ML17334B543

Forwards Addl Info Re Thermo-Lag Related Ampacity Derating Calculations,As Requested by NRC

ML17334B543
Person / Time
Site:	Cook
Issue date:	05/12/1995
From:	Fitzpatrick E INDIANA MICHIGAN POWER CO. (FORMERLY INDIANA & MICHIG
To:	NRC OFFICE OF INFORMATION RESOURCES MANAGEMENT (IRM)
References
AEP:NRC:0692DF, AEP:NRC:692DF, TAC-M85538, TAC-M85539, NUDOCS 9505190297
Download: ML17334B543 (136)

Text

RIGRITY CCELERATED RIDS PROCESSING)

REGULATORY INFORMATION DISTRIBUTION SYSTEM (RIDS)

ACCESSION NBR:9505190297 DOC.DATE: 95/05/12 NOTARIZED: NO DOCKET I FACIL:50-315 Donald C.

Cook Nuclear Power Plant, Unit 1, Indiana M

05000315 50-316 Donald C.

Cook Nuclear Power Plant, Unit 2, Indiana M

05000316 AUTH.NAME AUTHOR AFFILIATION FITZPATRICK,E.

Indiana Michigan Power Co. (formerly Indiana

& Michigan Ele P

RECIP.NAME RECIPIENT AFFILIATION Document Control Branch (Document Control Desk) ~)~

SUBJECT:

Forwards addi info'e Thermo-Lag related ampacity derating calculations, as requested by NRC 950306 ltr.

DISTRIBUTION CODE A029D COPIES RECEIVED:LTR ENCL SIZE:

TITLE: Generic Letter 92-008 Thermal-Lag 330 Fare Barrier 0,'OTES:

R RECIPIENT ID CODE/NAME PD3-1 LA HICKMAN,J INTERNA NRR/DRPW/PD3-1 RGN3

~...FILE EXTERNAL: NOAC COPIES LTTR ENCL 1

0 1

1 1

1 1

1 1

1 1

1 RECIPIENT ID CODE/NAME PD3-1 PD NRR/DE/EELB NRR/DSSA/SPLB NRC PDR COPIES LTTR ENCL 1

1 1

1 2

2 1

1 D

N i4OTE TO ALL"RIDS" RECIPIENT:TS:

PLEASE HELP VS TO REDUCE KV'iSTE!COYTACTTHE DOCL'ifEYTCONTROL DESk, ROOlif Pl-37 (EXT. 504-~OS3

) TO f;LlliflbATE YOL'R iAXIL'ROil DISTR IBUTIOYLIS'I'S I'OR DOCL'5 IEi'I'S YOL'OY,"I'ffI'.D!

TOTAL NUMBER OF COPIES REQUIRED:

LTTR 11 ENCL 10

Indiana Michigan Power Company P.O. Box 16631 Columbus, OH 43216 FI May 12, 1995 AEP:NRC:0692DF Docket Nos.:

50-315 50-316 U.

S. Nuclear Regulatory Commission ATTN:

Document Control Desk Washington, D. C.

20555 Gentlemen:

Donald C.

Cook Nuclear Plant Units 1 and 2

ADDITIONALINFORMATION REGARDING THERMO-LAG RELATED AMPACITY DERATING CALCULATIONS TAC NOS.

M85538 AND M85539 By your letter dated March 6,

1995, we were requested to submit representative ampacity derating calculations with respect to cables in raceways covered with Thermo-Lag used at Donald C. Cook Nuclear Plant.

The calculations and methodologies, including mathematical

models, are addressed in the attachments to this letter.

Attachment 1 provides an overall summary of our ampacity derating analyses.

Attachment 2 contains the basis of our mathematical model.

Attachment 3 contains cable tray allowable fill design criteria.

Attachment 4 provides an in-depth discussion of the development of the mathematical model and analysis.

Attachment 5

contains representative calculation results.

Attachment 6 provides results from tests used to verify the accuracy of our computer model.

Sincerely, Vice President cad Attachments ASQQjg 9505190297 95051'2 PDR ADOi K 050003i5 P

PDR

j I

U. S. Nuclear Regulatory Commission Page 2

AEP:NRC:0692DF CC; A. A. Blind G. Charnoff J.

B. Martin NFEM Section Chief NRC Resident Inspector

- Bridgman J.

R. Padgett

ATTACHMENT 1 TO AEP'NRC'0692DF

SUMMARY

OF AMPACITY DERATXNG ANALYSES

. ~ -9505190297

Attachment 1 to AEP:NRC:0692DF Page 1

1.0

~Back round In 'the early 1980's, compliance with 10CPRSO Appendix "R" was achieved for Cook Nuclear Plant (CNP) by enclosing certain raceways with Thermal Science Incorporated (TSI) Thermo-Lag 330-1 fire barriers.

Enclosing the power cable raceways with the TSI material increases the thermal resistance to ambient thus restricting the quantity of heat released, resulting in reduced conductor>> allowable ampacity.

Although TSI material specifications addressed specific percent derating for the cables in tray and conduit wrapped with Thermo-Lag barriers, AEPSC took an aggressive approach to independently determine the reduced allowable ampacities and documented that the full load currents for power cables in the TSI wrapped raceways at CNP did not exceed allowable derated ampacities.

2,0 Theoret ca ana s

s Mathematical mode The process included the development of a mathematical model based on the theoretical analysis and work done by Neher, McGrath, and Buller in their AIEE transactions papers57-660 and 50-52 (attachment 2).

This analysis is based on the phenomena of heat transfer with respect to energized cables and the effect on the ampacity.

The temperature rating of a cable is the maximum conductor temperature that will not cause excessive deterioration of the cable insulation over the expected life of the cable.

This maximum temperature limits the amount of heat which may be generated by a

conductor by resistive heating and therefore limits the amount of current the cable can carry.

Enclosing, the conductor within layers of material (i.e.,insulation,

raceway, or air space) increases the thermal resistance to the ambient heat sink and restricts the quantity of heat which may be transferred while still maintaining the maximum conductor temperature.

The objective then was to determine the allowable ampacity of cables in various raceway and fire protected raceway configurations based on the heat transfer through a thermal resistance while not exceeding the temperature rating of the cables under steady state conditions.

The phenomena of heat transfer with respect to energized cables and the effect on cable ampacity were examined.

Thi.s included:

Attachment 1 to AEP:NRC:0692DF Page 2

a) review of basic heat transfer mechanics, b) evaluation of previous work done in the areas of cable ampacity and heat transfer,,

c) analysis of the effects of conduction, convection and radiation with respect to CNP power cable installations, and d) development of heat transfer theory for low fillcable trays.

Per our design criteria (see attachment 3), the power cables installed in cable trays are positioned in a single layer with a minimum space between cables of 1/3 the diameter of the larger ad)acent cable.

Furthermore, the sum of cable diameters can not exceed 75% of the tray width.

The above criteria limits the number of power cables installed in a cable tray, thus limiting the total heat generated per foot and limiting the conductor derating.

3.0 Calculations A computer program was developed according to the criteria outlined in the mathematical model.

The program calculates the allowable ampacities for the power cables in the TSI wrapped raceways.

Assuming a

maximum allowable cable temperature of 90 C and an ambient temperature of 40'C, the maximum allowable heat generated(Q) was calculated for steady state conditions.

The allowable ampacity (I) was then calculated using the known relationship between Q and I.

The analysis and mathematical model are discussed in depth in attachment 4.

At CNP, the power cables in all TSI wrapped raceways were analyzed using this program and it was documented that the cable full load currents are within the calculated allowable ampacities.

Representative calculation results showing the allowable ampacities for the cable tray and conduit raceway design are included in attachment 5.

Attachment 1 to AEP:NRC:0692DF Page 3

4.0 Tests

Finally, a series of tests was conducted in 1983 at our Canton test lab to verify the accuracy of the computer model.

These tests simulated exact raceway loading conditions at CNP and demonstrated that the conductor temperatures for the TSI enclosed

. cables are within the temperature rating of the conductors:.

as. predicted by the computer model.

Refer to attachment 6

for the test report

¹CL-542 dated December 16, 1983. The highest conductor temperature recorded for the six tested configurations was 68.8'C. Cable trays and conduits were both included in this testing.

5.0

~Conclusio At CNP, the calculations for the cables enclosed with TSI Thermo-Lag 330-1 fire barriers demonstrated that:

a) the connected full load currents are well within calculated allowable ampacities, b) the calculated heat generated per foot of raceway is well under the calculated allowable heat generation per foot of raceway, and c) the raceway design criteria limits the total number of cables in a raceway such that the cable temperature ratings are not exceeded.

ATTACHMENT 2 TO AEP'NRC'0692DF AIEE TRANSACTIONS PAPERS57-660

& 50-52

'iy, k

l J.

• 4,

M. H. McGRATH i

'e

~e

,h a

N 1932 D. M. Simmons'ublished a

series of articles entitled, "Calculation ofthe EIcctricaI Problems ofUnderground Cables."

Over the intervening 25 years this work has achieved the status of a handbook on the subject.

During this period, however, there have been numer-ous dcvdopmcnts in the cable art, and much theoretical and experimental work has been done with a vievr to obtaining more accurate methods of evaluating the parametas involved.

The advent of the pipe-type cable system has emphasixed the desirability of a more rational method of calculating the performance of cables in duct in order that a realistic comparison may be maCk betmeen the twa systans.

In this paper the authors have en-deavored ta extend the vrork of Simmons by presenthig under one cover the basic principles involved, together vrith more recently developed procedures for han-dling such problems as the effec of the loading cyde and the temperature rise of cables in various types of duct stxuc; turcs.

Indudcd as wdl are expressions required in the evaluation of the basic paraxneters for certain specialixed allied procedures.

It is thought that, a mark of this type wiIIbe useful not only as a guide to engineers entering the Geld and as a reference to the more experienced, but particularly as a basis for setting up com-putation methods for the preparation of industry load capability and aw/d~ ratio compilations.

The calculation of the temperature rise of cable systans under essentially steady-state conditions, which includes the effect of operation under a repetitive load cycle, as opposed to transient temperature rises due to the sudden application of large amounts of laad, is a relatively simple procedure and involves only thc applica-tian af the therxnal equivalents of Ohm's and Kirchoff's Laws to a relatively simple thermal circuit.

Because this circuit usually has a number of parallel paths with heat Gams entering at several points, hovrcver, care must, be exercised in the method used of expressing the heat foms and thermal resistances

involved, and differing methods are used by various en-gineers.

The method employed in this paper has been selected after careful con-sideration as being the most cansistcnt and most readily handled over the full scope of the pxablan.

Alllosses willbe developed on the basis QONrs and temperature rises due to dielec-tric loss and to current-produced lasses mill bc treated separately, and, in the latter case, all heat Horns"miII be expressed in terms of thc current produced lossariginat-ing in one foot of conductor by means of multiplying factors which take into ac-count the added losses in the sheath and conduit.

In general, all thamal resistances miII be developed on the basis of the per con-ductor heat Qow through them.

In the case of underground cable systems, it is

'convenient to utilitc an effective thexxnal

'esistance for the earth portion of thc thcxxnaI circuit vrhich indudes the effect of the loading cyde and the mutual heat-ing cffcct af thc athcx'able of thc system, Allcables in the system wiIIbe considered t~ocsrry e eeoie Ided eetieiite eed to be operating under the same load cyde.

The system'of nomendature employed is in accordance withthat adopted by the Insulated Conductor Committee as stand'-

ard, and diffas appreciablyfrom that used inmany of thc references.

This system represents an attempt to utilize in sa far as possible the various symbols appearing in the Amaican Standards Association Standards for Eectxicai Quintities, Me-

chanics, Heat and Thaxna-Dynaxnics,

'and Hydraulics, when these symbols can be used without ambiguity.

Certain symbols which have long been 'used by cable engineers have been retained, even though they are in direct conQict mith the abaveementioned standards.

Nomenclature (AF) attainment factor, per unit (pu)

As<<cross-sectioht area of a shieldiag tape or skid rcire, square inches dr<<therznaI diffhhsivity. square inches pa hour CI<<conductor area, circular inches d<<distahhcc, inches'th etc. << from ceater of cable no. 1 to center of cable no. 2 etc.

Cks'tc.<<from center of cable no.

1 to image of cable no. 2 etc.

As etc.

from center of cable no.

1 to a poiat of icterfercace

.',."!7het Calculation of the Temperature Rise

an'd Load Capability of'able Systems

~

~

~

3. H. NEHER r.

MEMSER dhtlEE e

As'tc.<<frohn iauge of cable no.

1 to a point of intexfexeace D<<dhmcter, inches aq b.o Dcdaiasid D, <<Outxide Of Cahhduetar

~

Ds<<outside of ixhsulatioa Ds<<outside of sheath D<<,<<incan diameter of sheath Df<<outside of jacket Ds'<<effective (cixcuxnscribiag cirde) of several cables in contact Dp<<inside of duct wal4 pipe or conduit Dc<<dlaxneter at start of the earth portion of the thermal cixcchit Da<<fictitious diameter at vrhich the effect of loss hctor commences E<<line to neutral voltage, kilovolts (kv)

~<<coefficient of surface emissivity cr <<spccific inductive capacitance of insula-tloa

/<<frequency, cycles per secoad F, Fs,h<<pxxhducts of xatios of distances F(x) <<derived Bessei function'f x'Table III and Fhg. 1)

G<<geometric factor Gt <<applying to insulatioa resistance (Fige 2 of referexhce 1)

Gs<<applying to dielectric loss (Fig. 2 of reference 1)

Ght<<applying to a duct bank (Fig. 2)

I conductor current.

kiloampexes kd <<skin effect co?rection factor for annuhr and segxneatal conductors kp<<relative txanshrexse coadclc&ity hctox for caicuhting conductor pxoxihnity etfect J<<hy of a shielding tape or shd wire, inches L<<depth of reference cable below earth'

schxface, inches Lv<<depth to center of a duct bank (ox'ackfill),

inches (lf)<<load factor, per unit (LF)<<loss hctor, per unit ri number of conductors per cable xs'<<nuxaber of coaductoxs within a stated diaxneter N<<number of cables or cable 'groups in a systexn P<<perihneter of a duct bank or backfiJI, inches cos 4<<povrer factor of the insuhtion tfc<<ratio of the sum of the losses in the conductors and sheaths to the losses ia thc coaductoxs

'I tlc<<ratio of the sum of the losses hx the coadchctoxs, sheath and conduit to the losses in the conductors R<<electrica resistance, ohms Rsc <<dw resistance of conductor R

total aw resistixhce per conductor Rc<<dw resistance of sheath or of the parallel paths in a shield-skid vtrire assembly 8 << thexxnal resistance (per conductor losses) thexxnal ohm-feet 8s <<of iaschlatioa Af<<of jacket Rhd <<between cable surface aad schxxounding endosure Paper ST~, recomtaeadcd bT the hIBB Insulated Coaductors Committee aod approrcd bT the hIEE Tcchaiccl Operations Pepartmcac for presentation

~c the hlBB Summer Ccocrsl hfecttae. hfoocreal, Que.,'aosda, Juae 24-2S.

105T.

hfaauscript subhoittcd starch "0, 10ST; made aransbte for priociax hpril 18, 10$T.

J. If. Nausa ls eectb the phiaadclphta Elec&a Compcor. Philadelphia. Pa.. and hf. H. hfcCaam Is reich the Ccocral Cable Cocporacloo, Pcrth hmbor, ¹ J.

c'Ceher,.VcGrctliTerrlpercfnre crxd Load Ccpabilify oj Ccblc Systems QCTCnER lear

t

~

ajo OA9 OA4 OA7 OA4 005 Xo 2,5 IA 0.9 a4 0.7 0.4 g a5

~ a4

~~ 0.25 a2 O.I5 F(xv) j IF(x9)

I I! I I

i lii

~

~

I I

I

@xi I

l jr I

I I! I

'lji i

I i

~

s i.

I I!

II:(xj 0015 &

o Ip a009~ Iu 0004 0005 0~

hI OA03 00025 0002 I.O I.5 I.o 8

I O.IO 2 253 4

5 4 769IO l5 20 30 40 5060 4000 RucA Fig. l (above).

F(x) and F(xa') az functions of~/k Fig. q (right),

GI for 4 duct bank Wa~poztion developed in the conductor W,~portion developed in the sheath or shield W <<portion developed in the pipe or con-duit Wc ~ portioa deveiopal m the dielectzic X~~ mutual reactance, conductor to sheath or shield, microhms per foot Y~the incremen't of aw/dw ratio, pu Ya<<due to losses originating in the con-ductor, having components Yaa duc to shn efect and Y,jr due to prox-imity effect Ya ~due to losses originating in the sheath or shield, having compobeats YIa due t'o cizcuhting cuzrent cffect and Yi, due to eddy current effcct YIr~due'to losses originating in the pipe or conduit Ya~ due to losses originating in the amor General Considerations of the Thermal Circuit THs ~~TzoN op TsM2smTzzss Rzss The temperature rise of the conducmr of a cable above ambient temperature may be considered as being composed of a temperature rise due to its own losses, which may be divided into a rise due to current produced (PR) losses (hereinafter referred to merely as losses) in the, conduc-tor, sheath and conduit b,Ta and the risc produced by its dielectric loss hT4.

24~ of duct wall or asphalt mastic covering R~total between sheath aud diameter Da Including Rt, Rrc and Rc

~

~

~

R< ~between conduit and ambient

. R,'~effective between diameter Da and ambient earth including the cffects.

of loss factor and mutual heating by other cables Raa'~effective between conductor and ambient for conductor loss R4r' effcctive tzanslcnt thezznal resistance of cable systan Rca'~cffective between conductor aad am-bient for dielectric loss Rr,I~of the interference efect Rf4 ~ between a steam pipe and ambient earth p~clectrical resistivity, circular mil ohms per foot it thermal resistivity, degrees centigrade centimeters pcz'at't s~distance in a 3mnductor cable between the effective current center of the conductor and the axis of the cable, inches S~axial spacing between adjacent

cables, inches t, T~thickncss (as indicated).

inches T~ tanperature.

degrees centigrade Ta~of ambient air or earth Ta~ of conductor T~~mean temperature of medium AT~tcmpaature rise, degrees centigrade ATa~of conductor due to cturent produced losses hT4~of conductor due to dielectri loss tZTrxr~of a cable due to extraneous heat source r

infared tanpaature of zero resistance, degrees centigrade (C)

(used in correcting R4, and R, to tempera-tures other than 20 C)

Vs~wind velocity, miles per hour W~lozses developed in a cable, watts per conductor foot RATIO Lb/P Ta-Ta ~ hT,+4T4 degrees centigrade (1)

Each of them component temperature rises may be considered as the result. of a rate of heat flow expressed in watts oot throu a

ermal resistance dinthermalohm eet degzcescenti-gra 0 eet per watt); in other words, the Qow of one watt uniformly distributed.

over a conductor length ofone foot.

Since the losses occur at. several posi-tions in the cable system, the heat Bow in the thezznal circuit wB1 increase in steps.

Itis convenient to express all heat Qows in terms of the loss per foot ofconductor, and thus,,

aT,- WgRr+q,R,.+qA) degrees centigrade (2) in which W, represents the losses in one conductor and RI is the thermal resistance of the insulation, q> is the ratio of the sum of the losses in the conductors and sheath to the losses in the conductors, R<< is the total thamal resistance between sheath and cocdmt, q, is the ratio of the sum of the losses in conductors, sheath and conduit, to the conductor losses, and Ra Oerosss 1957 Nchcr, McGrathTcrnpcratarc arrd Load Capability of Cable Systcrrrs

ls the thermal resistance between tt e

<trconduit and ambient.

" In practice, the load carried by a cable is rarely constant and varies according to st daily load cycle having a load factor (lj).

Hence, the losses in the cable will vary according to the corresponding daily loss cycle having a loss factor (LF).

From an examination of a large number of load cycles and their corresponding load and loss factors, the follovringgeneral rda-tionship betvreen load factor and/ loss factor has been found to exist.'LF)

~ 0.3 (tf)+0.7 (tf)'er unit In order to determine the maximum temperature rise attained by a buried cable system under a repeated daily load cycle, the losses and resultant heat flows are calculated on the basis of the maxi-mum load (usually taken as the average current for that hour of the daily load cycle during which the average current is the highest, i.e. the daily maximum one-hour average load) on vrhich the loss factor is based and the heat Qow in the last part of the earth portion of the thermal circuit is reduced by the "factor (LF). If this reduction is considered to start at a point in the earth corresponding to the diameter D'quation 2 becomes t2Tc Wc(lt+qc~tc+qc(~cs+(LF)@c)l degrees centigrade (4)

In effect this means that the tempera-ture rise fitom conductor to'> is made to depend on the heat loss corresponding to the maximum load vrhereas the tempera-ture rise from diameter Dc to ambient is made to depend on the average loss over a 24-hour period.

Studies indicate that the procedure of assuming a fictitious critical diameter D> at which an abrupt change occurs in loss factor from 100% to actual will give results which very closely approximate those obtained by rigorous transient analysis.

For cables or duct in air where the thermal storage capacity of the system is relatively small, the maxi-mum temperature rise is based upon the heat Gow coizesponding to maximum load vrithout reduction of any part of the theimal circuit.

When a number of cables are installed dose together in the earth or in a duct bank, each cable wQI have a heating eEect upon all of the others.

In calculating the temperature rise of any one cable, it is convenient to handle the heating etfects of the other cables of the system by suitably inodifying the last term of equatiot 4.

This is permissible since it is assuined that all the cables are, carrying equal cur-rents and are operating on the same load cycle.

Thus for an P-cable system aTc Wc(A+qc~cc+qcfffcc+(LF)X (Bcc)+(N-I)N¹I) (5)

Wc(lt+qcIcc+qcRc')

degrees centigrade (Sh) where the tenn in parentheses is indicated by the etfective thamal resistance 8c'.

The temperature rise due to dielectric loss is a relatively small part of the total temperature rise of cable systems op-erating at the lower voltages, but at higher voltages it constitutes an appre-ciable part and must be consideretL Al-though the dielectric losses are dis-tributed throughout the insulation, itmay be shown that for single conductor cable and multiconductor shielded cable with round conductors the correct temperature rise ts obtained by considering for tran-sient and -steady. state that all of the dielectric loss Wtt occurs at the middle of the thermal resistince between conduc-tor and sheath or aitentateiy for steady-state conditions alone that 'the tempera-ture rise between conductor and sheath for a given loss in the dielectric is half as much as ifthat loss were in the conductor.

In the case of multiconductor belted cables, however the conductors are taken as the source of the dielectric loss.'he resulting temperature rise due to dielectric loss 42'tt may be expressed dTtt~ Wit's'egrees centigrade (6) in which the effective thermal resistance ib 'is based upon /It,8,and)4'(at unity loss factor) according to.the particular case.

The temperature rise at points in the cable system other than at. the con-ductor may be determined readily from the foregoing relationships.

THB ChiA'-UthTio)4 op Lohn ChPhnan)r fn many cases the permissible maxi-mum temperature of the conductor is Gxed and the magnitude of the conductor current goad capaMity) required to produce this temperature is desiretL Equation 5(A) may be written in the form ATc~I'24c(I+ yc)lcc'egrees centigrade (7) i which the qqaatity~lb, (1+ Y, qhieh ill be ev uate re resents the eE

've electn resistance of the con-ducto 'n hms and which vrhen multiplied by P (I in kiloamperes) vrillequal the loss Wc in watts per conduc-tor foot actually generated in the conduc-tor; and 8ec's the e(fectlve thermal resistance of the thermal circuit fIcc'IIt+qc8cc+qcffc'hermal ohm-feet (8)

From equation I it follows that I

+

lciloam eres 3 a,<I+ I;)~.

Ta6le I.

Electrical Resbtlvity of Various Materiab btaterlcl P

Cheater Mll Ohms per Foot at20C r, C Copper (100% IhCS') ~ ~ ~ ~ ~ ~ ~ ~ 10.371..... 234. S Aluminum (81% IhCS).e,

~

17.002.

~. ~.228. 1 Cotcmerelct Bronte (43.8% ~ ~. 23.8

~ ~ ~ ~.584 IhCS)

(90 Cu-10 Zo)

Bta$ 5 (2T.3% IhCS) ~ ~ ~. ~.. ~ ~ ~ 38.0

~ ~ ~ ~.912

( 0 Cu-30 Zu)

Lead (7.84%c IhCS)... ~. ~...132.3

. ~. ~.238

~ Isterssuoud hoaeale4 Copper StaodanL Calculatioa of Losses and Associated Parameters 37.9 Rc ~

'or Iesd at 50 C Dctttt (IIA) 4

~

for 61% aluminum at 50,C Dg 1

(IIB) vrhere Dcttt is the mean diameter of the sheath and t ts its thickness, both in inches Dccq ~Dc t laches (12)

The resistance of intercalated shields or skid wires may be determined from the expfcsstOQ rpc SDtet R, (pe: path) ) I+(

)

microhms per foot at 20 C (13) where A, is the cross section area of the Gac~Tio)i CF DN RBsisThNcxs The resistance of the conductor may be determined from the followingexpressions vrhich include a lay factor of 2%;

see able L 1.02 pc microhms per foot at 20 C CI (IO) 12.9 for 100% IACS copper CI conductor at 76 C (10A) 212

~for 61% IACS CI alumlautn at 75 C (IOB) vrhere CI represents the conductor size in Circular inCheS and Vrhere Pc rePreSentS the electrical resistivity in circular mil ohms per foot.

To determine the value of resistance at temperature T multiply the resistance at 20 C by (r+T)/(r+20) where r is the inferred temperature of Zero resistance.

The resistance of the sheath is given by the expressions pc R, ~

mlcrohms per foot at 20 C (II~

4Dcctt Kdhdr, hfcGra! h Terripdratnrd and Load Capability of Ccbfe Sys.'crrts QcToBBR 19o<

s

~

~'

~

tape or sl.id wire and l is its lay.

The over-all ':esistancc, of the shield and skid rwire assembly, particularly for.noninter-calated shields, should be determined by Jectrical measuremcnt when possible.

C~L.ctfuTioHoF Losslls It is convenient to develop expressions for thc losses in the conductor, sheath and pipe or conduit in terms of the components of the aoc/doc ratio of the cable system which may be expressed as followsl r(w R CIRcc 1+Yc+Ys+Fp (14)

The aoc/doc ratio at conductor is 1+ Yc and at sheath or shield is I+Y,+ Ys and atpipeorconduit is I+Y,+Ys+Yp The corresponding losses physically gen-erated in the conductor, sheath, and pipe are Ws I Rcs(l+ Yc) watts pcr conductor foot (IS)

Ws PRcc Ys watts Per conductor foot (16)

Wp ~I'24cYp watts per conductor foot (17)

'cisj>>

Il.

Recommended Values of k,cndks Conductor Construcuon Costing on Saends Treatment Lro Concentric round,.............Hone.....

~ ~. ~ ~.~...".Noae..............l.o

.....~.......1.0 Concentric round..............Tlo or enoy........

~. ~.None..........~...1.0

........~....1.0 Concentric round..............Hone.~...............

Yes...............l.o

.....~.......0.80 Compact round o

~

Noae

~

~ ~ Yes

~

~

~

I 0

~ ~

~

~

~ 0 0 Compact segmental.......,....Hone..................Noae..............0.43$

.............0.0 Compact segmental............Tin or aUoyoo Hone

....O.S

. ~..

0.7 Compact segmental............Hone..................Yes...............0.43$

.."...~.....0.37 Compact sector................Hone...............

~..Ycs...............l.o.............(secnotc)

Horns:

1.

The term "treated" denotes a completed conductor which has been subjected to a drylog and lmpregnat lng process simaer to that employed on paper power cahte.

2.

Proximny edect on compact sector conductors may be tahen as ose half of that for compact round having 'thc same cross scctloosl area asd Lnsutsuon thtchncss, 3.

Proximity CUcct on annular eooductors may be approdmsted by using the value for a concentdc round conductor of the same cross-cctfsnnsL area and spadng, The locressed diameter ol the annular type and the removal of metal from the center decreases the shin eifcct but, for a given adsl spsdng, tends to. result tn an lnaease ln proximity.

o 4.

The values listed above for compact scgmentsl refer to four segment constructtooa The uocoatcd treated" values msy also be tahcn as apphcabi ~ to four segment compact segmental with hoaow core (ap proximately 0.7$ inch dear).

For "uncoated treated" six segment houow core compact segmental limited test data lodicatcs ko and kp values of OA and OA respectively.

Tabl>> III. Skin Effect fn % in Solid Round Conductor lnd in Conventionel Round Concentric Str4nd Conductors 100 F(x), Skin Effect fo 3

4 5

d 7

d 9

his permits a ready determination of the losses if the segregated a-c/doc ratios are known, and conversely, the aoc/doc ratio is readily obtained after the values of Ycs Ys and Y< have been calculated.

Itfollows from the definitions of qs and qc that Wc+WC Yc qsw m]+

Wc 1+ Yc Wc+WC+ Wp Yr+Yp qc i+-

We 1+ Yc (18)

(ip)

The factor Y, is the sum of two compo-nents, Ymdue toskneffect and Y,p due proximity effect.

Wc ~lsRefc(1+ Ycc+ Ycp) watts per conductor foot (20)

(21) xs ~0.875

~

at 60 cycles

$ Rcc QRcr/ks (22) in which the factor hs depends upon the conductor construction.

For conventional conductors a

nctton F(x) may o tatne om Table'II or from the curves of Fig. 1 in terms of the ratio Rs,/h at 60 cycles.

For annual conductors solid or

~Srrotnate eIL The, (2$ )

in vrhich D, and Ds represent the outer The skin etfect may be determined from the skin effect function F(x)

~ Ycc~F(xr) 0.00...

0 Ol ~ ~ ~

0.04..

~

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0 $4o ~ ~

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23.03...

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~

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3$.44oo ~

38.8$...

42.3$...

4$.93...

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29.27, ~

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~ 30.21.

32.4$.. ~ 32.78... 33.11... 33.44...

3$ 78..

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35.TQ.

39.20e.

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49.94... 50.30...

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Ld.d2... 17.15..

17.30 19.28... I9.64...

19.80 21.93..

~ 22.20...

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41.29 ~. ~ 41.ds 44.49... 44.8$... 4$.21 48.11... 48.4T... 48.84

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2.$... LT.64...

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2,$.. ~ 2$.62oo ~

2.9.

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~

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~

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~

4.T... 93.$3..

4.8.

~. 97.13..

4.9..

~ L(tO.TL..

and inner diameters of the annular con-ductor.

In comparison with the rigorous Bcssel function solution for the skin effect in an isolated tubular conductor, it has been found that the 60~cle skin effect of annular conductor when computed by equation

'23 will not be in error by more than 0.01 in absolute magnitude for copper or aluminum IPCEA (Insulated Power Cable Engineers Association) Sled OcTOUUR 1957

%cher,.lfcGrcfhT~n(pcrc]nrc and Load Capability pf Cnbtc Sysfcfns 7M

6 as

~

I ~

Ta6I>> IV.

Mutual Reactance a160 Cyeiess Conyfudoe lo Sheath (or Shlelsf)

D~/28

--0 1

2 3

4 5

5 T

8 9

6 (2 S/D~) as in the case of lead sheaths.

<<~ 1+-

't

'I j 'I

~tj core conductors up through 5.0 CI and for hollow core concentrically stranded copper or aluminum oilrfiilled cable conductors up through 4.0 CI.

For values of xp below 3.5, a range vrhich appear to cover most cases of prac-tical Interest at povrer frequencies, the conductor proximity efect for cables in equilateral triangular, Eormation in the same or in mpaiat'te ducts may be cal-culated from the followingequation based on an approximate expression given by Arnold'equation

7) for a system of three homogeneous,

straight, parallel, solid conductors of circular cross section arranged in equilateral formation and carrying balanced 3-phase current remote from all other conductors or conducting material.

The empirical transverse con-ductance factor kp is introduced to make the expression applicable to stranded conductors.

Experimental results sug-gest the values of kp shown in Table IL Yep-F(xp)(-') X is)

+0.312 (24) 6.60 at 60 cyattt (25) e p

When the second term in the brackets is small vrith res pect to the Grst term as it usually is, equation 24 may be written at I

I m)5(De/S)t 1 Yep ~4F(xp)i J

F(x,)+om

~4(')

F(xp')

(24h)

()

Ijt'"

r 6

~

'li

'I vrhere the function F(xp') is showa in Fig. l.

The average proximity efect for con-ductors in cradle configuration in the same duct or in separate ducts in a forma-tion approximating a regular polygon may I

~

~

~

Ta6l>> V.

Speci8>> Intiuctiv>> (:apadlance of Insufations also be estimated from equation 24 and 24(A).

In such cases, S should be taken as the axial spacing betvreen adjacent conductors.

The factor Ys is the sum of tvro factors, Y<<due to circulating current efect and Y<<due to eddy current efects.

Ws I'Rd< Yes+Yes) watts p>>r conductor foot (26)

Because of the large sheath losses vrhich result from short~ited sheath opera-tion with appreciable separation between metallic sheathed single conductor cables, this mode ofoperation is usually restricted to triplex cable or three singie~nductor cables contained in the same duct.

The circulating current dfect in three metallic sheathed singlemnductor cables arranged in equilateral configuration is given by Rs/Ree 1+(Rs/Xw)s (27)

. When (R,/X~)t is large vrith respect to unity as usually is the case ofshielded non-leaded cables, equation 27 reduces to X~

Yse ~

approximately RIRde Xss ~0.882/ IOg 2S/Ds~

microhms per foot (28)

~52.9 Iog 2S/Dses microhms p>>r foot at 60 cydes (28A) where S is the axial spacing of adjacent cables.

For a cradled configuration X~

may be approximated f'rom 2.52S 0

/

S X ~52,9 log'-(

)

b,-S) microhins per foot at 60 cydes (29)

~52.9 log 2.3 S/Dyes approximately (29A)

Table IVprovides a convenient means foi determining X for cables in equilateral configuration.

The eddy~eat efect for single-coaductor cables in equilateral configura-tion with open~cuited sheaths is Materia)

Polyethyleae.................2.

3 Paper lasuiatlou (solid type)...3.

~ (1PCEh ea)ue)

Paper jose) atjoa (othee types)..3, ~.2 Rubber aod eubbee jjhe coos pounds....

~...............5 (lPCEh va)ue)

Varnished eaesbrje.........,,.S (IPCEh value) 3RI/Rde 1+-

(30) when (5.2 R,/J)'s large in respect to 1/5 0.4.

~."21 ~ 1. ~ ~ ~ 20.5,. ~ a19 9....r19 4.....18.9..".18.3.....1T.8...

~.ly.i..."15.9..".15.4 0.3.

~ ~ ~ ~ 2T.T. ~ ~ ~ 25 ~9...

~25.2" ~..23 '.....24 as. ". ~ 24. l."..23.5....

~22.9.....22.2.....21.5 0.2.....3T.0....33.9,.34.8.....33.8.

~...32.8.....31.9.....31.0.....30.1.....29.3.....28.4

0. 1"".52.9. " 50.T....48.T...

~.45.9.

~. ~.45.2..

~ ~.43.5.....42.1.....40.T*.

~ -.39.4

~ ~ ~ ~.3' roximattly at 60 cycles (30A)

When the sheaths ale short~ted, the sheath eddy loss mal be reduced and may be approximated by multiplyingequations 30 or 30(A) by the ratio R,'/(Res+Xmas)

In computing average eddy current for cradled configuration, S should be taken equal to the axial spacing and not to the geometric-mean spacing.

Equations 30 and 30(A) may be ural to compute the eddyment-,ef >>et for single-conductor cables installed in separate ducts.

Strictl s

ag, these uations a

ly onl to three cables in equilateral con-guration but can be used to estimate osses in e cable ou s when latter are so oriented as to a roximate a re lar polygon.

TEe eddyment efect for a 3-conduc-tor cable is given by ArnoId.'RI (2s/D~)'2s/Dsw)'1 4 +1 (2y/D~)s

~ ~ ~

5.2R, 16 +1 f

When (5.2R /f)i is hrge vrith respect to

unity, Y ~

approximately at 60 cyd>>s (31A) 3~1.155T+0.60Xthe Vgauge depth for compact sectors

<< 1.155T+0.58 D, foi round conductors iuy)

~ and T is the insulation thickness, indud-ing thickness of shieldiag tapes, iE any.

While equation 31(A) vrillsuKce for lead sheath cables, equation 31 should be used for aluminum sheaths.

On 3~nductor shielded paper lead cable it is customary to employ a 3-or 5-mil copper tape or bronze tape inter-calated vritha paper tape forshielding and binder purposes.

The lineal d-c resist-ance of a copper tape 5 mils by 0.75 inch is about 2,200 microhms per foot of tape at 20 ('he drc resistance per foot of cable will be equal to the lineal resist-ance of the tape multiplied by the lay correction factor as given by the expres-sion under the squ3:e.root sign in equation 13.

In practice the lay correction factor may vary froin 4 to 12 or more resulting In shielding and binder asscinbly resist-756

.i cher, McGrctl:Tcn:pcrc! arc and Load CaPability oj Cable Systcn;s QCTOBER 195I

}

s,

'I he ances of approximatdy 10,000 or more microi<ms per foot of cable.

Even on thc assumption that the assembly resist-ance is halved because ofcontact with ad-jacent conductors and the lead sheath computations made using equations 2?

~

and 30 shocv that the resulting circulating and eddy current losses are a fraction ot 1% on sizes ofpractical Interest.

For this reason it is customary to assume that the losses in the shielding and binder tapes of 3oconductor shielded paper lead cable are negligibleo In cases of nonleaded rub-ber power cables where lapped metallic tapes are frequently

employed, tube effects may be present and may materiaUy lower the resistance ofthe shielding assem-bly and hence increase the losses to a point where they are of practical signiG-CanCeo An exact determination of the pipe loss effect Yp in the case of single~nductor cables instaHed in nonmagnetic conduit or pipe is a rather involved procedure as indicated in reference 7.

Equation 31 may be used to obtain a rough estimate of Yp for cables in cradled formation on the bottom of a nonmagnetic pipe, how-ever by taking the average of the results obtained for wide triangular spacing with saa(Dp'-Ds)/2 and for dose tri-angle spacing at the center of the pipe with 2~0.578'DThe mean diameter of the pipe and its resistance per foot should be substituted forDr and R, respectively, For magnetic pipes or conduit the foUowing empirical reIationshipss may be employed 1.54s-0.115D p Yp ~

(3~nductor cable)

Ac (33) 0.89$ -0.115D p 4

dose triangular)

(34) 0.34$ +0. 175Dp Yp~

(single-conductor, 244 cradled)

( 5)

'These expressions apply to steel pipers and should be multiplied by 0.8 for iron conduit.s The expressions given for Y, and Ys above should be multiplied by 1.7 to Gnd the corresponding in-pipe effects for mag-netic pipe or conduit for both triangular and cradled conGgurations.

CALCULATIONOF DIELECTRIC LOSS The dielectric loss Ws for Saocdnetor shielded and a~in teaondnetor cable ts given by the expres'sion 0.00276Esrr cos c) lo

( Lr :D )/DQ"--.

-conductor foot at 60 cycles (36) and for 3~nductor belted cable by'.019E'c, cos c)

Wg~'atts per s

coccdccctor foot at 60 cydes (37) where Z is the phase to neutral voltage in kilovolts, er is the speciGc inductive capacitance of the insulation (Table V) T is its thickness and cos p is its power factor.

The geemetric facter Gs may be found from Fig. 2 of reference 1.

For compact sector conductors the di-electric loss may be taken equal to that for a concentric round conductor having the same cross-sectional area and insulation thickness.

r'eo Calculation of Thermal Resistance THERMALRESISTANCE OF THB INSULATION For a single conductor cable, r

I Rf 0.012tif log Df/Dc thermal ohm-feet (3S) where sic is the thermal resistivity of the insulation (Table VI) and Di is its diameter.

In multicoaductor cables there is a multipath heat Gow between the conductor and sheath.

The foUowing ex-pressionc represents an equivalent value which, when multiplied by the heat Gow from one conductor, will produce the actual tern peraturre devation ef the conductor above the sheath.

Bf~0.00522ifcGc thermal ohm-feel (39)

Values of the geometric factor Gs for 3-conductor belted and shidded cables are given in Fig. 2 and Table VIIIrespec-tively of reference l.

On large size sec-tor conductors with rdatively thin in-sulation waUs (i.eo ratios of insulation thidmess to conductor diameter of the order of 0.2 or less);

values of Gl for 3-conductor shielded cable as de(ermined by back calculation, on the basis of an assumed insulation resistivity, from lab-oratory heat-run temperature-rise

data, have not always confifmed theoretical values, and, in some cases, have yielded Gi values which approach those for a nonshielded, nonbelted construction.

T46fe Vl.

Thermal Resistivity of Various Ma(erich Material if, C Cm/W'acc paper fosulacloo (solid Cype)...T00 GFCEA value)

Varnished cambric.~....

~.. ~..000 (IPCEA value)

Paper iosulacloa (ocher cypes)..500-Mo Rubbct aod rubbct.lihe.. ~ ~ ~...$00 (IPCEh value)

JuCe aod Cessile prolectlve COVeffaeo ~

~

~ ~ ~ ~ ~ ~ ~

~ $00 Fiber duccoo ~ ~

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 480 Polycchyleae...............

~.4$0 Traaid'ce dticc

~ ~ ~ ~ ~ ~ ~ ~ ~

~ 200 Somasclcooooo

~ ~

~ ~ ~ ~ ~ ~ ~ ~

~ ~ 100 THBRNALRESISTANCE OF JACKETSr DUCT WALLs,ANUSo)MsTIc CohTINcs The equivalent thermal resistance of relatively thin cylindrical sections such as jackets and Gber duct waUs may'e determined from the expression

,/t N

g ~0.0104)a'(

)

thermal ohcn-feet (D-I)

(4O) with appropriate subscripts applied to 8,

sI, and D in vrhich D represents the outside diameter of the section and t its thickness.

rc'is the number ofconductors contained with the section contributing to the heat Gow through it.

THERMAL REslsThNcE BETwEEN CABLE SIFhcE ANU SIROUNnnfc PIPEs CONUUTT,.OR DUcr WALL Theoretical expressions for the thermal resistance between a cable surface and a surrounding endosure are given in refer-ence

10. ~ indicated in Appendix I, these have been simpliGed to the general form rcrdt

, thermal ohm-feet 1+(B+C1'm)Ds'41) in which dt, B, and C are constants, D,'epresents the equivalent diameter of the cable or group of cables andrs'the number of conductors contained within Ds'.

T~

is the mean temperature of the interven-ing medium.

The constants d4, B, and C Table Vil.

(:onsfcnts for Use in Equc(fons dt and 4I(A)

Coadlcloa B

c Aa mecalliccondulC...................IT

~......3.0.........0.0"0.........3.2.....

~ ~ ~ oo 10 In dbcr duet la air...................ly

.........2.1.........0.010.........$.0....." "0 ~ 33 Io dbcf duet lo cooetece..

~

~ ~ ~...,,. IT,,,....,.2.8...,..0.024......,..4.d..

~.0 2T Ia Craaidce duec la afr................ly

~, ~......3.0.........0.014.........4.4......

~ ~.0 2d Ia craosfce duec lo coucrecc...

~ ~ ~.....1T,.......2.0.....,...0,020,........3.T.......

~.0.2-Gas-&lied pipe cable ac 200 psl.........

3. 1.........1.10.........0.00$ 3,......,.2. I.......

~ ~ 0. 0$

Oil dlled pipe cable....~.............

0.$4......

~..0

.........0.004$.........2.1......

~ "2 ~ 4$

fye'1.00 Xdlameser of <<able for oae cable I.dsXdhmecer of eablc for cero cables 2.1$ Xdlamccct of cable for Chree cables 2.$0Xdlamcccr of cable for four cables OcTQBER 1957 Kci:cr, If(GraK Tern pcratffre arid Load Capcbili!y of Cable Systems foi

15.6n','Kaz'/D,')

t<<+I.Gal+0.OIGTT)l thertnal ohm.feet (42) log +(LF) log F In this equation ATrepresents the. differ-thcrtnal ohm.feet (44) ence between the cable surface tempera-ture T, and ambient air temperature T, in degrees centigrade, T~ the. average of in which D< is th 'ter at which the portion oE the therm ctrcuit com-

'hese temperatures and c the coe6icient of mene'.and tt Is the num of con uc-tors contained within D,. 'he Gctitious diameter D>> at which the effect of loss factor commences is a function of the diffusivityofthemedium a and the length of the loss cyde.c emissivity of the cable surface.

Assum-ing representative.

values of T,~60 and T>>~30 C, and a range in D,'f from 2 to 10 inches, equation 42 may be simpliGed to 9.5n',

thermal obtn<<feet (42A)

D,~1.02> ct(length of cyde in hours) inches (45)

The empirical development o! this equa-tion is discussed in Appendix IIL For a daily loss cyde and a representative value of a~2.75 square inches per hour for earth, D>> is equal to 8.3 inches. Itshould be noted that the value of D, obtained Erom equation 45 is applicable for pipe diameters exceeding D in which case the Grst term of equatioa 44 is negative.

The factor F accounts for the mutual heating effect of the other cables of the cable system, and consists of the product'f the ratios of the distance from the, reference cable to the image of each of the other cables to the distance to that

cable, Thus, The value of c may be taken as ual to 0.95 or i

c nduits or ucts, and painted or braided surfaces, an 0.2 to 0.5 for lead and aluminum sheaths, depending upon whether the, surface is bright or corroded.

It is interesting to note that equation 42(A) checks thc IPCEA method of determining R, very dosdy with c~0.41 for diameters up to 3.5 inches.

In the IPCEA method 8, ~

0.00411 n'3/D~'here 9~050+314 D~'or D,'-1.75 lacbes and B 1,200 for Imrger values of Dt'I FEOTrvE. TaEBMhL RESIsThNcE BETWEEN ChBLES, DUCTS, OR PII'ESy AD AhfBIENT EhRTH

( t ~ c tt.~t>> )

As previously indicated, an efFective thermal resistance 8<'ay be employed to represent the earth portion of the thermal ci:cuit in the case of buried cable systems.

This effective thermal resistattce includes the effect oE loss factor ana, in the case of a m 'lticable installation, also the mutual F~.

~. (N-Itertas)

(46)

It willbe noted that the value of F will va~

depending upon which cable is sdected as the reference, and the maxi-mum conductor temperature wi11 occur in the cable for which 4LF/D>> is maxi-given in Table VIIhave been determined.

heating dfects of the other cables of the from the experimental data given in refer-system.

In the case of cables in a con-cnces 10 anti Il.

crete duct bank, it is desirable to further If representative values of T~~60 C recognizcadifferencebetweenthe thermal are assumed, equation 41 reduces to resistivity oE the concrete rrc and thc tt'ri'hermal resistivity of the surrounding

,thermal obm-feet (41A) earthA.

The thermal resistance between any It should be noted that in the case of point in the earth surrounding a buried ducts, A,e is calculated to the inside ofthe cable and ambient earth is given by the duct wall and the thermal resistance of expression'c the duct wall should be added to obtain EE>>c ~0.012ts, Iog tt'/8 thermal obm-Feet (4>)

y, ERMhL RBsIsThNcE PRost ChBLEs>

m which p~

th th al ti ty ofthe

't 't Ta is e

tance from the image CoNDUITs~ oR DUcTs SUsPENDBD IN earth rlr is of the cable to the point P, and d is the The thermal resistance R, b tweendistance Erom the cable center to 2'.

cables,conduits,orductssuspendedinstill From this equation and the principles air may be determined from the Following discussed in references 3, 12, and 13, the expression which is developed in Ap-following expressions may be devdoped, pendix L a

licable to directly buried cables.and to~i;type'-cab es.

c gC 8>>'.~0.012Pgtt'X mum. N refers to the number oE cables or pipes, and Fis equal to unity when N~l.

When the cable @stem is contained within a concrete enydope such as a

duct bank, the effect of the differing thermal resistivity of the concrete en-velope is conveniently handled by Grst as-suming that the thermal resistivity of the medium i that of concrete rF, through-out and then correcting that. portion ly-ing beyond the concrete envelope to the thermal resistivity of the earth i4.

Thus 1'g

~0.012tI,+'$(

c

(.3;[i. '-. (in')~))'~

ohm-feet'44A)

The geometric factor Gc, as dcvdoped

- in Appendix Ilis a function of the depth to the center of the concrete cndosure Q and its perimeter P, and may be found conveniently from Fig. 2 in terms of the ratio 4/2'nd the ratio of the longest to short dimension'of the endosure.

For buried cable systems T, shbuld be taken as the ambient temperature at the depth of the hottest cable.

As indicated m

reference 12, the expressions used throughout this paper for the thermal resistance and temperature rise of buried cable systems are based on the hypothe-sis suggested by Keaaelly applied in accordance with the principle. of super-position.

According to this hypothesis, the isothermal-heat Qow Gdd and tem-perature rise at any point in the soil sur-rounding a buried cable can be represented by the steady-state solution for the heat Qow between two paraM cylinders (constituting a heat source and sink) located in a vertical plane in an inGnite medium of uniform temperature and thermal resistivity with an axial separa-tion between cylinders of twice the actual depth of burial and with source and sink respectively generating and absorbing heat at identical rates, thereby resulting in the temperature of thc horizontal mid-plane between cylinders (Le., correspond-ing to the surface of the earth) remaining.

by symmetry, undisturbed.

The principle of superposition, as applied to the case at hand, can be stated in thmnal terms as follows:

IE the ther-mal network has more than one source of temperatu:e rise, the heat that Qows at any point, or the temperature drop be-tween any two points, is the sum of the heat Qows and temperature drops at

. these points which would exist if each source of temperature rise were conside:ed separatdy.

In the case at hand, the sources of beat Qow and temperature rise to be supcrimposed are, namdy, the heat 7OS rober, DfcGratlsTemperatttre and Loatf Capability of Cable Syste":s OcTooER 1957

from the cable, the outward Qovr of heat from thc core of. the earth, and thc in-ward h(at Qovr solar radiation, and, when

present, the heat Qow from interfering sources.

By employing as the ambient temperature in the calculations thc tem-perature at the depth of burial of the hottest

cable, the combined heat Qow from earth core and solar radiation sources is superimposed upon that produced at the surface of the hottest cable by the heat Qow from that cable and interfering sources vrhich are calculated separately with all other heat Qows absent.

The combinedheat Qovr from earth core and solar sources results in an earth tempera-ture which decreases withdepth insummer; increases.vrith depth in winter; remains about constant at any given depth on the average over a year; approximates con-stancy at all depths at midseason, and in turn results in Qovr of heat from cable sources to earth's surfac, directly to suz-face in midseason and winter and in-directly to surface in summer.

Factors vrhich tend to invalidate the combined Kennelly-superposition princi-ple method are departure of the tempera-ture of the surface of earth from a true isothermal (as evidenced by melting of snovr in vrinter directly over a buried steam main) and nonuniformity of thermal resistivity (due to such phe-nognena as radial and vertical migration of moisture).

The extent to which the Kennelly-superposition principle method is invalidated, however, is not of practical importance provided that an over-all or effective thermal resistivity is employedin the Kennelly equation.

Special Conditions Although the majority oE cable tem-perature calculations may be made by the foregoing procedure, conditions fre-.

quently arise vrhich require somewhat specialized treatment.

Some of these are covered herein.

EMERCENCY RATINCS Under emergency conditions it is fre-quently necessary to exceed the stated normal temperature limitof the conductor T, and to set an emergency tempegature limit T,'. If the duration of the emer-gency is Iong enough for steady-state con-ditions to obtain, ~then the emergency rating I'ay be found by equation 9

substituting T<'or T< and correcting ~,

or the increased conductor temperature.

If the duration of thc emergency is less than that required for steady. state con-ditions to obtain, the emergency rating of the line may be determined from Tc'-I'~1+ YcXN~'-R<<')-(2's+

Z (1+.Yg)8<<'n which 8<<g's thc effectiv transient thermal resistance of the cable system for the stated period of time.

Procedures for calcuhting E,g'or times up to several hours are given in reference 14, and for Ipper times in references 15-17.

~

~

C THE EFIECT.op ExTIumoUs HEAT SOUECEs In the case of multicable installations the assumption has been made that all cables are of the same size and are sim-ilarly loade<<L When this is not,the case the temperature risc or load capability ofone particular equal cable group may be determined by treating the heating effect of other cable groups separately, intro-

. ducing an interference temperature rise dTgg in equations 1 and 9.

Thus T,-T~~dT<+dTc+dT<<~g degrees centigrade (1A)

T~-(T(<<+dTa+ d Tg>> g)

I~

gg(1+ Yc)~ca'iloamperes (9A) in which dTg,g represents the sum of a number of interference effects, for each ofvrhich.

d2 <<>>g (IVa/LF)+IVclksg degrees centigrade (48)

Ag<<<~0.012<<r,>>'Iog Fg,g thermal ohm-Eeet (49)

((Egg'X<<E<<g'X<<E<<<<')" (EN<<'~

)

(<<Eg<<X(E<<<<X(E<<g)

"<<EN<<

(50) where the parameters apply to each sys-tem vrhich may be considered as a unit.

For cables in duct A.g 0.012>>'(r<<log F<<g+N(ggg-rr<<%l thegnud ohm-Eeet (49A)

Because of the mutual heating betvreen cable groups, the temperature rise of the interferin groups should be recheci:ed.

If all the cable groups arc to be given mutually compatible ratings, it is neces-sary to evaluate IV< for each group by successive approximations, or by setting up a system of simultaneous equations, substituting for W, its value by equation 15 and solving for I.

In case dT<<ng or a component of it is produced by an adjacent steam main, thc temperature of the steam Trather than the heat Qow from it is usually given.

Thus dT<<>>g

~gag degrees centigrade (Sl )

I kiloagnpeges (47) vrhere 8<<

is the thermal resistance be-tween the steam pipe and ambient earth.

A RIAL CABLEs In the case 'of aerial cables it may be desirable to consider both the cffects of solar radiation which increases the tem-perature rise and the effect of thc vrind which decreases it.gg Under maximum sunlight conditions, a lead-sheathed cable vrill absorb about 4.3 watts per foot per inch of profiIe" which must be returned to the atmosphere through thc thermal resistance 8,/>>r.

This effect is con-veniently treated as an interference temperature rise according to the rela-tionship dT<<((<< ~4.3Dg'/I,/>>r degrees centigrade (47A)

For blacI: surfaces this value should bc increased about, 75%.

As indicated in Appendix II,the follow-ing expression for l(I, may be used where V>> is the'velocity ofthc vrind in miles per hour 3.5>>'

'(~V/D,'+0.62 )

thermal ohm-feet (42B)

UsE CF Low-R'EsrsTIvITY Bane.L In cases where thc thermal resistivity of the earth is excessively high, the value of 8,r may be reduced by bacldiiling the trench with soil or sand having a lower value of thermal resistivity.

Equation 44(A) may be used for this case ifr r, the thermal resistivity of the bacldill is sub-stituted for grg, and Q applies to the zone having the bacldili in place of thc.

zone occupied by the concrete.

SINOLE-CCNDUcroa C((1BLES IN DUcT wITH SCLIDLY BCNDED SHEhTHS The relatively large and unequal sheath losses in the three phases vrhich may result from this type of operation may be deter-mined from Table VIoE reference

1. It vrillbe noted that Yrgg ~

g 'gcg ~

~

IS vrhere expressgons for I>gg/P etc., appear in the table.

The resulting unequal values of Y,ia the three phases vrillyield unequal values of (Eand equation 5 becomes for phase no. 1, the instance given as equa-tion 5(A) on the following page.

OCTOBEE 1957 3 crgcr, rf&GraligTerr:pcrafggrc a>>d Load Gxpabil<<Iy of Cab!c Systcr>>s 759

4Tci We[/fi+rfrsI/fre+/fe.+(LP)/f,pj+

. 'fq<<(fF)kpe]

thermal ohm-feet (SA) where qra Is the average of qrsI qrs> and qrs.

Table VIII. Coustanls for Use in Eque6on 53 Arerase AT ARMORED CABl.EB In multiconductor armored cables a

loss occurs in the armor which may be considered as an alternate to the conduit or pipe loss. If the armor is nonmag-netic, the component of armor loss Ya to be used instead of Yp in equations 14 and 19 may be caIculated by the equa-tions for sheath loss substituting the resistance and mean diameter of the armor for those of the sheath.

In cal-culating the armor resistance, account should be taken of the spiralling"effect for which equation 13 suitably modified may be used. If the armor Is mag-

netic, one would expect an mcreasc in the factors Y, and Y, in equation 14 since this occurs in the case of magnetic conduit.

Unfortunately, no simple:

pro-'edure, is available for calculating these effects.

A rough estimate of the induc-tive effects may be made by using the pro-cedure given above for magnetic conduit.

A simple method of approximating the losses in single conductor cables vrithsteel-wirc armor at spacings ordinarily,em-ployed in submarine installations is to as-sume that thc combined sheath and armor current is equal to'the conductor current.s The effective a.c resistance of the armor'ay be tdcen as 30 to 60% greater than its d-c resistance corrected for lay as in-dicated above.

Ifmore accurate calcula-tions are desired references 19 and 20 willbe found usehl.

EPPEcT oP F0RcED CooUNG The temperature risc of cables in pipes or tunnels may be reduced by forcing air axially along the system.

SimiIarly, in the case of oil-Glied pipe cable, oil may be circulated through the pipe.

Under these conditions, the temperature rise is not uniform dong the cable and increases in the dir'ection of EIow of the cooling medium.

The solution of this problem is discussed in reference 21.

based upon all of the data avaihbie and including the effect of the temperature of thc intervening medium.

The theoretical expression for the case where the intervening medium h dr or gas as presented in reference 10 snay be genenI.

Ised in thc following form:

and a range of 150-350 for De'T~ equation 54 reduces to equation 41 <<ith the values of A, B, and C given in Table VIZ.

In thc case of cables or yipes suspended in still air, the heat loss by ndhtion may be dctcrauncd by the Stchn-Bolznsann forsnuh rs',',

+b+cT~

(53) rs'W(radhtion)

~0,139Ds eKTa+273)e (Ta+273)ej10>>

watts ycr foot (55)

E,cathe effective thcrsnd reshtsuce be-tween cable and enclosure in thclnul obm-Eeet D,'~ the uble diameter or equivaIcnt dhsneter of three cables us Inches 4T~the tempcnture dIEfcrenthI in degrees centigrade P~thc prcssure In atmospheres T~~mesn tesnperature of the medium in degrees centigrade rs'~nusnber of conductors Involved The constants a, b, and c in thh equation have been established empiYicdlyas follows:

Conslderusg b+cTe as a constant for the

moment, the analysis given in reference 10 results in a value of a~0.07.

With a thus established, the data given ui reference 10 for cable in pipe, 2nd in reference 11 for cable in aber and txauslte ducts were andyzcd in sinuhr nunner to give the values of b and c which are shown in Table VIIL In order to avoid a reltentivc calcuhtloa procedure, it is desirable to assume a value Ear 41 since its actual value will depend upon ffre and the heat flow.

Fortunately, as 4T occurs to the 1/4 power in equation 53, the use of an average value as Iadicated in Table VIIIwill not introduce a serious

error, By further restrictissg the range of D,'o I-I Inches Eor cable in duct or coaduic and to 3"5 inches for pipe-type cables, equation 53 is reduced to equation 41.

where e

is the coeKcicnt of emisslvity of the cable or yipe surfaces Over the limited temperature nssge in which wc are Interested, equation 55 snsy be shnplificd to" rs'W (radiation) ~0.102Ds'4Te X (1+0.01671 ~)

watts pcr foot (SSA)

Over the same tempenture nnge the heat loss by convection from horixoatal cables or pipes is given with sufficient acciuacy by the expression rs'W(convection) ~0854 De'dT(dT/De') +e watts yer foot (56) m which the numcrica1 constant 0.064 has been selected for the best Eit with the carefully deternsined test results reported by'cilaunss on 12, 3.5 aud IQB-Inch dhmctcr bhck pipes (e~0.95).

Inci-

dentally, this value also represents the best Eit with the test data on 1~5 inch diameter bhck pipes reported by Rosch."

For vertical cables or pipes the value oE this numeriesI constant may be hicrcased by 22%"

Combiniag equations 55(A) 2nd 56 we obtain the relationship 4T rs'W(total) 15,8rs'r'K AT/Dr') a+1.6e(I+0.0167') I then'hm.feet (42)

Cable lu suetatuc couduls,...............0.07..

~.~.......0. 121...........0.0017..:.

~.. ~....20 Cable lu sber duce lu air..................0.07............0.03d...........0.0000............%

Cable lu dberdu<<t lu coucrete..

~..~.......0.07...,......0.043....

~~.....0.0014.....

~ ~. ~.20 Cable la srauslse duct lu afr................0.07............0.08tl..

~~......,0.0008.........

~..20 Cable lu trauslie duct lu coucrete..~.....

~ ~.0.07....,

~ ~.....0.079....~.....,0.0010..,.

~ ~ ~...20 Gas.elled pipe type cable at 200 pal.........0.07.,.....,..0.121...........0.0017............10 Appendix I Development of Equations 41, 42, and Table VIX Theoretical 2nd semicmpiricd expressions for the thermal rcslstarice between cables surd als eaclosirsg pipe or duct wail are given in refercricc 10.

Further data on the thermal resistance between cables arid Sber and tnrssitc ducts are given in ref-erericc 11.

For purposes of cable cating, it is desirable to develop staudardhcd expressions for these thermal resistances rs'A Are~, thcrmd ohm-Eeet (41) in which the values of the constants A,

B, arid C appear ln Table VII.

Ia the case of oil.6Iled pipe cable, the analysis givers ia referesicc 10 gives the following expression rs'.60+0.025(Dr" T~'dT)

~'hermal ohm-Eeet (54)

Assumiug aa avenge value of 4T~7 C If the cable h subjected to wind having a velocity of V>> miles pcr hour, the follow-ing cxprcssiors derived from the work of Schurig and Prick" should be substituted for the convectiors comyoricnt.

rs'IV(coavectiors) ~0.286Dr'4Tv Vu/De'atts per foot (56A)

Combining equations 55(A) arid 56(A) with T~~45 C 4T 3.5rs's'IV(mlsl)

D;(QV/D;+0.62e) thermal ehm-Eeet (42B) 760 iVeLer, yrlcGrc!r' Terrperafare and Load Capabilily o/ Cable Svs.'eras Ar-,nnm. 1057

g, g

Appendix'l Table IX.

Compadsoa of Values of go (+F) for Sinusoidal Loss Cydes at 30$

Loss Factor Da<<8.3 Inches.

As indicated in the Chird paper of reference 3. however, theorcQcally D/c shouM vary as the square root of the product of the dilfusivity and thc thne length of the loading cyde.

Hence as thc diifusivitywas taken as 2.?5 square inches pel hour ia the above, Da << Ig02X VacXlength of cyde in hours mches (45)

Table IX presents a comparison of the values of per cent attainmcnt factor for sinusoidal loss cydes at 30% loss factor as calculated by equations 45, 66, 62(A), and 63 and as they appear in Table IIof the Grst paper of reference 3.

Appendix"IY.'Cafculaations for Representative Ca6le Systems Determination of the Geometric Factor Gi for Duct Eanld Considering the surface of the duct bank to act as an isothermal cirde of radius ra, the thermal resistance between the duct bank and the earth's surface wUI be a logarithmh function of ri and Li the distance of the center'f the bank bdow the surface.

Using the long form of the Kennelly FonnuhLs we may deflne the geometric factor Gi as Li+O'Li'-ri'i<<

log ri

~og Igr/ro+O/(gr/ro)'-gl (gg>

In order to evaluate rb in"'terms of 'the dimensions of a rectangular duct bank, let the snuiier dimension of the bank be x and the larger dimension bP'y.

The radius of a cizde inscribed within the duct bank touching the sides is lifddI Desccfpdou, Srst<<u laches Ifehec ShsakllaV/lseugea pipe.... 53/53... dl/d2...d3/dd pipe.....dd/dd... 50/57....53/50 plpe..... 55/5... SO/58.. ~.54/53 plpe. o ~..58/58... 5 l/50...55/53 cable. ~ e ~

\\ ~ ~ ~ 80/80

~le'....77j75.

~ '.77/75....77/77 cableo ~ o oT1/71 cableoooo

~ ~ ~ ~ ~ ~ ~ 53/52 cablcoo

~. ~ ~ ~ ~ ~ ~ ~ o75/74 cable............77/Td cable....83/80...83/81 cable....Td/74...74/173 cable....TO/55.

~.To/5T cable.. ~.d0/54. ~. 55/54..51/53 I ~ ~ ~ ~ ~ ~ 4 5 Iloo

~ ee 5 d IIIoooooo 8 5 Iveoooo ~ 10 d Vo ~ ooo ~ ~ 0 d VIe ~

~ ~ ~ 1 5 VII~ eeo ~ I 0 VIII.... 2.0 IXooo oo 3 0 Xo ~ ooo ~ 3 4 Xa

~ roe 3 4 XI ~ oooo 3 T XII eoo 4 2 XIII 4.d a Dhduglelcy<<4.7 scuse>> lucha pcr hour.

15-Kv 350-NCN3<<Conductor

. Shielded Compact Sector Paper and Lead Cable Suspended in Air D, <<0.618 (equivalent round);

V<<gauge depth <<0.539 inch Dc <<2.129; T<<0.175 inch; l<<0.120 inch 12.9 /234.5+SIN cg

ggcgg,

(

0250(234.5+75)

<<37.6 microhms per foot (Eq. 10A)

Deca 2.129-0.120 2.009 inches (Eq. 12) fs <<x/2 (58) and the radius of a hrger cirde embracing the four corners is

/

O/x'+g'r rr 2

Lct us assume thaC the cirde of radius ri lies between these circles and the nugnitude of ra Is such Chat it divides the thernul resistance between rl and rs in direct rehtion to the portions of the heat Geld between rs and rs occupied and unoccupied by'he duct bank.

Thus th~~1 cQcult co~I9SSSS3 Equation 62 may be written in the form 8 '-8 +8 +(LFXd -8) thernul ohmofeet (62A)

In terms of the attainment factor (cfF), one may write (AF)~ca (ciFXNcc+/t¹)

thernul ohmofect (63)

Equating equations 62(A) and 63 obtains Che rehtionship Bcc<<(1-x)8¹-x/t<< thernul ohm.feet (64) where 37.9 C

'ggr roiororrroo 2.009(0.120) pcr foot at 50 C (Eq. 11A) kg <<1.0; kr<<0.6 (equivalent round)

(Table II) lac/>c <<37.6g Ycc O.OM (Eq. 21 and Fig. 1)

$<<0.616+2(0.175+0.008) <<0.982 inches J4Jkp <<62.6; F(xp') <<0.003 (Fig. 1)

Ycp<<4 0 003 <<0.002 (Eq. 24A, and aote to Table II) 1+ Yc<<1+0.008+0.002 <<1.010 s <<1.155(0. 175+0.OOS)+0.60(0.539)

<<0.534 inch (Eq. 32) 396 2(0.534)1 s

Yc<<Y¹<<

(

<<0.019 15?(3T.6) 2.009 J

(Eq. 31A) n xy-~ s f rsN log-r(log-)

or

~ ~**-.)(.)~ 'xy/

rsN tog (log-)

ri grss-r,s)(

r<)

from 'which log fi<<(

<<) log (I+

+log-2A~ y)

(

xs) 2 (40)

It is desirable to derive ri hl terms of the perimeter P of the duct bank.

Thus P <<2(x+y)<<4- (1+y/x) 2 I-(cfF) x<<1-(LF)

(45)

Since 8¹ <<0.012/s'p log Dc/Dc

~

thermal ohm-feet (44) and therefore 83 log Dc/Dc <<,KI-x)/tca-x/eccl

>>'/I (47)

P log-log 2

4(1+y/x)

(41)

Thc flrst paper of reference 3 presents the results of a study m which a number of typical daily loss cydes and also sinu-soidal loss cydes of the same loss factor were applied to a number of typical buried cable systems.

The results indicated that in all cases the sinusoidal loss cycle of the same loss factor adequately expressed the maximum temperature rise which was obtained with any of the actual loss cycles considered.

An analysis by equations 65 and 6T of the calcuhted values of attaiameot factors for sinusoidal loss cycles given in Table II and tile corresPoading cable systcra Pscamo etcrs given in Table I of the Grst papa'f reference 3 yields a most probable value of The curves of Fig. 2 have been developed from equations 57, 60, and 81 for several values of the ratio y/x.

It should be noted in passing that thc value of ri<<

0.112P used in reference 13 applies to a y/x ratio of about 2/1 only.

R/Rcc <<1.010+0.019 <<L029 (Eq. 14) qg<<qc<<I+

'<<1.019 (Eqs. 18-19) 0.019 1.010 c,<<3.7(Table V); E<<15/Q<<S.T; cos y <<0.022 Appendix ill 0.00276 (8.7)'f3.7(0.022)i 2(Q. 175)+O.BSC 0.681

<<0.094 watt per coaductor foot (Eq. 36 and text)

(Vote:

Ia computiag dielectric loss on Empirical Evaluation of D, In order to evaluate the effect of a cyclic load upon the maximum temperature rise of a cable system simply, it is customary to assume chat the heat Gow in the Goal

~

portion of the thermal circuit is reduced+

by a factor equal to the loss factor of the cydic Ioado The point at which this reduction commences may be conveniently expressed in terms of a Gctitious diameter Dao Thus Aca'<<Dec+(LF)/tcs thcrnul ohm-feet (42)

For greater accuracy, it is desuable to establish the value of Dc empiricaily rather than to assume that Ds is equal to the hich the earth i~con o hn~nggc ~ 10 Ar %I,M.o~/l.

7 ~/.

g ~,

o ~

4 r 4 / -a g/g.'r.

C / :g.

• <<a gir'a"<<t I

l'

sector conductors, the equivalent diameter of the conductor is tatcen equal to that of a concentric round conductor, Le.,

0.681 inch for 350 MCM.)

700 (Table VI); Gr ~0.45 (Table VIIIof reference 1)

~r 0.00522(700(0.45) }

1.64 thermal ohm-feet (Eq. 39) n'3;

~ ~0.41 (assumed) 9.5(3) 1+1.7(2.129(0.41+0.41)]

~7.18 thermal ohm.feet (Eq. 42A)

Nca ~1 64;+1.019(?. 18) ~8.96 thermal ohm-feet (Eq. 8) dT<~0;094(0.82+7.18) ~0.75 C (Eq. 6)

T, ~40 C (assumed)

I 81-(40+0.8) 37.6(1.010(8.96)1

~0.344 kiloampere (Eq. 9)

If the cable is outdoors in sunlight and subjected to an 0.84 mile per hour wind 3.5(3) 2.129(V 0.84/2.129+0.62(0.41)i

~5.59 thermal ohm-feet (Eq. 42B)

. Ace' 1.64+1.019(5.59) ~7.34 thermal ohm-feet (Eq. 8)

ATrrrr (4.3)(2.129)()

17.1 C

/5.59 i (3)

(Eq. 47A) dg c96'e cla" Lc4X5

/'r )

images

~ s J

dg

~ 96/"

dt

~ c 87.5" cc.

78 5.

3e.

I b

~ 43.5 Te <<30 C (assumed)

)81-(30+0.6+17.1) y (37.6)(1.010)(7.34)

~0.346 lriloampere (Eq. 9)

In this particuhr case the net effect of sohr radiation and an 0.84 mile per hour wind is to effectively raise thc ambient temperature by 10

degrees, which is a rough estimating'alue commonly usecL It should be noted,'owever, that this willnot always be true, and the procedure outlined above is preferable.'4 rcc ~

69-Kv Ir500-MENSingle-"

Conductor Oil-Filled Cable in Duct Two identical cable circuits will be considered in a 2 by 3 fiber and concrete duct structure having the dimensions shown in Fig. 3.

De~0.600; De~ 1.543l Dr~2.113; T O.N; D, 2.373; r 0.130 inches 12.9 Te~75 Cl Rec~

~8.60 1.50 p, microhms per foot (Eq. 10A)

Dna ~2.373-0.)30~2.243 inches (Eq. 12) 37.9 Rc (2 243)(0

30) ~ 130 microhms per foot at 50 C (Eq. llA) 1.543 -O.BOO(1.543+1.2003 c 1.543+0.600(1.543+0.600J 0.72; k~

O.S (Eq. 23 and Table il) 5 I.O on 69-lcv

$,500.MCM ci: pre/kc ~ll9r'cc ~0.075 (Eq. 21 and Fig. 1)

$~9.0 (Fig. 3) i Rec/4~

10.75'(x~')~0.075 (Fig. 1)

Ycrr 4(

)

0075 0007 (Eq 24A)

(9.0) 1+ Yc ~ 1+0.075+0.007 < li082 Assuming the. sheaths to be openwircuited, Yea ~0 1+-

'.006:"(Eq. 30A)

Rec/Rcr ~~ 1 082+0 006 1 088 (Eq 14) 0.006

~

1.082 qc aqc w1+.

],006 (Eqs. 18-19)

I ~

cr ~ (Table V); 8 ~69.'y 3 ~40; cos 4 ~0.005 0.00276(40) r(3.5.'(0.005) 2.113 log 1.543 0.57 watt per cond ctor foot (Eq. 30)

Fig. 3.

Assumed duct bonk conR9uratlon for typical calculations tj

4. if oil@lied cable (Appendix lV) 7R'?

rVchrr, N'd7rrrflrTrrrr6crahurc and Load Caoabrvitv of Cable Svsfrrrrs QCTOBBR 1957

I

2 iv'h 2;(

Pg <<5.0 (Table VI) aTc 0.57(0.45+1.75+0.24+4.63) 4.0 C 2.113

~

(Eq. 6) 88<<0.012 550 log~

~

~

> 45r Wcj (lr X8 BQX1.082) <<9 31 Ir

<<0.90 thermal ohm-foot 6((Eq. 38) r watts per conductor foot (Eq. 1S) 4Trf6g<<(9.31Irr KI.QOBX0.80)+0.5?l)3.81 2.37+087

<<2>17'+28.5Irs degrees centigrade in thermal ohm-feet (Eq. 41A) circuit no. 2 (Eq. 48$

irc<<480 (Table VI); 1<<0.25;

- Simihr calculations for the second circuit cp.,

Dc<<5.0+0.5<<5.50 for aber duct yield the foUowing values.

0.0104(480X0.25) lgc'.18; 4T<<<3.4; Wgg<<17.44IEE',

5.50-0M

~

4T(,g <<1.71+53.2IE'n circuit no. 1 120(asumed);

jfc 85 (TableVI)'...

~ :.(9.31)(6.$ 5) 0.715-0.859I22 (Eq. 9A)

. -(-.)('-:)('=".)('-)("=) ';, ':-"'"..";".";;,",....

<<42,200 (Fig. 3 and Eq. 46)

Solving simultaneously Ir<<0.714; Ir<<

1>(P 0.483; hs:

0.487 kiloampere.

2(18+27) 18 0>

0 87 (Ptg 2) 138-Kv 2000-2,102( 2(fgh-Pressure 5z~

Oil-Filled Pipe-Type Cable 8.625-

'c'(at 80% loss factor)

(0.012)(85)(l)X Inch&utside-Diameter Pipe 8.3 I 4(43.5) log.+0.80log[~42~)J)+

The cable shielding will consist of an hrtercalated 7/8(0.003)-inch bronxe tape 0.012(120-85X1)(6)(0.80)(0.87) l.inch lay and a single 0.1(02)-inch D-

<<6.79 thermal ohm-feet (Eq. 44A,)

shaped brass skid <<IreLS-inch ly.

The cables will lie in cradled conBguration.

Ec'at unity loss factor) <<8.44

~

~

th hm.feet (Eq. 44A)

Dc<<1.632; Dr<<2.642> T<<0.505; 16 Egg.

l2 p

R'gtg'0.90+1.00$

(1.7k+0.24+6.79) 72 ther<<) ehtu feet (Eu. 8) 7 70 <. 8 (189)(234 5+70 )

4'.57(

+L?4+0.24+8.44 8M 625 microhms per foot (Eq. 10A)

<<6.2 C (Eq. B)

ForshfeIdfngtape448<<7/8(0.003)<<0.00263l f<<I.Q; p<<23.8; 2 <<564 (Table 1)

Tc 25 C assumed),

75-(25+62) 23.8

(

(2.68

)',60(1.082)(9.72) 4(0.00263)$

(

1 j

<<0.696 kiioampere (Eq. 9) 564+50)

) <<62,900 mlcrohms To illustrate the case where the cable 564+20'ircuits are not Identical, consider the'er foot at 50 C (Eq. 13) second circuit to have

?50-MC'hf con-ductors.

For the erst circuit

. 'or skid wiregg r(Q 1)2 Q Q157 P <<3; (IF) <<0.80 (assumed);

(

l<<1.5; p<<38; r<<912 (Table I)

F<< <<92.4 (Eq. 46) 9 9

38E.

(2.6Br)2 R,

1+ X (8

t log+0.80 log (

92.4) J+

8.3 A(43.5) r I

<<11,100 microhms S.S

(

8.3

. )J 0.012(120-8SX1X3)(0.80X0.87) per foot at 50 C (Eq. 13) 5

~

~

<<3.74 thermal ohm-feet (Eq. 44A) l (62.9)(II.I)1 R, (net) <<L-JI>000

(

L(62.9X11.1)J

<<9,435 microhms per foot at 50 C k8<<0.435; kp <<0.35 (Table II) 0.012(1) X (85 log 456-;3(120-85)(0.87))

Rcg/kg <<14.6l Ycg <<0.052(L7) <<0.088

<<3.81 thermal ohrn feet. r (Eq, 49)

(Eq. 21, Fig. I, and text) ls l4'.90+1.006(1."4+0.24+3.74)

S 2.66+0.10

2. 6; Rc /k 17.2;

<<6.65 therrrral ohm.feet (Eq. S)

F(KP') <<0.035 (Fig. 1)

/1.632% 8 Ycp<<4(

)

(0 035X1 7) 0 083

( 2.76)

(Eq. 24A and text) 1+ Yc<<1+0 088+0.083 <<1.1?1 52.9leg (2.3X2.76) 2.66

<<20.0 microhms per foot (Eq. 29A)

(20.0) 2(1.7)

Yg<<Ygc<<<<0011 (Eq. 2?A and text)

Y (0 34X2.76)+(0.1?SX8.13) 6.35 (Eq. 35)

Rcc/Rcc <<1 171+0.011+0272 L554 (Eq. 14) 0.011 0.011+0.372

~

1.171

'.171 I~ (Eqs. 18-19) cr<<3.5 (Table V);.E <<138/Q3 <<80; cos p <<0.005 0.00276(80)2(3.5X0.005) 2.642 log 1.632

<<1.48 watts per conductor foot (Eq. 3B)

A<<550 (Table VI); 8r 0.012X

(

2.642(

550 log') <<128 thermal

'.1.632) ohm-feet (Eq. 38)

>>2<<3; Dc'.15(2.66) 5.72; 3(2.1)

Ru 77 there.tet 5.72+2.45 ohm-foot (Eq. 41A) ptr<<100 (Table VI); t<<O.SO; D,<<8.83+1.0 9.63 for 1/2-inch wall of asphalt mastic 0.0104(100X3XQ.SO) 9.63-0.50

<<0.17 thermal ohm.foot (Eq. 40)

Assume pc<<80, I <<36 inches, (LF)<<0.85; II<<1, F 1

88'(at 85% loss factor) 0.012(80)(3) X log

+0.85 log (1)

<<2.85 thermal ohm.feet (Eq. 44) 80'at unity loss factor) <<3.38 thermal obm.feet (Eq. 44)

Pgcg<<1.38+1.M9(0.7?)+

1.327(0.17+2.85)

<<6.1? thermal ohrn-feet (Eq. 8) 4Tc <<1.48(0.69+0.5 5 -,'0.17+3.3S) <<7.4 C (Eq. B)

Tc <<25 C (assumed);

70-(25'7.4) 4 3 (6.35X1.171X6.17)

<<0.905 ki!osmpere (Eq. 9)

References 1.

Catcocattox or tna Euactstcu.

Pooka,sxs ar UNoskokoaNO Casass, D. )tL Shameae.

Tbc Electric Iosraol, Bast Pittsburgh.

Pa May Nor. 1032.

Loca Pactoa axo EttotvaLsxt Hoaas

Coxraaso, P. H. Buiier, C. A. Woodrau; Ztec.

tricot W'orld, Ncw York,¹ Y., vai. 02, ao. 2, 1028 pp. 50-60.

3.

Stxroctatt ox Tsitrskatasa Rms or Casters, AIRE Caauaittee Report.

AIEE Tre>aroctio>tl>

vol. 72, yt. III,Juae 1053, pp. ~L 4.

h-C Rsarstaxcs or Ssoxaxraa Caucus nt Srsst. Prrs. L Meycrhotr, O. S. Eager, Jr.

Ibid.,

raL 68, pt. II, 1049, pp. 815-34.

d.

Pkorttxttv Enact ix Souo axo Hotaoer Romeo Coxooctoas, A, H. M. Araeid>>

Ieur>tot, Iaaututioa ol Eicctticai Eagiacecs,

Laodoa, Eagiaad, vol. 88, pt. Il, Aug. 1941, pp. 340 59. o, Eaov&aaksxv Loaass nc Mattress Parka.

INaotatso La*~russo Cast,aa, haxoaso ar>o Uxakxokso, Cakavtxo Baaaxcsa 3-Prtaas

Caaksxv, A. H. 5>L Arnot*

Ibid., yt. I. Peb.

1941, pp. 52-63.

T.

Ptrs Loecss M

Norocaoxsttc

Ptrs, MeyerhotL AIEE Trouracliosr, vaL T2, yt. III, Dcc. 1053, yp. 1260-T$,

8.

A>>C Rsarstaxcs or Prrs-Casts Svatsxs

>>mt Ssoxaxtaa Coxaactoks, AD1E Commiuee ReyerL lbQ ~ roL Tl> pt. III,Ja>L 1952, pp. 30 414.

AN Rsstataxcs or Coxrsuttoxar. Staaxo Pa>>as Caucus nt Noxxstaaue Duct axo ue Iaou Coxomt, R. W. Burteu> ItL Morda Ibid.,

voL 74, pt. 111, Occ. 1055, yy. ION 23.

10.

Tas Tasaxu. Rsetstaxcs Batvrssx Cosc,ss axo a Saakoauonto Piro oa Duct Waar F> H>>

Boiler, J. H. Zcher.

IbQ., vaL dy, yt. I. 1050, pp. 34~9.

11.

Haav Ta*xsrsa Stout ox Po>>sa Casus Ducts axo Deer heaaxsc,tss, Paul Cceebicr, Ouy F. Baraett.

Ibt>L, voL 69, pt. L 1050, pp.

SST 57.

12.

Trts Tsxrseataas Rtss or Baatso Casuas axttPtrss. J. K, Ireher, lbi>L, voL 68, pt. I. 1940, yp. 9-21.

13. Tas Taurus*toss Ries or Case,ss nt a

, Doer Baxr, J. H. Neher>>

Ibidpp. ~0.

-.14.

Ott Faow axo Pasaaaas Caacouattoxs roa S~Ntatxso Ott> Fttuso Casas Svstaxs>>

B. H. Bauer. J. H. Ifeher> P. O. Weutstoa>>

lb>>d.>

vaL 75, yt. III,hpr. 1055, pp. ISHl4 1$.

Tasaxax. Tkaxarsuts oN Boktso Castaa, F. P Bailer.

IS@., vaL TO, yt. I, 10SI, pp. 4~.

ld. Tas Dstsaxtxattox or Tsxrsaatoks Taaxatsxts nt Cast,s Svatsxs sv Msaxs or ax ANaaooaa Coxrotak>> J. H. )Ichor.

Ibid., yt. II, 1051, pp. 1361-T1.

17.

h Stxrurtso M*tasxattcaL Paocsaaka roa Datsaxtxtxo tas Taaxatkxt Tsxrskataas Rtssor Casut Svstsxs.J.H, Irchcr IbQ, vol.

72, pt. IILhug. 10$3, pp. 712-1S.

~ IiL Tss Hsattxo or C>tacks Exroaso to tas Sax tx Raas, E>> B. Wedmere.

leuc>>oL Iaatitu ttoa at Electrical Eagloccra, vcL TS,

1034, pp.

737&L 10.

Loaaas tx hat>ossa Stxaas~xaactok>

La~russo h>>C Cast.ss, O. R. Schurig> H P.

KuehuL F. H. Buuer.

AIEE Trc>>roctk>ur> rai.

48, hpr. 1020, yp 417~.

2tL CostaisotroN to tas Svaov or Loaass axo or Ssar4>ooottox or StuoasCoxuoctoa Ak xoaso Caaass, I Boaoae.

Zt>ttrol>cairo, Miiaa, Italy, 1931, y, 2.

2L hattnctaa, Coouxo or Poxsa Cast.s, F. H.

Bauer.

ALEE Troarcctlear, vai. Tl, yt. 111, hug.

19S2, pp. ~l.

22 Soar acs Hs*TTaaNSxiaaIQK>> R>> K,Henaiaa Tio>tt>xticer, htacricaa Society at hfcchaoicci Bagiaecrv. Neer York,¹ YroL 51, pt I, 1020.

pp. 287~

23.

Tss Caakaxt-CakkvLvo Caracttv or Ros ssa.INsuaatso Coxoacroaa.

S. J. Roach.

AIEE Trout>xrioor, raL ST, hyr. 1038, pp. 15~7.

24.

Hsatnto *No Coaksut~kttxo Car*cttv 0'

Baa' Couattctoks rok Oataooa Sskvics>

O. R. Schurig, O.

W. Prick.

Ce>>>rot Zfcclric R>rserr, Scrtcaectady, ¹ YvaL 33, 1930, y. 141.

Discussion C. C. Barnes (Central Electricity Authority, Londan, Enghnd):

This paper is an excel-lent. and up-~te study of a most hnpar-tant subject.

Par 25 yeirs D. M.

Simmons'rticled have been used for fundamental Study on current rating problems, but the numeraug cable deveiapmentg aud changes in indtaihtian techniques introduced in recent years have made a modern assess-ment af this subject very neccsgary.

The essential duty af a power cable is that it should transmit the maximum current (ar power) far Specified instaihtian canditiang.

There are three main factarg which deter-mine the safe continuous current that a cable willcarry.

1.

The maximum yertnidgible temperature at which itg campanentg may be aperated with a reaganable factor of safety.

E.

Thc heatMiggipathtg yrapertieg af the cable.

3.

The instalhtian canditians and ambient condithn5 obtaining.

In Great Britain the basic relerencc document is ERA (The British Electthal and AHied Industries Regeirch Asgachtha) reyatt F/TI31t published in 1939, and in 1955 revised current tutiag tables for solid-type cables up ta and including 33 kv were pubHshed in ERA report F/TI83.

A more detailed rcport sumtnarhing the method of computing current ratings far SOHd-type, ail GHed, and gas.preggure cables is naw being GnaHted and mn be published as ERA rcport F/TI87 satne time in 1958.

Until recent years currertt ratings in eat Britain have usually bten considered an a continuous basis, but the ltnpartance of taltittg into consideration cycHc ratings hag naw been eirefuny studied, since con-tinued high metal priced have forced cable users to revietr carefully the effects of cyclic laadings.

A report has recently been issued in which a simple methad h yre-gcnted for the rapid calcuhthn of cycHc ratings.'able V giveg Specific inductive capaci-tance values far yaper ast paper htguhtion (SOHd type), 3.7 (IPCEA value);

paper inguhtian (Other type), 33-4A Is it pad-sible ta Hdt the other types and their apyrapriate Specific inductive capacitance values or alternatively gunply use an average Specific htductive capacitance value af 3.7, far etample> for aH types af paper inguhthn?

Reference 15 made ta the adaption of the hypothesis suggested by KenneHy as the bash of the papu this ig'a logical approach but it appears ta dEer fiant the basis of computing ratings hitherto adopted in the United States.

An ampHGcatian of the autharg'iewpoint aa this important issue wiHbe >>deemed.

With reference ta the use af low-resittivity bttchfiH, recent Studies in Great Britain have Shown that the method of bachGHing cable trenches deserves careful cangideta thn as atteathn ta this point can result in incretset up ta 20% iu had currents.

Equatha 43 gives the thettnal resistance between any point in the etrth Surrounding a buried cable and ambient earth. It is Table X.

Tempetblute Llmib for 8eHed; Screened-cnd HSL f'-Type Cebiet LaM Direct or la A)r Ia Ducts Syeteai Voltage aad Tyye ai Cable Lead Sheathed Armored Ua-armored Aiamiaum Sheathed Armeured or Ua-armored Lead Sheathed Ua Armored armored Atom)asm Sheathed Armored er Ua armored 1.1 kr Stogie>cate..

F 80

~ ~ ~ ~ ~

~ 80

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ ~

~ ~ ~ 60>> ~ ~ ~ ~ ~ ~ ~

Ttria aad multicoce baited.>> ~ ~ ~ 80

~

~ ~ ~

SO>> ~ ~ ~ ~ ~

~ ~ 80

~ ~ ~ ~ ~ \\ ~ 80

~

\\ >>60

~

~

~

80 2.3 kr aad 5.5 kr Siagtehae

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~

~

~ ~ 80

~ ~ ~ ~ ~ ~ ~ 80

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ ~ ~ ~

~ 50

~ ~

>> ~ ~

SO Thf~rc baited type

~

~ ~

~ ~ ~ ~ 80

~ >>

~ ~ ~ ~ >>80

~ ~ ~ ~ ~ ~ ~ 80

~ ~ ~ ~

~ ~

SO

~ ~

~ ~ ~ ~ >>60

~ ~ ~ ~ ~ ~ ~ 80 11 kr Siagic~..

~.......70.........70.....................50.........70 Threncoee belted type.......

~..SS.....,...5$...,.....65...,......5$.........50.........d5 Three>>care acrceacd type..~.....> 0..~......TO.........TO,........70.........50.....,...TO 22 kv Static~re..

..5$.........6$............

~........$ 0....

~.

~ ~.5$

Three-care betted type..........SS.........SS,...........,........$

5.....,...50 Threescore icrceocd type........6$.........55.........5$..........5$.........$ 0....... "5$

Tht~c lSLI or Shl)........65...................

A$..........65....................55 33 kr (ccrccacd)

Static~re..

.55.

50 Three core HSL...............OS.

.65

~ Mccauccd ia degrcca ccatigrade.

t Hachttatcc separate lead.

I Separate iced rheatbcd.

1 Separate alumtouaa sheathed.

not

clear, however, what value of soil thermal resistivity is used in this expression and information on this important point ls desirable.

In Great Britain a value of soil thermal resistivity (g) of 120 C cm/watg is generaHy used but further test data are being slowly acquired.'nd where tests have indicated that a lower value, e.g90 C cm/watt, is justified. this value is used.

Current loading

~ tables in ERA report F/T183 provide data for soil thermal resistivity values of 90 and 120 C an/watt, and correction factors for other values o! soil thermal resistivity are also provided.

In the United States buried cables are usually pulled into duct banks, but there must be many cases where'irect

burial, as aormaHy,.used in Great Britain, wiH result in lower'instaHation coits.

Formulas dealing with this instaHation technique are a desirable addition.

Permissible tem-perature limits for the various types ot cables and instalhtion conditions used in the United States will be a helpful ap-pendix, and itis suggested that this informa-tion should be added to the paper.

For comparison

purposes, the limits recom-mended in Great Britain are summariged in Table X and in the foHowingl Phstic-insuhted power cables............

70 C maximum conductor temperature Gas-pressure and oH-HHed cable systems

(<< types).

85 C maxiniunl conductor temperature Finally, it will be helpEul to know if adoption of the formulas in the paper wiH necessitate revision or ampliHcation of existing rating tables and, iE so, when the revised tables will be published.

REpERBBcas 1 ~

CQRRRNT RATcvo or CAsass roa TRANS sccsscoN

• ND DcstacsonoN, S. Whitehead, E. E.

Huichfngs.

Rcporh Rcfcrcrccr P/PfJl, The Bcfffsh Efccccfcaf aad Allied fodusccfes Reseacch cfssocfa cion. Lcaihechesd.

Eogtaad, 1939; also Jo rsel, fastftutfoo of Elcetcfcal Baglaeecs,

Loadon, Bagland, vol. 83, 1938, p. $ 1T.

2.

Tss CAaeoaanoN or Ctcuc RAToco PActoas roa Case,ss LAco Dcaact oa sN Doers, E Golden berg.

Precccdfacc, foscffusfon of Electrical Eagf

seers, Leaden, Eaglaod, TOL 104, pe. C, 195T, p.

154.

H. Goldenberg (Electrical Research Asso-chtion, Leathcrhead, England):

The cal-cuhtion of cable ratings ls a subject of prime Importance to cable engineers.

Nevertheless, it seems that until recently the American standard work on this subject has been that of Simmons,'hile the corresponding British standard work has been recorded by Whitehead and Hutch-lngs.

These papers have been supple-mented by scattered pubHshed papers.

including developments deaHng with cyclic loading.

The paper by 3fr. Neher and Mr. Mc-

" Grath records up to date American cable-rating practice in a manner that will prove invaluable to engineers for many years to cocne.

It is a pleasing feature that the authors are espcciaHy competent to deal with this subject in view of their valuable contributions to the cable-rating field over a number of years.

Modern British cable rating prsctice has recently been recorded in an ERA reports deaHng with continuous current ratings.

and in two IEE (Institution of Electrical Engineers) papersc>

(based on ERA reports) deaHng with cycHc hacHng, but the majority of this work ls in process of printing and pub Hcation.

An obvious dHEerence in British and American technique is the method of cycHc rating factor calculation.

Mr. Neher and Mr. McGrath'5 method is based on an equivalence between typical daily loss cycles and sinusoidal loss cydes of the same loss factor, while a method recently hftro-duced in Britain'4 takes full account of the form of a daily load cyde.

Both methods are considerably shorter than any that have been available'itherto.

Nevertheless

-,without further study I would not feel certain that for British.type cables, subject to their typical daily cycles, the Eorm of the cycHc load can be ade-quately taken into account by use of the loss factor independently of the cycHc load wave form giving rise to it. In hct the conclusion reached in my second IEE

'paper,s is that a knowledge of the cyclic load wave form for thc 6 hours6.944444e-5 days <br />0.00167 hours <br />9.920635e-6 weeks <br />2.283e-6 months <br /> prior to peak conductoi temperature, together with the loss

factor, are adequate for cycHc rating hctor cdcuhtion.

However, it would be unhir to assess any of the rehtive merits of the two methods prior to the publication of one of them.

The difference between Britbh and American cable rating technique is not so marked for continuous current rating cal-cuhtion as might appear to be the case at Grst sight.

In hct, such dilferences as exist are principally due to the dHIerent types of cables employed on each side of the Athntic, and to the diiferent standard aw frequencies in use.

Nevertheless a

comparison o! the present paper with the ERA report dealing with continuous current ratingss gives rise to certain observations.

The present paper fs principaHy.directed to the calcuhtion OE a single current rating, but one use to which it might weH be put is the hrge-scale preparation of current rating tables, with rating hctors for non-standard conditions.

For such an applica-tion it Is often preferable to introduce explicit formuhs for the rating factors, as these formulas might be independent oE some of the thermal resistances or loss factors involved, with a consequent saving in calculation time.

The method employed for external ther-mal resistance calculation for grouped cables hid direct in the ground differs somewhat from that.recolnmended in a recent paper of mine.c For the preparation OE group rating factors for the more com-monly occurring groups of cables dealt with in an ERA report,s the combination of certain simpli6ed external thermal

'esistance formuhs and my recommended method has led to i substantial saving In calculation time. I do not favor the introduction cf a geometric mean distance, or its equivalent, as it is inconvenient for unequally loaded cables.

A brief rcsucn6 of other points is that the thermal resistivity values given in Table VI for thermal resistance calculation are generally somewhat lower than the corresponding British

values, that the proximity effect on cylindrical hoHoir conductors appears to mc to be best ob-tained from Arnold'5 paper.s that where sheath and nonferrous reinforcement losses occur a paraHel combination oE sheath and reinforcement resistance permits the cal-cuhtion of a single loss factor. that a simple formula has been derived for the external thermal resistance of one of three cables in trefoil touching Eormation hid direct in the ground,'nd that sector colrecriion factors are often used ia British practice for 3~re cable rating calcuhtions.

REFEaasfcss 1.

See ccfeceaee 1 of the paper.

2.

See cefeceaee 1 of bfc. Basses'fscossfoa.

Tss CAacoaano>> or Cosnsccoos RAnsos AND RAnND FActoas roa TRANacccsscoN AND DistacsictioN CAaass. K Galdeabefg Rcpers Rcfcnucr P/Tlry Elbl, Irsedea, Eoglaad, (ta be published).

4.

Sce cefcccace 2 of Mr. Bacncs'fscossfoa.

5.

Tss CAacoaanoN or Ctcccc RAnND PAccoas AND EicsRDSNCT LDADcso roa ONR oa Moss CAscss LAiDDcRsct oa Dc Ducts, K, Gold enbecg.

$feeorrepA cco. 3$l, fastftosfon ol Efcoscfcsf Engi-neers, July 1951.

8.

Tss Esctsavao Tssauaa Rosie TANcs or Boacso CAai ss, E. Goldenbecg.

Eceeccc Jeurccef, London, England, vof. $4, ao. 1, Fcb. 195T, p. 38.

T CQRRSNT RAIQcos roa

~ PArsa TNslKATRD C*sass To B.S.480, 1954; VARNcsssoCANsasc INsccLATSD CAÃ.ss To B.S. $98, 1955.

Rcport, Rc fcnacc P/I'lpp, The British Efccccfcal and AQfcd industries Research hssocfasfeo, Leachcchcad, Eag lead.

8.

See reference 5 of ihc papa.

Elwood A. Church (Boston Edison Com-pany, Bostoni Mass.): The authors present a hrge amount of useful data and formulas for the calcuhtion of cable thermal con-stants and suggest a new approach to the problem of calcuhtion of temperature rise for various loss factofs including steady-load or 100% loss hctor.

Cable engineers usually agree on the hctors to be taken into account and the methods of calculation for steady loads.

However, there appears still to be disagreement on the problem o!

cyclic loading.

At the AIEE General Meethig in January

1953, a

group of papers'as presented suggesting various approaches to the problems of cycHc loading on buried cables and on pipe-type cable.

Of the methods suggested in these

papers, the one which appealed to the author the most was Mr.

Neher's methocl using sinusoidal loss cycles.

In his paper it was shoitn that this method yields reasonably accurate results for the higher loss factors.

For a low loss hctor sharply peaked cycle the results are not a5 accllrate A modification of this method would be to represent the load cyde more accurately by splitting it into harmonics and com-puting the temperature rise Eor each harmonic separately.

This eatails more work. but with modern methods of machine calcuhtion it is cconocnical to use the most accurate method available and let the rnachine perforni the hborious cal-culations.

In fact, it takes very little more time on the machine when the more rigorous methods are used instead of, any of the approximate methods which have been suggested.

The author has invcsligslcd. the various methods of catculalioa of the cyclic com-ponecit of temperature rise of l,250-5ICM

P

'i>P Pa v e

C 4 ~

1 4

Tab/c Xt.

Thermal Impedance FuacQons 1,250.MCM 115-Kv Csb/c Enclosed /n 6s)to-Inchucx/dc-I}/eactcr P/pc Tab/e XIII. Maximum Temyctature R/ce for Cyclic Loading

'armonic Ts/C}o To/f)o I s/(/o yo/C}o oo............... 8.03/o'...........d.ss/o'...........s.pyio

...........s.so/o't......,........lo.

sdlos

......,.....9. 08/Oo

~ 8. $0/Oo

....,.......8.03/Oo I............. 2.88/-30............1.57/

43............1.24/-$ 4..~.........0.031-51 2

>~......,......

2.20/<<38..........1,19/

54.....~......O.S2/-58.... ~~.... ~.O.ST/-77 3 "~ ~.. ~.~......

1.94/

43o............0.94/

dto............o.dl/

79o............0.39/ /-87 4

e ~. ~ ~.e" ~..... 1.58/ -50'............O.Td/ <<dyo............0.48/

87'............0.20/

95

~ Steady.state componcaC for s/agic pipe fSteady.state compoaenc for c<<o pipes, 18 inches apart.

Qo<<<<acts copper ioss pct coaduccot pot foot Ts<<'cctopctacute tise of conductor 7's<<tcmpotaiute t(sa of shiddiag tape Ts<<cern pctacute tfse of oil ia pipe 2'o<<Cetapctatute tise of pipe Coaductot P/pe Method Tempctacute, C Tetapetacute, C

of Ca)-

ca/ac/oa I Pfpe 2 Pipes

.I P/pe 2 Pipes For Loss Cyde I 1.......39.1.....49.2......24.1

....34.3 2.......30.8.....40.0......24.5

....34.8 3.......30.0.....$ 0.1......23.2e..

~.33.4e For Loss Cyde 2 I ~......30.0.....37.5......

17. I.:..23.8 2.......32.d.....30.2......18.2

....24.9 3.......32.8.....39.5......15.xe....22.8e These dgutcs do aoc iaciude the Ccmpctacute cise due co die)acetic ioss, <<hfch would be added co the

~ccady.state compoacaL

~ These ste acetate ccmpctacutcs.

It is aoc possible Co compute the maximum ccmpctaxute of the pipe by this method.

115-kv cables enclosed in 6s/s-inchwutslde-dianxeter pipe buried in the earth.

The results of three such methods Eor two representative load cycles are presented in this discussion for comparison.

The three methods compared are:

(1) the Harmonic method using Bessel Eunctions to compute the heat-Qow constants of the cable for each harmonic of the temperature cycle, (2) the sinusoidal method suggested by'r. Ncher in his 1953 paper, and (3) the latest method suggested by Mr. Neher and Mr. McOrath in their current paper.

Space in this dhcussion does not permit a complete derivation of the heat-Bow equa; tions for the hazznonic components of the heat-Bow cycle, but only the results, as calculated by an IBM (Intenutlocul Business Machines) 550, are tabuhtecl in Table XL It may be noted that the znachine tiznc to solve the eight simul-taneous equations necessary tor the solution oE the tempecatures and heat Gows for each hazmonlc was approximately 5 minutes per znatrix, with a separate solution neces-sary for each harmonic.

The whole cost of the job m rental tinxe on the machine and punching the data oa the cards for msertlon in the machine was $ 150 Eor three Tab/c X/I.

Hannon/c Componea/s of Loss Cycles Loss Cyde I Loss Cyde 2 Hat

Loss, Phase

Loss, Phase moa/c Watts hac(e, Waus Aag(~,

Desto so Decrees 0.......4.03...............2.54 I~ ~

~2500231

~ ~

2....... 1. 10..... +30......0.43...... +IS$

3.......0.20.....

00......0.do......+

ds 4.......0.$ 3..... +40......0.53......

3$

Bxamp(e:

The equation of loss cydc I using the fotegoiag data is as foiiooom (staximum Qo<<d.d

<<acts ptt toot ptt coaduccot}

Qo<<4.03+2.$ 0 sin oot+I.IO sin (sot+30o)+

0."-0 sia (3ot-00o)+0.$ 3 sia (sc t+40o) <<ates Cottespoadiag ccmpttscute cycle fot cooduccot tempstacutc is ss folio<<s fot ~ siagie pipe: (I taxi.

mum Ti <<35.lo) 7's<<32.4+7.24 sia (ut-30')+2.$ 7 sin (<<ot 8 )+

0.30 sia (3<<t 133') +0,80 sla (4a T')

dcgttcs ccadgtsdc Sere time<<5,00 a,cs. ia the fotegoiog expressions.

ditferent sizes of cable (a total of 12 ma-trixes).

The cost of pzogzanuning was small since the generai program for solutioa of complex simultaneous equations was already avaihble in the IBM library, and only a small amount of work was necessary to set up this particular problem.

The components ot the loss cycles with which the data in Table XI was multiplied to obtain thc tempezature cycles are given in Table XII. These loss cycles are iHus-trated in Pigs.

4 and 5, with the cocre-syonding temperature cycles of the con-ductor and yiye, In aH future calcuhtions of this soct, it is planned to cany the programming stiH further and have the machine calculate the temperature cycle for each size of cable and detecznine its maximum value.

Thh has been estimated to cost approxinutely

$500 for programming and $15 extza per size of cable to compute, Usually only the temperature of the conductor and the pipe are signiGcant in calculation ot the current.carrying capa-bility but the electronic calcuhtor auto-matlcaHy computes the other va/ucs'sted in Table XI. and they are recozded Eor whatever use may be made of them.

A tabu/ation of maximum temperatures for the foregoing two load cycles and the three dHfecent. methods of calculation Hsced previously are tabulated in Table XIII in the same order.

Examination of this table wHI reveal that the sinusoidal method yields results which are nearer to the znore accurate harmonic method tlun thc htest method proposed in thc paper.

The agreement between the various methods is seen to be better at the higher loss factors.

It may be argued that the agrcemcnt is close enough between the three methods for aH practical purposes and that the accuzacy of the original thermal constants from which the computations were made does not warrant the extra work necessary to use the harznonic method.

However, the danger in using an approximate method is that someone unEacniliar with its deriva-tion and its limitations wiliuse it where it does not apply.

The author does not con-sider thc agrecznent close enough for 40 fo loss factor.

The computation ot the pipe Ietnpctature is just as important as the conductor tcm-pezatures, especially in summer when high earth temperatures prevail and where higher daily loss hctozs arc more likely to be encountered:

If the earth next to the pipe exceeds an avenge of 50 C, there is danger of drying out the soH causing thezmal instability.

Ca/culations ot cur-rent~ying capability should take this liznit into account.

Rxcysaxcwcx I.

Sce tefcteacc 3 of the paper.

K J. Wiseman (The Okonite Company, Passaic, ¹ J.):

The authors are to be conunended for thh very Gne technical paper.

Thc nial for aa up-bxhtc com-.

pihtioa ot engineering fonnuhs and con-stants for the calcuhtioa of current-cacrylng capacities of cables has been of increasing importance every year.

When Dr. Simmons wrote his series of yayccs about 25 years ago we might say the electrical cable industry was young in engineering knowledge, the types of cable furnished were not too great in number, and the characteristics of the cables mere not too well known.

Today our knowledge of cable design, materials, ancl operating conditions along with new types of cables is hr ia advance ot 25 years ago.

We have been using the tonnuhs as they became knowa and it was desizable to bring theta together in one phce and, in addition, aH of us who have occasion to make these calculations wiH be using the same fozznuhs and electrical and theznul constants.

Also, this paper <<iH be of great help to younger men coming into the cable in-dustry.

Although ic summarizes the formulas, anyone stishing to get a dearer appreciation of che text can refer to the bibliograyhy and study che original papers.

To cnake any tare of this kind gencraHy useful, it is desirable that the procedure be easy to follow sad the formulas readily applied.

Theo recital fonnu/as involving higher mathematics can be used, but they take time, and vcr).olccn it is not possible to take the tune to stock up a case.

Aga/n conditions ot inscsi/scion ate varlab/e daily, so if we atcczapc io mal'e a Geld check ot ca/cuhcions wc can Gad dL~ctcrtccs; there/ore, cxaccnes) 'co 3 high degree is

l l

5

~

~ t' 4

I 4 "~ ~

~ ~

'1 J

~r l

II

3 100 100 X

~ ao O

~ao CD O. 20 A

~do E

~

X

>dO O

l-ao z

ux rD co O 20 AVE.I Xc-..,r..",,

a

~

A.M.

tiM Flg. 4.

Loss and temperature cycles for 75%%uo load factor> Qlllullcf load cycle Ftg. 5.

Loss and temperature cydes for 60%%uo load factor winter load cycle Values same as in F>g. 4 C4~coppcr toss cycle Tx~tcmpcraturc ol conductor Tc~tcmpcraturc of pipe Tcmpcrdturcs are ln per cent of copper tcmpcraturc corrcspond-tng to steady load equal to the maximum.

not necessary.

It has been suggested thaC it is now possible to use computers on these problems.

This is true for those who have a computer, but here also time is taken for setting up the probtan for the computer.

Also we must show how to calcuhte the currents and in a Eorm thaC willbe used.

Vou willnote thaC many of Che focmuhs are new to mast ot you.

These fonnuhs were developed to make the calculations easily and quickly and yet do not cause a

large error in the ttnat answer from the highly theoretical formula. It is natural that the formulas may bc a compromise and some may feel that a particular formula Chat they use may bc superior to that recom-mended.

Likewise the thermal constants may be a coxnpromisa This is true as far as I am concerned, yet we are witting to accept the recommendattons given in Che paper.

The calcuhtion of the various losses existing tn a cable systan and thc location of these losses is well done and should bc carefully studied by all new engineers.

The section dealing with the calculation of some of the thermal resistances need careful study in order to appreciate than as they depart from the usual manna'n which a thermal resistances are calculated.

For example:

the thermal resistance between a cable and a surrounding wall, such as a duct wall or a pipe; see equations 41 and 41(A).

Heretofore, we used 2>a~

0.00411 B/D, and referred to as thc IPCEA method.

This has been revised to take into consideration the condition existing and the materials.

Equation 41(A) is a general one, and by inserting the correct values of >4'nd B's given in Table I, we can get R>.

This is an example of how we can accept a compromise in order to get agrecmcnc.

We ac Okonite made tests years ago co determine the thermal constants for the oil or gas medium sur-rounding cables in a pipe.

Wc tried to use the cylindrical log fornxuta and found the apparent thermal resistivity varied due to the convection effects of the oil.

IE we took the simple formula R>a~

1.60/D where D is the diameter over che shielding tape we found we goC good agreement with test.

We neglected tan-

~

perature effects as the actual value of Rra as coxnpaxed to thc thermal resistance of the hsuhtion is very tow, many times in the order of one. tenth; therefore, temperature effects are small.

For a gas medium using 200 pounds per square inch me use the equation 8>a 2.58/D.

How do these focmuhe cocnpase with equation 41(A) proposed by the authors)

Consider two cases, one having a diam-eter over the shieiding tape of 1 inch and another having a diameter ot 2.5 inches.

The Eollowing table compares the two types of equations.

Dtameter ~

Diameter ~

1 loch,

XAlaches, Thermal Thermal OhmrPoot Ohm-Pool on..... {

Ohoaite......t.do t.o.r....o.da t.o.f.

Nehcr aad...1.3r

...0.80 Ohoaite......2.5d Co.t.... 1.03 C.o.f.

Nehcr aad...2.22

...1.04 htcCraxh Caa

~ ~ ~

Thc differences are not great and when considered in relation to the total thecmal resistance, they are negligible.

We can accepC the authors'quations.

I am ghd to see the authors phce thc duct system in proper rehtionship to a buried cable system and that the same soil thermal resistivity will be used when making comparisons.

This was the weak-ness in the cluct heating constants originally set up by iVELA and hter known's IPCEA constants.

Also a better under-standing of the effect of multiple cab'tcs in a duct bank is obtainable, and th>> decermina-tion of the cable having th>> highest thermal resistance is possible.

Appendix III discusses the'derivatton of Dr, a fictitious diameter in the soil up to which it is assumed that a steady heat load exists and outside which the loss factor of the load is taken into considera-tion. I have not been able to accepC this assumption.

It is an endeavor to obtain a thermal cesistance for the soil that will check with a study that Messcs.

Neher, Butter, Shanklin and myselE made and is referred to in reference 3 in the bibEography of this paper.

A study of the previous papers will show thac the attahiment factor is not exactly the same for att types of cables studied and all shapes of load

curves, The authors tabulate in Table IX a comparison of the attainment tactor for three methods of calcuhtion for a loss Eactor of 30%

Eor several cable designs.

Rather than give results for one loss factor only, it would have been betta'f they had covered the cange of loss factors which were studied in 1953.

It these attainment fac-tors were plotted against loss factor as I did in my paper, it would have been noted that a straight line could be drawn giving a good representation of how (>4F) varies with loss

factor, naxnely,

(>4F)~0.43+

0.57 (t/) for my method.

This equation follows the plot of (AF) and loss factor vay well down to about 35% loss factor, and in some cases, it gave a higher value and other cases a lower value than actually calculatecL The (4F) values I reported are based on careful calculations from thc exact load curve and no assumption that a single ine wave curve can be taken as representuxg any load cucve.

As it isa rarity that cables are designed for loss hctors as low as 30% (50% toad factor).

my formula gives results as accurate as when using D, and easier to use.

However, for the sake of uaiforniity in methods of calculation, we wilt accept the authors'ethod.

In thh connection, I ivould like to raise a question which I hope will be taken up by others interested in this subject.

The use of the equxciou involving Da is an Annn>r>oo 1OA ~

Arrhrr 1 fr/ rn>CTrrrhr n> ~>rr n>>rf I'na:< I nnnVl~'t>> ~

,attesnpt to tn'crease the thernut resistance and have arrived at catatn condusions, for the soil for cables or small pipe sixes; some of mhich are discussed in the following hi other

words, the computed value oE paragraph.

th emu! resistance is too Iow.

Is it not The determination of thc losses m the IHldy that vre are leaving out of our equa-conductor, shield, sheath or pipe, and the tion a term involving a surface contact dielectric have been weH estabHshcd by between thc surface of the cable or pipe the authors and bear no furth and the saiL Thisis term would be of the Thc calculation of the thelmal resistances no er comment.

cables sasne fostn as we now use for the case of of direct buried bl d 'l es in air, namely, 8~0.00411 B/D.

instalhtions appear to have'een well soil thermal res If we add this term to the log fortuna Eor founded; althou h the hod E

resistance, we willget a higher at the effect of cyclic loading scans to bc total resistance and the Inliuence of the in question amottgst the various investiga-diameter of the cable or pipe willbe greater, toss (reference 3 of the paper).

However, the tower the diameter.

It vriH be neces-as Ear as duct bank Instathttons are con-sary to determine the value of B.

Thc cerned, the difference between the NELA idea of such a tenn is showa in the paper'r IPCEA current rating method and that Table I the by Mr. Matha and his coauthors.

In proposed by the authors is so t th t y give same thermal data one cannot help but <<onder at the dearth grea a

obtahtcd frotn tests made by them on a of practical data h the paper.

pipe-type cable.

They give a value of ln reading references 10, 12, 13. 16. and B for surface of Somastic to wata'f 218 17 of, the. paper,"there scans to be very thermal ohms pa cm'. I like this.

Is it little data on cable 'temperature measurc-not likely that wc have a surface resisttvity ments takal in th 6dd ch thecahleandthesoHmtmmedtate by the various utilities when the NELA c,

sQ as mas doric values mere established.

The work re-RBFEMtNCts ported in these reEerences ts almost atl theoretical, and laboratory measuranents 1.

Bottrtava.aa powaa ttotttrrtssa*norr Hton.

an,an~ogue mends u~ ~ ~ appr d

Voc TAOC Ciaoa SjtrotÃsy R Js MathafJ Pe Js

MaCattoa, E. Dautlrtlatt.

AIEE Traarrurtoas, I am gi to u dets t there a movement afoot to have this Neher-McGrath method accepted and to revise the IPCEA current rating tables accord-E. K Thomas (ConsoHdated Edison Com-htgty. I am not sure that this is the case-pany of New York, Inc., New York, N. Y.):

The authors are tobe congratutated in setting up mathanatical equations to evaluate load We have used the method given in thc gret that no mention was made of the pio paper to compute the current sathtg of ncerworkbyWathceE.~ketnthemtddte quite a number of high-voltage cable cir-1920's on the nthg of cables mstated m

~ts h a duct bank md 5 d complete dh-duct bank

. Th work, I bdieve, f -

agrcanent mith the NELA or IPCEA ntshed thc b

~u of ~btc rating of thc nicthod. In every case the Neher.McGrath NELA and present IPCEA published rat-method results in a hrger conductor stxe Ings of cable.

The work of Zirke was pre-for a given current tathtg, m some cases before thc AIEE anti pubHshcd in as much as 30% morc conductor metal is Journal 1

required by the Neher-McGtath method.

The work on ratings of cabte by Ktrke.

Ha h mhere our di a ~ begins.

One 5dd m~

of two things prevaHsl eitha Mr. ¹her meats in the New Yorlc City area and tater and Mr. McGrath have cotstered the nonfcrroQs lnctat maske't or they arc attanpting to make a pipe. type cable carry which lead to the NELAIPCEA satin the same load as a dua-bank tnstaHatton.

Yet on the face of it, it is incomprehensible Qse of pipe-type cable.

Zt should be hom anyone can conceive o! a ~nductor obvious that the answer obtained by high-voltage cable (and a Pipe-type cable mathenuttcai solution is never any better assumptions ou which the equa colnpCtlng On a current sating basis with gona are dcvdoped and the constants used single.conductor high-voltage cables sePa-vrith the equations.

ratdy spaced in a duct bank where aw I bdtcve the actual heat ttow in under losses are a minimum and heat dissipation g

d cable sy t~ h constd~bly mo~

a ~m~

In either event we ~ot complex than has been assumed in this undastand why so much thne should bc paper and, therefore, actual ratings which

~ spent on devdoping a ncm method of cur-are obtained may be dHIcrcnt from those rent sating calculation for. duct-bank obtained by this calculation, systelns without Gsst having at least obtained some actual In - service field Rzt ttttstvcts measuranents to substantiate their l.

fosmtttas.

~iuu Caactraanorl or Caaaa Tattraaazoaas On thc other hand, we must sincerely commend the authors for attanpting to arrive at a realistic comparison between duct-bank and direct-buried systans.

It D. Short ts unfortunate, however, that in doing so ort (Canada Wire and Cable they have not based their formttta dcvdop-ompany, Toronto, Ont., Canada):

Sevant ment on extensive 5dd survey data as was oE the engineer mho worL with me at Can-done at the time thc NELA duct constants ada Wire have been studying the Neher.

were established.

MCGrath a a over th P P e past few months, The only way in which we have as yet, been able to make the Neher-McGrath method tsack with the old and well proved NELAmethod is to reduce the soil thermal resistivity to the order'of 40 C to 75 C cm/lratt.

The actual value which one mould use to ttsrive at the same conductol sixe as detamined by the NELA method appears to depced upon the number of cables in the duct bank and the value of thc daHy load factor chosen.

In contradis-tinction, Mr. Neher in reference 13 of the papa'tates that his method agrees within 10% of thc NELA method if a pa~75 C cm matt is used.

We have nude some calcutattons of the thalnal resistance of cables in a duct bank from thc sheath to ground (or sink) using the

¹her-McGrath

~ method and the average conditions on <<hich the NELAduct constants were obtained.

Thc average conditions were:

I.

Most of the measurements were taken tinder paved streets with the depth of pave-ment between 10 and 12 inches.

2.

Majority of ducts wac made of fibre.

3.

Avaage duct inner diasneter ~3.75 inches.

• Concrete spacer between ducts 2

inches, with duct..watt~1/4.tach, 3-inch outer concrete sheIL Spacing between duct centres ~6t/t inches.

5.

Average depth of busial to top of duct bank ~30 inches.

6.

Most measurements with ~nductor lead sheathed cables fran 2 inches to 3 inches outside diameter.

Avaage diameter 2S inches.

7.

AH Ioaded cables in outside ducts, all equaHy loaded.

8.

Soil thatnat resistivity (i>> situ) ~

120 C cm/watt.

Two cases mere studied and the results are summasixed in the foHomingl Care I Thrcc cables in 2 by 2 duct bank (onc of lourcr ducts crnpty).

. NELA Valtte (Le. 4.93/D,'+LrNH3 Loss factor........100%o..62.5%o..33%

Rthc g thamal/

ohns-feet.......5.09

..3.92

..3.00 Neher-McGtath Value Loss Eactor, 100%o 62,5%,33%

Upper cables Rths s thalnal

/ohms. feet...

~ ~.6.68..5.02

..3.71 Lower cable Rths.s" """"6-63 -.4-99

..3.70 Average values....6.66

..6.01

..3.71 In order for Nehcr-McGlath values of therlnal resistances to be equal to NELA values, soil resistivity would have to be; At 100% loss tactor p, 65 C an/watt At 62.5% loss factor p< ~60 C cm/watt At 33.0%o toss factor pa ~45 C an/watt Case IlSix cables in 2 uridc by 3 dccp duct bank.

NELA Value Loss factor...... 100%..62.5%..33.0%

Rths-z thermal

/ohms-feet....6.89

..5.05%..3.60

¹her-MCGrxth Value Loss factor...... 100%..62.5%..33.0%

Jt/cher, rtfcGrathTcmpcratttrc and Load Capability rsf Cable Systcnls OCTOBER 1957

~ <

P k

Lt

~

I~

I'p per layer Rths d ther-mal/ohms- "

feet..........10.23..7.24

..4.88 Middle layer Rths-d ther-mal/ohms-feet..........10.95..7.69

..5.12 Lower layer Rthc d ther-mal/ohms-feet..........10.63,.7.49

..5.02 Average values.. 10.60..7.47

..5.01 In order for Neher-McGrath values of thermal resistances to be equal to NELA values, soil resistivity would have to be:

At 100% loss hctor p,~53 C cm/watt At 62.5% loss factor pe~50 C cm/Iratt At 33% loss factor p, 43 C cm/watt

~<

Other calcuhtions on slngle~nductor high-voltage cables varying in conductor size from 300 to 1,150 MCM instaHed in outside ducts in a normal duct-bank systens It was necessary to assutne a pe~75 C

cm/watt in order to make the Neher-McGrath fozmuhs agree with the current ratings calcuhted by the NELAmethod.

The NELA method is of course strictly empirical and thc duct constants deter-mined from an average of a large number of 6eld surveys.

It has been in use for well over 25 years; and there must of a consequence be many thousands oE miles of cables operating at current ratings cal-culated by the use of these duct constants.

So far as our experience in Canada is con-cerned we know of no hot-spot failures with high-voltage cables in duct-bank instalh-tions.

On the contrary one is led to read with great interest the recent paper by Brookes and Stazrs.t Do the authors expect utility engineers operating duct-bank instaHations to adopt the method put forward in the paper and forthwith reduce their loads accordingly!

This is a question of great importance, and we should have a categorical statement from the authors in this speci6c regard.

In Appendh IV the authors give a speci-men calcuhtion for a typical duct-bank htstaHation and also a similar calcuhtion for a pipe-type instaHation.

In the one they use a pe of 120 and in the other a pe of 80.

Would the authors enlighten me on the significance of these two different values for p,.

On this point Dr. Wiseman stated in his discussion of the paper that he was glad to leam that. we can now base the duct-bank calcuhtions on the same basis of pe as pipe-type cable, but the authors have not done this in their Appendhc IV.

The use of the Kennelly fozmuh in the practical case of cablet buried in the earth is at best an approximation.

For'the theoretical case ofa heat source in a medium that is homogeneous, of uniform resistivity and temperature, the formula would apply.

However, for the practinl case of cables in the euth, there is considerable deviation'rom the ideal case such as honunifozzn medium, seasonal variation of temperature gradient in the earth. nonuniform distribu-tion of. moisture in the

earth, moisture migration, and other factors, which render the Kennelly formula more or less inac-curate.

Thus in its use one must bear in mind these limitations.

In Europe the Kennelly formula has been'used extensively, but thc apparent thermal resistivity Inserte in the calcuh-tions are based on that value obtained irt ziltr, as measure4 in accordance with reconunended methods.

To get a very accurate value of the apparent thczznal resistivity, it seems that the method to be used should exactly duplicate the cable and its operating conditions; Le., thc same diameter as the cable, the same watts loss dissipated, the same depth oE burial. and at the titne when the thermal conditions arc most onerous.

Thus in the calcuhtion of thermal resistance Erom cable to ambient, it appears that the Kennelly fozmuh can be used to a high degree of accuracy if an apparent thermal resistivity of the soil in situ is used.

This measurement should automatically take into account aH the factors that otherwise limit thc KenneHy formula to a theoretical exercise.

There has been a great deal"o!.investiga-tion into the infiuence of moisture on soil resistivity.

However, as yet there seems to be no general agreement on another basic problen, and that is the direction of the heat Qow.

The authors and others maintain that the heat Qow is to the surface o! the euth whereas other investigators claim sotne heat Qow is downwards to a deep isothermal, about 30 to 50 feet below the earth's surhce.

In reference 12 Mr.

Neher obtains the heat 6eld pattern by superimposing the Geld based on the Kennelly fomtula on the temperature gradient. It is obvious from the Geld

~

patterns that in the summer the heat Qow is predominantly

down, whereas in the.

winter the heat Qow is to the surface.

The authors give no quantitative method of evaluating the cffect of the temperature gradient on the apparent soil resistivity.

This could be one of the reasons foz'he difference between the resistivity as meas-ured in the laboratory and h the field.

An indication of the effect of change of apparent thcrnul resistivity h shown in a

paper by de

Haas, SandiEord, and Camezon,t wherein the dfect oE introducing a deep isothcmzal (ground water) in combi-nation with the euth's surface as the sink has a theznul resistance oE approximately 25% less than iE the earth's surface was the o=ly sink, This would indicate that the thermal resistivity of the medium is changed whereas the change in tempera-ture cHstributlon due to the temperature gradient should be investigated.

It should be enphasized that the Ken-nelly formula is applicable to steady-state conditions only.

The authors redize this, of course, and attempt to ccnnpcnsate for this shortmming by applying a cydical loading factor to the external thermal path.

The factor they usc h based upon measured values obtained on direct buried and/or pipe-type cables.

Since thc thezznal cucuit of a duct bank is quite dHferent from that of direct buried cables, we do not agree that thh satne cyclical Ioadhg factor (as measured on direct buried cables) can be applied to a duct.bank instalhtioa.

FinaHy it is pertinent to point out that thc KenncHy formuh is premised upon aH the heat energy Qowing to the earth' surface.

One must thea ask the authors what they mean by ambient soil tempera-ture.

Theoretiedly at least the tempera-

'ure of the earth at the cable depth of burial is not thc ambient to be used in the

'enneHy formuh if the sink is the earth' surface.

Why is thc euth's surface tem-perature not the tzue ambient to use when applying the Kennelly fozmuh?

Is the British usc of a 2/3 factor in reaHty a correction for the virtual sink temperature.

or sink tenperatures if the deep Isothcmul theory is valid.

L TssaxAL ANU MaatANTOAL PaoaLax oN 128 Kr Ptas CASLS TN Nsw Jaaaar, h. S. BrooLee, T. B. Starre.

A188 'Frearerrioar, roL TC, pt. 111, Oat. LOST, pp. TT2%4 2

AN ANotooos SoLUTIoN or CASLs Hsar PLow Paoatsaa, B. de Eaaa.

P. J. Saadtford, A, Vf. Vf. Caceeros ISfd., roL Td, pt. 111, Jaae IOSS, pp. 215-22.

F. O. WoHaston (British Columbia Engi-neering Company, Ltd., Vancouver, B. C.,

Canada):

This discussion is confined to the parts of the paper dealing with cables in ducts.

The paper is in many respects most adtnirable, notably the coverage of sLin dfect in conductors. of special types, proximity and eddy current elfects, muttuI heating effect oE multicable instalhtions, and the diect of extraneous heat sources.

For the 6rst time these are aH adequately treated in onc paper.

The methods of edculation

must, however, be critically examined before being acceptecL I am disturbed to Gnd that the methods given for rating cables in ducts lead to sub-stantially hrger conductor sizes than does the IPCEA-NELA method.

By thc IPCEA-MELAmethod I mean the method given in an Anaconda publication.t believe this method is identical to that used in preparing the existing IPCEA. cur-rent mtings for cables.

The Neher-McGzath method leads to much higher values for the duct heating constant (the thezznaI resistance from duct.bank to eazth ambient) than does the IPCEA-NELA method, when the thezznal resistivity of the euth is taken as 120 C an/watt in the Neher-McGrath calcuh-tion.

The value to bc used for earth theznul resistivity is of paramount izn-portance and wiH be discussed in more detail later.

A few Qlustrations of the differenc between the two methods wQI Gzst be given.

The Gzst application of the Neher-McGrath method which we made was to detezznine the conductor size for a pro-posed 230-Lw cable instaHation.

The cal-culated conductor size was 1,500 MCM, whereas by the IPCEA-NELA method the calcuhted size was 1,150 MCM.

Some 42 mQes of cable were involved in the proposed

project, so the Neher-McGrath result would have meant substantial extra cost for the cable compared to the IPCEA-NELA zcstdt.

In another tnztazcc, thc Ncbcr MCGzath method was used to determine the required size of cable leads for a 75.mva trans-forzner.

The calculated size was so large as to be considered physicaffy Impractlad, whereas by the IPCEA.NELA method the calcuhted size was pzactied.

Rather than risL possible trouble H the IPCEA-NELA result were

adopted, it was decided to use aerial bus instead of cable for these leuis.

In a third case, the cable leads of a 50-mva 13.S-L>'enerator were to be changed OCTOBER 1967

%cher, iVcGraffs

'Tcrrtpcrafurc at:d Load Capabtl Ey of Cable Sys.'crtts 769

< l'~l-1 $l C

h l

~ r'

Table XIV. It was necessary to measure the air temperature in an occupied duct.

since there werc no empty ducts.

The loading on the machine vras recorded and the current division between the six cables was detcsmhscd.

The maximum departure from equal loading of the two cables on each phase was only 2%.

After 5 days the duct air temperature was 43 C.

The ambient ground temperature was 19.5 C at the same depth as the center of thc duct bank, Dividing thc temperature rise by 1/6 of the total losses, a thermal re-sistance of 4.6 ohms is obtained.

Table So s>>

i Iz ss ~l2us,g cn rrs.

'1.'.Qi..'.QI

~

~

5 sr ZRsrrzrff, OVCZ nr covcagrg.

ZU shows the thermal resistances pertinent to this case as dctesmincd by the Neher-McGrath method and the IPCEA-NELA znethod.

The expcrisnental value (occuyied duct air to earth ambient ot Table XV) is in good agrcemcnc with the IPCEA-NELA value given in "duct wall to earth ambient" of Table XV, while the ¹her-Fig. 6.

Cross section of duct bank because the associated

~o-Lw step-up transfosmcr was being rephccd with a 345.kv unit.

The existing leads consist of two 2,500-MCM cables per phase installed in a Mucc bank.

hccording to the Neher;McGrath method, these cables should be approximately 3,500 MCM each ifthc AEIC allowable temperature of 'F6 C is not to be exceeded at full load in sununer tiine.

The unit has run at full load for long periods on many occasions since going into service in 1949. If our applica-tion of the Neher-McGrath method is correct, one'must conclude that the existing cables have been severely overloaded many times during their service period of 8 years.

No evidence o! such overloading has been seen; the cables have been entirely trouble-Free.

There are toro other units at this plant, identical in all respects to the one described above except that one of than has been in service slightly longer, the other not quite as Iong.

No trouble has occurred on the leads of these units.

It was decided to make a temperature survey to establish the correct facts.

The unit was run at full load for 5 days.

Test results showed that the duct structure atcaisscd equilibrisun temperature in 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.. The bulb of a recording thcsxnom-cter was inserted 20 Eeet in the bottom xniddle duct.

The details ot the duct bank and cable are, given in Pig. 6 and value i! the two methods arc to give the same results, as is obvious by inspection of Table XV. The Neher-McGrath value should be lower than our experimental

value, since the fosmcr represents the thczmd resistance from the outside surface of the occupied duct wall to earth ambient, while the htter represents this same re-sistance plus the thcsmal resistance from occupied duct air to the outside surface ot the occupied duct wan.

One is not entitled,to say that the dis-crepancy between the Nchcr-McGsath value and the IPCEA-NELA value is real unless the value ot the specific thermal reshtivity of the earth ps is the same for both.

The ¹her-MCGsath value in the tabulation is obtained when a value ot earth thermal resistivity ps m 120 C cm/watt and thcsmal resistivity of concrete ps~85 are used m equation 44(A} ot the paper.

There has ncvcr bccn asly general agrec-meat on what value of earth thcsmal resistivity is inherent in the IPCEA-NELA duct constants.

Several years ago Mr.

G. B. Shank!in and his coworkers in the General Electric Company investigated this extensively and concluded that the value is about 180 C an/watt.

If this conclusion is correct the discrepancy be-twom thc Nchcr-MCGzath result and the IPCEA-NELA duct heating constant is Table XIY. Cable and l.oss Data 2,500.MCM Scgiaentol Copper Condsrctorr Pepcr inzuf4tcd.teed-Sheoshed Solid-Type, 13.8 Kv real and serious.

Our test result cited above does not give any information on this point because the earth thczsnal re-sistivity was not measured, due to lack of facilities.

If the discrcyaucy is real, one h led to question the soundness of the Kennelly formula used by thc authors.

It is based on the premise that all heat generated in the cable escapes to tbe surface of the earth.

Some ccnnpetent engineers have argued chat part of the heat escapes by another path, namely to a sink deep in the earth.

Mathe-maticd development of this premise gives a result for the thermal resistance between duct bank and earth that is only about two-thirds as large as the result by th Curreas Daring Teat, hmpercs Wa Sic Loss Per Boot of Cable Cable zfo.

2..............

0TS...............

5.13 5...........

~..1,020...............

S.T3 Total 30.50 Per cable average S. 1 Roses:

hmbleat earsh tom peraiure durlag teat was 10.5 C.

Cables are paired 2-3 for h-phase, CH for B-phase, 5-5 for C-phase.

D(ameser over <<oaductor, laches............2.000 Cotton tape shicxaess. laches...............0.01T zasulssloa thichaess, laches................0.210

'lameser over insulation, laches............2.4S4 sppcr tape shichaess, laches..............0.003 obeaib ihichaess, inches...................0.12$

Over.all diaescser. laches..................2.T10 h< resissanee at 5$ C~$.41 (Xo>>) ohms.face Kennelly formula.

hccording to this, we might expect the Nehcr.McGrath method to agree with the NELA value iE the carch thcrznd resistivity is taken equal to 2/3X 180~120 C crn/watt in equation 44(A}.

It turns out thac agreement occurs when

.McGsath value is much higher.

The

='-:Neher-McGrath

• value should be ap-proximatciy equal to the IPCEA-NELA Table XY.

ThcrnNl Resistances Pertaining to Test

'hermal Eeshsaaee, lfehet IPCEh Ezperi-C pcr Watsrryoos Mcarash Tfgch mensal Znsuiasioa...~........0.73

..".O.TS Shesih so dues....'....1,52,....1.82 Duct wall.............0.13 Duce wall io carsh

~mblen!............8.7$ >>.~...4.0 Occupied duce air so earth ambient........

..4.51

>> Calculased from criuasfoa44(hj usiag p>>~120 C cmlwasz.

the earth resistbrity is taken as 55 C an/

watt in equation 44(h). It does not sean likely that the value of 55 is representative of typical sail around duct banks.

Many measurements in several laboratories have>-~-

consistently shown that the specific thczma1 1 r'esistivity of earth varies frosn about 100 C cm/watt Eor a moisture content. of 15%, to about 300 or 400 C cm/watt for sero moisture content.

A value of 180 C cm/watt seems fairly representative of average conditions. I conclude that the validity of the ¹her.McGrath method of cdcuhting the thcrznd resistance from duct bank to earth. ambient should be desnon-strated by tests whczchs the <<arth thermal resistivity is dcfinitcly known.

Have the authozs verified their findings by such tests?

RETERENCE t.

Caaaaaz Raznros roa Baaczasoc Cosa nncroaL Anaconda Pssrrsstfen C4t, McCcaw-Hi0 BooL Compaar, Zoc Rew Yes¹ Y., erst edlcfoa, Ocs. 1042.

J. K, Ifcher and M. ILMCGratht We are indebted to Mr. Baznes and Mr. Golden-berg for their dscuszions in which they summarize the present cable rating prac-tkcs in Great Britain and point out some diifcrcnccs with hmczicxn practice.

Prom this it would'ppeaz'hat in most respects the practices in the taro countries are shnihr.

While the method ot handhng group cable ratings developed by'x; Goldenberg may appear to difFer hoax the method ot the paper, actually both methods arc derived from the same basic prhxciplcs and should give identical results for the sazne set of conditions.

To answer their questions with regard to tcsnpcrature lnnits and the relationship of this paper to the published rating tables, we may say that IPCEA, in collaboration with the AIEE, has under active con-sideration a xevision of the existing current rating tables based on the methods of cal-cuhtion set !orth in this paper.

The tem-yerature limits wfii be those dready'dopted by IPCEA, AEIC,ctc.. in industry spcclfications.

Mr. Church has outlined a procedure for determining the effect of the loading cyme on cable ratings which will be, we fear, an cnigsna to znost cable engineers despite the fact that ic represents a

chdlenge to those mathmssatically inc8ned.

Mr.

Goldcnbcrg also has referred to a different buc nevertheless machcsnatically involved procedure for doing this.

For uorsnal cable calcuhtions, the crcmmsdous asnount ot computations required for each individual 7TO 1Vcher, McGrathTerrs perature and broad Capabihty of Cable Systerrss OCTOBER 1951

a a ~

~

ee 0

1

casi,'is simply not warranted

<<ven iE a digital computer mere available to the cable engineer.

If the application of a particular load cycle to a given cable system is to be studied, we suggest that this may be done more

siniply, morc

rapidly, and more economically by using an analog computer designed for the purpose.

We feel, how-ever, that the accuracy of thc method given in the paper as compared to aB exact caI-culations which we have examined, includ-ing those of Mr. Church, is suificient, par-ticularly in view of the fact that any par-ticular load cycle may never repeat itself.

The method given in the paper is an approximation, admittedly, but it has been derived from the same fundamental prin-ciples which underlie Mr. Church's method through a

series of careMIy considered simplifications.

It should be understood that there is nothing sacred about. the value of 8.3 inches used for the fictitious diameter Dc.

This value happens to be the best single value to use based on the studies described in reference 3.

For Mr. Church's case values of 7.1 for thc 75% load factor cycle, and of 5.1 for the 60% load factor cycle are indicated.

The errors in using 8.3, however, amount to only 2 and 5%

high, respectively, m the conductor loss component of conductor temperature

rise, which would be offset by a 10% error in the value of earth thermal resistivity ein-ployed.

Dr. Wiseman's conunents in this con-nection are most interesting since he has often expressed the opinion

that, prac-tically, it was sufiicient to consider Dc to be equal to Ds, or in other words to apply the loss factor to aB of the earth portion oE the thezmal circuit.

We can agree with this in respect to pipe-type

cables, but, as he has indicated, we do not consider this further simplification desirable in the case of small directly buried cables.

Neither do we consider the forznuia which he gives for obtaining attainment factor directly fram loss factor suitable in this case.

This is readBy apparent fram Fig. 2 af the Grst paper of reference 3 in our paper.

Since the use of Dc has considerable theoretical justification in our opinion, we feel that it should be made a part of the general procedure Eor calcuhting the effect.

of the loading cycle.

The introduction of an additional thermal resistance to care for surface effects be-tween cable and earth is an entirely differ-ent nutter since this will increase the temperature rise both for steady and for cyclic loads, whereas the use of D> is intended to give the correct result for cyclic loads on the assumption that the total thermal resistance in the circuit which is unchanged by the value of Dc is correct for steady loading. It is quite possible that such a surface effect term is present and that it may attain an appreciable magnitude in the case of small directly buried cables.

We concur in the hope that this matter wBI be investigated further.

Ivfr. Thomas has noted the pioneer work of W. B. Kirke in connection with cable in duct and indicates that this worL: formed thc basis of the present NELA-IPCEA method.

Employing a duct bank con-Gguration such as shown by Wollaston and utilizing equations 14 and 17 of the Kirke

article, we Gnd that Kiri:e would use a

resultant thermal resistance from loaded duct mall to earth ambient of 9.0 for the worst soil in metropolitan New York and 6.00 for the best soiL These values, when compared with NELA constant of 4.9, scarcely confirm Mr. Thomas'tatement to the effect that the present IPCEA-NELA method is based on or is even closely rehted to Kirke's work, While Kirke made some attempt to take into account the configuratioa o! the duct bank structure, he did not utilize resistivity as

such, and as previously indicated we believe that a knowledge of this and other parameters ignored by Kirke is essential to a realistic method o! handling this problem, par-tlcuhrly when one considers the problem of comparison between different types o!

+steals.

hs Mr. Thomas has suggested, the heat Qom in a duct structure is complex, but this complexity results from the superposition of a number of heat Bows any one of which, due to a particular cable, is readily deter-mined as indicated in reference 12.

We are not interested in these heat Qoms frcr zc, but only in the resulting temperature difference betNreen a reference cable and ambient and the corresponding thermal resistance which is fully expressed by the relatively simple equation given.

True, the situation is complicated by the concrete envelope, but here extensive studies, both mathematical and on a Geld plotter, in-dicate that the equation 44(A) is sufii~

ciently accurate in view of the inherent errors in Gxing the earth resistivity and loss factor in a particular situation.

Mr. Short, at the start of his discussion, states in effect that he considers the method for determining the load capability.of direct earth-buried or pipe-type cable to be "mell founded" for a 100% load factor but, because of questions raised by various investigators in reference 3 of our paper.

does not seem to be too sure, that this is the case for other load and loss factors.

hll four investigators mho undertooL to itudy the problem for the Insuhted Con-ductor Comniittee, however, are on record as recommending or agreeing to the method given in the present paper.

In accepting the given method for buried and pipe-type cable, Mr. Short does not seem to realize that this method is based on the Kennelly fozmula because in the latter portion of his discussion he questions thc applicability oE this premise to current rating determina-tions for any type of underground instalh-tion, and proceeds to attempt to resurrect a nuinber of the ghosts which plagued the Insuhted Conductor Committee some 10 years ago when the latter started worL: an a critical review of the basic parameters involved iu load capability calculation.

These ghosts were subsequently hid to rest, at least to the satisfaction of the vast nujority of engineers in this country.

Even at that time the Kennelly forznuh had been in existence for over 50 years.

Despite the fact that this fozmuia is based on scientific principles found in most text books on physics and electrical engineering, some cable engineers had misgivings as to its applicability mainly because calculations by it did not appear to checL with measure-znents in the Geld.

This situation is dis.

cussed in reference 12 of our paper wherein it is shown that the disagreement was not due to the fozznula but to the fact that the 6eld meauraaents had not been carrie to a steady

state, and that laboratory determinations of the earth resistivity were not representative of thc soil in situ.

Also, the appareqt discrepancy (which appears because thc direction oE heat Qow implied in the Eozmu!a Is toward the surface whereas in summer the total heat Qow in the earth is obviausly in the reverse direc-tion) is explained by the application of the principle of superposition to the separate heat Gelds involved.

As a result, cable

engmeezs, with very fem exceptions, have accepted the formula for cakulations in-volving pipe-type and directly buried cable systems.

The method of handling cables in duct, given ia the paper, is a logical extension of the priaciples under-lying the Kennelly fozmuIa in order to include in the calculations tmo very im-portant variables which are not a part of the NELA-IPCEA.method, namely the duct. configuration and the thermal sistivity of the surrounding soB.

This method is also not new. It mas Gzst described by N. P. BaBey ia a paper in 1929'nd subsequently ia reference 13 of our paper.

Mr. Short also mentions the two-thirds factor, another resurrected ghost of the past.

Long'go the British established that the two.thirds factor represents a

diffezence between laboratory and in cits measurements of soil resistivity and that it does not stem from any lack ofapplicability of the Kennelly formula to the pzablezn.

Numerous British publications point out that the tmo-thirds factor is not to be used where the resistivity is measured in sits by buried sphere or by long or short cylinder.

In addition, in recent years the British have developed a new laboratory sampling procedure'hich checks not only with the buzied sphere, the buried cylhider, the transient

needle, but in addition also checks with results obtained on loaded cable installations.

Another ghost mentioned by Mr. Short is the deep isothermal approach (a proposal which mas Grst suggested by Levy in 1930)'iting the de Kus, Sandiford, and Camezans paper to give new life to this old suggestion.

However, in so doing Mr. Short faBs to point out that the deep Isothermal in this case consists of a conducting paint electrode of an analogue model connected electricaliy to another electrode representing the earth's surface and hence simulating a

lfrruiing (not stationary) ground water sink, a somewhat unusual condition that is scaredy pertinent to the problem at hand.

Incidentally, Table I of this paper gives results of an excellent analog check of the given method as applied to a duct bank.

We wish to assure Mr. Short that we have not cornered the nonferrous metal

market, nor are we saymg that three single~nductor cables of a given size insuBed in a buried pipe must have the same rating as three conductors of the same size Installed in separate ducts.

We should point out, however, that this has been a rule af thumb for the past 10 years or more and there are now many zniles af high.voltage pipe cable in successful service which are rated and are being operated at a load capability level which Mr. Short considers incomprehensible.

Mr. Short's dilemma results solely from OCTOBER 1957 Nchcr, hfcGratliT'crnpcraturc and Load Capabih.'.; of Cable Systcrnz 771

~ - eat 'd'i lt

o the Eact that he is attempting to compare the r,cults of calcrdations made under a

~

~

~

~

set of assumed conditions with the results of a procedure for which those same condi-tions are not stated and in fact are unknown.

This Is a situation which existed imme-cHately EoHowing the waz and is one of the ghosts previously nzentioned.

Conductor size determinations for cable in duct utHizfng the NELA constants require no knowledge nor consideration o! soil re-sistivity as such.

On the other hand. such determinations for pipe-type cable systems by any practical method require a speciflc numerica assumption to be made as to the value oE soil resistivity in order to anive at an answer.

By taking the stand that the concealed resistivity in thc NELA constants is 120 oz'ore, iC is thus possible to obtain, an advantage in favor of duct-Iay cable.

Furthermore, because oE the use of cable spacing factors and earth and concrete thermal resfstivltles in the proposed method, it mill be obvious that calcuhtions by the given method will check with those of the IPCEA method only for certain combina-tions oE the variable parameters in the methosL Since these parameters were not Gxed and in Fact are now'nknown as re-gards the NELA duct heating constants, it is obviously hnpossible to make a factual comparison o! the results obtained by thc two methods.

Here

again, by assuming earth resistivities oE 120 or 180 as both Mr.

Short and Mr. WoHaston have done, thc given method wHI result in hrger conductor sizes than the IPCEA method.

Despite the Fact that both Mr. Short and Mr. Thomas refer to the presumably large amounC of Factual data which underlie the NELA duct constants, we have been unable to ascertain the specfflc'conditions on which these constants were based nor is there any indication Chat earth resistivity mcaswements were taken as a part of the data.

About aH that can be done, there-fore, Is to assume representative cable and duct conflguzations and then to caIcuhte the earth resistiviCy required in the given method to match thc value calculated by the IPCEA method.

We cannot agree to the values given as "the average condi-tions on which the NELA duct constants

~vere obtained" as stated by Mr. Short.

Rather, vre believe that the conditions assumed in reference 18 are much more representative, on'the basis of which an average earth resistivity of 75 was obtained at 100% load Factor.

We take the position.

therefore, that the validity of the proposed method is not to be judged by whether or not the calcuh-tions made by it using parameters arbi-trarily picked by Mr. Short (or by Mr.

Wolhston) agree with calculations made by the IPCEA method.

Rather we feel that the applicability of the IPCEA method to a particular case depends upon how well it checks with the method which we have

proposed, and which takes into account more properly the essential param-eters which are pertineuC to the case aC hand.

With respect to Mr. Short's speciflc

question, we hope that utility engineers mill,adopt the proposed method but we do not think that they will Gnd it necessary to reduce loads unless they have very high values o! earth resistivity.

Regarding the need for reduction in loads on existing

drcuits, iC should be kept in mind that it is only rehtively recently that AEIC spedflcatfons have made provision Eor Increased permissible temperature Hmits Eor emergency periods, and for the greater portion of the period that these emergency limits have been in efect the nuznber of companies who have utiHzed them is relatively smaH.

As a result, the greater portion oE the cables now in service have" been sdected on the basis that normal

~permissible copper temperature would not, be exceeded under emergency conditions.

Moreover, in recent years a number of ass zsfra measurements have been made with the tzansient

needle, the

sphere, or the burie cylinder.

Theoretical studies have shown that measurement of ultimate soil resistivity can be obtained readily vrith such devices.

WhHe in many cases these have been made in connection with pipe-type cable instalhtions, they apply equaHy weH to duct bank instalhtions in so far as the resistivity o! the soil itself is con-caned.

The values in general range fronz 50 to 100 with some higher values as the exception at certain times of the year.

Moreover, over the past decade a number oE pipe type InstaHatlons have been in-staHed in this country with design re-sistivities in the 70 to 90 range.

Under the circumstances, we do not believe that it will be found necessary in most cases to reduce the loads on existing circuits.

However.

we do believe that engineers mill be well advised to take steps to ascer-tain the valuei o! thermal resistivity which are applicable for their conditions because with the more liberal use of emergency temperature limits and the tendency for shiEC in many areas in the load peaL from winter to summer, the existing margin may be reduced to a lovr level hc the not too distant Euture.

The values of soil resistivity of 80 and 120 used in the examples of Appendix IV were chosen merely Eor purposes of iHustra-tion and the value of 120 rather than 80 was used in thc duct Iay case in order to emphasize the effect of a difference between the resistivity o! earth at 120 and concrete at 85.

Unlike Mr. Short, Mr. Wolhston is very careful in his discussion to make it quite dear that his comments relating to a

comparison of the results obtained by the given method and the NELA-IPCEA method is preznised on his own arbitrary assumption of a concealed soil resistivity of 120 in the NELA constants and on bis impression, presumably based hrgcly on an unpublished 1947 memorandum by G. B. Shanklin, that a resistivity of 180 is representative of average conditions; conse-quently, the value of 55 which was obtained by back calcuhtion from the given method utIHzing his test results indicates a dis-crepancy ia the method.

We believe that if Mr. Wolhston wiH consult somcrs of the many references which have appeared in the technical litemture over the past few years on determinations of soil re-sistivity h connection with experimental duct bank, buried cable and pipe-type cable InstaHations, either alone or in conjunction with buried cylinders, spheres or transient needles, that he will Gnd that there is no longer any justiflcatfon for an Inferred resistivity oE the order of 120 in the NELA constants or for his impression that a re-o sistivity of 180 is representative of average conditions.

In as much as no actual measurement was made of soil resistivity at the sIte at which Mr. WOHaston obtained an indicated value of 55, there are, of course, several possible explanations that suggest themselves.

As-suming the tern peratur'e measurements werc made accurately.

perhaps the soil actually had a resistivity of this order of magnitude.

From recent studies on soils and the effects o! such matters as composi-

tion, density, compaction, particle

size, etc., it Is evident that it is very difGcult to estimate the resistivity of a soil fronc appearance alone.

Alternatively, it could be that the measured value of resistivity is not the ultimate value as a constant load applied for 5 days would not suflice to bring the duct structure to its ulthnate teznpera-ture rise over ambient, unless, o! course, it bad been canying substantially fuH load for some thne prior to the test in question.

Mr. Wolhston mentions that the tempera-ture was measured 20 feet from the nzan-hole but does noC indicate the length of the duct zun orf which the test was conducted.

This raises a question as to vrhether in his particular case, there could have been any aHeviatioa of temperature rise by longi-tudinal heat flow or, alternatively. by longi-tudinal convection effects such as were Found in the tests made with ducts open and plugged.'s psasscss 1.

HsAT Paow roose UscosaoaoUND Etscralc Powso

CAsass, Neil P

Baser, AEEE Troar ocrroer, voL 48. Jao. 1020. pp. 15&45.

2.

hN EvAAUAcrosc ov Two Rarro bfavsroos ov hsssssQco zsrs TosaMAl Rssrsrsvtvv or Soral W.

Marcosrsrd, E.

blochrrar rcf.

/o reer, lascrcncroa ol Elcccri<<al Eazlacers.

London.

Eacland. vol. 103, pt. h, no. CZ, Ocz. 103d, p. 433.

3.

CAsan Hoarrsco Uc Uscoeaoaoowo DUcrs.

R. D. Levy.

Ccacrer Erccrrlc Ecvrcsc, Schcncccadrr BL Y., hpr. 1030, p. 230.

4.

See reference 2 ol Mr. Shocc's drscnsslon.

S ToktoaAcnao Rrso Aoo CUaaoscv Ravnco or CAsass LArn'sc DocTsz E Bo Wedrnote> E Eo Horchlass,

Rcporr, Rr/rrcrrcc P/T

los, The Bclrlsh Electrical aod hrricd industries Research hssoelacloa, Loadoa, Eazla'ad, 1035.

""2 Ndhdr, sVcGraffi7drrrsrrr!Urn crt Ter> Crrsntrr:rsr nr /

nln Vvrlrmr Ar vn rs o cr 1 rrX7

THXS PAGE XNTENTXONALLYLEFT BLANK

1

~

C e

i I

0

~

F. H. BULLER *-."=J-rH. NEHER MEM8Ert AlEE MEMEER AIEE O

NE step in the calculation of under-ground cable temperatures involves the determination of the temperature rise of the.cable surface above the immediately surrounding inclosure such as a duct struc-ture or a gas-or oil-flied pipe.

Since the intervening medimn is a Quid, the mode of heat transfer simultaneously involves convection, conduction, and radiation.

The semiempirical methods now in use for this determination in the case of cables in duct are not entirely satisfactory, and vrith the advent of gas-or oil-fliedpipe-type cables there has arisen a definite need for a method of evaluation for these cable types as weU.

Because of the complex nature of the problem and the number of independent variables vrhich are present, it is imprac-tical to cover completely all possible com-'inations which may be met within prac-tice solely by tests.

By developing a

theoretical relationship between the vari-ables, however, it is possible to develop procedures by which the test data avail-able may be analyzed in such a way that relatively simple working expressions may be derived which may be applied with suflicient accuracy over the entire working range.

The theoretical relationship for the case of cables in duct was recently pre-sented in a paper by one of the authors.'n the present paper this rehitionship has been extended to cover oil and gas pipe systems as tvell, and from the test data presented the requisite working expres-sions for thermal resistance or surface re-sistivity factors have been obtained.

Theoretical Considerations The theoretical rckitionships given in Appendix II of reference 1 for the case of cables in duct have been expressed more completely to account for the physical characteristics of the media involved in Appendix I of this paper.

The resulting equations for the the therinal conductiv-ity betvreen cable and duct or pipe vrith air or gas as the intervening medium are Q

0.092 Ds

"/'sT'/'P'/'sT 1,39+Dr /Dd 0.0213

, +0.102Ds'c(1+0.0167Tm)

IogtsD4/Ds'atts per degree centigrade foot (1) and with oil as the medium Q,

0.053D "/'nT'/ T '/s 0.116

(oII)',

+

CsT 1.39+Dr'/D4 logisD4/Ds'atts per degree centigrade foot (2)

For a single cable D,'aa D the diameter of the cable.

For three cables in the pipe or duct it is customary to base D,'n the circumscribing circle of the cables in tri-angular configuration, D,'m.15 D,. For tvro cables the relationshiP Dsraal.65 D, is satisfactory.

It will be noted that the primary vari-able in equation I is Dr As a result sllb-sequent analysis and development i>>ill be facilitated if this equation is written in the equivalent form Q

0.092 CsT'/sP

/'s'aT Ds"/'(1.39+Dr'D4)

, +0.102c(1+0.0167Tm) 0.0213 D,'og D4/Ds'atts per degree ccntigrad>> foot inch (1A)

From the method of derivation which assulnes a coaxial arrangement of the cable within the duct or pipe, the numeri-cal constants of the first two terms oi equations I, 1(A), and 2 must be con-sidered as being approximate only. They will serve, however, to evaluate the rela-Btdlcr, iVchcrThcrnrcf Rcsislancc The Thermal Resistance Between Cables

<>.

ever, when calcuhting a cable rating, with a fixed copper temperature of the order of 70 degrees to SO degrees centigrade, th>>

range of this variable is very small, and an accuracy of the order of 3 per cent tn >

per cent may be expected.

In the case of equation 2, the conduc.

Paper 50 Sz, reeommcoded by the AiEE lated Cooductors Commsttce aad approved the Alas Tcchnical protram Committee ior pres'otatioa at tbc hlEE Winter Qcacrat hfcctinc.

He>> YoA, H. Y.. January 30.February

3. I93".

Sfaauscript subcaitted October sl. t949:

available ior priories December y, 19t9.

F. H. Eot,tca is <<ith tbe General Electric Com'aay.

Scbcoeetady.

H. Yand J. H.

<<ith the philadelphia Elcetrie company.

Fhna'elphi

~, Pa.

AIEE TEAishcTtoHs

r

Table l.

Test Data on Gas-Riled Pip>> Type Cable Systems Teat Itumber Source Q

al'/ 7'/

D'r p

Q a7 i'

a'7 D,"I

'able 1L Test Data on Cables ln Rber and Trantlte Ducts Encased ln Concrete Test Itomber Source Q

a7'I 7'I D

l D,'Dr Q al','al'I 5........Bareoseher........Fiber.......o.d9....3.S

.... 1.0.... d.4.....0.228........1.T4 1.7....11.8.....0.203........2.03 2.5.. ~.IS.L.....0.235........2.

LT 4.4...24.8.....0.25T......

.2.44 S.d....34.2.....0.281........2.SS 8.1...39.T.....0.295........2.78 12.3.. ~.Sd.1.....0.318........3.00

1. 13....3.5.... 1.0.... 4.$.. ~..0.20l ~.......1.41 1.7.. ~. 7.1...7.0.207.....

~..1.$ 9 4.S..

~.Id.3. ~...0.248........1.9S 8.0....30.4.....0.233........2.28 11.0.. ~.32.8.....0.300.

~ ~.....2.32 14.8....48.S.....0.288........2.82 18.8....$ 2.4.....0.28$........2.dl 18.4....S8.7.....0.278........2.89 3.13....3.5.... 0.9.... I.d.....o. 194........0.S4 I.T.... 3.2.....0.173........1.00 2.4.... 3.8.....0.203........1.0$

4.5.... 7.7.....0. 188.....

~ ~.1.75 8.1....12.1.....0.213..a.....1.40

)4.8....21.9.....0.217........1.53 S........Jobos-Matteille....Piber.......s 38

~ ~ 3 SS 12 5 ld 8

~ 0 220

~ ~ ~ ~ a I 50 14.9....19.2.....0.230..

~.. ~ a.l.sd LT.S....21.7.....0.238........1.$

9 T........Johns-MaosiILe.... Traosite....3.38....3.88....1d.T....18.9.....0.292........1.50 19.8, 19.4.....0,299...... 1.$ 5 23.3....22.0.....0.314........1.50 2d.4....24.$.....0.318......

~. I.di tion term constitutes about 24 per cent of the total for a typical oil pipe installation.

Variation is more important than is the case with the gas.pipe cable, but is still within tolerable limits.

One peculiar phenomenon has been ob-served.

The ratio of DJDQ', which ap-pears in the conduction term aIso, ap-pears in the first {convection) tenn of equations 1 and 2 but in such a way that a change in this ratio produces an oppo-

site, though lesser,'ffect on the total value of these equations.

A minimum error should, therefore, prevail when the conduction term is treated as a constant if the denominator of the convection term also is treated as a constant.

This procedure will simplify the convection tenn but it willhave the effect of approxi-mately halving its numerical constant as compared with equations 1 and'2 since the numerical value of the denominator omitted is in the order of two.

ActuaUy the test datC was analyzed both with and without this simplification, and no ap-parent change in consistency in the re-sults was observed.

Analysis of Test Data It follows from the preceding discussion that the test data for cables in duct and for gas filled pipe. type installations may be analyzed by plotting the observed values of Q

CaT'I'pV'~

'gainst x~

(4)

DD'II?"

D ID/D The data given in Table I were compiled from tests on gas.fille pipe. type cable systems by The Detroit Edison Com-pany,'he General Electric Company, I.....Detroit Bdlsota Compaay....3.42...8.07...

I

. ~.23.4...20

...$2....0.34......1.$ 8 7.8...27.3...15.8...$ 1....0.51......4.08 14.8...28.8...13.1...$ 1....0.84......5.34 28.9... 17.1...50....0.49......5.71 28.9... 14.4...$ L....0.59......$.48 27.5...14.0...51....0.$ 8......$.43 2..

~ ~.Ceoerai BieetrieCompsoy...3.92...8.07...

1,7...

7 3... 8.2.,39.. 0.30...

I.d4 Il.i". 9.T...4$....0.30......1.83 IS.2... 12.4...50....0.31......1.73 7.8... 8.8... 4.7...39....0.37......2.92 11.5... T.0...43....0.42......3.22 14.9... 8.9.

~.4S....0.43...

~..3.42 11.2... 5:8...40...;0.49..'.::;4;22 ""

1$.9. ~

8.0...4$. ~,0.$ 1 ~ ~. ~.4.$ S 3.....Ceoeral Cable Corporatioo...4.90...d.07...14.8...2$.9... 9.2...$ d...'.0.'ST'.."..'.'.4'.47.

4.....General Electric Compaay...4.90...8.07...14.8...23.1...11.8...44....0.40......4.77 and the General Cable Corporation. These data are plotted in Figure 1 and the values of a and b in equation 3 are established as a~0.0?0; baeOM.

Table II presents similar data for cables in single dty fiber and Transite ducts in concrete taken from the Barcnschera and Johns Manville tests dis-cussed in reference 1.

These data also are plotted in Figure 1 where it will be seen that the Transite duct points fall on the gas in pipe calve, but the fiber duct points result in a different curve having the same value of a~0.07 but 5~0.10.

This difference may be explained by the fact that the duct wall departs from an isothermal as a result of the relatively high thermal resistance of the materials used, that of the dly fiber being consider-ably higher than that of the transite.'he test data for oil-filled pipe-type cable systems from tests by The Detroit Edison Company,'he General Electric Company, and the Okonite Company are presented in Table III and plotted in Figure 2. In this case, the analysis has beenmade by plotting the observed values of y~'itainst x~DQ"i'CaTi'Tea '5)

CDT and results in the values of am0.026 b ~0.60 in equation 3.

It willbe seen from the analysis of the test data that the agreement.

between theoretical and observed numerical con-stants of the simplified convection term is extremely good in the case of oil as the medium, but in the case of gas, the ob-served value of 0.07 is somewhat higher than the expected value of about 0.046.

This is rather surprising since tests num-ber 2 (with gas) and number 9 (with oil) which are consistently dose to the es-tablished curves in Figures 1 and 2 were made with the same physical setup which remained unchanged throughout the tests except for the change in the media employed.

Therefore, we should expect the ratio of values obtained to be the same as the ratio of the numerical con-stants of the convection terms in equa-tions 1 and 2.

This discrepancy seems to be due to the fact that in the case of several cables within the pipe, a condition of the major-ityof test data, there is an additional cir-culation of the gas between the cables themselves which is not properly ac-counted for by the use of an equivalent diameter for thc three cables, but which is apparently not effective when a more viscous medium such as oil is employed.

As indicated before, however, a high degree of accuracy is not required, and it is 1960, VoLUME 69 Brtllcr, NchcrThcrrrral Rest'slancc 343

R,

~ 4

Table lll.

Test Data on Oil Filled pipe Type Cabfc Sysleras S.e" o ~.rietraiae ~. e~........

~ e ~....4.83...8.07" 0.....o.Ceaerel Slleetrio CogaPsay...3.02...8.07 10.......0boaire Cogapeay...

.....4.50...5.13 25.2..

o 8.0....40....2.04.

~.~...e194 S.S..

~ 3.0....37....2.19..eo....

$5 ll~ 4 ~ ~ e 4 ~5...

~ 44..

~.2.55. ~

e ~

50 lb.5... 6.8....48....2.88........

70 4.1... 2.$....25.... 1.55......

43 0.4'. 4.4....31....2.14...,..

. 58 0.4 ~.. 5.4....21....1.75......, 53.$

l.l... 7.$....38....2.81.....

~.. 70 21.6... 8.8....41....2.45...

~.... 8$.6 3$.2... 11.4....50....3.00........105 34.9...11.7....48....2.08.

.132 felt that a working expression based on the foregoing analysis mill be sufficiently accurate.

Worhing Ezpressions

= -

-'n formulating the thermal resistance between cable and duct, itis customary to express this resistance in terms of an equivalent surface resistivity factor, as-suming that the entire resistance was concentrated at the cable surface, accord-ing to the expression Hgc 0.00411,thermal ohm feet (6) p Dg'n which p is expressed in degrees centi-grade square centimeters per watt.

Since Hgc~ chT//Q it follows from equation 6 that Dg'chT p

243 degree centigrade centimeter Q

per watt (7) and v

~ ~ L

~

a Ka'(QDg"Tm')'+24 feet (ll)

The value of p from equations 9 and 10 is plotted in Figure" 3 as a function of (Q'P/Dg')'

and the, value of Z,c from equation ll appears in Figure 4 as a function on (QD,"T')'.

Also indi-cated on these figures are the values'f these parameters for typical conditions.

In the case of cable in fiber duct, the thermal resistance of the duct wall is appreciable and should be accounted for.

This is most readily accomplished by modifying equation 6 to include this re-

.sistance.

Thus a7 Tost 0

lratabor Source D'a 0

4T T

ol',/doT'/dT /i Fpa'(Gber) 0.00411,+0.33thernial ohm pD,'eet (12) in which the second term represents the difference in thesmal resistance between a 4-inch fiber duct aad the corresponding section of concrete which itreplaces.

Discussion of Values for Cables in Duct It wiH be seen that the method of de-termining the thermal resistance between

'able an'd duct presented herein differs somewhat from the method given in reference 1, although the results are sub-stantially the same for terra cotta and fibre ducts.

For Transite

ducts, the values of thermal resistancI: derived in a more fundamental manner in the present

paper, are slightly lower than those appearing in the reference, being equal to those assumed for terra cotta.

it will be reoaUed that the reasoniag used in developing eigebraio eapressions for these, va ues assumes an isothermal duet wall.

The test data presented in Figurc 1 ~

Analysis of lest data for cables in duct-and gas@lied pipes 0

pl/tQI/d 4T '~0.253

/, (degrees centigrade)'/'8)

It is thus possible to develop working ex-pressions in terms of p in the case of cables in duct-or gas-filled pipe by sub-stituting equations 7 and 8 in equations 3 and 4 with the appropriate values of o and b.

In the case of oil-filled pipe a simpler expression is obtained in terms of FI,a.

For cables in single dry fiber ducts 13,700 p

Q /i

/g d e gre e s c en 1i p/e ~

+$ 7 D,'rade square centimeters per walt (9)

For cables in other types of single dry os

~ 4 Os oT oR 13,700 p

.,/,,/,

degrees ccuti-p/'11.3 D,'radesquare cciitimclers per walt (10)

For cables in oil.filled pipe 0

0 ev'r"

p,v Bullcr, ÃchcrThermal Rcsisksncc A,lEE TR~wsocTlo~s

~Q"aad plotted in Figure I, how-

> "dicate a.good correlation even 4~,there is substantial deviation from

,@/assumed isothermal as indicated by e hi'sic data on which the table is based.

iliathe range covered by the data, in-

'ag the departure from the isother-m changes the resulting constants some-ha't but does aot invalidate the method lrf."analysis.

'.;.Itfollows therefore that a considerable tion in P for cables in single-fibre

..may be expected depending upon

.Qative thermal resistivities of the wail and-theisurroundiag

medium,

'ther. data which has come to the

'. atteation confirms this.

Thus

~e'of Fi uct s~oul asidered as an u limit.

y, the application o the values ca foi single ducts to the case of cables

.;multiduct structure, depends upon Qect which the total heat field has in

'er changing the temperature gradi-

'tj'i'around the individual duct waHs.

e.data given by Smith ia his discussion 7(ence 1 indicates a value of p for

'riuitiple-fiber ducts in concrete corre-

"adiag dosely to the curve for cable

~mar:

~ ~

pe indicated in reference I,

addi-aI:.test data taken on multiple-duct blies are desirable to definitdy lish the limitsunder these conditions.

'reasons also indicated in reference I values are not directly coinparable

'ithe values adopted by the Insulated ower'Cable Engineers Associations and "aot directly adaptable to their calcula-oir'procedure, X":

nclusioas t":.~The theoretical relationships between

'various quaatities involved in the eQee-

,:thermal resistance between cables and

surrounding single duct or pipe have been

'eveloped ia a

manner which properly

'ts for 'the simultaneous modes ol heat cr by convection, conduction, and tlon.

I.'Ily means of these relationships certain 0:

~.

test data on cables in duct and in gas-and od.fiiled pipes have been analyted and work.

g,curves are'. presented for determining the

'resistance lor any particular case

~

.. maY be encountered in practice.

.~j'-'Under typical conditions representative

. es of the equivalent surface resistivity 4 for use in equation B are 800 degree

,.tlgrade square centimeters per watt lor fcs.'n pipe, single dry terra cotta or

,fslte ducts at atmospheric

pressure, 450 Scabies in gas-filled pipe. type installa-at 200 pounds per square inch, and 350 Ies in oil fillcdpipe type installation.

tative values of IS for cables in dry fiber ducts willvary from 850 to 100.

~..'Vot.vwit GO Mf J, ~,'\\

p8 0

Q.T Appendix l.

Theoretical

'evelopment of Thermal Con-ductivity 6etween Concentric Isothermal Cyclinders with Gas or Oil as the!ntervening Medium The mechanism of heat transfer between a cylindrical radiator and an enveloping iso-thernial enclosure through an intervening Quid medium is such that a portion of the total heat Qow Q is carried by convection Q<<, a portion by conduction Qrc, and thc re-mainder by radiarion Qi.

ln fOrmuhting the components of thc thermal circuit.

thcrcfore, it is morc convenient to <<ork in terms of thermal conductanccs rather than thermal resistances since the foriner quanti-ties are directly ad<liiivc. Thus, if 3T is the temperature drop in degrees centigrade across the circuit Q

Qcr Qcc Qi

++watts perdegrcccenti-aT aT aT aT

'grade foot (13)

Figuic 2.

Anclysis of lest cfctc for cc6lcs in oil4lfccfpipe The phenomenon of convection involves the conception of the temperature drop being conccntratcd in two films, one at the surface of the cylindrical radiator of diame-ter substantially equal to the diameter of the radiator D, in inches, and one at the surface ol the enclosing isothermal surface which will be considered also being cylindrical of diameter Dc.

The following formula based on McAdams'equation 42, page 251, 1st edition only) is applicable to either film.

Q<< ~ 12"DI 'GATI'I'Kwatts pcr foot (14) in which DI ic in inches, and

/d'c gh i'

~ (

-)

watts pcr centimeter '~'c-(')

grees centigrade '~'15)

Thc significancc ol the components ol equation 15 and rcprcsentativc values lor gas (air or nitrogen) and Suniso number B oil are given in Table lv.

Bullcr, IVchcrThcnnal Rcsisfancc 340 0

lo '0 so 40 so Co 70 eo 90 00 no lao l30 0','T~

T

gooo g

Iaoo

TYPICAL, a

IO OF CA P<<l 81 E u IL IN OUCT 5

1100 BLE I

~ eeoO N FIBRF OUC 4 I Ised/Og+.33 doe 243 Nsd Os

~a NO OUCT CABLE IN PIPEs EAAA COTTA A TAANSITE-1w2$

OF cy oa.

<<4.$

FILLE T v'S O PIPE 0

aoo LE IN PIPE S FIL 5.1, TYPICAL Of CA PIPE AT 200 P.

2S Os 4.$

LE 20 40 40 oo goo uo lao goo goo goo rgo 240 Zoo taiy,s Ts>'A Figure 3 (left).

Values ol p foc cables in dcy single dgccfs and gao-filled pipe Rgure 4(above).

Yafueo of Hga for cables in oif-flllecfpipe 0 x,a,o,a la aa L4 aa Le 2 4 J.o xa 3.4 3.4 s ~

Ao 42 fo"P/0; l'*

In the case of air or inert gas, these physi-cal propesties are substantially independent of temperature over the working range but the density is a direct function of the pressure.

Thus, ifP represents the prcssure in acmospheres, from equation 15 Kcaa0.000755P'/'atts per centimeter

'/'egrees centigrade '/'l6)

When oil Is employed as the medium thc physical constants are substantially inde-pendent of prcssure and tempesatures with the exception of the viscosity which for the type of oil cornrnonly employed (Suniso number

6) may be taken as varying in-versely as th>> cube of the temperature ac-cording to the rehtionship 94,000 grams per ccncimetcr second (17)

The value of K for oil thus becomes K~

0.000434Teg'/'accs per centimeter'/'egrees centigrade '/'18)

~ ~

ao

• x 2 4 ao 4.4 Aa 44 SO 4.2 The solution of equation 14 for the two 6lms ia series and mith equation 16 or IS substituted therein is given with sufficient accuracy by the expressions Qcr Dc dT'/'P'

(gas) m0.092 watts pes de-dT 1.39+Dc/Dc grec centigrade foot (19) degree centigrade foot (20)

From a theoretical standpoint the ex.

pression for the conduction component should take into account any eccentricity between the cyiindsical radiator and the enveloping isothermal enclosure.

In the practical case of cables in duce or pipe the cables willnot rest uniformly on the bottom of the duct, and also in the case of a non-metallic duct the duct Ieafi is not strictly maintained as an Isothermal.

Since these effects cannot be evaluated, the familiar expressioa for the resistance between two concentric cylinders in terms of the dimen-sions of the cylinders and the thermal re-sistivity of che medium millbe used.

Thus Q

0 0213

( 011CL4LC40gra

(gas)

'aas per degree dT loggo Dc/Dc centigrade fooc (21)

Qcgr 0.116

'goal) walls par degree d T loggo Da/Dc centigrade foot (22)

The radiation component with gas as the medium is given with sufficient accuracy by the followingexpression based on McAdamss equation 5, page 61, Gsst editioI),

I 0 cNIAc~~

(gas) aa0.102Dgc(1+0.0167Teg) watts d1 per degree centigrade foot (23) in which e is the emissivity coefficient of the surface of the cable and T<< is the average tenlperature of the medium.

The radiation term is ineffective cohen oil is the medium.

The over.all thermal conductivity is ob-tained by substituting equations 19, 21, and 23 or equations 20 and 22 in equation 13.

Table IV Appendix IL List of SymI3ots Symbol Quaaiity Oaa al SO C OllalsOC p........... Tbcrcasi resiscivicy...........,........C cm/<<atc.......

3 900..........

~ ~.TIS ga.......e...Average absolute viscogicy.............grains/cm scc.....,

0.000l95........0.75 a..~........ Deasicy..

.grams/cmg......,..

0.00l'lo P.......0.904 Cr. ~ ~ ~. ~ ~ ~ ~ ~ Specific bess ac coascaac pressure......,<<acc see/C.......

~.

0.99S

~ ~.. ~. ~....2.IO graga S........... Aeeeleratiaa due tO gravity.......... Cm/SCC1...........990.

~

~. ~ ~ ~ ~

~ ~.990 r.s......,.. TIgcrgnal eocil'ieicnt oi ~cpaasion........ I/C.......

~ ~, ~ ~

~ ~ ~ 0 OOSIO.

~ ~ ~ ~ ~ ~ ~.0.00008 Q~totaf heat floggr from equivalent sheath to duct wall or pipe in watts per foot d7 aw temperature drop in degrees centigrade P aa prcssure in atmos pheres D, ~diameter of the sheath ininches Dc'<<equivalent diacnetcr of a group of cables in inches Da ~inside diameter of chc duct wall or pipe in inches Buflcr, /I/cIIcrTr'crrnal Rcsisfancc 3, IEE TILAwsAcTIo85

T~'~averag>> t>>mperature of the medium in degrees centigrade coefficient of emissivity of the cable.sur-face r and y~rectanguhr coordinates a and b~>>xperim>>ntally determined con-stants H,a ~thermal resistance between equiva-lent sheath and duct wallor pipe in ther-mal ohm fe>>t Hsa'~equivalent thermal resistance be-tween equivalent sheath and Gbrc duct wall including the increased tb>>imal re.

sistivity of the duct wall over that of the surrounding mediuln in thermal ohm feet J)~equivalent surface resistivity factor in degre>>s centigrade square centimeters per watt sI ~ thermal resistivity in.degrc>>s centigrade cciltlnic'ters pcf wa'tt

'verage absolute viscosity in grams per centimeters second 8~density in grams per cubic centisneter C~speciffc heat at constant pressure in watt seconds per degree centigrade gram g

acceleration duc to gravity in centimeters per second squared c~ th>>rmal coefficient of expansion in centi-meters per centimeter degree centigrade E~a factor dependent upon the physical constants of the medium in watts per c>>ntim>>t>>r'ia degrees centigrade'<<.

a References 1,

TNR TaxtRRATVRR RIRR ot CARO'Rs IN A Dvcr BANC, J H. Licker. AlEE Transassions, volume 08, part 1, 1049, pages 840-40.

2.

HRAT TRAicsaisstoN (book) W, H. Mchdams, htcCsaas.Hill Book Company, )re>> York. Lc. Y.,

dsst editloo, 1033.

3.

TIIRRNAI CRARAcraatsTIcsoF A 120 Vv HICII'aessvaa Gas.PIu.ao CARI R lnsTAt tATICN, W. D. Sandcsson, J. Sticker, M. H. Mcasath.

AlEE 1 raasassiaas, volume dT, Psst 1, 1948, pages 487-08.

4.

A Srvor ot TKR TaiitaaATvae Dts'salsa Tio'I IN EI Rcsasc CARtas IN UaocacRovao Dvcrs, P. J. Baseacches.

T'assis, Depastmeot ol Electsical Eagioecsing, Uaivessity ol Wisconsin (hfadlaon, Wis.), 192S.

S.

CvaaRNT CARRTINo CAFAcITT oF LNtaao.

NATRO PAFSR, RVS ~ RR ANO VARNISKRO CANRRIC 1Nsw.ATRo CAaaas.

Pablisasion lruaIb<r P 2P.

Cgd, lasulatcd Pores Cable Eagineess Association (Nciv York, H. Y.), dsst cditioa, 1043.

Discussion R. H. Norris and Mrs. B. O. Buckhtnd (Gen>>ral Electric Company, Schenectady, N. Y.): Eiftci>>nt work in the heat.transfer field on a variety of applications requires awareness of the definitions and units, in order Lo avoid confusion and misunder-standing.

In this paper and other papers written by cable engineers, confusion arises as to th>>>>acct meaning of th>> expression "thermal resistivity."

R>>sistivity as nor-mally deffncd (by the American Standards Association (ASA) for cxasnple) is a prop-erty of a substance and is not affected by its geometry; for example, the resistivity of copper has a constant value at any spcciffed temperature, while its resistance dep<<nds on

, its site and shape.

Then the us>> of thc word "resistivity" for surface phenomena is a misuse of thc terra.

To show ho>>

Lhc distinction between resistance and resistivity caters into lhc picture.

the thermal circuit for a single-conductor cable in air is given in Figure 1 of the discussion.

In this Ggure, iso, l,a, and ra are tempera-tures of copper,

sheath, and ambient. re-spectively, 8 is insulation thickness, p

is thermal resistivity of thc insuhting material, sf z, is the log mean area of the fnsuhtion for heat Gow, s(sa is sheath area, and fic and igs are the cabl>> engineers'erms for "sur-face resistivity" for free convection and radiation.

Each fraction in thc Figuri is thc th>>rmal resistance; and when resist-ances and temperatures arc known, the heat dissipation of the cable is known.

But in order for the resistances to be dimensionally consistent, th>> dimensions ofp must bediffer-ent from thc dimensions of l), and therefore p and ff should not be called by thc same nanlc Since the d>>Gnitlon of p as thermal resis-tivityconforms to ASA standards, it might bc better to denote ll as th>>rmal resistance of a unit surface.

Its reciprocal h, is de6ncd as surface heat transfer coclffcient, or alter-natively as surface Ghn conductance.

The concept of ~ conductance is particuhrly applicable here, as the total Glm conduct-ance is the sum of hr and hc. and therefore numerically easier to handle.

The units of length used in the paper seem to be a mixture of metric and engineering units.

A combination of square centi-meters with feet has no logical basis.

Ifany cable dimensions were expr>>ss>>d in centi-

meters, the mixture lvould bc logical al-though not standard; but since dimensions are not so expressed, it seems time to aban-don this practice and use the engineerin system of units throughout.

It is therefore proposed that the AIEE Cominittee on Insuiat>>d Conductors take steps to p>>rsuade its adherents to become familiar with ASA standards and to use them <<here they apply.

IL W. Burrell (Consolidated Edison Com-pany of Neir York, Inc., New YorL, N. Y.):

The authors have presented a desirable elaboration of Appendix Il of a previous paper by Mr. N>>h>>r.'lthough the ap-proach to the problem is uot changed, the lnaterial presented in the Appendix referred to is of sufficient importance to justify a more detailed presentation.

ILis apparent to those engaged in the 6eld of cable heating that the Insulated Poirer Cable Engineers Association recommended value of l), while perhaps sufficiently conser-vative for general design, lacks Lhc flexibility needed in comparing alternative construc-tions.

Precise determinations of ig 'or various types of inslalhtions may noL be possible because of inherent variations in the physical constants involved;

however, as additional test data are compiled. the n,

Aw Flgvse l. 'hesincl circuit fos single conductor in ~ is probable range of ig, for a particular case, will be better understood, Lh>>reby making possible more realistic comparisons.

The authors chrify our conception of the dfect of the various parameters involved in the temperature drop between cable surface and duct or pipe walL For a given system of cables in duct or pipe, the th>>rmaf resistance willdecrease sensibly with increasing watts loss.

W. B. Kirk>>iintroduced this modiffcation which is taken into account in determining cable ratings for the Consolidat>>d Edison systcfn As one follows the assumptions made in this paper, there appear various points to which exception. might be taken

.on the ground that they are not substantiated, for exampl>>l the assumption of the same constant in the expression for the convection Ghn at (he cable surface and at the inner duct wall, the treatment of conduction on thc basis of a concentric system, and the arbitrary assumption of an cmlssivity co-

>>fffcient of the cable surface of 1.0.

Yet, the important point ls that putting all of these various assumptions together in the particular form given in the paper, the over-all end result does produce expressions which are reasonably satisfactory.

It is unfortunate that, while the basic equations and the selection of parameters hard a reasonably sound theoretical basis, the Gnal working expressions given are essentially empirical and do not allow an accurate determination of the separate effect of the three modes of heat transfer.

On the average, the calcuhted values of QfcaT for the oil-6lled

pipes, gas-611>>d pipes, and cable in duct are about 5 per cent 15 per cent. and 55 per cent higher, respec tively, than the measured vahtes given

'ables I, II.and IIIof the paper.

Special-ists in the 6eld of cable heating would be interested in knowing which component or components are responsible for these dis-crepancies so that >>xtrapoLttion into new Gelds could be Inade with conffdence.

It is stated in the paper that the agree-ment between theoretical and empirical numerical constants of the simplified con-vection term is dose for the case of an oil medium, but is off appreciably for the case of a gas medium.

It also can bc said that the conduction.radLttion constant agrees lvith theory for the case of a gas medium; however, for the case of an oil medium. the constant theoretically app>>ars to range from 0.60, as given in the paper, to n>>arly twice that value, depending upon the values of D,'and Da involved.

From the over-all standpoint, it neverthe-less appears chat the expressions for J) and H,a. as given in equations 9, 10, and 11 of the paper are quite workable and agree with test data as well as could reasonably be ex-pected.

A high degree of accuracy in the calculation of allowable current ratings of cables is not yct to be expected but impor-tant worL has been done in the past fcw years in chrifyingour understanding of heat flow through duct stluctur>>s and the earth, and this paper is an important contribution to such understanding.

RBFBRBNcas 1.

See selcsence 1 ol the paper.

2.

TK~ Caacvaastoa ot Caata Tallteaafva ~ s IN Svaw*r Ducts. W. B. Xlske.

AlEE Joaraal.

volume 40, 1030, pace SSS.

1950, VOLUME G9 Bisllcr, iYchcrTher>>tnf Rcsisfasscc 347

f' a>>

lie I ~

R. J. Wlseman (The Okonite Companyc Passaic, N. J.): I like thc author's paper very much.

It explains the three methods of heat flow from a cable to a surrounding

mediutn, nameiy, conduction, convection, and radlaticn.

Also, they give the various parameters which influenec each factor namely, cable diimeter, temperature, and temperature difference, and viscosity of the medium.

The various formulas look quite "formidable when we note terms raised to fractional powers.

It is not easy to obtain thc constants for each formuh as they are dependent on condicions not easily calcuhble so it is necessary to gec test data and work back to nurnerics which will give the de-sired results.

It so happens that as all three modes of heat transfer are funccioning at che same time, a change in dimensioning tends to work in opposite directions, reduc-ing thereby.chc,effect of diame(er.

AIso the range in temperature is not great and as we take the one. fourth power ot temperature difference and three fourths power of temperature, the variation with tempera.

ture is not great.

About two years ago we decided to re-study the thermal constants tre obtained when we originally set up thc Oilostatic cable system.

At that time we used the cylindrical log forlnula of ra(io of internal pipe diatneter to circumscribed circle over the assembled conductors, and also a con-stant which was a function of the tempera-ture.

Our more recent tests showed chat the thermal resistance was almost independent

~ of temperature (a variation of abo'ut 10 per cent between 30 and 61 degrees centigrade) for an oil pressure zone and a very few per cent for a gas pressure zone at 200 pounds per square inch.

Wc also noted that within the accuracy of testing we could safely assume the thermal resistance to vary as inversely as the diameter of the shielding tape over the insulation.

As a result, we have sec up two simple formulas for the determination of the thermal resist-ance of che pressure zone for three cables in a pipe, namely, for oil pressure system H~1.60/D thermal ohms per foot per con-ductor where, D is thc diameter in inches over the shielding tape; and H~2.58/D thermal ohms per foot per conductor for a gas pressure zone operating at 200 pounds pcr square inch.

You willflnd these values of thermal resistance for the pressure zones amply accurate.

As the authors refer to the surface resis-tivity factor P, the values of 4 comparable to che above constants in H~0.00411 tt/D are IS 390 tor an oil.pressure system as cora-pared to 350 given by the authors and P~

827 for a gas pressure system at 200 pounds per square inch as compared to 450 given by the authors.

We are qutte confldent in our values and have been'sin'g'theiii foi 'over a year.

in the paper, since this analysis gives the order of magnitude contributed by each of the three mechanisms of heat transfer.

The authors have assumed for cable in duct that the component of the thermal con-ductivityduc to radiation can be treated as a constant in the range of normal operating temperatures.

Only the component duc to convection was considered as variable with changing cable diameter and heat flow.

This assumption does not lead to a true pic.

ture of the variation in thermal resis(ivity with heat flow, or more fundamen(ally, with cable tetnperature.

Mr. Darnctt and 1 have stated in our papert that the decrease in thertnal resistivity with increasing sheath temperature is caused primarily by varia-tion in the radiation component of heat transfer, and that the effect of temperature variations on convection are negligible over the normal operating range.. This state-menC is verified by calculations based upon equation 1A of the Huller-Ychcr paper, which is repeated here:

(

q i 0.0920,T'/P'i

+

(Ih)

Di'ciTg Da'(1 39+Dc /Dd)

(convection) 0.0213

~

t+0.102c(l +00 167T>>t)

Di'og Dd/Dc'"d t.

)

(radiation) in watts per degree centigrade toot inch.

The emissivity factor, c, is assumed to be unity at attnospheric pressure.

Table I of the discussion lists two repre-sentative sheath temperatures from our test data on flber duct in concrete, and these temperatures might very well be represent-ative of the operating range ofa cable.

The term (Q/D,'hT) evaluated in equation 1A is inversely proportional to the surface resistivity factor, tt.

The three terms in the equation give thc thermal conductivity components due to convection, conduction, and radiation respec-tively.

As we increase the sheath tempera-ture over the range showa, the increase in the radiation tenn produced by substituting our experimental data in the Buller-ocher equation is five times grezCer than that of the convection term.

This shows that the experimentally obsetved decrease in tt over this range is due ahnost entirely to the in-crease in the radiation tetm.

These cal-culations are based, of course, on the rather large cable size that we employed in our tests.

A smaller cable size willincrease the effect ot the convection term only slightly, however, and not nearly enough to make its variation with temperature equal to Chat of the radhtion term.

Identical calculations with our data on Transitc in concrete, Transite in air, and fiber in air, show simihr relative variations in the radiation and coti-vection terms.

The authors have neglected thc variation in radiation component of conductivity with tempenture, pointing ouC thac these varia-tions are quite smalL This is justlfiable from a practical stand point.

However, the variations in the convection component with temperature also should be neglected for practical considerations, since, as is shown in Table 1 of thc discussion this factor is even smaller thart thc change in the radia-tion tenn.

This would considerably sirn-plifythe Bailer-Heber equations for the sur-face resistivity factor.

ln their equations 9 and 10, (he surface resistivity factor. f4 depends upon thc fourth root of the heac flow.

This does noc have much significancc smce it is based upon the variation in thc convection tenn, a second order elfccc com-pared with the radiation term.

Similarly the dependence of ti upon the square root of the sheath diameter is doubtful, since chc change from.a fourth root to a square rooc dependence in the convection term also was based on the very small change in convection conductivity with temperature.

The foregoing discussion tras confined to cable in duct with air as the intervening fluid.

Its applicability to cable in gas-filled

'pipe at high pressures, where convection becomes the principal mechanism of heat transter, requires further study.

The authors have done an excellent job in helping co establish the theoretical ground-work necessary to both encourage and guide experimental workers in the duct heating problem.

RBFERENCE l.

Hear TU*ttsrcx Srvov ott Powea Cast.a Dvcts atto Dvcr Assctcstses.

Pau(

Gteeblcr, GU7 P. Batoctt.

AlZZ 7 vaatoctioat, rolutoe 09, pan I, 1950, paces $$7-07.

I i'

~I r

a h

0 ri L.

~ y i

tc Table l.

Gtecblet-Becne((

Da( ~

ts

h. H. Kidder (Philadelphia Electric Com-pany, Phihdelphia.

Pa.):

This paper by Buller and Neher, together with two pre.

vious papers by Mr. Neher,4t completes presentation of the steady-state considera-tions involved in a project which was started about four years ago when Philadelphia Electric Company interested Mr. archer in undertahng an investigation of funda-mental relationships.'s necessary to dc(er-mine approximately what pipe.cype cable circuit load ratings would be accurately comparable with thc load ratings of con-ventional cable circuits in ducts.

The thermal resistance through the spaces between the cable sheaths and the pipe or f'uct wall inclosures is an important link in the thermal circuit. Ithad beenhoped that a general rehtionship could be developed in i',

such a form thac all of che differences bc-

>> ~ I Pavl Greebler (Johns Manville Corpora-tion, Manville, N. J.):

In this paper the authors have contributed imrncnscly to-ward an understanding of the mechanistns of heat transfer from (he cable to ics sur-rounding pipe or duct avail.

The theoreti-cal analysis was necessarily based upon thc simplifying assumption of a coaxial cable in duce arrangetnent.

This does not, however, detract from thc value of the analysis given Lead Sheath Temperature Coclde Duct Meso V/all Sot(ace Temperature Temperatureullet Nehet Temperature Eeuatloo lA Drop Cooccctlou Radlatloo ar Tctm Term Gteeblet Barnet t Data tt lo 'C(cm)'/>>

dd.2...

77.2...

...40.$...........50.$...

...5$.0,....,.....0$.4...

~ ~ ~ ld. l. ~..., 0 0dx...o. Ipd....

~ ~.990

~..22.0.....,.0 005...0.2ls

~...,..020 loctcaac 0 00$...0.0l5,...,.. 00~ decrease Temperatures acc lo dcrtccc ceodetadc.

Thc latldc duct >>att cut(ace temperature lc au avctaee value.

,'34S Bttftcr, /V'cJtcrThcrnaf Rest'stattcc AIEE TRANSACTIONS

~ '

~ '

~(

~ q, e

Si 6 1 ~

~

~

s tween cables in air in ducts and cables in high-pressure gas or oil-flied pipes could be explained in terms of the physical constants ich characterize the respective fiuids and oertinent geomctricat relationships.

method presented by Buller and has approximately achieval this re-sult, at least to the extent of permitting the correlation of data obtained by various in-vestigators at various tiines in various con-

'structions.

It does not disturb ine par-ticularly to find that there is some apparent difference between the elects of Transite and fiber duct walls, respectively, under the conditions which prevailed at the time the tests were made.

I think we should hesitate to attach much significancc to these appar-ent differences because there was no attempt to control the moisture content in thc fiber or the Transite, or even to make the tests under conditions comparable to those to bc expected in the usual exposures to natural but variable moisture conditions to bc en-countered in underground structures.

The significant point is that Buller and Neher have obtained a correlation ivhich now per-mits estimating the thermal resistance froin cable to pipeor duct wall with sufficicut

accuracy, so that little, if any, practical iinprovement in cable load ratings can be gained by introducing furgher refinements in their analysis of this part of the thermal circuit.

RspsRBNcss I.

Taa Tassraa*ruaa Rise or Bvaiao C*n,as Auo Piras, J. H Neher.

AlEE Troasersioar, olume il8, pact 1, 1040, pages 0-1T.

Sce relcreace 1 ol the paper.

F. H. Buller and J. H. Neher: Mr. Norris and Mrs. Bucldand have taken us somewhat to task for our apparent'inconsistency in expressing our physical units in one system and our geometric units in another.

For better or worse it has long been the custom in cable rating procedure to express the physical units involved in the watt-second-centimeter-gram

system, and to ~ express length's in feet and diameters in inches.

In developing our equations itwould have been more consistent to have expressed the latter quantities also in centimeters, and thea to have converted the final expressions to'he system of measurement used in practice.

Wc chose to use the mixed system through-out, however, in order thag the reader might be able to use any equation in thc drvelop-ment, directly, without encountering the uncertainty which inevitably arises as to whether you multiplyor divide by the trans-formation constants.

The usc of the tarn "surface resistivity factor" is a slightly different matter. and as our sncntors have yoin]ed.out, it has dimen-sions which are not those of true, or volu-

metric, "resistivity."

Here

again, this nomenclature has been hallowed by tiinc and is thoroughly understood by cable engi ~

~ ~

neers, for whom this paper was written. It should be stressed, however, that this "sur-rvce resistivity" is not a

fundamental rsical quantity, in the sense that volu-

..ctric resistivity is; but as pointed out, is the resistance of a unit surface of a flin which, purely for purposes of convenience, is assumed arbitrarily to represent the entire thermal resistance of the composite heat transfer elects operating in the r'egion be-tween cable sheath and duct wall. 'ltis un-fortunate that we do not have a more dis-tinctive name for it.

Mr.Burrell has presented a thoughtfuldis-cussion of the assumptions which we have made in developing the theory used for corrdating the test data.

In this respect, a book by Prof. McAdamst gives a constant for the convection film on thc outside of a cylindrical surface in a free medium which is about 20 pcr cent lower than that for the in-side of a pipe and which we have used for both films.

Wc have not distinguishal be-tween the Lwoconstants because no informa-tion is given as to thc values of these can-stants when the cylinder is placed within the pipe.

While a formula for the conduc.

lion component in a nonwoncentric system is given by Whitehead and Hutchings't is far too complicated to use in this analysis,

'and itreduces substantially to the concentric formula which we have employed except for extremely small separations between the cylinders at one point.

Further there is considerable experimental evidence to sup-port the assumption that the emissivity constant is substantially unity for the types of cable surfaces employed.

Discrepancies were expectal, because of the assumptions which had to be made, a'nd because the physical location of the cables within the pipe cannot be controlled.

We have used assumptions and theory only to obtain a

sensible understanding of the problem with which we have to deal and to determine ivhat simplifications can justifi-ably be made in order to obtain practical worhng expressions.

These working ex-pressions were then developed directly from actual tests rather than from theory.

We do not share Mr. Burrell's desire for working expressions of sufficient complexity to identify the separate elects of the three modes of heat transfer.

Dr. Wiseman's simplified formulas for calculating her (on a per cable basis) for three 'cables in an oil-flied pipe or in a gas-filledpipe at 200 pounds per square inch are very intaesting and similar formulas may be derived from Figures 3 and 4 of the paper assuming that Q, P, and T~ have Gxed typical values.

Unfortunately Dr. Wise-man's derivation of the equivalent P in his formulas gives values ivhich are not com-parable to P as defined in this paper.

The corresponding rehtionship forP as defined in the paper is hgc 0.004110 3

2.15DN and this yields P 290 for the oil.pressure system and P ~ 450 for the gas-pressure sys-tem We cannot accept his formula for the oil system since its corresponding value on a total heat'iow basis is" Hrc" 1.15/Dr'hich is equivalent to Q/dT ~ 3.9 for Dr' 4.5.

Noae of the tests cited in Table~

IIIof the paper give an('upport for so high a value.

Dr. Wiseman also assumes that the over-all thermal resistance varies inversely with the diameter whereas we believe that a more representative variation may be deduced from the slope of the curves of Figures 3 and 4 in the vicinity of the typical operatirg points.

Thus for Q 25 watts per foot and T~

50 degrees centigrade, we derive the simplified expressions H,c (oil)~0.70/De"/s thermal ohm teeL (I)

Hrc (gas at 200 psi) ~1.20/(Dr')'l thermal ohin feet (2)

The conesponding equations on a per cable basis and with three cables in thc pipe are 1.44 2.07 hrc~= and hrc m respectively Qp (D )

~ s Figures 3 and 4 are intended to give prac-tical working values ofhce or Hrd over a wide range of operating conditions.

Mr. Grecb-ler is right in pointing out that the elect of temperature variations upon the radiation component is considerably greater than the effect of variations in the convection tenn which is the essential variant in Figure 3.

The inclusion of the temperature of thc medium in thc ivorking expressions would vastfy coinplicate them, however, and as a practical matter this is unnecessary.

In all of the Greebler.Barnett data't will be observed that P varies inversely as Q'/<

within the accuracy of measurement.

The dependence of P upon Dr cannot be evalu-ated from this data since only a single value of D, was employed, but since the convection term theoretically varies directly as Q'/</D'/s we believe that the temperatssre variation in the radiation term which Greebler has men tioned will be accounted for with su%cient accuracy by expressing the Greebler-Barnett data for fiber and Transite ducts in the form Ji(fiber) <<1120Ds'/'/Q'/'egrees centi-grade square centimeters per watt (3) lf(Transite) m990Dr'/'/Q'/'egrees centi-grade square centimeters per ivatt (4)

This will have the elect of changing the slope of the curves <<hen plotted in ac-cordance with Figure 3.'he coiresponding values of Hrc assuming '

worhng value of Q m 10 watts per foot Hrc (Gber) m(2.59/Dr'/ )+0.33 thermal ohm feet (5)

Hrc (Transite) 2M/D, I'hermal ohin feet (8)

While further theoretical and experimen-tal work may well be undertaken in order to clear up some of the apparent discrepancies between theory and practice and to yidd more factual data on thc pafonnancc of cables in duct; we agree with Mr. Kidder that little of any practical improvement in cable load ratings will result.

We do not wish to discourage further elorts in this direction, but we feel that it is sufficient to base cable ratings on Figures 3 and 4 of the paper or more simply on equations (1, 2, 5, and,8) just given.

Rspsasscss 1

See ccfcreace 2 ol the paper.

2, Cvaaairr Rarsuo or C*ai,as roa TaaNsaus siou auo Disraiavrsou, Se Whitehead, B. E Huichlags.

sources lastliutioa ol Electrical Baciaecrs (toodoa, Eagieod),

volume 83, 1038.

cqueiioa 10.3, page 531.

3.

Hear Taausraa Srvov oN Porvaa Caai.a Doers auo Doer Assausaas, Paul Greebler, Gus

p. Beraeu.

AIEE Trcareaioas, volume 80. pert

'1, 1030. paCes 337-5Z.

C. 'Dlscussioa br J.

H. Lleher ol cclcreace 3

~bOve pegCs 385~

1950, VOL.URIB 69 Bsdlcr. >VchcrThc.-nsal Ress'starve

ATTACHMENT 3 TO AEP:NRC:0692DF CABLE TRAY ALLOWABLE FILL DESIGN STANDARD

e ~ l p ~

sir mao P

~ J 2.

In all tvpe trays, cables shall be placed in the travs in a neat workmanship like manner.

Crossing of cables shall be avoided, cable oile-uos shall be keot to a minimum and cables shall not extend above the top of the tray.

(a)

When installing cables in a power t ay place the oower cables in a single layer soaced approximately 1/3 the O.D.

(outside diameter of the cables) apart.

See Figure l.

(b)

The surmtation of the O.D. of the power cables

~ shall not exceed 75% of the tray width.

See Table 1 for maximum allowable fill.

3.

When installing cables in control and ~strILRoentation tr y total cross sectional area of installed cables shall not exceed 40% of the trav cross sectional area.

See Table 2

for maximum allowable fill.

4.

When it is necessary to exceed the maximum allowable fill approval from the responsible cable engineer is required.

0 FOR SPACING OISTAHCE KTWEEH CAMS 5EE HOTE5 I IZ.MLOW FIGURE f

POWER CABLE SPACIAI6 NOTES:

f.

FOR CASLES OF EQIAL QL,SPACIH6 I& 0 EIL Z. FOR CAELES OF UHEOUAL CLL SPAQH& IS I/A clL 0F LARGER )casLE.

~

TRAY WIDTH ALLOVYABLE FII.I.

9 TABLE I

POWER TRAY MA1IMUAIFILL TRAY Vj IOTN ALLOWASLE FIU.

HI<& TRAY 26.8 AI.I.OWAOLi FILI.

Ii.

HIGH TRAY 57.6 w<

TABLE Z

~

CONTROL ( INSTRUMENTATION TRAY MAXIMllMPILL HoTES:

L AS TRAY FILL APPROACHES ITS ALLCWA8I ~ UAIIT THE FIELD SHALL'TAHE NOTE It CAELES ARE REACHIH6 OVER THE'SIDES CF 'M TiIAY(Eli.OUE TI5 POOI4Y TTAIHEO CASLES). IF HECESSARY, IM flED,AT ITS OWA OISCRETION SHALL INSTALL Coal.

TRAY SIOEMARO PER I-Z-EOS C 39(POS-.IIII).

Z.

IN EATREAIE CASES oR VIHERE SIOEOOAROS c'AH HOT SG IIISTAuZO,&E, FIELO 5HAu.

INPORM THE 'ELECTRICAI PLANT ACTION Td CLONIC 'THC ThaY.

IND(ANAcl IVtCHlGAN ELECT. CO.

D.C.COOK NUCLEAR PLANT Pos - I I9I.O c.LECTRICAI PLANT OESIGN SECTION REVISION-CI PI ANT OESIGN STANOARO CABLE TRAY A<<ONABL= =Al APP O OR. i'. C ICH.LIST, I OATH'I-I'-54 AM-RIC'N E' RIC PC'A'KR S=RVICK CORP.

I 1 EOS g

y.QISH I

OI.

I

ATTACHMENT 4 TO AEP:NRC:0692DF ANALYSES AND MATHEMATICALMODELS This attachment includes the pertinent sections of the report on ampacity program development.

The original report and the computer program were developed by the Electrical Section team members

AEPSC, New York.

l

V y ~

APPENDIX A

THEORETICAL DEVELOPMENT OF HEAT TRANSFER PHENOMENA WITH RESPECT TO CABLE AMPACITY IN LOW FILL CABLE TRAYS A.l REVIEW OF BASIC HEAT TRANSFER MECHANISMS Heat energy will flow through or from a body by means of three different mechanisms:

Conduction is the flow of heat from a point of higher temperature to a point of lower temperature, through a body or from one body to another body in contact, without signizicant molecular movement.

The equation for one dimensional steady state thermal conduction for a solid of constant cross sectional area is q =kA b,T cd X

Where: qk A

bT =

X Conductive heat transfer.

Thermal conductivity Area normal to heat transfer flow Temperature difzerence Thickness of solid Convection is the flow of heat away from the surface of a heated body by the motion of the surrounding fluid (gas or liquid).

When the motion of the fluid is produced mechanically, the action is known as forced convection.

When the motion of the fluid is produced by differences in the fluid density resulting from temperature differences, the action is known as natural convection.

The equation for heat transfer by means of natural convection is:

(2)

Where:qhcv ATss Ta Convective heat transfer Convective heat transfer coefficient Surface area of the body Surface temperature of the body Ambient temperature of the surround-ing fluid.

Any body at a temperature greater than absolute zero will lose heat in the form of radian" energy.

Likewise any body will absorb heat radiatec from any other heated body.

The net exchange of heat is proportional to the difference of the forth power of the'r absolute temperatures.

The net transfer of energy by raciation from a body to ambient or from a body to a surrounding body separated by a nonabsorbing medium is given by

(3)

Where:

q

=

Radiant heat transfer Stefan Boltzman constant

(

=

Surface emissivity (a factor between zero and unity, unity being a perfect emitter-or "black body")

A

=

Surface area of radiator s

Absoluter temperature of surface s

of radiator.

Absolute temperature of ambient a

or of surrounding body.

In actuality, the transfer of heat will be the result of the summation of conductive, convective and radiant transmission mechanisms or:

@=a

+q

+q (4)

Where:

Q= the total heat transfer A.2 HEAT FLOW IN CABLE TRAYS Presently, IPCEA Standard P-54-440 is the industry benchmark for cable ampacities in open tgp tray.

Much of this standard is based on work done by Stolpe The ampacities presented in this standard depend heavily on the assumption that the cables are tightly packed and that there is no air flow through the cable bundle.

The cable bundle is treated as a

homogeneous rectangular mass with uniform heat generation.

Based on the above criteria, the allowable watts per linear foot of cable tray is found to be constant for a given total cross-sectional area of cables (at a given b,T).

Referring to the fundamental equations for heat transfer outlined in the previous section, it is clear that conductive heat transfer is the governing heat transfer mechanism.

That is to say, allowable heat loss is inversely proportional to the thickness (i.e.,

cross-sectional area) of the body through which the heat, flows, for a given b,T.

When a cable tray is filled with cables to a depth of one layer or less, the assumption can be made that each cable wil'e exposed to a free flow of air.

In this case the above treatment of heat transfer does not apply.

For low cable tray fills, convective and radiant heat transfer are the governinc mechanism.

If this is true, the allowable heat loss per linea" foot of cable trav will.be constant for a given total surface area of cables as per equations (2) and (3)

~

Tne valica"ron of the above theory which is developed in the next sect'on is the major emphasis of this discussion.

A.3 HEAT TRANSFER PHENOMENA FOR CABLE TRAYS WITH LOW FILL Theory:

When a cable tray is filled to a depth less than or equal to one layer of cables, the maximum allowable heat loss will be constant for a given total cable surface area at constant aT.

An initial assumption will be made that the above theory is true.

Experimental data will be used to validate this assumption.

It will then be shown that the ampacity for any cable in the tray may be found based on the allowable heat loss.

The problem will be simplified by initially assuming that the tray contains only one size cable and that each cable is carrying the same current.

In this analysis, per unit area refers to per unit area of cable tray.

The total cable surface area pei unit area is:

A = nTt'd s

Where:

As n

d (4)

Total cable surface area P.U.

Number of 3 P cables per unit area Diameter of each cable P.U.

The percentage fillof the tray can be defined as the summation of the per unit cable diameters or:

F

=

nd (5)

Note tha" this differs from the industry standard of defining percentage fillbased on the summation of the cables cross-sectional areas.

From examination of equations (4) and (5) it is clear that the surface area A will be constant for a given percentage fillF.

The total heat generated per unit area by resistive heating of the cables is:

Q

=

3n I R

2 (6)

Where:

Q I

Rac Total heat generated per unit area.

Conductor current a.c. resistance of conductor per unit length.

Rearranging equation (5) n = F/d (7)

Substituting in equation (6)

Q = I R

3F 2

d ac (8).

Solving for the current (9) or (9a)

According to the initial assumption Q will be constant for a given surface area that is to say, a certain oercentaae fill.

Therefore a plot of l va ~dRac for a given percent fillahoulc yield a straight line through the origin with slope equal to Q 3F.

Plots of I vs.

Rac are shown in Figure A-1 for several raceway configurations at a constant tray fillof 67%,.

This data was determined experimentally at AEP's Canton Test Lab (see Appendix C).

As predicted, the plots are linear and pass through the oiigin.

The maximum allowable heat for this tray fillmay be determined from the slope of the plots as shown below:

(10)

A.4 CALCULATION OF AMPACITY In the previous section it was shown that the total allowable heat, Q,

was constant for a given percentage tray fill. In order to eliminate hot spots caused by locallv intense heat

sources, this allowable heat genera"ion should be distributed uniformly across the occupied area of the tray-This concept of uniform heat distribution is discussed in depth by Stolpe in Reference 2.

However, whereas Stolpe's analysis required a uniform heat distribution per unit volume (for tightly packed cable trays),

the calculation of ampacity for low filltrays is dependent upon a uniform heat distribution per unit area of filled tray.

FIGURE A-I 700 ventilated tray with ventilated co 600 500 solid tray with solid cover I

400 ventilated tray with 1 hour1.157407e-5 days <br />2.777778e-4 hours <br />1.653439e-6 weeks <br />3.805e-7 months <br /> fire barrier system 300 200 100 20 40 I

100 120

A.4 CALCULATION OF AMPACITY (contd).,

Figure A-2 illustrates the differing requirements of uniform heat distribution.

As per Stolpe's analysis of tightly packed trays, seven Ol2 cables occupy the same volume as one 4/0 cable and thus the heat generated by the two configurations should be equivalent under uniform heat distribution conditions.

For low filltrays, three il2 cables occupy the same area of tray surface as one 4/0

-..cable and therefore must generate the equivalent total heat.

A discussion of this effect on the effective diameter of the cable group is given in Appendix B.

Keeping in mind the concept of uniform heat distribution and rearranging equation,(8) it can be shown that:

d 3I R

=

F Q

(ll) or the heat produced by the resistive heating phase cable is equal to the percentage of the

heat, Q,

as determined by the area that cable in the cable trays.

of one three total allo~able

occupies, d/F, The allowable ampacity of any cable in tray can be calculated if the allowable heat is known for a specified tray fill, from equation (9):

(9)

The determination of allowable heat for various tray fills and raceway configurations is discussed in Appendix B, Computer Model.

FlGURE A-2 effective Equivalent heat sources for tightly packed trays as per Stolpe in Reference 2.

Equivalent heat sources for lot. ill cable travs

~

~

~.>>a eke

~

B.2 Program Development The heat transmission of cables contained in a rectangular tray enclosed with multiple layers of fire barrier material is quite complex and extremely difficult to model.

Therefore, an assumption was made:

treat the rectangular tray and fire barriers as cylindrical sections with the equivalent surface area.

Initially, the validity of this assumption was questionable.

However, because of the excellent correlation between computer data and test data,. it. is,felt that this approximation is sound.

.Utilizing the previous assumption, the program was developed based on the excellent work done by Neher and McGrath in reference 3 and Buller and Neher in reference 4.

Throughout this section, the concept of "thermal resistance" and "thermal resistivity" will be used, these terms being the inverse of thermal conductance and thermal conductivity respectively.

It is often easier to visualize thermal resistance analogous to resistance in an electrical circuit, with the thermal resistance of each medium be'ng in series, and with the conductive, convective anc radiant resistance acting in parallel through each medium.

A typical thermal circuit is shown in Fig. Bl.

The equation for load capability as developed in reference 3

is given by the following equation:

in equation (12)

T (T

+ ~Td) c a

Rd 1+7) dc c

ca (12)

Tc D Td dc conductor current (kiloamps) conductor temperature

( C) 0 ambient temperature

( C) 0 0

dielectric losses in conductor

( C)

D.C. resistance (microhms/ft. )

increment of ac/dc ratio Rca effective thermal resistance conductor to ambient (thermal ohms-ft.)

1cd 2cd Rlcv R2cv Ta R2 T

T

= Q(R

+

R

)

c

.a 1

2 where:

Tc ~ conductor temperature (typically 90 C)

'a

= ambient temperature (typically 40 C)

Q

= heat energy (watts p.u.)

1 1

1 1

+

+

Rl Rlcd R3 Rl 1

1 1

1

+

+

2 2 cd 2cv R2r (R in thermal ohm p. u, )

In the above thermalcircuit the conductive, convective and radiant thermal resistance components through each medium are added in parallel.

The equivalent thermal resistance of each mediumi Rl and R2 are added in series.

FIGURE 8-1

'B.2.1 Determination of Electrical Resistance The D.C. resistance of a conductor may be found from the following expression:

Rg~ =

p< [(r+ r )i( c + 201]

where:

p,

=

electrical resistivity of conductor (circular MZL OHMS/FT at 20 C)

CI =

circular inch area Y =

inferred temaerature of zero resistance

( C)

The factor 1 + Y may be determine if the ac/dc ratio is known c

R /Rd= 1+I +Y+YP (14) where:

Y

=

increment of ac/dc ratio at shield s

Y

=

increment of ac/dc ratio at pipe or conduit Y will be zero provided shields are'pen-circuited and Y

will be negligable in light of the fact that most cables in a tPay will be three phase twisted conductor.

Therefore equation (14) reduces to ac dc 1+ Yc B.2.2 Determination of Thermal Resistance (14a)

If shield and pipe losses are neglected as previously discussed, the total thermal resistance conductor to ambient, Rca will be the summation of the individual thermal resistances of each medium (i.e., insulation, jacket, air space, etc.).

The thermal resistance of the insulation may be calculated by the following 0 ~ 012 ( j log (Dj/D )

where:

R.

=

thermal resistance of insulation (thermal ohms-ft. )

p >

=

thermal resistivity

(

C CM/watt)

D.

=

diameter over insulation (IN. )

3.

D

=

diameter of conductor (IN.)

c (16)

The thermal resistance through relatively thin cylinders (i.e, cable jacke), tray, fire barrier) may be calculated from the following equation R = 0.0104 n n'D-t,>

3

where:

R

=

thermal resistance of the section (thermal ohms-ft. )

thermal resistivity of the section

(

C CM/WATT).

n' number of conductors contained within the section.

thickness of the section (IN.)

D'

.outside diameter of the section The heat transfer between surfaces separated by a "dead-air" space involves the mechanisms of conduction convection and radiation.

Each corres'ponding t'hermal resistance mast be added in parallel to obtain the effective thermal resistance.

However, in this case it is simplier to take the inverse of the conductances added in series.

Using the equations developed in reference 4:

C d =

lcd

=

0.0213 aT lo~go /D'),

D 'ET

DT (17)

(18)

Cr

=

'2r AT where:

C 0.102 D'

(1 + 0.016 Tm)

(19) thermal conductance due to conduction, convection and radiation respectively (watts/ C-ft) respective heat loss (watts/ft)

~T

=

temperature drop through the air space

(

D' outside diameter o

inner surface (IN.)

D" =

inside diameter of outer surface (lb.)

P

=

pressure of air (ATM.)

surface emissivity of inner surface T

=

mean temperature of air space

( C) 0 m

At this point, some clarification is necessary concerning the equivalent diameter o

the cable or cable group, the equivalent diameter of a 3 twisted conductor cable is obtained by multiplving the individual cable diameters by 2.15.

This factor will act to increase the calculated thermal resistance which is what would be expected due to the close spacing of a 3TC cable.

4 NI

~ ~~

The effective diameter of the cable bundle should be obtained by multiplying the effective cable diameter (or jacket diameter) by the number of three phase cables in the tray.

This will be D'hen calculating the thermal resistance of the air space inside the tray.

The effect is to use the, cable surface area to calculate the heat loss, which is in accordance with the theory discussed in Appendix A.

The thermal resistance per conductor will be the total number of conductors divided by the total thermal conductance.

If 1 atmosphere pressure is assumed the thermal resistance of the air space will be given by the expression.

n' log D" D')

'he thermal resistance from the last surface to ambient, in still air can be found from the following equation derived in reference 3.

1

[( ~ T/D"'"

+ 1.6 p (1 + 0.0167 Tm)]

III where:

D

= outside diameter of outer surface (21)

As previously stated, the total thermal resistance conductor to ambient, R'ill be the summation of the individual thermal resistances thrSugh each medium.

B.2.3 Determination of dielectric losses From reference 3:

Td = Wd Rda (22) where:

Wd W.

=

dielectric loss d

thermal resistivity based on da individual thermal resistivities at unity power factor.

0.00276 E

cos g

2 log DEJ (23) where:

E

=

phase to neutral voltage (KV)

(

=

specific inductive capacitance of insulatio.-.

r cos P

=

power factor of insulation D ~i =

diameter of insulation (in. )

I

~

Rd

=

R R./2 (24)

B. 3 Fire Barrier Ampacity Derating (FBAD2)

The program FBAD2 was developed according to the criteria outlined in section B.2.

A program listing is included in section B.4.

When running the program for cables in ventilated tray with covers, enclosed in Fire Barrier Material it was determined that the thermal effects of the tray was insignificant and could be neglected.

This agreed, with the results of tests at Canton (see Appendix C).

When a ventilated tray without a cover is enclosed in a Fire Barrier material, the thermal resistance introduced by the tray is negligable.

Therefore the tray should not be input as a "layer" in the program.

The assumptions used to develop this program require that the tray be filled to less than or equal to one layer of cables.

Therefore the number of circuits entered multiplied by the cable diameter should be less than or equal to the tray width.

'When entering "N" the number of layers, the cable insulation and jacket should not be entered as a layer.

The program is designed to account for their effect.

B. 3.1 N

Data Input The data required for running the program is as follows:

The number of layers of material enclosing the cable.

See B.3 D (I)

The equivalent diameter of layer I in inches.

T (I)

S (I)

E (I)

P (I)

The thickness of layer I in inches.

The dead air space outside of layer I in inches.

Enter

~ "1" if the air space is ambient air.

Note: Enter '1" o~nl for ambient air.

The emissivity of surface I.

The emissivity is a number less than or equal to 1, used to determine the radiant losses, 1

being a perfect radiator (black body).

See reference 1 for additional information.

The thermal resistivity of layer I in C-cm/watt.

0 Note:

The variables D(I), T(I), S(I), E(I) and P(I) shall be entered for each layer input.

A

~ i e

~

w J

Tl

=

Conductor temperature in oC.

T2

=

Ambient Temperature in C.

P

=

Electrical resistivity of the conductor in circular mil ohms per foot.

See Reference 3.

TO

=

Inferred temperature of zero resistance for the conductor material. 'ee Referenec 3.

V

=

Line to line voltage in KV.

El

=

Specific.-inductive capacitance of the insulation.

See Reference 3.

Fl

=

Power factor of the insulation.

T5

=

Thickness of the cable jacket in inches.

P5

=

Thermal resistivity of the cable jacket in C-cm/watt.

Nl

=

The number of conductors per cable.

C

=

Area of the conductor in circular inches.

DO

=

The conductor diameter in inches.

DI

=

The insulation diameter in inches.

Pl

=

The thermal resistivity of the insulation in C-cm/watt.

A

=

The AC/DC ratio ES

=

The emissivity of the cable surface.

D5

=

The diameter of the cable in inches.

B.4 Computer printout:

FBAD2 B.4. l The program FBAD2 is stored in the Warner Computer System under the access code for Electrical Plant Design Section.

B.4.2 Program Listing:

If 4

References 1.

Heat Transmission, W.H. McAdams.

McGraw-Hill Book Company, New York, N.Y., second edition, 1942.

3.

"Ampacities for Cables in Randomly Filled Trays," J. Stolpe.

IEEE Transactions, Paper 70 TP 557 PWR.

"The Calculation of the Temperature Rise and Load Capability of Cable Systems,"

J.H. Neher and M.H. McGrath.

AlEE Transactions, Paper 57-660.

4 "The Thermal Resistance Between Cables and a Surrounding Pipe or Duct Wall, " F.H. Buller and J.H. Neher.

AZEE Transactions, Paper 50-52.

Appendix l.

g 5.

6.

"Engineering Data for Copper and Aluminum Conductor Electrical Cables,"

The Okonite Company.

Okonite Bulletin EHB-78.

Pg.

5.

g cables in Trays Traversing Firestops or Wrapped in Fireproofing," O.M. Esteves.

ZEEE Transactions Paper 82 JPGC 601-3.

7.

"Ampacities Cables in Open-top Cable Trays,"

ZPCEA NEMA Standards Publication.

IPCEA Pub No..P-54-440~Second Edition);

NEMA Pub.

No.

WC 5 - 975.

8.

9.

Industrial Heat Transfer, Alfred Schack, Dr.

Ing. John Wiley

Sons, Inc. 1933.

Pg.

18 TSZ response to AEP questionaire from Marilyn Grau to R.H.

Bozgo dated September 29, 1982.

ATTACHMENT 5 TO AEP:NRC:0692DF REPRESENTATIVE AMPACITY DERATING CALCULATION RESULTS

Cable Tray: 1AZ-P8 Total Heat Generation Per Foot of Raceway:

Calculated Allowable:

36.98 Watts/Ft.

Actual:

9.70 Watts/Ft.

Connected Load Calculated 1470 R

1469 R

8067 R

8024 R

8187 R

8026 R

8027 R

2349 R

• 1476 R

1488 R

1991 R

16666 R-2 3

TC 412 CU 3

TC 412 CU 3 TC 412 CU 3

TC 412 CU 3

TC 412 CU 3

TC 412 CU 3

TC 412 CU 3

TC 412 CU 3

TC 412 CU 3

TC 412 CU 3

TC 42 AL 3

TC 412 CU 3.8 16.0 1.2 1.1 17.0 2.7 1.2 1.9 20.0 60.0 2.5 21.58 21.58 21.58 21.58 21.58 21.58 21.58 21.58 21.58'0.67 21.58

• CABLE CUT IN TRAY AND TAPED

Dc 6 F035. 92 I. 5 Zev

.5 CH&c'.a mC).

Ch BLh r VPa BCpc//p. zp H.P,

+W.

KVA.

/'4.7'

/r-g BobT ~

~Bo Z s8v' goZ6 N gOZ 7 rZ 234.5 I 7@

/ /c//

/Z.

/c<c< ~-z C

/2 9 ci/

<C /

9rc 9C

/z 3 c

/2 c

/z 3

c

/z 9 c

/

S C

/

C 2

C

/

cr cl A/G u

D4 G 6')b

+

acg u

0 9g 092 0 92 0 32 0 32 O 3c

~$ 2 03z Cu 0

2-092 w'

'P2 DP 0 92 E

R sr OT 0

1

/)N //

R CO 0- 0/

E'

/

/H 7 u

P s

Cy-R K

/7' H

COL,

-2 /

-2/

R/

P iP ge7

/7

//

. //P 2

//H /

/

//P /-

P go P

C) 8P QI5

CABLE N CONDUIT CONNECTED LOAD CALCULATED ALLOWABLE a2KCI5X ESRZBLet

+8003 R-1

• 8004 R-1

• S004 G-1 8026 R-1 8505 R-l 8506R-,1

<<8003 R-2

~8004 R-2

• 8004 G-2 8154 G-2 8155 G-2

+8744 R-2

+5ZV CABLE 4%

~

4N 4H 0

4N 4%

4N 1 s 1 II 4w 3

TC 42 SH-AL 3

TC 42 SH-AL 3

TC 42 SH-AL 3

TC 412 CU 3

TC 412 CU 3

TC 412 CU 3

TC f2 SH-AL 3 TC 42 SH-AL 3

TC 42 SH-AL 3

TC 412 CU 3

TC 412 CU 3

TC f2 SH-AT 57.5 3.32 64.6 4.20 64.6 4-20 2.7

.045 2.6

.042 2.6 042 57.5 3 32 64.6 4.20 59 3-50 2.6 042 2.6

.042 71.9 5.20 99.04 99 04 99 04

25. 85

25. S5 25.85 99 04 99.04 99 04

25. S5 25.85 99.04 9.S6 9.86 9.86 4.14 4.14 4.14 9.86 9.86 9.86 4.14 4.14 9.86 NOTES:

1.

ALL CABLES ARE 600V EXCEPT AS NOTED.

2.

CABLE FLA (FUEL LOAD AMP) AND MPACITY IS GlVZN.IN MPS.

3.

AMBIENT TEMPERATURE WAS TAKEN TO BE 40 C

~

~

c888E'YPE OiD

>~asH, FL8 FZP KV8 Ml lM =L 2.

~u gP HP

~P aB.

XP P 2 2.d gP 9

ATTACHMENT 6 TO AEP:NRC:0692DF RESULTS FROM TEST REPORT gCL-542

4

~,

C e

g Page I of~

TEST REPORT American Electric Power Service Corp.

Canton Laboratory P.O.

Box 487

Canton, Ohio 44701 ltle:

AMPACITY TEST FOR POWER CABLES es t o.

CL-542 December 16, 1983 Test By:

L.J. Balanti;J.

P. McCallin Report By:

L. J. Balanti Approved By:

- - A. P. Litsky blade For:

AEPS Corp.

Sponsor:

W. F. Wilson - New York Tes t Comp le ted,: November 18, 1983 g0 C)

Cl 0

CL E

Cl I

ZNTRODVCTZON For compliance with 10CFR50, Appendix R at the D. C.

Cook Nuclear Plant, tests were conducted on power and control cables enclosed in a TSZ, Znc. one-hour fire barrier system.

The results of-the test will be compared to computer-generated data to determine the validity of the computer model on heat run flow and cable ampacity.

II.

OBJECTIVE go

~~

4J E

0 g

The test objective was to simulate as closely as possible the actual conditions of tray and conduit runs proposed for Cook Plant and determine the final conductor temperature for the specified amperage and tray fill.

ZII.

TEST METEOD The generalized test method consisted of:

l.

Installing cables.

2.

Attaching thermocouples.

3.

Enclosing the TSZ fire barrier system.

4.

Applying the specified amperages.

5.

Maintaining a constant ambient temperature of 400C.

6-Monitoring the temperature rise and final conductor temperature.

Copies To:

T. O. Argenta/B.

R. Larson Canton B. J.

Ware - Columbus C. B. Charlton - Canton T. E. King - Columbus S.

R.

Kekane - Columbus

TEST METHOD (Cont 'd. )

The detailed test procedure was as follows:

Equipment Cable Tray and Cover 1.1.1.

Cable tray was galvanized steel, expanded metal bottom; size 12" x 6" x 8'-0" Long.

1.1.2.

Cable tray cover was galvanized steel, ventilated 12" wide.

1.1.3.

10'-0 Original tray length cut to 8'-0" to accommodate installation in environmental chamber.

1.1.4.

Tray cover attached to tray by using 510 x 3/8" Parker-Kalon type B (Z) with "H" head.

1.2.

Conduit 1.2.2.

4" I.D. Galvanized rigid steel.

1" I.D. Thinwall EMT 1.2.3.

Conduits cut to 8'-0" to conform with cable tray length and installation in chamber.

1.3 fire Barrier Envelope 1.3.1.

Thermo-Lag 330-1. subliming coating manufactured by TSI, Inc. for a one hour barrier.

Thickness of barrier was

.500" (+.125",

.000").

1.3.2.

1.3.3.

1.3.4.

1.4.

Prefabricated panels 6'-0" x 4.6 Prefabricated conduit sections.

Steel banding.

Cables The following cables were used for testing:

324 339 344 348 3101 3102 3103 3104 3120 3TC 012 Cu 600 V

3TC N6 Al 600 V

3TC N4 Al 600 V

3TC 02 Al 600 V

3TC 14 Al 5 kV shielded 3TC N2 Al 5 kV shielded 3TC '2/0 Al 5 kV shielded 3TC N4/0 Al 5 kV shielded 4/C 512 Cu 600 V.

~

~

1

Test Setup 2.1 Raceway 2.1.1.

Cable tray and conduit were supoorted aoproximately 2'-6" above floor to allow for natural ventilation.

2.1.2.

Raceway ends were sealed durinc the test with thermal insulating material to orevent heat loss through these areas.

Note:

This procedure could cause excessive heating of the cables passing through the thermal seal; therefore, all temperature readings were taken a minimum of 1'-0" from the thermal seal.

2.2 TSl One Hour Fire Barrier System 2.2.1.

The tray envelope was constructed of the pre-fabricated panels, cut so as to fit as shown in the Appendix (see Figure fl).

2.2.2.

2.3 The conduits were encased in the prefabricated sections.

Thermocouoles 2.3.1.

T-Type thermocouples were used to measure tempera-tures of the following:

A.

Ambient air B.

Too and bottom of the fire barrier envelope C.

Air space in tray D.

Conductors.

2.3.2.

Thermocouples were installed on the inward side of the conductor in a triplex arrangement (see Figure 2).

A hole was bored in the insulation and the the mocouples were placed on the conductor.

2.3.3.

Thermocouples were imbedded in Omegatherm 201 high thermal conductivity paste.

2.3.4.

Thermocouples were installed in a position located on the cables in the cente.

of the tray where:

A.

B ~

Heat generation is greatest.

-: ar dissipation is the least (see Figure 3).

~ t y, 1

'I

~ s ~

~

2.3.5.

The minimum number of thermocouples used to measure the conductor temperature was two (2) per cable circuit installed in the tray and five (5) for single cables installed in the conduit.

2.4.

Cables 2.4.1.

Cables were positioned in the cable tray in a single layer in such a position that there was a minimum spacing of 1/3 the diameter of the larger adjacent cable'.'Cables were then secured with "Ty-Raps".

3.

Test Procedure 3.1 Each test consisted of installing the cables in the tray in one of six (6) configurations as specified in the test request.

3.2 Once the proper setup was attained, cables were subjected to a load of three phase, 60 Hz sinusoidal current as specified in Section 4 ~

3.3 Ambient temperature was set to 40oC.

3.4.

Temperature rise of the cables was recorded on an Esterline Angus Hodel PD-2064 data acquisit-ion system at 4-hour intervals until the cable temperatures stabilized.

3.5.

The voltage and amperage of each circuit was monitored periodically throughout the test.

4 ~

Test Configurations 4.1 Test SI Circuit No.

Ztem No.

Description Runs in Tray Ampacity 324 3TCr 12 Cu 324

'TCr12 Cu 348 3TC02 Al 324 3TC512 Cu 3.8 20.0 60.0 0

f 4

j p

I H

t

2.3.5.

The minimum number of thermocouples used to measure the conductor temperature was two (2) per cable circuit installed in the tray and five (5) for single cables installed in the conduit.

2.4.

Cables 2.4.1.

Cables were positioned in the cable'tray in a single layer in such a position that there was a minimum spacing of 1/3 the diameter of the larger adjacent cable.

Cables were then secured with "Ty-Raps".

Test Procedure 3.1 Each test consisted of installing the cables in the tray in one of six (6) configurations as specified in the test request.

3.2 Once the proper setup was attained, cables were subjected to a load of three phase, 60 Hz sinusoidal current as specified in Section 4.

3.3 Ambient temperature was set to 40oC.

3.4.

Temperature rise of the cables was recorded on an Esterline Angus Model PD-2064 data acquisit-ion system at 4-hour intervals until the cable temperatures stabilized.

3.5.

The voltage and amperage of each circuit was monitored periodically throughout the test.

Test Configurations 4.1 Test fl 324 3TC 12 Cu 7

324 3TC~412 Cu 3

348 3TC~2 Al 1

324 3TC e~ l2 Cu 1

3.8 20.0 60.0 0

P

4.2 Test 02 Circuit No.

Item No.

Description Runs in Tray Ampacity 324 324 324 348 3120 344 3TC512 Cu 3TCI12 Cu 3TC012 Cu 3TC$ 12 Cu 4/C412 Cu 3TC54 Al

.17

.71 2.8 6.8 6.8 53.0 4.3 Test 43 Circuit No.

Item No.

Description Runs in Tray Ampacity 324 324 3120 324 3120 324 339 339 344 344 348 324 3TCf12 Cu 3TC$ 12 Cu 4/C012 CU 3TC012 CLI 4/C012 Cu 3TC 12 Cu 3TC$ 6 Al 3TC56 Al 3TC54 Al 3TC54 Al 3TC02 Al 3TC012 Cu 5

5 1

2 2

2 1

1 1

1 2

1

.71 2.8 6.8 6.8 16.0 16.0 16.0 36.0 36.0 53.0 60.0 0

4.4 Test N4 4.5 Cable Size:

3TCN12 Cu 600 V.

Conduit Size:

1" I.D. EMI Ampacity:

2 amps.

Test 05 4.6 Cable Size:

3TC52 Al 5 kV shielded with grounded.

Conduit Size:

4" I.D. Galv. rigid.

Ampacity:

72 amps.

Test 56 one end Circuit No.

Item No.

3101 3102 3103 3104 3TCV4 Al Sh.

3TCI2 Al Sh.

3TC02/0 Al Sh.

3TC54/0 Al Sh.

20 25 40 50

IV-TEST RESULTS The complete temperature recordings are tabulated along with test comments on computer printouts and listed under data sheets in the Appendix.

The final conductor temperatures for each test are listed below:

Test No.

Cable Ampacity (ampm)

Runs in Tray Highest Conductor Temperature (o C) 3TCC12 Cu m

3TCC2 Al 3TC)12 Cu m

4/C512 Cu 3TCT'4 3TCN12 Cu 4/CR12 Cu

~I 3TCe6 Al 3TCt4 Al m

3TC52 Al 3TCC12 CU 3TC02 Al 3TCS4 Al 3TC52 Al 3TCC2/0 Al 3TCm4/0 Al 3.8 20.0 60.0

.17

.71 2.8 6.8 6.8 53.0

.71 2.8'.8 16.0 6.8 16.0 16.0 36.0 36.0 53.0 60.0 2.0 72.0 20 25 40 50 45.6 59.7 55.7 42.6 42.7 45.1 44.4 43.9 58.3 54.6 57.9 60.4 67.3 55.2*

62.7*

57.6 65.9*

57.9*

68.8 63.7 42.9 65.0 45.6 45.4 45.5 44.5

• Thermocouple installed on insulation, not conductor

0

V.

DISCUSSION Due to a limited supply of variable power sources, several circuits were consoLidated.

In all cases, the loads were met or exceeded those that were originally requested.

As per the original request, conductors were placed in the cable tray in a single layer in such a position that there was a minimum spacing of ll3 the diameter of the larger adjacent cable.'lthough this probably is not the best simulation of actual conditions, it was one criterion of the test request.

During Test f3, the amount of cables made it impossible to follow this criterion.

It was followed as closely as possible and the results can be viewed in the Appendix under "Photographs".

All results contained in this report were forwarded to W. F. Wilson, New York, immediately upon completion of the test.

Any questions pertaining to the actual test results as compared to the computer-generated data should be directed to him.

VI.

APPENDIX A.

Data sheets B.

Test setuo C.

Photographs.

v f

J

~

~

l.)

":. )

v. )

Lc. )

5. )

G. )

7. )

Q

)

9. )

18. )

11.

3 1:". )

1 i, ~ )

14. )

15. )

fE. )

COMMENTS

- TEST No. l TEST 1

CL 6

~ 11/Sl/8~

IME IS 4:29 A.M.

START A=. 785V B=. 798V C=. 81 BVi A'

~. 8 AMP START A=. 7~2V B=.G57V C=i.82Vv ALL GG AMP START A='. 17V B=i. i4V C='.19V~

ALL 28 AMP CHANNEL ~9= AMBIENT CHAN

'=TRAY TOP~ "=TRAY BOTTQ,, 4=AIR N

. RAY CHANNEL, E, 7.ARE ON SG AMP CIRCUIT CHANNEL 5~ 8 APE ON 28 AM. CIRCUIT ALL OTHER CHANNELS ON

. 8 AMP CIRCUIT CURR END A 3. 9 B 3. 9 C ~. 9

'OLT END A

. 878 B. 805 C

. 867 CURR END A 59. 2 B 59. 5 C 59. ~

VOLT END A.818 B.7','

1 ~ 8" CUP.R END A 28. 4 B 28.:"

C 28. 2.

VOLT END A 1 ~ "'8 B f. 418 C l. 259 END TEST Nf CL-542 ff/f/8Z CL-512

1

~

~

TEST No.

ESTEr~: it1E Al'uGUS DATA TINE CH..m CHc2 CHIC CH84 CHÃ5 CHNS CHN7 cH5aa CH".1=.

84:28 84 4~

85: 15 8 c' 4c HF:1

~

8S: 45 87: 15 87:45 8n

~ ac 8n o4c 89,15 8Q 1 8

~

ac'8:45 11 a~

11-45 12,15 ls e ~ 45 14 4l~

ic ~ 1 c 15: 45

17. "

19. 4 on4 2S. 4 rsn s

o &a

28. 7 "8

~8. "

i8.:"

8 5

~8. S Z8. 9 va. 1 v~a.

1

~a

~

<e C';. 4

'9

48. 4

48. 5

41. r 4 8

41. e

41. 4

~ ha A [

41a 1

41.

1

41. 4

41. S

41. E 41

~

4g c

41. S

41. 5

41. "

r

<<J ~

s s

="8. a

~S. 5 41

48. 7

41. ""

48. 7

41. 4

41. 9 42.

1

41. 8

41. F 42.

1 4r. 5

41. 9

41. 8 4 2 ~

4r. "

41. 9

41. 9 Ja 7 r8

4. 1

<<an

~aCI ~ I

41. E 4 or ~ M 44.

1

44. S 44a 8

45. 4 45a 5

45. S

45. 8

45. S 4c'

45. 9

45. 9 45 ~ a

45. 9

45. 9

45. 9 4E

25. 5 4,.4.

49. 5c Jar ~ J 55a 9 57o

57. 8

58. 9 59.

1 59.

1 59 5S.

='9.

7

59. u

59. "

59. i

59. ~

ca 7

59. 4

59. 5

"'5. S

'E. 4 44a 1

9

51. 7

54. 4

54. 9 55

55. "

c'cJo J 55 a cc'

55. S c'5 c'J.

S 55a 7 sr5o 7 4v. "

48

58. 4 4

Jara Jv. S c'4 54.

1

54. 1 54a 4.

54a v c'4 54a E 54a 5 c'4 c'4.

S 54a 5

54. S

54. S 54

~ 5

<<Jo M 49 5~. 9 5F. 1

57. S 58.

~

59. 2 59

59. 2

59. s

59. J

59. 2

59. 4

.59. 5

59. 5

59. 4

59. 4

59. S

59. 4 c'9 c'

c c

J ~

o So 8 5 4 0

c'os

~ ~ J

41. 9 4v ~ ar

44. "

44. 4

44. 4

44. 7

44. S

44. 9 li.4. 9

44. 9 45 4c' 4c 4J5a ~

4c

45. ~

4i c'5. 4

45. 4

25. S ZS 4.1. '.

4r.5 4-V. J~

4:". S 4" 8 44

44. 1 44.

1 44.

~J

44. 2

44. '"

44

44. "

44. v 44.

"-'4.2 erc'Ja h

~ a

~~4. 5 vS. 5n 42.

a 8

4... r 4~e ~ J 4J. 7 4 ". 7 4~. 7 4"v. 9 44 4.4.

1.

44. 1 44.

1 4". 9 44.

1 44.

1 T<s lr=

~r7~ cia~

~

C ".17 CH~18 CHUB CH.5 CH CH

.7 CH.:" CH".6 CH~'7 CH/s33.

84: r8 84-45 8 c' 8 c' 4

c'S:

1.5 GS-45 87- '5 87:45 fpn ~ 1 c'n a4c'9:

15 89 18o 15

'8 ~ 45 11: 15 11 ass

~

g c' a ~ 4 c'olc r4 4~

~ C

~

1 C

~ C e

4C're'

<<J ~ eJ "4. S vS. F

48. E 4s s

4n 4.1 4v 4..4 4er o 4....

4

~

c'".

S 4.. S c':.

S 4

. E, rac c

<<Jo

~5. S MSa 5 41a 4 4"r. S 4<<

4v. S c'".8 4". 7 4e

~ ~ 8n 4e s ~ Cl 44 4sso 8n 44, 1

4..9 9

e ecJo J

~4. 7

~rSo 7 41.

1

42. 9 4

~.9 4v.

~

4i o, ~ S 4~. 4 4'. 7 4:". 7 4,,7

~ 8 4.. 7 4r. 7 4/s

/

7 4.

~.::-:

~ 5. S

~9 4

o C'z.

a 4.1 4... 5 4v. 5 4~. S 4 o ~ c' o ~ 5 4... 7 Q

4e. ~. ~ 7

l. -..3 4..9 4~. 9 4i

~ 8 l 4.

1

<e C

.,8, 2 v5. 9

~9. 9 4

44

44. 4 44...

44. E, 4lr.. 7 44i 44o 8

44. 9

44. 8

44. a

44. E 44 n n

4 c'4. 7 4i /.

38.

1 vS.

1 48.

1 4..,4.

44i

44. "

44.

lr.4. S

44. 7

44. 7

44. 8

44. 7

44. 7

44. 5

44. 7

44. 7

44. 5 4 /s Rc'

~8

~S 48 4n c

4". 9 c'4.8

44. 7 4

c'5.

1

45. 4 45.

~

45.

4Jo

45. S 4ic';

4c; c'

.9. a v4. S

-.n 48

42. 1 9

4". '"

4'. 4n 4s s ~ S 4i, 7 4.. Sn

44. 1n 4...9 4". 9 4v. 9 44

4. ~.9 le 4 nc n

<<iJo IJ

"8. S sr7 41.

1 4'". 4

44. 8

45. 5 4c5.

S

45. 9 4i8 ~

'S..~

4E. 4 4S 4S.

4F.

'8o4 48s r4.

"7. 9

48. 8

48. 48 48.

='8.

4 41.

~~

48. 8

48. S

48. 7

48. 7 41

48. 9

48. 7

48. 4

48. 4

48. 8

48. S

48. 7 4a.1 4

CL-54".

1 ~

3 a

~

~

~. )

4, )

-. )

C

)

7 ~ )

B. )

9.?

)

'1.)'.)

1~,)

1 4

)

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7. )

1B

)

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2i7i ~ )

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'.'7 ~ )

~+I

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"9. )

a8.

3

~1. )

COl'll<<ENTS TEST No 2

THERM1 AMB-. Ek'T t'CH~9)

THERMr".'OP TRAY Rl lvr'OT Of1 TRAY THE

-4 AIR S ACE CURR STAR:

A.2 8." C.2 VOLT STAR.'

~ 815 8

~ 81B C.82B CURR START A.9 B.9 C.9 VO' STAPT A.84B 8.848 C.8 5 CURR START A G. B 8 S. B C E.B VOLT START A

. 471 8

. 478 C. 558 CURR S ART A ".B B 2.B C

~.B VOLT START A. ~89 B. '"7 C.>8E CUR% START A 5~.8 8 5.8 C 5~.8 VQ:

START A 1. 587 8 '. ~7B C

. B86 CL-54" TEST Fr'2 1'/~/B~

START 8515 VOLT END A.8189 8.8147 C. 8.48 CL'R END ALL. 28AMP VOLT END A. 84BS 8

. 8496 C

. 8559 CUR CUR END A.B8 B.88 C.B8 VOLT END A.49S 8.58 C.S8 VOLT "END A.:2" 8.~5

~

C VO' END A

1. 572 9

1. 4B2 C. B~B CUR EtlD ALL 5~. 8 AMPS END TEST 2 CL 562 1688 TIME CH 9i 1B. 2E."'7t 2B '7 ON

='. B A...

CIRCU T CH

~ B ON 5" A:"lP CIPCUIT CH Bs 7 ON:-:'

CABLE~

S. B AMP CIRCUIT CH

'8~ '

QN 4/C CABLE~

F. B AMP CIRCUIT CH 17i ~E ON.17 AMP CIPCU CH 11~ 28~ 25 QN.71 AMP CIRCUIT CL-542

r t

~s

~

a,

~ I t=*

~

W j

TEST No.

ESTERLINE ANGUS DATA TTtlE CHUG CH CHir "

CH 4 CH 5 CH"6 CH 7 CH CH-9 CH" 18 CH <<

Gc

~ 4c Gc-1 86:4

~

87-}5 87-45 88-1 88-45 GS 1

89-45}c 18 4 11:15 ii:45 1.

~

~ c

~ o J 1 +ro4c 1":45

'4:45 1c

~ ic

.9. 6 VG vG. "

8 5 v8. 8 V}

v1.

"='i

~

V'}o

~}. 5

"}.5 v}. 4 o 1 1 ~

vi ~

re. 7 v76. 4

>>,g 48

48. 4

48. 5

48. 5

48. 7

48. 9 414}. 1

48. 8

48. 9 4}. }

41

~

1

48. 8

41. 2 v.7

>>6 8

'v. 4

>>9 P\\

484}. "

41. 7 4}. 4

41. ""

4}. 4

41. 7

41. 9

41. 5 4}o 6 4>>+

41. 4

~ 7 e>>9 v4.

='7

~ 6

':"9. 7

48. 9 41

~ 8 4". 4 4

~

c 4

~.9 4". 9 4r. 9

42. 9 4v.

1 4". 1 4V 4v. "

V>>J ~

4v. 6 49o 4 4~>> ~

&So

~

'ho

'6.9

&7>>

57. 6 57>> 7 57o 7 ce ee C

~J8 Se cw QGo Se.

1 se.

'n

>>J Vo

21. 4 o 4 5

48. 5

41. 98 4..4 4v 4 4v. 9 4'. 9 4.9 4>>4 44 44.

1 44 44 44>> 4 44.

1 2}. 8 r9, 1

"4. 6

.e. 4

48. 7

41. 9 4<. 4 4v. 6

, ~ 9 4",8 44>> 1 44.

1

44. 1 44.

1

44. 4 44

44. ~

4~o 8 4n. 9 C>>

e A~o 54 ~

1 cc c VSo V c6

56. v c6 c

56. 9

56. 9 S6. 9 57o o

57

57. 1

57. 1 S7, 1

err@

v8 v4>>. 9

>> euo 48 41

~

41. 8 4r. 4

42. 6 4r. 9 4v. 1

42. 9 4V 1.

4u 4>o.

er p

'e

~ ~

~

8. 4 iS. 6 n

>>euo V

48. 5

41. 6 4J

~

~

4

~.7 4

~.4 4v. 4 4v. 6 4

~.4 4m>> ~ 6 4v. 7 4v. 6 4v. 7

>>rP

~

vG a4. 7 v7. 9

'z9

48. 9

41. 6 e

42. 4

42. 6

42. 5

42. 6

42. 5 4'

6

42. 4

42. 6 4r. 7

42. 7 T1i1E CHO}

CHN}7 CH~18 CH-..28 CH-.. 25 CH026 Chill l7 C."t02nv CHOZ6 CHOi7 CHN'9 85: 45 QC

~

o c u

'6:45 87 87:45 88: 15 88:45 89: 15 89: 45

}8-}5

}8:45 11: 'S

':45 1 r-15 1.2: 45

}v:}5 O

~

1 4 4c 15.15 o

e

~ ~

vG. 7 v9 48 8 4...

'='V.'"

4

~. 7 4v. 8 4

~~

~ c 4>>

e ~ Vn 4>>

e ~ V 4..6 4u. 9

+ P'e

~ >>9 c v79. V

48. 9

41. "

41. 5 4}. 7

41. 8 Cl 42.

1 4}o 9 42.

1 42.

1 "6.

1',

uo

48. 6

41. 4 4( f ~

42. 4 4r. 4

42. 7

42. 7 42 9 4r,7 4ro 8 4ro 9 4.

4 '.

29. 4 i4. 5 V7>> 5 v9. 4 48 4}o "

41.. E

41. 7 4>>

e 4'

~

1 42.

1 4

~

4-'. 4 42

~1

'7

~

~

.4. 6

'7. 6

48. 4 41.

1 4}. 5n 4~>> ~

1 4r. 4 4-'. 4 4r. 4 4r. 4 or o "i. 5

6. 7 "9. 5 42.

1 4>>~r 7 4v.

1 4". 5 4..4 4:.. 6 4...7 4l>>7n 9

n p

~ V~

}.4 41.

1, 4ro 1

42 ~ 7 4..

4". 4 4v 4 4i. 5 4..., 7 4u ~

4.'. 7 4

c

.0. 4

=-e.

48o 5 4a. S

. ~

1 4v. 1 4

4 er 4.~.

4>e ~

.9. 6 "4. 6

='7 7

48. 6 41

~ 2 8

41. 9 4

~

4>>r 4r. 4

42. 4

42. 5 4r. 5 oo>>4

~ ~>

a7. 4

48. F

42. 5 4.". 4 44.

1

44. 4 44>> 7 45.

1n 45

44. 9

44. 9n

44. 8 45.

1.

45.

1 Vdo u v~9. 6 48

48. 6

48. 7

48. 8

48. 5 48..i

48. 7

48. 9

48. 7

48. 7

48. 5

48. 7

48. 5

48. 7

48. 7 48 CL-542

r

~

~ '

4 ~.:

5. )

E.?

7

)

C )

9. )

18. )

i~. )

14. )

15. )

16. )

'7. )

1 ~v'. )

19

)

28. )

'r 1

~ )

)

5o )

2h

)

27. )

='9. )

~3. )

'1. )

~...?

24

)

u5. )

f.:.. ~..',;

~

t'

~sh, (LI i

TP >. gt g ~Q, P HA 'MEL 4

Rc.Y P !ic.'A'E Ofl THE INSU'TION NQT THL CONDUCTOR CURP, START A 5~. 8 8

5~~. 8 C 5". 8 VOLT STAR:

A. 64'

. 744 C. 697 CURR STAR:

A >E. 8 8 ~6.8 C ~6.8 VO'. T START A 1.5 8 1.45 C '.6 CURR START A 2.9 8 2. 9 C =.9 VOLT START A.~96 8. ~99 C.426 CJRR START A 16..

8

16. ~

C16.

'OLT START A 1.9-7 8 2. 8.

C i. 9m~

CUq~ cTART A78 86 9

C 78 VQ'T STAPT A.Er 8 -61 C 6 CURR S

ART A.9 8.8 C.8 YO'

'START A.16 8.16 C.16 CURR START A 56.8 8 57.=.

e VOLT START A.64 8

. E4 C.67

. 7'MP CKT 512 CHAN'S iii17~25

2. 8 AMP CKT..12 CH'S 9. 18'1 26 27 26 m91 &7

6. 8 AMP CKT 4/C CH' 18'2

6. 8 AMP CKT "-'= CH'S

~8 16 O'"IP CKT

..6 CH'S

='

24 A~P CKT 4/C CH' "2 ZZ

'6 Af"P CKT ~12 CH'S "E. -'6

"6. 8 AiiP CKT N4 CH'S 28~ iB

==. e f.~P CKT."6 CH S -.4, ~5

.:.. 8

~MP CKT "4 CH'

5. 8

68. 8 AMP CKT 12 CH'S 6~ 7 CURR END A 47.4 8

2.8 C 57.7 VOL'.

c.ND A

. 643 8

. 692 C.712 CUR%

c.~D A ~E,.6 8 ~6.7 C 36.2 VOLT END A i. 5 9 8 1 ~ 465 C

1-687 CURP.

END A 2.9 8

~. "" C 2. 9 VQL T END A.416 8.414 C.441 CUR..

END A 16. 2 8 '6. ~

C 16.

1 VOLT END A

~. 48 8 2. 84 C 2.26 CURR END A 6.7 8 6.8 C 7.8 VOLT END A.594 8.628 C.6 7 CURR END A 8.9 8 8.9 C 8. S VOLT END A. 11,7 8. 1.2 C

. 1'5 CURR ENID A 55. E 8 5'. 8 C 55.9 VOLT END A

. 6 "8 8

. 585 C.697 END Q.=

TEST R~ CL-542r '/1 'Sv 14 5

Y W

~

'L s

TEST NO.

ESTER1 ENE ANGUS DATA T 1'NE CHI8 CH-..

CH0 CH 4 CH CH-"..6 CH.7 CH-..B CH".9 CH"18 CH4 QC ~ 4C 86 ~ 1 C 86:45 87:15 87-45 8S:15 8n ~ () c 89: 15 89 45 }8-15 1,8-45 }1-15 11-45 ier ~ ic:r-45 ~ 1 c 1=-.: 45 C' ~ ~ <<J rB. 9 29. 1

29. 9 u8. 4 "8. 7 V8. 7

>8. 8 u8 ~ 'v <<8<<8 >8. 6 .:"8. 4 <<ree I Q ~ u '1. 5 VE. 6

9. "

41. 1 4r. 6 6 4...7 44. -'4... 44<< 4

44. 6 44, 6 44<< 5 44.

~

44. 6 u4.

1 v9. 7 4r. 7 4<< e ~ ld 44, 7

44. 5 8

44. 9

45. u 4c

45. 6

44. 8 45.

1 >>7o 5 C ~J 1J ~ IJ 4r. 4

47. 7

~ r C'e ~J ' 54o 2 C'C <<J IJ C'C J ~ IJ

55. 8

55. 6 sJsJ ~ 7 5>>' 7 55o 7

55. 8

24. v

48. 4

58. 9 c,'7

61. 4

65. 5

66. 7

67. 6

67. 9 GB. 4

67. 9

67. 6 67 c

67. F 67.

1 F7 r4. 4

5. 4 5n

56. 6

59. 4

68. 9 Gr.

1 6" Ev. 4 Gu. 7 Gv. 4 Ei. 1 Gc 6sr ~ <<J

62. 9 Gn n4 e<<5a 7 5.

~ 1

56. 7

59. 4

68. 9 Er. 1 6". 4 Gv. 6 E".4 Gv. 1 F.1 6u ~

Gu. 1 2r4

48. 6 5}. 5 CQI 62.

~ F4 EG. v

67. 6

68. 8 69 GB. 7

68. u

68. 4

68. 4

68. =

68. 1 ~8, n u'U ~ u

44. 8 49 'r

51. 8 54 ~ 5J CC'5.

4

55. 5

55. 7

55. 6

55. 6

55. 6

55. 6

29. 7

%7o 7 44

48. 5

58. 9 c'IJ<<

~ ~ 5v ~ 5 5 aJ ~ 7 c'4 S4 v 54o 4 54 ~ 5 54o 5

54. 5

54. 5 54o 5 r9

<<7o

47. 5

58. 2 5}. S 5ra 6 5<<re 70

~J' ~ u 5~. 9 5Z ~ '9 c'<< 5u. 7 TItlE CHN}'Hn'15 CH=: 7 CHN}8 Cl-'-'28 CH-.. ri CIJI'P'e CH-.. 4 CHvr25 CHr. 25 CHc' 85-'45 86:15 86-45 87e}5 87-45 88:15 8ne45 89:15 8a:45 '8 1 18-45 11: 1,5 11-45 '-15 12-45 }u:}5 1 4c

24. 4

29. 8 VB 48 9

51. u C'JI '

W'4. 4 C'/D C'C <<J sJ ~ sJ <<J C5 a 1 5<<J ~ a 55e 1. C'C ~e <<J <<J ~ >>r VG. 7

45. 4

51. 8 c6

58. 4 68 FG. 8 FJ8a a

68. 5 e

u 'i. 1 6'8. 9

61. 2 68 uo

68. 8 l

C'}. 4 45 u

47. 6

49. ",

49. 7 c8 C1 C'1

<<e }.2 C' ~ <<J

51. ""

C1 c 1 24 cSo 7 4c

49. 7 C'e e

~J ~ <<J 5>>I ~ 7

54. 6 C'O';

<<J <<J ~ >>' 6 55o 5 CC

55. 6

<<J 5/ ~ 4 55<< 4 c'1 AG. 9 c' <<J ~ e CJ<< e ~ 55

55. 6

56. 9 57o>>

57 a c7 4 57e 5 c'7 c'7.5 57o<<e

57. 4 r4. 4 1

~ 1

48. 5

46. 8 c1

~ Il'<< ~ CC' <<J <<J ~ <<J

56. u

57. 6

57. 7

57. 4 c7 J/

57. 4

~J7<< ee r4

41. 4 48 52 54

5. 9

56. i 56e 5

56. 7

55. 9 c5 Q

57

56. 9 5F. 7

55. 7

~ 4. 4

47. 7

51. 8 55o cc 6 r

~J<<Jo u CC' <<J <<J ~ u C'C <<Jm o cC 5F. 1 uh 5c 24 ~ u <<rue u

44. 4 4IB. 4 51 5='. 7 5u ~ Na 54 C'/e C'J>>

~

54. 6

54. 5

54. 6

54. 5 54o 5

54. 5

24. 4 r9. 4 e'.IB<< 7

45. 5 52a 5 c4

55. 1 5p. 5 SDo 8 C6<<

1 cC 5 9 C Q <<J>> ~ V 'r4. urt

45. 5

49. 7 c'n

~ <<J 54o 1 54o 7 C'J sJ ~ <<J 5s/e 5 cE C'/5 >><<J ~ u cc n <<J <<J ~ 5<<Je 9 C'JQ s PS 7 CL-542

~ ~ ~ ~ ~ 1 I ~ ~ 7

Csgr ~ - C PL/!~, 1 s i <os Qglll>> CHN S PC' 4 C' ( 8S:45 87:15 87:4c~ 8' 1 c'S-45 89-15 89-45 18:'5 18-4 11 ei5 '1-45 1": 1.5 '-15 1:": 45 'r4. 4 ='9. 7 4c c'8 C'!>>>> ~ 7 Oa 5S. 7 5S. 9 7 r sJ s ~ 57. 'J ~ ~

57. '::

57 c'7 c 7 r>>4 c =:9. S .n 1 4S 58a 5 e! ae>> ~ >>r 54 S 7 5Se 1 cS c 5S. 7 5S. 7 C'I <Ge s Cl 5B, 7 5Sa E 56e 5 4 4':.'. 5

49. "

5S. 4

59. 'r e5>> ~ 7 S8.

1 S8, 4 S8 SQ..:. SQ. ~ S+ S8. ='8. '.:4. 4 .r'. 1

41. 4

47. 7 51.

i-'~. 9 OsJe 8

55. S 55 a Fr O'

5Ee 1 cS 55a 9 5F. 1

56. 1 rr

~ ~ Ii r sl 45 8 5'. 9 C'Ca! ~ < c'7 4 59 5S CCs &4l rer

58. u~

L Q 5 >>L QSa 4 ~~7 1

47. "

54e 1 sJ Aa S8 4i S'. S 7 Ei. 9 g r' 1 Sr. 1 E". ='t o C 4>>gl c C'C rs ada>> DMe Ss ~ 1 F -'. 4, S:-'. 9 S4. r S4. 5 S4. 8 E4. 9 E4.. 8 S4. 7,

64. 9 S4i ~ 7 S4. S

>>rg, ~ I a QPJe S 4S. 9 C'C C'Je c9 c Si. S Sv. '" S~. S S5 S5. ~ Sc' E5. 9 S5. 6 S5. 7 E5. 7 S5. S S5. 7 4i 1 ~

51. S e!S e E='. 4 E4. 9 BS. 5

67. 5 SE. 7 S7 S7 V7

~ ~ F7. 1 P7 S7. 1 Su. 9 tS 7 ~ 41. 47. 51. 54. 5S. 5S. 57e 57. C'Pl 4Ga C'Q Wva 57a 57. 57. 57. 57 a 9 Ql C b Pl 9 7 % ~ ~ 47. 51 Qi ' C4e 55 a 57 a 57. 57 a 57. 57. CiP 57o 57. 57 a 9 9 Ql CHI:9 8C' 4C'S:'5 85: 45 87: 15 87:45 8G: '5 8g e 4c'9et 5 89: 45 '8-15 18-45 ':15 '1-45 1 r ~ 45 1 e ~ 1 C ~S. S 4>> Ql 48o 4

48. 5

48. 7

48. 7

48. 7

48. 7

48. 7

48. S 48

48. 9 4,1.

1

48. 9 41 0

C'542

~ ~ ~ ~

o ~ TEST NO. 4 E'ST=. LLNK ANGUS DATP T:: I"iE CHNS CH-:.'H-.: " CH-.. ~ CHI4 CHN5 CH-..S CHS7 CHNS CHI9 QW ~ Pg Se'9:88 89 'p 18:88 18:>8 11-88 11:. 8 ~ 88 ~ 8 1i:88 'i:~8 14:88 '::"8 <<'4 o Sl

26. 6 27, 6 Clo 6 r9. E:

38 Z8. ~ ~8. 4 'v,8 >8. 7 >8. 7 "6. 6 ~6. ~ ~9. 1 ~9. 5 o,9 0 v9. 9 ~9. 6 48 48 48, 1 48. 1

48. 2

~9. 8 c' oraJ ~ 7 ~ g w<Mo o 'Bo 4C mq ~ ~ v9. 9 v9. 9 48. "-'8. 5

48. 7 48 48 48 Ql 48 ~

..9. 4 "B. 4 ~o7 .9 48. 1

48. 5

48. 6 41

~ 5

41. 9

48. 5 41

41. 7

41. 7 2Q u5 4

\\ ~7o .7 ~ 9

"9. 4 48.

~

48. 4

48. 6 48

48. 8

48. S 41

48. 8

48. 5 7o M N7

<<>9o 5 48.;

48. 8

48. 7 41 41 41.

1

48. 9 4f. 1 "S. 1 i7. 1 7 9 "9. 7 48o 4

48. 5

48. 5

48. 7

41. 2

42. 9

48. 9 41

~ 1

48. 9

-6. 8 ~5 'VM o o,T 4 "9. 1 48 1

48. 2 48.

1

48. 5 48 48

41. 7 48.

~

48. 6 70

34. 7 i6. 9

~7. u v9. 1 48o 2

48. 5

48. 6

48. 6

48. 8

48. 9

48. 9 41 ~

1 48o 8 2".4 ~~So ~> i5. 6 ~6. 4 m5o 7 ~~7. u~

48. 5

~S. 4 v9. 1 "5. 7 COt"i."fENTS

i. )

='. )

s. )

4. )

C' TES! VOLT Ql [RA CHAN CURR 4 START A f'9.5 B 119.4 C i21. S START A 2.8 B '.8 C ~.8 9 NYALID CL 54'r TEST 4, FINISH A =.8 B 2. 8 C 2.8

m 0

TEST NO. 5 ESTERLINE ANGUS DATA TIME CH08 CHQi CH CH03 CHSA CH~S CHC7 CHC9 CHc18 CHn 1 1 CH51 ~ 8 e ~ cgr 8G 8G:4 89 ic 8aeAc 18:15 18 45 1> ~ 1 1 1 ~ 45 12 ~ 1 ~:45 1 ~:15 1':45 14: 15 14: 45 15: 15 19

21. 9

'r3e 4 .6. e p .e. F =9. 6 38,

38. 4

'8 7

38. 9 5-.45 Ic if3 I I

~6. 7 1

39. 7 ie. 6

39. 7 48, 1

48 AQ ~9 9 48 v9. un 9

39. 7

39. 9

~9. 9

39. 6 48 o'r o

34. 7

'7 3e. 4

39. 3 48, 2

Ai 4'. 5

41. e

41. 7

41. 4

41. 7 41

~ 6

35. 6 37, 1 e"v ~ 7 "9. 7

48. 4.

48. e

41. 5 4r. 4

42. 5

41. 9'

i. 7 4:

Are c Arr 7 Ai. 9 .7. 7 C 3-. 5 4r. 9 46. ~ Ae. A.

58. 4

51. e 52e 7 C i D~ ~

53o 7

53. 9

53. 9 54 4

54. 3

54. 5 "8. 1

47. 4 58.

7'3.5 CC opere oi 56e 6

57. e

58. 6 Ca U>> ~ o

59. 5

59. 7

59. 9 68

68. 3

'4 ~ .e 6

45. 9 51.

1 c5r rr

59. 9

61. 9

63. 3

63. e

64. 5

64. 3

64. 4

64. S

64. e 65 29e e

. c

41. e 46e 7

58. 6 C

5~. ~ 55e 3

56. 4

57. 4 cn erGe u

58. 6 erGe 9 59.

1

59. 3

59. 5

38. 2 "5 7 4

~.6 4e. 1 cr, Vo' 44o 0 57 cn DGo ~

59. =

68,

68. 5

68. 9

68. 9

68. 9

61. 2 61.

~

61. 5

31. 7

37. 4

44. 5 58 54

56. 9

58. 7

68. 4

68. 9 6'

62 n

62. 4 6

~o 6='. 7 6=. 8 6 I ~ 9o

34. 6 4'. 5

46. e 58e e 5ere 4 cS n

57. e 5n c 5ee 9

59. 4 59o 5

9. 6

59. 6

59. 7 59'. 9 1

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5. )

6. )

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n

9. )

COMMENTS TEST 5 CL-54 '8/28/e3 8738 VOLT START A. 5S9 B. 844 C. 611 CURR START A 72. 8 B 72. 8 C 7.. 8 CHN 1 " ON OUTSI DE h!SULATION '-A.lBIENT 2-TOP CONDUIT BOTTO!" CONDUIT 4-AIR SPACE YOLT FINISH A. 631 B -997 C -S57 CURR FIN1SH A 7.8 B 7.. 1 C 71.9 END TEST 5 CL 54= 18/ r8/83 1545 C -542

1. )

)

v. )

4. )

) E. )

7. )

8. )

9. )

i8. )

11. )

2 ~ 1". )

14. )

15. )

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17. )

18. )

19. )

28, ) CQ+gENTS - TEST NO. 6 CL-4':: TEST 8 .ND RU" ll/18 8 CHANNEL m9 AHBl+NT CHANNEL iRAY TOP CHANN"L ~ TRAY BQ.TQl'i CHANNEL 4 AIR SPAC-28 A."lP C!(7 CHANNELS 9 25 AMP CKT CHANiNELS 8 18 48 Ai~iP CKT CHANNELS 5~ 7 58 AilP CKT CHANNELS 18~ 28~ ~S CURR START A 28. ~ B 28. 4 C.8. ~ VOLT START A. 748 B . 769 C..'SS CURR START A.5. 4 B 25. 8 C "5. i VQl T S ART g j 88' 1 058 C 1, 59( CURR START A 48. ~ 8 48. 8 C 48. Z VOL. S ART A. 22K 8 . 214 C. 245 CUR% SiAR: A 53.8 8 58.8 C 58.8 VOLT START A. "84 B . "89 C.287 END TEST S biD /18/8 Tl!CE 1545 CURR c'!>D A ""8. 5 B 21. 5 C ~i. 1 VOLT END A. 78c B. 8~8 C.8~7 CURR END A 25. 4 B 25. Z C.5. = VQl T END A i. 31S ei l. 797 C 1.285 CURR END A 41. 1 8 08. 4 C 4F. 9 VOLT END A. 48 8 . "25 C. 25K CURR END A 58. 8 B 49. 8 C58.4 VOLT END A..'"7 B. 211, C.278 CL-S42

i. 4

TEST Ho. 6 ESTERL:NE ANGUS DATA CHC2 CHr-. CHc4 CHN5 CHi"-.7 CHCS CH=::9 CH018 CH: 1 CH 16 CH5'"8 8'c 85-45 86-1 ~ 86:4u 87:15 87:45 88-15 8S:45 89:1 89:45 18:15 18:45 '1:15 12o 15 iso 4c 15 '-45 14:45 f.5-15 1 c ~ 4c

21. 5 i7. 7 o9. 7

'49o u 48 Jg

48. 6

48. 7 "9. 4 uSo 48.

1

48. 9 48, 2 u9. 2 48, 1

48. 9

48. 7

>9. 4 4.8 a9. 1 <<8. 1 v9. 7 .9 c ZS YQ >9. 6 48. 1

48. 4 48, 'r

48. 7

41. u

41. 5

41. "

41. 1

41. 8

41. 6 41

~ 2

41. 5

41. u 41

~ 6

41. 5 ore

<<4 ~ So 8 u<< ~,.u 5 o6 5 u8. 1 u9. 4 48 or 41. 1

41. 8 4 Pg 4r. 7

, ~ 1 ..4v. r 44...4 4u. 6 4v. 5 5o <<6o 8 , 29.S g o'<<o J C'b/ ~ 4 ~ u7. 4

48. 6

41. 9 4r. 8 4 or ~

4.6

44. 1

44. 6

44. 8 4c

44. 9

45. u

45. 4

45. 4 4c c o Joe O7 o

~ ~ =-.8. 1 ,.:":". 9 C' 'sJ ~ u u7. 8 u9. 7 41 4Z. 1 4",4 4v. 8

44. 1 44o 6

44. 8

45. 1 44o 9

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45. 2

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24. 9 "r9. S C>

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"7. 9 4

41. 1

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44. 2

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48. 9 4 +r 4u. 4.

44

44. 4 44 Qi 45 ~

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37. 4 v9. 1

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43. 9

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41. 8 4r. 5 4u. 4 7

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1 45. ~ 4c 4c c 4c c wzc <<do V

26. 7

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59. 2

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4 ~.5 4r.9 l-.. 1 4". 5 4",9 4". 8 4~. 9 44. 1

44. "

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26. 7 29o 6 T5c

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48. 5

41. 5 4r. 7 4v. 5 4u 8 44 44.

~ 44. ~

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44. 4

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44. 5 TE IE CHOu6 CHOZS 85 '5 Qc

~ 4c 86: 15 86:45 87: 15 87: 45 8So 15 BS: 45 89: '5 89:45 18o 18'5 11 -15 11 -45 12: 15 ior 4c 1 1 1 lL:45 ico ic I co45 ac <<uo 5

6. 7 Q9 Ql u5. 4 "7.i Z9. u

48. 5 42.

1 7 4u. 2 7 p 44 44...

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48. 5

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48. 5 4$ o 5

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49. 0

48. 5

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48. 5 CL-542

Envelope Bottom for =fness Envelope Cover fahrica eQ

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