Fault current distribution in HV cable systems

E.Viel and H.Griffiths

Abstract: An acivanced analytical model is presented ibr the evaluation of ground return currents at substations fed by both three and single-core cable circuits. The circuit model includes the accurate treatment of an intermediate substation between tlic so~ircc and tlic fiulted substation, unlike Engineering Recoiiiiiieridiitioii EA S.34, which adopts ii inore sinipliliect approach. Through detailed parametric studies, the diffcrcnccs between the simplified and the inore acc;uratc treatment are quantified. Thc effects that variations in the key paraineters ~ cable length and type, substation earth impedances ~- liavc on thc niagnitutie of tlie groLmd return current are identified and explained.

List of symbols conductoi s (ovci head eaith wires aiid cablc slieatha), and

rise of earth potential of ii substation, V earth impedance of a substation, SZ earth impedance of substation A. B and c, Q total earth 1’atilt current. A component of If through remote trans- former neutrals, A component of /,. or of I/ returning through ground, A overliead earth wire longitudinal self impedance, Q/km mutual impedance between line conductor and earth wire (overhead lines), Q/ lm length of cablc circuit connecting subski- tion A to B and B lo C, 111 phase i sheath currcnt in cable circuit con- necting substation A to B and B to C, A cable sheath longitudinal self-impedance, SZ/l<lll mutual impedance between sheath i and sheath j (single-core cables), Q/km mutual impedance between cable conduc- tor iind sheath i (single-core cables), Q/lm mutual impedance between conductor and sheath (thrcc-core cables), Wkin sheath longitudinal DC resistance, Wkm soil resistivity, Qni centre to centre distance bctween conduc- tors/sheat hs in single-core cables, 11-I

1 Introduction

Under line-to-ground fault conditions, the fault curreiit returns to the source substation partly through neutral

0 IEE, 2000 ILE Proccwhgs onlinc no. 2OOo0404 DOL IO. 1@49/ip-gtd:2000@4~ Paper tirst rcccivcd 14th July I999 atid in rcviscd Tomi IOth Fccbl-uary 2NH) Thc atithors arc with the CmliIT School of Enginccritlg, Cal-dill‘ University, Ncwporl Road, PO Box 687, Cardill’CF2 3TD, U K

partly through earth via grounding structures (towers, grids). Tlie proportion of the f i d t current llowing througli a substalion carthing systcm ( ZVr) raises its potential with respect to remote ground. This potential V , is given by

Knowlecigc 01’ V,, ciiables the evaluation of step, touch and transfer potentials, which can ciiuse electric slioclcs to people and animals and damage to equipment. National aiid international stanciards require these potentials to be confined within acceptablc hinits during worst case hiilt conditions.

The evaluation of lx,. as a proporlion ol‘ the net fault cur- rent iiifeed Ir at substations fed from overliead lines is fairly straightforward. EA Engineering Reconinlendation S.34 [l] providcs values of lq,. according to the tower line type. A num ber of diffcrent analytical inethods also accounting for conductive effects, liave bcen devcloped to determine accu- rately thc fault current disti,ibution along overhead lines [2, 31.

However, Ibr substations fed by underground cables, Fault current distribution analysis is more complicated due to the following factors: (i) Cable circuits are relatively short (small loiigitudirial impedances), and thcrelbre is arfectcd significantly by the values of the terminating grid impedances; (ii) When single-cow cables arc employed, the three sheaths form three mutually coupled paths. Publications regarding detailed modelliiig of single-sheath cablc circuits arc available [4, 51, but an extensive treatment of three-sheath systems is needed.

Generally, to determine tlie ground rcturri current at the fault point, it is not essential to model the entire system. For practical purposes, the relevant part of the network is that part electrically near lo the fault. Therefore, the use of a two-substation model (faulted substation and equivalent source) with only one cable circuit is often sufficiently accu- rate. [ I ] provides nonioglariis and aiialytical relations for the evaluation of IT,. for a number of two-substation arrangements cinploying three-core and single-core paper insulated cables. Similarly, BS 7354 [h] based on [I] pro- vides expressions for the same arrangements and cable types.

However, recent case studies [7] have revealed limitations in tlie circuit rnodels based on [ 11, when applied to arrange-

(1) 1,’ I - ILJr I I z,. I

23 I

ineiits where the cable sheaths are grounded at intermediate substations located between the fault and the source. The value of the earth inipedanccs of the interniediatc substa- tions affects the fault currcnt distribution, and the use of a three-substation model inay be necessary.

In this paper, the fault currcnt distributions for three- substation arrangements are investigated for both three- core and single-core cables, without considering cross- bonding at this stage. For each configuration, detailed ana- lytical solutions are dcrived. The sensitivity of Iyl, to param- eter variations using the simplified models based on [I] and the improved models are presented. Finally, a two-substa- tion arrangcment is examined for three-core and single-corc cables.

2

A relatively straightforward method of evaluating Igi is required by engineers for carthing system design. Sevcral scientific publications provide detailed analytical models for overhead lines and cablc circuits [2, 3, 8, 91. [I , 61 are com- monly used in the UK Tor both system types.

Since overhead lines are gciierally relatively long, tlic magnitude of thc earth impedances of terminating substa- tions are sufficiently low in comparison to the system longi- tudinal impedaiiccs not to affect jK, significantly. Therefore, ZEl can be expressed simply in terms of the line parameters a s in [l]:

Determination of ground return current

[ I ] treats fault current distribution involving cable circuits by coilsidering only onc section of cable terminated and earthed at either end, referred to as points A and B. This model is employed for both three and single-core cables in three different variants, depending on the position of the fwlt and of the soul-ce with respect to the two terminating points. Nomograms are provided for the evaluation of ZE, for PICAS, PlLC and PILCSWA cables ranging in voltage froin 1 I ItV to 4001tV. Similarly, [6] provides simplified empirical formulae for the siiiiie variants and cable types, giving additional guidelines on the use of the formulae for other cable types.

When the sourcc and/or the fault arc located beyond thc cable section ends, the approaches in [ l , 61 imply that there is no metallic continuity beyond point A and/or B. In the following Sections, the validity of this assumption is investi- gated by comparison with models accounting for metallic paths back to source.

3 Three-core cable circuits

Fig. 1 represents a threc-substation arraiigenicnt employing a three-core cable. The sheath of the cable is terminated to ground at both the sending (SA) and receiving (S,) substa- tions, and also at the intermediate point (SB). For both the simplified and detailed models, it is assumed that the fault current I, flows only in the f'aulted phase. Since thc outer hessian layer of PILCSWA cables degrades once in contact with the soil, the steel armour is exposed to possiblc corro- sion and its longitudinal metallic continuity cannot be guar- anteed in practice. Therefore, in the following studies, the effect of the steel wire armour is neglected.

3. I Simplified model This model does not fully represciit the arrangement of Fig. 1, but only the section of length /B(- supplied by a remote source of infeed. The simplified model is shown in

232

Fig. 2 [ 11. The nietallic contiiiuity back to source (sheath between A and B) and the effect of the earth impedancc of substation A are neglected. In addition, this model only accounts for the resistive component of the earth grid impedances of substations B and C.

IAB IBC

I I phase I I

zmp,c

ZC

sheath -1

18

-- SB

I I I

'BC

I I phase I

tS8

The solution of Igi; Tor the circuit represented in Fig. 2 can be found by solving the following equations

If = I g r + IRC R c I ~ ~ - ~ J B C J B C + % m p , c l H C ' I j - RDIUC = 0

( 3 ) which yields

3.2 Advanced model This analylical model represents completely the system in Fig. I . It IS assumed that the same type of cablc is employed in each of the two sections of length lAH aiid /llc13.

Hcnce, the following set of network equations apply

If = I,, +Inc.

I j = I A + IAU Z e ~ I ~ - ~ ( ~ A B I A ~ + zmp,rlAijIj + Z,HIB = 0 z,c.I,, - dsr . Inc + z T , p , c l ~ c ~ I ~ - Z , ~ B = 0

= IAJ3 + 113

( 5 )

3.3 Parametric comparison Parametric studies were carried out on this system, compar- ing the simplified and improved models (eqns. 4 and 6) for a soil resistivity value of 100Qiii. FOW types of 331tV, 240nim' cable werc considered, naniely PILCSWA, PICAS, XLPE insulated copper-wire screened and XLPE insulated lead slieathed. The cable sclr and mutual imped- anccs were obtained using relations based on the Carsoii- Clem formulae [I] . The cable sheath dimensions and impedances employed in the paper are given in the Appen- dix.

3.3.1 Effect of cable type and length - simplified and advanced models: Fig. 3 shows 1 calculated by eqns. 4 and 6 as a fiinction of lJjc Ibr different cable types and lengths lilR, the other parameters being lixed. Note that the proximity effects between terminating substation grids, expected for very short cable circuits, are not accounted for in this paper.

6C

55

5c

45

4c

35 s .rl 30 0 -

25

20

15

10

5

.

, 0

I g c , km

' l { , , r l f0 / ( 7 f s ~ / / l /,,(, ~/ / l t / /,1,j /Or d;//&l'i'll/ C(i/>/e /.IyJC',S

PILCSWA . . XLPE Icad sl1e;llIl

. . XLPE copp"' SCI'CCll PICAS

Eqn. 4 ClII'vC:

(i) (ii) (iii) (iv) E q n 0 CLII'VC: (v), (vi). (vii) (km) = 5, 1 - 0.1 (viii). (ix), (x) I ( k i n ) 5, I , 0.1 (xi), (xii), (xiii) /.i,l (km) = 5 , I , 0. I (xiv), (xv). (xvi) /,,Is ( h i ) = 5, I, 0.1

The comparison over relatively short lIj(, (I,?(. < 5kin) shows a significant discrepancy between the results of the

/El: I'i.oc.-Geiiei~. Ti.~ii~\iii. l h / r i / i . , I ' I J / . 147, No. 4. , / i d \ , 211110

two equations. It is evidcnt that the simplificd niodcl con- siderably overestiinates / y r , increasingly as fDc, becomes shorter. Precisely, for IAH = l / ](, = 0. I Im, thc accurate eqii. 6 applied to PICAS cables yields l / q i . l = 1.2'%1, while eqn. 4 yields /!qrl = 50.2'%,.

(> %kin), the two equations give similar results, as cxpected from the asymp- totic analysis of the two relalions for lIjC - CO. The effect of

The c~irvcs show how, due to the lower longitudinal resistance of aluminiLirn sheaths, the use of PICAS cables yields a lower l / y l . l than for lead sheathed cables.

Note that for very long lcngths

is mol-e significant for small values of / l j c . .

3.3.2 Effect of lZeBl and lZecl - simplified and advanced models: Unlike long overhead lines, the value of tlic terniination impcdanccs in cable circuits inay aKcct significantly the f2iult current distribution and the inagnitude of / y l .

I n big. 4, Vri1 given by cqiis. 4 and 6 is represented as ii function of lZc,/ll for different values of lZ, I when PILC- SWA cables are employed.

e 50 m -

40

30

20

10

n

The two equations yield similar results Tor very low values of lZ,,Rl. For increasing IZ(,ni, cqri. 4 yields increasing l[q,. for all thrce values of lZ(,(>l, while eqn. 6 exhibits the opposite trend for low values of lZi,,.I.

For very low values of &,(., the simplified model (Fig. 2) includes a very low impedance ground path connecting the fault point and the source. Therefore, if either Z,, is high or is short (/ljc,zi~l,l,c is low and so is the induced current ID(,), l / x l . l is very close to I 00'%,. 'The overestimation given by the siiiiplilied model may be in excess of 70%.

233

3.3.3 Effect of /z,A/, /&/ and /Zec/ - advanced model: Fig. 5 shows lIgll as a function of lZl,Al given by eyn. 6 for four different values of Z,, and Z,,,. when PILC- SWA cablcs are employed. Each group of curves refers to a different value of Zl,,. and the curves are parametric in ZcB.

35

$? 30 + -

i_ m - 25

20

15

10

For increasing values of IZl,A/, If$ decreases unless lZ,,l is very low, in which case it remains almost constant. [ncreas- ing lZ(,cl results in a reduction in lIKl.l, while increasing lZc3,1 either increases or decreases lZgrl, depending on whether lZl,Al < lZl,(:l or lZ(,r,l > lZ~,c.i, respectivcly. This can be explained as follows.

Provided that in the two seclions the same type and length of cable are employed, when ZoA and Z1,(. are of the same value, the symmetry of thc circuit (see Fig. I ) yields Z, = 0. A high earth impedance at thc source substation (lZl,Al > lZ,,l) tends to force fgr back to the sourcc via the inter- mediate substation and the sheath of section AB. On the other hand, for low values of Zl,,f (lZelfl < lZl,(.1) the inter- mediate substation drains part of I,, through earth and back to source via Therefore, in the first case an increase in Z,, reduces Zxr and increases IBCf, while for lZeAl < IZcci, Zxr is higher for high values of &.

3.3.4 Effect of the phase angle of /zeA/, /z&/ and /Zec/: Fig. 6 shows /ZR,l when the phase angle of Z,,, changes from 0.5" to 60" for three different lengths I,(. The magnitude of ZgJ is virtually inscnsitive to this parameter. Again, [l] tends to overestimate lZKt 1, particularly Tor short /,(,. Unlike the results of eqn. 6, those of eqn. 4 are not significantly affected by the length lIjc. Similar results were found for variations in the phase angle of the other two earth impedances.

234

40

301

2o t 10 l 5 tl,(vll

0 6 12 18 24 30 36 42 48 54 60 deg

Fig.6 L % ~ . ~ i i i ~ t i ~ ~ o f ' p 1 /O .l'ypc -= NLC'SWA. = yktii, Eqn. 4 c11rvc: (i) (km) = 0. I (ii) / / J ( (kin) = 1 (iii) (km) = 5 Eqn. 6 ciirvc: (iv) 11,( (kin) = 0. I (v) in, (kin) = I (vi) I , , (kin) 5

4 Single-core cable circuits

111 installations employing single-core cablcs, the three sheaths are bonded together and connccted to earth at each leimitiation, forming three conductive paths mutually cou- pled and electrically in parallel. tn long circuits, the sheaths might also be cross-bonded at intermediate points in order to compensate for induced voltages during load conditions. 'The latter casc is not treated in this paper. However, the L I S ~ of single-core cables makes the fault current distribu- tion calculation more complicated, requiring more paralie- tcrs to be accounted for, such as the separation distance and the mutual coupling between thc cableshheaths. A three-substation system employing single-core cables is shown in Fig. 7.

The assumptions introduced in Section 3 regarding the fault current Z, and the treatment of PILCSWA cables are also made for this arrangement.

I E E Pi01 -Genrt iiun\tn Dic/ i ih , Vu/ I47 N o 4 J u h 2000

4. I Simplified model Assuming a remote source of infced supplying cable section BC, the simplified model shown in Fig. 8 is obtained [l].

IBC --______, phase I I

1 Znlp,l-2 3

sheaths

.

When the impedances of the cables are sniall compared to the earth grid impedances (short lnc andlor high carth impedances), the effect of the latter dominates. I n these cases, eqn. 9 cat1 be simplified to

If, in addition, RH s R , lIxr1 is approximately 50%.

4.2 Advanced model This analytical model refers to the complete system of Fig. 7. It is assumed that the three single-core cables are symmetrically disposed in a close trefoil formation, for which the mutual impedance between the faulted phase conductor and the sheaths in the healthy phases is inde- pendent of which phase is faulted. For cables laid in flat formation, this parameter would depend on whether the fault occurs in the central or in one of thc outer phases.

This paper only refers to arrangements using the same cable type in trefoil formation in the two sections of length IAB and lEC. Assuming phase 1 to be the faulted phase, thcn

~77x1,~ = zrn2,3 = z n i ~ j , ~ Z n t p , 2 = z m p , : < (11) Eqn. 1 1 implies that

I2BC IRBC

IaAB = 4 A R

IEE Proc . -Gc~i~'r . Truns~n. DDlrih., Vol. 147, Nu. 4. J~t ly 2f)flfI

The solution of the system iii eqn. 13 yields

whcrc

It is recognised that the above analytical relations will require extensive calculations for- the evaluation of Ig,. Techniques for simplifying these equations into a more readily useable yet accurate form for practising engineers are currently being developed.

4.3 Parametric comparison Parametric studies were conducted on this arrangement employing 240mm2 PILCSWA cables to compare the two modcls. The effect of employing different cable types can be seen in Section 3.3.1. The assumptions and reference val- ues employed here are the same as those of Section 3.3. A cable centre to centre distance D of 0.051~1 is assumed.

4.3.1 Effect of cable length - simplified and advanced models: The variation of lIK,l with Inc. is rep- resented in Fig. 9 for different lAB. As predicted above, for grid impedances of similar values and short lengths f B c , the simplified model gives Is, E: 50%. The difference between the results given by eqns. 9 aiid 14 Tor short cable lcngths can be of the order of 50%. The maximum variation in lZsll due to a change of I,], from 0.1 to 5km (when = 0.1) is 29.5% (employing three-core PILCSWA cables it would be

215

34.1%). As with three-core cables, varying IAl j does not sig- nificantly affect JKr.

6C

55

50

45

40

35 s Q 30

~

L 0 -

25

20

15

10

5

0 I I I I I I I I I I

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Igc, km

(i) Eqn 14 ctisve: (ii) LAO (kin) = 5 (iii) lilH (kni) = 2 (iv) (km) = I (v) (km) = 0.5 (vi) //la (kin) = 0. I

80

70

30

20

10 --c-c--_L (iv)

(V)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 IZeBIz 8

236

4.3.2 Effect of lZeBl and lZecl - simplified and advanced models: Fig. 10 shows the sensitivity of &,,.I to lZeBl for different values of lZ,cl. Unlike Fig. 4, the accurate solution yields decreasing 1 for increasing iZc,ljl, even for relatively high lZc>c.\. The discrepancy between the results of the two equations is grcater than for three-core cables and the overestimation given by the simplified model may reach 85'%1.

4.3.3 Effect of IZeAI, lZeBl and lZecl - advanced model: The scnsitivity of iZKll to variations in the earth impedances shown in Fig. 11 is similar to that found for three-core cables (cf. Fig. 5). However, for the same values of earth impedances and cable lengths, the usc of single core cable slightly reduccs the magnitude of IKl . This is due to the reduction in overall longitudinal sheath resistance and to the additional llow of current induced in the healthy sheaths by the mutual coiipling with the faulted phase con- d uctor.

30 0

27 5

25 0

- 2 m 2 2 5 b

20 0

17 5

15 0

12 5

10 0

7 5

I I

5.0' ' I I ' I I I '

lZeAI, 6 2

Fig. 11 Typc = PILCSWA, lAll = Curvc: (i), (v), (ix), (xiii) (ii). (vi), (x), (xiv) lZc,tl (9) = 0.1, I, 2. 4; I& (62) = 1 (iii), (vii), (xi), (xv) (iv), (viii), (xii), (xvi)

Sensitivity o'lfgrl io i~~,;.ai,fbr c//fi,rent lZ,,l cind l& j (eqn. 14) = Ikiii

(9) = 0.1, I, 2, 4; 1Zt:,.,? (B) = 0.01

(9) = 0.1, I, 2. 4; IZ,,l (9) = 2 ((2) = 0. I. I, 2, 4; \Z,# (8) = 4

The sensitivity of to the phase angle of the earth inipedances is very low, even for systems einploying single core-cables.

5 Two-substation arrangement

For completeness, it is worthwhile to examine the current distribution for the simpler two-substation arrangement shown in Fig. 12 for three-core cables. This model can be employed to analyse systems in which the Faulted subsla- tion (S,) is directly connected to the source substation (SA) without an intermediate earthing point at B. Accordingly, the expression of ZR,. for this circuit is

II single-core cables laid in trefoil are employed

Eqns. 16 and 17 could also be obtained fi-om cqns. 6 and 14, respectively. for Z,, ---5 W. Eqn. 16 is equivalent to eqii. l u in appendix B of [I], while eqn. 4 of the same appendix [ I ] reduces lo eqn. 17 once the simplification valid for tre- foil formation (eqn. 1 I ) is introduced.

‘AC

I I phase

sheath

Fig. 12

50

40

30

8 - - ~- . m -

20

10

0 0.01 0.01 1 10 100

IZ,A+Z,CI/IAC

Fig. 13 , fb l . t/ifii.l~c.rlt crhle t y / m

~ l ~ ’ ( ~ - ~ s ~ l / ~ . ~ t f ~ / ; ~ / ? crrrrr/zgwc.nt. Smsiriisitj, uf 1 io IZ(,,,, + Z , ,

Eqn. 16 3-corc ctirvc: (i) PILCSWA (iii) XCPE Icad shcaf (iv) XLPE coppcr scrccii (v) PICAS Eqn. 11 I-corc CLI~VC: (ii) 1’[LCSWA (vi) PICAS

Fig. 13 shows lIg,l as a fuiiction of the parameter IZ,,, + Zc,#Ac, using eqns. 16 and 17 for the same cable types of Sections 3.3 and 4.3 (curves I , 2, 3, 4 and 5) and for 33kV, fluid filled, single-core, 240mni’ PICAS cables (curve 6).

I E E Proc.-Geiier Tvr/iisni. Dixtrih., Vol. 147, No. 4, Jidi. 211011

The curves Iollow the same trend Cor all cable types, and the value of I&,l for IZc,,, + Zc,cl///,c + 0 is dictated by the cable self and mutual impedances. As expected, the cables with higher longitudinal per unit sheath resistance yield higher II,, I values. In addition, comparisons between curves 1 and 2 and bctwcen 5 and 6 show that single-core cables yield lower I than the corresponding size of three-core cables.

6 Conclusions

The paper has examined current distribution under earth fkiilt conditions for subslalions fed by three-core and sin- gle-core cable circuits. Arrangements with substations inter- mediate to the source and the faulted point are treated together with simpler two-substation systems.

A detailed analytical inodel is presented for the calcula- tion of the ground return current f,,,,., required for safety assessments of substations. The equations obtained here have been compared with simplified models through para- inclric analyses. Thcsc showed that the latter inay be inac- curate, especially for the short lengths of cable typically employed in actual systems. For specific combinations of the earth impedances, the einploynieiit of siniplified models may lead to overestimations of lIKrl by up to 90‘%,. It is sug- gested that the simplified models based on [I] are not employed 011 arrangeinclits where a cable section has a remote soiirce of iiifeed or a remote fault, for which thc paper provides accurate analytical expressions. The simpli- fication of these expressions into a inore readily useablc form is the aim of work currently undertaken by the authors.

Finally, the sensitivity of Ig, to changes in the key parain- eters has been illustrated, providing useful information to engineers engaged in such analysis.

7 Acknowledgments

The authors would like to thank EPSKC and Strategy & Solutions Ltd. Cor supporting this work, and also Dr Aziz Ahniad-Marican and Mr Giovanbattista Mattiussi for their contributions to some preliminary work.

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6

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8

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References

S.34: ‘A gtiitlc lor asscssing thc risc of cart11 potential at substation sites’. Electricity Association. Engineering Recoiiimendation, I986 VBIIMA. R., and MUKHBDKAR. E),: ‘Ground f k d t current distri- hiition in substations, towers and ground wires’, IRE/: T iwx I ’ m c r Appri/,, S,y.st., 1979, 98, pp. 724 -730 NAHMAN, J.M.: ‘Proximity cTlects on the ground Ihult current dis- tribution within the carthing system formed hy a suhstation and the associated transmission lines’, IRE Proc C: Gencv. ‘frr/ii,s/ii. DisIrih, 1988, 135, (G), pp. 497-502 GUVEN, A.N., and SEBO, S A . : ‘Analysis of ground fatilt ctirrcnt distribution along tinderground cables’, / /<LE Trcu1.s. Po iw IMiv., 1986, PWRD-I, (4). pp. %I5 I’OPOVIC, L.M.: ‘I’ractical method lor evaluating ground I h l t .

rent distrihution iii slation supplicd by iiii tiiihoiiiogeneous line’, If 7i(iii.s. /’otwr De/iii,, 1997, 12, (2), pp. 722-727 BS 7354 ‘Code of practice for design of high-voltage open-lcriiiinal stations’. BSI Standard, I990 VIEL, E., and GKIE‘F‘ITHS, H.: ‘Determination of grotitid rcturii currents Tor earth faults Ted by metal sli~itlic~/scrcciie[t cables. A case study’. I’rocccdiiigs 0 1 33rd Universities Power Enginccring confcr- ence, UPEC ‘98, Edinburgh, UK, 1998, pp. 715 718 NAIiMAN, J.M., and DOIIDEVIC:, V.: ‘Distribution of zero scqucncc currents for earth faults occurring along transmission lines and proximity efl‘ccts’, lB/i Proc.. C, Gwier. Trcms/77. Distrih., 1993, 140, (5), pp. 427-432 NAHMAN, J.M.: ‘Earthing cll‘ccts of coated ~ i i i d ~ r g ~ ~ ~ i i i d cables with iiietallic shields honctcd to earth clcctrodcs’, /EE h o c . C, Geiwr. ’ l i ~ m s r ~ i . / M i h , 1997, 144, ( I ) , pp. 2630

231

9 Appendix: Cable dimensions and impedances

Table 1 summarises the dimensions and impedances of the cables employed in the paper. For three-core PICAS and

PILCSWA cables, the values of impedance stated in the table on p. 26 of [I] were employed, while for the other cable types, calculations were made based on manufactur- ers’ data using the Carson-Clem relations [l].

Table 1: Cable sheath dimensions and impedances

Cable type Three-core cables Single-core cables

33kV240mm2 ri,mm r,mm z,Q/km z,,, Q/km r;, m m r,, mm z, Q/km z,;,~, Q/km z,,;, Q/km

PL 0.396+j0.63 0.049+j0.63 18.60 20.60 0.918+.j0.673 0.049+j0.618 0.049+j0.673

PA 0.174+j0.652 0.049+j0.652 17.10 18.00 0.334+j0.683 0.049+j0.618 0.049+j0.683

XL 41.79 44.59 0.331+j0.626 0.049+j0.624

xc 42.78 46.15 0.261+j0.624 0.049+j0.624

PL = PILCSWA, XL = XLPE lead sheath, XC = XLPB copper screen, PA = PICAS, ri = inner radius, ro = outer radius

238 IEE Proc-Gene,. Trmsm. lAstrili.a Vol. 147, No. 4, .July 2000