths. Clearly, 'Cc' can be inserted only after thealphabets 'A ' , b' and 'c'. All possible return paths canbe generated by continuing the above procedure.

I

I

FiP 2

e

We illustrate the results obtained so far by means ofan example. A cable with a single tee-joint togetherwith the cable dimensions, the cable parameters andthe simulated pulse-echo response are shown in Fig.3. For ease of reference, the time axis for the pulse

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response diagram has been converted into a distanceaxis (for the pulse-echo return path) according to (3).The positions of occurrences of the echoes within anecho distance of 300 metres can be identified bytracing all possible routes of echoes in the waydescribed above. To start, we see that there are onlythree routes (i.e. 'Aa', AuAa', 'AuAuAa') made up of'A' and 'a' only and are of total distance < 300m. Wethen go on to insert one or more ' B b after an 'A' togive 'ABba', 'ABbBba', 'ABbBbBba', 'ABbuAa','AaABba' while observing the 300m distanceconstraint. This process can be continued byinserting ' C r ' to produce all possible routes of echoeswith a path length less than 300m and the result(sorted by distance) is given in Table 2. Themagnitude of each pulse can be calculated as aproduct of the appropriate transmission and reflectioncoefficients according as the types of discontinuitiestraversed by the pulse along its path. The predictedpulse magnitudes are summarized in Table 2.

l

b

When comparing th e values obtained in Table 2withthe magnitudes of the pulse echoes exhibited in Fig.3, it should be noted that the injected pulse has avoltage magnitude (= 95) given by twice that of theinitial pulse shown in Fig. 3 due the voltage doublingeffect discussed in section 3. Pulse positions aremeasured at the left rising edge. It is observed thatthe results obtained based on the reflection andtransmission coefficients agree well with thesimulated response given in Fig. 3. The smallundulation at 280m is due to approximation errors inthe cable model used for simulation.

130m

Cable Parameters:R = 3. 25 x I O 4 RimL = 3.12 x 10 Hl m

C = 1. 4 x 10 "FlmG = 2 . 0 ~0 * IQm

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-40 IEcho Distance/ m

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before. Continuing this process, we can deduce thecable topology and it s dimensions completely.eturn Path Pulse'osition Pulse MagnitudeA x 5 = -31.73* x * x 9s = 42.2

3 3 )

~ x ~ x 9 5 =10.6( $ x ~ x ~ + ~ x ~95=28.1

Aa 80 m6. Cable FaultsABba 140m

160 m200 m

AaAa The method of reflection and the transmissioncoefficients can be extended to cables with two simplekinds of fault conditions.BbBba& ACra6.1 Series FaultABbaAa

&AaABba 22 0 m Consider a series fault of impedance Z , at apoint P of the cable as shown in Fig. 4. An incomingpulse reaching the point P from the left will see aload impedance of

240 m260m

AaAaAaABbCca &ACcBba &ABbBbBba z, = Z,$+Z "ACraAa &AaACca &

AaABbBba &ABbBbaAo &AB baABba

The reflection coefficient and the transmissioncoefficient can be calculated according as ( 5 ) arid (6):80m

zsz, +2Z"P =Table 25. Determination of Cable Dimensionsfrom Pulse-Echo Response

Making use of the results of the last section, wenow show that it is possible to determine the topologyand the dimensions of a healrhy cable by mecans of aninspection of the positions and the magnitudes of thepulse echoes in the order of their occurrences. Fig. 4First. we note that a healthy cable has only twopossible types of discontinuities, namely, an opencircuit and a tee joint. I f the first pulse has a positivemagnitude equal to twice the magnitude of theinjected pulse, then the cable is a straight cable oflength equal to half the path length travelled by thepulse, and in this case there is nothing more to bedone.

If the incoming pulse has voltage V . then the reflectedpulse has magnitude Vr = p V . The voltage of thetransmitted pulse before passing through the faultimpedance is T V . However, this transmitted pulsewill undergo a voltage drop due to the faultimpedance, and as a result, the voltage pulse thatemerges from the fault has a magnitude given by

If the first pulse is negative, then i t is reflected from atee joint and its magnitude should be equal to -2/3that of the injected pulse and the distance to the teejoint is determined by using (3). We next calculatethe magnitudes and positions of all the echoes due tomultiple reflections between the input terminal andthe tee joint. The calculated echoes are comparedwith the given pulse-echo response. The firstdiscrepancy indicates a pulse reflected from a newdiscontinuity not yet known and its location andnature (open circuit or tee joint) can be determined as

v,=z,V = 2zo v (10)ZS %, z, 2%,Hence we may define an effec'five transmissioncoefficient at a series fault to be

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6.2 Earth FaultConsider an earth fault with an impedance Z , at

a point P of the cable as shown in Fig. 5 . A voltagepulse reaching the point P will see a load impedance

Direct substitution into ( 5 ) and (6) shows that thereflection and the transmission coefficients are givenby

(13)Z022, +z,=22,

22, +zo 5 = (14)

If the incoming pulse has voltage V , then the reflectedpulse has voltage Vr = pV and the transmitted pulsehas voltage V , =TV .

dimensions of the cable up to the point of the faultcan be deduced. If the topology and th e dimensionsof the healthy cable are known or can be determinedusing a good core of the cable, then a directcomparison reveals the location and the nature of thefault. This illustrates how the features in a pulse-echo response can be used systematically for thediagnosis of simple types of fault conditions. We arecurrently conducting an investigation to extend themethod to general cases when the fault is less clearcutthan a short circuit or an open circuit, or if the faultoccurs at a tee joint.

8. ConclusionsIn this paper, we have shown that the positionand magnitude of each echo in the pulse response canbe determined by direct calculation if the cabletopology and dimensions are known. An algorithm is

obtained for solving the inverse problem ofdetermining the topology and dimensions of a healthycable from its pulse-echo response. Hence the pulse-echo response of a cable can be taken as a time-domain signature representation which completelycharacterizes the topology and the dimensions of thecable. We have also analyzed certain kinds of faultconditions by means of reflection and transmissioncoefficients, with a view towards using these resultsfor fault diagnosis.

9. ReferencesThe above analysis shows that the method oftransmission and reflection coefficients can be used todescribe the behaviour of a pulse at a series or anearth fault occumng at a point on a straight length ofa cable. If the fault occurs at a tee joint, the analysisis more complicated because it becomes necessary toconsider how the fault is physically distributedamong the branches of the cable at th e joint. Themethod discussed in this paper is still applicable butthe details are to lengthy to be presented here.

1. Lee, W.K. and Hung, Y.S. : Cable faultdiagnosis using signal processing techniques, Roc.Distribution 2000, vol. 2, pp. 43-48, Sydney,Australia, 199 1.2. Hung, Y.S. and Lee, W.K. and C.K. Hui :Signature representation of cables by pulse echoes,hoc. 9th Conf. on Electric Power Supply Industry,pp. 245249, Hong Kong, 1992.3. Cheng, D.K. : Field and Wave Electromagnetics,Addison Wesley, 1989.7. Fault Diagnosis

The results given so far already allow certaintypes of unambiguous faults (such as a complete shortcircuit or an open circuit) to be diagnosed. Forinstance, if a cable contains an open circuit at a pointalong a straight length of th e cable, then its pulse-echo response can be analyzed in th e same manner asthat of a healthy cable, and the topology and

4. Clegg. B.and Lord, N.G. : Modern cable-fault-location methods, hoc. IEE, vol. 122, No. 4, pp.403-408, 1975.

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signature representation of underground cables

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