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Section II Bare Aluminum Wire and Cable

Chapter 3

Engineering Design

This chapter describes lbe principal design features ofbare uninsulated conductors; however much lbat appliesto hare conductors also pertains to lbe metaUic part of insulated or covered conductors which are considered inSection III.Many types of bare conductors are in use depending on

application requirements. They may differ in electrical andphysical properties, configuration, method of assembly,and corrosion resistance. Certain general physical properties have been described in previous chapters. Detailedphysical and electrical properties of lbe various commercial sizes of bare conductors are listed in Chapter 4.For many years it has been the practice to employ codewords to identify and precisely define specific conductorconstructions and designs (conductor size, stranding,insulation type, voltage rating, neutral configuration andsize, number of phase conductors, type of assembly,etc.). In our text, code words are often used, as in theexample under Table 3-6 wherein the code word "Blue

bell" identifies a specific cable, in this case a 1,033,500cmil, 37 strand, bare aluminum 1350 conductor. Thesecode words are tabulated in Aluminum AssociationpUblications "Code Words for Underground DistributionCables" and "Code Words for Overhead AluminumElectrical Cables. "Symbols for types of aluminum conductors: AAC-all-aluminum conductors (of 1350 aluminum); AAAC-all-aluminum alloy-conductors (of 6201-T81); ACSR-aluminum-conductor steel-reinforced (steel wire reinforcement); ACAR-aluminum conductor aluminum alloy-reinforced (high strength 6201-T81 wire reinforcement).Except as otherwise referenced, ~ r a p h s and data intables are taken from Alcoa Aluminum Overhead Conductor Engineering Series handbooks.

Mechanical Design of Conduc:lorsAmerican Wire Gage (A WG)

This wire system, formerly known as Brown & Sharpe(B&S) gage, was introduced by J. R. Brown in 1857, andis now standard for wire in the United States. Successive

AWG numbered sizes represent the approximate reductionin diameter associated with each successive step of wiredrawing.Fig. 3-1 shows typical full-size cross-sections, andapproximate relationships between the sizes.For wire sizes larger than 4/0 AWG, the size is desig

nated in circular mils. Wire sizes of 4/0 AWG andsmaller also are often designated in cir mils. One cir milis the area of a circle I mil (0.001 in.) diameter; that is, thearea in cir mils equals diameter-in-mils squared.As one emil = "./4 sqmils (Eq.3-1) Area in cir mils 1.2732 X 10' X area in sq. in. Expressing diameter of wireD, in inches D = 1O-'cmil"orcmil I()6D' (Eq.3-2) Thus a solid round conductor of 1,000,000 cir mils has

an area of n/4 sq. in., and a diameter of 1.00 in.Stranded Conductors

Flexibility requirements for conductors vary widely. Theconductors accordingly may be either lengths of singlewires or a stranded group of smaller wires arranged in

30 #10 #1/0 #'10Nominal AWG Awe AWG AWGDiameter, mils 10 101.9 324.9 460.0Area, cmils 100 10,380 105,600 211,600

Approximate Relationships(I) An increase of three gage numbers doubles area andweight, and halves dc resistance.(2) An increase of six gage numbers doubles diameter.(3) An increase of ten gage numbers multiplies area andweight by 10 and divides de resistance by 10.Fig.3-1. Typical cross-sections ofsolid-round A WG-sizewires and approximare relationships. (Actual size.)

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bare aluminum wire and cablesome regular manner. In ellber case, the total crosssectional area of all component conducting wires determines the AWG or emil size of the assembled conductor.Concentric-Lay Stranding

Most bare power conductors are in concentric-laystranded form; that is, a single straight core wire is surrounded by one or more helically curved wires. The direction of twist of lay is usually reversed in adjacent layers.All wires of a given layer generally are of same diameter.The direction of lay is either right- or left-hand dependingon whether the top wire of the helix extends to right orleft as the conductor is viewed axially in the directionaway from the observer. The length of lay is the axiallength parallel to the center line of the assembled conductor of one turn of the helix of a single wire. Bare aluminum conductors conventionally have a right-hand lay onoutside layer.Ameriean practiee (ASTM) recognizes two classes ofbare concentric-lay stranded conductors, AA and A, theformer usually for bare-wire ov-erhead applications and thelatter for covered overhead lines.Still greater flexibility of stranded conductors, mostlyused for insulated conductors, are those with Class B, C,D, or even finer strandings. These have more wires for agiven size of conductor than used for Class AA or Astranding. Wires of softer temper than the usual harddrawn wires can be used. Added flexibility also may beobtained by using small braided wires or those in"bunched" arrangement.. The stranding arrangement of each class is also specifiedm ASTM Conductor Standards. Fig. 3-2 shows typicalexamples of concentric-lay stranded bare conductors forvarious degrees of flexibility.AAC/TW is a new design of all aluminum conductor

composed of shaped wires (Trapezoidal) in a compactconcentric-lay-stranded configuration. The design is described in ASTM B 778, and the properties are listed inTables 4-10 and 4-11.

Single layer 0.586 in. 007/w 7/.1953, (Class AA)

Two layer, 0.593 in. 0019/.1185, (Class A)

19/w

Three layer, 0.594 in. 0037/.0849, (Class B)37/w Fig. 3-2. Typical Examples of Concentric Lay Conduc tors. All 266.8 kcmil.(lllustrations are approximately to scale.}

TABLE 31 Strand Lengths VS Solid Conductor Lengths for ASTM B231

Incremental Increase fWeight and de Resistanof Stranded Over thaof Solid Conductors

Sizes 4.000,000 to 3,000,001 emil 4%Sizes 3,000,000 to 2,000,001 cmil 3%Sizes 2,000,000 emil or under 2%DifJerences Between Stranded and Solid Conductors

Because of the helical path of the strand layers this more length of metal in a given length of stranded coductor than in a solid round conductor of the same A Wsize, hence both the weight and de resistance pe r ulength are increased. The amount of increase for ali-alumnum conductors may be computed according to a methdescribed in ASTM B 231, or the standard incrementsincrease listed in Table 31 (also from ASTM B 231) mbe used.The tensile load on a conductor is not always equadiVided among the strands. This effect can reduce the toload at which the first strand breaks as compared wthat of a solid conductor of equal cross section. Hoever, this effect is more than offset by the fact that the utensile strength of commercially cold-drawn wire generaincreases as its diameter is reduced, as is evident bycomparison for H 19 stranded conductor in Table 3-2.According to ASTM Standards, aluminum conductthat are concentric-lay stranded of 1350 or 6201 allin the various tempers have their rated tensile stren(or minimum rated strength) taken as the followpercentages of the sum of the minimum average tensstrengths of the component wires, multiplied by ratfactors, as below:

7 wires per conductor One layer 9619 wires per conductor Two layers 9337 wires pe r conductor Three layers 9161 wires per conductor Four layers 9091 wires per conductor Five layers 8(and over) (and over)

Similarly, the rated strength of ACSR is obtained by plying rating factors of 96, 93, 91, and 90 percent, spectively, to the strengths of the aluminum wires of cductors having one, two, three, or four layers of aluminwires, and adding 96 percent of the minimum stress insteel wires at 1.0 percent elongation for cables having ocentral wire or a single layer of steel wires, and addingpercent of the minimum stress at 1.0 percent e longationthere are two layers of steel wires.All strengths are listed in pounds to three significfigures, and these strengths also apply to compact-rouconductors.

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engineering designSpecial Conductor Constructions

Large conductors requiring exceptional flexibility maybe of rope-lay construction, Rope-lay stranded cables areconcentric-lay stranded. utilizing component memberswhich are themselves either concentric stranded orbunched, Bunched members are cabled with the individualcomponents bearing no fixed geometric relationship between strands. Rope-lay stranded conductors may bestranded with subsequent layers reversing in direction.or may be unidirectional with all layers stranded in thesame direction but with different lay lengths.Some cables are designed to produce a smooth outersurface and reduced overall diameter for reducing iceloads, and under some conditions wind loading, Thestranded cables are smoothed in a compacting operationso that the outer strands loose their circularity; each strandkeys against its neighbor and many interstrand voids disappear. (Fig. 3-3) A similar result is commonly obtained byuse of trapezoidal strands that intertie with adjacentstrands to create a smooth, interlocking surface. (Fig. 3-7)Another cable design, expanded core concentric-layconductor. uses fibrous Or other material to increase thediameter and increase the ratio of surface area to metalcross-section or weight. (Fig. 3-3) Designed to minimizecorona at voltages above 300 kV. they provide a moreeconomical balance between cable diameter and currentcarrying capacity.A "bundled" conductor arrangement with two or mOreconductors in parallel. spaced a short distance apart. isalso frequently used for HV or EHV lines. Although theratio of radiating area to volume increases as the individualconductor size decreases, the design advantages of bundling are not wholly dependent upon ampacity. Normalradio interference, etc and the usual controlling designcharacteristics are discussed elseWhere, but the currentcarrying capacity relationship is similar. Thus, two 795kcmil ACSR Drake under typical conditions of spacingand temperature provide 24 percent more ampacity perkcmi! than a single 1780 kcmil ACSR Chukar.Composite Conductors

Composite conductors, conductors made up ofstrands of different alloys or different materials. are used

TABLE 3-2Strength of 1360-H19 Aluminum Conductors

ISu-andAWG Stranding :Oiam, In. Rated Strength, Lb

I

2 Solid.1 0.2576 12252 7 Strand: 0.0974 13502 19 Strand i 0.0591 1410

Calculated from ASTM B230 and B231.

Rope lay Concentric Stranded Conductor-

Compact Concentric Stranded Conductor

Expanded Core Concentric Stranded Conductor

Fig, 3-3. Typical cross-sections of some special conductorshapes..

where the required strength is greater than the strengthobtainable with I 350-H19 grade aluminum strands. Theprincipal kinds of composite conductors are (I) 1350stranded conductors reinforced by a core of steel wires(ACSR), (2) 1350 stranded conductors reinforced by aluminum-clad steel wires which may be in the core or distributed throughout the cable (ACSRIAW). Or (3) 1350stranded conductors reinforced by wires of high-strengthaluminum alloy (ACAR).Aluminum Conductor Steel Reinforced(A CSR) and Modifications

ACSR has been in common use for more than half acentury. It consists of a solid or stranded steel core Surrounded by strands of aluminum 1350. Table 3-3 comparesbreaking strengths of several all-aluminum stranded conductors with ACSR and one of hard-drawn copper, all ofapproximately equal d-c resistance. The principal economic factors involved are weight, strength. and cost.

Historically, the amount of steel used to obtain higherstrength soon increased to become a substantial portion ofACSR, but more recently as conductors became larger.the trend has been toward use of a smaller proportionof steel. To meet varying requirements. ACSR is available

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bare aluminum wire and cableTABLE 3-3

Comparison of Properties of Typical ACSR Conductor With Thoseof Similar All-Aluminum and Hard-Crawn Copper Stranded Conductors'

! de Re- ! RelativeSize

! !i Strand- Diam.sistance

Ohms per1000 fI

WeightIb per1000

RatedBreakingStrength

I

Strength Condueemil I Type ing In. at 20'C fI fb 0/0 tance

336.400394,500 ! 1350-H196201-T81 : 1919 0.6660.721 0.05140.0511 315.6370.3 6,15013,300 35.6 i 102.476.8 101.8336,400211,600 I ACSRHD Copper 30/77 ! 0.7410.522 0.05020.0516 : 527.1653.3 17,3009,154 100.0 100.052.9 102.8

'Abstracted from ASTM Standards and industry sources. Resistances are based on IACS,% conductiVities of 61.2% for 135Q..H19; 8% for steel; 52.5% for 6 2 0 1 ~ T 8 1 ; and 97.OCk for H.D. Copper. 500H19, although included in earli editions of this handbook, has been deleted from this edition because it is no longer commercially available,

in a wide range of steel content-from 7"1. by weightfor the 36/1 stranding to 40"10 for the 3017. Today, for thelarger-than-AWG sizes, the most used strandings are 18/1,4517, 7217. and 84/19. comprising a range of steel contentfrom II "10 to 18"10, and for the moderatelY higher strengthACSR 54/19, 54/7, and 2617 strandings are much used,having steel content of 26"1 26"1. and 31 "I" respectively.Typical stranding arrangements for ACSR and highstrength ACSR are depicted in Fig. 3-4. The high-strengthACSR. 8/1, 1217 and 16/19 strandings, are used mostlyfor overhead ground wires, extra long spans, river crossings. etc. Expanded ACSR, Fig. 3-6, is a conductor thediameter of which has been increased or expanded byaluminum skeletal wires between the steel core and theouter aluminum layers. This type of cable is used for linesabove 300 kV.The inner-core wires of ACSR may be of zinc-coated(galvanized) steel, available in standard weight Class Acoating or heavier coatings of Class B or Class C thickneSSes. Class B coatings are about twice the thickness ofClass A and Class C coatings about three times as thickas Class A. The inner cores may also be of aluminumcoated (aluminized) steel or aluminum-clad steel. Thelatter produces a conductor designated as ACSRIAW inwhich the aluminum cladding comprises 25 percent of thearea of the wire, with a minimum coating thickness of10 percent of overall radius. The reinforcing wires maybe in a central core or distributed throughout the cable.Galvanized or aluminized coats are thin, and are applied to reduce corrosion of the steel wires. The conductivity of these thin-coated core wires is about 8 percent(lACS). The apparent conductivity of ACSRIA W reinforcement wire is 20.3"1. (lACS).The incremental increase for dc resistance over that ofsolid round conductors, because of stranding of ACSR,

differs from that stated in Table 3-\, and depends On tyof stranding. The amount of increase also may be coputed according to a method described in ASTM B23Table V of B232 is reproduced on next page as Table 3-4A description of the method of computing rated breaing strength of ACSR found in ASTM B 232 is abstractin right-hand column of page 3-2.

ACSRlfW is a new design of ACSR composedshaped aluminum wires (Trapezoidal) stranded aroundstandard steel core. It is fully described in ASTM B 7and Tables 4-19 to 422.

Aluminum Conductor AlloyReinforced (ACAR)Another form of stranded composite conductor consi

of 1350-H19 strands reinforced by a core or by otherwdistributed wires of higher-strength 620 1-T81 alloy.The ASTM approved method for determining ACArated strength is described in ASTM B 524 as follow(The mentioned Table 4 is that of ASTM B 524.)

"The rated strength of completed conductors shall be taken the aggregate strength of the 1350 aluminum and aluminum alcomponents calculated as follows. The strength contribution oftbe 1a.luminum wires shall be taken as that percentage according wnumber of layers of 1350 aluminum wires indicated in Table 4 ofsum of tne strengths of the 1350-HI9 wires, calculated from thspecified nominal wire diameter and the appropriate specified minimaverage tensile strength given in ASTM Specification B 230. Tstrength contribution of the aluminum aHoy wires shall be taken as tpercentage, according to the number of layers of aluminum alwires. indicated in Table 4 of the sum of the strength of the aluminwires calculated from their specified nominal wire diameter and minimum stress as 1 percent extens.ion. This shall be considered. to

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@7 AliI S.AI!1 S. 8 AliI S.AI!1 S.

54 AI/19 S.

12 AliI S.6 AI!7 S.

42 AI/19 S.

18 AliI S. 36 AliI S.

38 AII19 S. 24 AI!7 S. 26 AI!7 S.

30 AI/19 S. 54 AI17 S. 30 AI!7 S.

45 AI17S. 21 AIl37 S. 16 Ali19 S.Fig. 3-4. Typical stranding arrangements of aluminumcable steel-reinforced (ACSR). The conductor size andampacity for any arrangement depends On the size of theind,vidual wires.

engineering design95 percent of the minimum average tensile strength specified for thewire diameter in Table 2 of ASTM Specification B 398, Rated strengthand breaking strength values shall be rounded-off to three significantfigures in the final value only. , ."

Because the 6201-T81 reinforcement wires in ACARmay be used in the core and/or for replacement of someof the J350-H19 wires in the strands, almost any desiredratio of reinforcement 1350-H19 wires is achieved, therebyobtaining a range of strength-conductance properties be-

TABLE 3-4A Increase, Percent, of Electrical Resistance of Aluminum Wires in ACSR of Various Strandings (Table 5, ASTM B 232) % de i % de

Stranding Resistance Stranding ResistanceI4217/1 1.5 2.54517/1 1-5 2.58/1 2.0 4817 2.5

18/1 2.0 5417 2.52.06/1 72/7 3.01217 2.5 16/19 2.52417 2.5 30/19 2.752617 2.5 : 54/19 3.030/7 2.75 76/19 3.084/19 3.0i

The above resistance factors also are usuaUy taken into account Intables of de resistance for ACSR.

TABLE 3-4BStrength Rating Factors

Extm.ct from ASTM Specification B 524 forConcentric-Lay-Stranded Aluminum Conductors.

Aluminum Alloy Reinforced (ACAR)(Referenced in ASTM B 524 as Table 4)

Stranding Rating Factor,.1350Numbe

62011'81r of Wires Number

1350of Layers'"620IT81

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bare aluminum wire and cable

KEYo 1350-H1g wire6201-T81 wire

4-1350 3-13503-6201 4-6201 15-13504-6201

12-13507-6201

30-13507-6201 24-135013-6201 18-13509-6201

42-135019-620154-1350 48-13507-6201 13-6201Strength/ Strength/ Strength/Stranding

4/3

Wt ratio26,000

Stranding3017

Wt ratio21,800

Stranding48/13

Wt ratio21,600

15/4 22,100 24/13 24,100 42119 23,5001217 25,100 18/19 26,800 5417 20,200Fig. 3-5. Typical stranding arrangements o f aluminum cable alloy-reinforced (A CAR). Assuming the reinforcement is6201- T81 alloy, and that individual wires are larger than 0.150 in. diameter the strength-weight ratios are as shown: (thestrengths are slightly higherifsmallerwires are usedJ_ The strengthlwt_ ratios compare rated strengthperASTMB 524and conductor weight in Iblft.

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engineering designtween constructions of all 1350-H19 wires or those of all6201-T81 wires, Fig. 3-5 depicts several stranding arrangements of ACAR cables of 1350-HI9 and 6201-T81wires.

The rating factors for various strandings of ACARusing 6201-T81 reinforcing wires are shown herewith asextracted from ASTM B 524. They are used as the basisfor calculating the properties of ACAR listed in Chapte r 4,International AnnealedCopper Standard

[n 1913 the International Electro-Technical Commission established an annealed copper standard (lACS)which in terms of weight resistivity specifies the resistanceof a copper wire I meter long that weighs one gram.Commercial hard drawn copper conductor is consideredas having conductivity of 97"l. lACS.Calculation of dc Resistance

USA practice is to exptess conductor conductivity in

19 x O,fRTl" STEEL WIRES

x 0,168" ALUMINUM WIRES -L.H. LAY &.4)( 0.168" ALUMINUM WIRESR.H. LAY

24 x 0.1591" ALUMINUM WIRES-LH, LAY

30 x 0.1591" ALUMINUM WIRESR,H, LAY

Fig. 3-6. Air-Expanded .4CSR. The size shown is 1595kcmi!. OD is 1.75 in. The diameter of equivalent regular.4CSR is 1.54 in,

Fig. 3-7. Composite conductors similar to A CSR also maybe manufactured by using trapezoidally shaped strandsas shown abovefo r selfdamping conductor.

terms of percent International Annealed Copper Standard(lACS) instead of in mhos (the unit of conductance).Resistivity is expressed as follows:

I IVolume Resistivity = pv = - R in which (Eq. 3-3)LI I = Cross-sectional areaL=LengthR = Resistance WWeight Resistivity = pw = - 2R in which (Eq. 34)LW = Weight

These resistivity constants may be stated in whateverform is required by the units used for area, length, weight,and resistance, and if these units are used consistently Rmay be obtained for any A, L, or W, by inverting thep,L PwL'equation; thus, from Eq. 3-3, R --;-- or --=,.- asWthe case may be.

Fo r USA practice, two volume resistivity constants' areused (Table 3-5):1. Ohm-cmillft, representing the resistance in ohms ofa round conductor 0.001 in. diameter 1 ft long.2. Ohm-sq in.lft, representing the resistance in ohmsof a conductor of I sq in, in cross-sectional area and 1 ftlong. This constant is sometimes multiplied by 1000 whichprovides ohms per 1000 ft.

"The resistivity constants are based on ohms when conductor isat AST:M Standard temperature of 20C (68 F). Some tables are basedon temperaLUfe of25"C, I f so. new resistivity constrants can be computedfor 25"C if considerable work is to be done (see Table 3 ~ 7 ) , ora temperature coefficient can be applied to the 20"C value of R"c toobtain that for 25"C, as below,

Multiply the 20" value by135!l-HI9 62.0% lACS 1.02048B5!l-H 19 6].0% lACS 1.02015620I-T-81 52,5% lACS 1.01734

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Equivalent Direct Current (de) Resistivity Values for Aluminum Wire Alloys at 20'C'

AlloyVolume

Conductivitypercent

lACSOhm-emil

per ft

Volume ResistivityOhm-mm2

per mOhms-in2per 1000 ft

WeightResistivityOhms-Ibper mile21350H19 61.2 16,946 0,02817 0,013310 435.13

6201T81 52,5 19.754 0,03284 0,015515 507,24Alumoweld 20,33 51,01 0,08481 0,04007 3191,2Steel 8,0 129,64 0,21552 0,10182 9574,0HD Copper 97,0 10,692 0,01777 0,0083974 902,27

Abstracted and calculated from ASTM Standards. For stranded conductors, resistance values obtained by use of these factors are to be increased by the stranding-increment ratio, per Table 31 for all aluminum conductors, or per Table 3-4A for ACSR. Example: Find de resistance at 20'C of one mile of Bluebell cable of 1,033,500 emil area of 1350 of 61,2% lACS conductivity, allowing 2% stranding increment,

' ., 3R5280XI6 .946x l ,0200883AIP YlI'lg reSistivity factor from Table 5, = = . ohms 1,033,500 It is customary to compute the conductor resistancefrom known resistance at 20C (68F), Some tables,however. specify resistance at 25C which are related to

lO'C values by the factors in footnote on page 3-7, or maybe read directly from Table 3-7, Temperature coefficientsfor 20C resistance values are in Table 3-6.Change of dc Resistance with Temperature

Over a moderate temperature range (OCC to 120CC)the resistance of a conductor increases lineatly with increase of temperature, thusR, = R, [1 + "" (T , - T,)] (Eq.35)

in whichR, = Resistance at temperature T,R, = Resistance at temperature T,"" = Temp, coefficient ofresistance at T,

Temperature-Resistance Coefficientsfo r Various Temperatures

From Eq. 3-5 it is apparent that the temperature coefficient for 20 D C cannot be used when the known resistance is at some other temperature, Fat this condition1"'x = --------- (Eq3-6)1 + (Tx - 20)

in which"" = Temp, coefficient at Tx deg C,0: ,. =Temperature coefficient at 20"C

Example: The 200C temperature coefficient 0:: $ l for 1350 { 6 L 2 ~ olACS) alloy is 0.00404. What is it for 509 C? Applying Eq, 36

1O,QQ)6()"'so = - - - - - - - - 1 ----+(50-20) 0,00404

For coefficients for other temperatures see Table ).7. Calculation of ac Resistance*

Skin effect is by convention regarded as inherent in thconductor itself; hence when the ac resistance of a conductor is stated, what is meant is the de resistance usuallin ohms, plus an increment that reflects the increased apparent resistance in the conductor caused solely by thskin-effect inequality of current density.

Skin effect results in a decrease of current density toward the center of a cylindrical conductor (the currentends to crowd to the surface),A longitudinal element of the conductor near center is

surrounded by more magnetic lines of force than is anelement near the rim, hence the induced counter-emf isgreater in the center element. The net driving emf at theReports of resistance and Kvar reactive requirements For large-sizr

t r a n s m i s s i o n ~ U n e conductors (single. [win. and expanded core} are inAlEE paper 5 9 ~ 8 9 7 power Appar(lW$ (md Systems. Docember 1959by Earl Hazan and AlEE paper 5841 C u r r e n ( ~ C a " ) ' i n g C(lpacity oACSR. February 1958. by H. E. House and P. D. Tuttle, Thesepapers also refer extensively to th(' effect on ampadty of wind velocityand temperature rise, For a complete listing of the formulas coveringthese resistivity relationships, see ASTM B 193, Table 3.

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engineering designTABLE 3-6

Temperature Coefficients of dc Resistance of Wire Materials C( x 20"C (68' F)(Abstracted from ASTM Standards)

Conductivi ty Temperature Coefficlent oc ,Material Percent lACS at m"C per degree CAluminum1350-H19 0,004041.2 0,00347Copper (h-d) 52.5201-T61 0,00361Alumoweid 97.0 0,00360Steel 20.33 0,00320.0Example: The resistance of one mile of Bluebell strandedconductor of 61.2% (lACS) 1350-H19 at 20(>C ,is 0.0883ohms. What i, it at 500C?Applying coefficient from Table 36

R50 =0;1lll83 [1 + 0.00404 (50-20)1 =0.0990 ohms

center element is thus reduced with consequent reductionof current density.The ratio of ac resistance to de resistance (R,,/Ru,) isalmost unity for small aU-aluminum conductors at powerfrequencies, regardless of load current. I t increases toabout 1.04 for the 1113.5 kcmil size and to about 1.09

in the 1590 kcmi! size.The ):>asic calcula\ions of R"/R,,, ratio have been madefor round wires and tubes of solid material, and thesevalues can be obtained from curves based on such calculations or tests. Fig. 3-8 shows R.,/Ru, ratios for solidround or tubular conductors, and they also may be applied for stranded conductors by treating the stranded c r o ~ section as if it were spHd.For use' of the curves of Fig. 3-8, R", is first obtainedand corrected for temperatore. Rae is then obtained fromthe R.,/Rd, ratio read from the chart.

Example: Allaluminum Bluebell stranded conductor of 1350-H19(61.2% lACS) has de resistance of 0.0188 ohms per 1000 II at5


10/26


Temperature Coefficients of dc Resistance of Wire Materials at Various Temperatures Alloy

Conductivity

TempoC 010202530405060708090

100

1350-H1961.2% lACS

.00440.00421

.00404

.00398

.00389.00374

.00361

.00348

.00336.00325.00315

.00306

6201-T8152.5% lACS

.00373.00359

.00347

.00341

.00335.00324

.00314

.00305

.00296.00287.00279

.00272

'Calculated per NBS Handbook .lOR Example: The resinanee of one mile of Bluebell stranded conductor of 1350-Hl9 alloy at SOOC is measured at 0.0990 ohmWhat is it at 200c? Applying the 5()0 coefficient from Table 3-7 in Eq. 3-5: R20 = 0.0990 [I + 0.00361 [20 - SOli = 0.0883 ohms.

TABLE 3-8 Comparison of Basic and Corrected RaclRdc Curlew Conductor (2) (3) (4). (5)

(1) Amps Resistance Basic Correc1lldLoad per multiplier RaclRdc Ratio iamp emil x 106 Fig. 3-7 Ratio (3) x (4)200 194 1.007 1.025 ! 1.032400 388 1.013 1.025 I 1.038600 581 1.018 1.025 1.044800 715 1.022 1.025 1.048

1000 960 1.025 1.025 1.051*If these current variations occur in a conductor whenambient temperature is constant, the operating temperaturewill increase with load. hence the basic Rac/Rdc ratio mustbe adjusted to reflect the variation of Rdc with temperature.Constants are available from the Aluminum Association thatfacilitate this adjustment of R.c/Roc ratio.

caused by this crowding is less than I percent, hence ordnarily can be neglected.Hysteresis and Eddy Current EfJects

Hysteresis and eddy current losses in conductors anadjacent metallic parts add to the effective a-c resistancTo supplY these losses, more power is required from thline. They are only important in large ampacity conductowhen magnetic material is used in suspension and deadend clamps. or similar items which are closely adjacent the conductor.

Usual tests that determine R"/R, , ratios for conductoas reported in tables of properties take into account anhysteresis or eddy-current loss that is in the conductitself, so no separate estimate of them is ordinarily rquired.The calculation of eddy-current and hysteresis loss adjacent metallic materials, (structures, housings, etc.)its estimate by tests is beyond the scope of this book.

Radiation LossThis component of power loss in a conductor is neglig

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engineering design

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I 1 I /'f / / /1)1 / I //I, / / / II JVI I I V /f.""U I1 / / / / / /fJ I / / / /' // / / / / / ./ ,/ ~ = 0 . B 8 1

' l '/.// / /// /Tn

/:..,..- / /.....-:: ........ : : : - r I~ : : : : - _ ~ = O 9 0

D ~ = O 9 2 10 ao a.V60 !RdcRdc in ohms per mileFig. 38. Skin-eDect factor for solid-round or tubular conductor at 60 Hz.

H. B. Woght. "Skin JIm n Tubu /wan d Flll t Cffdu


12/26


TABLE 3-SAComparison of R . IR Ratios for All-Aluminum and ASCR,266.S kcmi!, Single-Layer Conductors, and Equivalent 2-Layer ConductorResistance value in ohms per mileLight Load at 25C 75% Load at WC

Resistance Resistance RKiR. .Conductor Stranding dc ! 60 Hz RacfRck , dc 60 Hz Ratio

1350H19, 61.2% 7 , 0.349 I 0.350 0.364 0.366 1.005.+ !lACSi i6;7 1,42CSR (1 layer) 0.349 0.350 1.+ 0.384 0.545

!26;7CSR (2 layer) 0,349 0.349 1. 0.364 0.384 1.00i ,

ble at usual power frequencies; it becomes important onlyat radio and higher frequencies. Accordingly no methodof estimating such loss is considered herein.Corona"

Corona oCcurs when the potential of the conductor issuch that the dielectric strength of the surrounding airis exceeded. The air becomes ionized and bluish illuminated gaseous tufts or streamers appear around theconductor, being more pronounced where there areirregularities of the conductor surface. The dischargeis accompanied by the odor of ozone, and there maybe a hissing sound.Corona discharge from a bare conductor power linemay interfere with radio and TV reception, or adjacentcarrier and signal circuits.Bundled conductors are frequently used to obtain lowervoltage stress on the air insulation for voltages above3S0kV.Inductive and Capacitive ReactanceVariable current flow in an electrical conductor, eitheras alternating current or as a transient of any kind, givesrise to the parameters of inductance (usually expressed inmillihenrys) and capacitance (usually expressed in micro

farads) and their related properties of inductive andcapacitive reactance, usually expressed as ohms per mileand megohm-niiles, respectively, No energy loss is associated directly with these parameters, but the 90 out-ofphase voltage and current must be supplied to sustain themagnetic and electric fields created, so a slight increase'For further information regarding corona, see Standard HandboQkfor Electrical Engineers. McGraw-HiH Company. Sec. 14 which alSocontains references to the varioUs n:search paperS, An ex;;:eUem text

on corona and EHV line design is the EPRI Transmission LineReference Book. 345 i:V and above.

of I'R loss in the conductors occurs because of them.Inductance and capacitance, however, influence systemstability in high-voltage lines to a greater extent than resistance.Only the reactances that are related to the conductors,either as parts of a single-phase or a three-phase circuit,are considered herein. The total system reactance also In-cludes many factors not related to the conductors; amongthem leakage reactance of apparatus, and the extent thatautomatic tap-changing and powerfactor control are used.These system conditions are taken into account as a part

of circuit analysis for which a high degree of electricalengineering skill is required, and their consideration isbeyond the scope of this book.Inductiye Reactance

The inductance L of a circuit is a measure of thenumber of interlinkages of unit electric current withlines of magnetic flux produced by the current, bothexpressed in absolute units. L also is defined by e =L(dildt) in which dildt indicates the rate of change ofcurrent with time. L is the coefficient of proponionality,and e is the momentary induced voltage.The quantity X=2"f L, in which I is frequency in Hz. is

the in.ductive reactance, expressed in o h m s ~ but in phasonotation the inductive-reactance drop is perpendicular tothe resistllnce drop; that is, the current I in a conductorhaving both resistance and inductive reactance, but negligible capacitance, and at unity power factor isI E/ (R + jX) in which; = Vector operator (-1)'"(Eq.3-7)

E = Emf, volts, to neutralI = Current in conductorampX = Inductive reactance,3-12 ohms


13/26

engineering design1,04

,..- ..-.03 .-- .- _1 54 / 7 strondingl54/19..,.., .,.,.

/V/ ' " / ~ , , + 5 / 7 strandingl1 ,.V rn -.// ",1.0

200 400 60 0 800 1000 1200 1400 1600CURRENT DENSITY 60 HZ AMPERES PER MilLION eMi l OF ALUMINUM AREA

Fig. 3-9. Resistance multiplying factors for tktee-layer ACSR for aluminum conductivity of 62%. Without significant error.these ftlCtors also may be used for aluminum of 61.2% lACS conductivity. These data are used to reflect the increase in resistancedue to magnetizing effects o f the core.

Numerically (R + jX) = (R ' + X2)14 and is designated impedance, also expressed in ohms.Normally, computations of R and X for transmissionlines are made, for convenience, on the basis of unit

lengths, usually one mile. Tables are set up in this manner.The inductive reactances discussed herein and listed intables of conductor properties are suitable for calculationsof either positive- Or negative-sequence reactance, as employed for usual transmission and distribution circuits.Zero-sequence values, as required for unbalanced conditions or fault-currents, may be obtained by methods laterdescribed. Inasmuch as zero-sequence inductive reactanceis the principal factor that limits phase-to-ground faultcurrents, its value is important in conductor selection.Simplifying of reactance calculations is effected if thereactance is considered to be split into two terms ( I )

that due to flux within a radius of 1 ft (X,) including theinternal reactance within the conductor, and (2 ) that dueto the flux between 1 ft radius and the center of theequivalent return conductor-(X,,). A further simplifyingconvention is that the tabulation of the latter distance isthe distance between centers of the two conductors insteadof the distance from one-foot radius of One conductor to* First proposed by W. A. Lewis. See also W. A. Lewis andP. D. Tuttle, The Resistance and Reactance of Aluminum Con-ductors, Steel Rein/orced. Trans. AlEE, Vol. 77. Part IU, 1958.

the surface of the adjacent one; thus, there will be minusX" values tabulated for distance between conductors thatare less than 1 ft apart.Conductor spacing D for 3-phase circuits is the geo

metric mean distance (GMD) as later defined.The sum of the two terms (X , X,) is the requiredinductive reactance of the conductor X under usual loadconditions. The values also are useful as a basis for calculating impedance under fault conditions (zero-sequence).It is to be noted that X, is an inherent conductor electricalproperty, taking into account the reactance due to the fluxout to a distance of 1 ft from center of the conductor, andis so tabulated for round, stranded, and composite conductors, usually as ohms per mile. The values of X" however, depend on spacing of the conductors, and are unrelated to size of an individual conductor. Table 3-9 listsvalues of X. at 60 Hz based on separation distance between

centers of the conductors, in ohms per mile. The value forany other frequency is directly proportional; thus, for25 Hz it is 25/60 of the 60-Hz value.The conductor spacing for other than a simple two-conductor circuit is its geometric mean distance (GMD) inft. A few of the usual arrangements and their GMD's areshown in Table 3-10. If the spacing is unequal, the GMDis a geometric average value which, however, usually issatisfactory for preliminary calculations. Thus, in a flat

313


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bare aluminum wire and cableTABLE 39 Separation Component (X.) of Inductive Reactance

at 60 Hz (1) Ohms per Conductor per Mile Separation of Conductors

Inch. .feet 1 2 3 4 5 I 6 7 I 8 9 10 11 I0 -1 02 0.08413 0.13334 0.16825 0.19536 0.21747 0.2361

8 0.25239 0.266610 0.279411 0.291012 0.301513 0.311214 0.320215 0.328616 0.336417 0.343818 0.350719 0.357320 0.363521 0.369422 0.375123 0.380524 0.385625 0.390626 0.395327 0.399928 0.404329 0.408630 0.412731 0.416732 0.420533 0.424334 0.427935 0.431436 0.434837 0.438238 0.441439 0.444540 0.447641 0.450642 0.453543 0.458444 0.459245 0.461946 0.464647 0.467248 0.469749 0.4722

314

-0.2174 -0.1682 -0.0654 -0.04920.3015 -0.1333 -0.1062 -0.0841 -0.0349 -0.0221" -0.01060.Q735 0.0789.0097 0.0187 0.0271 0.0349 0.0423 0.0492 0.0568 0.0620 0.0679 0.1299.0891 0.0938 0.0984 0.1071 0.1112 0.1152 0.1227 0.1264.1028 0.11900.1399 0.1430 0.1657.1366 0.1461 0.1491 0.1520 0.1549 0.1577 0.1604 0.1631 0.1933.1707 0.1732 0.1756 0.1779 0.1802 0.1825 0.1847 0.1869 0.1891 0.19120.2012.1973 0.1993 0.2031 0.2050 0.2069 0.2087 0.2105 0.2123 0.2140 1 0.21570.2207 0.2332 0.2347.2191 0.2224 0.2240 0.2256 0.2271 0.2287 0.2302 0.2317 10.2376 0.2390 0.2404 0.2418 0.2431

From: Electrical Transmission and D i s t r i b u ~ tion Reference Book, Westinghouse ElectricCorporation, 1964.{I) From formula: at 60 Hz

Xd ; 0.2794 10gl 0 dd = separation in feet

0.2445 0.2458 0.2472 0.2485 0.2498 0.2511

3-phase arrangement of conductors A, e, and C with5 ft between A and e, 7 ft between Band C, and 12 fbetween A and C, the reactance voltage drop from anyconductor to neutral does not vary more rhan 2.2"!, fromthe voltage based on average D (A x B x C) A, Or 7.5 ft.Xa and Geometric Mean Radius (GMR)

The calculation of inductive reactance to a radius o1 ft (X.) is aided by the factor GMR, which representsthe radius of an infinitely thin tube the inductance owhich under the same current loading equals that of theconductor. For non-magnetic materials,

j 1X. = 0.2194 - loglo--- (Eq.3-8)60 GMRin whichX, = Inductive reactance to 1 ft radius, ohms/mileI = Frequency, Hz

GMR = Geometric mean radius, ftThe GMR of a single solid round conductor is 0.1788rin which r is radius of conductor in ft. Fig. 3-10 is a

curve showing GMR for an annular ring.The GMR of a stranded conductor without steel reinforcement or center voids is obtained by using the concepof concentric rings of solid round wires, each ring beinga specified G MD apart. *The GMR of a stranded multi-layer ACSR or an expanded all-aluminum conductor with hollow center is*FOr methods of calculation see reL at bottom of page 3-13.


15/26

1.0

0,95

0.90GMRr,

0.S5

0.600.n68

0.75

I/,

//, , /

I/ 8I /, I ,/ IIVV

o ,1 .2 .3 .4 .5 ,6 .7 .8 .9 1.0r,r,2= RATIO OF INSIDE; R:AOIUS TO OUTSIDE RADIUSr,

Fig. 310. GMR of annular rings.L F. WoQ


16/26

bare aluminum wire and cableCheck of X, 1X. = 0.2794 log, . 0.399 which checks table.0.0373Comparison with solid round

1.170GMR = 0.7788 X 0.0380 ft2X 12

1X, = 0.2794 X 10glO 0.3970.0380A corresponding size of ACSR, Curlew, diam. 1.246 in.is listed with X, of 0.385 and GMR of 0.0420 ft, therebyshowing the reduction of X, because of the hollow-tubeeffect and increased diameter, as per Eq. 3-8.The variation of X, for different cable constructions ofthe same size, according to standard tables of electricalproperties, is shown below for 266.8 kcmi! conductors:

X.Kind af Overall Ohms perCable Code Stranding diameter l


17/26

engineering designTABI.,E 3-11 of a single conductor, as previously noted,Zero-Sequence Resistance and Inductive or as taken from table.Reactance Factors (R.and X.lil)

Frequency tn 60 HzFrequency (f) 60HzResistivity (Pe ) ohms per conductor

Ohm-meter per mileAl l values Re 0.?8SS*

1 2.0505

1050 f 2.3432.4692.762

100' 2.888500

1,000 X'l 3.1813.3075,000 3.60010,000 3.726

Wl'Slilli'itOIm', "TroMmimanand DisltifxllicfI Hruvibwk. " 1964.! l) From formulas:

He = 0.2858X = 0.4191 -L log 77,760 60 p.-. 60 f where f = frequency

p. = resistivity (ohm-meter)* This is an average value which may be used in the absence of

definite information.

in which p, = ac resistivity of the earth return path inohm-meters (the resistance between thefaces of a one-meter cube of earth). Thisvalue depends on quality of the earth, andis in the range shown in Table 3-11, butan average value of 100 may be used inthe absence of definite information.f = Frequency, Hz

In addition, the zero-sequence reactance and impedanceis also affected by a mutual reactance term because ofnearby ground wires Or circuits. The zero-sequence impe-dance of one mile of a 3-phase transmission line withoutground wires, but with ground return, not including capacitance effects, isZ. =Roo +R, j (X, X. - 2Xd ) (Eq.3-11)in which Roo = ac resistance in ohms per phase per mileR. and X, are given by Eqs. 3-9 and 3-10 aboveX. and Xd are inductive reactances in ohms per mile

Example: Consider the arrangement below in which conductor isACSR 795 komi!, Drake, 60 Hz.r--15 1 t J 5 ~

From Eq. 3 ~ 9 = 0.2858, and X t = 2.888, ohms per mileFrom tables, Rill:< 0.1370 ohms per milt at 7 5 ~ C

X. 0.399 ohm, per mileX, = - I (0.3286 + 0.3286 + 004127) = 0.35663 ohms per mile in which Xd. at 15 ft is0,3286 and at 30 ft is 004127

Substituting in Eq. 3-11 for im:pedance ZoZ. = 0.1370 + 0.2858 + j(2.888 + 0.399 -2(0.3566)) ohms!

mile= 0.4228 + j 2.5738 ohms!mile = 2.608angleSO.67D.Shunt Capacilive Reactance

In long high-voltage transmission lines the distributedcapacitance caused by the electric field between and surrounding the conductors can attain high values whichmarkedly affect circuit properties; among them voltagedistribution, regulation, system stability, corona, lightningperformance, and transients set up by faulting or lineswitching.The shunt capacitive reactance of a conductor system

1is X' , =- - " - - -ohms (Eq.3-12)2"jCIn which if C is in farads; f is frequency Hz.It is customary in engineering work to express shuntcapacitance in microfarads per mile and X', the corresponding reactance in megohm-miles, usually for 60 Hz.The prime (' ) is affixed to the X' to prevent confusionwith X-values that represent inductive reactance.To obtain the megohms of shunt capacitive reactancethat controls charging current of a line longer than onemile, the listed megohm-miles value is to be divided bylength of line in miles; that is, for 100 miles of a line using795 kcmil 54/7 ACSR at a phase spacing of 20 ft, themegohms of shunt capacitive reactance which determinesthe charging current wiD be the listed 0.1805 megohmmiles divided by 100 or 0,001805 megohms (1805 ohms).Similar to the use of X a to represent inductive reactanceto radius of 1 ft and Xd to represent inductive reactancein the remaining space up to an adjacent conductor, thetotal capacitive reactance similarly may be divided intocomponents as follows:

3-17


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bare aluminum wire and cableTABLE 3-12Separation Component (X'd I of Capacitive Reactanceat 60 Hz II I Megohm-Miles Per Conductor

Separation of Conductors

feet!012345678910

111213141516171819202122232425262728293031323334353537383940414243444546474849

inches0 1 ! 2 3 4 5 6 7 8 9 10= 1-00.02060.03260.04110.04780.05320.05770.06170.06520.06830.07110.0737

0.07610.07830.08030.08230.08410.08580.08740.08890.09030.09170.09300.09430.09550.09670.09780.09890.09990.10090.10190.10280.10370.10460.10550.10630.10710.10790.10870.10940.11020.11090.11160.11230.11290.11360.11420.11490.1155.

-0.0737 -0.0532 -0.0411 -0.0326 -0.02600.0024 0.0046 0.0066 0.0085 0.01030.0218 0.0229 0.0241 0.0251 0.02620.0334 0.0342 0.0350 0.0357 0.03650.0417 0.0423 0.0429 0.0435 0.04410.0482 0.0487 0.0492 0.0497 0.05010.0536. 0.0540 0.0544 0.0548 0.05520.0581 i 0.0584 0.0588 0.0591 0.0594

From: Electrical Transmission and Distribu-tion Reference Book, Westinghouse ElectricCorporation, 1964.(1) From formula: for 60 Hz

X'd = 0.06831 log lOdd :::::: Separation in feet

-0.0206 -0.0160 -0.0085 -0.0054 -0.00260.01200.0120 0.0166 0.0180 0.0193.0136 0.01520.0272 0.0300 0.0309 0.0318.0282 0.02910.0372 0.0392 0.0399 0.0405.0379 0.0385 0.0467.0446 0.0452 0.0457 0.0462 0.04730.0519 0.0523 0.0527.0506 0.0510 0.0515 0.0570 0.0574.0555 0.0559 0.0567.0563 0.0611.0598 0.0608 0.0614.0601 0.0604

, 60 1 60X, = 0.0683 -loglO + 0.0683 -10glO dabf rn I (Eq.3-13in whichX' , = Capacitive reactance in megohm-miles per COn-ductor'n =Overall radius of conductor, Itd" = Separation distance to return conductor, tf = Frequency, HzThe left-hand term of the above two-term equationrepresents X'" the capacitive reactance lor 1 ft spacing

(to I-ft radius); the right-hand term represents X'd' theseparation component; both are in terms 01 megohm-miles.These two values have been tabulated lor 60 Hz. Thosefor X' , are listed in the tables of electrical properties ofconductors and those for X'd are in Table 3-12.Example: For 795 kcmil Drake, Ra.dius of conductor 0,1)461 ft

6(} Hz. 20 rt spacing.Substituting in the termS of Eq. 3 13

IX'. = 0.0683 108"-- = 0.0683 X 1.3365 = 0.09130.0461 megohmmiles X' , = 0.0683 log" 20 = 0.0683 X 1.3010 = 0.0889 megohm-miles X' , = 0.0913 + 0.0889 = 0.1802 megohm-miles

Zero-Sequence Capacitive ReactanceAn added term E', that affects zero-sequence capacitivereactance depends on distance above ground. I t is representedbyX',. = 0.0205 60 log", 2h in which h is height of cant ductor above ground, ft(Eq.3-14)

318


19/26

The zero-sequence capacitive reactance of one 3-phasecircuit without ground wires in terms of megohm-milesper conductor isX'o X', + X'd - 2X', (Eq, 3-15)

in which the terms have previously been defined,Capacitive Reactance of BundlcdConductors

The shunt capacitive reactance of bundled conductorscan be found from equations identical with those used inthe numerical example relating to inductive reactance ofbundled conductors (page 3-17), except a prime is addedto each X, Thus (X',)b and (X',,)b may then be used inplace of X'" and X'" in the corresponding equations forpositive- or zero-sequence inductive reactance,Ampacity of Bare Conductors'

The major considerations involving the current-carryingcapacity (ampacity) of overhead transmission conductorsare the effect of conductor heating by the current and theconsequent reduction of tensile strength, Most aluminumtransmission conductors are hard-drawn and operate overpredetermined ranges of maximum sags and tensions,Heating to relatively high temperatures for appreciabletime periods anneals the metal. thus reducing the yieldstrength and increasing elongation. Hence the ampacityof such conductors is generally stated to be the currentwhich under the assumed conditions of operation will notproduce sufficient heating to affect significantly the tensileproperties of the conductor.

Basic to the calculation is the establishment of an ambient temperature level. Obviously the ampacity is relatedto temperature rise. and the amount of the latter dependson temperature of the outside air.

lisual practice is to assume an ambient temperature of40'C for overhead conductors, and the tables and chartsherein are on that basis. However, lower ambients will befound in some applications, and the temperature rise for agiven operating temperature must be altered accordingly.The usual maximum operating temperature for tensioned bare conductors is 70 to 85'C, with 100'C andovcr permiSSlble only in limited emergencies.

Hear Balance:Temperature rise in a conductor ciepends on the balance between heat input (FR loss plus heat received fromsunsbine) and heat output (due to radiation from the COn-

ductor surface, and transfer because of convection of aircurrents). The heat loss arising from metallic conductionto supports is negligible, SO is ignored. When the temperature of the conductor rises to the point where heat output

* Conductor ampacity has been reported extensively by Schurigand Frick, W. H, McAdams. House and Tuttle and others, andtheir results checked by test programs, The brief treatment hereinis abstracted from many sources, principally the Alcoa AluminumOverhead Conductor Engineering Data book: Section 6.

engineering designequals heat input the temperature remains steady, and thecurrent for such condition is the ampacity for that temperature under the stated conditions,

The factors of importance that affect ampacity for agiven temperature are wind velocity, conductor surfaceemiSSivity, atmospheric pressure (which affects ampacityat high altitudes), and of course the ambient temperature,

Neglecting sunshine heat input. the heat balance may beexpressed asPRo,,, =0 (W .. ..;.. W,) A" both terms in watts/linear ft.

(Eq.3-16)and in which

W, Convection loss, watts/sq in. of conductorsurface

W, = Radiation loss, watts/sq in. of conductor surfaceA = Surface area of conductor per ft of length, sq in.R"rr = Total effective resistance per ft of conductor,ohms, including the resistance-equivalent ofpertinent components of loss under a-c conditions, (skin and proximity effects. reactance

components, etc,)which reduces to

~ - - = - " ' C " : ~ . ~ - .....- Xd(W,+W,) (Eq,3-16a)I = ~ - - - - - - - - - - - - - - - - - - - -0 f fin which d = Outside diameter of conductor, in.

i = Current for balanced condition (theampacity), amp

The convection heat loss W" depends on wind velocity,temperature risc, and atmospheric pressure (altitude), Theradiation heat loss W, is considered to depend on temperature rise and an emissivity constant , that expresses theability of the conductor to radiate internal heat.A perfect non-radiative surface would have, = : 0, anda body that radiates all heat would have, I. The emissivity factor < for aluminum conductor surfaces dependson the degree of oxidation and discoloration of surface,its roughness, and the stranding. Newly installed conductors mav have, as low as 0.23. and mav be 0.90 afterbeing ";elI-blackened after y e a r ~ of s e r v j ~ e . A value of, = 0.5 provides a safety factor for the majority of exposed conductors which have been installed for severalyears, This value (, "" 0.5) is used for the tables andcurves herein, which also show values based on a crosswind of 2 ft per sec (1 . 36 miles per hr) as well as forstill but unconfined air (Figs. 3-11 et seq).

The effect of sunlight and altitude as well as of variations of emissivity constants are shown by small auxiliarycurves of Fig. 3-15.The various factors entering the heat balance equationshave been summarized by one conductor engineeringgroup into the following:1. Convection Heat Loss (W,,) for 2 ft/sec wind, atsea level for 60C rise above 40C ambient.

3-19


20/26


TABLE 3-13Current Ratings for High-8trength ACSR with Single Layer ofAluminum Strands 40 C ambient = 0.5 emissivity; no sun.

!

Code Size Strandingame emil.Grouse 80,000 BAI- 1 St.

80,000 8AI- 1 St.Petrel 101,800 12AI- 7 St.

W, = 0.5388 (1.01 + 43.22 d V2) watts per ft oflength for d up to 1.6 in. diameter (q.3-17)W, = 22.15 dO' watts per ft of length for d 1.6 in.diameter and over (Eq. 3-18)

2. Convection Heat Loss (W,) for still air, at sea levelW, (still) 0.072 d75 6 t,'25 watts per ft oflength in which 6 t. is temperature rise aboveambient (Eq.3-19)

3. Radiation Heat Loss (W,) for 60eC rise above40C ambientW, - 6.73 d watts per ft of length for < 0.5 (anaverage emissivity for weathered conductors)(Eq.3-20)

4. Sun Heat Gain (W,)-to be subtracted from (W,+W,) in the above equations.W, = 3.0 d watts per ft of length for mid latitudes(Eq.3-21)

Wind Condition

2 ft per secStill Air2 It per sec

Current in AmperesTemp Rise Temp Rise Temp Rise

IDe 30e aoe23606 175 1661322630425

101,800 12AI- 7 St.Minorca 110,800 12AI- 7 St.

110,800 12AI- 7 St.Leghorn 134,600 12AI- 7 St.

134,600 12AI- 7 St.Guinea 159,000 12AI- 7 St.

159,000 12AI- 7 St.Dotterel 176,900 12AI- 7 St.

176,900 12AI- 7 St.Dorking 190,800 12AI- 7 St.

190,800 12AI- 7 St.Cochin 211,300 12AI- 7 St.

211,300 12AI- 7 St.Brahm. 203,200 16AI-19 St.

203,200 16AI-19 St.

Still Air2 ft per secStill Air2 I t per secStill Air2 f t per secStill Air2 ft per secStill Air2 It per secStill Air2 ft per secStill Air2 I t per secStill Air

7513279

14992

166104178111187117199126188120

1903327711201423143923162 352662628237485 , 28096394002960842219318233890129610

If the ambient temperature is less than 40C, a smachange in ampacity for a given temperature rise may bobtained because the resistance of the conductor is les(because of its reduced temperature). However, at thlower ambient and the same temperature rise, the radiateheat loss is less. The net result is that the current forgiven temperature is little changed over a considerablrange of ambient temperature.Ampacity of1350-HJ9AII-Aluminum ConduclOrand Standard-StrengtitACSR Conductors

Ampacity graphs for 1350 all-aluminum conductorsand Standard-Strength ACSR are shown in Figs. 3-1112, 13, and 14 for still air and for 2fps wind at 4I)Oambient for, =0.50 and 62.,. lACS aluminum withousunlight effect. For 61.2". lACS multiply by 0.994Small graphs of mUltiplying factors for sunlight, altitudeand emissivity corrections are shown in Fig. 3-15. ThW, and W, values for 600C rise are from Eqs. 3-17, -18and -20. The slope of the lines from the 60 0C valuesbased on experimental data.

320


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Ampacity of Single-Layer High-StrengthACSR Conductors

Table 3-13 can be used for ampacity values for highstrength ACSR in larger-than-A WG sizes for 10', 30',and 60'C rise. Values for intermediate temperatures maybe obtained by plotting tb,ese values on log-log paper similar to that used for Figs. 3-13 and 3-14.Ampacity of6201-T81 andACAR Conductors

Inasmuch as heat loss for a given temperature rise isproportional to conductor surface (or diameter) and heatinput is proportional to FR, the ampacity of any conductorof conductivity other than 62% lACS is found closelyper the following example:Find ampacity in still air for 30'C rise of 394.5 kemil(0.684 in. diam.) cable of 6201-T81 of 52.5 % lACS cOnductivity.

By interpolating in Fig. 3-11, the ampacity of 62"70 lACS1350 conductor of same diameter (if it could be obtained) would be 320 amp. Hence, the ampacity at52.5% lACS is 320 x (52.5/62.0)i!,; or 294 amp.'For ACAR which has wires of two conductivities, theequavalent conductivity value is used; thus, for 42119ACAR (1350 and 6201-T81) of 1.165 in. outside diameter,the "7. lACS conductivity of the ACAR conductor, if the1350 wires are 61.2"1. lACS, is(42 X 61.2 + 19 X 52.5) 161 = 58.5"70 lACSExamples of Ampacity Values Obtained from Figs. 3-11

to 15 Incl.The following typical examples illustrate the use of thevarious graphs:

I. Cable size 795 kemil ACSR 26n stranding, E =0.50, diam. 1.1 in. approx., wind of 2 ft per sec.What is ampacity for 35C rise, or 75C operatingtemperature?At top of Graph Fig. 3-14 note the diagonal line that

The method described is based solely on comparative [2ft Joss,and the values obtained are conservative. I f correction is madefor the slight change of Rt,/Rde ratio caused by change of i n ~ ductance. a slight increase of ampacity, of the order of 1% or 2%in this instance is: obtained.

engineering designextends downward from the designated size. It intersectsthe 35'C rise horizontal at 835 amp, which is the ampacity for the stated conditions.

2. For the cable of Example 1, what is ampacity ifaltitude is 10,000 ft with sun, and with emissivityfactor reduced to 0.23?Note: The multiplying factors of Fig. 315 are to be used. These

strktly are applicable only for l O O ~ C operating: temperature.but inasmuch as the ampadty diagonals on Fig. 13 are almoststraight lines. it is satisfactory to apply the muitipJying factorsdirectly to the 35"'C rise ampadty of 835 amp.The altitude factor with sun is taken from the left-handdiagram of Fig. 3-150 as being 0.83 (approx) for I . l in.diam., and the emissivity factor taken from the right-handdiagram with sun for, = 0.23 is 0.90. The desired ampacity is 835 X 0.83 X 0.90 = 630 amp.

Note: I f the multiplying factors are applied to the 60 Q Riseampacity. for conditions stated in Example 1, the unadjustedampacity is 1050 amperes. After applying the multiplying factors, this reduces to 1050 X 0,83 X Q,!'X) = 785 amp. EnteringFig. 314 at intersection of 60"C rise and 785 amp, and fonowAing down an imaginary diagonal that is parallel to an adjacentdiagonal, it is noted that ~ h i s intersects the 35"C line at 630amp. the same value as previously obtained.

Emissivity L imita tions for Figs. 3-11 10 3-14An emissivity of < = 0.5 is the maximum assumed forweathering conditions at high altitudes (l0,000 ft). Themaximum assumed emissivity for a fully weathered conductor in normal altitude is 0.91.Conductor EconomicsThe high cost of energy and generation facilities hasmade it very important that power losses be evaluatedwhen selecting the correct conductor size to be used ina given project. Construction and energy costs haveincreased dramatically during the past decade, and thistrend seems likely to continue. The Aluminum Association pUblication, "The Evaluation of Losses in CondUCtors." provides details on how such an economic analysiscouId be done.

3-21


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--


Chart A Chart Ba,Al t i tude Effec1 b. EmissivityEHect c. Eminivi ty Effe(:t Q, Alti 'ude E H ~ c t b,Emiuivity IHied .EII1'nl",i ty Efhtd10.000 f ~ e t no sun with svn

.. b. sbw.....IE$ . .Q WI!..U"t; !:> (123 0..918 I .85 .95

2.

2.I.

50.

51.00.5

0.

---NoSon -

SOO -\ I0.23 0..50. II 91

-----

.90. 1.0.0. 1.10 1.2080. .90.

10000 feet no SUfi "nth sun... 2.5..i 2.0D" ~ t 5 " xaUt ; ! to

910.5U0. .85 .95 .95 1.0.5 1.15 ,90 1.0

-0..50. I r0-- -No Sun - -

0..91 0.23..23 O.un\ -I \ I ~ I .75 .65 ,95 .65 .95 1.05 1.1 5 .So. .90. 1.0 .8 0 ,90 1.00 ,90 1.00 1.10 .85 .95

CURRINT CURRENT

A-For stranded 1350 in sti ll air. Fig. 3-11. B-For stranded 1350-wind 2 jps. Fig. 3-12.

Chart C Chart DQ , Altit'Ude fffec t b, Emissivity Effe :>I"0..5

50.

50.

NoSunS "

- - 0..50.- -- -- -

1023 0..50. 0..91 0.23 0..9- I I I \ , 1\ Z8 80. .80. .90. .9 0 1.00 UO 1-20 .85 .95 S5 .95 :95 l.OS l, 5 .90 to.75 .85 .95 .85 ,95 1.05 1.1.5 .SO ,90 to .80. .90 .90 1.00 i.10 .85 .95CURR ENT CURRNT

C-For stranded ACSR in still air. Fig. 3-13. D-For stranded ACSR-wind 2 jps. Fig. 3-14.

Fig. 315 (A, B, C, and D)-Multiplying factor for various conditions o f emissivity (,j, sun, and altitude.Multiply the ampacity value obtained from Figs. 3-11 to 3-14 for 600C rise inclusive by the applicable foctor at bottom of dicorresponding to the associated ampacity CUlVe.

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