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Lauri J. Hiivala and Carl C. Landinger
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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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650700750800900
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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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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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