23

3 ConductorsLauri J. Hiivala and Carl C. Landinger

CONTENTS

3.1 Introduction....................................................................................................243.2 MaterialConsiderations..................................................................................24

3.2.1 DirectCurrentResistance...................................................................253.2.2 Weight.................................................................................................253.2.3 Ampacity............................................................................................253.2.4 VoltageRegulation..............................................................................253.2.5 ShortCircuits......................................................................................253.2.6 OtherImportantFactors.....................................................................25

3.3 ConductorSizes..............................................................................................263.3.1 AmericanWireGauge(AWG)............................................................26

3.3.1.1 ShortcutsforEstimations.....................................................263.4 CircularMilSizes...........................................................................................273.5 MetricDesignations........................................................................................363.6 Stranding.........................................................................................................40

3.6.1 ConcentricStranding..........................................................................403.6.2 CompressedStranding........................................................................ 413.6.3 CompactStranding............................................................................. 423.6.4 BunchStranding................................................................................. 423.6.5 RopeStranding................................................................................... 423.6.6 SectorConductors............................................................................... 433.6.7 SegmentalConductors........................................................................443.6.8 AnnularConductors............................................................................ 453.6.9 UnilayConductors..............................................................................46

3.7 PhysicalandMechanicalProperties...............................................................463.7.1 ConductorProperties..........................................................................46

3.7.1.1 Copper..................................................................................463.7.1.2 Aluminum............................................................................463.7.1.3 ComparativeProperties,CopperversusAluminum............ 47

3.7.2 Temper................................................................................................ 473.7.2.1 Copper.................................................................................. 473.7.2.2 Aluminum............................................................................ 47

3.8 StrandBlocking..............................................................................................483.9 ElectricalCalculations....................................................................................48

3.9.1 ConductorDCResistance...................................................................483.9.2 ConductorACResistance................................................................... 49

24 Electrical Power Cable Engineering

3.1 INTRODUCTION

Thefundamentalconcernofpowercableengineeringistotransmitelectricalcurrent(power)economicallyandefficiently.Thechoiceoftheconductormaterial,size,anddesignmusttakeintoconsiderationsuchitemsas:

Ampacity(currentcarryingcapacity) Voltagestressattheconductor Voltageregulation Conductorlosses Bendingradiusandflexibility Overalleconomics Materialconsiderations Mechanicalproperties

3.2 MATERIALCONSIDERATIONS

Thereareseverallowresistivity(orhighconductivity)metalsthatmaybeusedasconductorsforpowercables.Examplesoftheseasrankedinorderofincreasedresis-tivityat20CareshowninTable3.1[1].

Consideringtheseresistivityfiguresandthecostofeachofthesematerials,copperandaluminumbecomethelogicalchoices.Assuch,theyarethedominantmetalsusedinthepowercableindustrytoday.

Whenchoosingbetweencopperandaluminumconductors,oneshouldcarefullycomparethepropertiesofthetwometals,aseachhasadvantagesthatmayoutweigh

3.9.3 SkinEffect.......................................................................................... 493.9.4 ProximityEffect.................................................................................503.9.5 CablesinMagneticMetallicConduit.................................................503.9.6 ResistanceatHigherFrequencies.......................................................50

References................................................................................................................ 51

TABLE3.1ResistivityofMetalsat20CMetal Ohm-mm2/m108 Ohm-cmil/ft106

Silver 1.629 9.80

Copper,annealed 1.724 10.371

Copper,harddrawn 1.777 10.69

Copper,tinned 1.7411.814 10.4710.91

Aluminum,soft,61.2%cond. 2.803 16.82

Aluminum,1/2hardtofullhard 2.828 16.946

Sodium 4.3 25.87

Nickel 7.8 46.9

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25Conductors

theotherundercertainconditions.Thepropertiesmostimportanttothecabledesignerareshowninthefollowingsections.

3.2.1 Directcurrentresistance

Theconductivityofaluminumisabout61.2%to62.0%ofthatofcopper.Therefore,analuminumconductormusthaveacross-sectionalareaabout1.6timesthatofacopperconductor tohave theequivalentDCresistance.Thisdifference inarea isapproximatelyequaltotwoAmericanwiregauge(AWG)sizes.

3.2.2 Weight

Oneofthemostimportantadvantagesofaluminum,otherthaneconomics,isitslowdensity.Aunitlengthofbarealuminumwireweighsonly48%asmuchasthesamelength of copper wire having an equivalent DC resistance. However, some of thisweightadvantageislostwhentheconductorisinsulated,becausemoreinsulationvol-umeisrequiredovertheequivalentaluminumwiretocoverthegreatercircumference.

3.2.3 ampacity

Thecurrentcarryingcapacity(ampacity)ofaluminumversuscopperconductorscanbecomparedbyreferringtomanydocuments.SeeChapter14fordetailsandrefer-ences,butobviouslyalargeraluminumcross-sectionalareaisrequiredtocarrythesamecurrentasacopperconductorascanbeseenfromTable3.1.

3.2.4 Voltageregulation

In alternating current (AC) circuits having small conductors (up to #2/0 AWG),andinallDCcircuits,theeffectofreactanceisnegligible.Equivalentvoltagedropresultswithanaluminumconductorthathasabout1.6timesthecross-sectionalareaofacopperconductor.

In AC circuits having larger conductors, however, skin and proximity effectsinfluencetheresistancevalue(ACtoDCratio,laterwrittenasAC/DCratio),andtheeffectofreactancebecomesimportant.Undertheseconditions,theconversionfactordropsslightly,reachingavalueofapproximately1.4.

3.2.5 shortcircuits

Considerationshouldalsobegiventopossibleshortcircuitconditions,sincecopperconductorshavehighercapabilitiesinshortcircuitoperation.However,whenmak-ingthiscomparison,thethermallimitsofthematerialsincontactwiththeconductor(e.g.,shields,insulation,coverings,jackets,etc.)mustbeconsidered.

3.2.6 otherimportantFactors

Additionalcaremustbetakenwhenmakingconnectionswithaluminumconduc-tors. Not only does the metal tend to creep, but it also oxidizes rapidly. When

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26 Electrical Power Cable Engineering

aluminum is exposed to air, a thin, corrosion-resistant, high dielectric strengthfilmquicklyforms.

When copper and aluminum conductors are connected together, special tech-niquesarerequiredinordertomakeasatisfactoryconnection.SeethediscussioninChapter13.

Aluminumisnotusedextensivelyingeneratingstation,substation,orportablecablesbecausethelowerbendinglifeofsmallstrandsofaluminumdoesnotalwaysmeetthemechanicalrequirementsofthosecables.Spaceisfrequentlyaconsider-ationatsuchlocationsalso.However,aluminumistheoverwhelmingchoiceforaer-ialconductorsbecauseofitshighconductivity-to-weightratioandforundergrounddistributionforeconomywherespaceisnotaconsideration.

The 8000 series aluminum alloys have found good acceptance in large com-mercial,institutional,andsomeindustrialapplications.Thesealloysofferreducedcoldflowandimprovedcreepresistance.Thisoffersgreaterretentionoftorqueatscrewdownterminalscommonlyusedinindoorplant.IntheUS,theNationalElectricalCode(NEC)callsfortheuseofthesealloysifaluminumistobeusedinanumberofwiretypesrecognizedbytheNEC.

Economicsofthecostofthetwometalsmust,ofcourse,beconsidered,butalwaysweighedafterthecostoftheoverlyingmaterialsisadded.

3.3 CONDUCTORSIZES

3.3.1 americanWiregauge(aWg)

Justasinanyindustry,astandardunitmustbeestablishedformeasuringthecon-ductorsizes.IntheUSandCanada,electricalconductorsaresizedusingtheAWGsystem.Thissystemisbasedonthefollowingdefinitions:

Thediameterofsize#0000AWG(usuallywritten#4/0AWGandsaidasfourought)is0.4600inchesforasolidconductor.

Thediameterofsize#36AWGis0.0050inches. Thereare38intermediatesizesgovernedbyageometricprogression.

Theratioofanydiametertothatofthenextsmallersizeis:

0 46000 0050

1 12293239 ..

.=

(3.1)

3.3.1.1 ShortcutsforEstimationsThesquareoftheaboveratio(theratioofdiametersofsuccessivesizes)is1.2610.Thus, an increase of one AWG size yields a 12.3% increase in diameter and anincreaseof26.1%inarea.AnincreaseoftwoAWGsizesresultsinachangeof1.261(or26.1%)indiameterand59%increaseinarea.

Thesixthpowerof1.122932 is2.0050orverynearly2.Therefore,changingsixAWGsizeswill approximatelydouble (orhalve) thediameter.Anotheruse-ful shortcut is that a #10 AWG wire has a diameter of approximately 0.1 inch,

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27Conductors

forcopperaresistanceof1ohmper1,000feetandaweightofabout10or31.4poundsper1,000feet.

Another convenient rule is basedon the fact that the tenthpowerof1.2610 is10.164orapproximately10.Thus,foreveryincreaseordecreaseof10gaugenum-bers(startinganywhereinthetable),thecross-sectionalarea,resistance,andweightaredividedormultipliedbyabout10.

Fromamanufacturingstandpoint,theAWGsizeshavetheconvenientpropertythatsuccessivesizesrepresentapproximatelyonereductionindiesizeinthewiredrawingoperation.

TheAWGsizeswereoriginallyknownastheBrownandSharpegage(B&S).TheBirminghamwiregage(BWG)isusedforsteelarmorwires.InBritain,wiresizeswerespecifiedbythestandardwiregage(SWG),andwerealsoknownasthenewBritishstandard(NBS).

3.4 CIRCULARMILSIZES

Sizeslargerthan#4/0AWGarespecifiedintermsofthetotalcross-sectionalareaoftheconductorandareexpressedincircularmils.Thismethodusesanarbitraryareaofaconductorthatisachievedbysquaring the diameterofasolidconductor.Thisdropsthe/4multiplierrequiredfortheactualareaofaroundconductor.Acircularmilisaunitofareaequaltotheareaofacirclehavingadiameterof1mil(1mil=0.001inch).Suchacirclehasanareaof0.7854(or/4)squaremils.Thus,awire10milsindiameterhasacross-sectionalareaof100circularmils.Likewise,1squareinch=4/times1,000,000=1,273,000circularmils.Forconvenience,thisisusuallyexpressedinthousandsofcircularmilsandabbreviatedkcmil.Thus,anareaof1squareinch=1,273kcmil.

A r= pi2

(3.2)

whereA=areaincircularmils;=3.1416;r=radiusin1/1,000ofaninch.TheabbreviationusedinthepastforthousandcircularmilswasMCM.The

SIabbreviationsformillion,M,andforcoulombs,C,areeasilyconfusedwiththisolderterm.Thus,thepreferredabbreviationiskcmilforthousandcircularmils.

The AWG/kcmil system is prevalent in North America (population over425million)andisalsousedtosomeextentinover65countriesintheworld.Themarketshareofcableproductssizedwiththissystemisestimatedatover30%($17.3billion)oftheworldmarketforpowerandcontrolwiresandcables.TheAWG/kcmilsystemisalsothereferencesizingsystemforallelectricalproductsandinstallationsinNorthAmerica.Assuchitrepresentsabasicelementoftheinfrastructure.Whenconsideredinconjunctionwithwiringdevices,connectors,andotherrelatedproducts,themarketaffectedbytheAWG/kcmilsystemissub-stantiallylarger[7].

Tables3.2and3.3providenominalDCresistanceandnominaldiametervaluesforsolidandconcentric-lay-strandedcopperandaluminumconductors.

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TABLE3.2ANominalDCResistanceinOhmsper1,000Feetat25CofSolidandConcentric-Lay-StrandedConductor

ConductorSizeAWGorkcmil

Solid Concentric-Lay-Stranded*

Aluminum Copper Aluminum Copper

Uncoated Coated ClassB,C,D

Uncoated Coated

ClassB,C,D ClassB ClassC ClassD

87654

1.050.8330.6610.5240.415

0.6400.5080.4030.3190.253

0.6590.5220.4140.3290.261

1.070.8510.6750.5340.424

0.6520.5190.4110.3250.258

0.6780.5380.4270.3380.269

0.6780.5380.4270.3390.269

0.6800.5380.4270.3390.269

3211/02/0

0.3290.2610.2070.1640.130

0.2010.1590.1260.1000.0794

0.2070.1640.1300.1020.0813

0.3340.2660.2110.1680.133

0.2050.1620.1290.1020.0810

0.2130.1690.1340.1060.0842

0.2130.1690.1340.1060.0842

0.2130.1690.1340.1060.0842

3/04/0250300350

0.1030.08190.06940.05780.0495

0.06300.0500

0.06450.0511

0.1050.08360.07070.05900.0505

0.06420.05100.04310.03600.0308

0.06670.05240.04480.03740.0320

0.06690.05300.04480.03740.0320

0.06690.05300.04480.03740.0320

400450500550600

0.04330.03850.0347

0.04420.03930.03540.03210.0295

0.02690.02400.02160.01960.0180

0.02770.02460.02220.02040.0187

0.02800.02490.02240.02040.0187

0.02800.02490.02240.02040.0187

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0.02720.02530.02360.02210.0196

0.01660.01540.01440.01350.0120

0.01710.01590.01480.01390.0123

0.01720.01600.01490.01400.0126

0.01730.01600.01500.01400.0126

1,0001,1001,2001,2501,300

0.01770.01610.01470.01410.0136

0.01080.009810.008990.008630.00830

0.01110.01010.009250.008880.00854

0.01110.01020.009340.008970.00861

0.01120.01020.009340.008970.00862

1,4001,5001,6001,7001,750

0.01260.01180.01110.01040.0101

0.007710.007190.006740.006340.00616

0.007930.007400.006940.006530.00634

0.007930.007400.007000.006590.00640

0.008010.007470.007000.006590.00640

1,8001,9002,0002,5003,000

0.009820.009310.008850.007150.00596

0.005990.005680.005390.004360.00363

0.006160.005840.005550.004480.00374

0.006160.005840.00555

0.006220.005890.00560

Source: ANSI/ICEAS-94-649,StandardforConcentricNeutralCablesRated5,00046,000Volts,2004.* Concentric-lay-strandedincludescompressedandcompactconductors.

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TABLE3.2B(METRIC)NominalDCResistanceinMilliohmsperMeterat25CofSolidandConcentric-Lay-StrandedConductor

ConductorSize

Solid Concentric-Lay-Stranded*

Aluminum Copper Aluminum Copper

AWGorkcmil mm2 Uncoated Coated ClassB,C,D

Uncoated Coated

ClassB,C,D ClassB ClassC ClassD

87654

8.3710.613.316.821.1

3.442.732.171.721.36

2.101.671.321.050.830

2.161.711.361.080.856

3.512.792.211.751.39

2.141.701.351.070.846

2.221.761.401.110.882

2.221.761.401.110.882

2.231.761.401.110.882

3211/02/0

26.733.642.453.567.4

1.080.8560.6790.5380.426

0.6590.5220.4130.3280.260

0.6790.5380.4260.3350.267

1.100.8720.6920.5510.436

0.6720.5310.4230.3350.266

0.6990.5540.4400.3480.276

0.6990.5540.4400.3480.276

0.6990.5540.4400.3480.276

3/04/0250300350

85.0107127152177

0.3380.2690.2280.1900.162

0.2070.164

0.2120.168

0.3440.2740.2320.1940.166

0.2110.1670.1410.1180.101

0.2190.1720.1470.1230.105

0.2190.1740.1470.1230.105

0.2190.1740.1470.1230.105

400450500550600

203228253279304

0.1420.1260.114

0.1450.1290.1160.1050.0968

0.08820.07870.07080.06430.0590

0.09090.08070.07280.06690.0613

0.09180.08170.07350.06690.0613

0.09180.08170.07350.06690.0613

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329355380405456

0.08920.08300.07740.07250.0643

0.05440.05050.04720.04430.0394

0.05610.05220.04850.04560.0403

0.05640.05250.04890.04590.0413

0.05670.05250.04920.04590.0413

1,0001,1001,2001,2501,300

507557608633659

0.05810.05280.04820.04620.0446

0.03540.03220.02950.02830.0272

0.03640.03310.03030.02910.0280

0.03640.03350.03060.02940.0282

0.03670.03350.03060.02940.0283

1,4001,5001,6001,7001,750

709760811861887

0.04130.03870.03640.03410.0331

0.02530.02360.02210.02080.0202

0.02600.02430.02280.02140.0208

0.02600.02430.02300.02160.0210

0.02630.02450.02300.02160.0210

1,8001,9002,0002,5003,000

9129631,0131,2661,520

0.03220.03050.02900.02350.0195

0.01960.01860.01770.01430.0119

0.02020.01920.01820.01470.0123

0.02020.01920.0182

0.02040.01930.0184

Source: ANSI/ICEAS-94-649,StandardforConcentricNeutralCablesRated5,00046,000Volts,2004.* Concentric-lay-strandedincludescompressedandcompactconductors.

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TABLE3.3ANominalDiametersforCopperandAluminumConductors

ConductorSize NominalDiameters(Inches)

AWG kcmil Solid

Concentric-Lay-StrandedCombination

UnilayUnilay

CompressedCompact* Compressed ClassB** ClassC ClassD

87654

16.5120.8226.2433.0941.74

0.12850.14430.16200.18190.2043

0.134

0.169

0.213

0.1410.1580.1780.2000.225

0.1460.1640.1840.2060.232

0.1480.1660.1860.2080.234

0.1480.1660.1860.2080.235

0.1430.1600.1790.2020.226

3211/02/0

52.6266.3683.69105.6133.1

0.22940.25760.28930.32490.3648

0.2380.2680.2990.3360.376

0.2520.2830.3220.3620.406

0.2600.2920.3320.3730.419

0.2630.2960.3330.3740.420

0.2640.2970.3330.3740.420

0.2540.2860.3210.3600.404

0.3130.3520.395

3/04/0

167.8211.6250300350

0.40960.46000.50000.54770.5916

0.4230.4750.5200.5700.616

0.4560.5120.5580.6110.661

0.4700.5280.5750.6300.681

0.4710.5290.5760.6310.681

0.4720.5300.5760.6310.682

0.4540.5100.5540.6070.656

0.4430.4980.5420.5940.641

400450500550600

0.63250.67080.7071

0.6590.7000.7360.7750.813

0.7060.7490.7890.8290.866

0.7280.7720.8130.8550.893

0.7290.7730.8140.8550.893

0.7290.7730.8150.8550.893

0.7010.7440.784

0.6850.7270.7660.8040.840

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0.8450.8770.9080.9380.999

0.9010.9350.9681.0001.061

0.9290.9640.9981.0311.094

0.9300.9650.9991.0321.093

0.9300.9650.9981.0321.095

0.8740.9070.9390.9691.028

1,0001,1001,2001,2501,300

1.060

1.1171.1731.2251.2511.276

1.1521.2091.2631.2891.315

1.1531.2101.2641.2901.316

1.1531.2111.2641.2901.316

1.0841.1371.1871.2121.236

1,4001,5001,6001,7001,750

1.3231.3701.4151.4591.480

1.3641.4121.4591.5041.526

1.3651.4131.4601.5041.527

1.3651.4131.4601.5041.527

1.2821.3271.3711.4131.434

1,8001,9002,0002,5003,000

1.5021.5421.5831.7691.938

1.5481.5901.6321.8241.998

1.5481.5901.6321.8241.999

1.5491.5911.6321.8241.999

1.4541.4941.533

Source: ANSI/ICEAS-94-649,StandardforConcentricNeutralCablesRated5,00046,000Volts,2004.* Diametersshownareforcompactround,compactmodifiedconcentric,andcompactsingleinputwire.** Diametersshownareforconcentricroundandmodifiedconcentric.

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TABLE3.3B(METRIC)NominalDiametersforCopperandAluminumConductors

ConductorSize NominalDiameters(mm)

AWGorkcmil mm2 Solid

Concentric-Lay-StrandedCombination

UnilayUnilay

CompressedCompact* Compressed ClassB** ClassC ClassD

87654

8.3710.613.316.821.1

3.263.674.114.625.19

3.40

4.29

5.41

3.584.014.525.085.72

3.714.174.675.235.89

3.764.224.725.285.94

3.764.224.725.315.97

3.634.064.555.135.74

3211/02/0

26.733.642.453.567.4

5.836.547.358.259.27

6.056.817.598.539.55

6.407.198.189.1910.3

6.607.428.439.4710.6

6.687.528.469.5010.7

6.717.548.469.5010.7

6.457.268.159.1410.3

7.958.9410.0

3/04/0250300350

85.0107127152177

10.411.712.713.915.0

10.712.113.214.515.6

11.613.014.215.516.8

11.913.414.616.017.3

12.013.414.616.017.3

12.013.514.616.017.3

11.312.613.815.116.3

400450500550600

203228253279304

16.117.018.0

16.717.818.719.720.7

17.919.020.021.122.0

18.519.620.721.722.7

18.519.620.721.722.7

18.519.620.721.722.7

17.418.519.520.421.3

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650700750800900

329355380405456

21.522.323.123.825.4

22.923.724.625.426.9

23.624.525.326.227.8

23.624.525.426.227.8

23.624.525.326.227.8

22.223.023.924.626.1

1,0001,1001,2001,2501,300

507557608633659

26.9

28.429.831.131.832.4

29.330.732.132.733.4

29.330.732.132.833.4

29.330.832.132.833.4

27.528.930.130.831.4

1,4001,5001,6001,7001,750

709760811861887

33.634.835.937.137.6

34.635.937.138.238.8

34.735.937.138.238.8

34.735.937.138.238.8

32.633.734.835.936.4

1,8001,9002,0002,5003,000

912963

1,0131,2661,520

38.239.240.244.949.2

39.340.441.546.350.7

39.340.441.546.350.8

39.340.441.546.350.8

36.937.938.9

Source: ANSI/ICEAS-94-649,StandardforConcentricNeutralCablesRated5,00046,000Volts,2004.* Diametersshownareforcompactround,compactmodifiedconcentric,andcompactsingleinputwire.**Diametersshownareforconcentricroundandmodifiedconcentric.

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36 Electrical Power Cable Engineering

3.5 METRICDESIGNATIONS

Except as noted above, most of the world uses the SI unit of square millimeters(mm2)todesignateconductorsize.TheInternationalElectrotechnicalCommissionhasadoptedIEC60228[8]todefinethesesizes.Animportantconsiderationisthatthesearenotprecisesizes.Forinstance,their50mm2conductorisactually47mm2.Toaccommodateeveryone,theIECstandardallowsasmuchasa20%variationinconductorareafromthesizedesignated.

InCanada,metricdesignationsareusedforallcabledimensionsexceptfortheconductorsize.ThevariationsinthetwosystemsaretoogreattouseanyoftheSIsizesasadirectsubstituteforstandardsizes.

ConductorsdescribedinIEC60228arespecifiedinmetricsizes.NorthAmericaandcertainotherregionsatpresentuseconductorsizesandcharacteristicsaccordingtotheAWGsystem,andthousandsofcircularmilsforlargersizes.TheuseofthesesizesiscurrentlyprescribedacrossNorthAmericaandelsewhereforinstallationsbysubnationalregulations.IECTC20cableproductstandardsdonotprescribecableswithAWG/kcmilconductors.

IECTC20recognizestheneedtoproduceasingle,harmonizedstandardforcon-ductorsthatistrulyinternational.Harmonization,inthisrespect,isunderstoodasthemergingofAWG-basedandmetric-basedsizestoproduceonerationalizedrangeofconductorsizesforpowercables.TC20alsorecognizesthatthedevelopmentofsuchaharmonizedstandardisalong-termproject.

Athree-stageapproach,whichwillculminateinasingleInternationalStandardforconductors,hasbeenagreed.

StageoneoftheapproachistoproduceatechnicalreportthatdefinestherangeofAWG/kcmilsizesthataretobeconsideredintheharmonizationprocess.

Stagetwooftheprocessistodevelopthistechnicalreportbystartingtheratio-nalizationprocess.ThetestmethodsandrequirementsinthistechnicalreportaretobealignedwiththoseinIEC60228.

The thirdandfinal stagewillbe toproduceaharmonized standard,basedonIEC60228andtheworkofthefirsttwostages,withasingle,rationalizedrangeofconductorsizes.Thepresentexpectationisthatthethirdstagewillnotbeachievedbefore2020.

IEC Technical Report 62602 provides resistance and dimensional details forAWGandthousandsofcircularmilssizesaswellasapproximateequivalentmetricnominalcross-sectionalareas[9].

Table3.4providesmaximumresistancevaluesforsolidClass1circular,annealedcopperandcircularorshapedaluminumandaluminumalloyconductorsforuseinsingle-coreandmulticorecables.Suchconductorsareavailable innominalcross-sectionalareasupto1,200mm2.

Likewise,Table3.5providesmaximumresistancevaluesforstrandedClass2circular,circularcompactedandshapedannealedcopperandaluminumandalumi-numalloyconductorsforuseinsingle-coreandmulticorecables.

It should be noted that maximum or minimum diameter requirements are notspecifiedinIEC60228.Instead,itgivesguidanceondimensionallimitsforthefol-lowingtypesofconductors,whichareincludedinthisstandard:

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37Conductors

TABLE3.4Class1SolidConductorsforSingle-CoreandMulticoreCables

1 2 3 4

NominalCross-SectionalAreamm2

MaximumResistanceofConductorat20C

Circular,AnnealedCopperConductors

Plain/kmMetal-Coated

/km

AluminumandAluminumAlloyConductors,Circular

orShapedc/km0.5 36.0 36.7

0.75 24.5 24.8

1.0 18.1 18.2

1.5 12.1 12.2

2.5 7.41 7.56

4 4.61 4.70

6 3.08 3.11

10 1.83 1.84 3.08a

16 1.15 1.16 1.91a

25 0.727b 1.20a

35 0.524b 0.868a

50 0.387b 0.641

70 0.268b 0.443

95 0.193b 0.320d

120 0.153b 0.253d

150 0.124b 0.206d

185 0.101b 0.164d

240 0.0775b 0.125d

300 0.0620b 0.100d

400 0.0465b 0.0778

500 0.0605

630 0.0469

800 0.0367

1,000 0.0291

1,200 0.0247

Source: IEC60228(Edition3.02004-11),Conductorsofinsulatedcables,Copyright2004IECGeneva,Switzerland.www.iec.ch

a Aluminumconductors10mm2to35mm2circularonly;see5.1.1c.b Seenoteto5.1.1b.c Seenoteto5.1.2.d For single-core cables, four sectoral shaped conductors may be assembled into a single circular

shapedconductor.Themaximumresistanceoftheassembledconductorshallbe25%ofthatoftheindividualcomponentconductors.

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TABLE3.5Class2StrandedConductorsforSingle-CoreandMulticoreCables

1 2 3 4 5 6 7 8 9 10

NominalCross-SectionalAreamm2

MinimumNumberofWiresintheConductor MaximumResistanceofConductorat20C

CircularCircular

Compacted Shaped AnnealedCopperConductorAluminumor

AluminumAlloyConductorc/kmCu Al Cu Al Cu Al

PlainWires/km

Metal-CoatedWires/km

0.5 7 36.0 36.7

0.75 7 24.5 24.8

1.0 7 18.1 18.2

1.5 7 6 12.1 12.2

2.5 7 6 7.41 7.56

4 7 6 4.61 4.70

6 7 6 3.08 3.11

10 7 7 6 6 1.83 1.84 3.08

16 7 7 6 6 1.15 1.16 1.91

25 7 7 6 6 6 6 0.727 0.734 1.20

35 7 7 6 6 6 6 0.524 0.529 0.868

50 19 19 6 6 6 6 0.387 0.391 0.641

70 19 19 12 12 12 12 0.268 0.270 0.443

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95 19 19 15 15 15 15 0.193 0.195 0.320

120 37 37 18 15 18 15 0.153 0.154 0.253

150 37 37 18 15 18 15 0.124 0.126 0.206

185 37 37 30 30 30 30 0.0991 0.100 0.164

240 37 37 34 30 34 30 0.0754 0.0762 0.125

300 61 61 34 30 34 30 0.0601 0.0607 0.100

400 61 61 53 53 53 53 0.0470 0.0475 0.0778

500 61 61 53 53 53 53 0.0366 0.0369 0.0605

630 91 91 53 53 53 53 0.0283 0.0286 0.0469

800 91 91 53 53 0.0221 0.0224 0.0367

1,000 91 91 53 53 0.0176 0.0177 0.0291

1,200 bbbbbb

0.0151 0.0151 0.0247

1,400 0.0129 0.0129 0.0212

1,600 0.0113 0.0113 0.0186

1,800 0.0101 0.0101 0.0165

2,000 0.0090 0.0090 0.0149

2,500 0.0072 0.0072 0.0127

Source: IEC60228(Edition3.02004-11),Conductorsofinsulatedcables,Copyright2004IECGeneva,Switzerland.www.iec.cha Thesesizesarenonpreferred.Othernonpreferredsizesarerecognizedforsomespecializedapplicationsbutarenotwithinthescopeofthisstandard.b Theminimumnumberofwiresforthesesizesisnotspecified.Thesesizesmaybeconstructedfrom4,5,or6equalsegments(Milliken).c Forstrandedaluminumalloyconductorshavingthesamenominalcross-sectionalareaasanaluminumconductor,theresistancevalueshouldbeagreed

betweenthemanufacturerandthepurchaser.

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40 Electrical Power Cable Engineering

1.circular solid conductors (Class 1) of copper, aluminum, and aluminumalloy;

2.circularandcompactedcircularstrandedconductors (Class2)ofcopper,aluminum,andaluminumalloy.

Thisisintendedasaguidetothemanufacturersofcablesandcableconnectorstoassistinensuringthattheconductorsandconnectorsaredimensionallycompatible.

3.6 STRANDING

Largersizesofsolidconductorsbecome toorigid to install, form,and terminate.Strandingbecomesthesolutionto thesedifficulties.Thepointatwhichstrandingshouldbeusedisdependentonthetypeofmetalaswellasthetemperofthatmetal.Copperconductorsarefrequentlystrandedat#6AWGandgreater.Aluminum,inthehalf-hardtemper,canbereadilyusedasasolidconductoruptoa#2/0AWGsize.

3.6.1 concentricstranDing

Thisisthetypicalchoiceforpowercableconductors.Thisconsistsofacentralwireorcoresurroundedbyoneormorelayersofhelicallyappliedwires.Eachadditionallayerhassixmorewiresthantheprecedinglayer.Exceptinunilay-strandedcon-ductors,eachlayerisappliedinadirectionoppositetothatofthelayerunderneath.Inthecaseofpowercableconductors,thecoreisasinglewireandallofthestrandshavethesamediameter.AsshowninFigure3.1,thefirstlayeroverthecorecontains6wires;thesecond,12;thethird,18;etc.Thedistancethatittakesforonestrandoftheconductortomakeonecompleterevolutionofthelayeriscalledthelengthof

Number of wireseach layer 54 48

4236

3024

1812 19

3761

91127

169217

271 Total numberof wires

3

5791113151719

Number of wiresacross diameter

16 7

FIGURE3.1 Concentricstandingrelationships.

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41Conductors

lay.TherequirementforthelengthoflayissetforthinASTMstandards[6]tobeneitherlessthan8normorethan16timestheoveralldiameter(OD)ofthatlayer.

In power cables, the standard stranding is ClassB. Standards require that theoutermostlayerbeofalefthandlay.Thismeansthatasyoulookalongtheaxisoftheconductor,theoutermostlayerofstrandsrolltowardtheleftastheyrecedefromtheobserver.Moreflexibilityisachievedbyincreasingthenumberofwiresintheconductor.ClassChasonemorelayerthanClassB;ClassDhasonemorelayerthanC.TheclassdesignationgoesuptoM(normallyusedforweldingcables,etc.).ThesearecoveredbyASTMstandards.

ClassCandDconductorshaveapproximatelythesameweightasaClassBandanODwithin3milsofClassB.ExamplesofClassB(standard),ClassC(flexible),andClassD(extraflexible)areshowninTable3.6withthenumberofstrandsanddiameterofeachstrand.

Thefollowingformulamaybeusedtocalculatethenumberofwiresinaconcen-tricstrandedconductor:

n N N= + +( )1 3 1 (3.3)

wheren=totalnumberofwires instrandedconductorandN=numberof layersaroundthecenterwire.

3.6.2 compresseDstranDing

Thisisthetermthatisusedtodescribeaslightdeformationofthelayerstoallowthelayerbeingappliedtoclosetightly.Thereisnoreductioninconductorarea.Thediameterofthefinishedconductorcanbereducednomorethan3%oftheequivalent

TABLE3.6ExamplesofClassB,C,andDStranding

Size ClassB ClassC ClassD

#2AWG 70.0974 190.0591 370.0424#4/0AWG 190.1055 370.0756 610.0589500kcmil 370.1162 610.0905 910.0741750kcmil 610.1109 910.0908 1270.0768

TABLE3.7GapsinOuterLayerofaStrandedConductor

TotalNumberofStrands AngleofGapat16OD19 8.30

37 100

61 100

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42 Electrical Power Cable Engineering

concentricstrand.Atypicalreductionisabout2.5%.ExamplesofgapsintheouterlayerforconcentricstrandedconductorsareshowninTable3.7.

Shorteningthelengthoflayontheouterlayercouldsolvetheproblembutwouldresultinhigherresistanceandwouldrequiremoreconductormaterial.

Compressed stranding is often the preferred construction, because concentricstranding,withitsdesignatedlaylength,createsaslightgapbetweentheouterstrandsofsuchaconductor.Lowerviscositymaterialsthatareextrudedoversuchaconductortendtofallintoanygapthatforms.Thisresultsinsurfaceirregularitiesthatcreateincreasedvoltagestressesandmakeitmoredifficulttostripoffthatlayer.

3.6.3 compactstranDing

Thisissimilartocompressedstrandingexceptthatadditionalformingisgiventotheconductorsothatthereductionindiameteristypically9%lessthantheconcen-tricstrandedconductor.Thisresultsinadiameternearingthatofasolidconductor.Someairspacesthatcanserveaschannelsformoisturemigrationarestillpresent.Themainadvantageofcompactconductorsisthereducedconductordiameter.

3.6.4 BunchstranDing

Thistermisappliedtoacollectionofstrandstwistedtogetherinthesamedirectionwithoutregardtothegeometricarrangement.Thisconstructionisusedwhenextremeflexibility is required for smallAWGsizes, suchasportable cables.Examplesofbunch-strandedconductorsarecordsforvacuumcleaners,extensioncordsforlawnmowers,etc.ExamplesofbunchstrandingareshowninTable3.8.

NotethatinClassKandMconductors,theindividualwirediametersareconstantandthecross-sectionalareaisdevelopedbyaddingasufficientnumberofwirestoprovidethetotalconductorarearequired.

3.6.5 ropestranDing

Thistermisappliedtoaconcentric-strandedconductor,eachofwhosecomponentstrandsisstranded.Thisisacombinationoftheconcentricconductorandabunch-strandedconductor.Thefinishedconductor ismadeupofanumberofgroupsof

TABLE3.8ExamplesofClassKandMStranding

ConductorSize ClassK ClassM

#16AWG 260.0100 650.0063#14AWG 410.0100 1040.0063#12AWG 650.0100 1680.0063

NoteinClassKandMthattheindividualwirediametersarecon-stant and the area is developed by adding a sufficient number ofwirestoprovidethetotalconductorarearequired.

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43Conductors

bunch- or concentric-stranded conductors assembled concentrically together. Theindividualgroupsaremadeupofanumberofwiresratherthanasingle,individualstrand.Arope-strandedconductorisdescribedbygivingthenumberofgroupslaidtogethertoformtheropeandthenumberofwiresineachgroup.

ClassesGandHaregenerallyusedonportablecablesforminingapplications.Classes I,L, andMutilizebunch-strandedmembersassembled intoaconcentricarrangement.Theindividualwiresizeisthesamewithmorewiresaddedasneces-sarytoprovidethearea.ClassIuses#24AWG(0.020inch)individualwires,ClassLuses#30AWG(0.010inch)individualwires,andClassMuses#34AWG(0.0063inch)individualwires.ClassIstrandingisgenerallyusedforrailroadapplicationsandClassesLandMareused forextremeportability suchasweldingcableandportablecords.

3.6.6 sectorconDuctors

Thesehaveacrosssectionapproximatingtheshapeofasectorofacircle.Atypicalthree-conductorcablehasthree120segmentsthatcombinetoformthebasiccircleofthefinishedcable.SuchcableshaveasmallerODthanthecorrespondingcablewithconcentricroundconductors,andexhibitlowerACresistanceduetoareductionoftheproximityeffect.

Forpaper-insulatedcables,thesectorconductorwasalmostalwaysstrandedandthencompactedinordertoachievethehighestpossibleratioofconductorareatocablearea.Thepreciseshapeanddimensionsvariedsomewhatbetweenthemanufacturers.

Figure3.2andTable3.9showthenominaldimensionsoftypicalcompactsectorconductors.

Forthecalculationofcablecapacitance,forinstance,anequivalentroundconductorisrequired.Overthe2/0AWGto750kcmilsizerange,thefollowingformulaholds:

D A=1 337. (3.4)

whereD=equivalentrounddiameter inmilsandA=areaofsectorconductor incircularmils.

D

E

B

H C VC 120

FIGURE3.2 Outlineoftypicalcompactsector.

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44 Electrical Power Cable Engineering

Sector conductors that are solid rather than stranded have been used forlow-voltagecablesonalimitedbasis.Thereisinterestinutilizingthistypeofconductorformedium-voltagecables,buttheyarenotavailableonacommercialbasisatthistime.

3.6.7 segmentalconDuctors

Theseareround,strandedconductorscomposedofthreeormoresegmentsthatareelectrically separated from each other by a thin layer of insulation around everyothersegment.Eachsegmentcarrieslesscurrentthanthetotalconductor,andthecurrentistransposedbetweeninnerandouterpositionsinthecompletedconductor.ThisconstructionhastheadvantageofloweringtheskineffectratioandhencetheACresistancebyhavinglessskineffectthanaconventionallystrandedconductor.

TABLE3.9NominalDimensionsof3/cCompactSectorConductor

Cond.AWG/kcmil

V-GageInch

V-Gage*Inch

BInch

CInch

DInch

EInch

1/0 0.288 0.462 0.080 0.080 0.504

2/0 0.323 0.520 0.085 0.085 0.540

3/0 0.364 0.592 0.100 0.100 0.584

4/0 0.417 0.660 0.111 0.090 0.595

4/0 0.410 0.660 0.117 0.090 0.770

250 0.455 0.720 0.118 0.220 0.635

250 0.447 0.720 0.125 0.220 0.812

300 0.497 0.784 0.130 0.179 0.678

300 0.490 0.784 0.138 0.179 0.852

350 0.539 0.834 0.151 0.259 0.718

350 0.532 0.834 0.151 0.259 0.890

400 0.572 0.902 0.147 0.244 0.754

400 0.566 0.902 0.158 0.244 0.928

500 0.642 1.018 0.155 0.207 0.820

500 0.635 1.018 0.167 0.207 1.000

600 0.700 1.120 0.165 0.210 0.882

600 0.690 1.120 0.178 0.210 1.050

750 0.780 1.280 0.163 0.284 0.970

750 0.767 1.280 0.185 0.284 1.140

800 0.806 1.324 0.164 0.224 0.890

800 0.795 1.324 0.176 0.224 1.083

900 0.854 1.405 0.170 0.236 1.040

900 0.842 1.405 0.180 0.236 1.110

1,000 0.900 1.500 0.137 0.300 1.008

1,000 0.899 1.500 0.192 0.300 1.266

* Denotesthecolumnthatappliesforinsulationthicknessover200mils.

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45Conductors

Thistypeofconductorshouldbeconsideredforlargesizessuchas1,000kcmilandabovethataretocarrylargeamountsofcurrent.

Thediametersoffour-segmentconductorsareapproximatelythesameasthatofClassBconcentric-strandedconductors(Table3.10).

3.6.8 annularconDuctors

Theseareround,strandedconductorswhosestrandsarelaidaroundacoreofrope,fibrousmaterial,helicalmetaltube,oratwistedI-beam.Thisconstructionhastheadvantage of lowering the total AC resistance for a given cross-sectional area ofconductorbyeliminatingthegreaterskineffectatthecenterofthecompletedcon-ductor.Wherespaceisavailable,annularconductorsmaybeeconomicaltousefor

TABLE3.10NominalDiametersforSegmentalCopperandAluminumConductors

ConductorSizeSegmentalConductorDiameter*

(FourSegments)

kcmil mm2 Inches mm

1,0001,1001,2001,2501,300

507557608633659

1.1401.1521.1951.2091.2351.2631.2601.2891.2851.315

29.029.330.430.731.432.132.032.732.633.4

1,4001,5001,6001,7001,750

709760811861887

1.3251.3641.3751.4121.4201.4591.4601.5041.4801.526

33.734.634.935.936.137.137.138.237.638.8

1,8001,9002,0002,2502,500

912963

1,0131,1401,266

1.5001.5481.5301.5901.5701.6321.6651.7301.7401.824

38.139.338.940.439.941.542.343.944.246.3

2,7503,0003,2503,5003,7504,000

1,3931,5201,6471,7731,9002,027

1.8301.9131.9101.9981.9852.0802.0852.1592.1502.2342.2252.309

46.548.648.550.750.452.853.054.854.656.756.558.6

4,2504,5004,7505,000

2,1542,2802,4072,534

2.2452.3782.3152.4482.3752.5162.4352.581

57.060.458.862.260.363.961.865.6

Source: ANSI/ICEAS-108-720,StandardforExtrudedInsulationPowerCablesRatedAbove46Through345kV,2004.

* Diameteroverbindertape.

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46 Electrical Power Cable Engineering

1,000kcmilcablesandaboveat60hertzandfor1,500kcmilcablesandaboveforlowerfrequenciessuchas25hertz.

3.6.9 unilayconDuctors

Unilayhas,asthenameimplies,allofitsstrandsappliedinthesamedirectionoflay.Adesignfrequentlyusedforlow-voltagepowercablesisthecombinationunilaywheretheouterlayerofstrandsarepartiallycomprisedofstrandshavingasmallerdiameterthantheotherstrands.Thismakesitpossibletoattainthesamediameterasacompactstrandedconductor.Themostcommonunilayconductorisacompact,8,000seriesaluminumalloy.

3.7 PHYSICALANDMECHANICALPROPERTIES

3.7.1 conDuctorproperties

Althoughhigh conductivity is oneof the important featuresof a good conductormaterial,otherfactorsmustbetakenintoaccount.Silverisaninterestingpossibilityforacableconductor.Itshighcostiscertainlyoneofthereasonstolookforothercandidates.Silverhasanotherdisadvantage,which is its lackofphysicalstrengththatisnecessaryforpullingthecablesintoconduits.

3.7.1.1 CopperImpuritieshaveaverydeleteriouseffectontheconductivityofcopper.Thespeci-fiedpurityofcopperforconductorsis100%.Smallamountsofimpurities,suchasphosphorousorarsenic,canreducetheconductivitytoaslowas80%.

3.7.1.2 AluminumElectrical conductor (EC) grade aluminum is also low in impurities, 99.5%purity or better. ASTM B 233 specifies the permissible impurity levels foraluminum[6].

TABLE3.11ComparativeProperties,CopperversusAluminum

Property UnitCopper,

AnnealedAlum,Hard

Drawn

Densityat20C Pounds/in3Grams/cm3

0.321178.890

0.09752.705

LinearTemp.Coef.ofExpansion

perFperC

9.4106

17.010612.8106

23.0106

MeltingPoint F 1981 12051215MeltingPoint C 1083 652657

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47Conductors

3.7.1.3 ComparativeProperties,CopperversusAluminumTable3.11comparesthepropertiesofannealedcopperandhard-drawnaluminum,whicharetypicallyusedforpowercableconductors.

3.7.2 temper

Drawing of the copper and aluminum rod into wire results in work hardeningofboth.Thisresults inaslightly lowerconductivityaswellasahigher temper.Stranding and compacting also increase the temperof the conductor. If amoreflexible conductor is required, annealing the metal may be desirable. This canbedoneeitherwhilethestrandisbeingdrawnorthefinishedconductormaybeannealedbyplacingareelofthefinishedconductorinanovenusuallyhavinganitrogenatmosphereandatanelevatedtemperatureforaspecifiedperiodoftime.

3.7.2.1 CopperASTMStandardsB1,B2,andB3coverthreetempersforcopperconductors:hard-drawn,medium-hard-drawn,andsoftorannealed,respectively.Soft-drawnisusu-allyspecifiedforinsulatedconductorsbecauseofitsflexibilityandeaseofhandlinginthefield.Medium-hard-drawnandhard-drawnareusuallyspecifiedforoverheadconductors.

3.7.2.2 AluminumASTMStandardsB231andB400coverconcentric-layandcompact-roundstrandedaluminumconductors,respectively.ASTMhasfivedesignationsforaluminumtempersasshowninTable3.12.Notethatsomeofthevaluesoverlap.Half-hardaluminumisusuallyspecifiedforsolidandfor8,000seriesalloyconductorsbecauseoftheneedforgreaterflexibility.Three-quarterandfull-hardareusuallyspecifiedforstrandedcables.

Itisimportanttoconsidertwofactorsbeforedecidingwhichtempershouldbespecified:

The increased cost of the energy and equipment required to anneal theconductor.

Evenwithamoreflexibleconductor,theoverallstiffnessoftheinsulatedcablemayonlybemarginallyimproved.

TABLE3.12AluminumTemper

1350AluminumTempers PSI103

FullSoft(H0) 8.514.0

1/4Hard(H12or22) 12.017.0

1/2Hard(H14or24) 15.020.0

3/4Hard(H16or26) 17.022.0

FullHard(H19) 22.529.0

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48 Electrical Power Cable Engineering

Overheadconductorsandcablesthatwillbepulledintolonglengthsfrequentlyutilize higher tempers in order to increase the tensile strength of the conductor.Examplesofcablesthatmightrequirehightensilestrengthconductorsareboreholecables,mineshaftcables,orextremelylongpullsoflargeconductors.

3.8 STRANDBLOCKING

Moisture in an insulated conductor has been shown to cause several problems.Aluminum,inthepresenceofwaterandintheabsenceofoxygen,willhydrolyze.Thus,ifwaterentersaninsulatedcablehavinganaluminumconductor,thealumi-numandwatercombinechemicallytoformaluminumhydroxideandhydrogengas.Thisconditionisaggravatedbyadeficiencyinoxygenintheinsulatedconductor.Thechemicalreactionis:

2 6 2 32 3 2Al H O Al OH H+ ( ) +

Aluminum hydroxide is a white, powdery material which is a good insulator.Manyusersofstrandedaluminumconductorsnowrequireblockedconductorsforthisreason.Waterblockingcomponents,suchaswater-swellabletapesandyarnsorsealants,incorporatedintotheintersticesofthestrandedconductoractasanimpedi-menttolongitudinalwaterpenetrationandthushelpretardthisformofdeterioration.Copperconductorsmay,ofcourse,alsobewater-blockedinthesamemanner.

Regardlessoftheconductormaterialanddegreeofcompaction,thereisstillsomeairspaceremainingintheintersticesofthestrandedconductor.Thisspacecanactasareservoirformoisturetocollectandhenceprovideasourceofwaterforwatertreeing.Water-blocked strandedconductors are frequently specified forundergroundcablestoreducethepossibilityofthishappening.Solidconductors,ofcourse,aretypicallyspecifiedforthesamereasonfor#2/0AWGandsmalleraluminumconductors.

3.9 ELECTRICALCALCULATIONS

3.9.1 conDuctorDcresistance

R C ADC at 25 1000 = , (3.5)

whereRDC=DCresistanceofconductorinohmsper1,000feetat25C;=resis-tivityofmetalinohmcircularmilsperfoot;forcopper=10.575cmil/ft(100%conductivity) at 25C; for aluminum=17.345cmil/ft (61.0% conductivity) at25C;A=conductorareaincircularmils.

Theresistanceofastrandedconductorismoredifficulttocalculate.Itisgenerallyassumedthatthecurrentisevenlydividedamongthestrandsanddoesnottransferfromonestrandtothenext.Forthisreason,theDCresistanceisbasedon:

Multiplythenumberofstrandsbythecross-sectionalareaofeachtakenper-pendiculartotheaxisofthatstrand.Theproductisthenthecross-sectionalareaoftheconductor.

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49Conductors

Comparethelengthofeachstrandtotheaxiallengthoftheconductor.Thisincreasedlengthisarithmeticallyaveraged.

TheDCresistanceofasolidconductorhavingthesameeffectivecross-sec-tionalareaismultipliedbytheaverageincreaseinlengthofthestrand.Theresultantisthecalculatedresistanceofthestrandedconductor.

Sinceresistanceisbasedontemperature,thefollowingformulaecorrectforothertemperaturesintherangemostcommonlyencountered:

Copper:

R R T

T2 12

1

234 5234 5

=+

+

.

. (3.6)

Aluminum:

R R T

T2 12

1

228 1228 1

=+

+

.

. (3.7)

whereR2=conductorresistanceattemperatureT2inC;R1=conductorresistanceattemperatureT1inC.

These formulasarebasedon the resistancecoefficientofcopperhaving100%conductivityandofaluminumhaving61.2%conductivity(InternationalAnnealedCopperStandard).

3.9.2 conDuctoracresistance

AconductoroffersagreaterresistancetotheflowofACthanitdoestoDC.ThisincreasedresistanceisgenerallyexpressedastheAC/DCresistanceratio.Thetwomajorfactorsforthisincreasearetheskineffectandtheproximityeffectofcloselyspacedcurrentcarryingconductors.Othermagneticeffectscanalsocauseanaddi-tionalincreaseinAC/DCresistanceratios.

R RAC DCAC/DC ratio= (3.8)

TheAC/DCresistanceratioisincreasedbylargerconductorsizesandhigherACfrequencies.

3.9.3 skineFFect

InACcircuits, thecurrenttendstodistributeitselfwithinaconductorsothat thecurrentdensitynearthesurfaceoftheconductorisgreaterthanthatatitscore.Thisphenomenonisknownasskineffect.Alongitudinalelementoftheconductornearthecenteroftheaxisissurroundedbymorelinesofmagneticforcethanneartherim.Thisresultsinanincreaseininductancetowardthecenter.Thedecreasedarea

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50 Electrical Power Cable Engineering

ofconductancecausesanapparentincreaseinresistance.At60hertz,thephenom-enonisnegligibleincopperconductorsizesof#2AWGandsmallerandaluminumsizesof#1/0AWGandsmaller.Astheconductorsizeincreases,thiseffectbecomesmoresignificant.

Thefollowingformulacanbeusedtogiveanapproximationofskineffectforroundconductorsat60hertz;anotherapproximationwillbegiveninChapter14.

Y

RCS=

+

11 188 82

.

.DC (3.9)

where YCS=skin effect expressed as a number to be added to the DC resistance;RDC=DCresistanceoftheconductorinmicro-ohmsperfootatoperatingtemperature.

3.9.4 proximityeFFect

IncloselyspacedACconductors,thereisatendencyforthecurrenttoshifttotheportionoftheconductorthatisawayfromtheotherconductorsofthatcable.Thisphenomenonisknownasproximityeffect.Thealternatingmagneticfieldlinkingthecurrentinoneisolatedconductorisdistortedbythecurrentinanadjacentconductor.Thisinturncausesanunevendistributionofthecurrentacrosstheconductorcrosssection.

Sinceskinandproximityeffectsarecumbersometocalculate,tableshavebeenestablishedtogivethesevaluesforcommonmodesofoperation[5].

3.9.5 caBlesinmagneticmetallicconDuit

Due to excessive hysteresis and eddy current losses, individual phases of an ACcircuitshouldnotbe installed inseparatemagneticmetalconduitsunderanycir-cumstances.Thisisbecauseofthehighinductanceofsuchaninstallation.Infact,separatephasesshouldnotpassthroughmagneticstructuressinceoverheatingcanoccur insuchasituation.Allphasesshouldpass throughanymagneticenclosuresimultaneously,sothatmaximumcancellationoftheresultantmagneticfieldoccurs.Thisgreatlyreducesthemagneticeffect.However,evenundertheseconditions,anincrease inskinandproximityeffectswilloccurbecauseof theproximityof themagneticmaterial.Therecanbesignificantlosseswhenlargeconductorsaresimplyplacednearthemagneticmaterials.

Cablesin50or60hertzACcircuitsshouldnotbeinstalledwitheachphaseinaseparatenonmagneticmetalconduitwhentheirconductorsizeis#4/0AWGorlargerduetohighcirculatingcurrentsintheconduit.Thiscausesasignificantdecreaseinthecableampacity.

3.9.6 resistanceathigherFrequencies

Cablesoperatingatfrequencieshigherthan60hertzmayneedtobeevaluatedforampacityandAC/DCratiosbecausetheycancausehighervoltagedropsthanmight

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51Conductors

be anticipated.Also at higher frequencies, an increase in the inductive reactancemayaffectvoltagedrops.Insulatedconductorsshouldnotbeinstalledinmetallicconduits,norshouldtheyberunclosetomagneticmaterials.

Forfrequenciesotherthan60hertz,acorrectionfactorisprovidedby:

x f R= 0 027678. DC (3.10)

wheref=frequencyinhertz,RDC=conductorDCresistanceatoperatingtempera-ture,inohmsper1,000feet.

Foradditionalinformationontheeffectsofhigherfrequency,seetheICEAreportinReference[3]andthecablemanufacturersmanuals[4,5].

REFERENCES

1. Kelly, L. J., 1995, adapted from class notes for Power Cable Engineering Clinic,UniversityofWisconsinMadison.

2. Landinger, C. C., 2001, adapted from class notes for Understanding Power CableCharacteristicsandApplications,UniversityofWisconsinMadison.

3. ICEA P-34-359, 1973, AC/DC Resistance Ratios at 60 Hz, Global EngineeringDocuments,15InvernessWayEast,Englewood,CO80112.

4. EngineeringDataforCopperandAluminumConductorElectricalCables,1990,TheOkoniteCompany,BulletinEHB-90.

5. Southwire Company Power Cable Manual,SecondEdition,1997,Carrollton,GA. 6. Annual Book of ASTM Standards, Vol. 02.03: Electrical Conductors. Section 2:

NonferrousMetalProducts,2010,ASTMInternational,100BarrHarborDrive,POBoxC700,WestConshohocken,PA,19428-2959USA.

7. IEC20/680/RVCResultofvotingon20/633/CDV:IEC60228Ed.3:ConductorsofInsulatedCables,2004,IECCentralOffice,3ruedeVaremb,P.O.Box131,CH-1211Geneva20,Switzerland.

8. IEC60228(Edition3.02004-11),ConductorsofInsulatedCables,2004,IECCentralOffice,3ruedeVaremb,P.O.Box131,CH-1211Geneva20,Switzerland.

9. IEC/TR62602(Edition1.02009-09),ConductorsofInsulatedCablesDataforAWGandkcmilSizes,2009,IECCentralOffice,3ruedeVaremb,P.O.Box131,CH-1211Geneva20,Switzerland.

10. ANSI/ICEA S-94-649, Standard for Concentric Neutral Cables Rated 5,000-46,000Volts,2004,GlobalEngineeringDocuments,15InvernessWayEast,Englewood,CO80112.

11. ANSI/ICEAS-108-720,StandardforExtrudedInsulationPowerCablesRatedAbove46Through345kV,2004,GlobalEngineeringDocuments, 15 InvernessWayEast,Englewood,CO80112.

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3.1 Introduction3.2 Material Considerations3.3 Conductor Sizes3.4 Circular Mil Sizes3.5 Metric Designations3.6 Stranding3.7 Physical and Mechanical Properties3.8 Strand Blocking3.9 Electrical CalculationsReferences