reactance calculation

7/27/2019 Reactance Calculation

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Section III Insulated Aluminum Conductors

Chapter 9

Engineering Design as Related to Cable Applications

The data in this chapter provide the application engineer with certain formulas and tables that can be used toadvantage when selecting cable for ordinary uses. It isassumed that he has available the latest National ElectricalCode (NEe), and that the helpful supplementary tablesprepared by wire and cable manufacturers to aid NECapplications are at hand. The mathematical basis for someof these tables is described herein, and a few are abstracted. The important comprehensive tables relating tocable construction, applications and ampacity issued byICEA-NEMA are also explained, Many equations andtables principally relating to cable design as distinct fromapplications are omitted, as beyond the scope of this book.

Descriptions of cable components and their functions,and of the various kinds of insulations, are in Chapters 7and 8,The design factors that inHuence the selection of asuitable aluminum cable are electrical, mechanical,thermal, ability to withstand unusual environments. am

pacity, short-circuit rating, and operational-costs, including investment charges. Some of Ihese factors are considered in this chapter.Cable Diameter

Most lists of cables show the outside diameter fromwhich a suitable duct size or other support provision maybe determined, sufficient to accommodate any distortionthat may occur in the cable because of thermal expansion,If the cable diameter is not known, it may be estimatedfrom the dimension of its elements as follows:

D, d + 2T for single conductor cable (Eq.9.1)D, 2(d + 2T) + 2t for round duplex cable(Eq. 9-2)D, 2.155 (d + 2T) + 2t for 3-conductor cable(Eq.9-3)Dr =2.414 (d + 2T) + 2t for four-conductor cable(Eq.9-4)

WhereD, = Inside diameter of sheathT Insulation thickness over the conductord Conductor diameter

Belt thickness (under outer sheath)

The diameters of cables of over four conductors contained within a single circular oUler sheath are obtained,either as round conductors or as twisted pairs, as follows:D, = f (d + 2T) + 21 (Eq.95)

where f the factor in Table 9-1, and other values areas above stated.Example: What is Ihe minimum diameter of [he inside of the outersheath of a 1 2 ~ c Q n d u c t o r 2/0 A WG aluminum cable whenconductors are assembled in parallel and in (wisted pain;, a s ~ u m i n gd = 0.419 In . T O.078io . 1 ....O.080In:rSubsdtuting in Eq. 9-5Fo r single parallel conductors (for 12 conductors. "f " == 4.155,

D, = 4,155 (0.419 + 0,156) + 0,160 = 2,55 in,Fo r twisted pairs (6 pairs, " f ' = 4.60):

D, = 4,6010.419 - 0,(56) + 0,160 2,81Duct, Conduit and Raceway Inslallalions

The terms "duct" and "conduit" may be used interchangeably to refer to non-metallic raceways made of suchmaterials as transite. fiber, concrete or plastic, Tubularmetallic raceways of steel or aluminum are generallydesignated "conduit." The cable is run loosely into theduct or conduit as distinct from having the metallic oulercovering closely fitting, as with a lead sheath, The electromagnetic field surrounding a cable carrying alternatingcurrent does nOI induce stray currents in a non-metallicraceway, but it does cause eddy-current loss in metallicconduit, and also hysteresis loss if the conduit is ofmagnetic material.

The eddy-current and hysteresis losses in conduit arereduced if the conduit contains the two Or three conductorsthat comprise a single circuit because their external fieldstend to canceL The fields, however, will not exactly balance because the conductors are not located at exactlythe same position with reference to the conduit wall,and also because of unbalanced loads, if any, in the conductors of the circuit,

Because the stray field surrounding a single conductoris not offset by an opposing field from an adjacent conductor. it is not customary to place a Single conductor ina metallic conduit by itself because of the resulting high9-1


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insulated aluminum conductorsTABLE 9-1Factor "r 'for Equation 9-5 for Use inDetermining Cable Diameter Where Cable has More than Four Conductors

Number ofConductors

or Pairs

SingleRound

Conductors

Factor I I f"

TwistedPairs

Number ofConductors

or Pairs

Factor " f"SingleRound

ConductorsTwisted

Pairs12345678910

1112131415

.

1.02.2.1552.4142.7003.0003.0003.3103.6104.0004.0004.1554.2404.4144.550

-2.4143.503.854.354.604.755.205.505.856.106.256.406.706.90

21222324252627282930

3132333435

5.3105.6105.6106.0006.0006.0006.1556.2406.2406.4146.5506.5506.7007.0007.000

8.108.258.458.808.959.159.259.359.509.70

9.809.95

10.2010.3010.35

1617181920

4.7005.0005.0005.0005.310

7.207.357.507.607.80

3637618191

7.0007.0009.000

10.55011.000

10.4010.50---

'Pairs cabled in the same direction of lay as the twist of the pairs.

losses. Instead, it is usual practice to place the cables thatcomprise a complete circuit in one conduit.A 3-phase circuit requires at least three conductors. Ifthe three-phase circuit includes a neutral, a fourth conductor is required. Three conductors also are suitablefor the usual 3-wire single-phase lighting circuit. Thethree conductors may be parallel side-by-side or they maybe triplexed as a spiraled assembly.The interior of a duct or conduit must be large enough

to accommodate cable flexing and distortion because ofthermal expansion. NEC and other Standards specifythe maximum number of cables of a given size that canbe installed within a raceway.92

Also, because cable ac/dc resistance ratio increases witcable size, it is sometimes advisable to divide a giveload among several parallel circuits as a means of reducinlosses, providing this practice can be economically justfied. The cable-loss ratio for the condition depictedFig. 9-1


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300.30IIIII 150.15 II oII oI

1.29 100 '" wo t~o /\I:g1J5 '50 !


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ins"lated aluminum conductorsTABLE 9-2 Comparison of Conductor Diameter and Approximate cable Outside Diameter of Typical Single, Class B Concentric-Stranded Aluminum Cables. Voltages are ac Line-to-Line with Grounded Neutral* Except as Stated

(See explanation at bottom of table regarding values in italics)SizeAWGorkcmil

6421

1/0

2/0

3/0

4/0

250350

500750

10001250150017502000

ConductorDiameter(inches)

0.1840.2320.2920.3320.3730.4180.4700.5280.5750.6810.8130.9981.1521.2891.4121.5261.632

Approx. Outside Diameter of Cable (inches) Thermosetting or Thermoplastic InsulationNonshielded Fully Shielded

600V lkV 5kV'H 5kV 15kV 25kV 35kV0.32 0.34 0.62 0.74

0.42 0.610.37 0.39 0.67 0.79

0.47 0.640.43 0.45 0.73 0.88 1.16

0.53 0.71 0.94 1.160.51 0.53 0.77 0.92 1.20 1.68

0.57 0.75 0.98 1.220.55 0.57 0.85 0.96 1.24 1.72

0.61 0.79 1.02 1.26 1.450.60 0.62 0.89 1.00 1.29 1.77

0.66 0.89 1.07 1.30 1.500.65 0.67 0.95 1.06 1.34 1.83

0.74 0.94 1.12 1.35 1.550.71 0.73 1.01 1.11 1.40 1.920.77 1.00 1.18 1.40 1.61

0.79 0.81 1.08 1.20 1.44 1.960.84 1.04 , 1.23 1.46 1.65

0.90 0.92 1.18 1.31 1.56 2.060.94 1.15 1.33 1.58 1.80

1.03 1.05 1.32 1.44 1.75 2.17,1.07 1.28 1.46 1.76 1.97

1.25 1.27 1.50 1.63 1.93 2.381.26 1.44 1.62 1.95 2.14

1.40 1.42 1.73 1.85 2.09 2.561.46 1.65 1.88 2.09 2.30

1.58 1.60 1.91 2.02 2.26 2.731.70 1.72 2.04 2.13 2.38 2.961.82 1.84 2.15 2.22 2.49 3.071.92 1.94 2.29 2.36 2.61 3.13

46kV

1.821.871.922.03

2.24

2.34

2.50

*For voltages through 5 kV the diameters also apply If the neutral IS ungrounded. For cables above 5 kV with ungroundedneutral or cables at 133% insulation level, consult manufacturer's lists.**The 5 kV nonshielded cable, as well as all shielded cables, have strand shielding.

The listed overall diameters of 600 volt cables are from Column may be included without increase of diameter. The values in italics4 of Table 5 of NEe (1981) and are fairly representative of Type for 5 kV and above are representative of cables with XLPE insulationTHW and triple-rated RHW /RHH/USE unjacketed cable with XLPE and include the thickness of pVC jackets on shielded cables. Theseinsulation; the values are increased by 0.02 in. for I kV. The values diameters do not apply to cable with metallic armor. in the other columns that are in regular type correspond closely Though the listed values are generally suitable for preliminary studies,with those listed in ICEA No. P-46-426, Vol. II, 1962, when increased imporant calculations should be made by use of actual diameter ofto allow for jackets. By omitting the jacket , sometimes a lead sheath the selected cable.

9-4


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engineering design as related to cable applicationsTABLE 9-3*

Resistance of Aluminum Cable with Thermosetting and Thermoplastic Insulation for Secondary DistributionVoltages (to 1 kV) at Various Temperatures an d Typical Conditions of Installation

Note: The metallic conduit is assumed to ba steel. If aluminum is used, the efleclive resistance is about the same asfor single conductor in nonmetallic conduit to 410 size, and for larger sizes is in the range %%-2% more than theresistance of the conductor in nonmetallic conduit, hence of lillie significance except in critical cases.

Class B-concentric strandsOhms per 1000 feet

r 60 Hz 8c-75'C I * 60 Hz ac-!lO'Class B 60 Hz ac-60'CMu Itl-Cond.ultiCond.Multi-Cond.One Single Cable One Single OneSingleable Cable

Conductor : or2or3r 2 or 3 Conductoronductor or2or3Single in Air, in Air,n Air, Single SingleBuried,uried, Conductors Conductorsuried, Conductors ! de or in de orinn One de or in in One in Oneat Nonmetallic at Nonmetallicetallic at ' Nonmetall ic Metallic MetallicWGor 90C Conduit0C Conduit Conduit i 75C Conduit Conduit Conduitcmi!

0.848 0.848.808 0.848.765 0.765 0.808.765 0.808 0.533 0.533.507 0.533,483 0.5070.483 0.507.483 0.422 0.422.402 0.422.402.382 0.382 0.382 0.402 0.319 0.335 0.335 0.335.319.303 0.303 0.3190.303 0.266 0.266.253 0.266.240 0.240 0.253.240 0.253 0.211 0.211.201 0.211.191 0.191 0.201.191 0.201/O 0.167 0.167.159 0.167.159.151 0.151 0.151 0.159/0 0.132 0,132.127 0.133.119 0.126.120 0.12610 0.119 0,102 0.105 0.106 0.107.101.0953 0.0963 0.10110 0.0954 0.089 0.0892 0,0908.0865,085.0806 0.0822.0808 0.084750: 0.0741 0.0744.072 0.0766,0708.0672 0.0686 0.Q70600 0.0674 0.0635.0623 0.0638 0.0654.057550 0.0578 0.0593 0.0605 0.0608 0.0556 0.0560.0552 0.05800 0.0504 0.0507 0.0525 0.0530 0.0533 0.0445.045 0.0448.0427 0.047200 0.0403 0.0428 0,0424.0406 0.037 0.0374.0381 0,040.0336 0.0370 0.0357.0340 0.035300 0.0337 0.0318 0.0322 0,0353.0320 0.030700 0.0288 0.0303.0292 0,0296.0317 0.0302 0,0333.0269 0.0302 0.0282 0.028850 0.0273 0.0222 0.0228,0212 0.0253 0.D265000 0.0201 0.0239 0.0218.0207

0.0186.0216 0.0178.0162 0.0228.0177250 0.0176 0.0215 0.0169 :0,0193 0.0148 0.0158.0135500 0.0184 0.D15 0.0203,0141.01430.0115 0.0177 0.0127 0.0137 0.0186750 0.0124 0.0168 0.0121 0.0131

0.0166 0,0111 0.0122.0101 0.0111 0.0173000 0.0158 0.0106 0.0117Calculated from ICEA Resistance Tables fo r Class B stranding and corrected for temperature,For higher voltages or other installation conditions, see Table 94.

95


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insulated aluminum conductorsExample: A I5-kV, 1000 kcmil Triple-xed rubber or thermoplasticinsulated cable, class B concentric stranding, in steel conduit at 75"C.with insulation pf of 0.035, 60 Hz ac, and with short


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c

TABLE 9-4 Factors fo r Estimating 60-Cycle addc Ratios for 1-kV and 1S-kV Insulated Aluminum Cable at 75"C fo r Constructions Nos_ 1.2. and 3 (page 9-6) with Thermosetting and Thermoplastic Insulation* (See Section B for Asbestos Insulation)

S :)nductor.eAWGo f

komi!

64:/1

I/O2/0JlO4/0250350500750

10001250150017502000

dc"Rois-tancoat 7SoC

808.507.319.:153.201.159.126.100.84.860.642.428.321.217.014.112.116.6

I... 1 kV .. 15 kV ~ ~ ~ ~ ~- - ' - = : - ~ ~ . Single C o n d u c t o r ~ l i r i P l e K . d ~ r l l d ~ u " t o l " 3.conductorsinole Conduct or I. TriplOKed.conductors 3 ConductorsIn Duct In Air, In Steel In Air, In Steel In Duct Of In Air, Duc' In Steel In Air, Duct InSteel

InAir or Buried Duct Conduit Duct Conduit InAir Buried or Buried Conduit or Buried Conduitor Buried or Buried

- - - - 'QSoc QS Roc Roc QS Qf R. QS R., QE R,," QS R" R.o QS Roc QE R" QS R", Qf x x x x x x xx x x x x x x x x x xx x x x x x x x x x x x x x x x x 1.004 x 1.006 x 1.003 x 1.004x x x x x x x x x x x x x x x x x 1.005 x L_ x 1.003 x 1.005x x x x x x x x x x x x x x x x x 1._ x 1.011 x 1.004 x 1.007x x x x x x x x x x x x x x x x x 1._ x 1.014 x 1.006 x 1.009x x x x x x x x x x x x x x x x x 1.010 x 1.019 x 1.005 x 1.01?x x x x x x x x x x 100.8 x x x x x x 1.015 x 1.025 x L010 l00.5? 1.017

84.90 x 84.90 l( 85.10 x 85.33 x 85.24 x 85.52 x 84.90 x 84.90 x 85.00 1.018 85.16 1.031 85.09 L012 135.27 U}2160.62 x 60.63 x 60.95 x 61.30 x 61.08 x 6LSO x 60.62 x 60.6 x 60.79 1.026 6104 1.047 60.87 L019 61.14 1.03142.64 x 42.66 )( 43.16 x 43,70 x 43.32 x 43.96 x 42.64 x 42.86 x 42.93 1.043 43.31 1.07 3 43.02 L029 43.44 1.04928.S4 x 28.67 )( 29.41 x 30.22 x 29.65 x JO.61 x 29.64 x 28.67 1.001 29.13 1.070 29.74 1.119 29.27 1.049 29.96 LOBO21.70 x 21.75 )( 22.79 x 23.89 x 23.09 x 24.41 x 21.70 1.001 21.75 1.001 22.41 1.102 23.26 1.167 22.61 1.069 23.58 1.11217.57 x 17.64 x x x x x 17.57 1.002 17.64 1.(){)214.86 x 14.96 )( x x x x 14.8Il 1.003 14.96 1.00312.95 x 13.07 x x x x x 12.95 1.005 13.07 1.00511.55 x 11.69 )( x x x x 11.55 1.006 11.69 1.006

- - - - - - ---------- - - - -All resistances are listed as microhms per ft. To convert to ohms per 1000 ft, point of f three places: thus, for 1000 kcmil. 21.2.u ohms/ft =: 0.0212 ohms per 1000 ft.The listed factors are from ICEA PUb. No. PA6-426 Vol. II, (1962). Faclors lor 5-kV, 8kV, and 25kV cable, are also listed in the ICEA publication. Ambienttemperatures 20C for duc t or directly buried, and 40C for air or conduit.

Factors listed under heading Rac are alternating current resistance value!> in microhms per f t including skin and proximity effects.factors listed under the heading as are the ratios of the sum of all cables losses (in conductor, insulation, shields, and sheaths) to losses in conduc tor alone (includingskin-proximity effects),Factors listed under heading OE are ratios of the sum of all cable and condu it losses (in conductor, insulation, shields, sheaths and conduit) to losses in conductor alone(including skin-proximity effects).If an "x" is rn any column headed Rac the factor is not significantly different from the corresponding dc resistance listed in the table. If an "x" in any column headed QSor QE the value 1.000 may be used.Example: For each cable of a ~ r i p l e ) ( e d assembly of three 750kcmilcables at 15 kV in a nonmagnetic non-metallic duc t, the (from table) is 29.13 microhms per ft., The corresponding acldc ratio i. 29.13/28.3 =1.029 for lhe conductor alone. The as ratio (from tablel is 1.070. The overall aclde ratio is 1.029 X 1.070 =1.10.The R. ff = 28.3 X 1.10'31.1 microhm. per ft."10


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insulated aluminum conductorsnum conduit is so small that ordinarily it can be neglectedin computations of acldc ratio where cables of one circuitare contained within a single conduit and each cable is410 size or smaller. For larger cables, a conservative estimate of overall acldc ratio with aluminum conduit containing a complete circuit is obtained by using a QE valueobtained as follows:

QE" QS. + (0.2 X (QE, (Eq.9-6)whereQE" = QE value for aluminum conduitQS. = QS value from Table 9-4 for nonmetallic ductQE .. = QE value from Table 9-4 for steel conduitExample: For the example appended to Table 9-4 the QS ratioat 75"C for duct is 1,070 and the QE ratio for steel conduit is1.19. The QE for aluminum conduit, applying Eq. 9-6 isQE" = 1.070 + (0.2 X (1.119 - 1.070)) 1.08The overall ac/dc ratio, using the value for conduit fromtable (29.13), is acide = (29.13i28.2) x 1.08 = 1.1I and R",28.3 x 1.11 = 31.4 microhm' per ft (0.0314 ohms per 1000 it).Series Inductive Reactance

The effect of series inductive reactance of a cable in acircuit is depicted by Fig. 9-2 (A and B) in which (A )shows volt-ampere vector relationship when the load powerfactor is almost 100%. and (B) shows it when load powerfactor is 80% (cos e= 0.80).

o

I

Fig. 9-2. Volt-Ampere Vector Relationship in CircuitHaving Cable with Inductive Reactance: (AJ for almost/00% p./.; (SJ for 80% pf.98

whereOE, = Voltage vector at supply endOEL = Voltage vector at load end01 = Current vectorix = V o l t a g e ~ d r o p vector due to inductive reactance

"x"ir = Voltage-drop vector due to resistance Hr"G Angle of lag of Ctirrent vector in relation to OE

As voltage drop ir is in phase with 01, ir will be paralleto 01; and as reactance drop ix is in quadrature with 01ix will be perpendicular to 01.The diagrams are drawn to accentuate the relationshipsIn practice the Ix vector is usually smaller than the ivector and the angle between OE, and OEL is smaller. Breference to (A l it is noted that vector OE, is almost thsame length as vector (EL + ir), bearing out the weUknown fact that inductive reactance does not significantlaffect voltage drop in circuits of 100% load power factorHowever, from (B) it is evident that Ix considerably affectvoltage drop (the difference between E, and ELl whethe power factor is significantly different from 10percent.Series-Inductive-Reactance Calculation

The voltage-drop effect caused by series inductive reactance requires consideration for insulated cables in whichthe go-and-return conductors are close together as whentriplexed or in duct or tray, and particularly if the loadpower factor is low. When cables are far apart, the inductive reactance is about the same as that of bare conductorsas described in Chapter 3.The similar shunt capacitive reactance in short lines omoderate Voltage usually may be neglected. Generally, ibecomes significant only for insulated long lines, say 10miles in length or over.In the usual circuit supplying non-inductive load or onoof lagging power factor, series inductive reactance in thsupply conductors causes voltage drop at the load end,if the load has leading power factor, such as with certainelectric furnaces, the series inductive reactance may nabe large enough to compensate for the capacitive reae'm1ceand the voltage in the load end would be gt: at" .nanat the sending end.Since the inductive reactance decreases with reduction ospacing between a conductor and the return conductor othe circuit which may be a ground, the minimum circuit inductance occurs when the inSUlation of both conductorstouch. The distance between the centers of the conductorsthen is twice the thickness of insulation and covering plusthe diameter of the metal conductor.The method of computing inductive reactance may beaccording to the X. Xd concept used in Chapter 3, but fosmall spacings it is convenient to apply Eq. 9-7, thus, fo


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2- or 3-conductors in non-magnetic duct or conduit:s

X = 2"f (0.0153 + 0.1404log,o-) X 10-3 .r (Eq.9-7)where

X Inductive reactance to neutral, of one conductor,ohms per lOOO ft.s = Spacing between centers of conductors, in.r = Radius of metal portion of the conductor, in., including strand shielding, if anyf = Frequency, Hz (It is convenient to use 377 for

2" X 60)The distance s (assumed average effective) for variousconductor arrangements is per following diagrams:

0 \ EQUILATERAL TRIANGLE ~ = AO O ~G'f RIGHT ANGLE TRIANGLE ! = 1.122A4-A-+1 AC) (9

UC)UI.... A-+I ... A-I>I SYMMETRICAL FLAT ! = 1.26A! = {AxSxC)1/3

A usefUl nomogram, Fig. 9-3,* aids use of Eq. 9-7. Inthe table of Corrections for Multi-Conductor Cables. theterm "sector" refers to a single conductor in which thestrands are arranged approximately as a 1200 section of acircle (see Fig. 8-2b). The designation "single conductor"refers to one of several single conductors of a single circuitthat lie loosely together in one conduit, not bound together Or are closely adjacent on a support. The increasefor "random lay" in this instance is the result of unequalspacing of the conductor in the conduit, perhaps caused bythermal flexing.Example 1: From Fig. 93 find reactance of each of three singleconductors in magnetic conduit. each 7SO kcmH, concentricstranded, The outside diameter of each cabJe is 2,00 in. which isabout average for a 15 kV c a b l e ~ thus the arrangement is equilateral with outer jackets touching. Draw line from 750 kcmil to2.00 in. spacing distance; it crosses the reactance scale at 0.038ohms per 1000 ft. The random*lay plus m a g n e t i c ~ c o n d u i t adjustment is 1..5. hence the reactance per conductor is 1..5 X 0,038 =0.OS7 ohms per 1000 ft. This value, multiplied by rms amperes inthe conductor. equals the ix drop to neutral in volts for that c o n ~ductor, per 1000 ft. length,

engineering design as related to cable applicationsExample 2: Using the nomogram find reactance of each conductor of a 3-conductor 6 0 0 ~ v o ! t cable, each 250 kcmil. concentricstranded, 0.890 in. diameter in nonmagnetic conduit. The c o n d u c ~tors are bound with tape as an equilateral triangie (triplexed). Theoutside diameter of each conductor is 0.89 in., which equals thespacing. From the nomogram the reactance is found to be 0.0315

ohms per 1000 ft. and from notation on the nomogram, nO r a n ~d o m ~ l a y correction is necessary. I f this cable is in a magneticconduit, the reactance will be 0.0315 X 1.149. or 0.0362 ohms pe T1000 Ft. The presence or shield current in shielded cables alters theinductive reactance predicted by Eq. 9 ~ 7 . Thus, care must be takenin the use or tables or nomograms neglecting this factor when dealingwith cables having low resistance shields.Supplementary Table for Series Inductive Reactance

For moderate insulation thicknesses, such as prevail insecondary distribution circuits. Table 9-5 provides closernumerical values for Eq. 9-7 than obtainable from thenomogram, but it is useful only for the particular conditionstated in the table; namely, that the separate single cooductol'S of one cireuit are loose in the conduit, though inapproximately equilateral arrangement. For any other ofIbe usual conditions applying to single- or multi-conductorcables. it is generally simpler to use the nomogram together with the adjustment factors noted upon it.

Example. Three 250 kcmil conductorS, each 0.890 in. diameter(insulation 155 mils thick) in non-magnetic conduit, a p p r o x i ~mateiy touching in equilateral arrangement. From Fig. 9 ~ 3 , thereactance per conductor to neutral is 0.0315 ohms per 1000 ft,which adjusted for random lay is 0.031.5 X 1.2 = 0.0378 ohms per1000 ft. Table 9-5 shows 0.0377. If these conductors are in amagnetic conduit, the adjustment factor is 1.5 t and the reactanceis increased to 0.0473 ohms per 1000 ft. Table 95 shows 0.0471.Reactance of Conductorson Rigid Cable Supports

If a multi-conductor cable is placed alongside anothermulti-conductor cable on a flat tray or other rigld Hat support, the inductive reactance of a conductor in that cableis not significantly increased by there being another similaradjacent cable, because the force fields around the conductors in each cable tend to neutralize, so there is littlemutual-inductance effect unless loads are unbalanced.However. if single conductors are alongside of each other.each will have an average reactance to neutral which canbe obtained from Fig. 9-3.Example. Assume three 250 k\.'mil, 6 0 0 ~ v o l t insulated s t e e l ~armored conductors arranged symmetrically fiat on 4 ~ i n . centers.

The effective spacing from diagram on page 9-9 is 1.26 X 4.0 ==5.0 in. From Fig. 9-3, the reactance is 0.072 ohms per 1000 ft,which because of the m a g n e t i c ~ a r m o r effect is increased by theapplicable factor 50% -20% (as there is nO random lay) or30% to 1.30 X 0.072 = 0.094 ohms per 1000 ft.Shunt Capacitive Reactance

Although the capacitance of an insulated conductor be-tween its outer grounded surface and its inner surface at* Source General Electric Company Data Book.

9-9


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insulated aluminum conductors

SIZECONDUCTOROIA, IN AWG OR KCMIL

INCHES SOliDc-c

SPACING IN INCHES 2.01.8I.S1.4

8

.$

.4

.314.2

.18 6.16.14.11.10

.OB

.06

.05.04 _18

20.03

2124.01

STRANDED20001m150012501000

;,l50SOD "-Sllil .......400 ...350 ........300 .........250 " ...DOOr- ___ ... ,-- ....oo --':-=r.DO0I246 CQRa(;TIQNS FOrtMULTICONDIJCTOR CAStES8

N n " ' ' ' Q g n ~ < : M a 9 M I ; ~Cond,. Bil'l(hu Bind.r10 s;" ROIJl!d So,,,,, Rel/ndkcmi l

12 t


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TABLE 9-5Inductive Reactance to Neutral

2,3, or 4 Single Conductor in Same Conduit Ohms Per 1000 Feet-GO Hz_ NONMAGNETIC CONDUIT (ALUMINUM) MAGNETIC CONDUIT (STEEL)

Conductor Covering Thickness (Insulation + Cover) Conductor Covering Thickness (Insulation + Cover)WIRESIZEAWGOR

kemil6421

1/02/03/04/0250300350400500600700750

MILSGO 80 95 110 125 140 155 170 190

_0404 - .0430 .0455.0386 .0402 .0424.0359 .0379 .0398

.0367 .0384 .0400 .0415 .0430 .0443

.0357 .0373 .0387 .0402 .0416 .0428

.0348 .0363 .0376 .0389 .0402 .0414

.0339 .0353 .0366 .0378 .0390 .0401

.0332 .0344 .0356 .0367 .0378 .0388.0338 .0349 .0360 .0370 .0380 .0390 .0399.0333 .0342 .0353 .0 363 .0372 .0381 .0390.0328 .0337 .0347 .0356 .0364 .0373 .0382.0324 .0333 .0342 .0351 .0359 .0367 .0375.0318 .0326 .0334 .0343 .0350 .0358 .0365.0321 .0329 .0336 .0343 .0350 .0357

.0317 .0324 .0331 .0338 .0345 .0351

.0315 .0322 .0329 .0335 .0342 .0349

WIRESIZEAW GOR MILS

kcmil 60 80 95 110 125 140 155 1706 .0505 .0537 .05684 .0475 .0503 .05302 .0449 .0473 .04971 .0458 .0480 .0500 .0519 .0538 .0554

1/0 .0446 .0466 .0484 .0502 .0520 .05352/0 .0435 .0453 .0470 .0487 .0503 .05173/ 0 .0424 .0442 .0459 .0473 .0488 .05014/0 .0415 .0431 .0445 .0459 .0473 .0486250 .0423 .0436 .0450 .0453 .0475 .0487300 .0416 .0428 .0441 .0453 .0464 .0475350 .0410 .0421 .0433 .0445 .0456 .0467400 .0405 .0416 .0427 .0439 .0449 .0459500 .0397 .0407 .0418 .0428 .0438 .0447600 .0401 .0411 .0420 .0429 .0438700 .0397 .0405 .0414 .0422 .0431750 .0394 .0403 .0411 .0419 .0428-

190

.0499

.0482

.0477

.0469

.0457.0447

.0439'

.0436

The above tabular values include 20% adjustment for random lay of single conductors in a nonmagnetic conduit and a 50% adjustment for random-lay and magnetic effect in sleelconduit. If the conductors are part of a multi-conductor cable with fixed spacing. multiply the tabular values in the left-hand section by 0.833. For the right-hand section in such a casemulliply the adjusted left-hand section values by the magnetic-binder adjustment factors shown in Fig. 9-3. Thus, for a triplexed 250 kcmil cable with minimum 155 mils insulation' thickness of each conductor, the reactance when in non-magnetic conduitis 0.0380 x 0.0833 = 0.0316 ohms per 1000 ft., and when in magnetic circuit is 0.0316 x 1.149 = 0.0363 ohms per 1000 ft.

-(),-


12/30

insulated aluminum conductorscircuit potential is a factor that influences voliage drop andregulation in long runs of heavily insulated high-voltagecable, it is not often of significance for usual lengths ofinsulated conductor at moderate voltages, hence for usualcalculations at distribution voltages the capacitive reactance may be ignored.

As noted in Appendix 8-A, the shunt capacitivereactance is obtained from the 60-Hz capacitanceas follows:

X'=- (Eq.9-8)2" I C".where X' shunt capacitive reactance for stated lengthof insulated conductor in ohms (it will be half as muchfor twice the length)C" = Capacitance on 60-Hz basis of the insulationin farads. (I f C" is in microfarads, X' will be in megohms.)I = Frequency, HzThe shunt capacitance C" of a round insulated conductor with outer surface of the insulation (or shield) atground potential is a function of dielectric constant andof insulation thickness, On 60-Hz basis, as follows:

Coo 0.00736 X f , X___ _ (Eq.9-9)log,o (D/d)

where E f Dielectric constant of insulating materialD = Diameter over insulation or underinsulation grounded shield, if anyd == Diameter under the insulationC" Capacitance in microfarads per 1000 ft, on60-Hz basis

Example, No. 410 AW G aluminum single conductor, 19-str'ands;conductor diam, 0,528 in: outside diam. 0.684 in.; Eo, "" 6.5.From Eq, 9-9eft 0,00736 x 6.5 X log" (0,684/0,528)= 0.426 microfarads per 1000 It.Because capacitive reactance, as described, is a distributed shunt reactance, and the corresponding inductivereactance is a series reactance, they cannot directly be

veotorially added (o r subtracted), Approximate methodsof combining them for voltage-drop calculations are employedbased 'oii-lumpli1g the total capacitance a t one ormore points of the line. Description of such methods is

'" The value Er 6.5 is typical of synthetic rubber RHW insulation,For i g h ~ m o l e c u l a r ~ w e i g h t polyethylene a value 2.3 is used for estimatesand similarly 2.3 for cross-linked polyethylene. A range of values forvarious insulations is in Tables 8-1, and

912

beyond the scope of this book. The value. however, winot exceed that represented by the combined vector reactance in ohms, computed as follows:2" ILVector X + X' = - - - - - , . - (Eq.9-1O[(2 IT f ) ' L C]where

L = Series inductance of the conductor to neutral, henrys

C = Shunt capacitance of the conductor to neutrafaradsf= HzThe inductance in henrys is obtained from inductive reactance, Eq. 9-7, or nomogram Fig; 9-3 and dividing b377. The capacitance is obtained directly from thnomogram, Fig. 9-4, after multiplying by dielectric constant, noting however, that tlle microfarads so obtainemust be converted to farads before use in Eq. 9-10.Whether or not the capacitive reactance is of sucamount that it should be taken into account for calculatioof voltage drop and regulation is readily detemlined bEq. 9- ro, which is an approximation of its maximumeffect In the large majority of circuits employing alumnum insulated conductors it will be found that no furtheanalysis beyond that indicated by Eq. 9-10 will affect thresults significantly, and in most cases the capacitive reactance can be ignored.

Voltage-DropThe size of a conductor for a given installation is governed by the permissible voltage drop or the permissiblampacity. In long runs, voltage-drop often is the decidinfactor, and for short runs and large currents. ampacitwill govern.The NEC (1981) voltage-drop limitation provides thathe size of a conductor in either a feeder or branch circumust be such that the voltage drop will not exceed 3%from source to the last outlet in the feeder or branch circuit, and that the combined voltage drop of feeder anbranch in series will not exceed 5 % from source to thJast outlet of the longest combination of feeder and branchRules also are given in NEC for estimating loads wher

they are unknown at time of installation,For most voltage-drop calculations only resistance, inductive reactance, and load power factor have to be considered (see Fig. 9-2). The relation is as follows for stated length of run (from source to load only):Volts drop IZ = J (R cos 0 + X sin 0)where (Eq.91II = Current per conductor, rms ampZ = Impedance to neutral, ohms


13/30

R == Resistance, at stated temperature, ohmsX = Series inductive reactance, ohmsQ = Angle of lag of current vector in relation to emfvector for load endThe load power factor, expressed as a decimal fraction,equals cos 9, from which sin e can be read from table,or computed from sin 9 = {I-cos:! g)!Ii .Example, A 3-phase 480 Y/277 volt 60-Hz feeder circuit 250kcmil single conductors with grounded neutral is in aluminumnonmagnetic conduit of a 600ft run, carrying ISO amp per conductor at 80% load lagging power factor. The insulation is 6/64in. thick (94 mils). What is voltage drop. and percent drop at

7S


14/30

---------- -----


108654

1 ]118Q.5II.S.;on 114wz!! 113r- D,20-

on:l --:> 0.1?;

QOi0,060,05aD.003D.Q2

0,01

Fig. 9-4. Nomogram for 60-Hz capacitance across conductor insulation for ]000 It length after immersion inwater lor one hour at 25'C.The nomogram. above. is a ready means of finding the

6 O - H ~ capacitance C" when dielectric constant is known.The insulation thickness used when applying the nomogram is the thickness from conductor surface to the insulation shield, if any; not the thickness through an outerjacket or covering.

d,o,Co -3,10 1,5

0,0110 1l0)),5 0,94

0,054.0 D,1Iti45 0,015 0,'06

JI9 D.l .E10

w D,) -w5.,0,4 "0 is5 0'> ..30 0,6 040 --- -- u-,8 0'"zto 0Oll uISO 10O

)00

I56810

Note: The capacitance Cal; in microfarads per 1000 ft is obtained bmultiplying tbe scale value of Cn x dielectric constant Er

Example: For 4 / 0 ~ 1 9 cable dia. 0.528 in. 0.078 in. insulatiothickness; dielectric constant Er = 6.5; intersection wi.th middle linshows 66 X 1()-3, which multiplied by 6.5 = 0.429 microfaradper 1000 ft.

9-14


15/30

engineering design as related to cable applicationsTABLE 96

"V " Factors for Calculation of LinetoLine Voltage Drop for 3Phase 60 Hz Circuits or DirectCurrent Circuits.Multiplying factors are included for calculations of voltage drop in singlephase Circuits, and for singlephaseor 3phase circuits to neutral. All voltage drops are valid up to and including conductor temperature of 75C.

"V"-Volts Drop pe r Amp per 100 Ft. of RunNONMAGNETIC STEEL CONDUITLUMINUM CONDUITSIZE ANDAWG : MAGNETIC Or LOAD % LAGGING POWER FACTOR LOAD % LAGGING POWER FACTOR: CONDUIT.'cmil 70 80 90 9S 100 90 95 ! 100e 70 80

12 .380 .485 .509 .533 .616 .381 .485 .510 .533433 .435 !0 .241 .274274 .305 .322 .336 .388 .243 .218 .323 .336!8 .153 .195 .20417'1 .193 .203 .211 .244 .155 .176 .2116 .101 .113 .132 .156 . 114 .125 .132 .135125 .136 .1024 .065 .081 .084084 .099 .066 .075 .086072 .080 .0852 .043 .051 .054 .044 .052 .054047 .053 .062 .048 .053! .035 .039 .041 .049043 .043 .036 .040 .042 .043 .043

I/O .029 .034 .033 .035 .035 .034032 .035 .034 .039 .0302/0 .024 .026 .028 .027 .031 .027 .027027 .025 .028 .028I/0 .017 .022 .023 .023 .022 .025 .022 .023 .024 .023 .022

.017 .018 .018 .017 .020 1.017 .018 .018 .018 .017/0 .016 .015 .015 .014 .016 .016 .016 .016 .016 .014014 .01550.012013 .013 .013 .012 .013 .014 .014 .014 .01401300

.013 .012012 .012 .011 .010 .012 .013 .013 .01050 .012.010 .0089 .012 .012 .012 .011 .0093011 .01000 .011 I .011 .0087 .010 .010 .00860091 .0072 .0082 .011 .007600 .0094 .0094 ! .00900085 .0085 .0081 .0076 .0060 .010 .0097 .0095 .006300 .0068

.0051 .0094 .0084 .007800 .008 .0078 .0072 .0068 .0069 .0090 .0056750 .0077 .0075 .0069 .0049 .0055 .00870064 .0091 .0081 .0075 .0053i I iAPPLICABLE FORMULAS:

'V ' X AMPS. X RUN DISTANCE(ft)% VOLTS DRbp LINE TO LINE VOLTS % VOLTS DROP X LINE TO LINE VOLTS RUN DISTANCE Y'XAMPS.% VOLTS DROP X LINE TO LINE VOLTS"V " FACTOR

RUN DISTANCE X AMPS.

Voltage drop requirements fo r feeders and branch circuits are given in NEe 1987 articles 21S-2(b) and 2J()19(a) respectively.

NOTES:(a) For single-phase line-lo-line voltage drop, multiply the "V " factor from the table by 1.155.(bl For single- or 3*phase line-to-neutral voltage drop, multiply the "V " factor from the table by 0.577 using line to

neutral voltage.

915


16/30

insulated aluminum conductorsthat have the usual types of insulation and that areinstalled as cables in the various kinds of environmentsfound in today's power systems. A more recent publicationaddressing URD/UD Style Cables is ICEA P-53-426.

Chapter 10 of this handbook contains ampacity tables,largely based on these ICEA tables, for many applications of insulated conductors.A few cable types do not have ampacities listed in theabove-mentioned ICEA publications. Ampacity tablesfor these have since been issued as follows:

A. Ampacities for primary underground residential distribution cables of two-conductor concentric-neutraltype, for direct burial and for installation in duct at20C ambient, polyethylene insulated and XLPE insulated. This table also includes a section for suchcables in air at 400C ambient, taken in part fromICEA Pub. S-61-402 2nd ed.The values in this table relating to aluminum are shownin Tables 10-9 A and 10-9B-

E. A table similar to Table 10-9, except it is for 85'Cand Butyl-rubber insulation (ICEA Pub. S-1981, Jan. 1966 revision). This table shows values forburied cable of about 5 % higher ampacity than thevalues for PE insulation in Table 10-9, and when induct about 9% higher ampacity. The values for airinstallation a


17/30

engineering design as related to coble opplicationsFor thermoplastic insulations (polyvinyl chloridesand plain polyethylenes) 150c CRubber, rubber-like, and varnished cambric 200 cCCross-linked polyethylene and EPR 250cC

Figs. 9-5, 9-6, and 9-7 show the time in cycles (60Hz basis) that a short-circuit current of stated value canbe withstood. on basis of 75 0 C operating temperatureprior to the fault, without its temperature exceeding thespecified upper limit. Special analysis is required if thecircuit is protected in part by current-limiting fuses.

The diagrams are based ,m the assumption that no heatis emitted from the conductor metal during the short timethat the fault current flows; that is. the basis is the some ,I>that employed for short-circuit calculations of bare-conductor as described in Chapter 6.

The upper temperature limits established for the variousinsulations not only reflect the ahility of the insulation towithstand the high temperature, but they also take into

account the rise in temperature of the insulation after thefault has been cleared and the heat conknt of the con-ductor tr3nsfers to the insulation. That is, after the faulthas cleared and the conductor cools, the insulation slowJyincreases in temperature to some point that is lower thanthe peak temperature of the conductor itself (150 0 , 200 0 ,Or 250C as the case may be), yet not so high that theinsulation is damaged.Example: Assume the maximum falllt-clcadng time is 30 cycles.including allowance for One reclose of the imerrupling device,Also assome that the fault oCcurs sufficiently far from the conductor being considered so there is no arcing burn-down effector insulation breakdown that causes current to How through shieldor sheath, What allowance for fauH current can be made for :1single 4/0 cable insulated for 150C, 200C, and 2 5 0 ~ C maximum -.:.onductor temperature, if maximum operating temperatu:"ebefore fault is 75"C?

By reference to Fig. 9 ~ 5 j the intersection of vertical line above4/0 and diagonal line for 30 cycles is at 10,400 amp for lS0"'C

Ah o for Fig. it is 12 j 500 am p for 200 QCand for Fig it is 14,.900 amp for 2 5 0 ~ C

TABLE 9-7Abstract of ICEA Standards for Maximum Emergency-Load and Short-Circuit-Load Temperatures for Insulations Listed in

Tables 8-2, 8-3 an d 84

InsulatmnNormalloadTemper"1!'re, Emergency-LoadTemperature'".,

Short..(ircuitTemperatureof CableConductor: (less. than 30 '5&..) 0c

Polwlny!chlorideiMrmoplasticpolyethyleneRubber-insulated53.7 to 53.17On Table 8-2

607575

607075808590

859595 (0-5kV)90 (SOOl35kV)8585 (over SkV)95 (0-5kV)90 (5001.skVI95 (over 15kVl105 (05kV)100 (5001-15kV)130

I 150I 200250hermosettingcross-linkedpolyethylene

and EPR

"'For short circuit capability of c cable shields. see lCEA P-45-482,

9-17


18/30


10080

6050

40

30

20

(/ )wa:w "::; 10"ogJ 85 6If - 5I!z 4wa:a:13 3'=::::Joa:(3 2f a:

~(/ )

.8

.6

.5.4.3

.2

SHORT CIRCUIT CURRENTS FOR INSULATED CABLES

/ / / "V/ V / / / V / V'

/ / V / // / / V V "V/ ' / V / V V / / / // V V V / V V V/ / / / V V/ /~ / / / /V v ~ / / ~ Vv ~ _, / / /V "VV //V

,v.J;. ",V",


19/30

engineering design as related to cable applicationsSHORT CIRCUIT CURRENTS FOR INSULATED CABLES

10080

60504030

20(J)i l la::UJc.::;

~ 10o~ 85 6J:.... 5I!z 4a::a 3t:::::Joa::13 2....~(J)

.8

.6

.5

.3

.2

v y VI V V / V , I/ V / 1/

/ ' r / V / / /V / V Y V'i / V / L V V / / V , I/ ' // / / / VV / / , I/ . / / V / Y VV V/ / /VvV /Vi/';/ //, / V//~ / V / / VV / IT ~ / /// /,I... / '/ t."..J:. v""''> /V / /V / !v' ",0;> ~


20/30

insulated aluminum conductorsSHORT CIRCUIT CURRENTS FOR INSULATED CABLES

.8 // I

.6 V /.5 /. 4 f o f - - - - , ~ - - + _ - - + _ -

f!]2 t =0.0125 log [T I +228JLA [T, +228WHERE

I = SHORT CIRCUIT CURRENT,AMPERESA = CONDUCTOR AREA, CIRCULAR MILSt = TIME OF SHORT CIRCUIT, SECONDS TI= MAXIMUM OPERATING TEMPERATURE,75CT2= MAXIMUM SHORT CIRCUIT TEMPERATURE,250C. 3 ~ - - + - - - + - - - - r - - - - - T - ~ - r - - r - I - ' - - r - I r - . - ~ r - - r ~ - r r r ~

i i i2 ~ ____ ~ ___L_____ L ___ ~ _ ~ - L _ _ ~ ~ ~ _ _ ~ L - ~ L - ~ - L - L U - ~10 I I/O 210 310 4/0 250 350 500 750 1000KCMIL

CONDUCTOR SIZE Fig. 9-7. Short circuit currents for insulated cables (250C maximum).

9-20


21/30

APPENDIX 9-AExplanation of ICEAIEEE Tables of Ampacityof Insulated Aluminum Cables For Various

Conditions of InstallationBased on 1978 Edition, ICEA. Pub. No. P ~ 4 6 4 2 6 ; IEEE Pub, No. S-t35'"

A working knowledge of these tables is almost essentialfor economic studies of alternative proposals of cable selection because they embody comprehensive ampacitytemperature ratings for most of the types of cables andmethods of installation currently used. The tables foraluminum cables comprise 317 pages, the result of years ofresearch by leading authorities (see footnote on page913). Although most of the space in the book is devotedto cables above the 600-volt NEC range, many of the l-kVratings provide comparative values that are useful, evenwhere NEC requirements are mandatory.Space does' not permit inclusion of the tables them'selves. and the originating bodies control their distribution. However, an abstract of the tables is included

along with an explanation of their use. See also theampacity tables in Chapter 10.For aluminum conductors, the ampacity tables aregrouped according to kind of insulation, method of installation, kV ratings, and conductor operating and ambienttemperature. Sets of constants are provided that enableadjustment of the ampaciry rating for conditions differingfrom those for which the table is compiled. Not everyclassification is inciuded in every group, because somecombinations are not practicable. The following are principal groups for thermosetting or thermoplastic insula

tions.Cable types: Single-conductor cable; triplexed cable,comprising three insulated conductors in equilateral arrangement held in position by tape or by spiraling arounda neutral; three-conductor cable, comprising three insulated conductors in equilateral arrangement, all surrounded"The description of the l C E A ~ I E E E tables herein, and elsewherein this publication, that contain abstracts from the tables arereproduced by permission of the C:OpyrigtH owner, Insulated CableEngineers Associalion (formerly IPCEA). These tables. originallypUblished in 1962. were reissued unchanged in 1978,

by a circular sheath which gives tbe assembly the appearance of a round cable. See also Note 1. Illustrations ofmany cable types are in Cbapter 10.The inclusion of a neutral conductor in triplexed orthree-conductor cable does not affect the ampacity rating.Also a two-conductor cable has the ratings of a triplexedcable if the conductor assembly has an overall sheath. Allampacity ratings are those of One conductor of a triplexed

or three-conductor assembly.Installation Methods (See Figs. 9A-1 and 9A-2 forspacing, etc.)Single conductor cable: in air; three cables in a 3-or4-duct bank; six cables in a 6-duct bank; nine cables in a9-duct bank; three cables ciosely adjacent directly buried;six cables in two-circuits directly buried. This cable is notexpected to be installed singly in a steel conduit.Triplexed cable: in air; in conduit exposed to air; andin duct-bank arrangements as described for single-conductor cable with the addition that One cable can be installed in a single duct; and one or two cables may bedirectly buried.Three-conductor cable in same arrangements as listedabove for triplexed cable.Voltage: 1,8, 15.25 kVOperating temperature: 60, 65, 70, 75, 80, 85, and

90'C where applicable.Ambient temperature: 20'C in duct or for direct burial;40'C in air or exposed conduit.

Notes:L ICEA-NEMA has since published additional ampactty tablesfor N'o*conductor concentric-neutral aluminum cable for URD

Ampacities for cables in open-top cable uays are found inICEA Pub. P54-440, Aug, 1979.

9-21


22/30

covered and insulated wire and cable

19"X 19"DUCT BANK(bJ

(c )NOTE -H INDICATES THE HOTTEST CABLE 33.4" X 33.4" DUCT BANK

(d )Fig. 9A-1. Arrangements of 1, 3, 6, and 9 cables in underground duct, as basis forampacily calculations.

~ i & W ~

0i611

24'0BURIED 3 CONDUCTOR BURIED SINGLE CONDUCTOR CABLESCABLES OR PIPES 101 Ibl

NOTE-H INDICATES THE HOTTEST CABLE

Fig. 9A-2. Arrangements of buried cables, as basis for ampacity calculations.

BURIED TRIPLEX CABLESlei

(as well as for air installation), This type of cable has spiral three-wire 3 ~ p h a s e circuit. bare e ~ t e r i o r r o u n d ~ w i r e copper neutral, suitable for direct earth burial (see Table 10-9), 3, The ICEA-IEEE set of tables also includes ampacity rating2. The term "one-ciruit" refers to two or three cooducfors of for low- and high-pressure gas-fiHed and o i l ~ f m e d cables of tha single circuit, with or wIthout an extra- conductor for neutral. kinds in limited commercial or e x ~ r i m e n t a l use with aluminuthat comprise a two.-wire or three-wire single-phase circuit. or 3. conductors.

922


23/30

Description of Typical Section ofIeEA-IEEE Ampacity Table

For explanation of these tables, a typical section is reproduced as Table 9A-l from top of page 167 of Vol. I I onaluminum conductors. The three cables in duct bank are arranged and spaced according to Fig. 9A-l(b), in whichthe cables in each duct are Single, and the duct bank is below ground as shown. The lining of the duct is nonmetallic.The designations RHo.-60, RHo.-90 and RHo-120signify Earth Thermal Resistivity in terms of 60, 90', and120C--centimeters per watt (CO-em/watt). Thus, earth

of RHo.-60 thermal resistivity transmits a given amount ofheat at a lower temperature than will RHo-l20 earth,hence a cable in a duct buried in aggregate or earth ofRHO 60 resistivity will have a higher ampacity tban if theduct were buried in earth of higher thermal resistivity.Where the earth thermal resistivity is unknown, ICEAsuggestS using the RHo.-90 values.

The designations 30LF, 50LF, 75LF, and JOOLF signify Load Factor; that is, the ratio of average load to peakload according to customary practice of electric powerutilities when determining average load factor. The increased ampacity for low load factors is the result of theheat-sink property of the earth surrounding the conductors or the duct block. Thus, as load increases to a peak,the temperature of the conductor does not rise as rapidlyas if it were exposed to air. Load factor variations ofampacity are not shown in the tables that apply to cablessuspended in ai r or are in conduit exposed to air (see Table9 A-2). In selecting the LF value, consideration must begiven to futnre load factors during the expected life of thecable; thus, initial conditions may indicate that the ampacity corresponding to 30LF is satisfactory, but perhapsthe cable should be selected on the basis of 75LF orlOOLF because during the period of load growth, suitableload dispatching may tend to flatten any peaks that existearly in the life of the cable.

Associated with load factor is a Loss Factor. Thus, atypical load curve of 50LF will have peaks and Valleys.I f the PR loss for one day is obtained from such a curve,it probably will be about 33 percent of the 12R loss if theload were constant Empirical loss factors correspondingto the various assumed LF's are 0.15, 0.33, 0.625, and1.00 loss factors for 30LF, 50LF, 75LF, and lOOLFvalues, respectively.

The three right-hand columns of Table 9A-1 are headed DELTA TD for 0.035 power factor (of insulation),applying to RHo.-60, .90, and -120 conditions. TheDelta TD values signify dielectric-loss temperature rise.For cables of equal dielectric constant, these values varyin direct proportion to insulation power factor. Any valueof ampacity I appearing in the table may be corrected fora change of operating or ambient temperature or of insulation power factor by use of the following expression inwhich the prime mark indicates the desired new values:

engineering design as related to cable applicationsIT', T'. - Delta TO' 228.1 +T,

l ' = I V------ X - ~ amperesT, T. - Delta TD 228.1 T',(Eq. 9A-l)Where I = Ampacity as listed; and l ' = AmpaCity undernew condition;

T, = Conductor temperature, Co as listed; andT' c is same, under new conditions;

T. =Ambient temperature, CO as listed; and T'. issame, under new conditions;Delta TD factor is as listed; and Delta TD' is sameunder new conditions (Delta TD varies oulywhen there is a change of dielectric constant

or power factor of the insulation).When ambient temperature only is changed, Eq. 9A-lbecomes

DeltaID/' = I IT, - 7' , amperes (Eq. 9A-2), T, - T. - Delta TD

It will be noted that Eqs. 9A-I and 9A-2 contain noprovision for adjustment for variation of RHO. values orfor load factors. These adjustments are obtained by use ofthe curves of Figs. 9A-3 and 9A-4, as described on thecurve sheets.Examples:L The 4/ 0 ampacity under RHO-90 and 75LF conditions for70e C conductor temperature and 20"C ambient, from Table9A-l, is 252 amperes. What is it 30"C ambient? Here applyEq.9A-2;1'=252 X i -.;..-.;..-.:.....- = 225 amperes

2. The cable of example 1 (before adjustment for change ofambient) has an insulation power factor of 0.035 and insulationdielectric constant of 4.7, accQrding to the data accompanying theICEA tables for rubber and plastic insulation. What is theampacity at 5 5 ~ C for conductor, with lS"C ambient, i f dielectricconstant is 5.5 and power factor is 0.020?0.02 X 5.5The adjusted Delt. TD' = 0.79 X = 0.530.035 X 4.7Applying Eq. 9A-2 and substituting:1---------------/' = 252 X I 55 - 15 - 0.53 X 228.1 + 70 232 amperes'V 70 - 20 0.79 228.1 + 55

Interpolation Cham jor Variation of RHOand Load Factor

I f the values of RHO. and LF differ from those used in923


24/30

insulated aluminum conductorsTABLE 9A-'Ampacities of Single Conductor Concentric Stranded Rubber Insulated Cable in Ducts, DELTA TO FOR

eOND. RHOSOSIZE 30LF I50LF 175LF 1100LFRHO90

30lF I50LF 175LF l'OOLF 30lF RHO12O150LF ! 75LF Ii00LF .0350 PF AND R60 I 90 I 1ALUMINUM CONDUCTOR CONCENTRIC STRANOI I3 CASLES IN DUCT SANK 15 KV - 70 C CONDUCTOR 20 CAMSIENT EARTH

2 144 140 134 127 143 137 129 121 141 134 125 116 0.55 0.61 0165 160 153 145 153 157 148 138 162 154 143 132 0.57 0.64 0I/O 190 184 175 166 188 180 169 158 186 176 164 151 0.60 0.68 02/0 218 210 200 189 215 206 193 180 213 201 186 171 0.63 0.71 03/0 250 241 229 216 247 236 220 205 244 230 213 195 0.66 0.75 04/0 287 277 263 247 284 271 252 234 280 I 264 243 222 0.70 I 0.79 0

250 317 306 289 272 313 298 277 256 309 291 267 244 0.72 0.83 0350 389 374 353 330 384 364 337 : 311 379 355 324 294 0.79 0.90 1500 463 463 434 404 476 449 414 380 469 437 397 359 0.86 0.99 1750 617 589 549 509 607 570 522 476 597 553 499 448 0.95 1.10 11000 734 697 648 598 720 674 614 557 708 653 585 523 1.02 1.20 11250 536 793 734 675 820 765 694 : 628 805 739 860 588 1.04 1.22 11500 927 877 810 743 908 845 764 1 689 891 816 : 725 645 1.10 1.29 11750 1010 954 878 804 989 918 827 744 969 885 1 784 , 695 1.15 1.36 12000 1086 1023 940 858 1062 963 884 793 1040 L ~ J 837 1.... 740 1.19 1.41 1See text for explanation of Delta TO values.the tables, the charts of Fig. 9A-3 may be used for interpolation Or extrapolation for values of RHO and LF forcables installed in duct banks, and those of Fig, 9A--4 maybe used for directly buried cables. For both sets of chartsthe upper family of curves shows variation of ampacity forLF-lOO in terms of I " the ampacity for RHO-60 and LF50. Each curve is designated for a particular ratio 1,//"where I, is the ampacity at RHO-120 and LF-IOO. Thelower family of curves shows the relationship betweenRHO and LF which will give substantially the sameampacity as the indicated value of RHO at LF-IOO.Example:3. Assume that it is desired to :find the ampacity of tbe 4/0 cableof Table 9A-l at RHO-J40 and LF-60. The base values and ratioare as follows:

11 = ampacity at RH0..60 and LF-50. from table, ::::::::; 277 amperes1'1 = ampacity at RHO-120 and L F ~ l 0 0 % . from table = 222amperesRatio l,/!, 222/277 0,80

Enter lower section of Fig, 9A3 at RHO140 and LF-60, Theintersection lies on curve for RHO-50 at lOOLF. FoUowing thevalue vertically to the upper family of curves at intersection of

-HO-50 and lr:.!ll = 0.80, the corresponding value of F (at leIS 0.91. The desired ampacity for RHO-J40 and LF-60 is0.91 x 277 = 252 amperes

Tables tor Installation in Air or inConduit Exposed 10 AirI f there is no heat-sink effect, as when cables are in dubank or directly buried, the ampacity table is in simplform than the one used for Table 9A-1. The sample showas Table 9A-2 is for Triplexed rubber-insulated cable air. Ampacities for all listed voltages are in a single sectioof the table for given temperature.

Trip/exeQ vs Three-Conductor Cable: A triplexed cablFig. 9A-2(c) comprises three single conductors arrangequiJaterally as shown; the assembly may be taped to messenger or grounded neutral as a preassembled aericable or in duct, or directly buried. A thrce-conductcable, Fig, 9A-2(a) is similar, except that the assembof three conductors is surrounded by a jacket or sheathform a cylindrical exterior. Because the radiating insulatinsurface exposed to ambient temperature is greater in triplex cable, the ampacity rating of the triplex cable is th9-24


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TABLE 9A:2Triplexed Concentric Stranded Rubber Insulated CableIn Air-Isolated Circuit 40 C Ambient AirCONDo VOLTAGE kV VOLTAGE kVSIZE ,1 8 15 25 8 15 25AMPACITV DELTA TO

ALUMINUM CONDUCTOR CONCENTRIC STRAND CONDUCTOR TEMPERATURE 75C INSULATION P F .0350

44 0.169 654 78 85 0.170.19 0.4412 115106 129 133 135 0.19 0.45 0.81123

149 153 155 0.20 0.46 0.83/O 143172 175 178 0.21 0.48 0.85/0 165 204 0.21 0.49 0.8798 202/0 192229 :::.13 235 0.22 0.50 0.89/0 224

0.9160 0.23 0.5250 251 254318 0.23 0.54 0.9450 312

I315 I

500 392 392 395 394 0.24 0.56 0.98750 512 502 504 500 0.26 0.59 1.03

589 0.26 0.61 1.050001612 595 I 594 ,The Delta TD factors are used for adjustments when thereis a change of dielectric constant. See text for furtherexplanation.

reater. These relations are shown by theollowing comparison:AmperesAmpaciJy fo r 1 kV 4/Q AWG Triplex 3-CoruJucrorcable at 60f>C Ca&le Cable

20"C ambientIn duct bank 191 173Directly buried 240 22740"C ambientIn air 174 149

In conduit. in air 144 133Ambient Temperature: It is assumed that there is no windnd no solar radiation. An average 40C ambient for airs suitable for initial ampacity estimates, subject to adjustby applying Eq. 9A-2. A similar average for underround duct bank is 20C ambient. The increased amhould be evaluated when the economics of URD for agiven installation are considered.

engineering design as related 10 cable applicationsConstruction oj Cables Used as Basis jar A mpacity Tables:Metallic insulation shielding is a part of rubber andthe""oplastic cables listed as 8-kV and above. Ampacitiesfor lead-sheathed rubber and thermoplastic cables assumemetallic shielding. Nonmetallic jackets, if any, are assumed with rubber, thermoplastic, and asbestus (AVA)insulations. Depth for direct burial and duct banks areas in FIg. 9A-j and 9A-2. Open-circuit sheath operationis assumed for single-conductor cables with metallicsheaths, installed in separated ducts or directly buriedwith separation. Ampacity values for short circuit sheathoperation of single-conductor cables, including the effectof circulating current losses, are available in ICEAPub. P-53426. Short-circuited sheaths or shields, if used,are assumed for each conductor of triplexed cables withrubber and thermoplastic insulations. The insulation thicknesses for cables with rubber and thermoplastic insulationsare according to ICEA S-19-81 (Fourth Edition revised)and S-61-402 (Second Edition revised). The insulationpower factor for rubber and thermoplastic insulations istaken as 0.035 (3Vi %), but adjustment for other valuesmay be made by applying Eq. 9A-1. This assumed powerfactur applies to this insulation after some years of useunder average conditions. A lower power factor may beexpected with new cables, but use of the higher value isrecommended for estimates. An average Dielectric Constant for the rubber and thermoplastic insulation afteryears of use is assumed as 4.5, and this value also appliesto cables with neoprene or plastic jackets.Supplementary Constants

The set of ampacity tables also includes supplementarytables of design constants that can be used for computingampacity for non-tabulated conditions. These are all for75C, and include the following values:

PD Outside diameter, inchesWD =Dielectric loss, watts per conductor foot =W.RI = Thermal resistance of insulation, thermal ohm-

it = RlRSD = Thermal resistance between cable and duct

IVall, or pipe (R. ) , or air for cable in air (R,), thermalohm-feetQS Ratio of sum of the losses in the conductors andsheaths or shields to the losses in the conductorsOE = Ratio of the sum of the losses in the conducturs,sheath or shield, and pipe to losses in the conductors.Rae = ac resistance of the conductor, including skin

and proximity effects only, microhms pe r foot.Note: The Symbol R with line over top designates thermalresistance '

The values in these tables of constants are helpful in moreways than merely for computing ampacity values. They

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I i::

i no

I ~ __ _I - _ ~ : :

n '0 20 30 60 10 ro iO 10 10 HO iO iO 11 In dORHO

Fig. 9A-3. Interpolation chart jo r cables in a duel bank. I, = ampacity jo r RHO-90, 50 LF,' I, = ampaciRHO-nO, 100 LF; desired ampacity = F X Ii'926


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--

engineering design as related to cable applications

50 1\ .\ : :1.55 ~ ~ I

"'

0 ~ ~ I ! .1.I 15 ,1,\ ~ ~ "- - 1 10o. - ~ ~ " .......... - i :' - - I '\ ,". " ........ .......... - - T - r-- 01--._1 - \." ."' " .......... ~ " ...... i'- r-- -, ,'---l- " , "" I" .......... : - ~ - i"--..i - o.I " !' , I" .......... i ........ "--.. r-"--..i5 , ........ r---... j ........r-.'....... r- 0I : t'-... ~ r- - .........r-,..i'- ,.......r-. --r- -05 -........J. -.. - I r---... r ........ .......... --r-- -Q0 "'-..J. -.I ~ .......... -1"' -0-. - O.I I -r- . r

00o.,.95

.8 .90

OJS

80.1S

.00 .1065.60

5,I o.501 1 I

, I01

10 10 20' 30 40 50 60 ' 10 !l0 90 IfJO 110 1ZO 130 140 150 GO 10 180 1'90 200\ 1\ 1\ 1\ \ \1\ [ \ \.. ii\.. '"l"'l"" "" ."' .""'- l"'- ['-.... ~\ \ \ \ \ 1\ , '\. '\.1'\.' '" " "- ",,-'r--: i.........0\ \ !\ \ \ \ "' "" ~ .........\ ." "" ~ r....... ~5! !\ \ ,\,'\. ' \ """, "" i'-" ~ " :--. .......,\ \ \ 1\ "."...'\. ." i'-" " ..........i" ..... ..........--.5 1\\ \ \ '"\1," " "\. '" " .......... ......." ...........0 \' 1\ 1\ '\. " .","", " .......... ....... .......... --.....5 1 \ "' ..... ~ --.::: ..... .......... --.. ........... ........., " \ ~ \ " '" " ........." --.. i'- --..5o! \ ~ \ '"\ '" ......... " ......... -........ ".....: \ :-., "- t'- "l i'- ......... -........ "-..\ "" " I l" I- -........ ........r-...o. " .......... - " i i '" r-. r........ - I" " , -l ''1-- 1-I :030 10 10 30 '0 50 60 10 80 90 100 110 110 130 "0 150 160 110 180 190 100

~"~Q:;

RHO9A-4. interpolation chart for pipe-type and directly buried cables h = ampacity for RH0-60, 50 LF; 1, = amfor RHO-l20, 100 LF; desired ampacity = F XII'

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insulated aluminum conductorsrepresent the results of research, both experimental andanalytical, relating to single as well as closely adjacent conductors, values that are difficUlt to find in usual sources.

Example: A lOO)-kcmil 1350-HJ9 aluminum cable of 61-s:trandshas de resistance at 20"C of 17.34 microhms per ft ; at 7S"C itis 19.44 microhms per ft. The ac resistance, including skin andproximity effects


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Articles 310 and 318 of the 1987 edition of the NECimpose more restrictive regulations than those providedby the rCEA.Note No.8 of Article 310 states: Where the numberof conductors in a raceway or cable exceeds three, theampacity shall be as given in Tables 310-16, -18, -22, -26to -31, but the maximum allowable load current of eachconductor shall be reduced as shown in the followingtable:

engineering design as related to cable applicationsTABLE 9A-6

NEC Derating Factors Where Conductors in Raceway or Cable Exceed Three Percent of Values inNumber of Tables 310-16, -18, -22Conductors -26 to-31

4 thru 6 807mru 24 70251hru 42 6043 and aboveExceptions to the table above are provlded In the above-referencedNEe Articles and should be adhered to when installations fall underNEe jurisdiction.

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reactance calculation

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