_ _______ _ _ _ _____ _ ________________ JICABLE '99

A6.4The additional losses in the metallic screens of high voltage cablesDEJEAN P.M .• O bies Pirelli, Sens, France

FONTANA M .• REMY c.. ZACCONE E.• Pirelli Cavi S.pA. Mi lano. Italy

Abstract :The continuously increasing request lor electricpower implies a correct d imensioning 01 thecables conductor. The choice 01 cables withlarger cross-sectional areas is a consequence ofthis,in order to reduce the energy losses.An analytical st udy 01 the losses generated in themetallic screens has been do ne, it allows anappropriate ca lculation 01 the cabl e currentcarrying capacity applicable to copper wi rescreened H.V. extruded ca bles. The study hasbeen carried out lor EPR insulated cables but canalso be extended to XlPE insulated cables up to400 kV.

1 - Introduction

For oi l li lled o r impregnated pa per insulat edtrad itional cables, as weil as in so me t yp es 01modern extruded ins ulated ca bles, the metallicscreen is normally constituted by an impervi ouslead alloy or corrugated aluminium shea th, thatcombines the lollowing electrical and protectivelunct ions:a) limiting the electrical lield; carrying thecapacitive and leakage current , carrying the earthl ault current 01 the system and en su ring in somecases the cont inuity 01 the earthing.b) Protecting lrom possible accidentai electriccontacts with the core and preserve the insulationaga inst the ent rance 01 mo isture andcontaminat ing agents that may be pre sent in thecab le surroundings.Th e we il proven experience gained Irom the earlysixt ies wi t h Ethylene Propylene Rubber (EPR)insulat ion ha s demonstrated that this cables donot need any w ater barrier. This is a consequence01 the good resistance 01 the insulation tomo isture that has also been conlirmed by longterm water treeing tests carried out in laboratory.This property allow s to design a cable w ithoutany metall ic sheath , replaced by a copper wires ort ape s screen. A large amount 01 132 kV cablesmade w it h t his design have already beensuc ce sslull y installed since the seventies and arecurrently used now by ENEl up to the voltage 01150 kV .

Résumé:la demande sans cesse croissante d'énerg ieélectrique nécessite un dimensionnement correctdes conducteurs de s câbles . la conséquence enest le choix de câbles avec des conducteurs desection plus grande et conçus pour réduirel ortement les pertes d 'é ne rgieCette étude analytique des pertes générées dansles écrans mét alliques permet un calcul co rrectde la ca pacité de transport des câbles H.T . àisolation EPR et éc ran li ls cuivre , et peut êtreétendue également aux câbles X l PE jusqu'à 400kV .

Figure 1 - 150 kV E PR copper wi re sc reen cablewith large conductor

Additional los ses in the screenThe current Ilowing in the conductor generates inthe cable metallic screen currents that causeadditional losses due to the Joule elfect. Theselosses will cu mulate with the conductor los sesgiving the result 01 reducing the cable permissiblecurrent capacity .The thermal equilibrium 01 a single-core cable inwhich the current Ilows is obtained lrom thelollowing lormula:9c - 0... := (Wc + 112 Wo) Tl + (Wc + Wo + Wsl (1 3 + T..I

Where the symbols are those indicated andcalculated accordingly the IEC 60287 st an dard"Calculation 01 the continuous current rating 01cables (100 % load Factor)" [ 1 JTaking into consideration the metallic screentosses , these are expressed as a lunction 01 the

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lasses in the conduc tor by the relation W s = ÀW cw here À is the rat io between the tota l lasses inthe sc reen and the total lasses in the conductor.Since the current is a cam mon parameter, thisrelation ca n be reduced ta an equiva len taddit ional resi st ance of t he conductor expectedas a ratio (À) comp ared w ith the originalco nd uc to r resistance or in absolut e va lue (Ol m i asused f or t he fo llowing considerations.Scr een lasses can be c lassified in two types, theones ca us ed by t he circulating current , called À'and those ca used by the eddy currents , called À".Using the terminology of t he IEC St andard n O60287 w e ca n therefore w rit e:

À= À' + À"À' is due t a the induced c irculating current in t he

sc reen that can be eliminated or strongly reducedby ado pt ing spec ial metallic screen bondingarr angements (single point bonding or crossbond ing l [2].À" are the edd y current lasses and are not on lylin ked ta the conduct or and meta llic screengeomet ric dimensions but also ta the conductivityof t he sc reen .For HV or VHV ca bles insta lled in sys t ems withvery high earth fault cu rren ts , the met allic screensmu st be design ed t a have a suitable total cross­sect ion area capa ble to susta in these currents.When using a m et allic sheath as a screen it ' slarge thi ckness im plies th at the eddy currentlasses ca n reach va lues of 10 - 30 % and can notbe eliminated , sa reduc ing the conductor rating by5 - 15 % . Using a metallic screen co nstituted bycoppe r wi res (see fig . 1) having an electri cal crosssec ti onal area equivalent ta the metallic sheathsthis paper prove s that the eddy current lasses À"are practi cally negligible.Th e IEC St andard n ? 60287 provides fullinf ormati on on how t a ca lculate eddy currentlas ses for continuous tubular sheaths, w ith andw it ho ut reinforcing t apes . For copper wiressc reens there is no proper calculati on method andnormally f or these type of screens they areassumed ta be simi lar ta an equivalent t ub ularsheath of the same size . This ass umption is notcomplet ely valid bec ause it does not take intoaccount the real geometry of this type of screen.ln fact , a wi re screen is a set of small c ross­sec t ion individual elements and cannat bemo de lled by a single element even if it has thesame global c ross-sec t ion . Exactly as the metalsheets in th e magnetic circuit of a transformerhave a different behaviour fram the one of an"equivalent " bulk nucleus . Using the basic t heory[3, 4 , 51, from w hich the IEC st andard n ? 60287th eory has been obtained, sa me approximat epractical form ulae are here under reported .Confirmation of t hese practica l formu lae can be

ob tained in [141 where more compli catedformulae are reported.

2 - An alytical co nsiderations

The fun dam ental config urations of t he magneticfie ld for the ca lculation of induced lasses in thescreens (as for the skin and proximity effects inthe conductors) are:1 coaxial, current inside the screen; (current in

the conductor of the same phase);E current outside the screen, parallel with the

cable axis, in a single-phase system; (currentin the other cond uctor);

T cu rrents inside and outside the screen, pa ralle lwith the cable axis , symmet rica l and ba lancedin a three-phase system (currents in the threeconductors)

The ex isting ca lculation methods caver the wholerange of l, E, T co nfigurations in case ofhomogeneous t ubular screens and have beenintroduced in the present standards. Th is t heoryhas then been applied also ta w ire and /or tapescreens helically applied .

General points on open helicesThe mai n di fferenc e between the open heli xes(eit her tapes or wires) case and the tube one isthat the induced currents inside the singleelement are subjected ta cross-section reduc t ionalong their path in comparison with w hat isadmit t ed in a tubular structure .Therefore , the formulae developed for the specialcases have bee n based on the carefu l study ofgeometry and currents paths and balancedbetween complex models and simple formulae inarder ta reach an acceptable approximation level.Generally speaking, reference ta the tubularst ructure has always been made fo r it 'smathemat ics and schematisation simplicity or onlybecause it is the formai reference ta the standard .The comparison between helixes and tubes (seetables 1, and 2) has been made on thedimensions (diameter, thickness/area) andmateria l (conductivity, cr pa rameter) as weil as the

equ iva lence of t he dimensions and specificlongitudinal resist ance (O /m , r parameter) .

Formula e developmentThe screen structures constituted by an openhelical applied tape (Tape), or non-touch ing andhelical applied wires (Wires) or more real isticall ywi res with a counter heli x tape (Wires + tape)have bee n ana lysed for bath co nfigurations E and1. The results were compared with those of asimilar t ube using t he approximate and the exactformulae, and also apply ing the IEC me t hod .Th e complete study and the developm ent of theformulae ca n be f aun d in [14].

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3 - Results analysis

Comparison of the formulaeThe formulae developed in this study for thepractical case of copper wires plus counter helixtapes are reported in the tables 1 and 3,comparison can be made with the equivalent tubereported in table 2.We emphasised the expressions of the resistanceequivalent to the los ses induced in one meter ofthe screen (related to the main conductor). Theselosses are expressed either as a function of theconductivity, either as a function of the screensspecifie resistance, for the formai comparisonwith the formula relevant for the "equivalent"tube.When looking at the formulae developed in thetables some interesting remarks can be made:

TubesAs known the proximity effect (E) highly prevailsover the skin effect (1) as expressed by the ratioREIRI , not very different fram (D/S)2 (see Table 2).RE is the additional resistance equivalent to los sesinduced by the praximity effect, and RI the samefor the skin effect.

TapesFor tapes the ratio RE/RI praves to be > > 1 andclosely related to the ratio valid for tubes.

Wiresln case of wires the ratio RE/RI = D2 /4d 2 is lessbut not to far from the unit. D is the screendiameter and d is the inter-axial distance of thescreen. When comparing the expressions withthose of equivalent tubes, it is possible to verifythat the losses in configuration 1 (Rwires/Rtube =3a 2/4s 2 ) , being a the diameter of the wire and sthe thickness of the tube, remain of the sameoroer of magnitude or are comparable. Whereasthe losses in configurations E (Rwires/Rtube =3a 2/4d 2 ) are significantly lower and comparablethe ones of configuration 1.Note: the deciding factor for obtaining such areduction is the wire diameter. In fact, dividingthe same cross-section (corresponding to r, thescreen resistance per unit length) in n wireshaving a diameter (a), the los ses in bothconfigurations E and 1 will reduce according to a2

(or 1/n 2r.These results are in perfect accordance with theonly data founded till now in the literature on thissubject. [11 J.

Wires + tapeln this case it is not possible to comparepositively the expressions because they are toocomplicated (see Table 1); therefore reference ismade to the following numerical example.

Comparison of the numerical resultsThe numerical comparison has been carried out ina practical case.We have considered the data of an extruded cable132 kV - 1 x 1200 mm" with a copper wirescreen and counter helix tape for calculating theequivalent resistances using ail the methods wehave up to here developedThe numerical values used for the calculation are:

WiresD = 87 10-3 m (mean diameter of the screen)p = 0.87 m (a = 19.4°) (wire lay length and

application angle)d = 96.5 10-3 m (distance between the cable

axis)cr = 5.56 10+7Q-'m-' (copper conductivity)n = 105 (number of screen wires)rf = 120 10-6 Q/m (screen resistance)a = 1.35 10-3 m (wire diameter)Il = 110 = 4 1t 10-7 H/mf = 50 Hz

Tape:D = 89 10-3 m (mean diameter of the counter

helix)b = 15 10-3 m (tape width)s = 0.07 10-3 m (tape thickness)p = 77.8 10-3 m (a = 83°) (tape lay length and

application angle)rn = 65 10-3 Q/ m (tape resistance)

The results of the calculations are shown in figure2. The additional equivalent resistances areshown as reference to the resistance of the phaseconductor.The comparison of the above mentionedexpressions for the different cases and of thenumerical results for a typical case, relevant forthe conventional calculation method as indicatedin IEC 60287, shows that:

• The appraximate expressions to calculate thelosses in wires are enough accurate;

• The losses calculated in wires (either exactly,or either approximately) are less than 0.01 %of the conductor resistance and mainly due tothe phase internai current;

• The losses calculated in wires when applyingsystematically the IEC formulae (which arequite appropriate in case of tubes), are of 3 or4 orders of magnitude higher (from 20 to 30% of the conductor losses);

• The losses calculated approximately in thetape by its self have the same order of

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importance as the ones in wires, but slightlyhigher;

• The losses calculated in the tape by its selfwhen applying systematically the IEC formulae(0.1 %) are slightly higher (Iess than an orderof magnitude) than the ones calculated as justdescribed above;

• The losses calculated approximately (byexcess) for wires + tapes meshes, « 0.1 %)are a little higher than losses calculated in bothelements taken separately, and a little lessthan the value calculated for the tape by itsself with the IEC formulae.

• Experimental checking of calculations requiresan AC measurement of additional resistanceswith a device that has an accuracy ::; 10-8 Q/m[13]. '

The comparison of exact losses in configurationsl, E, T, shows that the difference between asingle-phase (E) and a three phases (T) isgenerally 'Iow. This justifies using at first theapproximate formulae nEn for a three phasessystem also when the purpose is only todetermine the order of the losses magnitude.

Log 10 of equivalent additional resistance­Q/m

Figure - 2Lasses indueed in the wire + tape sereen, calculatedby various methods and shown like the decimallogarithm of equivalent additional resistance in QI mCond = conductor resistance1 = Wires/tape according to IEC 2872 = Tube equivalent to wires, approx.3 = Tube equivalent to wires, exact4 = Wire. 0 1.35 mm approx.5 = Wire. 0 1.35 mm exact6 = strips 1.2 X 1.2 mm, approx.7 = Tape according to IEC 287.8 = Tubeequivalent tQ tape, approx.9 = single tape, approx.10 = meshes tape + single wires

o-2

, , 1, , 1 c::::I, , 1, , 1

:=~ 1 ,

1

~ E := :""", 1

I3T , = :E§"', ,OI+T , ,

, :œz::lr::=s3 1 1, 1 1, , , 1, , ",.: 1

1, , , ,, ,= """": 1, 1, ,

1 1,, , c;:=' 1

1,1 ,, , ,1 1

I~ , '= 1 1, ,1 1

:~, ,

=: 1, 1

: ,

~,, 1

: : , ,

1

2

3

4

5

6

7

8

9

10

- 16 - 14 - 12 - 10 - 8 - 6 - 4

eond.

4 - Conclusion

The basic finding is that the calculationaccording to the IEC 60287 method is notsuitable and too pessimistic when applied toscreen wires. Therefore, for such cases it isbetter to analyse them with the approximateformulae for wires and for tape separately (seeTable 3), or to apply the IEC formula only to the

tape. These calculations generally allow us tocon sider the additional losses in the screen wiresas virtually negligible (for e.g. < 1 %). Whenthese losses cannot be considered as negligible itwill be then worth calculating the contribution ofthe wires + tape meshes and verifying theapproximation level of these results.The method developed on this paper can be thebase for the formalisation of a new work itemproposai at international standardisation javel.

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TABLE 1

Calculation formulae for resistances equivalent to induced losses in wires + tape.

(wires)

III U

Config.

/JE"config.

cr parameter (conductivity)

7r 3- fi2 f2 cr !- k cos" ex (tape)3 D

+ ~ fi2 f2 cr~ n16 D 2

(wires)

. 2sm a

7rD 4n--+--bsp ita 2

r parameter (resistance)

With k

r,

b

:TrDcosa1

ab s cosa

filling factor for tapes.

resistance per unit length for a tape

4resistance per unit length for a wire

Cf7ra2

COSa

7r D 4 n---+ --::-3 b s p 7r a

2

7r 2 CT sin 2 a

Other parametersdefined in the numerical example.

TABLE 2

resistances equivalent to induced losses in tubes.

cr parameter (conductivity) r parameter (resistance)3 1. fi2 f2 ~

S2:Tr S

RI _ fi2 f2 cr-- -3 D 3 r D2

!!- fi2 f2 cr sD3

~ fi2 f2 ~ D 2

RE 12 d 2 12 r d 2

1r=--­

CT:TrDs

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TABLE 3

Table for separated losses valuation of screen elements ( tape, wires)(conductivity)

Configuration 1(RI)Tape TC

112 f2 0'S3

k cos?«- -3 D

Wire a = 0 TC a4

longitudinal -1l2 f2 0' -n16 D2

a < "" 50 a 4TC 2 f2 a

long lay -Il 0'-- n cos a

length 16 D 2

a"" > 80 aIr a4 sinla

short lay -:"'1l2 f2 O'-n--length 32 D 2 cosa

5 - References

[1] IEC 60-287 Standard « Calculation of theContinuous Current Rating of Cables (100%Load Factor) »

[2] ELECTRA N° 28 & N° 47 « The design ofspecially bonded cable systems»

[3] Dwight « Proximity effect in wires and thintubes» AIEE Trans., vol 42, 1923, p.850

[4] Arnold « Proximity effect in solid andhollow round conductors» J.I.E.E. vol 881941,p.349

[5] Pirelli Report U. T. n. 188, Dec1954[6] Neher, Mc Grath « The calculation of the

temperature rise and load capability of cablesystems» AIEE Trans., vol 76, 1957

[7] CERL Report RD/LIN 132174 « Eddy currentlosses in isolated tubes ». 1974

[8] EPRI Report EL-2256 « Determination of ACconductor and tube losses in pipe-typecable systems », Pirelli Cable Corp., 1982

[9] EPRI Report EL-3624 « Designer'shandbook for forced-cooled HPOF pipe-type

Configuration E (RE)Short helix sD 3

b»nD/2 TC- 112 f2 0' 7 k12

Long helix sD 3

b«nD/2 TC 112 f2 0'-- lècosa-3 dl

longitudinal TC a 4

- 112 f2 0' n64 d 2

Touching phases 41 Ir a- -1l2 f2 0'-- n

Minimum value 9 16 Dl4

Ir a- 112 f2 0' -- n

Maximum value 16 Dl

Long strip~ 112 f2 0'

sb 3

(p » b) --12 dl

cable systems ». Underground systems lnc.,1984

[10] Pirelli Report RTLR 974, Mar. 1965[11] K. Watanabe & ethers, « Application of

corrugated stainless steel sheath to highvoltage XLPE cable ». Fujikura TechnicalReview 1994

[12] E. Meyer, L Silvera « Eddy current shieldingand heating, reduction of dissipation forvery low temperature experiments in thepresence of magnetic field ripple« Rev.Scie. Inst. 60 (9), Sept. 1989,p.2964

[13] S. Fleshler, P. Metra & others« Measurement of true ac power loss of Bi­2223 composite tapes using the transporttechnique « submitted to Applied PhysicsLetters, Aug. 1995.

[14] M. Fontana, P. Metra, E. Zaccone « Leperdite addizionali negli schermi a fili deicavi di alta tensione » r L'energia ElettricaVol. 72 N° 6 Nov. Dic. 1995

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