,

i~

-< )~ ..~.-A'....:.~.,j'r

;-..".j}

-".~.j~~.~;,

~L.''

, .

.~r

;~

H. E. HOUSEMEMBER ,4.IEE

Synopsis: Current-temperature charac-teristics of stranded-aluminum conductorsteel reinforced, known throughout theindustry as ACSR, have been investigated.The effects of surface conditions, windvelocity, altitude, and solar radiation areillustrated for a widely used size of con-ductor; curves of current-carryingcapacityversus conductor outside diameter aregiven for designconditionsof 75 C (degreescentigrade) conductor temperature and25 C ambient temperature at 2-fps (feetper second) wind velocity, Necessaryformulas and tables to permit computationof current values for any set of operatingconditions are included. Computed valuesof current are in close agreement with testdata which have obtained by AluminumCompany of America (Alcoa) and otherinvestigators.

SINCE first introduced by Alcoa in1909, the use of ACSR for overhead

electric power transmission lines hasgrown steadily until it has almost re-placed copper for such use. In most newconstruction, aluminum instead of copperis being used for overhead distributionconductors. Because of the presence ofthe steel core in ACSR and its consequenteffect on the electrical characteristics ofthe conductor, considerable test work hasbeen carried on throughout the years toevaluate effective resistance. This isneeded to compute the current-carryingcapacity of the conductor. Early in-vestigations were carried out by Work forAlcoa at the Carnegie Institute of Tech-nology, Pittsburgh, Pa.! The well-knownpublications of Luke' and Schurig andFrick 3 were followed periodically byothers,4-8 indicating a strong and con-tinued interest in the subject.

Results of tests for the determination ofthe emissivity of stranded-aluminum con-ductors for surface conditions of both newand weathered conductors were reportedin 1956.9

Tests to determine the effective 60-cycleresistance of a great variety of sizes and.strandings of ACSR have been carried

Paper 58-41, recommended by the AlEE Trans-mission and Distribution Committee and approvedby the AlEE Technical Operation. Department forpresentation at the AlEE Winter General Meeting.New York. N. Y.• February 2-7. 1958. Manu-script submitted October 16. 1957; made availablefor printing November 6. 1957.

H. E. HOUSE and P. D. TUTTLE are with AlcoaReeeerch Laboratori~. Massena, N. Y.

FEBRUARY 1959

out at the Alcoa Research Laboratories atMassena, N. Y. Conductors were strungunder tension on a 120-ft (foot) test span.Values of 60-cycle resistance were meas-ured up to a conductor temperature of200 C or 3,000 amperes/square inch if200 C temperature was not reached.The method which was used in thesetests. is described by Tompkins, Jones,and Tuttle.!O

A co-operative research program be-tween the· Illinois Institute of Tech-nology, Chicago, Ill., and Alcoa ResearchLaboratories has been completed.P-PThe results of this work provide a meansof accurate computations of reactanceand resistance for ACSR of any combi-nation of aluminum and steel stranding.

Because of the tremendous growth ofthe electrical utility industry, there re-main very few long transmission lines inthe eastern part of the United States .Lines that were once long have beenlooped into newly constructed sub-stations. The load on these short trans-mission lines is limited by the heating ofthe conductors rather than by stabilityand voltage regulation, as was the caseas late as the 1930's. For this reason, anaccurate understanding of the thermalcapabilities of the conductors is more im-portant than ever before.

The formula developed by McAdantsU

for convected-heat lossof single horizontaltubes and wires has been found to giveaccurate convected-heat loss for strandedconductors. This formula has been com-bined with the results of emissivity tests'and data on solar radiation, 14. 16 and field-test data on absorption of solar and skyradiation on outdoor test spans ofstranded conductors, in order to evaluatethe current-carrying capacity of ACSR.With accurate values of a-c resistance fora variety of strandings, it is now possibleto compute the current a conductor willcarry for any given set of conditions oftemperature, wind velocity, surface con-dition, and altitude above sea level,both with and without the effect of thesun.

Heat-Balance Equation of ElectricalConductors

Under steady-state conditions of windvelocity, temperature, solar radiation,

and electric current, the following equa-tion is valid

(1)

or

I",,~ge~g,-g,

where qe is convected-heat loss, q, isradiated-heat loss, I is the current inamperes, r is the effective arc resistancein ohms/ft of conductor, and q. is theamount of heat received from solar andsky radiation. Each heat quantity in theequation is expressed in watts/lineal ft ofconductor.

(lA)

CONVECTBD-HEAT Loss

The fundamental relationship for con-vected-heat loss of single horizontal tubesand wires is given by McAdants (see refer-ence 13, p. 220). This is expressed bythe diniensionless equation

io, (DoG)o.n- =0.32+0.43 -k, ~I

where hDo/k, is the Nusselt number, andDrIJ/1l1 is the Reynolds number for anyset of conditions. This formula is recom-mended for Reynolds numbers rangingfrom 0.1 to 1,000which include air veloci-ties up to 2 fps for conductors up to 1.3-inch diameter.

The units used in electrical engineeringare watts, degrees centigrade, and feet.Accordingly, h, the surface coefficient ofheat transfer, is expressed in watts/sq(square) ft/C; Do is conductor outsidediameter in ft; k, is the thermal conduc-tivity of air, (watts) (ft)/(sq ft) (C); Gis the mass velocity of air in Ib (pounds)/hr (hour) (sq ft) cross section, orthe product of air density PI in lb/ft'times the velocity V in ft/hr. Thequantity III is the absolute viscosity ofair in Ib-mass/ft-hr. Density, viscosity,and thermal conductivity are at thetemperature of the air film given by therelationship

(2)

where Ie is the conductor temperature andt,. is the temperature of surrounding airin C.

Then, for DOPIV/llf=O.l to 1,000,

•q. = [ 0.32+0.43( D:: V)o.n] X

kf1rDo ( ) ()"1J; t.-t,. 3

By simplifying and expressing conduc-tor diameter D in inches, the followingequation is obtained

House, Tuttle+Current-Carrying Capacity of A CSR 1169

Table I, Viscosity, Density at See Level to 15,000 Ft, and Therm.1 Conductivity of Air

Temperature AbsoluteVlseo.ltJ.

IIIC I:DeuitJ, ", Thermal

Conductlrit7.tJSe. Level 5,000 Ft 10,000 fa 15,000 Ft

32. . .. 0.. .278 55.55 0.0.15 0.0807. . .0.0671. 0.0564 0.0455 O.00739• 1.... 5 278 59.73 0.0.21. 0.0793 0.0660 0.00545 0.0447 0.00750SO 10 283 64.14 0.04.27 0.0779 0.0648. . .0.0535 O. 0439 0.0076269 16 288 68.80 0.0433 0.0765 0.0636 0.0526 0.0431 0.0077368 20 293 73.70 0.0439 0.0752 0.0626 0.0517 0.042 •..... 0.0078477 25 298 •... 78.86 0.0444 0.07.0 0.0616 0.0508 0.0.17 0.007958G 30 303 84.29 O. 0450 O. 0728 O. 0606 O. 0500 O. 0.11. O. 0080795 35 308 89.99 0.0456 0.0716 0.0596 0.0492 0.0404 0.00818

104 ....• 0 313 95.98 0.0461 0.0704 0.0586 0.0484 0.0397 0.00830113 ....• 5 318 102.26 0.0467 0.0693 0.0577 0.0476 0.0391 0.00841122 50 323 108.85 O. 0473 0.0683 0.0568 0.0469 O. 0385 O. 00852131. 55 328 115.74 O. 0478 0.0672 0.0559 0.0462 0.0379 0.00864140 .. " 60 333 122.96 0.0484 O. 0661. 0.0550 O. 0454 0.0373 0.00875149 .. " 65 338 130.52 O. 0489 O. 0662 O. 0542 O. 0448 0.0367 O. 00886158 70 343 138.41 0.0494 0.0643 0.0535 0.0442 0.0363 0.00898167 75 348 146.66 0.0500. '" .0.0634 0.0527 0.0436 0.0358 0.00909176 80 353 155.27 0.0505 0.0627 0.0522 00431. 00354 0.00921185 85 358 164.26 0.0510 0.0616 0.0513 0.0423 0.0347 0.00932194 90 363 173.63 0.0515 0.0608 0.0506 0.0418 0.0343 0.00943203 95 368 183.40 O. 0521. O. 0599 0.0498 O. 0412 0.0338 O. 00952212 100 373 193.57 O. 0526 0.0591. 0.0492 0.0406 0.0333 O. 00\;66

• Degrees Fahrenheit.~f = absolute viscosity. Ib/(hr)(ft). computed from formula in reference 17.p/ = density, Ib of air/ft'. computed from data given in reference 18.R/ = thermal conductivity of air. watts/(sq ft)(C) at 11- (1.+/0)/2. reference 13. Table Xl.10 = ambient temperature C.te= conductor temperature C.

g. =[ 1.01+0.371(D::vtU

}/(te-ta)

watts/lineal ft of conductor (3A)

For Reynolds numbers from 1,000 to.50,000 the following empirical formula isrecommended by McAdams

hDo= O.24(DoG)O .•k, PI

Expressing this in a manner similar toequation 3(A) gives

0.24lr(DPI V)o .•q. = 4.45 -;;; k/(t.-ta)

watts/ft of conductor (4)

(D V)O"=0.1695 ;: k,(t.-ta)

watts/ft of conductor (4A)

Values for P" PI, and klare given in Table1.

For convected-heat loss in still air thefollowing formula checks closely with testdata obtained at Alcoa Research Labora-tories in a room free from drafts.

q. =0.072DO·71(t.-t4)1.21

watts/It of conductor (4B)

where D is conductor diameter in inches,te conductor temperature in C, and ta is thetemperature of the surrounding air inC.

RADIATED-HEAT Loss OF CONDUCTOR

The radiated-heat loss of a conductoris given by the expression

where (1 is the Stefan-Boltzmann constant,

which expressed in electrical engineeringunits is 0.5275X 10-8 watts/sq ft/K4,where K is temperature in degreesKelvin or C+273.16 The quantity E isthe thermal-emissivity constant which fornew conductor is 0.23 and for flat-blackwell-weathered conductor 0.91 or possi-bly higher. The area of a circumscribingcylinder A is expressed in sq ft. Convert-ing to conductor outside diameter ininches with temperature in K gives

== 0.5275X 10-1 rDE (K '-K ')qr 12 e a

where K. is conductor temperature andKa is air temperature in K.

Simplifying gives

Qr=O.138D{ (~)4-(~;o)'Jwatts/ft of conductor (SB)

Values of (K/lOO)' are given in Table 1.

SoLAR-HEAT GAIN OF THE CONDUCTOR

Because of the large amounts of powerused by air-conditioning equipment, manypower utilities in the Northern Hemi-

Table II, He.t-Trlnsmlulon Factor forAltitudes Above Sea Level·

Elevation AboveSea Level, Ft

MultipUer forValue. ill Table m

sphere are having lhe yearly peak: loads ';during July and August. ra,ther than ·iDecember and ~January,." fhe 'effeCt' of ~.isolarradiatioD ..-ODconductor' 'Wn~ra- ,;;1ture is more 'bpporta'ht thkn" Wbre' be~"1cause its maximum intensity now'OCcurs . .at the same time as the peak: load .

The amount of heat received by a flat Vsurface perpendicular to the sun's rays andlocated outside the earth's atmosphere isapproximately 123 watts/sq ft of surface.However, because of the earth's atmos-phere, part of this energy is absorbedbefore reaching the earth. Points of highaltitude of, e.g., 10.000 ft, such as existin the Rocky Mountain area, receiveabout 25% more solar energy than sea-level areas; see Table II. The amountof solar heat received by a conductoralso depends on the altitude of the sunabove the horizon and the effective angleof incidence between the direct rays of thesun and the exposed surface. In addi-tion to direct radiation, heat is radiatedfrom the sky to the object. This quantityalso varies with the sun's altitude.Atmospheric contamination has a markedeffect on the solar heat received.

Considerable work has been done in thefield of solar-energy studies, in connectionwith the heating of buildings, as a sourceof power, and relative to the solar-heatgain required to be absorbed by air-conditioning systems. 14. 16

The amount of heat received from thesun and sky may be expressed as

(6)

(5)

0 ............•............ 1.006.000 ...........•... " 1.16

10.000 ..••..................... 1.2515.000 ....................•.... 1.30

(SA)where QD is direct solar radiation andQd is sky radiation, both in watts/sq ft;A'is the projected area of the conductor,and a is the solar-absorption coefficient.Outdoor tests at Massena indicate this is0.23 for new conductor and 0.97 for blackconductor. For simplicity in computa-

• Souree, reference 15.

T.bl. III. Total Heat Received by Surflceat Se. Level Normal to Sun's Rays·

Q., Watts/Sq FtSolar

Altitude,H••Decreea

ClearAtmosphere

lDdu.trialAtmosphere

5 21. 7 12.610 40.2 ,22.315 , 54.2 30.520 , 64 .•........ , 39.225 71.6, ,46.630 , 77,0 , .53.035 81.6 67.540 84.8 61.545 , .. 87 .•. , 64.550 90.0 67.560 92.9 .. , 71.670 95.0, 75.2SO ••..•.•.••••... 95.8 77 .•90 •....•......... 96.4 78.9

• Seuree, referenee 14.

1170 House, Tuttle-Current-Carrying Capacity of A CSR FEBRUARY 1959

{)

Table IV. Altitude and Azimuth in Degrees<of'Sun .t Varioul Latitudes at Declination of!l.O Degrees, Northern Heml.phere, June

10 .nd July 3*

Local SUJI Time

Decree& 10:00 A.M.North

Latitude He z,2:00 P.M.

Be Zc

12 Noon

H. Zc

20 ..•. 62 78 ~ •.. 0 62 28225 .•.. 62 88 88 1SO 62 27230 ••.. 62 98 83 180 62 26235 .... 61. 107 78 180 61. 25340 ••.. 60 1Ib 73 180 60 24545 •... 57 122 68 180 57 23850 .... 54 128 li3 1SO 54 23260 •... 47 137 'i3 180 47 22370 .... 40 143 43 180 40 :H7

••Source, references 19 and 20.

tion, Table III shows total heat receivedfrom both direct and sky radiation forboth clear and industrial atmosphere.This introduces a small amount of erroras sky radiation does not depend on theangle of incidence. However, this errorcannot be detected in the final value ofconductor current. In the case of around, horizontally placed conductor, theangle 8 is given by

D=cos-1[cos n, cos (Z.-ZI») (6A)

where He is the altitude of the sun abovethe horizon, Ze is the azimuth of the sun,and ZI is the azimuth of the conductor(north-south line ZI=1800). See TableIV for altitude and azimuth of sun atvarious latitudes.

Computation of Current-CarryingCapacity

Combining the various components ofheat loss and heat gain, the followingformula results

1-

SAMPLE COMPUTATION

In the sample computation the follow-ing conditious apply:

Drake conductor, 795 MCM (thousandcircular mils), 26/7 ACSR, (new)

wind velocity =2 fps at sea levelair temperature=25 C=t ••conductor temperature =75 C =1.conductor outside diameter =1.108 inchesconductor a-c resistance=0.0265 ohm/

1,000 ft

K.=75°+273=348°Ka =25° +273 =298°t,=(75+25)/2=50E=O.23p,=0.0683 (Table I),u,=0.0473 (Table I)k,=0.OO852 (Table I)V=3,600X2=7,200 ft/hr

,By substituting these values, the follow-ing results:

~000r--------'----'------.----r---'---------'----'

2000~------~----~-----+--~~--~------~~--~NEW CONDUCTOR10.000 FT. El..- SUN INEW CONDUCTOR- SUNNEW CONDUCTOR- NO SUN JBLACK CONDUCTOR- SUNBLACK CONDUCTOR- NO SUN

Ii:

100,~ ~ ~ ~~~~1 ----~-------7----~0.1 0.2 O.~ 0.5 0.7 I

CONDUCTOR DIAMETER - INCHES! I I I I I I I I I II ill: I!

:::: "CQ CQ ClI",

I I i I•.~ •• 1'.

(7)

!Ie (

- [ 1.01+O.371( 1.108XO.0683X7,2000'-'~~jr.

g,-20.95W'~'!k····l:f~t~~!l;!IT •••0.138X 1.l08XO.23(146.66-78.86)

-2.37 watts/ft (9)

Assume the following: azimuth of line135 degrees, latitude 35 degrees north,clear atmosphere, 12 noon ..

H.=78°Ze=I80°ZI=135°

Q,=95+0.6=95.6 watts/It! (10)

8 =cos-1[cos 78Xcos (180° -135°»). =cos-1 0.147=81.55° (11)

sin 81.55° =0.986

1.108!I,=0.23XO.986X95.6X12

=2.01 watts/ft (12)

= ~120.95+2.37 -2.01 =897 am eresI 1 0.0265XI0-1 p

(13)

Current-Carrying Capacity CurvesCurves have been computed (Fig. 1)

for the following design conditions: 25C ambient temperature, 75 C conductortemperature, and 2-fps wind velocity, forACSR for sizes front no. 6 ACSR 6/1 to3,364 MCM 108/37. A total of four

ZS·C AMBIENT TEI/PERATUIIE75·C CONDUCTOR TEl/PERATURE

COMPUTEDVALUES

o600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800

CURRENT AMPERES - 60 cps

Fig. 1 (left). Cunent-carrylng capacity of ACSR with various .urfaceand ambient conditions

Fig. 2 (above). Current.c.rrying capacity of 795 MCM 26/7 ACSRversus wind velocity

FEBRUARY 1959 House, Tuttle-Current-Carrying Capacity of A CSR 1171

'"a.oo<D

<JlWffiooo~~----------------~~~~~~~----+---~Q. 25·C AMBIENT TEMPERATURE~ 75° C CONDUCTORTEMPERATURE~700r2~F~1~/S~E~C~.W~IN~Dr-__ -, ~ __ ~~~~ -+ ~~ I~Q.500r-------~----4_-----+--~~---r--------+_--~t3 I'

~>= i~ ~OO t------- L_<tu~Z~ 200r-----cr:::>u

0 I

,. -:

0 \ :I,···

~

.,\ i;j= IeOIOO:CIe· 75 Clr,Ie' 50·C

1

~ ~/I

I ~ 1//I

I i ~ -,I

~ ~I

~~I

I I~ ~"~ t:--.-f--

I.

0.5

•..'"'"ILoo2II:

'"Q.

(I)

::E::z::oIwuz~.,ViWII:II:o...o::;)ozou

0.30

0.20

0.10

0.07

0.05

0.03

0.02

0.01

0.0050.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

CONDUCTOR OUTSIDE DIAMETER - INCHESI'

r I I II I I I I I I 1 1/ I I I I •...'"•....II>

•... ,..'"

Q,.. ,.. •... ,.. •...•... •... ••..•....•.... t- :::: I, ' •.... , •...., -, .....••. .., , .•. :::IE,.::::,:::::: '" "'''' '" "'''' '"••. on ••. III

II>:::::::: "UtU' t.D CD N NN N NN N on I I .•. <), , ,

I I , I I 111M') I I ::EUH.oU)~1 I 1 I II> ••. on ..I I I t~~~~ <D •. ~N 0 0"'r-: t- ..,'" on '" II> '"CD..-"'--N""'" '" "'''' •... 0", '" ..,o~ s ~ '"•••• N "'''' .. "'''' •... "'..:.: ,..;

Fig. 3. A-c resistance at 60 Cpt of ACSR at three conductor temperatures

curves givesperformance for ACSR underthe following conditions:

1. Black conductor, no sun, sea level.2, 3. Black conductor, sun; and newconductor, no sun; sea level.4. New conductor, sun, sea level.5. New conductor, elevation of 10,000ft.

In computing sun effect, a value of 85watts/sq it was used for total radiationand (J=75°, giving an effective heat fromthe sun of 82 watts/sq ft.

It is significant that there is a definitediscontinuity in the curves between thesizes 4/0 ACSR 6/1 and 226.8 MCMACSR 26/7. This is explained by theincreased magnetizing effect on the steelcore; the current in the single layer ofaluminum strands gives rise to eddy-current and hysteresis losses in thesteel core which in turn cause a markedincrease in effective a-c resistance. Inthe case of more than one layer of alu-minum strands with the spiraling in theopposite direction in each successivelayer,the magnetizing effect is almost entirelycancelled.

Effect of Wind Velocity onCurrent-Carrying Capacity

Drake 795 MCM ACSR 26/7 has beenselected to illustrate the effect of increas-ing wind velocity, other conditions re-maining constant. Ambient temperaturewas taken at 25 C and conductor tempera-ture 75 C. Curves are shown in Fig. 2for new and black conductor, both withand without the effect of sun, and newconductor at lO,OOO-ftelevation. Notethat for black conductor with sun effect,the increase in current capacity of 2-fpsvelocity over still air is 143%. The in-crease from 2 fps to 5 miles per houris 13.0%. A design wind velocity of 2 fps,

a value based on considerable test data, 1,~as been~o~~~9-t1y usecl:thro\!gl1ou,tthe,mdustry,'.; . ···~if'e.re r&n a 'Safe:maximum; .;;

,·:." ...,j,,":-\\'C

Effect ~jltttbient',l'eU,lperature'onCurrent-Cariyirig Capacity-

New Drake conductor has been selectedto illustrate the effect of changing ambienttemperature, with the sun effectneglected,at a constant current of 1,000.amperes.This is shown in the following.

AmbientTemperature,

C

Ct'nductorTemperature,

CTemperature

Rise, C

0 57 5725 83 5840 101 ..........•.•. 61

It is evident that the effect of selectingan ambient only slightly different from astandard design value will have littleeffect on the actual temperature rise asillustrated by the foregoing example inwhich a 40 C change in ambient only in-creased the temperature rise 4 C. Thisincrease is still less when sun effect istaken into account, because this tends tocancel the effect of radiated-heat loss,leaving only convected-heat loss, whichvaries approximately with temperaturerise, to balance to 12r loss.

Test Data on 6O-Cps A-C Resistanceof ACSR

To enable the engineer to compute thecurrent-carrying capacity, recently ob-tained test data on the 60-cps (cycle-per-second) a-c resistance (covering the com-plete range of sizes of AcSR) are given inFig. 3, in the form of curves for 50 C, 75C, and 100 C conductor temperature.These values were obtained in a draftlessroom on 120-ft spans under tension at anambient temperature of approximately20 C. The temperature of the conductorwas determined by taking the averagetemperature of a number of thermo-couples.

Two variables affect the a-c resistanceof ACSR. The effect of increase in con-ductor temperature is to increase the

Table V. Current-Carrying Capacity at 60 Cps, Amperes

New Condition

Sun No Sun

Black ConditionFro'" Chart inReference IACSR Sun No Sun

----------------------------------------------------------------1.590 MCM 54/19" 1.430 1.482 1.564 ..•..... 1.762 ·· .I.~OO795 MCM 54/7"......... .. 941....... 9:3 1.020 1.130 ··· .. · 160No.46/1....... 149 · 1.,1.......... 155........ 165.... 48------------------------------------------------------

1172 House, Tuttle--Current-Carrying Capacity of ACSR FEBRUARY 1959 .

dItI,

resistance of the conductor with an in-, crease in conductor temperature. An in-

crease in conductor temperature may becaused by either increased ambient tem-perature or increased current. Eddy-current and hysteresis losses in the coreincrease the effective a-c resistancenoticeably for single-aluminum-layer con-ductors, as previously explained. Themagnetic loss component of a-c resistanceincreases with an increase in currentuntil the point of magnetic saturation hasbeen reached, after which there is no fur-ther increase in this component. Thisparticular behavior of ACSR is dealtwith fully by Lewis and Tuttle.!'

s.

re

Comparison of Revised Current-Carrying Capacity with PreviouslyPublished Temperature-Rise Data

.gaIeis·n'1-

isIS

to-s,~hre

-~-~

:e ,--,'

neb--r-11-

in75~e.:ssan-lyorge10-

lee.n-he

The current-carrying capacity curvespublished by Alcoa in 19461 are based onan ambient temperature of 40 C and awind velocity of 2 fps. Accordingly,current-carrying capacity of three typicalsizes of ACSR have been computed bythe method presented in this paper forboth new and black conductor, with andwithout the effect of sun, assuming aconductor temperature of 100 C or a 60C rise, and 2-fps wind velocity; see TableV.

Previously published information, al-though limited in scope, appears to beconservative. In general, a conductorweathers rather rapidly the first year ofoperation, so that it can be expected tooperate at a lower temperature thana new conductor. However, in certainareas of the western part of the UnitedStates, high-voltage conductors have beenobserved to stay bright for many years.For this reason, thermal-radiation andsolar-absorption characteristics may varyconsiderably in different geographicallocations. The new data presented repre-sent limiting conditions for new andweathered conductors.

Conclusions

The necessary formulas, curves, andtables have been presented which willenable transmission engineers to select thesize of ACSR most suitable for their re-quirements. It is believed that the datagiven to illustrate the effect of the sun areof importance in light of the fact thatmany system peak loads are now occur-ring in the daytime during the summermonths, because of air-conditioning andpumping-equipment loads.

Computed values of current-carryingcapacity at sea level are in close agree-

inI

19 FEBRUARY 1959 House. Tuttle-Current-Carrying Capacity of ACSR 1173

meht with test data obtained by theAlcoa Research Laboratories and thoseobserved by other organizations.

References1. ELBCTlUCAL CSARACTB&ISTICS 01' ACSR (.pamphlet). Aluminum Company of America,Pittsburgh, Pa., May 1946.

2. CURRBNT CAlUlYINO CAPACITY OP WUBS ANDCABLBS, Georre E. Luke. Westi,.,house Ele",i,Jou",al, Pittsburgh, Pa., Apr. 1923.

3. HBATINO AND CUBUNT CAlUlYINO CAPACITY01' BARB CONDUCTOI<8 1'01< OUTDOOR SBRVICII,O. R. Schurig. C. W. Prick. Ge,..,al Elecl,i, Re-view, Schenectady, N. Y .• vol. 33, Mar. 1930.

4. DBTBRMlNINO CUJUlBNT RATINOS OF OVBR-HEAD CONDUCTORS,PARTS I AND II, H. P. Seelye,A. L. Malmstrom. Electric Lighl and PowerChicago, Ill., Dec. 1943.5. SAPB RATINOS FOR OVBIlHRAD LINB CONDUC-TORS, Leonard M. Olmsted. AI EE Transactions,vol. 62, 1943, pp. 845-53.

6. ELBCTRICAL HBATINO CSARACTBRISTICS OFOVBRHBAD CONDUCTORS, PARTS I-IV, E. E.George. Electr" Lighl o,.d Power, Dec. 1944;Jan. 1945; Apr. 1945; Dec. 1945.

7. CURRBNT CARRYINO CAPACITY OF OVBRRBADCONDUCTORS, H. A. EnOl. Elecl,i,ol World, NewYork, N. Y., May 15, 1943.

8. CURRBNT CARRYINO CAPACITY OF ACSRCONDUCTORS,]. H. Waghome. V. E. Ogorodaikov.AlEE Transactions, vol. 70, pt. II, 1951, pp.1159-62.

9. EMISSIVITY AND ITS EpPBCT ON TRB CURRBNT'CARRYINO CAPACITY OF STRANDBD ALUKINUllCONDUCTORS, C. S. Taylor, H. E. House. lbid.,vol. 75, pt. III, Oct. 1956, pp. 970-76.

10. MBASURBMBNTS OF RBSISTANCB AND RBACT-ANCB 01' EXPANDBD ACSR, ]oel Tompkins. B. L.]one s, P. D. Tuttle. Ibid., vol. 74. pt. III, June1955, pp. 368-75.

11. THB RBSISTANCB AND RBACTANCB OF ALmn·NUll CONDUCTORS, STBBL RBINPORCBD, W. A.Lewis, P. D. Tuttle. rus., pp. 1189-1215 0

this issue.

12. TBB MAGNBTIC PI<OPBRTIBS OF ACSR CouWrRB, T. W. Matsch. W. A. Lewis. iu«, pp.1178-89 of this issue.

13. HBAT TRANSMISSION (book), W. H. MeAdalllll.McGraw-Hili Book Company, Inc., New York,N. Y., second edition, 1942.

14. HBATINO, VBNTILATINO AND AIR CONDITION-INO GUIDB 1956. American Society of Heating andAir Conditioning Engineers, New York, N. Y.,1956.

15. POWBR FROII SoLAR ENBROY, ]. I. Yellot.Transactioi •• , American Society of MechanicalEngineer'S, New York, N_ Y., vol. 79. no. 6, Aug,1957, pp. 1349-57.

16. A RBVIBW OF TmrltlolAL RADIATION CON-STANTS, N. W. Snyder. Ibid., vol. 76, 1954, pp.537-39.

17. TSB VISCOSITY, TSBRIIAL CONDUCTrvITY ANDPRANDTL NUKIIBI< POI< ArB AND OTBBR GASBS,]. HiI.earath. Y. S. Toulonkisn. iu«, pp. 967-981.

18. FAN ENGINBBRING, Richud D. Mason, editor.Buffalo Forge Company, Buffalo, N. Y., fifthedition, 1948.

19. TSB AlmRICAN NAUTICAL ALMANAC 1957.U. S. Naval Observatory, Washington. D. C .• 1957.

20. SIOHT RBnuCTloN TABLBS 1'01< AIR NAVIOA'TION, VOLS. II, III. PIlbUcatiMt 1<0. 249, U. S.Navy Hydrographic OfIi«, Washington, D. C.,1957.21. BARLOW'S T ABLBS, L. ]. Comrie, editor.Chemical Publisbing Company, New York, N. Y.,fourth edition, 1944.

22. TSBRMAL RADIATION TABLBS AND ApPLICA'TIONS, R.· V. Dunkle. Transll&/io1JS, AmericanSociety of Mechanical Engineers, vol. 76. 1954,pp.549-52.

23. GAS TABLBS (book), ]. H. Keenan, J. Kaye.John Wfley & Sons, Inc., New York, N. Y., 1948.

24. PltOPOSBD STANDAIlD SoLAI< RADIATIONCUltVBS !'OR ENOINBBRINO USB, Parry Moon.

Journal. Franklin Institute, Pnitadetphia, Pa.,vol. 23, no. 5, Nov. 194~. pp. 583-617.

25. HBAT TIlANSKi9810M' AS INl'LUBNCBD BYH •. A'!· CAPACITY AND. -SoiA-I< RADIATION, P•. C.HoUCbtOD, 1. L. 'BlAchhaw, B.I II: Pugh. P.IIcDermott. Pap., 1<0. 923, T,ansactio,,,, Ameri-can Society of Reatinc and. Ventllatlnr Encl-neets. New York. N. Y.;']an. 1932.

26. A RATIONAL H&AT GAIN MamoD FOR TIBDBTBRMlNATtON OP Au CONDITIONINO COOLINGLoADS, F. H. Paust, L. Levine, P. O. UrblllL.Jou11,al, Heating, Piping and Air ConditionincSection, Ibid., Aug. 1935.

"

----.'----

Discussion

W. A. Morgan (Washington Water PowerCompany. Spokane, Wash.): The authorsare to be commended for the thoroughnesswith which they have considered the factorswhich may affect the heat balance of aconductor that is carrying alternating elec-tric current with the usual prescribed limitsof conductor temperature and ambienttemperature. Particularly, the effect ofsunshine is noted.

However. the application and operatingengineer is in need of published data orguides which should be forthcoming frommanufacturers of ACSR and all-aluminumconductors as to the effects of loading abovethe currents which give the usual tempera-ture rises. Obviously there is a time-currentrelationship for such overloads, i.e., theshorter the time the greater is the amount ofcurrent that may be allowed to flow abovethat which would just give the desired tem-perature rise. Specifically. there is prob-ably a temperature somewhat above 75 Cwhere continuous operation would causea reduction in the tensile strength. anothertemperature where the tensile strengthwould be reduced 5% if operated at thattemperature a specific time, etc. Or, are weto assume that aluminum has not agreedupon temperature limit and will lose somepercentage of its tensile strength if operatedcontinuously at even 75 C?

There are data available for determininghow much a transformer may be overloadedunder emergency conditions without jeop-ardizing its life. or, in some cases a calculatedloss-of-life expectancy may be calculated andis acceptable. Similarly. it is desirable toknow how much a conductor may be over-loaded during an emergency and for howlong. For example, assume that one oftwo parallel circuits is out of service andit is desired to carry an overload current(say 25% above the rated value whichwould give 75 C conductor temperature)over the daily peak rather than to cut offcustomers.

Perhaps the steel reinforcing will providefor most of the loss of margin of tensilestrength in ACSR conductors. But, a11-aluminum conductor may be particularlyvulnerable to overload currents, and. if it is,perhaps we should know its critical conduc-tor temperatures or time-current overloadcharacteristics.

E. E. George (Ebasco Services Inc.,Little Rock, Ark.): The authors havedone an excellent job in utilizing pre-

vious analyses of val.ious componentsof heat transmission and in presenting asummary in final usable form. It appearsthat the accuracy of the new formulas isconsiderably greater than that of the inputdata generally available in the field, espe-cially as regards average surface conditionson the conductors.

The results are for a wind velocity of 2fps. While this is a relatively low windvelocity, it will be noted from Fig. 2 thatcarrying capacity ¢ith a wind of 2 Ips (orabout 1.4 miles per hour) is about 30%greater than in still air. This may be dueto the discontinuity between turbulent andlaminar flow and to the complex interactionof air currents due to convection and thosedue to external wind. These factors havebothered all investigators in this field.

Some of us think that the limiting condi-tion of still air or zero wind should be coveredin conductor heating tables, because thiscondition frequently occurs on hot summerafternoons under humid conditions preced-ing a storm. Such conditions are also re-sponsible for high peaks on the powersystems due to full operation of air condi-tioners.

It would also be helpful if engineers con-nected with research on copper conductorswould present figures on copper comparableto those in this paper on ACSR, utilizingthe latest available data on heat-trans-mission components.

It is to be hoped that the authors willcontinue their investigations and publishtheir results, including studies of sleet pre-vention and sleet melting. Massena, N. Y.,(location of Alcoa Research Laboratories) isfavorably situated for both natural and con-trolled tests concerned with the problem ofsleet on conductors.

R. W. Caswell and Lawrence Yule (Com-monwealth Edison Company, Chicago,Ill.): The authors are to be commended forpresenting a constructive paper on an im-portant subject.

The Commonwealth Edison Companyhare recently sponsored an investigation atone of the universities relative to tempera-ture rise of conductors when high currentsare used in order to melt ice from trans-mission lines. In this study, based onlaboratory tests, a formula was developedfor determining temperature rise of a con-ductor due to a specified current undergiven weather conditions. This formula issimilar in form to equation 7 in the paper.While the authors use data developed byMcAdams for determining convected-heatloss, the study by the university indicatesthat slightly different values should beused than those resulting from McAdams'work.

A comparison of the temperature risecalculated by each method for a given setof conditions shows that the two methodsgive different values. This means that acurrent value calculated by one methodas not being harmful to ACSR may actuallyraise the temperature above the desiredvalue.

We do not say that one method is correctand the other is incorrect but merely pointout that additional study is advisable todetermine the proper constants to be usedin calculating temperature rise.

In the authors' paper the assumption is

1174

made that the temperature of ACSR shouldnot exceed 75 C. In the interest of makingtbe most effective use of ACSR it may beadvisable under some conditions and fora limited time to exceed tbis temperature. .

In order that the users may fully evaluatethe results of doing this, it would be helpfulif data were furnished as to effect onstrength and sag characteristics of ACSRif the 75 C is exceeded for different lengthsof time.

This suggestion merely indicates thatadditional information would be benefi-cial.

Earl Hazan (Kaiser Aluminum and Chem-ical Corporation, Spokane, Wash.): Thispaper deals with a subject vital to thoseutility engineers who are faced with theproblem of determining their line capacitieson a realistic basis in the face of phenomenalload growth on their systems. The problem,of determining electrical characteristics ofACSR conductors, has been the subject ofexhaustive investigation by the ConductorLaboratory of the Department of Metal-lurgical Research, Kaiser Aluminum andChemical Corporation. It seems aproposto supplement the data presented in thispaper and to comment on the results ob-tained.

BACKGROUND

The program being carried on by theConductor Laboratory has resulted indata which describe the a-c and doc resist-ance characteristics of a conductor, its cur-rent rating, overload characteristics, andcomparison of ratings between bright andblack surfaces. In assessing the data ob-tained it was noticed that the conventionalformulas by Schurig and Frick (seereference3 of tbe paper) could be used with faircorrespondence to test results for a brightconductor, but were not reliable in check-ing results for a black conductor. Furtherinvestigation showed that Schurig and Frickbad developed their formulas for bare copperconductor whose emissivity was 0.5, whichis about double the value for a brightaluminum conductor. This emissivity fac-tor was used indiscriminately for aluminumconductors, at the time when ACSR andall-aluminum lines were beginning to beused in quantity. In retrospect it wasrealized that since the heat lost by radiationusing the Schurig-Frick formulas wastwice the correct value, then some compensa-tion must have been built into their formulafor convected-heat loss.

At this point we made a comprehensiveanalvsis of all those conductors which hadbeen-tested by the Conductor Laboratory todetermine the best relationship betweenour test data and analytical expressionswhich would describe the conductor per-formance. It was determined that theMcAdams formula (see reference 13 of thepaper) for heat loss from convection gave asatisfactory approximation of observed re-sults within the limits of experimental ac-curacy. This formula, being applicable forthe several wind speeds at which the conduc-tors had been tested, was adopted for gen-eral use by the Laboratory, and it wasrecommended at that time that the currentratings in the Kaiser Electrical Conduc-tor Technical Manual be revised on thatbasis.

CURRENT-RATING FORMULAS

Our formulas differ slightly from thosepresented by House and Tuttle, but theseare lmainly differences in fdrtD .. :Por·~-ample, it was found "thailOi' -&inductortemperatures in the range between' 40 C and110 C average values 'may be used for thefollowing constants: lAb the absolute vis-cosity of air; p" the density of air, and K"the thermal conductivity for air. Theseconstant values, reduced to electrical units.and substituted into the general McAdamsformula yielded the following equation forheat loss due to forced convection in watts/sq inch of surface.

W.7.645X 1O-·~[0.32+0.43(355. 7VD)UI)

D

where

~ = temperature difference between ambientand conductor, C

V=wind velocity, fpsD=conductor diameter, inches

The utility of this form lies in the factthat all unknowns are readily available forsubstitution in the formula.

The corresponding formula for heat lossdue to radiation in watts/sq inch of surfaceis

W,=36.8t [C,~o)·-C,~~o)·Jwhere

E = emissivity in per centT=conductor temperature, KTo=ambient temperature, K

The current rating can then be calculated.neglecting solar effects, by the formula

1= J3.77XlO'(W,+ W.)D

" «;where

W,= beat loss due to radiation, watts/sq inchW.= heat loss due to convection, watts/sq

inchD=conductor diameter, inchesRoc= a-c resistance at the temperature of the

conductor, ohms/1,OOO ft

Now, first of all, how does this set ofsimplified formulas check the more exactformulas presented in the paper? If theeffect of solar radiation is eliminated fromequation 13 for the Drake 795 MCM 26/7ACSR, a current rating of 938 amperes isobtained using the formulas presented by theauthors. Using similar formulas, in simpli-fied form, as just discussed, the rating isfound to be 933 amperes, a difference ofabout 1/2%.

Second, how do the simplified formulascheck actual test results for several differentwind speeds and several different conductortemperatures ?

Details are listed in Table VI, of a com-parison made for three ACSR conductorswhose data were arbitrarily selected fromall of the conductors tested by the labora-tory to date.

It will be observed that close correspond-ence exists between calculated and test data.indicating the validity of the formulas. It

House, Tuttle-Current-Carrying Capacity of ACSR FEBRUARY 1959

e

'J

:t)r

5S

.e

~\d. J

chsq

he

ofrct.he-rn; /7is

.heJli-isof

:lasent-tor

.m-orsom-ra-

nd-~jita,

It

)59

. . Table VI. Calculated and Observed Current Ratings, Amperes

Wind Speed - 2.0 FPS Wind Speed •••'Z.O FPs ': c".Wind Speed-3.a FPS

Per CeatConductor TutedConductor Difference, Difference,

Temperature, C Calculated Observed Per Cent Calculated Obsetnd Per Cut Calculated Observed

{50 747 760 1.7 868 , .. 890 2,5 848, 870 2.6

Cardinal. 54/7. 954 MCM....... 76 1.017 1.020 0.3 1.180 1.190 0.8 1.169 1.170 04 100 1.204 1.240 3.0 1.394 1.400 0.4 1.403 1.390 0.9

{50 741 760 2.6 861 875•....... 1.6 840 850 1.2

Rail. 45/7. 954 MCM........... 75 1.006 1.016 0.9 1.167 1.170 0.3 1.155 1.170......•. 1.3100 1.188 1.210 1.9 1.376 1.375 0.1. 1.383 1.390 0.6

{50 790 800 1.3 918 920 0.2 875 870 0.6

Curlew. 54/7. 1.033.5MCM..... 75 1.072 1.090 1.7 •....... 1.243 1.255 1.0 1.199...•.. 1.190 0.8100 1.265 1.300 2.8 1.464 1.485 1.4 1.431 1.460 2.0

should be observed, further, that in generalthe test results give higher values of currentrating than do either set of formulas. It isfor this reason that we desire to produce acomprehensive set of experimental data onall bare conductors.

SOLARRADIATION

The effect of solar radiation has beenneglected by many authors who dismiss thesun's effect as being negligible at the operat-ing temperatures of the conductor. H. A.Enos of American Gas and Electric ServiceCorporation proposed as early as 1943 thatthis effect be included in the heat-balanceequation for determining current rating ofa conductor. The authors show the effectof solar radiation, and demonstrate that itshould be considered. Our own calculationsshow that this is a valid proposal; that, in-deed, the sun's radiation is not so small asto be disregarded.

In the calculation of heat absorbed by theconductor from the sun, however, we haveassumed that the solar constant includedthe small contributions from other heavenlybodies and the sky. Furthermore, the sky,being at a temperature of about -50 C orso. actually represents a heat sink ratherthan a heat source. For this reason we havedivided our radiated-heat loss into two parts,half of the radiation from the conductorbeing lost to the surroundings which are atambient temperature. say 25 C, and halfbeing lost to the sky (on a clear day) whosetemperature is, say, - 50 C.

In computational form, therefore, W" theheat loss due to radiation on a clear day,would be

TV,""" {[ (I.£o),~(d&;),]+[ (I.£o)';(;;foo)']}

where

T=conductor temperature, KTo=ambient temperature. KT,= sky temperature, K

In making the computation for the•current-carrying capacity of a conductor insun on a clear day, therefore, the form pro-posed by the authors may be carried outwith the slight modification suggested inthe foregoing.

Using this equation, we have calculated

FEBRUARY 1959

the ratings of a few conductors when ex-posed to direct sunlight on a clear day.The results indicated a derating of from 2%to 4% for a bright conductor, and a deratingof from 15% to 18% for a black conductor.In comparing ratings of bright and blackconductors, with ·and without solar radia-tion. the authors show that these conductorsmay be derated 1% t03%, and 10% to 14%,respectively. The importance of the solareffect is demonstrated by the close agree-ment between both sets of data.

A-C RESISTANCEOFACSR CONDUCTORSIn the calculation of current rating, the a-c

resistance of the conductor is required atthe temperature of the conductor. Thishas been the elusive unknown for ACSRconductors because the effect of the steelcore has not been completely determined.In checking the curves of Fig. 3 with testdata for four sizes of conductors, which wehave tested and which are included in thefigure, we find exact agreement between theresistance data we have accumulated andthose presented in the curves.

SUMMARYIn summary, then, I believe the authors

should be commended for making availablethese data and calculating procedures. Ithink that the simplified forms proposed inthis discussion should be considered as alter-native methods for calculating currentratings. The subject of calculating theeffect of sun on the current rating needs fur-ther clarification with respect to sky radia-tion and sky temperature. Finally, I find itinteresting that two separate organizationshave been studying the same problem alongexactly parallel lines, and while our investi-gations have not yet been completed, I mustpoint out that in substance, we have checked,experimentally. the conclusions reached bythe authors. It is apropos to suggest. there-fore. that an Industry Committee be formedto consider the suggestion already made toour own organization. We feel that exist-ing current-rating tables should be revisedto reflect the more realistic values for stand-ard conditions of 75 C conductor tempera-ture, 25 C ambient temperature, and acrosswind velocity of 2 fps.

W. M. Pickslay (Pacific Gas and ElectricCompany, San Francisco, Calif.): Theauthors are to be commended for an excel-lent condensation from a large volume ofavailable literature of a relatively simple

and easy method of calculation of the cur-rent-temperature characteristics of overheadconductors.

The theory of convective-heat transfer isextremely complex mathematically and,in general, has been most successfullytreated by the methods of dimensionalanalysis. These involve nondimensionalnumbers, such as the Reynolds and Nusseltnumbers mentioned, as well as three othersof importance. the Prandtl, Stanton, andGrashof numbers.! For specific solu-tions, test data are required to inter-relate these numbers, and large amountsof such data have been accumulated. Theresulting formulas are, therefore, semi-empirical and usually restricted in applica-tion to a limited range of conditions. Con-sequently, while the authors state thatvalues computed by their complete formula7 are in close agreement with test results,it would greatly increase the formula'svalue if comparisons of test and comparedresults with suitable variation of the im-portant parameters were to be published.

With respect to radiation-heat loss fromthe conductor, the authors' approximationassumes all radiation to the earth's atmos-phere at a temperature equal to the ambi-ent. This is theoretically indefensible sinceby far the largest proportion of the atmos-phere. i.e., nitrogen and oxygen, is trans-parent to thermal radiation.' Moreover,air temperature with height above sea levelvaries greatly as does the temperature ofsurrounding terrain. Consequently, thenet radiated heat will be considerably re-duced where the line traverses a narrowrocky canyon than where it crosses opencultivated fields. A more accurate ex-pression for this term is given by Enos inreference 7 of the paper. The authors'reasons for the apparent gross simplifica-tion would be of interest .

It is suspected that the aforementionedarises from the relative magnitudes of con-vection and radiation-heat loss, approxi-mately nine to one, in the sample calcula-tion. These are of the expected order forthe 2-fps crosswind assumed. However,it has been a matter of some surprise to thisdiscusser that this wind velocity, originallybased upon weather conditions in Schenec-tady, N. Y., in 1928and 1929,is as generallyaccepted as it appears to have been. Closeexamination of U.S. Weather Bureau datafor the central valley of California hasshown that the hotter the summer day.the greater probability that there will beappreciable wind velocities above the fric-tion layer by the middle of the afternoon.

House, Tuttle-Current-Carrying Capacity of A CSR 1175

STRESS-RUPTURESTREN;THOF EC-HIt

10.o0o,-----,- -, -r-r- '

TEHS'LEPROPERTIU

.. ~ ~'--I:c !0:

i 10~~~~~~~~---~~---t_----_r---~---+_----~~ " •.11.000j----'>~-+--------fti:ccltO.OOO I--------+~~----+------+_------_l••....cit 11,000 I--------+--~._\__V'd-------+_------__l•.x..czr 10,000 j------+----\:'\-'H-\-""'----t_------j..•.•...J

0;~ .,000 I-------+--------~~o:::::-~~--+---------j..

40 .-----t.•-=----l----+-..:::....ct--..:::.....,..-l------=:,_--!...--=~o_I_:-,-."-.-.-

IOO-HltS.

TEMPERATURE DEG.C.0~,.~--7..0~-~7=.--~'O~0--~,~,.~-~,~.0~--J.,,~.---~,~00~-~

O~O------~,O~O------.~O~O------~.~O~O-----~.O.HEATINOTEIIPERATURE.T.OEO.C

Fig. 4. Stress-rupture curves of EC H18 at elevated temperatures

Similar conditions should be expected inother areas even of different topographysince on clear summer days the afternoonbreezes appear to be produced by themorning heating of the ground and loweratmosphere.

It, therefore, appears that when conductortemperature is a limiting design considera-tion, there will be occasions to use consider-ably smaller values than 2 fps for crosswindvelocities particularly when the line is pro-tected by hills, buildings, or trees, and thusbelow the friction layer. This poses a prob-lem in that there is an area between O-fpsand approximately 1/2-fps wind velocitywhere the conductor temperature rise isindeterminate. In this region, convection-heat loss is by a combination of both freeand forced convection, a circumstancenot amenable to treatment with presenttheory.

Because of this indeterminate area, undercircumstances similar to those indicated,the authors' formula 4(B) for q. should beused instead of 4(A). This is perhaps not soimportant for ACSR because of the presenceof the steel core, but is vital for copper andall-aluminum transmission conductors wherestrengths and clearances must be main-tained.

IC-HIIAT VARIOUSTEIIPERATURU

Fig. 6. Tensile strength of EC H19 at heating temperature for variollllengths of time at that temperature

REFERENCE

1. HEAT TRANSPBR PRENO:llBNA (book), R. C. L.Bosworth. John Wiley & Sons, Inc., New York,N. Y., 1952.

H. E. House and p, D. Tuttle: We arepleased to note the interest aroused by ourpaper as evidenced by the comments of thevarious discussers, whom we thank for theirremarks. In the following closure, someremarks made relative to one discussion mayapply to others and will not be repeated.

To reply to Mr. Morgan, we would firststate that the 75 C temperature was chosensimply as a reasonable operating tempera-ture. It is somewhat higher than that forwhich a new line would normally be de-signed but was not intended to indicate alimiting temperature. For both copper andaluminum, the 75 C temperature is one thatresults in loss of strength at a very low ratebut not a zero rate.

Mr. Morgan's request for loss of strengthat elevated temperatures can best be

answered by reference to the accompany-ing curves. Fig. 4 shows the rupture Limeof EC (electrical conductor grade) winunder various conditions of load and ternperature. For example, at 100 C, a wincontinuously loaded to 48% of its originatensile strength (measured at room temperature) will fail in 1,000 hr ; a loading 0

56% will cause failure in 100 hr. Fig.;shows the reduction in strength of EC wir-with temperature for various times. Th-tensile strengths are all measured at rOODtemperature. Thus at 100 C, a wire wildrop to 96% of its original strength in 10,hr, 94% in 1,000hr, and 90% in 10,000hr.

Fig. 6 is similar to Fig. 5 except thstrengths are given in terms of the actuatensile strength at the temperature undeconsideration. Thus at 150 C, the tensilstrength will decrease in 1,000 hr to 16,15-psi (pounds per square inch), 87% of itvalue of 18,600 psi after only 1/2 hr at thatemperature.

Fig. 7 is a plot similar to Fig. 6 but for aelectrical-conductor aluminum alloy. I

.1000r------------r------------r-----~T=E=N~S~=E~pc~0=P=E~R~T~~S-----,OF

ALUMINUIIALLOY CONDUCTORAT VARIOUSTEIIPE~ATURE5

l00r-----~~~~=_~~------~------------+-----------~~ tlOOO

% .....• 0:Z "... ..0: C.. 10 0:•. ~ 10000•. ••~ ..." ..Z ..••.. 00 C..J 0; 11000C •.;::~ %..... .•0 40

Z.. ... 10000TENSILEPROPERTIES cz ..•. •.u EC-H" •.a:•. ..J.. AT ROOIITEMPERATURE 0;

20 Z1000•...

0 00 100 300 400 0 100 100 100

HEATING TEMPERATUIU, T. OE8. C.

Fig. 5. Tensile strength of EC H19 at room temperature for varioustimes of heating at elevated temperatures

Fig. 7. Tensile strength of a typical electrlcal-c:ondudor alumintalloy at heating temperature for various lengths of time at that t

perature t1

.0000r-----~~--_r------------r-----------_r----------~

r-----------~----~~~~~~~~----~---------__li

HEATINGTEllPERATURE.DEG.C

1176 House, Tuttle-Current-Carrying Capacity of A CSR FEBRUARY 19~i

/TYPIC •••L STRESS- ST •••••IN CU••V! IFO ••••• CIII •••n!ll

•••NNE •••LlNG 0' •••LUIlINUIl

4 /- V

V/

/

//

.. .: '0.•

10

'0

oo .00' .001 .001 .004 .001 .001

UNIT DEFORIlATION -INCHES/INCH.001

this case, at 150 C, the tensile strength willdecrease in 1,000 hr to 22,900 psi, 91.5% ofits value of 25,000 psi for 1/2-hr heating atthat temperature. These strength reduc-tions, as for the EC, are cumulative andirreversible.

Fig. 8 shows the final "increasing" curvefrom a repeated stress-strain test on no.1/0 American Wire Gauge ACSR that hadbeen subjected to a temperature of 350C for 1/2 hr. This temperature is sufficient

/'~ to completely anneal the aluminum (Fig.. ) 5). During the stress-strain test the cable

~ had been held 1/2 hr at 30%, 1 hr at 45%,and 1 hr at 60% of its rated strength, withrelief to zero stress after each of theseholding stresses. The presented curveshows the subsequent increasing load test(that is commonly carried to failure). Thepoint to observe here is that, up to a stressof approximately 40% of the original ratedultimate, the plot is a straight line, in-dicating that the full tension load is beingcarried by the steel. The succeeding up-ward bend in the curve shows the effect ofthe aluminum strands taking up a share ofthe load.

Such a drastic thermal load cannot beenvisaged for transmission lines, but thisextreme case is presented to emphasize theunique characteristic of ACSR that canallow severe mechanical and electrical load-ing with only a minor change in totalstrength and a similar minor change in sagupon resumption of normal operation.

In reply to Mr. George, we have notedthat change in wind velocity at low speedshas much more effect than similar percent-age changes at higher velocities. This isindicated in Fig. 2 and we do not believeit is attributable merely to a change fromlaminar to turbulent flow. It is truethat the higher velocities result in vortexformation on the lee of the conductor, butin regard to heat transfer, the given for-

~ mulas hold very well in spite of this effect.':Actually, the air velocity because of natural

""-"'" convection in free air is of the order of 0.4fps when the conductor is at a reasonableoperating temperature. Outdoors, even

FEBRUARY 1959

Fig. 8. Final load-Ing curve (see text)of repeated stress-str.ln test at roomtemperature on no.1/0 American WireGauge 6/1 ACSRafter heating at

350 C for 1/2hr

the stillest day, there is more air movementthan one might suspect and this, coupledwith natural convection, could easily reach2 fps which actually is an extremely low andtherefore conservative velocity. However,for conditions that involve convection cool-ing due only to the heat of the conductoritself, formula 4(B) will give very closeresults.

To turn to the discussion by Mr. Caswelland Mr. Yule, we would stress that thedifferences in the computed results by ourformula and that referred to in the discussionare small and that they differ in their ac-curacy depending on the particular fieldconditions being considered; i.e., one for-mula checks the test results closer than theother under one set of conditions, while, fora different set, the formulas are reversedin their approximation to the actual testfigures. In all cases, however, it may besafely stated that the accuracy of thecomputed result is dependent on the fielddata and is not limited by the formulas.This is a point that Mr. George stated verywell in the first paragraph of his discussion.

We would again emphasize there was noattempt to indicate and no assumption wasmade that 75 C was the limiting ACSRtemperature. It was simply a reasonablecompromise between the frequently useddesign temperature of 50 C and the gen-erally recommended normal maximum 100C operating temperature. It was felt anintermediate temperature such as this wouldbe most useful in the curves given, which weassumed might be used for estimation pur-poses.

We are pleased to have Mr. Hazan'sagreement with our results. It is quiteusual for an engineer to simplify and tab-ulate constants for formulas frequently usedand, where the current-carrying formulais used often, a table of values for k,(p,1iJ,)o.n can be easily prepared. In thepreparation of a paper such as this, there isalways the question of how much reductionshould be made in the formulas. In thiscase we felt it was preferable to show theinfluence of the individual parameters, leav-

ing the further easy simplification to thetreader.

Considerable time was spent reviewing theeffect of the earth and sky on the radiationfrom the conductor with the decision that anexpression involving the ambient tempera-ture alone (rather than earth, sky, andambient) was preferable if the requisiteaccuracy could be obtained in the finalresult.This proved to be possible, no doubt partlybecause radiation loss is the smaller com-ponent of total thermal loss. The morecomplex expression proposed by Mr. Hazancan be used, if desired, or even more com-plicated ones taking into account thereflectance of the earth. However, refine-ments for increased accuracy seem war-ranted only in the case of the larger con-vection component of loss.

Some of the foregoing remarks also applyto the discussion by Mr. Pickslay. Thepaper was written from the viewpoint of theoperating engineer, whose chief interest isallowable current. Therefore the treatmenthas not stressed the theoretical, althoughample references to fundamental sourceshave been given. We did not feel that adiscussion of the theoretical parameterswould add to the purpose of the paper. Wedo appreciate Mr. Pickslay's interest, how-ever, and in due course, another paper maybe written to compare the present derivablevalues of the dimensionless parameters withprevious recommendations.

With regard to radiation loss, it is (as Mr.Pickslay points out) the smaller part of thetotal loss, even under free-air conditions,when one is computing on the basis ofmaximum allowable temperature. Fur-ther, the air temperature is readily avail-able to an operator while earth and skytemperatures are not. Considering thevariation in terrain a given line may traverse,the impossibility in most cases of choosingan average earth temperature (or even theworst) at a given time becomes apparent.Therefore, while the effect of the earthexists-as source, sink, or reflector+-con-sideration of it would add complications tothe formula with no useful increase in theaccuracy of the result.

Wind conditions, of course, vary widely invarious sections of the country, the localtopography having considerable effect. Itis also surprising what wind velocities maybe experienced 40 or 50 ft above the groundeven when, at ground level, dead calm seemsto prevail. True dead calm is a highly un-usual condition but if expected to exist overpart of a line, then the allowable currentshould be based on this section and theformula 4(B) for free convection would prob-ably be better. For free convection we havenoted the vertical air currents to be about0.4 fps at the usual maximum allowabletemperature so that even the slightestalmospheric air movement will bring thetotal convection currents out of the 0- to1/2-fps range of concern to Mr. Pickslay.As can be appreciated, the nominal designvelocity of 2 fps is very conservative and notrouble should be experienced if this valueis used. We recognize Mr. Pickslay's con-cern in the case of copper or aluminum con-ductors and a rather broad review of thecharacteristics of aluminum has been givenpreviously in this closure and the outstand-ing virtue of ACSR pointed out.

House, Tuttle-Current-Carrying Capacity of A CSR 1177

-,:'-w'j'cnt-CarryingCapacity of ACSR

H. E. HOUSE'.l'EN2'a ~

"-.;cps'.s: C=-r-ent-t=~ .charac:-_~ of ~..x=ded-~ conductor~ ~or=d. ~-~t the

, ....;u..<:t-:yas ACSR, !:a v e been bn:stigated.'..'Je 'C~ cf smf,,-= c:ori01ticos. ~d

!~'''':'Y.alt.irnde, and solar ra6tion are, '-"~~ for a ...-icldy o:sed size of con-

~C.T; S~'!:S of=t<a..-r:rin~ capaci:ty: =}; CO!lcbctor 0Ut5i2.e Cia..:.:=te:r are

",=~=g:;::I =cL~....s oi ,~ c Cc:...:G•-: :....9"aCt::) roo<iuc'..or ~e aud~:'·(;-~t t~ at 2':"'ps (led. ~~2.J ",,=d .ei-oc-ty. ~, J; -J~ a....::;;j t.ab:es to pcr=tt az:::JpOta.tivn0: ==t ..-.ili:e:s for <my set of cpe::-.ci:lgC) .:,.Jj.:5=.s ••..re ~clnC-ed.. Cox::!prrt<':rl values:-,' c-,:~ are n close ~ ...-it.htest',3.~ ",;:nc: h..•.e ~ by ~=~cj •.-a::IY vi ..d.=X:a (~) =d other.f •".ert:.; 4>'" o:rs.

r:'~ CE f... s~ L::!L.0C::x:eC. b: .=.lcoa i::J.~ 1~)9. tl;e '.:5e cf ..!.~ f.-::;;: ~;:~e!~ ....•-:C ~er L":<:· ~--:""I CoO b=.sj;!'uwr::. ~ izrtil rt m -;.'ost re-i.;l~--::-dc-op:..x:ricr SX::::=;e.. .- =.."St:;xw~..:::~ 2~z:::t ~~~ ci CC·P:'~;5 t~ -.:scd far ~~~ c...~ticn

'J~ •• '. ~_ Becznse c;f :l.~~~ce of:-,c " "·~·'-c-::-·e:'" :\r,~ ",-.n =c-_ '~~,~t_ _. "'-0.-_ ~ _~~'--_~'--:':..J~;;~ G::J 11:"" c:~ C::z..-d.-..e.::--,-~ cf

oeen C"~~ on t~ v-..gr,<ro.1t Ge yes:; toevaluate ~e- ...~ ,.e resistazce, T.cis isneeded to cozrpute ~ ~t~6::a?~ty ci tr.e cr,.,6ctC!'. iZly in-;,...4ig->-L;:=.,.-c=-e cz..~ =t t:r ~crl:: for~=at tl::.e0L~ I::S'trTt:z"t~ci Tech-iology, ~c.bu:r:5h, P2..1 TI:e ••~wn)c!::::lic:2..Lo= of Lcl:~ azd Sci:n.:rig and~rick3 .•••ere followed pe:-=.oc5c:illy by;!_he.-S,4--1~Dcati:::lg a strong azd con-~::;..:ec~:::~c~ in t.he ~b.5ect-

~e~uJ::soi L~...5for t1:edete.-~O!l vihe e:IJ~-si.-j!y ci s:::-a:::;ced-dL'J~= COI!-

'uctors fer =t~ cor:.OLXcs of both ne..,-.rd ~e3~ 'condcctors were reported!J 1956.'Tests i.0cet=~e the ~cc-.i....-et'J...<:ycle

esistazce cf a f:- cat ~-i;:ty ci sizes and:.rc_!1.G...:p uS ACSR have Leezi carr'ied

I

"_'J:''':' !~l. :c-:"'O=::::;;~~ by ~ B=:3. T:-.a::..lo-··:~loOl . D-~~~!:o()'~ Co::::..=.~~ r..::to a.;'~T"~y tb e ~ 7~::==c-....! O-.r=":';O=~ .0?a;-~~t f':..<

~;:~~<r~:::;.- ~. ~~: ..·~~;;;:~·~-~~5~.).!~~~::=-::,;t S~:1-=:;e-1 Oc:1)~ 1-:'. 195i; :=-__ ~r 2....,-.an.:-;e~rv:i:;t:-=:. :-:C'\'f'=~ 6. 19.:'7.

'. E. P.on-a aX P. D. TC'"t":"'L.!: are .-:-~ .J..~C'?&

~-:.arC'!:J !.."=';:-(""t.:.~. ~.~.~~. ~;_ j,",

P. D. TUTILEMEMBER AlEE

out at the Alcoa Research Laboratories at)..Iasse:na,N. Y. Conductors were strungunder tension on a 12O-ft(foot) test span,Values of 6O'q:cle resistance were meas-ured up to. a conductor temperature of200 Cor. 3,000 amperes/square inch if200 C temperature was not reached.The method which was used b thesetests is described by Tompkins, Jones,and Tuttle..-

A co-operative research program be-tween the Illinois Institute of Tech-nology, Chicago, Tll., and Alcoa ResearchLaboratories has been COlDpleted.ll•12

The results of this work provide a meansof accurate ccmprrtations of reactanceand resistance far ACSR of any combi-nation of aluminmn and steel stranding.

Because of the tremendous growth of6e eJectr-ic21utility mO!stry. there re-=::n .-ery few :long tr a=::ssion lines int1le ~teI'n pz.-rt of fr.-e l7r:cite<L§!?-tes.Lir-es that were once Icng have beenlr..nped into ne.,qy constructed sub-stations. T= load on these snort trans------~----.----~-- --.r;:i~.on).inesis fu::?~?y_t.be _bea~g_~tie conductors rather 62.D by stability~.:;X~l~e reg'S:.ti~~: as-~as-thec:a..~as I2"t;; 2S the 19':::0·5.-- Fc~ this'reason, 'an~rnte' ~~~~g of tile thermalcapabilities of the conductors is more im-portant than ever before. .

The fo=lia ~oped by ~fc.-\da:nslSfer corrvected-beat loss of si:;.glehorizontaltubes and wires has been found to giveaccurate convected-beat loss for strandedconductors. This formula has been CQ!Il-

bi!:-edwith the results of emissivity tests'and data O!lsolar radiation.u.1$ and field-test data on absorption of solar and skyradiation on outdoor test spans ofstranded conductors, in order to evaluatethe current-carrying capacity of ACSR.\\-rth accurate values of a-c resistance fora variety of strandings, it is now possibleto compute the current a conductor willCi...--ry for an}' given set of conditions oftemperature, wind velocity, surface con-dition, and altitude above sea level,both with and without the efiect of the

Heat-Balance Equation of ElectricalConductors

'L'4lCtI steady-state coaditions, of windnJr'\.--1ty, t ercperature, solar radiation,

and electric current, the following equa·tion is valid

(I)'

(IA)

where g. is convected-beat 1~, g, isradiated-beat loss, I is the current inamperes, r is the effective a-c resistancein ohms/ft of conductor, and q, is theamount of heat received from solar 3I!dsky radiation. .Each heat quantity in theequation is expressed in wattsflineal it ofconductor •

,I!~"~The fundamental relationship for COIF" . l;

veered-heat loss of single horizontal tubes tand wires is given by Mddams (see refer- ,. ~ence 13, p, 220). This is expressed by '" ~the dimensionless equation Y'o4!~)J. Q "' i.hD (DoG)UI' \ -.~ ~-'-0.32+0-43 - (2) htc t<;' ,It, PI . Sc,~ \Jt (1Cj l

• 1-") (;'I-\\l~~ ~where l:J?o/k ,IS the N usselt mnnber, and . I ~::;3 )'DoG/PI is the Reynolds number for any • OJset of conditions, This formula is reco:;n- '" _ .mended far Reynolds numbers rangingfrom 0,1 to 1,000 which include air veloci-ties up to 2 fps for conductors up to 1.3-inch diameter.

The units used in electrical engineeringare watts, degrees centigrade, and feet.Accordingly. 1:. tile surface coefficient of 'heat tr ansfer, is e.-.;pressed in "a tts; sq(square) ft/C; Do is conductor outsidediameter in ft; k, is the thermal conduc-tivity of air, (watts) (ft)/{sq ft) (C); G'is the mass velocity of air in Ib (pounds)/hr (hour) (sq ft) cross section, orthe product of air density Pr in 1b/ft'times the Velocity V in ft/hr. Thequantity PI is tile absolute viscosity ofair in lb-mass/ft-hr. Density, viscosity,and thermal conductiTIty are at thetemperature of the air film given by therelationship

r

where Ie is the conductor temperature andt" is the temperature of surrounding airin C.

Then, for Dop,V/}l,=O,l to 1,000,

[" -, (--;'p1V) •...] -- Xvq,= 0.32+0,43 ----;;;- X

k,..;D. ( ) (3)-- I,-Ia

Do

t,

B)' simplifying and expressing conduc-tor diameter D ia inches, the iollowingequation is obtained

1169

-. I'~.' '>

,- cThennaJ

CODdu~tifltr.11:,Sea L••.• I .5,000 Pt 10,OOO)'t 1:1,000 Pt

3:!.... 0 .• '.273. __• 5.5.SS ..••. 0.04IS .. _•• 0.0801 ••. 0.01\71. , .• 0.OSs. .••. 0.045S •••.• 0.00739• 1. . . • 5 .... 278 .•.. 59.73 ..••. 0.0411. ...• 0.0793 ..•. 0.0660 .•.. 0. O~S ..•• 0. 0447 .•••• 0.00750SO.... 10 .•.. 2S3 ..•. M.H ... _ .0.tH27 ..••• 0.0779 ..•. O.CMS .•. 0.0535 ..... 0.043D ..••. 0.00762SD..• , IS •••. ZSS .••• e8.SO •.••. 0.~ .•••. 0.076S ••.• 0.0636 •••. 0.0526 •••. 0.0431. •••. 0.0017368 .••• 20 .••. ??3 .... 73.70 ..•.. 0.O-t39 ••••. 0.0752 .•.. 0.0626 ...• 0.0517 ..•• 0.0424 .••. 0.OO7M77 •••• ~ ••.• 2:18.••• 78.M •.••. O.C+U ••••• 0.0740 •••. 0.0616 •.•. 0.0508 .••. 0.0417 •.••. 0.0079586 ..•. 3O.••• 3i'J3.•.• M.~ .••.. 0.04-S0 ..•.. 0.072S •... 0.0606 .•.. 0.0,500 •.•. 0.0411. •.•. 0.0080795 ...• 35 ••.. 3f'.-8 •••• ~. 99..••. 0.0456 ..••. 0.0716 •.•. 0.0596 .••• 0.0492 •... 0.0404 •.•.. 0.OOS18

104 .••. 40 ••.. 313 .... 95.98 ..... 0.0461. .... 0.0704 .••. 0.0586 •••• 0.0484 .••. 0.0397 •••.. 0.00830113 .. " U.... 3IS ..•. 102.24 •.••• 0.0467 •.••. 0.0/193 •.•. 0.0577 .••• 0.0476 .• , .0.0391. ., •. 0. 008-U12.2.••. SO•••• 323 •••• 108. 8.5 .••.. 0.0473 .•••. O. 0683 .... 0. 056S .•.• 0. 046D..•. O. 0385 .••.. 0. OC852131. ••• 5.5 •••• 3:23.... 115.74 ..••. 0.tH7S ..... 0.0672 •••. O. 0559 •••• 0.0462 .•.. O. 0379 .•••. 0. (081)4140 .••• ro .... 333 •... 1z.? 1liI••••. 0. MM .••.. 0.0661. ... O.0550 .•.. 0.04S. ..•. 0.0373 .•... 0.00875149 ••.• 65 •••• 33.8.•.. 130.52 ..... 0.O-t89 0. 06,52...• 0. 0542 .•.. 0.0448 .... 0.0367 .•..• 0.00886158 .. " 70•... 343 .•.. 138.41. ..•. O.O-t14 O. 06-43..•. O.053.S.... 0.OH2 ..•• 0.0363 ...•. 0.00898167 ••.• 7,; ...• 348 ...• 1!a.&5 ..•.. 0.0s00 ...•. 0.0634 ..•. 0.05Z7 ..•. 0.C436 0.035S ..•.. 0.~176.; .. SO •••• 3.53.... 1.;..;.:n ..... 0.0~ ..... 0.0627 .... 0.0,522 .... 00431. 00354 .... 0.0092118.3..•• 85 .•.. 3.58...• 11>4.26..•.. G. 0510 ...•• 0.0616 .•.. 0.0513 .••• 0.0423 0.0347 ..••. O. 009321')4 .•.• ~ ..•. 353 ...• 173. 63 ...•. 0. 051S .•.•. 0.0608 ..•• 0.0506 ..•• 0. 041S .•.. 0.0343 .•••. O.OO9t3203 .. " 95 ••.. 3C8 •••. 183.~ ..... O.0521. •••. O. 0599 ..•. 0.049S .... 0.0412 .••. 0.033S .•... 0.00952212 .•.. 100 ...• :r.:l ...• 193.57 ...•. 0.C52e •..•. 0.0591. •.. 0.0492 ..•• 0.0406 .••. O. 0333 ..•.. 0. OC!;66

.,

• "_0.-

·D.gndlF~~-a~"te~ty.l!:>/(l=r)(f-.J. ="';><lted froro formula in refer ence 17.n-d.l>:rity. 1b ol "-'rIft'. ccespczed fro<:>da..ta.giv~ in reference 18.l/- thcn=J ~.t7 of a.ir, ~(sq ft)(C) at '1- (L.+l ••)/2. reference 13. Table Xl.1-.- a.m~ ~-=-e C.Ie - cood -oc:rc t= pcr.o.tn:re C.

g.=[ LOl-TO.371(D::})l-U},,<t,,-t&)~illnea1 ;t of conductor (3A)

~For R...."T"-:cid.s ~ fro::n 1,000 to:20,000 ~ following ~ :ormula isre~c....."-d ~y :-Id.d=s

J:D. ,DoG)O"-=0'" -It, -- N

E~ this in a taanz er similar toequation 3(A) gives

. O~(D-;>'~'"q.=--_ -- k/.4-t",)4.45 . PI

watts/It of ~cuctor (4)

"=(l.1695(IJP/ V)'" ij{t,,-~}, ~,

watts/It of conductor (4A)

Values for PI, pi. and k,are givrea in Table1.

":'i

For convected-heat loss in still air thefollowing formula checks cl~31!lLte$~data obtained at Alcoa Research L~~!"~-~-------------.-.--.--tories in a room free from Grafts.-------- -g. =O.072VO·~tc-t/l)1.~

watts/It of conductor (4B)

Iwhere D is conductor diameter in inches,t,conductor temperature in C, and t" is thetemperature of the surrounding air inC.RADL-\'IED-HEAT Loss O? Co:-'-Ut:CTOR

The radiated-beat loss of a conductoris given by the expression

where a is the Stefan-Bol tzmann constant,

Values of (K/lOO)4 are given in Table I.

SoLA,R-HE~T GAIN OF THE CONDUCT0!k(/Vo_tor~ul4lS ~ive.,l') ~u"'if1·FrH:. f°-F-----------------

Because of the large amounts of powerusedbyall~nrutlorwn:geqwprrn;lt,m~ipower.. ~t~hies .iIi·.toe ''Northern . Hemi-

which expressed in electrical engineering .units is 0.5275X 10-:1 watts/sq ft/K·,where K is temperature in degreesKelvin or C+273.lS The quantity f isthe thermal-emissivity constant which for:new conductor is 0.23 and for flat-blackwell--weathered conductor 0.91 or possi-bly higher. The m-eaof a circumscribingcylinder A is expressed in sq ft. Convert-ing to conductor outside diameter ininches with temperature in K gives

_ 0.5Z75XIO-1 -.rD~(K 4-K I)qr- 12 ,/I

(SA)

where ~ is conductor temperature and.K.. is air temperature in K.

Simplifying gives

gr=O.l38D{ (~o'o)'-(~;o)']watts/It of conductor (SB)

T••ble II. Heal-Transmhsion Faclor fOf

Altitudes Above Sea level-

El evarion AboveSea Level, Fe

Multiplier forValues in Table ill

(5)

0 .•...•.•.•.•.•••..•.••.•. 1.005.000 ••••...•..••.••.•...•••.• 1.!~

10.000 .•••••••••.•.••••..••••.• 1._"15.000 ..•••.••.•.••••.•••••••.• 1.30

• Socece, rtJucn~ 15.

-, . .~. ,,',~{~'jL~~<f;(·~~,~,i~sphere e ~ving; the')' .!l~{.J,ulr··ari~~

,,' Dece.m~_andJ~~lr: .. tct,>()f ..solar radiatiol) 5:on~&0. biipwi:•.•..lure is more important:Uiin-:'bi(or-;-~cause its maxiwumini.e~it):' nowoccuiS~~e ~ ~h~jo:ad. '-" •

The amount of beat received bX a Batsurface perpendicular to the sun's rays and~ outside the earth'satmospliere'r,approximately 123 watts/sq ft of SUif~.However, because of the earili"sifmos-phere, part of this energy is absorbedbefore reaching the earth. ~oinls of highaltitude of, e.g., 10,000 ft,such as emt

:::; ~ Rocky Mountain area; .!!-a;iveen about 25P'a....Pl~ solM_.~~e.rgythan sea-

level areas; see Table II. "Thea;-;~;untOf solar-heat r~yed by.a_rondus!oralso depe;~~ the altitude of the sunabOvetbehoriz~~d the 'eff~ti~e-aiigleOfinc1clencebetween\h.e·direc't rays of thesu:n-aDdtE.-e·· exPOSed" Surf a£e~_. ln~'addi-:tion to dlrect' nutiiiion,' heat is radiatedfrom the sky to the obJ~t::' This quantityalso varies----wlth- the ~s -altit;·dt:.Atmosph~c c';;;~i~~ti-o; h~-;·;~k.edeffect on the Solarbeat received, .

Considerable work has been do;e in thefield of solar-energy studies, in connectioowith the heating of buildings, as a sourceof power, and relativeto the .solar-heatgain required to be absorbed by air- -conditioning systems.l~.U

The amount of beat received from thesun and sky may be expressed as

(0)

where QD is direct solar radiation andQ4 is sky radiation, both in watts/sq ft;A I is the projected area of the conductor •and Q....is~e solar-absorption coefficient.!h!!~~-t~~iSat':MaSseDai;;dicate thiS is.Q..23.io..r.ne}:LC()nAY.~tQu.nd0.97 for black.c;9nductor. ..E2!~j?licityin comput4-

Tabl. III. Tolal He.t Received by Surf"ccat Sea l~el Normal to Sun's RIIYS- .

Q., Watts/Sq FtSoW-

Altitude,Be. DegrMs

ClearAtmosphere.

5 ........•.•.... 21.7 •..•.•..••••• 1~.610 ....•...••..•.. 40.2 .....•.....•• 22.315 ............•.. 54.2 ...•.......•. 30.620 .....•......... 64.4 .•....•...••. 3~.725 ...........•... 71.5 ....•.•...... 46.630 77 .0 .•.......•••. b3.035 ............•.. 81.S , ~•. 540 .......•.... _.. 8j.8 ......••..... 61.545 ........••..... 81.4 .•.• ~•.• ·.;••.. 64.5SO •..•••• ; ••••••• 00.0 .•.••••.••••. 67.660 .....•.•...•••. 92.9 ..••••••• ·•••. 71.6

·X 70•••.•••••••..•• 95.0 ..•••••• :.;•••• :75.2SO•..•••••..••.•. 1l5.8 .•.••.•.••.•• ;77 ••90•..••••••••.••. 96.4 .•..••.•••••• 789

';"'~". }\!6b>d., ...dAxmvtL p. ~.• ; (.", l"~ Vu;OClS utiNda to( Otc:t_tioft 01... ~'~ ~, NorthUlt Heno~e, 1-.

. 10 at>d Jgly 3·

~ .. " ...---------------::. lO:OOAJL.

':P:!1. .!=:.e.. :s. Ie

2:OOP~

:!I .••. I32 •••• ;'8 ..•.. 87.•• O.•••. s:z .••. ~:-..;••• _~._ •• S8 .••.. J;:S .•• ISO ••••• ~ ••.. 27%::O: ••• t.:? •••. 98 •••. &3.•. 1W ••••• 62 .••. 2:<i2:>s•••. 61. ..• 1Q7.•..• ;'8 ... UO ..•.. 61. ... 2.53:J)••• .1:.0 .••. !I.!> ..••. ;-;) ••• lSO ••••• GIJ •.• :!~~.,).... s:' .... lZZ .•... 68 ... I~ ..•.. S7 .... 2ZB.'>il••.. <>4•••• 123 .•••• 1'3 ••• t~ ..... ~ .•.. ~050 •••• .f7 ••.. 137 ..••. S3 ... 1~ ..•.. -47•..• ::::23~O.•.. +0 .... 1-13.•••• .;3 .•• ISO.••.. 4;).••• :!li'

t!o:l, T.ilile III ~ toW bear receivedL-= t«h &ect aud ~ rh't:iiilfDrboth ~ ~d r-dl:sn""@~~TIris ~...d::u<= a ~~ or e:-ror2S sky ;~ ooes ncL &pe::.d on thel't%'"ie a: ~&nc- ~. i:ES error-~cannot be defected Xi!tile ';;"""1 .-due ofcondoctor ="e:JL h & esse of a:-ucnd,Xz:-iz.ol:~ piau:rl =6ctor, theangle =:s.~ by

6"o..."'S-'~ c-s E'c={.z:.:-ZI}1 (6.\)

w1:~~:s& ;:;i.:, CcGt::e=~tile: hcci-...c'!l.,Z~ is & c " ,6 ci ~ sun,~'-"-""1 :s we az-7::;=t;, of -::be conductor(D"",,~,~i..=.1J.~ Z;= IS},,). See TableIV l~ 2L~Ge c-:c ;:,: ·111·c=i sun atvarices ~l2.!ibC-€:S-

Computation, • Current-CarryingCapacity

Combining the various components ofheat loss and beat gain. the followingformula results

1-l[l'Ol~.37I(D;;vtn};{t._t.)+

~ Ol={ (fciot-(Foo)']-g,(7)

s'-\ldJ>LE Coxztrrartox

In tile sample computation the follow-ing conditioos apply:

Drake condDctor, 795 :'>IOr (thousandcircnlar T""Js). 26/7 ACSR.. (ncw)

-.rind vekx:ity -2 ips at sea Ieodair 1.emper.I.~-25 c-i.condnctor t=p=I..tI:re-75 C=t~conductor o~Wde <liam~ = LI08 inchescondnct.or a-c ~~O.o-J6.5 ohm!

1,(0) it ~. '1S Co

By ;;ubstitu:i::~ oc:e .-".1;:::0, the follow-~ results;

-a.oo"-'

o i: i~~~O:~--------~----~~~~~--~--~--------------~r-: ,=." 1(.) i

, !I

Ie,.:: !~ ~z ')! -c C.7 •

:et,::U:7:R ;;'':'.'J,£-;-~q - I~C-:C:S

'- '-, , , ".0 .. "''' ,, • I 5c .. ~-.• .• .•.:::oI!:?.•.

5~----~--.----r--~--~---.----r---TJ~,--r.~--,I

I I~ 40 I~:---L--~--~~--~--+---~--~-J~--J¥?-~I---;•••~ ••E'wco-n.cTOII 10,000 ,.T.EL.-'_ I

!EW c;c..::..c;TOII - SUNIoI(W CC>lC<)CTOR - NO SUI! J I

; :~~;;:O~~~;::~SUN ~ - -I- . '.~ 30 !---!--+---+----t---f---+~__2'_<~'-I--;----ir--i1:; u·c AWl!JCl(T TE ••PERA'ruIt£~ 7~·C «>MOOCTOIITE••PE"",....!

J •~ 20 I-----+----t---+---+------t----cf-!--#'?--.;-....::...--;-:.---;----;

~ I J> "! -5 j -,3 10 1-----7----;---+--~~-#S«'-:.......:----;---:....---..:..I-___r'-----:w>oz3'

f~· ~." '..' . : . ::, ; ' .. ~"';~__

[.. (1.l08xo.0683X7.200V·!'1 c-'

.- 1.014-0.371 . ~,. 0.0473' .<i.-d"" >. ,; . -~. 0.00852.><50:::'-(8) ',/

q. ~2lJ.95 ,~atts/lt t~:·(~~)q, -O.l3SX LlOSX0.23(146.66-78..86) .

"",2.37 watts/h (9)

Assume the following: azimuth of line ..135 degrees, latitude 35 degrees north,clear atmosphere, 12 noon.

H~-78·Z.,-I80-Z,=135-

Q. -95+{1.6 -95.6 watts/ftl

S=cos-1[cos 7SXcos (180°_135°»)-=cos-10.147=81.55°

(to)

f· .....(11)-.. .

sin 81.550 =0.936 "r~,....., 1.108q.=0.23Xo.SS6X95.6X12 .

\.',~2.01 watts/it

\(12)

'~- .•.Current-Carrying Capacity Curves

Curves have been computed (Fig. 1)for the following design conditions: 25C ambient temperature, 75 C conductortemperature, and 2-fps ••ind velocity, for.ACSR for sizes from no. 6 .",CSR 6/1 to3,364 xrcxr 108/37. A total or four

~EO VALUES

o(,O~ soc 1000 1200 1400 1600 16:)0 2000 2:r.>O 2~OO ~o 2~

ClRRENT AJ.OFEP.£S- 60 cps

3Fig. 1 (Idt). Curanl,c<'lrrying c~~city of ACSR with various IIJrfacc

and ambiflll conditions

fig. 2 (sbcve), CIJrrent;c<'lrrying c,,~city of 795 MCM 26f1 ACS~venus wind .•.e1CKity

~, }

I ,"-"

I

I-....•....•...oo2a:•••e,<It:::E~oIwuz~-I-.~ii)wc:a:oI-o::>azoo

,Q50rt-~-1----+----r---4~--4----+----+---~--~~--~---+--~

0.30r-_~.~~--~~---+----r---1----+----+----+----~--~--~--~0.201--l(I\~-r--+--+_-J_-.l--+--+--t--+--+---!, ;;:-tc -IOO·CI/;-tc·75·Ct/r: tc' 50·C0.10r--+-~-~~--+---~-T¥;[7f--r---r----f--I---+---I----+~

~.07 t---+--+~~-+/-H/;ljrt--+-+-...f---+--+---~I-------{0.osr--+---r-~~~~~-+--+-~--+--+--4-~t--4

.~,0.03~--~---+----~~~~-4----+----+----~--~--~----4---~

~~ 0.••....••....• 57 ••••••••.•.••. cr0.02~--+----4----t----+---~ ...•~~~....J-~----+----+----l-----+-~---4--~~::::::::::::::1~::::::: :~.:::::~

~~ ~\, -,~ .Jt is erident that the effect of selec~0.01t--t--i--+--+--+---+---+~<,"';:~~~----l:::----}--+-----4 an ambient on1I~@dent fr~

-..:::::::::::::-:::::::-;~- ~~esigr: ~Jne will have little

o.oos~__~__~~~L- __ ~ __ ~~ __ J-__~ L- __ -L __ ~L- __ ~ __ -J ~og.the~~ ~~!~~02 0.4 0.6 0.8 1.0 1.2 l4 1.6 1.8 2.0 2.2 2.4 2.5. i!ln.strated bv the i~~g ~~l~n

. CONDUCTOR OUTSIDE DIAMETER - II'OCHES lrlcicll a ¢J C ClJa.I:L.--e·inambient onlv :n-~~ tbe ~d:Irre ri..c.e'4Y·-ifisbcf2..'-e is stiil'less wi!en. Sun"6ect istaken E::ito acconnt, bec:;"se tills tends tocancel the e5ect of r...diated-btat loss,Ieaving only correected-beat loss, which.•cries approxiraately with temperaturerise, to balance to T-rk:ss.

, I I II I I r I I I II I I II

••••... :;::•.. .r:;' CDI Io 0'" .•.~~

Fig. 3. A-c reslstence lit 60 cps of ACSR lit t},ree conductor temperatures

Effect of Wmd Velocity onCurrent-Carrying Capacity

Effect'of Ambient Temperature onCurrent-Carrying Capacity

Xew DT2ke conductor has been selectedto illustrate the effect of changing ambienttemperature, ..nth the ~ effect De~lect~!t a m~"1'''J~ curren.,!~_~_~~.This is shown in the following.

AI::!bientTe:::openture.

C

CondoctGrl'e.t:l~tu.re,

C

curves givesperformance for ACSR underthe following conditions:

1. Black conductor, no sun, sea level.'2, 3. Black conductor, sun; and newconductor, no sun; sea Ievel,

4. New conductor, sun, sea level.5. New conductor, elevation of 10,000 it.

In computing sun effect, a value of 85. ~atts/sg It was used for total radiation

and 8 = 75O,~v1ng an effective beat fromthe sun of 82 watts/~gjJ;. - ..---.

It is signifu;gntthat there is a definitediscontinuity in the curves between thesi~3- ~JL.PJ1_and 226.8 MCMACSR 26/7. This is explained by theincreased magnetiziD"g effect on the steel<;;e; the current ~ the singl~~)'er -;;raluminum strands gives rise to eddy-current and hysteresis lossesin thesteel core which in turn cause a markedincrease in effective a-c resistance. !!!.the case of more than one layer of alu-~2.~~~th the spiraling in ~~posite dir~t~~ i:D each sucressi\"~ayer,~.agne.tiE!1g ~!!.ect is alm~t entir~!x

~--------------~----------------------~--------------

Test Data on 6O-Cps A-C ResistanceofACSR

To eIl2bk the ~e!:!eer to compute tilecnrrent-carrying capacity, recently ob-tained test data C£I. the 6(kps (cycle-per-second) a-c resSta~ (covering the ceca-plete range of sizes of ACSR) are give.:1:r.Fig. 3, in the form of carves for 50 C. 75C. and 100 C conductor temperature.These values were obtained in a dr.J'tl"'S.\room on 120-ft spans under tension at I ,

ambient temperature of approximate :'20 C. The temperature of the condr-;wasdeten:nined by taking ilip. avr;".temperature of a number of tbe-, ,couples,

Two variables wed the a-c resiste-of ACSR. The effect of increase in ~ductor temperature is to increase t.~ .

. Drake 795 MCM ACSR 16/7 has beense~toillUStraletlie effect of in~~{_~iL vei~!y:~~~iiditions ~maining constant. Amblen t temperaturewastaKen'at25 C and conductor tempera-ture 75 C. Curves are shownin Fig. 2for Dew and black conductor. both withand without the effect of sun. and Dewconductor at IO,OOO--ft elevation. .Kot.ethat for black conductor with sun efi'ect:.~ei.q Oluent cap..eCty of 2-~velocity over still air is H3%. The in-crease fWD\. ..2 fps to-:5.; miles per houris 13.0%.(Aa~d..Y~IocitYOf2~

7.'S~-V JCf.(:

Table V. Cu"~t.c.rrying Ca~ at 60 Cps, ~l'IIperes---------------------------------------------------

ACSRNew eo..ditiOJl

F""", Ch: z 'J:.~:c:_eJ).: • ~No SOD

1,690 MCM 54//9 .•..•....... I,43t1 ••• _ ••• 1.487 •••••••••• 1.M4..•..••• 1.7G:? .•.•••••• 1.:C~7115 MCM 54/1............. 941 ••••••• 9<'3 .••••••••• 1.CY.!O 1.130 ~.No.46/1 •...•..••••...•.•.• 1019•••••••• IS1. .•.•••••. 1~ •••••••• 165 .••••••••• }.o'

~•.,- ..t::!:'f! of ~ c.oodocta with an m.._ .':~.;: i..., C!-s:d--A;'.oc ~ An in-

" .: '-. ~ i.:: CC!rlDCtCC ~ may bec.u_'~! by t::i:..'-.eT ~ ambient tem-

-..-::~Xe or ~ carrent, :&!dy-. ( I ~ and hyste:-e::s5ksses ia the c::or'e

. -~ : ~_~~ tbe effective a-c resistance-", :-;-,-',;: ~:>17fur ~al.'.;'i,. iim-~}-er con-':} \D~;, as previoosly- explained.. Thei.."l~·~c loss ~t of a-c ~:r.cr2-"CS ••-jfu an i:ncr6;.se ill Cl..1I!=1:

"::. t:' L:e point of :r=.gne&: sat:uration bas. :n rf-'"~ after which ther-e is DO fur-

. _~.-c.: i=t:::ax in t!ns ~ Tl:Csj:::.rt£=L,--'r~ of ACSR is dealt;,-:th b-Tly by I..ewis a:cl Tuttle..u

~(;mf a,;son of Revised Cur:rent-Carrying Capady wirll PreviouslyPnblished Temperatzrre-Rise Data

rr; ----+ - - '.•.oe \..LU...l ~-<=:....:g czpadty carves~}1:.b~ by ..!1coa ~ l~ = based on••.•'l~~ci~CE:ndawind ~ocity Gi 2 i;:s.. ~.

''.:tLrre:rt-c2.L,.5 Cg ~ ci t1:::cetyF.calsizes of 3.<::9. ~ ..beea =;;ut::d bythe =6od I-~ ::...,.thS p<o:peIfoeboth ::,ew =d bl2d: c:c=X=ctr:r. ,.j'-clt z=dwithout the e::ec!: of =. 2S .~"g aconductor t.. !.ere, d: of iCi) C or a Ws ::=~ =cl2--,~..=--.:i >6::v"':t..'; seeT~~'J.' )

~ __ , 'L'C-"-_ .•.•• - • _.~..-!e,.~........:Sv ~1-'~ ==c==::!~~0!l, ~th '~..crl' --~~~~ =-:--ve,~~C'JLL~~ In ~ a cr-!bc",-,.~~ a;,;c,-;,Y ..L1e :"'st ye:ar vioperation, so ilia! it = be e:yected tocpcrate at a ~ ~~ ~a new~. ::o~. 0. cert::m~eas oi Ge western part of the Gnite:dStates. high-vt:~<>e CO"'-«bctors bave beenobserved to sta Y l..:gIrt fc;c ::r=IJ' yea:-s.For t:h:<; reason, t:::er=..L,.--a.cEation ~~~ .•.tlou cl=-..c...eri5tics =y~-yconsi~~:'" c· e:re:n!: 6~ -. b5clIocatiocs, Tbe =-- Cata presented repre-~:-;U-fu:::itL::.g c:onOti<mS for DeW aadweathered co:::-Guct.oos..

The IC:f:£f:SSZ!} fcrrrrnlas, C'..:....~ andtables ZzVl: been presented ,,!::ic.h w-JIeaable t7, <: .iss::OD. ~~ to select thesize lei ,ACSR most s:ri21:e for their re-qi1:r~t=:ts... It is 1:-e::: ••.•.. ed that the dataj\'en to :I!....strat.e tl:-ce5ert cf tbe san "-'.-e~of ,. F-~ce in E;!:t 0: we ic.ct t1:2.tm? ..~ .~ •.-ste=l ;~ 1~ c..:e DO';\""CtCLJ-

r::lJ n L:::.-<! 6.yL~ ci~-=g t.he s.....,.,-:-:-er·10:Jt.!;..;, ::.ecz-se 01 2Z-<cr'=tiroing ~d~::::i;i~~~..L~t !cx=..ds..Cc;:-:::::'-.l:ed"'-2~es c·j c:..r:ent-ca..rr)ug·JAct:i ~t sea le'\c! c:.re n close agrc.e-

Llt'..' with test data obtained 'by the'" J-'a4J; Frankli" lc~tu,te. 3~elPbJa'.,!;"'.: ..<.I·,;"· ,;-,;.. ~. '.,,01. 23. DO. S. XOY. 1940. PI'. ~17. ,.

.A.lro. Research I..aboc-atoOes and those .••• •• ' c:. 'r .," ,.,' .. -, _. .,. •••T TItA ••..,.Xl$S.lO~ AS' !(P1,U.,.,CRO .1' . ~ '"

observed by other ocganizations. BItA.T CuAClTT ",,0 Sot.n ~lAT10lf. F. "'Co:, .Bou&!>lba. J. L Blacksha_. It. U. PuP. P.McDermott.. PIIP"'''''' 9Z.1. Trll.,utw'lI. A:nuJ-eau Socirty of H_ti,,( and VeutDatior RDP.Dt-U~. Xew 1<O<'k. X. V .• 1aD. 1932-

26_ A. R.t.n~Al. BRAT CAlK MBTBOO PO. YB•DIIT1<'OC:DlAnO,. or A»t Co>lDtTtOHIHO COOL1NOLoAt>S.P. H. FaDst. L LenD-e. F. O. Urban.JovrtcD1, Heatinr. PipiDl and Air ConditioniorSKtiou. Iind .• ~.ur. 1935.

ReferencesL ~c.u. ~ or Acsot (apoa=;X:Id). A••.emi....... Coa:.;>a.D,. of ~~ Pa... May 1946.

:!. Ct;a..kJ<XT~Tn<O Cu.u::rrr OP WtaJtS ••.•••••~ ~.E. Luh. Wat;.~ EkdricJ~ r~ Pa... Apr. 1~23.

3.. RLt..TDOC •••....,. Cuna:.cT C4u.TtO<Q ~.LOTT

or l!AltS Co.!u>OOottS 7QI 00T:>00. Sz:rnca"0_ 2.. ~ c.. W. Frici. Cn=d El<dnc IU-";c.,,.~y.:S. Y_ Tlll. 33. Y.ar. 1930.

~ ~ Ct:latDrT JU.n>rcs 0" ~-J!tt4l> CCnll.OCOItS, P..u:rs I .en> U. H. P. ~e.J;... L ~ ~ LiIC1 ••&4 PD'IKT.~.m..D=.1~5.. ~ R,,:=<cs XlIIt ~ l.n<'s ~~ ~ M. Ob=ot.ed.. .A.IEE. Trc~.••ez, ~ 194..J. PP- 84.5-63..

s.. ~cu. liJ<A.r:o<o C=u..o.~ oP~ Cos!>OG 00dI. ?v:.rs I-IV. E. E.G-ecqe.. ~ ~irf td PC'K>CT, Dee, J~;10=- 19-1S; A:;r- !~5; Dee.. ~

r. ~~~..c:rTCP~Co=>ocro~ :a:. A...E.::ooc. ~ W.".!4. ~~

·Ycrl:,.:S_ Y_ Yay U. 1...043.

tL ~ ~ ~A.CTr Cf7 A.CSa~J..H.w~V.E.O~Y...!TEE TrtT'.c'ion. Tel.. 70, ;>t.. n. 1951. 7,).!'!-~-6:!.

1. ~..ua> L-" E7T=::r C>:'<~ C<;z~-~ Cu-..c:= OP S-:LoL'<O>lO .!.Ltnc:lCl:lC~-c:ro:u;.. c.. So TA~ 2.. E. Roese. l~ -e

--=L 7S. ?t- III. Oez, 1~ ;>;>- !;7!}-';' o.:::'l.. ¥~ 01' R=.L'OO .•...,., RLr..cT-...s= <? E=~ ~ Joel To=;>D=., !i.. L.:-=. P. D. T~ r~ -rei.. 7!. ~t.. ill. J=e::;05. p;>- scs-rs,C;.~t..j 7~ ~..L.""o '"J ~.L"'u Ct~~·~ Co..--<D-t:'crc-it.S. ~:-=-Z!.. ~·.aD. "W • ..L~-s. P. D. T~~ n-a.. 17- !!S9-J:::!S 0:-~~ ,

~-z;r ~~ ;?Jw~ OF .!.CSR Co;uT. w. ~ VI. A- I..:...:s.. ll>i4_~.

~l;-~ 01 t=s i=::>e.

u.. ~ ~'<9C55:"'" ,~. W. 2.. Yc.A6=s.).U:C.. •.• _E3il :3oolI:: W=;:>c:>Y. be.... ~.".. Y cck,.~_Y_~~19-U.

!~ HJ...oTDOC.'~ ~ _1.,3 Co,,-"Ir.i:IO<-~G=,.l~_ ~~ofR~&:>dAS ~ ~ ~ew York. S_ Y_L~

lS. l'oc'l<lt.-=nc 5oL.AJt E!O:2GT. 1. L Y~~~ • .!.=~ ~ of >1e<:b.:c:X:U:'£ .•.....•.~ew York. :So Yo. Tel.. .9, 1>0. 6. bz.c.3•••• po;>. l~.

l3... A ~ 07 TlI::DuuL lU.DunO!'l eo-""~"<'r5, 3. W_S::::yd= niL. ~ 76. 19.).!.~.>3"'~.ro_ ~ V~. 7'B:31luL Co"-,,t:<:TTVTIY .L~?1L-=n. ~DO.lI::it 7'01<Aa .1...'0> OnnrR G~c:zs.J.. E:ia=ntl1, Y. So Toa~ l~ .• pp. ~.-s-:n.l3. rAS E"~-=>USG. Ricb.rd D. MAse,,- eC..~.:sc.::a.!o r= Cc=~, BtdVo. ~. Y.• ~u~ 1945.

:.3. T,,~ ",~CA.N ~ .•.t7J1c:.u. N..>u....'iAC 1~57.C_ s, ~•..-.J O~tory ••••••tlhin.-tDu, D. C. 19.57.

!!1 5::':"'3'T R~'Cc:-tQ~ T.,I..E.L..E3)""Ox Am 'SA~C"'·-:-...O!'C', \C'~ n. III. P2£b!ic.c!~ ?'-O. 249. 'C. S.:~~ Eyc..-o;:£;>Oc 05~ W""':::'::r-O[1, D. c..-$::;>,.

::I.. E .•.·•.:...o•• ·s T A.!'~ L J. Co==--1~. K;-...ot.Q=5e>.! ?::!b'.;,c=nc Co=;>a,,", ~c" York. ~. Y .•~G~ eC;-j~. l~(" -

X!.. TE..!'-X.A!.. ~_! ...:il ..,r.O~ T.I.3:...rs /0...••• :> _.••.l"r_~.&. .•.

7.:';-:<" :t. V. D--nl;:~e. Tr~~uJ;r:u. A",~~..6.tJ' of M<"""'-l<:->l EQP:~ ,..,l. 76. 11lS4,;?- ~~.s2.:!.., G~ T u,--,." (boo-t). ]. R. XNO::.an,]. lUy-e.J'>C=:J ...-::I<;r & ""::.s., L-.::.. !,,,,,..York. !'. V .• l9-tSo

!!-I_ P:l.oP"'C'S.£~ ST •...'-:::tA.2.D Sot....A.& RAD!..A7:.0!II(

Ct:"'T"Y"-S rc,-lit !::St;~Z;:a~O 1.j~lS.. Pa.rrt M.~D ••

•Discussion

". ~: . r _ -r"

W. A- Morgan (Washington Water Power, "Company. Spokane, Wash.): The authors--are to be commended for the thoroughnesswith which they have considered the Iactors'Which may affect the heat balance of fi"conductor that is carrying alternating elec-tric current with the usual prescribed limits .of conductor temperature and ambienttemperature, Particularly. the effect ofsunshine is Doted.

However, we application and operatingengineer is in need of published data orguides which should be forthcoming from .manufacturers of ACSR and all-aluminumconductors as to the effects of loading above' .,...--the currents which give the usual tempera-ture rises. Obviously there isa time-currentrelationship for such overloads, i.e., theshorter the time the greater Isthe amount ofcurrent that may be allowed to flow abovethat "web ••ould just give the desired tem-perature rise, Specifically, there is prob-ably a temperature somewhat above 75 Cwhere confinuous operation would causea reduction in the tensile strength, anothertemperature where the tensile strengthwould be reduced 5% if operated at thattemperature a specifictime, etc. Or. are weto assume that aluminum bas not agreedupon temperature limit and will lose somepercentage of its tensile strength jf operatedcontin1lously at even 75 Cl .

There are data available for determining,how much a transformer may be overloadedunder emergency conditions without jeop-ardizing its Iife, or, in some casesa calculatedIoss-of-ille expectancy may be calculated andis acceptable. Similarly, it is desirable toknow bow much a conductor may be over-loaded during an emergency and for bowlong. For example. assume that one oftwo parallel circuits is out of service andit is desired to carry an overload current(say 2.5% above the rated .value whichwould give 75 C conductor temperature)over the daily peak rather than to cut offcustomers.

Perhaps the steel reinforcing will providefor most of the loss of margin of tensilestrength in ACSR conductors. But, all-aluminum conductor may be particularly...-uloerableto o"erload currents. and. if it is,perhaps we should 1.."110 •• its critical conduc- .,tor temperatures or time-current overloa~characteristics.

~

ilf

.'jI,

l:':. l:':. Georxe (Ebasco &-. ices Inc..Little Rock. Ark.): The :;lutboxsbavecone an e:cc:-ellentjob ;:i utilizin' pre-

",n::n « ,....,.....,..,. 1173u

. -. -

. "';.- .":.~ vious analyses of various componentsoi heat tran5fDission and in presenting asumm:uy in final usable fonn. It appearsthat the a.ccuracy of the new formulas isconsiderably greater than that of the inputdata generally available in the field, espe-cially as regards average surface conditionson the conductors. •

The results _are for a wind velocity of 2fps. """hile this is a relatively low windvelocity, it will be noted from Fig. 2 thatcarrying capa.cify ~ a wind of 2 fps (or .:about 1.4 miles per hour) is about 30%greater than in still air. This may be:dueto the discooti::nity between turbulent andIaminar flow and to the complex interaction.of air currents due to convection and thosedoe to uteP-..3l wind. These factors havebothered all in..-est:igators in this field.

Some of us t1rinJr:that the limiting condi-tion of still air or zero wind should be coveredin conductor heating tables, because thiscondition frequently occurs on hot summerafternoons under hnmid conditions preced-ing a storm, Scch conditions are also re-sponsible foc hip peaks on the powersystems due to full Operation of air condi-tioners,

It woold also be he1pfnl if engineers con-nected ..-i:;::h research on copper conductors .would pr=t:Eg-c= on copper comparableto those 1:1 t:::3 paper on .:lCSR. u tiliziugthe lat= 2..-~ data. on !:eat-traDs-mission =;x:ce::::ts.

It is to be ~ th.t De authors ~"i11continne ~ h>esti,:sa.tions and publishtheir r=!ts.. bcln&~ studies of sleet pre-vention aad ~ :De1ti!lg..~Ia.ss=a. N. Y.•(location "r _-\k:oaResearch Laboratories) isfavorably s>· _;..A for both natural and con-trolled tests cooceraed with the problem ofsleet on cocdcctcrs;

',~.-::

I

R. w. Cas;vciI znd Lawrence Ycle (Com-monwealth ECi..~ Company, Chicago,Ill.}: Thea:cr1:orsare to be commended forpresenting a. cocstrt-ctive paper on an im-portant sci>ject.

The Commonwealth Edison Companyhare recently sponsored an investigation atoae of the universities relative to tempera-ture rise of conductors when high currentsare used in order to melt ice from trans-mission lines. In this study, based onlaboratory tests. a formula was developed.for determining temperature rise of a con-ductor due to a specified current undergiven weather conditions. This formula issimilar in form to equation 7 in the paper.'\\."hile the authors use data developed byMe.Adams for determining convected-heatloss, the stndy by the university indicatesthat slightly different values should beused than those resulting from Me.Adams"work.

A comparison of the temperature risecalculated by each method for a given setof conditions shows th.at the t••o methodsgive different values, This means that acurrent value calculated by one methodas not being harmful to ACSR may actuallyraise the temperature above the desiredvalue'.

We do not say that one method is correctam, .•..e other is incorrect but rnerelv pointOut that additicnal study is advU;ble toliet ... e:tnune l:.~~ proper constants to be used1ll c:a'~" .~... .r .~~au.u~~ :npaature rise, •

D the autbors .•...""lyel"the assumption is

made that the temperature of ACSR shouldnot exceed 75 C. In the interest of makin,the most effective use of ACSR it may beadvisable under some conditions and fora limited time to exceed this temperature,

In order that the users may fully evaluatethe results of doing this, it would be helpfulif data were furnished as to e£l'ect Onstrength and sag cbaracteristics of ACSRif the 75 C is exceeded for different lengthsof time.

This suggestion merely indicates thatadditional information would be bene.fi.cia!.

Earl Hazan (Kaiser Aluminum and Chem-ical Corporation, Spokane. Wash.): Thispaper deals with a subject vital to thoseutility engineers who are faced with theproblem of determining their line capacitieson a realistic basis in the face of phenomenalload growth on their systems. The problem.of determining electrical characteristics ofACSR conductors, has been the subject ofexhaustive Investigation by the ConductorLaboratory of the Department of MeW-Iurgieal Research, Kaiser Aluminum andChemical Corporation. It seems aproposto supplement the data presented in thispaper and to comment on the results ob--tained.

•• • ~- "e ,

The program being carried on by theConductor Laboratory has resulted indata which describe the a-c and d-e resist-ance characteristics of a conductor, its cur-rent rating, overload' characteristics, andcomparison of ratings between bright andblack surfaces. In assessing the data ob--tained it was noticed that the conventionalformulas y !lung an n see erence3 of the paper) could be used with faircorrespondence to test results for a brightconductor, but were not reliable in check-ing results for a black conductor. Furtherinvestigation showed that Schurig and Frickhad developed their formulas for bare copperconductor whose emissivity was 0.5, wlllch.is about double the value for a brightaluminum conductor. This emissivity fae-tor was used indiscrimlnately for aluminumconductors, at the time when ACSR andall-aluminum lines were beginning to beused in quantity. In retrospect it was

(

realized that since the heat lost by radiationusing the Schurig-Frick formulas wastwice the correct value, then some compensa-tion must have been built into their formulafor convected-heat loss.

At this point we made a comprehensiveanalysis of all those conductors which hadbeen tested by the Conductor Laboratory todetermine the best relationship betweenour test data and analytical expressionswhich would describe the conductor per-formance. It was determined that theMcAdams formula (see reference 13 of thepaper) for heat loss from convection gave asat isfactory approximation of observed re-sults within the limits of experimental ac-curacy. This formula, being applicable forthe several wind speeds at which the conduc-tors had been tested. was adopted for gen-eral use by the Laboratory, and it wasrecommended at that time that the currentratings in the Kaiser Electrical Conduc-tor Technical Manual be revised On thatbasis.

• • r -~ '; -;~iL~~~':'(C~s)fl'-luTIJolG FoR>fULAs ; ,'-: .

Our formulas dilr~ ~light1yi~om thosepresented by House and' Tuttle, but theseare roainIy differences ill' form. For ez-ample. it was found that for conductorttmpe:ratures in the range between 40 C and110 C average values may be used for thefollowing constants: 1'/, the absolute vis.cosity of air; PI, the density of air, and X/,the thermal conductivity for air. 'Tbeseconstant values. reduced to electrical units,and substituted into the general McAdamJformula yielded the following equation forbeat Joss due to forced convection in watts/sq inch of surface.

We7.645X 1O-4M[0.32+0.43(355.7 VD)UlJ

- Dwhere

l1!~temper-aturedi.fference between ambientand conductor, C •.

V=wind velocity, £Ps \.":D=conductor diametet,'· in~es

The utility of this form lies in the factthat all unknowns are readily available forsubstitution in the formula.

The corresponding formula for heat lossdue to radiation in watts/sq inch of surfaceis ''''' __ .

Wr=36.8f[(~)(-(.2L)C]1,000 1,000

where

e=em.issivity in per centT=conductor temperature, KT.=ambient temperature, K .

The curren t rating can then be calcul ared,neglecting solar effects, by the formula

{3.77XIO'(W,+ Wc)DI=~ R.u

where

Wr= heat loss due to radiation, watt.s/sq inchWe=heat loss due to convection, watts/sq

inchD=conductor diameter, inchesP-==a~resistanceat the temperature of the

conductor. ohms/l,OOOh

. Now, first of all, how does this set ofsimplified formulas check the more exactformulas presented in the paper? If theeffect of solar radiation is eliminated from

. equation 13 for the Drake i95 MCM 26/1_~CSR, a current rating of 938 amperes isobtained Usingthe formulas presented by theauthors. Using similar formulas, in simpli-fied form. as just discussed, the rating isfound to be 933 amperes, a difference ofabout 1/2~. .

Second, how do the simplified Iormulascheck actual test results for several differentwind speeds and several different conductortemperatures?

Details are listed ill Table VI. of a corn-parison made for three ACSR conductors'whose data were arbitrarily selected {COrti

all of the conductors tested by the labora-tory to date.

,] It will be observed that dose correspond-I ence exists between calculated and test d"t",.• indicating the validity of the forraulns, It

,.--- L- . _

..Ud S~-2.0 fPS

Conductor Teete"eo••dactor I>i6erenu, D'~e=:e.

T~mperature, C C&kalaled Oblene" Per Cent YI<1!J.tH Obltned Per Cc: CaJc:al&t~ Obv.:T~

r- {50, ....•.•. ".1 ...•.. 760 1.7 ,,·. SSS ....•• sso 2.5 ......•. S45 !70 ".2.~\ ina], 54/7.954 MeM....... 15 ..•...... 1.011•... ,,1.020 0.3 1.160 1.1PO.. "'" .0.8 1.1('~ 1.!70 u

. 100.•••..•.. 1.204 ••.. ".1.240 ......•. 3.0 1,39 •....•. 1,~ ..•..•.. 0 .•........ 1.4C3 I,roO O.~

{<60•••••.••• 74.1•••••• 7GO•••••••. 2.& •.•.•••• SOL ••••• S15 .•••••.. I.& ••...••• S(O. __•••• tiSO•••.•••. 1.2

Rall, 45/7, 954 MCM........... 75••••.•... 1.006 .• '" .1.015 .•..•••. 0.9 (161 ...•.. 1.1iO .•.••... O.! 1.155 •..... I,liO 1.3. _ 100 1.1S! 1.210 .....•.• 1.9 1.37& 1.3Ts .••••... 0.1. 1.383 1.~iO ...••... 0.5

{

50 ..•••.•.. 790 : 800 ....••.. 1.3 918 ....•• 9:!O..••••.. 0.2 /;75 ••.••• 6.0 0.6Curle•••54/1.1,033.5MCM..... 15•..•..... 1.0;2 ••.... 1.090 •....•.. 1.7 1.2-(3 1,255 •.•..... 1.0 1,lP? ..•... 1.1S-0•....... 0.5

. . '. 100••••.•••. 1.265 ••••.. 1,300 •.•.•..• 2.8 1.'64 •..•.. I.{gj .•••.••• 1.4. •...•... 1•• 31. •.... 1,4-50 2.0

should be observed, further. that in generalthe test results give higher values of current;rating than do either set of formulas. It isfor this reason that we desire to produce acomprehensive set of experimental data oaall bare conductors.

SoLAR. RADIATION

The effect of' solar radiation bas beenneglected by many authors who dismiss the

_.sun's effect as being negligible at the operat-ing temperatures of the conductor. H.. A-Enos of American Gas and Electric ServiceCorporation proposed as early as 1943 thatthis effect be included in the heat-balanceequation for determining current ratmg ofa conductor. The authors show the effectof solar radiation, and demonstrate that itshould be considered. Our own calculationssbow that this is a valid proposal; that, 0-deed, the sun's radiation is not so small asto be disregarded.

~ the calculation of heat absorbed by theCJ ictor from the sun, however. we have.c ed that the solar constant includedtlie 'small contributions from other heavenlybodies and the sky, Furthermore, the sl.-v.being at a temperature of about -50 C ~so, actually represents a heat sink ratherthan a heat source. For this reason we havedivided our radiated-beat loss into two parts,half of the radiation from the conductor'being lost to the surroundings which are atambient temperature. say 25 C. and halfbeing lost to the sky (on a clear day) whosetemperature is, say, -50 C.

In computational form. therefore. Wr, thebeat loss due to radiation on a' clear davwould be .,

W.-30.8' [(I.£o),~(~)]+

[(~):-(~)']where

T=conductor temperature, KTo=ambient temperature, KT/~sky. temperature, K

In making the computation for thecur~t-carryiDg capacity of a conductor insuo a clear day, therefore, the form pro-rL-:;", by the authors may be carried outwW the slight modification suggested mthe foregoing.

Using tbis equation ••••e have calculated

.FEBRU~RY 1959

the ratings of a few conductors when ex-posed to direct sunlight CJ:l a' clear day,

IThe results indicated a derating of from 2%to 4% for a b7-i.shtconductor. and a derat.ingof from 15% to 18% for a black conductor.In comparing ratings of bright and blackconductors • with and without solar radia-tion, the author-s show that these conductorsmay be derated 1% to 3%. and 10% to g%,respectively. The importance of the solar

. effect is dernCT:!~ted by the close agree-ment between both sets of data.

A-C RESISTA."CE OF Acs.~Coxnccroas

In the caJcnlztion of ==t rating, the a-cresistance of rhe conductor is recnired at.the temperatzre of the =~. Thishas been the elusive =.l::::::!<TK"Il Io: ACSRconductor s because the So:1: of the steelcore bas not been completely d~ed.In checking the curves of FIg. 3 with testdata for four sizes of conductors, r~ .••.ehave tested and which are included i::ItheEc.~e. we find exact agreerneat between theresistance data 'l<'ehave =~"'c~ed andthose presented in the cc..rves,

SonuRv

In summary, then. I believe De arrthorssho-uldbe comroended for ~ ar-.3ableth= data and calcnlating pr-oce:d=es.. Ithink that the simplified tcrn::lS proposed hthis discussion should be considered as alter-native methods for calcnlating ccrrentratings. The sabject of c:alc:I1ati::tgtheeffect of sun on the current raring needs fur-ther clarification with respect to sky radia-tion and sl.-ytemperature, FroaJ1y.I find itinteresting that two separate ~tionshave been studying the S21Deprobkm alongexactly parallel lines. and ..mile om-in>esti-gations have not yet been completed, I mustpoint out that in substance, we have checked,experimentally, the conclusions ~ bythe authors. It is apropos to suggest. there-fOR, that an Industry Committee be formedto consider the saggest.ion already made toour own organization, V:e feel that exist-ing current-rating tables should be revisedto reflect the more realistic values for stand-ard eondit ions of 75 C conductor tempera.t=-e, 25 C ambient temperature, and att0S8\;nd velocity of 2 fps.

W. M. Pickslay (Pacific Gas and ElectrieCompany. San Francisco. Calif.): Theauthors are to be commended for an excel-lent condensation from a large volume ofavailable literature of a relatively simple

and eessv =60<1 of ~'~2'io:l of we CC"-

:rent-~~,,----=e ~c::tci-..ics of C~tr,"e:<.deonduzt ors,

~~e--h= t:r~~.'~Jy =pie:x Cr'-"c·r.-l1:;:, =.c..'in LC=-d. has beea =:Y.lSt ~.J..~.treated bv Uie =-~ of d!=---=io=lanalysis, -Toese b..-c.{,e n<r...di~--Si--.r~=k-s. =6 as t1:~~<-kis =d ~~~ ~erl, as well as tbr-ee othersof i=;.-r..zo:k~ the ~.l. S;•.~c.t.or=.dGr~ ~l Fc£ specific "sol11-tio=. ~ data are Te:iU-~ to inter-rclate ~ numbers, ~ Ic..~ ~.sof sx:1: C=.a bave b=::l n==7ted. Tbe~ f=clas are, ilie::-d"xe. ~c:Jp:' i=1 u;& ns:=!Iy res:=ic:ted i::;. 2.p~&2-tion to a li=n.t:d r~ ~ ~-5. Con-sequ="y. "':-d'e ~ :=iliors =te ~ ..valnes =r=ted by ili6- =pGe f=:ili.7 are i:J. c= ~ -.r-i-";' ~ results;it \E"cc.::d t7e=.1y i::lo-ee...<;e~ f=::!a'svalue ii coo;=ison-s of t!::St :=d cc:::;:;>2-~results ....-i:.h=itab~ " •..-2ti~ 0[ we io-porta:rt ;t=<-:eten ...-e:-e.to be p:::~~=d.

v,-rr.= ~ to r~::i?:!-"!.-=- k-ss fro:::lthe ~cr. the •.~~~-=-s' ~u.:a= a1J r~ to e ez:-:::::'"atzaos-~ca~~=lro~c-~'eat, T6 is ~-y ~-=---:ke ~by for De lz.~ p:-o;x:rti= of ~ a=as-pbere, Le., k Of>= =d =:X=. is tracs-pan:::tt to ti=221 I2r;;":i-n:O ~Gi'"t:O'<C.arr- t=per4I::"e ".-itl: }-,...:~ ~ sea J=dvaries g:-=1y as does ~ t="".--c.t='e ofS<!U0Cl:U&::g t=-cia. ~. theDe! ra&ted heat ...-iIlbe c:o=iC-e:-eb!y re-docr:d ~ the li:= ~ a n..a..~rocky ~ than ~ it: cresses oyc::1cnlti-r-c.U:d fidds.. A mere a=-c.te a-p1essOO for tl:is t= is Pe:1 b: Enos inrefereoce 7 of the paper, The atIt!Y.lr-S'reasons for the appoaeut UOSS ~J3ca- .tion wccl:i be of interest-

It is s::nspectcl that the d'~ed'arises from ~ rdarlTe ~tS of con-l"l!Ctioa and k-adiation-he:zt Joss, ~=tdy cine to ooe, in the simpk c:alcnla-bon. Tbese are of t:be expected order forthe 2-fps c055 ••iud assnraed, Ho~,it bas be= a matter of some sm-priseto tJ:::isd.!scn= t!:at this wrind ..-cloc:ity,crigl=!!ybased tq>= ...-ezthe:rcouditi::os in Schenec-tady, 1". Y~ b LQ28and 1929, is as ~.accepted as it: ~ to Cz"e been. ClCEeexamina.tiao of Us. \\.=~ B=u Gall.for the c=ttal va1lt:. of Calif omia 4ssh<Tt<u that the ~ the =-= Cay,the gr=Ur probabili1y th.al. there ...-ill be .a~e. ~d vclocitie:s zlxrrc the fric...titm layer by the middk of the ~ : -.~."'::-"

s le~:' ~x:.=:-:.:--:-_. -

...oJ

~ce..."~'"ooc~c

Or~ ..0.-cZOW..Ie:.......,J..z...•......

o•...z...u

'"...•..

ISlRtSS.AU'TUA£ STR(NG1H I

OF EC-HI.

I !"1

I

i..'to

0OS 5' n

.....•.IO-HJltI.

IOO-J·dtl.

tOO rz::s "0

TU-O£AA,UR£ ore.e,"s zoo

Fig. 4. S!rHS-flJpfure curves of EC H18 at elevaled ternperetures

Similar conditions should be expected inother areas even of different topographysince on clear summer days the afternoonbreezes appear· to be produced by themorning heating of the ground and loweratmosphere.

It, therefore, appears that when conductortemperature is a limiting design considera-tion, there will be occasions to use consider-ably smaller values than 2 fps for crosswindvelocities particularly when the line is pro-tected by hills, buildings, or trees, and thusbelow the friction layer. This poses a prob-lem in that there is an area between O-fpsand approximately 1/2-fps wind velocitywhere the conductor temperature rise isindeterminate. In this region, convection-beat loss is by a combination of both freeand forced convection. a circumstancenot amenable to treatment with presenttheory.

Because of this indeterminate area, undercircumstances similar to those indicated.the authors' formula 4(B) for qe should beused instead of 4(A). This is perhaps not soimportant for ACSR because of the presenceof the steel core, but is vital for copper andall-aluminum transmission conductors wherestrengths and clearances must be main-tained.

------- -.

••••OOr----

~ IS.OOO ~--~'c--...;...------wc:>..ccW&.. ''',000••....!;;;1'.OOOf-------+---V\-\~~~-----+_-----~•.%..o~'"•......•..I

0;~•..

1·... ·l------+----'-ITr-\-~_:_---t_-----_1

1.000

REFERBNCB

1. thAT TltANSPBlt PImNOlOP.<A (book), R.. C. L.Bosworth. John Wil<y & Sons, I:cc... :S-c••. Yoclc.N. Y., 1952.

.LO-----------~L-------~2--------~.L~~~-~~~~r~~a>€..I.noo; T~TV'U:.T.O£S.~ ------

Fig. 6. Tensile stnnsth of EC H19 ri ~ns km~retu~ (0( V61b~

. lengths of ti •••• Gt tN.t ttmpenture ~

H. E. House and P_ D. Tuttle ; We arepleased to Dote the interest aroused by ourpaper as evidenced by the comments of thevarious discussers, whom we thank for theirremarks. In the following closure, so:neremarks made relative to one discussion mavapply to others and will not be repeated, -

To reply to ·Mr. Morgan, we would firstslate that the 75 C temperature was chosensimply as a reasonable operating tempera-ture. It is somewhat. higher than that. forwhich a new line would normally be de-signed but was Dot intended to indicate alimiting temperatur-e, For both copper andaluminum, the 75 C t=peraf:u..re is one iliatresults in loss of st:r=gth at a very 10.••.ratebut not a zero rate.

Mr. Morgan's request for loss of strengthat elevated temperatures can best be

00.:z:..'"zw«l- I.....:!z..•..

10~( •>=

I•..0 -....z

-r->, ...ue

V•.

00

0 •

. - ~ ....=s ••ced by reference to tlle =illpan~-- .reg carves, F'ig; 4 shows the rupture tw-: •of EC (e:k:ct:ri=l Conductor grade) wireunder'varioos ~ of load and tc_ -pe=.t=e.. For example, at 100 C. a wire<:tXItinnoaslyloaded to 48% of its orig!.ndt=s:le str-~ (==red at room !.trJ-·~) will fall h 1,000 hr; a ~oiG.ing , '55% will cacse iai1C-e i:t 100 cr. :5"~. ,;shows 6e red-=tio::t n strength of EC v,1. \!

~ ternperaznre far various fimes, TI'"t.....,s•.'e ~..b.s are a!1 measured at ·rOO'·1

~tn:re. Thzis at 100 C. a ~ w~c....-vp to 9>3%of its ociPal strength ill.l;;';h. ~% ol.OC() hr, =C. 00% in 10,0001-"

rIg. 6 is ~ to FIg. 5 ezcept t.~.est=-=g6s = P-= =: ~ of the ac.=:!~ st!=.&-o. ~ 6e ~ =..d...:o:o.si..~ T= at 150 C. the w.!: ~~.s,..-t;l decrease i:: I.OOObr to 16,1:).)psi (pocmQs per ~ inch). 87% cI ;05• .<1= of 18,&Xl psi ;,..~ o:I1y1/2 hr a!".~~

rIg..7 is a pbt ~ to Fig. 6 b:rt ro.' .~~l.c::ooti:actoI 2.ln:mim:.m aJlc.y. : 1

"••00I'r-----------~------------~----------~--~--------TD$l.L ~rrarw....-...&U..OY~

••T~TE~U •.•"~S.oooor_----~~~_+------------~----------,_--~------

~ ~~r-----------_+~~~c_----r-----------4L----------...c::>•..•c~r~r_----------_+----~~~~~~~~----~----------~:aw~~..•

..,,

" ~~r_----------_+------~~_\~.-~~----~----------.•.r..o~~ tO~r_----------_+----------~~~~r_~~~----------~~~0;'"w•..

• '=".-------_L-------.,..!.----.:.....--:- •..I.o.---- --

IIO.~ T~T._.T.K&..C.

Fig. 7. TenJiJe rlrtngtb of • typ;at dedric.ol-<onouc:".u •..Fig. S. Tensile s!tensth of EC H19 <!It room temperature for variou$ alloy lit huting fcmpa.~ foe y...oo.u knSlhs of time _~.~.

____ ~ G__m~~~o~f_~~t~.~!~in~g~.~I~.J~ty~d~!~td~t~~~m~p~e~r~a~tu=r~es~ ~.~p1O~~'OX~~t~ ~~ _

rr><S>L£ l'1'OP£Rnu

[C·••"

..r ~oo"TE"P£~ATURE

_ t1>O $00

tf(ATIIJlQ TEIoII"[JtIoTlJ'!'!:. OE~.C

~!~. f Vi..J

.:r-t?'::.Al. ST'IOLS:$-S"TlUoa ~ , II-, FOIt ac:s. ATTDI

A"~O'_

~.I _I v I ,.

I vI r V , I I,

'YI I -J . I-

- YI I'· I

.r",:.,"!; ..0~:::!

I:,..;

o

"

Fi,. 8. Fi,...1r~d-in, CWVt (~ text)01 l't'pUitd stn;u.Jb.in test .t roo.,.tcm~ltwc on no.1/0 Ammall Wi,.G.u,c 6/1 ACSRJtc:r ,hulin, _t

350 C For1/2 ht

this case, at 15)C.De ~ st=gU ..••.•:ndecrease i::J. LO:;() h.- to 22,.9:0 ;S. 9L5S; dits vc:~ d 25;:00 ~ fer 1/2-:3- ~~ z:tfut t=pe::= e.. T= ~~d:1 r::C:::c-tions, as foc t::e :=:c. ~ =~ =dirr::~~

Fig..Sc:~~~1'-~~from 2. ~~ ~~ ~ O:l ::0..1/0 .•...,..--== ~re G<,-~ .:!.CS3.. Lbzt ~be:n ~-e..--!.ed ~ 2. t---:-c ~ e ~ ~5I)CJ·~('2=_ T;::S~~=!3~ro{:. . F>.>~;.tr ~ ~ c!~~ {F~,)),~& ~e =-=-:; ....6 = ±e C?'~',a.

had ~ b:e:1d 1/2 1:: ?_'t 0'j-;{-. J =- at .f5:=C .•8.!ld f ~ 2t ~ d i-:.s ~~ S:=-~JJ.. r--t...h..1e1~c.f,to zero stress ~~~ ee-:'" of c£:Se·;'old.i::::g ~~ T= ~ cc-.esl::.w:; u.e =~ ~g !oarl .~(6t !3 co=ly ~ to fc~). 7bepoint to coserve bere is ~:~ t:Q ;:0 a ~"F ?y:-ua::.=tby ~ of t.::e cr~ razeddti=7.:; u,e pkJt !s 2. =;p,t ~ D-dica ~ t1::at t.::e .fcil t.e::Sic.o lD<!d is ~~~ by u,e steel. The ~g Q-ward be::d 3';:e cnrve s::.:;ws u.e e:5ect.oit!Je 2 T., . '. "" I strc:::nds ~ u;> 2. s1:t2re 01the load,

Su21 a cra.~ ti:::.. !..:.>:.lk2d c:21:nOt been•..is-~-=rl for t::-a='s9co lim:s. bat 1±::sLo.~=.:: easeis;r.=ted to~~ ~lL'iq= C::"2-2C~ 01 •.t.CSR that C2.1:l

a;;:Hf ~ =-'-:<"'=01 a::.C. cit:L:..ica1 JC2.d-:'-1,,' -..7'JI o::Uya ~o:- cn"''''ge in tG"'c2l

~..:-:!~~~ azsd 2. s!7T'1~r .t::U::"~rC""2""t-ge D $2.g-t) ;4JI: r~;'ton of ~~ ~.:tion..

i":! ~7 to ~[r. G-::c:-ge. ~ h-;-e ncced•.:,It c•...;:-~ i:: ~d ve:!o~ at!a:rw ~na; :-::::6 wv.e e5ect t'"',,- "'='= percezrt-~..;.~ ,:~:!ge:s Got. bjg~ .e...!cci:5es. T'h...js:Smcp!<:c 0 F'~.2 =d "'e 0:::-0Ylt b--...Ee.ei; is ~:::;.'b-=t.2~!e ~lT t~ a c1--.:. .•..•ge £-00

ia:::.~ t~ tr!rO::Ue::J.t fo:·w... It i:s t:'1:.-ejat :.:.e ::.i6::tr •.~:ci-~'-:s 1',==--::11 i::J. \'c:-t=

~o~·-------.i:: on :=e Ie-:=: c! ~e C\..·i::H.:=C-....Dr. b'G"t

!1 (7 --=. to l=~ tr.a::Sf:!".Ge gi.= kr-.)Ol)Y{.:·r.c. .-e::y wtll b s;::~e of ..::..!s eta...!.~t~21:.-.t..:l!: a.i:- ~eJ(ciryt..:c2..=.-'~cf nanr-d"I::l't"cc-....:()~ i:J i:-ee ~ is <J tbc:e CJ:""t!er c.f 0.4'1:.• -r.~t:: ~e: cr..cCtX:'tc;-is at 2 ~~~~!-e

';:>e:"c:7:J?; te::J;.c.-a~r:.!'e.. O=d~:rs,. r.-=

~ ~ da.-. ~ is more air movementC= one ~ s:::spect and this, coopled~~ ~ ~ cocld easily reach2 f:;s ~ act:=Ily is an =t:-=ly low 2..Dd

~C£e cccservztive n:kci:ty_ HOWl!"Yer.for ~ C2t !...t .o1.-e convection cool-Cg C= ocly tD ~ beat of th condnctor~ f~ ~(3) "Kill give v cry close=.lts.

'To tzzrn to ~ ~ by ~!r. Caswella=l. ~!r. Ycle. "In: •• ould stress that thec::= i:I ~ cocrpnted resalts by ow-fa: ·'··3~r~~~d~tont..hedi..cc-~.()nare c-"'""~ azd r'-z· they dCer in their ac-=-dCJ' clepe::::.Ci::.g co the particular fieldc:o::Yi,"::i.-= b-:::::::::&=siclered; i.e., one for-~'"' ci:.e:::h6e t.~ r=lts closer thaa the~ =e-c ooe see: cf co~..s. while. fora. Gf=t set, '6e for=1as are reversedIn G6- 2.~ to the actual test~~ es. In a!1 C2..'=. however, it may besaidy str..ed C::at t.b.e accuracy of theULll;xrt:cd r=1t is dependent on the feldCa::a =d is not E:::::irted by the for=las.'IbS is a p...~ t.b.;u~_ Cecrge stated .c=)0~ ~ tbe ~ pa::-"4=ph of his discussion,

Vi"e .ocld ~ erzrphasize there "2S no .an~ to i::x5cate and no assumption wasn=e-f! .~t 75 C lOfd.S the li::niting ACSRt=J=""c..b::re.. It was simply a reasonablec=p:ccise between the frequently usedrl~g:l ternperatnre of 50 C and the gen-aal.'y reccrcznended normal maximum 100C ~C2.ri:Jg teraperatnre, It."as felt ani::r''''=eC~te ternperatnre such as t.hiswouldbe ~~ cseful 0 ~ curves given, wh.iGI weass-..=ed might be csed for estima tion pur-~•..---

We ar e p~=-<;t:<j to have lli. Hazan'sa~f"e==t wi-..b. o:::r results. It is quite=~ir:;;- = e.::.&i== to siffiplify and tab-:::2",€:=-,.-StE.::ts for f=uks f::-cque....,tlyu.<.eda:::o, 'Q;;"=e:-e ~e C"::----re.nt-c2.rrying fon:::l'ulais us~i of:o, a t:.!:lle ,of .alues for kt<Pr/~~l'" = ~ ="}y prepared. In ~e~~yc..-a.~J:l of a ~;;er such as this, ~tl~ is~""2Y; t.::e ~;:esu~ of how =:l\:ch recuctloll:lz:r.12~ :::.e ::;.ai ~ i:I Lbe fOm.'lulas. In th isC::'5~ -..:e f~t it '<'as ~erable to sboW' thee:=;lCc-e oi;'::~=nc:..'>idualpara!Ileters, Ie:n·-

in,; the Ct;rtbcr f!3.SY simpliOCali&n to thereader.

ConsiCen.ble time was spent reviewing theeffect of the earth and sky OD the radiationfrom tbe cooductor with the decision that anexpre;ssio;1in..-ohing the ambient tempera-ture alone (rather than earth, sky, andambient) w-as preferable if the requisiteaccuracy could be obtained iD the final result.This proved to be possible, no doubt partlybecause radiation loss is the smaller com-ponent of total thermal loss. The morecomplex expression proposed by Mr. Hazancan be used, if desired, or even more corn-plicat.ed ooes t.alcing eto account thereflectance of the earth. However, refine-men 15 for i::x:reased 2.CC11.raCYseem war-ranted OI:.t'y in the case of the larger con-vection component of loss.

Some of De foregoing remarks also apply f. "_.

to the d...~0ll by Mr. Pickslay, The "paper was written from the viewpoint of qle------ope=ting engineer, whose chief interest isallowable ccrrent, Therefore the treatmenthas not ~:::sed the theoretical, althougb:ample re!= to fundamental sourcesbave been given, We did not feel. that adiscussion cf the theoretical parameterswould add to the purpose of the paper. Wedo appreciate :Mr. Pickslay's interest. how-ever, and i:I clue course. another paper maybe written to compare t.b.epresent derivablevalues of ~-e dimensionless parameters withprevious recommendations, ,

"\1,-:-..h regard to radiation loss. it is (as MI. ~-Pickslay poizrts out) the smaller part of thetotal loss. even under free-air conditions,when oae is computing on the basis ofmaximam allowable temperature. Fur-ther, the ~ temperature is readily avail-able to an operator "bile earth and sl-ytemperatures are not, Considering thevariat.ion b terrain a given line may traverse,the i~~J:jt:r in most cases of choosingan 2n::"2.E;e earth temperature (or even theworst) at a given time becomes apparent.·Therefore, .••..hile the effect of the earthexists-v-as socrce, sink, or reflector-s-con-sideration c.f it would add complications tothe formula ..:th no useful increase in theaccuracy of the result.

'Wind cocdirions, of course. vary widely inva..•rices ~~ of the country, the- Jocal- -:..- ..topography bxing considerable effect •. Itis aL"O SUIp"ising "hat wind velocities maybe experienced ~ or 50 ft above the groundeven whea, at ground Ievel, dead calm seemsto prevail, True dead calm is a highly un-usual condition but if expected to exist overpart of a iCe. then the allowable current,should be based on this section and theformula 4(B) for free convection wouldprob-ablv be better. For free convection we havenoted the vertical air currents to be aboutOA Ips at tbe usual maximum allowabletemperature so t.b.at even the slightestalmospberic air movement will bring thetotal coavecrion currents out of the 0- to1/2-fps rang e of con= to ~1r. Pickslay,,\s c.w be 2.PPfeciated, we nominal design\"f:Ir<:i~ oi ~ fps is Ye.ry con:<en'ative and notrouble !2::cdd be eXpcr1e:lced if tJUs valueis u5Cd. "\\'e H:cOg7JUe~fr. Picks!a)"s con·cern b tlle C"_<.eof copper or aluminum COil·ducto:-s a::d a rather broad ~\"iew of thecbaracte..-ist.:.:::s of aluminum bas ~n gh-enpre'-iousl~- in this c!osuTe and the outstand-ing \-!rtt;e of .\CSR poi..'1ted out. .

,•iE

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IEEE 1 ransacrions on Power Apparatus and Systems, Vol. PAS· 104, No, 10, Ocrobe •. :I~5,_ ~. 4

SIMPLIFIED HODEL FOR STEADY STATEAND REAL-TIME AMPACITY Of OVERHEAD CONDUCTORS

R. L. Rehberg*W. Z. BlackMember, IEEE

School of Mechanical EnyineeringGeorgia Institute of Technolo~y

Atlanta, Georgia

ABSTRACTRecently the utility industry has recognized that

there are substantial economic advantages that can beachieved by knowing the real-time temperature of aconductor when it is subjected to variations incurrent and weather conditions. Unfortunately. real-time thermal models for the calculation of temperatureof overhead conductors are usually quite complex~This paper proposes a simplified transient ampacitymodel that overcomes this difficulty. The modelpreo i ct s both the steady state and transient thermalbehavi or of conductors that are subjected to a stepchange in current. The simplified modei providesresults that are within 15 percent of a more complex,detailed transient ampacity model.

Parameters which affect the transient thermalcharacteristics of overhead conductors aredi scussed. VaI ues needed for input to the mode 1 areprovided for a wide range of conductor sizes.CaI cu 1ated time cons tants range between severa 1rninutes for a sma II conductor in a moderate wi nd toover one-half hour for a larye conductor in a calmwind.

The real-time ampacity model is sufficientlysimple that i.t can be used to easi Iy predict thetemperature history of a conductor during an emeryencytransient in the current. A fURTRAN program isprovided in the Appendix to aid in solviny thetransient equations. The Appendix also containssample calculations that illustrate the application ofthe real-time model to practical ampacity problems.

INTRODUCTIONSteady state models' for conductor ampacity have

been widely used throughout the electric powerindustry and they remain the backbone for most design

*Presently employed by T.V.A., Norris, Tennessee •

35 ~~ 236-5 A paper recommended and approvedby the IEEE Transmission and Distribution Committeeof the IEEE Power Engineering Society for presenta-tion at the IEEE/PES 1985 Winter Heeting, New York,l,ewYork, Februa ry 3 - 8, 1985. }!3nuscript submit-ted August 31, 1984; made availab10 for printingJanuary 10, 1985.

and operating' decisions relating to the thermalbehavior of overhead systems. These models assumethat each change in conductor current is 1mmedi ate 1yfollowed by a corresponding change in conductortemperature. In reality the temperature of theconductor changes gradua lly over a peri od of timeafter a change in current. This delay is a result ofthe thermal capacitance of the conductor which is afunction of environ~ental and physical factors.

Real-time ampacity models account for conductorcapacitance and they therefore can revea I increasedsystem capacity, particul arly under emer qency loadinyconditions, that would otherwise remain \i'nutilizedwhen a steady state ampac i ty model is employed. Theenergy stored in the conductor 'duri ng the time of thetrans i ent is often su ffi c i ent to provi de the operatortime to make more effective load management decisionsbefore the conductor reaches a predetermined limitinytemperature. Armed with a real-time ampac i ty model,an operating engineer can efficiently and safelydistribute eneryy over the transmission networkwithout exceedi ny sag I imits or without jeopardi zi nythe strength of the conductors. .

A real-time ampacity model can provide otheradvantages to an ope rat i ny engi neer. Steady stateampacity models, ,ased on a set of conservativeweather parameters, may often predi ct that major tielines between utilities operate at their ultimatecapacity. If a real-time rating program is applied tothe same lines, it will frequently reveal a strikinglydi fferent conclusion. By using actual weatherconditions and by accounting for the thermal capacityof the line, the real-time program can show a reservecapacity for transmission Of power and thereby providethe operator with a potential' to generate increasedrevenue.' .

A real-time ampacity program helps not only theoperating engineer, but it also provides a useful andvaluable tool for planning and design engineers. If aplanner or designer has a knowledge of the transientthermal behavior of the overhead network, he is betterable to make capital intensive decisions. Forexample, a real-time ampac ity model could yreatlyinfluence the decision between purchasiny additionalright-of-way and installing a new line or simplyutilizing an established line coupled with resagging,reconductoring or rebuilding the existing towers.

The initial work on the steady state ampacitymodels first appeared in.the 1920'S [1-5], even thouyhextensi ve work had been completed 'prior to that t imeon the convective heat transfer from cylinders toair. Thermal models for the calculation of- theconductor temperature became more sophisticated [6-12]and riatu ra lly more comp Ii cated to use. Rea l-t i"".

0018·9510/85/IOOO-2942S01.00© 1985 IEEE

•

Itinys of ove~head conductors 'were introduced [13-21)1 the 1950's. At the present time most transientnpac~' 0 models are so complex that they require theid .' digit~l computer for their solution. Theume. • complexity associated with a' real-timeatiny ~rogram IS a distinct disadvantage and it,will~viously discouraye some from .ttempting to use real-ime rating results. ", '

This paper describes a simplified thermal modelhat ~ttempts to overcome this problem. ~ It proposes a.i mpIifi ed rat i ng program that can be used to predi ctloth steady state and transient conductor:emperatu res. The fi na 1 product is a simple computer .Jrogram that requires a minimum a~ount of program 0'

j nput and provi des both steady state conductortemperatures as well as the, complete 'transientbehavior of the conductor including a predicted timeconstant when the conductor is subjected to a stepchange in current. A Cbpy of a FORTRANprogram thatcan be used to solve for these parameter-s fs includedin the Appendix. While .the assumptions made in thesimplified analysis pre~ent consideration, of time,arying weather conditions" the analysis, issuf f i c ient Iy complete that [t can be used over a wide~ange of conductor des fgns and for a comp Iete set ofweather conditions. . ,

millRY "The time varying temperature of an energiied

over-need conductor can -be determi hed by app Iyi ny thepr t nc tp l e of conservation of energy' to a unit 'lengthof conductor. T)1e re su It. is an energy ba 1 ance whi chequates the di fference between the energy input intothe conductor and the eMergy transferred from thesurface of the conduct or to the energy stored withinthe conductors, ,Qstor~d' The maj or contri bu~ i on tohei' •........input to the conductor is a result of' I R heatge \ion within the conductor •. By, comparison, asomE!-it'l1at minor cont r ibut ion to energy tnput vto theconductor is the radiant solar energy absorbed at thesurface of the conductor, Qsolar' The two means bywhi ch heat is removed from the conductor' are the,convection to the ambient, air, Qco v» and emittedradiation to the surroundings, Qrad' ~he conservationof energy, therefore, stipulateS that

,.Q ' .: 12R '+ Q ~ ' 'Q (1)

stored - AC' solar - rad - conv

To carry the ane lys i s further. severalassumptions can be made at this point. Flrst theconductor is assumed to bel isothermal at an averagetemperature, T, at any instant in time; That is, anytemperature gradients within the conductor areneglected. This assumption is reasonable because theconductor consists of, met e l l ic strands that are goodconductors of both'cu~rent and heat. As long as thestrands remain in. good thermal contact, the radialresistance to the conduction of heat,to the surface ofthe conductor is far less than the resistance to heatflow from the surface of the conductor. Thereforetemperature gradients 'within the conductor will benegligible. However, if,' the conductor temperaturereaches such a l evel, that the strands' begin toseparate from each other and bird caging becomesevident, then the isothermal assumption wi II becomeless accurate and temperature gradients within theconductor must be taken into consideration.

A second assumption considers the AC resistanceof the conductor to be a linear function of conductort.f!.lJlperature. This assumption is very accurate in the

]e of temperatures expected during normal operationoverhead lines. Errors which result from this

assumption are practically nonexistent fortemperatures between OOC and 1500C. At temperatLlresnear 2~00C the errors caused by using a linear

2943

~",,-.'

res i stance express i on rather, than II more accurate"hi gher order curve. can resu I t in Pf8di ct ectemperatures which are in error by as much as '5 C [22]for a typical conductor under reasonable operatingcond it ions , Furthermore, if· the simplified analysis1s used to calculate, time constants when emergencycurrents. produce conductor temperatures aboveapproximately 1500C, sizeable errors can result fromthe assumption of a linear resistance-temperaturerelationship. ,

,To simplify the, radiation terms in theccnservat icn of energy 'equation, three additionalassumpt ions are made. Fi rst, the surroundi ngs whi chcontri bute i nci dent radi ant energy on the conductorhave an average temperature, T ,which is the same,asthe ambient air temperature.~ Second, only directsolar energy is considered and solar energy which isfirst reflected from the surroundings before strikingthe conductor is neglected. ' A final Simplification isprovided by using a two-band model for the radiationexchange. -The propert i es of the conductor importantto the energy balance are the infraredemi s s iv ity, e: , which ,influences the amount ofradiant enerJy emitted from the conductor and thesolar absorbtivity, a ", which governs the amount ofthe sun's energy ttrat" is' absorbed by the li ne ,Finally if KirChhoff's radiation law is applied, theemissivity and absorptivity of the outer surface ofthe conductor can be equated or e: = a •" ,By, app iyi ng these assumpt ~ons, s the terms inEquation 1 can be, written in mathematical form. Thestored ener~y in'a unit length of conductor is

Q ,dT (2)stored = m c~ dt

where m' is the mass per unit I ength of conductor andcis the spec ifi c heat at constant pressure of thecGnductor material. ,For a composite conductor such asan ACSR conductor consisting of one material used forload bearing purposes and another material for currentcarrying purposes, the m'cp term is calculated asfollows:

m'c = (m'c) + (m'c )p p st p alum

'The mass of each component per unit length of theconductor is a commonly tabulated value which isavai lable in the Tables of Chapter 4 of Reference23. . Recommended values for the specific heat ofconductor materials are

(3)

cp 954 J/lqj.oC for aluminumcp 424 J/kg.oC for coppercp 477 J/kg.oC for steel

The, heat generated by the current passing throughthe conductor becomes

2 12(A + BT) (4)I RACwhere the AC resistance has been replaced by a linearfunction of the conductor temperature. The symbol, Ais the AC resistance of a unit length of conductor atuOC and the symbol B is the temperature coefficient ofresistance which describes, how rapidly the ACres is tance changes with temperatu re. If B = 0, theCOhductor is assumed to have a resistance that isindependent of temperature. Values for A and B mustinclude effects such as lay of the strands, skineffeCt and proximity effect, if they are important.Discussion of these factors is included in Chapter 3of Reference 23.

The absorbed so I ar energy per uni t I ength ofconductor 1s

-,f ::---:,

": !i:Ij "

I"

II;i!

~ ;.~

.• t-I'~ if.

, 'i •£i J 'E .I:: ,;

! : ,"

" u:' -Ii: ;~:i;~!,'tt'i-~ ,~

];f"~ '1::,~,

'Ii~-...

, ~~.j.

i i, ~i' ~

1\ ':11

1 ~;t'I ~~. "\:.

r

tI

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'(

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, ',.-)

-2944'I

Qsolar "' llas Q~~n= DcsQ~~n ' (5)

where Q" is the solar energy per unit area incidenton the ~HPfdce of the conductor and 0 is the conductordiameter.

The convective heat transfer rate per unit lengt~of conductor is •

Qconv = 11 Dh(T - T...l

where his the convect i ve heat trans fer coeffi c i entwhich is predominately a function of the velocity anddirection of air across the surface of the conductor.

The net radiant exchange between the surface ofthe conductor and the surroundings at atemperature T~ is,

Qrad = nDc10(T4 T~4)

whe2e ~ is the Stefan-Boltzmann constant (5.67 x 10-8W/m ·K ).

Substituting Equations 2 and 4 through 7 into theenergy balance given by Equation I, results in anequation which can be solved for both the steady stateand transient temperature of the conductor.

12(A+BT) + DcsQ~~n- nDh(T - T...l

4 4- nDc10 (T - Teo )

Equation 8 'is an ordinary differential equation'that can be solved for the temperature, T, of theconductor. Unfortunately this equation is non-linear,as a, result of the emitted radiation term, and asimple, closed-form solution is not practical.However, if the radi at ion term could be "linearized",a simple solution does exist. Fortunately conductorsoperate over such a relatively limited temperaturerange that linearization of the radiation term can beachi eved wi th an acceptably sma 11 error in thecalculated conductor temperature. Linearization ofthe radi at i on term is made even more acceptab 1e whenthe influence of radiation on the conductortemperature is considered.

Figure 1 shows the percentage of energy leaving aLinnet conductor (26/" 336 kcmil) loaded at aconstant current of 555 amps by beth the convect i veand radiative modes of heat transfer as a function ofthe wind velocity. The two upper curves in Figure 1show the conductor temperature for two conditions:one curve2 assumes an incident solar energy rate of1000 W/m and the other' shows the conductortemperature when no solar energy is incident on theline. These curves show that i nc i dent so Iar energycauses the' temperature of the Linnet conductor toincrease by no more than 100C at low wind velocitiesand only about 20C at higher velocities.' The lowerportion of the figure shows that convection representsthe vast majority of heat removed from the conductor,partlcularly at moderate wind velocities. For \~indvelocities above 3 m/s (6.7 mph) the emitted radiationfrom the conductor accounts for approximately 1Upercent of the ener~y leaving the line~ These factorssuygest that linearization of the emitted radiationterm wi 11 not cause unacceptable errors in theresulting analysis.

The non-linear radiation term in the energybalance, Equation 8, can be replaced with a tenn thatis linear with temperature or

dTm'cp df

4 4T - Teo = E(T - T~) (9)

where E represents a consta~t. Ihe value for E can bedetermined by plotting T - T as a function of

T - T as shown 1n Figure~. Typical valuesGO

(6 )

90°

Ua,0.~UJf- 60a::0f-U::>0z0u

300~ 100~£...a::0

75f-U::>0z0u 50~a::u,>- 25(!)a::u),zUJ

00

VELOCITY (M.P.H.)10 155

~,0/

I~

i~

Iig(i~~

i~,I~·. .

II~~,Ir-~'f!,Il~ti-

~>.-r&~

--i1~¥

8 102 4 6 12

(7)

(8)

10." - 122 468

VELOCITY (MIS)

Fioure 1. Steady State Temperature and Percent ofEnergy leaving a linnet Conductor as aFunction of Air Velocity.

for T ranae 'between OoC and 40°C and conductortemperatur~s usually fa II between oOe and lOOoC abovethe ambient air temperature. Selecting two points on

. the curves shown in Figure 2 is sufficient todetermine values of E to be used in Equation 9. Ifthe linear curve and the fourth order curve are made

35

30I

FOURTH ORDER CURVE (T.,:400 C)LINEAR APPROXIMATION (T.,: 40° C)

2M- FOURTH ORDER CURVE (T.,: 20°C)LINEAR APPROXIMATION (T.,: 20°C)FOURTH ORDER CURVE' (T.,: OOC)LiNEAR APPROXIMATION (T.,: 0° C)

I. 20~

...Q>< 15~I•f-~ 10

5

0a 25 50 75 100TooT•• (OC or K)

125~~¥:

Fiyure 2. Linearization of the Radiation Emitted from -~an Overhead Conductor. _fl

"'-",~~ =e~~'~i.''''~

to f nt er s e .c at values of T -T equal to 1000e andOOC, the values for E are,

...

E 1.95 x 108 K3 for T 400e

') E 1.65 x 108 K3 for T" 2goeE 1.38 x 108 K3 for r: o e

These three va Iues call be used to express E as afunction of T so the linearization can be used for anarbitrary value of T 'The result is...

E = 1.38 x'108 + 1.39 x 106 T (10)...for T in °e and E in K3• The linearized radiationterm becomes

T4 , 1..,4 = (1.38 x 1~8 + 1.39 x 106 T.J(T - T.J (11)

for the range of temper.atures encountered in the caseof energized overhead conductors.

, With the linearized radiation term, Equation 8now becomes a linear, ordinary differential equationand a sol uti on for thecbnductor temperature can beobtained by conventional 'mathematical methods. Forthe analysis and results which follow, we will assumethat initially the conductor carries a preload currentof II and that at time.t = 0 the con~uctorissubjected to a step change ln current to a flnal valueof 12, The initial steady state conductor temperaturecorresponding to the preload current II is T1• !hefinal steady state conductor temperature correspondlngto the final overload current 12 is T2' The'initialcondition necessary to solve the differential equationis therefore

T = T1 @ t = 0 (12 )

Finally the values for m', c , h, T ,£, £1' and0" are all assumed to remaiR constant Juring the

-r-r--; ,t ~MRsi ent response of the conductor •."••.J The solution for the steady state temperature of

...,.the conductor can be 'obtai ned by set t i ng dTfdt = 0 andsolving Equation 8 for 1. The initial steady stateconductor temperature for the preload current II is

I2A' DO"1 , + £s sun

where

(13)

A = A + BT ... (14)

Similarly the steady state conductor temperaturecorresponding to the overload current 12 is given by

2 • "12 A + £s D 0sun(15)T..

Duringtemperaturebetween thetemperatureconductor is

the'transient portion of the solution, theof the conductor varies exponentiallyinitial temperature Tl and its final

T2' The time constant, tc' for the

m'c p (16 )l1hD + £ll1DaE I 28- 2

The transient temperature of the conductor which is( initially energized to a current of II and at t = 0 is

subjected to a step change in current to 12 can beexpressed in terms of the time constant as

(17 )

~945•• ,J-,_ •

The time constant of a conductor ,1s a ~impleparameter whi en can be used to quant i tati ~e lypredi ctthe transient thermal behavior of, an. overheedconductor. The value for the time constant physicallyrelates a time in which the conductor will respond to63 percent of the total temperature rise when it 1ssubjected to a step change in current. ' Larger valuesfor the time constant are indicative of a conductorwhose temperature responds more slowly to changes incurrent., while small time constants are indicative ofcondi t ions whi ch provi de a rapi d change 1n conductortemperature •

Equations 13, 15, 16, and 17 reveal theparameters whi ch i nfl uence both the steady state andtrans i ent thermal behavi or of energi zed conductors.The single parameter which proves to be,' the mostcritical in determining the time constant andtemperature of the conductor is the convective heat

"t r-ans Ier coefficient, h. While the variation in theheat transfer coefficient is explored in'greater Aepthin the next section. it is important to note here thatan increase in h wi 11 I ead to lower conductortemperatures (see Equations 13 and 15) and sma)lervalues of the time constant (see Equation .16). 'Thevalue for h is influenced mostly by the velocity of,the wind across the conductor and to a l~sser degreeby the direction of the wind as it crosses theconductor~

The weather has other, less important, influenceson the thermal behavior of .the conductor.' Theintensit~ of the sun ~~creases ~he temperature of theconductor. although_ it does not affect the timeconstant of the conductor. That is. the, response "QJthe conductor to a given change in current isindependent of the i ntens i ty of the sun even thoughthe initial end ultimate steady state operatingtemperatu res of the conductor depend upon theintensity of the sun at the ,location of the line.

The va I ue for the ainb ient ai r temperature has amodest effect on the thermal behavior of theconductor. The va 1ue for A' changes wi th T.., (seeEquation 14) and the value for E is also a functionof T (see Equation 10).

""The product of the mass and specifi c heat of theconductor i nfl uences the time constant of theconductor, but it has no effect- on the steady statetemperatu res of the conductor. As ~xpec~ed, 1aryerconductors contain a greater thermal lnertla and theyrespond more slowly to a change in heat input.

Examination of Equation 16 reveals severalinterest i ng cone 1 us ions about the va I ue of the timeconstant. All other fdctors being equal. the responseto an emergency current transient is the same duringthe daytime or the ni ght i me; that is. tci s not afunction of Q" • The time constant is also not afunct i on of 1.'h~ pre load current ~ II' and if theresistance of the conductor is assumed independent oftemperature (6 = 0). then the time constan~ is notinfluenced by the overload current, 12' Stnce thechange in conductor resistance is small over theant i c i pat ed ranye of conductor temp~rature~, we wouldexpect the time constant to be practlcally lndependentof the preload and emergency currents during thetransient period. Finally.' since the emittedradiation plays a minor role in removing heat from theconductor when compared to the convect ion, we woul dexpect t to be most affected by the weather asspecifiect'by the wind velocity and direction and lessby the ambient a i r temperature, the conductor currentand the radiative properties of the conductor.

At this point it is natural to question theaccuracy of the simpl i fied model, p~rticularl! ~heerrors caused by linearizing the emltted radlatlonterm. The, sophisticated thermal model reported inReference 20 has resulted in a complex computer

I

• 2946t

program callable of predi ct i ng conductor ampac it i es.The comp l ex program is not limited by the assumptionsused in the simplified analysis. The complex programretains the fourth order radiation term, it considersconductor and air properties to be functions oftemperature and it Cdn calculate the conductor thermalbehavior for aay variation in sun intensity, weatherconditions and conductor current. Using this programas a standard of comparison, it is easy to determinethe errors that result from the assumptions used inthe' simplified analysis.

Figure 3 shows the comparison between the resultsof the complex analysis and the simplified model whenthey are app lied to two different conductor sizes.The first case is a Linnet conductor (26/7, 336 kcmil)with no incident sun, a cross-wind of 0.61 m/s (2ft/sec), a preload current of 555 amps. and anemergency current of 832.5 amps. These currentscorr-espond to an emergency current overload of 5U.pe rcent (12/Il = 1.5). The complex program yields atime constant of 10.03 minutes and the simplifiedanalysis provides a value of tc from Equation 16 of10.83 minutes or a difference of 8 percent. Thedifference between the steady state values for Tl andT2 given by E9uations 13 and 15 and values from thecomplex analys~s are less than 40C. .

As an example of results for a larger conductor,a Falcon (54/19,1590 kcmil) conductor was selected.The initial current was 1525 amps and the finalcurrent was 2288 amps, or 12/11 = 1.5. As in the caseof . the Linnet conductor, the calculations wereperformed for no i nc i dent. ener qy from the sun and awind velocity of U.61 m/s (2 ft/sec). The simplifiedanalysis provides a time constant of 30.6 minutes andthe complex model gives a time constant of 26.5

175r-------------------------------------,555 AMPS, t,= 10.0 MIN555 AMPS,t,= 10.8 MIN

150

t)e.wa::~ 125I-~a::wc..~WI-

100

FALCON' ~= 1525 AMPS,I,= 26.5MINFALCON li= 1525 AMPS,I,= 3O.6MIN

NO SUN~.=0.7 -I =0.5 T••=25°CCROSS FLOW WINDV=0.61 MIS (2 FT/S)r.zr, = 1.5

75o 120 .150

Figure 3. Comparison of Results Predicted by ComplexAnalysis (Ref. 20) and Simplified Analysis.

minutes or a difference of 15 percent; The differencebetween the steady state temperature values were lessthan 70C.

Numerous other comparisons were made between theIlredictions of the simplified analysis and the morecomplete, complex model. For all cases considered thesimpl Hied analysis provided values for steady statetemperature rise above ambient that were within 10

;;f

percent of the more accurate mooel. ,.rhe· Simplifiedanalysis also predicted time const ents that wen~consistently within 15 percent of ~he values providedby the complex model. A sumnary of these comparisonsare provided in Table 1.

Considering the magnitude of errors that resultfrom the si mp1 ifyi ng assumptions, the simp Ie ana lys isin the form of Equations 13, 15, 16 and 17 provides astraight forward and accurate way to determine thethermal behavior of an overhead conductor withoutresorting to a complex digital computer solution.However, the solution of these equations requires aknowledge of the convective and radiative rates fromthe surface of the conductor. These two modes of heattransfer are discussed in the fQllowing paragraphs.

RadiationThe two radiative' properties. needed in the

thermal model are the solar ana infrared 'emissivity ofthe surface of the conductbr. The emi ss i vity is theratio of the radiant energy emitted by a surface tothe radiant ener qy emitted by a black sur-r ace at thesame temperature. The emissivity depends upon the ~material of the emitting surface, its temperature, "surface condition and wavelength distribution of the 1emitted energy. Since the temperature of a conductor ~,'rarely exceeds 1500C, the.' emitted energy lies

ipredominantly in the infrared wavelength ranges. As aresult, the appropriate emissivity for use in the !~emitted radiated energy term is the infrared;emissivity; \'.~- !

Table l. Comparison of Time Constants Calculated byComplex Analysis and Simplified Analysis.

Conductor Daytime Condit~ons Nightime Conditions(Q" . =1000 W/m ) (Q~un = 0)sun _

S;'mple Complex Simple ComplexAnalysis Analysls Analysis Ane lys i s

lPartrldge 8.U4 7.86 9.26 8.64

Linnet 9.35 9.09 10.83 10.03Hawle 11.81 11.41 13.86 12.56

Roole 13.83 13.36 16.34 14.73

Drake 16.44 15.83 19.50 17.44

Finch 19.92 19.00 23.90 21.13

Martin 22.66 21.5U 27 .47 23.92

Falcon 25.14 23.86 30.63 26.50.- ,

I2/I 1 = 1.5, &1 = 0.5, £~ = 0.7 ,11 Value based op 75°C conduct~r temperature,

T = 250C, V = 0.61 m/s (2 ft/sec) cross flow..• .. -

Two studies [25, 26] considered a la'rge number ofACSR samples removed from service. The results showedthat the emissivity of the aluminum ranged between0.23 for a new conductor to 0.98 for an aged, heavilyoxidized surface. As expected, the measured

'emissivity data showed -a Significant amount ofscatter. Nevertheless the emissivity values can bepredicted with enough accuracy for the purposes of anapproximate ampacity model. The recom~ended curvefrom Reference 25, for ACSR conductors energized abovel~ leV in most industrial, as well as rural atmospheresis

0.70 YJl 0.23 + 1.2Z + Y (l8)

.-

{

where Y is the age of the conductor in years. For, ACSI{ conductors energized below 15 kV, the emissivity

variation with conductor age was determined to be1.38Y

&1 = U.23 + 75.5 + Y~.....J

for 0 ( Y ( 95 •like aluminum conductor!, the infrared emissivity

for copper conductors is a function of the surfacecontamination and the extent of oxidization of theconductor surface. The following values arerecommended [23 and 27] for use in ampac itycalculations utilizing copper conductors.

(19)

0.800.50U.300.03

for black, heavily oxidized surfacesfor normally oxidized surfacesfor lightly oxidized surfacesfor polished, new surfaces

-The incident radiant energy on the conductor liespredominantly in the wavelength range from the visibleportion of the spectrum into the ~ear infrared.Applying Kirchhoff's radiation law WhlCh states thatthe monochromatic absorptivity and emissivity of asurface are equal, the parameter which dictates thepercent of the total incident _ solar energy .tha.t . isabsorbed by the conductor is therefore the emt s s tv i tyin the short wavelength ranges. For purposes of thispaper this emissivity is - referred to as th.e ~o~aremissivity, & • The trend in the solar emt s s t vt tycan be predi hed wi th some reI i abil ity by observi ngthe color of the conductor. Surfaces which are highlycorroded and dark in co 1or tend to have va I ues ofemissivity approaching 1.0. Hore polished and hiyhlyreflecting surfaces have much lower emissivities •.

Values for the solar emissivity for both alum1numand copper conductors can be approximated by using the-------,~ts presented in Reference [29]

\.

W

with the restriction that & <1.0 •The final radiative parameter that influences the

ampacity and transient rating of an overhead c~nductoris Q" •. the rate of solar energy per unt t areainci~~Rt on the surface of the conductor. Thisparameter is a complex function of the orientation ofthe line relative to the pos it lori of the sun , theextent of cloud cover and the composition of theatmosphere. A detailed discussion of these parametersis presented in Part III of Reference .16. T~eincident solar energy zxternal to the at~osphere 15approximately 1353 W/m. The solar r-adt at t on thatreaches the surface of the earth is part i allyattenuated by the atmosphere and it is composed of adirect or beam component and a diffuse component. Forthe purposes of a simplified analysis, it issufficient to consider only the di rect component ofradiation striking the conductor and to consider onlya constant value for incident solar energy. Theresults shown in Figures 4 and 5 aid in selecting asuitable value for Q" • Figure 4 shows U.S. averagesummert ime i nci dent s~21 ar energy va 1 ues measured atthe surface of the earth. Figure 5 shows the sameval~es for a winter mon~h. The ~aximum U.S. valul fori nC1dent solar energy 1s approx 1mate ly 1000 W/m andthis value will be used in the illustrations whichfollow to give an indication of the greatest effectthat the sun can have on rat i ngs of overheadconductors.

~."~V An accurate model for determi ni ng the convect i ve

heat transfer coefficient is imperative for anaccurate predict ion of the thermal behavior of anoverhead conductor. Unfortunately the convective heat

2947

-------------------------.----------------~

Figure 4. Approximate Solar Energy Per Unit Area in,-W/m~ Incident on the Surface of the EarthDuri~g June (Adapted From [28]).

Figure' 5. Approximate Solar Energy Per Unit Area inW/m~ Incident on the Surface of the EarthDuring February (Adapted from [28]).

transfer from a conductor is a complex phenomena thatdoes not easi ly lend itself .to a simple analysis. Asthe wind velocity approaches zero, the heat transferfrom the conductor occurs bj free convection and theconvection heat transfer coefficient in terms of theNusselt number, Nu, is given by a functionalrelationship which can be written in terms of theGrashof number, Gr, and the Prandtl number, Pr, or

where

Nu = qGr,pr)

Nu = hD/j(

3ye(T - T.JD

2v

(20)

Gr

and=~Pr k

For common sizes of overhead conductors and forsurface temperatures between OOC and 1000e it can beshown that

and for this range of GrPr the Nusselt number for freeconvection to air from a horizontal cylinder is given

2948

by [27]Nu = 0.53 (GrPr)1/4 (21)

-t.to the axis of the conductor given ~y Equation 2~.

An approximate expression for the forcedconvection heat transfer coefficient can be obtainedin terms of the wind velocity and the conductordiameter once the average air properties aredetermined. Usin~ air properties at an average airtemperature of 50 C, the express i on for the forcedconvection heat transfer coefficient for flow of airperpendicularly across a horizontal cylinder is given'~ \

2 1h = 0.~272 10[2.217+0.652 logVO+0.0355(logVD) ] (27)~

where V is the wind velocity in m/s and 0 is the outer:diameter of the conductor in m. t

RESULTS ~-.. !JThe simpl ified thermal model for the benavi or of.*'

overhead conductors permi ts the ca 1cu tat i on of both)approximate steady state ampacity values and tiffi~constants for a wide variety of conductor sizes an!:i:1environmental conditions. To t l l us tr at e the use or~the simplified. analysis fora range of conducto~~sizes, ei ght represent at i ve AG?R conductors wer~selected between 267 kcmil and 1590 kcmil. Th~properties of the conductors are listed in Table 2.'4Using these eight conductors, the free convection hea~transfer coefficients calculated by .usirig Equation 2~are plotted in Figure 6. The forced convection heat.ltransfer coefficients as a function of cross-flow win~velocity for the eight conductors can be determined bf1using Equation 27 •. The results are summarized il-.Figure 7. ..

A detailed study of equations and the parameterswhich are used in these .equations shows that th~convective mode of heat transfer completely dominate~the heat transfer leaving the conductor. -Therefor~those factors whi ch di cate the va 1ue of the convect h~heat transfer coefti cient have the greatest i nfl uenc~on the ampacity of an overhead conductor as well asihow that conductor responds therma lly to a change iicurrent. Whil e the conductor emi ss i v ity , absorpt i vi t::cand incident solar flux affect the temperature of th~conductor. . the i nfl uence of these parameters o~thermal behavior of the conductor is secondary to tt-,~influence produced by the convection parameters. i

12 .~.

JJ~

i~\"~

HORIZONTAL CYLINDER IN AIRAVERAGE AIR TEMP = 50° C

This expression can be further simplifiedthe properties of air are constant at antemperature of approximately 500C.•

by assumingaverage e i r

10

6

4L- __-L1 -L -L -L ~ j20 40 60 80 IOC~

T-T.(OC) 1Free Convecti on Heat Trans fer Coeffi ci ents f ~Typical Overhead Conductors. I

~•I~f;

Figure 6.

k = 0.0272 W/m~C0.896 x 108 1 _

m3•oCPr = 0.71

v = 1.85 x 10-5 m2/s

~2

"

Subst i tut i ng these propert i es into Equation 21followed by simplification results in

r - Th = 1.287 ( ~ )1/4 (22)

when T - Tis in °c a nd the outer diameter of theconductor.~D is in m.

A computational difficulty exists in freeconvect i on that does not exi st in the case of forcedconvection. Equation 22 shows that the freeconvection heat transfer coefficient depends upon the"t emper atur-e of the conductor. However, thetemperature of the conductor cannot be calculated fromEquat i on 13. until the va 1 ue for his known.Therefore. the problem requires an iterative solutioninvolving repeated calculations of h ·and T untilconvergence is satisfied. This difficulty does notarise in forced flow. because the convective heattransfer coefficient is independent of conductortemperature as long as thermodynamic properties of airare assumed to be independent of temperature. Toavoid the iterative procedure, the computer program inthe Appendix assumes a value for T - T of 500Cwhenever predicting conductor temperatures in freeconvection conditions. . Therefore. free convectiontemperatures and time constants computed ·by theprogram are to be considered as only approximatevalues. If a particular problem involves conditionswhich produce a conductor temperature rise aboveambient that is significantly different from 50oC,then an iterative proce~ure i~ suggested for moreaccurate results.

When the wind velocity across the conductor isnot zero, the heat transfer to the air occurs byforced convection and the relationship for the Nusseltnumber becomes a function of ·both the dimensionlessReynoldS and Prandtl numbers or

where

Nu = g(Re.Pr)

Re = ~ y .

(23)

(24)

For forced convection from a horizontal cylinder toair flowing perpendicular to the axis of the cylinder,the Nusselt number correlat-ion can be estimated by theexpression (See Ref. 16).

Nu=10[-0.07043+0.3153 10gRe+0.03553(logRe)2) (25)

For wind di rections other than perpendicular to theconductor. Equation 25 can be corrected by us i ng theexpression [16]

NU{w) _ (26)Nu(w=O) - 1.194 - sinw - 0.194cos2w + 0.368sin2w

where w is the anyle betw~en the normal to the· surfaceof the conductor and the direction of the air flowingacross the conductor. The denominator in Equation 26,Nu(w=O). is the Nusselt number for flow perpendicular

fable Z. Propertles ot Common ASCI< Conductors

Conductor Dia* Area* Strandi ng I".ass* Mass* AxlO~* Bx107** m'c ***Designation Steel Aluminum p

m kcmil kq/m kg/m orm/m ohm/m > °c Jim' °cPartridge 0.01631 267 26/7 0.1726 0.3750 1.885 8.369 440Linnet 0.01831 336 26/7 0.2165 0.4719 1.493 6.627 553Hawk 0.02179 477 26/7 0.3081 0.6697 1.050 4.721 786Wook 0.02482 636 24/7 0.3259 0.8929 0.7995 3.563 1007Drake 0.02814 795 26/7 0.5134 1 .1161 0.6378 2.818 1309Finch 0.03284 1113 54/19 0.5596 1.5700 0.4656 2.054 1764Mart in 0.03617 1351 54/19 0.6801 1.9048 0.3868 1.722 2141F?-lcan 0.03924 1590 54/19 0.8006 2.2427 0.3294 1.467 2520

:~ed from Table 4-14A of Reference 23* dapted from Table II of Reference 24**Ca1culated from Equation 3 using recommended cp values.

V(M.P.Hj

120~O~ __ T5 TIO~ __ TI5__ ~2TO__ ~2r5~~~ __ ~-,(

30

HOR IZONT AL CYLINDERCROSSFLOW WINDAVERAGE AIR TEMP=50oe

90 .

60

O~------~------~---- L- ~o 4 8 12

V (Mlpl16

Fi gu re 7. Forced Convection Heat Transfer Coefficientfor Typical Overhead Conductors.

The single factor which provides the greatestir~ence on the conductor ampacity is the windv~ ty.·A typical example of the effect· of the windvet6~;ty on the time constant is shown in Figure 8 fora Drake conductor with a preload current of 1005 amps.The time constant increases as the wind velocitydecreases and as the current overload increases.However the time constant. is pract ica 11y .independentof overload current for moderate wind velocities aboveabout 3 m/s (10 ft/sec). These results imply that aconductor requi res more time to reach its ult imatesteady state temperature as the wind veloc itydecreases and as the overload current increases,particularly at low wind velocities. Theseconclusions should not be misinterpreted. Simplybecause the time constant increases does not mean thatan operator has a greater amount of time before aconductor reaches a temperature that can create aclearance problem. For example, a decrease in windvelocity increases the conductor time constant, but it

2949

also increases the final steady state conductortemperature. Therefore even though the· conductorrequi res a greater time. to reach its ultimatetemperature, it can reach a predetermined limitingtemperature sooner at lower wind velocities.

The influence of conductor size on the timeconstant for a current overload of 50 percent abovethe 750c ampacity value is shown in Figure 9. Thelarger conductors ·with,their greater thermal inertiaprovide for greater time constants. For theconditions given in the figure, the minimum timeconstant is s1 ight ly over one minute for 267 kcmilPartridge conductor in a wind with a velocity of about12 m/s (27 rnph}, The largest time constant is greaterthan one-half hour for the 1590 kcmil Falcon conductorinca 1m air.

r

·35 .DRAKE CONDUCTOR.. ~s ·=0.7 "1=0.5 Tm=25°C·1 = 1005 AMPS

CROSS FLOW WIND30

_U)WI-::) 25~::eI- 20z<I:l-(/)z

150c..>

w::EI- 10

5

0La 1.2

.... -

V= 3.05 MIS (10 FT IS)~

V=6.10 MIS (20 FT/S)

2.01.4 1.6

Figure 8. Time Constants for a Drake Conductor.ACKNOWLEDGEMENT .

The authors would like to thank Georgia PowerCompany for provi ding fundi ng for the development of

. the deta i1ed computer program reported in Re f'er ences20, 21 and 22.

. ., .

;, .

2950

3S0

30

(i)w 25~::>z~

20~Z<l~IJ)z IS0uw~~ 10

5

00

5V(M.PH"

10 15 20 25

Ir/I, = 1.5•• =0.7 -1=0.5T••=2SoCCROSSFLOW WIND

PARTRIDGELINNETHAWKROOKDRAKEFINCHMARTINFALCON

2 4 6V (MIS)

8

Fiyure 9. Time Constants as a Function of WindVelocity for Typical ACSR Conductors.

REFERENCES

1.

';.. /

2.

.,3.

4.

5.

(

George E. Luke, "Current Carryi ng Capac i ty ofWire~ and Cables," Westinghouse ElectricJournal, PittSburgh, Pa., April 1923.

"A General Formula for Calculating theTemperature: of Electric Heated Wires," TheElectric Keview, Vol. 95, No. 2405, pp. 989-YO,Dec. 1923.R. J. C. Wood, "Heating of Large Steel '.:oredAluminum Conductors," AlEE lrans., Vol. 43, pp.12t>8-62, 1924.

W. M. Woll and J. A. Gable, "Current CarryingCapacity of Bare Cab l ss ," The Electric Journal,Vol. 23, No. II, pp. 557-59, Nov.,1926.

A. V.· Zeerleder 'and P. Bourgeois, "Effect ofTemperatures' Attained in Overhead Electric.

'Transmission Cables," Journal Inst. of .Metals,Vol. 42, pp. 321-27, 1929. .

6. 0'. R. Schur iq and C•. W. Fr ick ; "Heating andCurrent .:. Carry; ng Capacity of Bare Conductorsfor Outdoor Services," General. Electric Review,Schenectady, N.Y., Vol. 33, No.3, pp. 141-57,14arch 1930.

7. H. A. Enos, "Current Carryi ng Capacity of Over-head Conductors," Electric World, New York,N.Y., pp. 60-63, May 1943.

8. J. H. Waghorne and V. E. Oqor odn ik ov , "Cu rrentCarrying Capacity of ACSK Conductors," AlEETrans., Vol. 70, Part II, pp. 1159-62, 1951.

9. H. E. House and P. D. Tuttle, "Current-Carry1ngCapacity of ACSR,M AlEE Trans., PAS Vol. 78,Part Ill, pp. 1169-78, Feb. 19t>9.

12

t •

10. Earl Hazen, ·Extra~High~Voltage Single and Tw{nBundle Conductors, Electric Characteristics anc!'Conductor Selection," AlEE Trans., Vol. 78 pp.1425-34, Dec. 1959.

11. G. M. Beers, S. R. Gilligan, H. W. Lis and J. M.Schamberger, "Transmission Conductor Ratings,"AlEE Trans., Vol. 82 • pp. 767-7':>, Oct. 1963.

:;D. O. Koval and Roy Billington, "Det.ermf nat ion fof Transmission Line Ampacities by Probability $and Numerical Methods," IEEE Trans. PAS, Vol. .'89, No.7, pp. 14B5-92, Sept./Oct. 1970. •.•Glenn A. Davidson, Thomas E. Donoho, Pierre R. ~H. Landrieu, Robert 1. McElhaney ano r John H.bSaeger, "Short-Time Thermal Ratings for' Bare jOverhead Conductors," IEEE Trans."PAS Vol. 88"No.3, pp. 194-99. March lY69. .!

. . . ~V. T. Morgan, "Rat i ng of. Bare Overh,.ead Conduc- itors for Intermittent and Cyclic Currents." iProc. lEE, Vol. 116. No.8.:. pp. 1361-75, Aug. I1969. . ~

V. T. Morgan, ~Rating 6f Conductors for Short- ,..Duration Currents," Proc. lEE, "Vol. 118. No•3/4, pp. 555~69.Mar./Apr. 1971." .

Murray W. Davis", "A New Thermal Rating liApproach: The Rea I Ti me The rma IRati R-9 Sys t em jfor Strategic Overhead Conductor Transmission ILines." IEEE Trans •• PAS; Part I, Vol. 96, No••3, pp. 803-09. 11ay/June 1977; Part II, Vol. 96, ~No.3. pp. 810-25, May/June 1977; Part III. Vol. 097, No.2. pp. 444-55, 11ar./Apri I 1978; Part IV, !jii:3;aper F-79 710-15; Part V, IEEE Paper F79 1:

11'...

V. 1. Moryan, "The. Uns teady-State C"urrent Rat i nyof Bare Overhead Conductors ." Inst. of· Enqr s , ,Elec. Engr. Trans •• Vol. 16. Vol. 3, pp. 114-19,198U.

t;11<~

12.

13.

14.

15.

16.

17.

18. Stephen D. Foss, Sheng H. Lin and Roosevelt A.Fernandes, "Dynamic Thermal Line Ratings, PartI. Dynamic Ampacity Rating Algorithm," IEEETrans., PAS. Vol. 102, No.6. pp. 1858-64, June1983.

19. Stephen D. Foss~ Sheng H. Lin, Howard R.St i llwell and Roosevelt A. Fernandes, "DynamicThermal Line Ratings, Part II. Conductor Temper-ature Sensor and Laboratory Field Test Evalua- ttlon," IEEE Fr-ans , ,' PAS, Vol. 102, No.6, pp ,1865-76. June 19

t83. •.

W. Z. Black and W. R. 8yrd, "Real-Time Ampacity~'odel for Overhead Lines," IEEE Trans., PAS,Vol. 102, No.7, pp. 2289-93, July 1983. ,

I.,i~

"~

I&Ii£'"£

I1

20.

21. R. A. ~ush, W. Z. Black, T. C. Champion III. W.R. Byrd, "Experimental Verification of a Real-Time Program for the Determination of Tempera-ture and Sag of Overhead Li nes, U IEEE Trans.,PAS, Vol. 102. No.7. pp. 2284-88. July 1983.

22. Robert L. Rehberg,' "High Temperature Ampacityand Sag Model for ACSK Conductors", M.S. Thesis,School of Mechanical Engineering, GeorgiaInstitute of Technoloyy. Atlanta. GA, Dec. 1983.

23. A I umt nurn Electrical Conductor Handbook ,SecondEdition. The Aluminum Association, WaShin!ltooD.C., 1982,

•• 2952

~~ Quantity ~rogram

Symbolm'c MCPp0 OIA

./ A A

B B£1 EPSI£s EPSSII 1112 12Q~~n QSUNT'"

TlNFV VINF(0) OMEGA

Table 3. Input Variables to Simplified Ampacity ProgramI 1

Description

Product of mass per unit length and specific heat for the conductorOuter diameter of cortductorAC electric resistance per unit length of conductor at OoCTemperature coefficient of resistance of conductor defined by Equation 4Emissivity of conductor surface for infrared wavelengthsEmissivity of conductor surface for solar wavelengths

amps Preload current ~ r~,/mmP~ Emergency current jl" Solar energy per unit area incident on the conductor i°c Ambient air temperature ~,m/=-----_ Ambient air velocity .. tdegrees Angle between air veloc~ty vector and normal to axis "of conducto t

~ ~~~ (0_<_(o)_<9_0_0_)~~ __ ~ ~~~ __ ~ __ ~~ ~~--~f5X, "W/Ji" ,--lOX, "W/Hu• 7'1., UW/H" , 7X, "W/H" ,9X, "W/H" .sx, i:

2 "W/II".8X. "W/II") tPROPERTIES Of AIR AT AN AVERAGE TEIIP Of 50 DEG.C •NUBAR, - 1.85E-OS· ~KBAR - 0.0272 ,..•.- ~GBETA - 8.96E+07 tPI! - 0.71 . ,~PI - 3.14159 ',.,

.SIGMA - 5.67E-08 ~APR - A+S*TINf ~PISIGE - 24.58+0.2476*TINfIf (vINf .CT. 0.5) CO TO 35 !CALCULATION Of CRJ.SHOf NUMBER (GR) AND HEAT TRANSfER f.COEffICIENT (H) fOR fREE CONVECTION fOR WIND VELOCITIES ~LESS THAN 0.5 11/5. tCR - CBETA*(50.-TINf)*(DIA**3.) ..,NU - 0.53*(GR*PR)**0.25· .ooro~ '. . • I~CALCULATION Of THE REYNOLDS NUIIBER (REy) AND HEAT '.':.TRANSfER COEffICIENT (H) fOR fORCED FLOW ASSUIIINC WIND :VELOCITIES GREATER THAN 0.5 II/S.

35 REY - VINf*DIA/NUBAR ~,."BB - ALOGI0(REY) FNUO - 10.0*(-0.07043+0.3153*B8+0.03553*5B*BB)OI~EGA - 0IlECA*0.017453 .

'.llIO - 2.*OIlEGANU - NUO*·(l.194-SIN (0IlEGA)-0.194··'COS(rvo) +0.368*SIN (1\0'0»

40 H - NU*KBAR/DIAPIHD - PI*H*DIABI2SQ - aaI2*12 -BIISQ '- B*II*JIEPSIGE - EPSI~PISIGE*DIAaIGX' - PiHD-BIISQ+EPSIGEBIGY - PIHD-BI2SQ+EPSIGEEOO - EPSS"DIA·QSUNCALCULATION Of STEADY STATE PRELOAD TEIIPERATURE (T1)AND EIIERGEN.CYTEKPERATURE (T2).Tl - TlNf+«APR*ll*ll-EDQ)/BIGl()T2 - IINF+«APR*12*12+EOO)/BIGY)CALCLTLATION Of TIllE CONSTANT (TC) •.TC - IICP/(BIGY*60.) ,CALCULATION Of PRELOAD CONVECTION (QCl). ~~RGENCTCONVECTION (QC2) AND ABSORBED SOLAR ENERGY (QABS).QCI - PIHD*(Tl-TINf") .QC2 - PIHD'(r2-TINF)QABS - EOOCOEff.- PI*DIA*EPSI'SIGHACALCULATION Of PRELOAD NET RADIATION (QNETI) AND L~RGENCrNET RADIATION (QNEI2).QNETl .;.COEff*«Tl"273.2)*·".-(TlI'IF+273.2)**".) I~QNETl - COEff*«T2+273.2)**".-(TINf+273.2)·*4.). _CALCULATION Of PRELOAD Ah~ EHERGENCY INTERNAL GENERATION(QGEN i AND QCEN2) jjQGENI - (A+S*T1)*Il*Jl -!~~~ (;.3~~+~;~;~:i~:~~QCI.QC2.QABS.QNETI.QNET2.QGENI,QG!X' ;

30 ~~~~r (1IFII.2) IEND ~

i

Units

J/oC mmohrns/mobms/m °c

INPUT INFORMATION ***** _ C

CONDUCTOR PROPERTIESMCP= 1309.0 J/M DEG.CDIA= .028140 METERSA= .637800E-04 OHMS/MB= .281800E-06 OH~S/M DEG.CEPSI= .500EPSS= .700PRELOAD AND EMERGENCY CURR6NTS11= 850.0 AMPS12= 1300.0 AMPSWEATHER CONDITIONSQSUN= 1000.0 W/SQ MTINF= 30.0 DEG.CVINFc 2.240 MISOMEGA= 45.0 DEGS.

CCC

CCC

***** OUTPUT INFORMATION *****ORIG TEJoPFlf'W..TEM> TlI-ECONST HT COEFF ORIG COW Flf'W..COWDEG C DEG C t1N. W/M*M"'C W/M W/M58.90 94.02 9.85 25.34 64.75 143.43

SJN ABS ORIG Ern FINN..un ORIG G:N Fi NftL G:NW/M. W/M W/M W/M W/M

19.70 9.31 24.40 58.07 152.57PROGRAK..KAIN (INPUT, OUTPUT. TAPE6-INPUT, TAPE7-0UTPUT)REAL IICP.II,I2.NUBAR.Y.BAR.NU,NUO .READ (6,*) IICP.DIA,A,B.EPSI.EPSS.Il,I2.QSUN.TINf.VINf.0IlEGAWR lTE (7.5) lie?,DIA. A. 8.EPSI. EPSS. 11; 12.QSUN, TINf. VINf. OMEGA

5 FOR.'iAT(lOX." ••••••* INPUT INFORMATION """"./1,I "CONDUCTOR PP.O?ERiIES" .1/. "IICf';".rio.r.v J/II DEG.C". /,2 ·'D1A-",flO.6.u HETERSII,I."A-u,t:12.6," OH.'iS/H",/.3 "B-".EI2.6," OHHs/~ DEG.C".I."EPSI-".f"5.3.1,4 "EPSS·" .rs. 3.//. "PRELOAD AND E.~ERGENCY CURRENTS" ./1.S tlll-".FB.l," AMPS",/."12-II,rS.l," AMPS",II, I

6 "WEATHER CO":lIrIOtlS".r), "osux-", f8.1." 'W/SQ II".1.7 "TINy-H.f8.1." DEG.C".I."VISf-",f8.3." II/S".I.8 "OIlEGA-".f7.I," DEGS.".I/f)

WR IrE (7.20)20 fORMAT (20X,"••••• OUTPUT INFORMATION •••••••:/1.

1 ~x."oRrG TEIIP".2X."fINAL TEIIP".2X."TIXE COl/ST".2X,2 "HT COEfl'''.2X,''ORIGCOIlY".2X,"fINAL COIlV".2X,3 IISUN ABS".2Jt."CJ\JG E..HIT".3x,"FINAL £111T" ,to 2X. "OR IG GEN", zx, "fI NAL GEl'''.)

WRITE 0.23)25 fORMAT (6X,"DEG C",7X,"OtG C",7X."l1IN.",SX,"W/I1·X.C".

cC·

C

cC

CC

cC

• 2953

tT

I-tor..t~--~------------------------------------------------------------------------------------------~

luant1ty

.f" ...•. '.'~

Iif,-

Qconv.lQconv.2QsolarQrad.l

. Qrad 2'2 •{I. RAC)l

(r2RAC)2

ProgramSymbolTlT2TCH

QClQC2QABSQNETlQNET2QGE;NlQGEN2

Table 4. Output Variables from Simplified Ampacity program

Units Description

°c°cminW/m2 .oCW/mW/mW/mW/mW/mW/mW/m

.Steady (conductor temperature~Steady conductor temperature

.Conductor time constantConvective heat. transfer coefficient for air flow over conductorConvective heat flow from unit length of conductor at preload conditionsConvective heat flow from unit length of conductor at emergency conditi~nsSolar energy absorbed by a unit length of conductor, . .

Net radiation emitted from a unit length o~ conductor at preload conditionsNet ·radiation emitted from a unit length of conductor at emergency conditionsHeat generated within unit length of 'conductor at preload condt t tonsHeat generated withi n a unit 1ength .of conductor at emergency condi t ions

corresponding to preload current. 11correspondi n,g to emergency current. 12

, J

Correction to "Lightning Surge Anal)'sis in a Multi Conductor Systemfor Substation Insulation Design"

JzOzawa, E. Ohsaki, M. Ishii, S. Kojima, H. Ishihara, T. Kouno, andT. Kawamura

In the above paper l, there was a omission from item (6) of the discus-sion by A. M. Mousa on page 2253. The correction should have appearedas follows: .6. Unlike this paper, the method mostly used in North America [AlEE

Working Group (1963) and Clayton & Powell (1958)] assumes nearlightning strokes (both direct hits and backflashes) tQ be preventedthrough proper shielding and grounding. The maximum 'magnitudeof the incoming lightning surge is then taken equal to 1.2 times thefull wave insulation level of the line, and the rate of rise is determin-ed in terms of the distance between the substation and the origin pointof the surge. That information is then used to determine the permissibleseparation between the surge arresters and the protected equipment.

Manuscript received February 25, 1985

1 J. Ozawa, E. Ohsaki, M. Ishii, S. Kojima, H. Ishihara, T. Kouno,and T. Kawamura, IEEE Trans. Power App, Syst., vol. PAS-I04, no.8, pp. 2244-2254, August 1985.

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