ML17334B543

Forwards Addl Info Re Thermo-Lag Related Ampacity Derating Calculations,As Requested by NRC 950306 Ltr

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

RIG RITY 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 COPIES RECIPIENT COPIES ID CODE/NAME LTTR ENCL ID CODE/NAME LTTR ENCL PD3-1 LA 1 0 PD3-1 PD 1 1 HICKMAN,J 1 1 INTERNA 1 1 NRR/DE/EELB 1 1 NRR/DRPW/PD3-1 1 1 NRR/DSSA/SPLB 2 2 RGN3 ~ ...FILE 1 1 EXTERNAL: NOAC 1 1 NRC PDR 1 1 D

N i4OTE TO ALL"RIDS" RECIPIENT:TS:

PLEASE HELP VS TO REDUCE KV'iSTE! COYTACT THE DOCL'ifEYTCONTROL DESk, ROOlif Pl-37 (EXT. 504-~OS3 ) TO f;LlliflbATE YOL'R iAXIL'ROil DISTR I BUTIOY LIS'I'S I'OR DOCL'5 I Ei'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 ADDITIONAL INFORMATION 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 criteria. Attachment 4 provides an in-depth discussion of the fill design 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 ASQQ jg 9505190297 95051'2 PDR ADOi K 050003i5 P PDR

j I U. S. Nuclear Regulatory Commission AEP:NRC:0692DF Page 2 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 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:

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 trays.

of heat transfer theory for low fillcable 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.

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, As'tc.<<frohn iauge of cable no. 1 to a

.',."!7het Calculation of the Temperature Rise point of intexfexeace D <<dhmcter, inches aq b.o Dcdaiasid

an'd Load Capability of'able Systems D, <<Outxide Of Cahhduetar Ds<<outside of ixhsulatioa

~

Ds<<outside of sheath

~ D<<,<<incan diameter of sheath 3.~ H. NEHER

~ M. H. McGRATH Df<<outside of jacket r . MEMSER dhtlEE Ds'<<effective (cixcuxnscribiag cirde) of e

several cables in contact Dp<<inside of duct wal4 pipe or conduit Dc<<dlaxneter at start of the earth portion N 1932 D. M. Simmons'ublished a sideration as being the most cansistcnt of the thermal cixcchit a series of articles entitled, "Calculation and most readily handled over the full Da<<fictitious diameter at vrhich the effect of the EIcctricaI Problems of Underground scope of the pxablan. of loss hctor commences Cables." Over the intervening 25 years Alllosses willbe developed on the basis E<<line to neutral voltage, kilovolts (kv)

~ <<coefficient of surface emissivity this work has achieved the status of a cr <<spccific inductive capacitance of insula-handbook on the subject. During this QONrs and temperature rises due to dielec- tloa period, however, there have been numer- tric loss and to current-produced lasses mill /<<frequency, cycles per secoad ous dcvdopmcnts in the cable art, and bc treated separately, and, in the latter F, Fs,h<<pxxhducts of xatios of distances much theoretical and experimental work case, all heat Horns"miII be expressed in F(x) <<derived Bessei function'f x'Table has been done with a vievr to obtaining terms of thc current produced lossariginat-III and Fhg. 1)

G<<geometric factor more accurate methods of evaluating the ing in one foot of conductor by means of Gt <<applying to insulatioa resistance (Fige 2 i

'e parametas involved. The advent of the multiplying factors which take into ac- of referexhce 1) e pipe-type cable system has emphasixed count the added losses in the sheath and Gs<<applying to dielectric loss (Fig. 2 of

~

reference 1) the desirability of a more rational method conduit.

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

,h of calculating the performance of cables in duct in order that a realistic comparison In general, all thamal resistances miII be developed on the basis of the per con-I conductor current. kiloampexes kd <<skin effect co?rection factor for annuhr may be maCk betmeen the twa systans. ductor heat Qow through them. In the and segxneatal conductors kp<<relative txanshrexse coadclc&ity hctox In this paper the authors have en- case of underground cable systems, it is for caicuhting conductor pxoxihnity deavored ta extend the vrork of Simmons 'convenient to utilitc an effective thexxnal etfect by presenthig under one cover the basic 'esistance for the earth portion of thc J<<hy of a shielding tape or shd wire, inches principles involved, together vrith more thcxxnaI circuit vrhich indudes the effect L<<depth of reference cable below earth' of the loading cyde and the mutual heat- schxface, inches .

recently developed procedures for han- Lv<<depth to center of a duct bank dling such problems as the effec of the ing cffcct af thc athcx'able of thc system, inches (ox'ackfill),

loading cyde and the temperature rise Allcables in the system wiIIbe considered (lf)<<load factor, per unit of cables in various types of duct stxuc; t~ocsrry e eeoie Ided eetieiite eed to be (LF) <<loss hctor, per unit turcs. Indudcd as wdl are expressions operating under the same load cyde. ri number of conductors per cable The system'of nomendature employed xs'<<nuxaber of coaductoxs within a stated required in the evaluation of the basic diaxneter paraxneters for certain specialixed allied is in accordance with that adopted by the N<<number of cables or cable 'groups in a procedures. It is thought that, a mark of Insulated Conductor Committee as stand'- systexn this type wiII be useful not only a guide as ard, and diffas appreciablyfrom that used P<<perihneter of a duct bank or backfiJI, inches to engineers entering the Geld and as a in many of thc references. This system cos 4<<povrer factor of the insuhtion reference to the more experienced, but represents an attempt to utilize in sa far tfc<<ratio of the sum of the losses in the particularly as a basis for setting up com- as possible the various symbols appearing conductors and sheaths to the losses putation methods for the preparation of in the Amaican Standards Association ia thc coaductoxs 'I industry load capability and aw/d~ ratio Standards for Eectxicai Quintities, Me- tlc<<ratio of the sum of the losses hx the chanics, Heat and Thaxna-Dynaxnics, coadchctoxs, sheath and conduit to compilations. the losses in the conductors The calculation of the temperature rise

'and Hydraulics, when these symbols can R <<electrica resistance, ohms of cable systans under essentially steady- be used without ambiguity. Certain Rsc <<dw resistance of conductor state conditions, which includes the effect symbols which have long been 'used by R total aw resistixhce per conductor cable engineers have been retained, even Rc<<dw resistance of sheath or of the of operation under a repetitive load cycle, parallel paths in a shield-skid vtrire as opposed to transient temperature rises though they are in direct conQict mith assembly due to the sudden application of large the abaveementioned standards. 8 << thexxnal resistance (per conductor losses) amounts of laad, is a relatively simple thexxnal ohm-feet procedure and involves only thc applica-Nomenclature 8s <<of iaschlatioa Af<<of jacket tian af the therxnal equivalents of Ohm's (AF) attainment factor, per unit (pu) Rhd <<between cable surface aad schxxounding and Kirchoff's Laws to a relatively simple As<<cross-sectioht area of a shieldiag tape endosure thermal circuit. Because this circuit or skid rcire, square inches usually has a number of parallel paths dr<<therznaI diffhhsivity. square inches pa hour Paper ST~, recomtaeadcd bT the hIBB Insulated with heat Gams entering at several points, Coaductors Committee aod approrcd bT the hIEE CI<<conductor area, circular inches Tcchaiccl Operations Pepartmcac for presentation hovrcver, care must, be exercised in the d<<distahhcc, ~ c the hlBB Summer Ccocrsl hfecttae. hfoocreal, etc. << from ceater of cable no. 1 to center Que.,'aosda, Juae 24-2S. 105T. hfaauscript inches'th method used of expressing the heat foms subhoittcd starch "0, 10ST; made aransbte for and thermal resistances involved, and of cable no. 2 etc. priociax hpril 18, 10$ T.

Cks'tc.<<from center of cable no. 1 to differing methods are used by various en- image of cable no. 2 etc. J. If. Nausa ls eectb the phiaadclphta Elec&a gineers. The method employed in this Compcor. Philadelphia. Pa.. and hf. H. hfcCaam paper has been selected after careful con-As etc. from center of cable no. 1 to a poiat of icterfercace hmbor, ¹ Is reich the Ccocral Cable Cocporacloo, Pcrth J.

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

t ~

ajo OA9 Xo OA4 OA7 OA4 2,5 005 IF(x9) I.5 j

I.o I I! I I.O I i lii 8 IA 0015 o Ip I

0.9 a009~ Iu a4 ~ ~ I i I 0.7 0.4  ; I I i ~ s g a5

@xi I l jr 0004 0005

~ a4

'lji I I I! I i. I I! 0~

OA03 hI

~~ 0.25 00025 a2 0002 F(xv) I I:(xj O.I5 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 24~ of duct wall or asphalt mastic covering R~total between sheath aud diameter Da Including~ Rt, Rrc and Rc RATIO Lb/P R< ~between conduit and ambient

~

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

of loss factor and mutual heating by Wa~poztion developed in the conductor other cables W,~portion developed in the sheath or Raa'~effective between conductor and shield Ta-Ta ~ hT,+4T4 degrees centigrade ambient for conductor loss W <<portion developed in the pipe or con- (1)

R4r' effcctive tzanslcnt thezznal resistance duit of cable systan Wc ~ portioa deveiopal m the dielectzic Each of them component temperature Rca'~cffective between conductor aad am- X~ ~ mutual reactance, conductor to sheath rises may be considered as the result. of a bient for dielectric loss or shield, microhms per foot Rr,I~of the interference efect Y~the incremen't of aw/dw ratio, pu rate of heat flow expressed in watts Rf4 ~ between a steam pipe and ambient Ya<<due to losses originating in the con- oot throu a ermal resistance earth ductor, having components Yaa duc dinthermalohm eet degzcescenti-p~clectrical resistivity, circular mil ohms to shn efect and Y,jr due to prox- gra 0 eet per watt); in other words, the per foot imity effect it thermal resistivity, degrees centigrade Ya ~due to losses originating in the sheath centimeters pcz'at't or shield, having compobeats YIa Qow of one watt uniformly distributed.

s~distance in a 3mnductor cable between due t'o cizcuhting cuzrent cffect and over a conductor length of one foot.

the effective current center of the Yi, due to eddy current effcct YIr~due'to losses originating in the pipe Since the losses occur at. several posi-conductor and the axis of the cable, inches or conduit tions in the cable system, the heat Bow in S~axial spacing between adjacent cables, Ya ~ due to losses originating in the amor the thezznal circuit wB1 increase in steps.

inches It is convenient to express all heat Qows in t, T~thickncss (as indicated). inches General Considerations of the terms of the loss per foot of conductor, and T~ tanperature. degrees centigrade thus,,

Ta~of ambient air or earth Thermal Circuit Ta~ of conductor aT,- WgRr+q,R,.+qA)

T~~mean temperature of medium THs ~~TzoN op TsM2smTzzss AT~tcmpaature rise, degrees centigrade degrees centigrade (2)

Rzss ATa~of conductor due to cturent produced losses The temperature rise of the conducmr in which W, represents the losses in one hT4~of conductor due to dielectri loss of a cable above ambient temperature may conductor and RI is the thermal resistance tZTrxr~of a cable due to extraneous heat of the insulation, q> is the ratio of the source be considered as being composed of a r infared tanpaature of zero resistance, temperature rise due to its own losses, sum of the losses in the conductors and degrees centigrade (C) (used in which may be divided into a rise due to sheath to the losses in the conductors, correcting R4, and R, to tempera- current produced (PR) losses (hereinafter R<< is the total thamal resistance between tures other than 20 C) sheath and cocdmt, q, is the ratio of the Vs~wind velocity, miles per hour referred to merely as losses) in the, conduc-W~lozses developed in a cable, watts per tor, sheath and conduit b,Ta and the risc sum of the losses in conductors, sheath and conductor foot produced by its dielectric loss hT4. conduit, to the conductor losses, and Ra Oerosss 1957 Nchcr, McGrath Tcrnpcratarc arrd Load Capability of Cable Systcrrrs

ls the thermal resistance between tt e aTc Wc(A+qc~cc+qcfffcc+(LF) X Ta6le I. Electrical Resbtlvity of Various

is made to the electrical resistivity in circular mil case. The temperature rise at points in ohms per foot. To determine the value of depend on the heat loss corresponding to the cable system other than at. the con- resistance at temperature T multiply the the maximum load vrhereas the tempera- ductor may be determined readily from resistance at 20 C by (r+T)/(r+20) ture rise from diameter Dc to ambient is the foregoing relationships. where r is the inferred temperature of made to depend on the average loss over a THB ChiA'-UthTio)4 op Lohn ChPhnan)r Zero resistance. 24-hour period. Studies indicate that the The resistance of the sheath is given procedure of assuming a fictitious critical fn many cases the permissible maxi-diameter D> at which an abrupt change occurs in loss factor from 100% to actual will give results which very closely mum temperature of the conductor is Gxed and the magnitude of the conductor current goad capaMity) required to R, ~ by the expressions pc 4Dcctt mlcrohms per foot at 20 C (II~ approximate those obtained by rigorous transient analysis. For cables or duct in air where the thermal storage capacity produce this temperature is desiretL Equation 5(A) may be written in the form Rc ~ 37.9'or Dctttt Iesd at 50 C (IIA) ATc ~I'24c(I+ of the system is relatively small, the maxi-mum temperature rise is based upon the yc)lcc'egrees centigrade (7) ~4 Dg 1 for 61% aluminum at 50,C heat Gow coizesponding to maximum load i which the qqaatity~lb, (1+ Y, qhieh (IIB) vrithout reduction of any part of the ill be ev uate re resents the theimal circuit. When a number of cables are installed eE ducto 'n 've electn hms resistance of the con-vrhen multiplied by P (I in kiloamperes) and which vrhere Dcttt is the mean diameter of the sheath and t ts its thickness, both in inches dose together in the earth or in a duct bank, each cable wQI have a heating eEect vrillequal the loss Wc in watts per conduc- Dccq ~Dc t laches (12) upon all of the others. In calculating tor foot actually generated in the conduc-the temperature rise of any one cable, it is tor; and 8ec's the e(fectlve thermal The resistance of intercalated shields convenient to handle the heating etfects of resistance of the thermal circuit or skid wires may be determined from the ) expfcsstOQ the other cables of the system by suitably fIcc'IIt+qc8cc+qcffc'hermal ohm-feet inodifying the last term of equatiot 4. This is permissible since it is assuined From equation I it follows that (8) R, (pe: path) )I+( rpc SDtet that all the cables are, carrying equal cur- I microhms per foot at 20 C (13) rents and are operating on the same load + lciloam eres cycle. Thus for an P-cable system 3 a,<I+ I;)~. where A, is the cross section area of the Kdhdr, hfcGra! h Terri pdratnrd and Load Capability of Ccbfe Sys.'crrts QcToBBR 19o< s ~ ~' ~ tape or sl.id wire and l is its lay. The Il. Recommended Values of k,cndks 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.ctfuTioH oF Losslls 'cisj>> Conductor Construcuon Costing on Saends Concentric round,.............Hone..... ~ ~ . ~ ~ .~...".Noae..............l.o Concentric round..............Tlo or enoy........ ~ . .None..........~...1.0 Treatment ~ Concentric round..............Hone.~............... Yes...............l.o .....~.......0.80 Compact round o ~ Noae ~ ~ ~ Yes ~ ~ ~ I0 Lro .....~.......1.0 ........~....1.0 ~ ~ ~ ~ ~ 0 0 It is convenient to develop expressions for thc losses in the conductor, sheath and Compact segmental.......,....Hone..................Noae..............0.43$ Compact segmental............Tin or aUoyoo Compact segmental............Hone..................Yes...............0.43$ Hone ....O.S .~ .. .............0.0 .."...~.....0.37 0.7 Compact sector................Hone............... ~ ..Ycs...............l.o.............(secnotc) pipe or conduit in terms of the components of the aoc/doc ratio of the cable system Horns:

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

r(w R CIRcc 1+Yc+Ys+Fp (14) 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, The aoc/doc ratio at conductor is 1+ Yc 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 and at sheath or shield is I+ Y,+ Ys 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 and atpipeorconduit is I+Y,+Ys+Yp 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 The corresponding losses physically gen- test data lodicatcs ko and kp values of OA and OA respectively. erated in the conductor, sheath, and pipe are Ws I Rcs(l+ Yc) watts pcr conductor foot Tabl>> III. Skin Effect fn % in Solid Round Conductor lnd in Conventionel Round Concentric Str4nd Conductors (IS) 100 F(x), Skin Effect fo Ws PRcc Ys watts Per conductor foot (16) Wp ~I'24cYp watts per conductor foot (17) 3 4 5 d 7 d 9 his permits a ready determination of the 0.3... 0.00... 0.00... 0.01 .. ~ 0.01... O.OL.. 0.01... 0.01... 0.01... 0.01... 0.01 losses if the segregated a-c/doc ratios are 0.4... 0,01... 0 Ol ~ 0.02. . ~ ~~ ~ 0.02... 0.02... 0.02... 0.02... 0.03... 0.03... 0.03 O.S... 0.03". 0.04.. 2.as' 0.04... ~ 0.04... 0.0$ ... 0.0$ ... 0.0$ ... 0.00... 0.05... 0.00 known, and conversely, the aoc/doc ratio 0.0.. 0.07... ~ 0.08... 0.08... 0.09... 0. 10... 0.10. 0.11... 0.11.;. 0.12 is readily obtained after the values of Ycs 0.7... 0.12... 0,13... 0.14... ~ 0.1$ . ~ . 0.10.. ~ 0.17... 0.18... 0.19... 0.19... 0.20 0.8... 0.2L. . ~ ~ 0.24. . ~ 0.2$ ... 0.20. ~ ~ 0.2$ ... 0.29... 0.30oo ~ 0.3L... 0.33 Ys and Y< have been calculated. 0 9 0 34 ' ~ O.sd... 0.38.. ~ 0.39... 0.41. .~ 0.43... 0.4$ . 0.4T... 0.4$ ... 0.$ 0 It 1.0' Oo62.", 0 $ 4o ~ ~ 0.60... 0.$ 8... 0.01... 0.03... 0.0$ ... 0.08... 0.70... 0.73 follows from the definitions of qs and ~ e I I ~ ~ 0 Tdo O.T9... 0.81.. ~ O.dl... 0.87... ~ 0.90... 0.94... 0 97 I 00' I 03 that 1.2... I OT... 1.11... 1.14 . ~ 1.18. ~ ~ 1.22... '1.25.. ~ 1.30.. 1.34. ~ . 1.3$ ... 1.42 qc 1.3" ~, 1.47". I S2o ~ ~ 1.50... 1.01". L.dd... ~ 1.71." I.Td... 1.81o ~ 1.8'. 1.92 1.4.. I.OT. 2.02.. ~ 2.08. ~ ~ 2. 14... 2.20... 2.20... 2.32.. ~ 2.39.. 2.4$ ... 2,$ 2 Wc+WC Yc ~ 1.5... 2.$ 8... ~ ~ 2.93... 3.01... 3.08... S.td... qsw m]+ (18) . 2.72oo ~ 2.79.. ~ 2.6$ . ~ . 3.40oo ~ 3.49... 3.6T." S.dd... 3.7$ ... 3.$ 3.. ~ 3.92. ~ . 3.24 4.11 1+ Yc 4.02oo i+- Wc ~ 1.7.. 4.21... 4.30... 4.40... 4oso... 4.50... 4.TO... 4.81... 4.91... 6.02... d.13 5 '2 ~ $ .94... d.od... ~ Wc+WC+ Wp Yr+ Yp 1.6... $ .24... 6.3$ ... $ 4To ~ 6 6' ~ 6 TO ~ ~ ~ ~ 0.19.. ~ 0.31 qc (ip) d,syoo 0.70... 0.83... 0.97... 7.11... 7,24.. 7.38. ~ . 7.53.. 7.07 We 1+ Yc 2.0... T.S2... T.Q0.. ~ 8.11... 8.25... $ .42... 8.$ 7... 8.73.a. $ .89. ~~ 9.0$ .. ~ 9.21 2.1... 9.38" . 9,71... 9.88... 10.0$ .. 10.22.. 10.40... 10.$ 8. 10.70.. 10,94 The factor Y, is the sum of two compo- 2.2.. 11.13" ~ 11.3lo o ~ 11.50... Ll.d9... 11.88. ~ . 12.07. . 12.27... ~ ~ 12.4T. 12.0T. I'2.67 2.3... 13.07. ~ . 13.27... 13.48. ~ . 13.08... 13.90... 14.11... 14.33... I4.'$4.'.. ll.'70.'.. ll.'9$ nents, Ymdue toskneffect and Y,p due 2.4.. ~ 15.21... IS.43. ~ . 1$ .00... LS.SO. ~ ~ lb.12... 10.3$ ... 1$ .$ 8.. Ld.d2... 17.15.. 17.30 2.$ ... LT.64... IT.78... 1$ .03... 18,27... 18.$ 2o.. LdoTS... 19.03o ~ . 19.28... I9.64... 19.80 proximity effect. 2.0... 20.00... 20.32... 20.$ 8o ~, 20.8$ .. ~ 21.12o,. 21.38... 21.0$ ... 21.93.. ~ 22.20... 22.48 2,7... 22.TS... 23.03... 23.31... 23.50... 23.88... 24.17. ~ ~ 24. 4$ . ~ . 24.T4 ~ ~2$ .03, 2$ .33 Wc ~lsRefc(1+ Ycc+ Ycp) 2,$ .. ~ 2$ .62oo ~ 2$ . 02. ~ 25.21... 20.$ L... 25.8L... 2741... 2T.42... 2.9. 28. 0$ . ~ 2$ .90... 29.27, ~ 29,$ 8... 29.90. ~ 30.21. 30.$ 3... 30.$ $ oo ~ 31.17... 31.49 watts per conductor foot (20) 3.0... 31.$ 1... 32.13... 32.4$ .. ~ 32.78... 33.11... 33.44... 33.7T. o ~ 34.10... 34.43o.. 34.TT 3.1... 3$ .10. 3$ .44oo ~ 3$ 78.. 30.11.3d.4$ .. 35.TQ. ST.13... 3T.4T. ~ . 3T.$ 2.. ~ 38.10 The skin etfect may be determined from 3.2... 3$ .$ 0... 38.8$ ... 39.20e. ~ 39.$ $ ... 39 89... 40.24... 40.$ 9... 40.94. 41.29 . ~ ~ 41.ds the skin effect function F(x) 3.3... 42.00. ~ . 42.3$ ... 42.71... 43.05... 43.42... 43.78... 4l.li... 44.49... 44.8$ ... 4$ .21 ~ 3.4., 8.5.. ~ 4$ .$ 7oo 4$ .93... 49.20... 49.$ 7... 40.29oo ~ 40,0d... 47.02... 47.38... 47.74... 48.11... 48.4T... 48.84 49.94... 50.30... $ 0.07... $ 1.04... 51.40... $ 1.77... 62.14... 62.$ 1 'k:::: ".::::::::: ~ Ycc~F(xr) (21) 3.0... $ 2.8$ ... S3.2$ ... .02... 63.99... 64.35... Si.T3... 5$ .10... $$ .'4$ .".. ss.'Ss.".. Sa.'2 3.7... $ 0.59... Sd.90.. d .33... ST.TL .. $ 8.08... 58.4$ ... $ 8.82... $ 9.20.. ~ $ 9.$ 7.. ~ d9.94 xs ~0.875 ~ QRcr/ks at Rcc 60 cycles 3.8... 3.9... 4,0... 00.31 .. 00.09... 04.OS... 07.79... 01.00... 01.44... al.dl... a2.18... d2.$ 0... d'3.93. 03.30.. 03.dd 04.80... 0$ . 17... 0$ .$ $ . ~ 0$ .92... 00.29... 00.07oo ~ 07.04... 07.41 ~ as.'la."..'1.89... 0$ .$ 3. . 08,91. ~ ~ 09.28... 09.0$ .. ~ 70.40... 70.7T... 71.14 (22) 4.1.. 4,2... ~ TL.$2. 7$ .23... " Ts. 00. 72.20. ~ . 72.03... 73.00. 73.38. 73.7$ ... T4.12... 74.49... 74.80 7$ .9T... 7d.34... 7d.TI... 77.0$ .o ~ T7.4$ ... TT,82, ~ T8.19... 78.50 in which the factor hs depends upon the 4.3., 4,4... ~ 78.93... 82.01... ~ 70.30... 79. 0T... 80. 04... 80. 41 .. ~ 80.7S. SL.L4 .. 61.$ 1.. ~ $ 1.8S... 82.2$ ~ 82.98..r 83.3$ ... 83.01... 84.08. . 84.4$ ..o 84.dl... 8$ .18 .. 8$ . 5$ . 8$ . 91 ~ ~ ~ conductor construction. For solid or 4.$ ... 80.28 ' ~ ST.OI.. 87.37.. ST.73... 8$ .10.. 88.40... 88.82... 89.19... 89.$ S 4,0. 89.91., 90.2$ ... 90.04.. 91.00... 91.37,. 91.73. 92.09... 92.4$ ... 92.81... 93.17 conductors ~Srrotnate ~ ~ ~ conventional a 4.T... 93.$ 3.. 93.89... 94.2$ ... Ol.dl... 94.97... 9$ .33... 9$ .09... 90.0$ ... 90.41... Od.TT eIL The, 4.8. . 97.13.. ~ 97.49... 97.8$ ... 98.21... 98.$ 7... 98.92... 99.2$ ... 99.d4...100.00...100.3$ 4.9.. L(tO.TL.. ~ IOL.OT... 101.42...101.78".102.14...102.49." 102.$ $ ... 103. 21... 103.$ 0... 103. 92 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 and inner diameters of the annular con- annular conductor when computed by ductor. In comparison with the rigorous equation '23 will not be in error by more (2$ ) Bcssel function solution for the skin effect than 0.01 in absolute magnitude for in an isolated tubular conductor, it has copper or aluminum IPCEA (Insulated in vrhich D, and Ds represent the outer been found that the 60~cle skin effect of Power Cable Engineers Association) Sled OcTOUUR 1957 %cher, .lfcGrcfh T~n(pcrc]nrc and Load Capability pf Cnbtc Sysfcfns 7M 6 as ~ Ta6I>> IV. Mutual Reactance a160 Cyeiess Conyfudoe lo Sheath (or Shlelsf) (2 S/D~) as in the case of lead sheaths. I~ D~/28 6 --0 1 2 3 4 5 5 T 8 9 <<~ 1+- 0.4. ."21 1. 20.5,. a19 9....r19 4.....18.9..".18.3.....1T.8... .ly.i..."15.9..".15.4 roximattly at 60 cycles (30A) 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. " When the sheaths ale short~ted, the 50.T....48.T... .45.9. . .45.2.. .43.5.....42.1.....40.T*. -.39.4

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ .3' sheath eddy loss mal be reduced and may be approximated by multiplying equations 30 or 30(A) by the ratio core conductors up through 5.0 CI and for also be estimated from equation 24 and hollow core concentrically stranded copper 24(A). In such cases, S should be taken R,'/(Res+Xmas) or aluminum oilrfiilled cable conductors as the axial spacing betvreen adjacent up through 4.0 CI. conductors. In computing average eddy current for For values of xp below 3.5, a range The factor Ys is the sum of tvro factors, cradled configuration, S should be taken vrhich appear to cover most cases of prac- Y<<due to circulating current efect and equal to the axial spacing and not to the tical Interest at povrer frequencies, the geometric-mean spacing. Equations 30 Y<<due to eddy current efects. conductor proximity efect for cables in and 30(A) may be ural to compute the Ws I'Rd< Yes+Yes) eddyment-,ef >>et for single-conductor equilateral triangular, Eormation in the watts p>>r conductor foot (26) cables installed in separate ducts. same or in mpaiat'te ducts may be cal-culated from the following equation based Because of the large sheath losses vrhich Strictl s ag, these uations a ly on an approximate expression given by result from short~ited sheath opera- onl to three cables in equilateral con-Arnold'equation 7) for a system of tion with appreciable separation between guration but can be used to estimate three homogeneous, straight, parallel, metallic sheathed single conductor cables, osses in e cable ou s when latter are solid conductors of circular cross section this mode of operation is usually restricted so oriented as to a roximate a re lar 't arranged in equilateral formation and to triplex cable or three singie~nductor polygon. 'I cables contained in the same duct. The TEe eddyment efect for a 3-conduc-j 'I carrying balanced 3-phase current remote from all other conductors or conducting circulating current dfect in three metallic tor cable is given by ~ tj ArnoId.'RI material. The empirical transverse con- sheathed singlemnductor cables arranged ductance factor kp is introduced to make the expression applicable to stranded conductors. Experimental results sug-in equilateral configuration is given by Rs/Ree (27) (2s/D~)'2s/Dsw)'1 4 +1 1+(Rs/Xw)s (2y/D~)s gest the values of kp shown in Table IL Yep-F(xp)(-') X . When (R,/X~)t is large vrith respect to unity as usually is the case of shielded non-16 5.2R, f +1 ~ ~ ~ is) leaded cables, equation 27 reduces to 6.60 +0.312 (24) Yse ~ X~ RIRde approximately When (5.2R unity, ~ /f)i is hrge vrith respect to at 60 cyattt (25) Xss ~0.882/ IOg 2S/Ds~ Y e p microhms per foot (28) approximately at 60 cyd>>s (31A) When the second term in the brackets ~52.9 Iog 2S/Dses is small vrith res pect to the Grst term as it microhms p>>r foot at 60 cydes (28A) 3~1.155T+0.60Xthe V gauge depth for usually is, equation 24 may be written compact sectors where S is the axial spacing of adjacent << 1.155T+0.58 D, foi round conductors m)5(De/S)t Yep ~4F(xp)i I 1 cables. For a cradled configuration X~ iuy) jt'" '-( I F(x,)+om J may be approximated f'rom and T is the insulation thickness, indud- ~4( () / ~ r ') F(xp') (24h) X ~52,9 log 2.52S 0 S ing thickness of shieldiag tapes, iE any. 6 b,-S)) While equation 31(A) vrillsuKce for lead ~ 'li vrhere the function F(xp') is showa in microhins per foot at 60 cydes (29) sheath cables, equation 31 should be used 'I Fig. l. for aluminum sheaths. ~52.9 log 2.3 S/Dyes The average proximity efect for con- On 3~nductor shielded paper lead ductors in cradle configuration in the approximately (29A) at I cable it is customary to employ a 3- or 5-same duct or in separate ducts in a forma- Table IV provides a convenient means foi mil copper tape or bronze tape inter-tion approximating a regular polygon may determining X for cables in equilateral calated vrith a paper tape for shielding and configuration. binder purposes. The lineal d-c resist-I~ ~ ~ The eddy~eat efect for single- ance of a copper tape 5 mils by 0.75 inch Ta6l>> V. Speci8>> Intiuctiv>> (:apadlance of coaductor cables in equilateral configura- is about 2,200 microhms per foot of tape Insufations tion with open~cuited sheaths is at 20 ('he drc resistance per foot 3RI/Rde of cable will be equal to the lineal resist-Materia) ance of the tape multiplied by the lay correction factor as given by the expres-Polyethyleae.................2. Paper lasuiatlou (solid type)...3. Paper jose) atjoa (othee types) ..3, Rubber aod eubbee jjhe coos 3 ~ (1PCEh ea)ue) ~.2 1+- (30) sion under the squ3:e.root sign in equation

13. In practice the lay correction factor pounds.... ~ ...............5 (lPCEh va)ue) may vary froin 4 to 12 or more resulting Varnished eaesbrje.........,,.S (IPCEh value) when (5.2 R,/J)'s large in respect to 1/5 In shielding and binder asscinbly resist-756 .i cher, McGrctl: Tcn:pcrc! arc and Load CaPability oj Cable Systcn;s QCTOBER 195I

} s, he . 'I 'atts ances of approximatdy 10,000 or more and for 3~nductor belted cable T46fe Vl. Thermal Resistivity of Various microi<ms per foot of cable. Even on Ma(erich cos by'.019E'c, c) thc assumption that the assembly resist- Wg~ per ance is halved because of contact with ad- s Material if, C Cm/W'acc jacent conductors and the lead sheath coccdccctor foot at 60 cydes (37) computations made using equations 2? where Z is the phase to neutral voltage paper fosulacloo (solid Cy pe)...T00 GFCEA value) Varnished cambric.~.... ~ .. ~ ..000 (IPCEA value) ~ and 30 shocv that the resulting circulating in kilovolts, er is the speciGc inductive Paper iosulacloa (ocher cy pes) ..500-Mo and eddy current losses are a fraction ot capacitance of the insulation (Table V) T Rubbct aod rubbct.lihe.. ~ ~ ~...$ 00 (IPCEh value) JuCe aod Cessile prolectlve 1% on sizes of practical Interest. For this is its thickness and cos p is its power factor. COVeffaeo ~ ~ ~~ ~ ~~~~ ~ $ 00 reason it is customary to assume that the The geemetric facter Gs may be found Fiber duccoo ~ ~ ~ ~~ ~~ ~ ~ ~~ ~ ~ ~ ~ ~ 480 Polycchyleae............... ~ .4$ 0 losses in the shielding and binder tapes from Fig. 2 of reference 1. Traaid'ce dticc ~~~ ~ ~ ~~~~ ~ 200 of 3oconductor shielded paper lead cable Somasclcooooo 100 For compact sector conductors the di- ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ are negligibleo In cases of nonleaded rub- electric loss may be taken equal to that for ber power cables where lapped metallic a concentric round conductor having the tapes are frequently employed, tube same cross-sectional area and insulation effects may be present and may materiaUy thickness. THBRNAL RESISTANCE OF JACKETSr DUCT lower the resistance of the shielding assem- r'eo WALLs, ANU So)MsTIc CohTINcs bly and hence increase the losses to a Calculation of Thermal Resistance The equivalent thermal resistance of point where they are of practical signiG-CanCeo relatively thin cylindrical sections such as jackets and Gber duct waUs may'e THERMALRESISTANCE OF THB INSULATION An exact determination of the pipe loss effect Yp in the case of single~nductor For a single conductor cable, determined from the expression ,/tthermal ohcn-feet r cables instaHed in nonmagnetic conduit I Rf 0.012tif log Df/Dc thermal ohm-feet N or pipe is a rather involved procedure (3S) g ~0.0104)a'((D-I) . as indicated in reference 7. Equation 31 ) where sic is the thermal resistivity of the (4O) may be used to obtain a rough estimate insulation (Table VI) and Di is its of Yp for cables in cradled formation on with appropriate subscripts applied to the bottom of a nonmagnetic pipe, how-diameter. In multicoaductor cables 8, sI, and D in vrhich D represents the there is a multipath heat Gow between the ever by taking the average of the results outside diameter of the section and t its conductor and sheath. The foUowing ex-obtained for wide triangular spacing thickness. rc'is the number of conductors with saa(Dp'-Ds)/2 and for dose tri- pressionc represents an equivalent value contained with the section contributing which, when multiplied by the heat Gow angle spacing at the center of the pipe to the heat Gow through it. with 2~0.578'DThe mean diameter of from one conductor, will produce the actual tern peraturre devation ef the THERMAL REslsThNcE BETwEEN CABLE the pipe and its resistance per foot should conductor above the sheath. SIFhcE ANU SIROUNnnfc PIPEs be substituted for Dr and R, respectively, For magnetic pipes or conduit the Bf ~0.00522ifcGc thermal ohm-feel (39) CONUUTT,.OR DUcr WALL foUowing empirical reIationshipss may be Theoretical expressions for the thermal Values of the geometric factor Gs for 3-employed resistance between a cable surface and a conductor belted and shidded cables are 1.54s-0.115D p given in Fig. 2 and Table VIII respec- surrounding endosure are given in refer-Yp ~ Ac (3~nductor cable) tively of reference l. On large size sec- ence 10. ~ indicated in Appendix I, these have been simpliGed to the general (33) tor conductors with rdatively thin in-0.89$ -0.115D p sulation waUs (i.eo ratios of insulation form 4 thidmess to conductor diameter of the rcrdt , thermal ohm-feet dose triangular) (34) order of 0.2 or less); values of Gl for 3-conductor shielded cable as de(ermined 1+(B+C1'm)Ds'41) 0.34$ +0. 175D p Yp ~ (single-conductor, by back calculation, on the basis of an 244 assumed insulation resistivity, from lab- in which dt, B, and C are constants, cradled) ( 5) oratory heat-run temperature-rise data, the equivalent diameter of the D,'epresents 'These expressions apply to steel pipers have not always confifmed theoretical cable or group of cables andrs'the number and should be multiplied by 0.8 for iron values, and, in some cases, have yielded of conductors contained within Ds'. T~ conduit.s Gi values which approach those for a is the mean temperature of the interven-The expressions given for Y, and Ys nonshielded, nonbelted construction. ing medium. The constants d4, B, and C above should be multiplied by 1.7 to Gnd the corresponding in-pipe effects for mag- Table Vil. (:onsfcnts for Use in Equc(fons dt and 4I(A) netic pipe or conduit for both triangular and cradled conGgurations. Coadlcloa B c Aa CALCULATIONOF DIELECTRIC LOSS mecalliccondulC...................IT ~......3.0 .........0.0"0 .........3.2..... ~ ~ ~ oo 10 In dbcr duet la air...................ly .........2.1 .........0.010 .........$ .0....." "0 33 ~ The dielectric loss Ws for Saocdnetor 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 ~ shielded and a~in teaondnetor cable ts Ia craosfce duec lo coucrecc... ~ ~.....1T,.......2.0 .....,...0,020,........3.T....... ~ .0.2-given by the expres'sion ~ 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$ ~ ~ 0.00276Esrr cos c) fye'1.00 Xdlameser of <<able for oae cable lo ( Lr :D )/DQ"--. I.dsXdhmecer of eablc for cero cables 2.1$ Xdlamccct of cable for Chree cables -conductor foot at 60 cycles (36) 2.$ 0Xdlamcccr of cable for four cables OcTQBER 1957 Kci:cr, If(GraK Tern pcratffre arid Load Capcbili!y of Cable Systems foi given in Table VII have been determined. heating dfects of the other cables of the mum. N refers to the number oE cables or from the experimental data given in refer- system. In the case of cables in a con- pipes, and F is equal to unity when N~ l. cnces 10 anti Il. crete duct bank, it is desirable to further When the cable @stem is contained If representative values of T~~60 C recognizcadifferencebetweenthe thermal within a concrete enydope such as a tt'ri'hermal are assumed, equation 41 reduces to ,thermal obm-feet (41A) resistivity oE the concrete rrc and thc earthA. resistivity of the surrounding The thermal resistance between any 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 It should be noted that in the case of point in the earth surrounding a buried medium i that of concrete rF, through-ducts, A,e is calculated to the inside of the cable and ambient earth is given by the out and then correcting that. portion ly-duct wall and the thermal resistance of expression'c ing beyond the concrete envelope to the the duct wall should be added to obtain thermal resistivity of the earth i4. Thus EE>>c ~0.012ts, Iog tt'/8 thermal obm-Feet 1'g (4>) ~0.012tI,+'$( c 't 't y, Ta ERMhL RBsIsThNcE CoNDUITs~ oR DUcTs SUsPENDBD IN PRost ChBLEs> m which p~ th th earth rlr is e al ti ty o f the tance from the image (.3;[i. '-. (in')~))'~ of the cable to the point P, and d is the The thermal resistance R, b tweendistance Erom the cable center to 2'. ohm-feet'44A) cables,conduits,orductssuspendedinstill From this equation and the principles The geometric factor Gc, as dcvdoped air may be determined from the Following discussed in references 3, 12, and 13, the - in Appendix Il is a function of the depth expression which is developed in Ap- following expressions may be devdoped, to the center of the concrete cndosure pendix L a licable to directly buried cables .and to~i;type'-cab es. Q and its perimeter P, and may be found gCc conveniently from Fig. 2 in terms of the t<<+I.Gal+0.OIGTT)l 15.6n','Kaz'/D,') 8>>'.~0.012Pgtt'X ratio 4/2'nd the ratio of the longest to short dimension'of the endosure. thertnal ohm.feet (42) log +(LF) log F For buried cable systems T, shbuld be In this equation AT represents the. differ- taken as the ambient temperature at the ence between the cable surface tempera- thcrtnal ohm.feet (44) depth of the hottest cable. As indicated ture T, and ambient air temperature T, in degrees centigrade, T~ the. average of in which D< is th 'ter at which the m reference 12, the expressions used throughout this paper for the thermal temperatures and c the coe6icient of portion oE the therm ctrcuit com-mene'.and tt>> Is the num 'hese of con uc- resistance and temperature rise of buried emissivity of the cable surface. Assum- 'he cable systems are based on the hypothe-tors contained within D,. Gctitious ing representative. values of T,~60 and sis suggested by Keaaelly applied in T>>~30 C, and a range in D,'f from 2 diameter D>> at which the effect of loss factor commences is a function of the accordance with the principle. of super-to 10 inches, equation 42 may be simpliGed position. According to this hypothesis, to diffusivityof themedium a and the length of the loss cyde.c the isothermal-heat Qow Gdd and tem-9.5n', perature rise at any point in the soil sur-thermal obtn<<feet D, ~1.02> ct(length of cyde in hours) rounding a buried cable can be represented (42A) inches (45) by the steady-state solution for the heat Qow between two paraM cylinders The value of c may be taken as ual The empirical development o! this equa- (constituting a heat source and sink) to 0.95 or i c nduits or ucts, and tion is discussed in Appendix IIL For a located in a vertical plane in an inGnite painted or braided surfaces, an 0.2 daily loss cyde and a representative value medium of uniform temperature and to 0.5 for lead and aluminum sheaths, of a~2.75 square inches per hour for thermal resistivity with an axial separa-depending upon whether the, surface is earth, D>> is equal to 8.3 inches. It should tion between cylinders of twice the actual bright or corroded. It is interesting to be noted that the value of D, obtained depth of burial and with source and sink note that equation 42(A) checks thc Erom equation 45 is applicable for pipe respectively generating and absorbing IPCEA method of determining R, very diameters exceeding D in which case the heat at identical rates, thereby resulting dosdy with c~0.41 for diameters up to Grst term of equatioa 44 is negative. in the temperature of thc horizontal mid-3.5 inches. In the IPCEA method 8, ~ The factor F accounts for the mutual plane between cylinders (Le., correspond-0.00411 n'3/D~'here 9~050+314 D~'or heating effect of the other cables of the ing to the surface of the earth) remaining. cable system, and consists of the product'f by symmetry, undisturbed. D,'-1.75 lacbes and B 1,200 for Imrger the ratios of the distance from the, The principle of superposition, as values of reference cable to the image of each applied to the case at hand, can be stated Dt'I of the other cables to the distance to that in thmnal terms as follows: IE the ther-FEOTrvE. TaEBMhL RESIsThNcE cable, Thus, mal network has more than one source of BETWEEN ChBLES, DUCTS, OR PII'ESy AD AhfBIENT EhRTH ( t c tt.~t>> ) ~ F~ . . ~ (N-I tertas) temperatu:e rise, the heat that Qows at any point, or the temperature drop be-As previously indicated, an efFective (46) tween any two points, is the sum of the thermal resistance 8<'ay be employed to heat Qows and temperature drops at represent the earth portion of the thermal It will be noted that the value of F will . these points which would exist if each ci:cuit in the case of buried cable systems. va~ depending upon which cable is source of temperature rise were conside:ed This effective thermal resistattce includes sdected as the reference, and the maxi- separatdy. In the case at hand, the the effect oE loss factor ana, in the case of mum conductor temperature wi11 occur sources of beat Qow and temperature rise a m 'lticable installation, also the mutual in the cable for which 4LF/D>> is maxi- to be supcrimposed are, namdy, the heat 7OS rober, DfcGratls Temperatttre and Loatf Capability of Cable Syste":s OcTooER 1957 from the cable, the outward Qovr of heat Tc'-I'~1+ YcXN~'-R<<') -(2's+ I from thc core of. the earth, and thc in- kiloagnpeges (47) ward h(at Qovr solar radiation, and, when Z (1+.Yg)8<<'n present, the heat Qow from interfering which 8<<g's thc effectiv transient sources. By employing as the ambient thermal resistance of the cable system for vrhere 8<< is the thermal resistance be-temperature in the calculations thc tem- the stated period of time. Procedures tween the steam pipe and ambient earth. perature at the depth of burial of the for calcuhting E,g'or times up to several hottest cable, the combined heat Qow hours are given in reference 14, and for A RIAL CABLEs ~ from earth core and solar radiation sources ~ Ipper times in references 15-17. In the case 'of aerial cables it may be is superimposed upon that produced at C THE EFIECT.op ExTIumoUs HEAT desirable to consider both the cffects of the surface of the hottest cable by the SOUECEs . solar radiation which increases the tem-heat Qow from that cable and interfering perature rise and the effect of thc vrind sources vrhich are calculated separately In the case of multicable installations which decreases it.gg Under maximum with all other heat Qows absent. The the assumption has been made that all sunlight conditions, a lead-sheathed cable combinedheat Qovr from earth core and cables are of the same size and are sim-vrill absorb about 4.3 watts per foot per solar sources results in an earth tempera- ilarly loade<<L When this is not,the case inch of profiIe" which must be returned ture which decreases with depth in summer; the temperature risc or load capability to the atmosphere through thc thermal increases.vrith depth in winter; remains of one particular equal cable group may be resistance 8,/>>r. This effect is con-about constant at any given depth on the determined by treating the heating effect veniently treated as an interference average over a year; approximates con- of other cable groups separately, intro- temperature rise according to the rela-stancy at all depths at midseason, and . ducing an interference temperature rise tionship in turn results in Qovr of heat from cable dTgg in equations 1 and 9. Thus sources to earth's surfac, directly to suz- dT<<((<< ~4.3Dg'/I,/>>r face in midseason and winter and in- T,-T~~dT<+dTc+dT<<~g degrees centigrade (47A) degrees centigrade (1A) directly to surface in summer. For blacI: surfaces this value should bc Factors vrhich tend to invalidate the I~ T~-(T(<<+d Ta+ d Tg>> g) increased about, 75%. combined Kennelly-superposition princi- gg(1+ As indicated in Appendix II, the follow-ple method are departure of the tempera- Yc)~ca'iloamperes (9A) ing expression for l(I, may be used where ture of the surface of earth from a true in which dTg,g represents the sum of a V>> is the'velocity of thc vrind in miles per isothermal (as evidenced by melting of number of interference effects, for each hour snovr in vrinter directly over a buried steam main) and nonuniformity of ofvrhich . 3.5>>' thermal resistivity (due to such phe- d2 <<>>g (IVa/LF)+IVclksg '(~V/D,'+0.62 ) nognena as radial and vertical migration degrees centigrade (48) thermal ohm-feet (42B) of moisture). The extent to which the Ag<<<~0.012<<r,>>'Iog Fg,g thermal ohm-Eeet UsE CF Low-R'EsrsTIvITY Bane.L Kennelly-superposition principle method (49) is invalidated, however, is not of practical In cases where thc thermal resistivity importance provided that an over-all or ((Egg'X<<E<<g'X<<E<<<<')" (EN<<'~ ) of the earth is excessively high, the value effective thermal resistivity is employedin (<<Eg<<X(E<<<<X(E<<g) "<<EN<< of 8,r may be reduced by bacldiiling the the Kennelly equation. (50) trench with soil or sand having a lower where the parameters apply to each sys- value of thermal resistivity. Equation Special Conditions tem vrhich may be considered as a unit. 44(A) may be used for this case if r r, the For cables in duct thermal resistivity of the bacldill is sub-Although the majority oE cable tem- stituted for grg, and Q applies to the perature calculations may be made by A.g 0.012>>'(r<<log F<<g+N(ggg-rr<<%l zone having the bacldili in place of thc. the foregoing procedure, conditions fre-. thegnud ohm-Eeet (49A) zone occupied by the concrete. quently arise vrhich require somewhat Because of the mutual heating betvreen specialized treatment. Some of these cable groups, the temperature rise of the SINOLE-CCNDUcroa C((1BLES IN DUcT are covered herein. interferin groups should be recheci:ed. wITH SCLIDLY BCNDED SHEhTHS If all the cable groups arc to be given The relatively large and unequal sheath EMERCENCY RATINCS mutually compatible ratings, it is neces- losses in the three phases vrhich may result Under emergency conditions it is fre- sary to evaluate IV< for each group by from this type of operation may be deter-quently necessary to exceed the stated successive approximations, or by setting mined from Table VI oE reference 1. It normal temperature limitof the conductor up a system of simultaneous equations, vrill be noted that T, and to set an emergency tempegature substituting for W, its value by equation limit T,'. If the duration of the emer- 15 and solving for I. Yrgg ~ 'gcg ~ gency is Iong enough for steady-state con- In case dT<<ng or a component of it is g ditions to obtain, ~then the emergency produced by an adjacent steam main, thc ~ IS rating I'ay be found by equation 9 temperature of the steam Trather than the heat Qow from it is usually given. substituting T<'or T< and correcting ~, Thus vrhere expressgons for I>gg/P etc., appear or the increased conductor temperature. in the table. The resulting unequal values If the duration of thc emergency is less dT<<>>g of Y, ia the three phases vrillyield unequal than that required for steady. state con- values of (Eand equation 5 becomes for ditions to obtain, the emergency rating ~gag phase no. 1, the instance given as equa-of the line may be determined from degrees centigrade (Sl ) 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+ Table VIII. Coustanls for Use in Eque6on 53 . 'fq<<(f F)kpe] thermal ohm-feet (SA) Arerase where qra Is the average of qrsI qrs> and qrs. AT ARMORED CABl.EB Cable lu suetatuc couduls,...............0.07.. ~ .~.......0. 121...........0.0017..:. ~ .. ~ ....20 Cable lu sber duce lu air..................0.07............0.03d...........0.0000............% In multiconductor armored cables a Cable lu dberdu<<t lu coucrete.. ~ ..~.......0.07...,......0.043.... ~ ~.....0.0014..... ~ ~ . ~ .20 loss occurs in the armor which may be 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 considered as an alternate to the conduit Gas.elled pipe type cable at 200 pal.........0.07.,....., ..0.121...........0.0017............10 or pipe loss. If the armor is nonmag-netic, the component of armor loss Ya to be used instead of Yp in equations 14 based upon all of the data avaihbie and and a range of 150-350 for De'T~ equation and 19 may be caIculated by the equa- including the effect of the temperature of 54 reduces to equation 41 <<ith the values tions for sheath loss substituting the thc intervening medium. of A, B, and C given in Table VIZ . resistance and mean diameter of the The theoretical expression for the case In thc case of cables or yipes suspended armor for those of the sheath. In cal- where the intervening medium h dr or gas in still air, the heat loss by ndhtion may as presented in reference 10 snay be genenI. be dctcrauncd by the Stchn-Bolznsann culating the armor resistance, account Ised in thc following form: forsnuh should be taken of the spiralling"effect for which equation 13 suitably modified rs'W(radhtion) If the armor Is mag- (53) ~0,139Ds eKTa+273)e (Ta+273)ej10>> may be used. rs',' netic, one would expect an mcreasc in +b+cT~ watts ycr foot (55) the factors Y, and Y, in equation 14 since this occurs in the case of magnetic where e is the coeKcicnt of emisslvity of the cable or yipe surfaces Over the conduit. Unfortunately, no simple: E,cathe effective thcrsnd reshtsuce be- limited temperature nssge in which wc are is available for calculating these pro-'edure, tween cable and enclosure in thclnul Interested, equation 55 snsy be shnplificd obm-Eeet to" effects. A rough estimate of the induc- D,'~ the uble diameter or equivaIcnt tive effects may be made by using the pro- dhsneter of three cables us Inches rs'W (radiation) ~0.102Ds'4Te X cedure given above for magnetic conduit. 4T~the tempcnture dIEfcrenthI in degrees (1+0.01671 ~) watts pcr foot (SSA) A simple method of approximating the centigrade losses in single conductor cables vrith steel- P~thc prcssure In atmospheres Over the same tempenture nnge the T~~mesn tesnperature of the medium in heat loss by convection from horixoatal wirc armor at spacings ordinarily,em- degrees centigrade cables or pipes is given with sufficient ployed in submarine installations is to as- rs'~nusnber of conductors Involved acciuacy by the expression sume that thc combined sheath and armor The constants a, b, and c in thh equation rs'W(convection) ~0854 De'dT(dT/De') +e current is equal to'the conductor current.s have been established empiYicdly as follows: watts yer foot (56) The effective a.c resistance of the armor'ay Conslderusg b+cTe as a constant for the be tdcen as 30 to 60% greater than moment, the analysis given in reference m which the numcrica1 constant 0.064 its d-c resistance corrected for lay as in- 10 results in a value of a~0.07. With a has been selected for the best Eit with the dicated above. If more accurate calcula- thus established, the data given ui reference carefully deternsined test results reported tions are desired references 19 and 20 10 for cable in pipe, 2nd in reference 11 by'cilaunss on 12, 3.5 aud IQB-Inch for cable in aber and txauslte ducts were dhmctcr bhck pipes (e~0.95). Inci-willbe found usehl. andyzcd in sinuhr nunner to give the dentally, this value also represents the values of b and c which are shown in Table best Eit with the test data on 1~5 inch EPPEcT oP F0RcED CooUNG VIIL diameter bhck pipes reported by Rosch." In order to avoid a reltentivc calcuhtloa For vertical cables or pipes the value oE The temperature risc of cables in pipes procedure, it is desirable to assume a value this numeriesI constant may be hicrcased or tunnels may be reduced by forcing air Ear 41 since its actual value will depend by 22%" axially along the system. SimiIarly, in upon ffre and the heat flow. Fortunately, Combiniag equations 55(A) 2nd 56 we as 4T occurs to the 1/4 power in equation obtain the relationship the case of oil-Glied pipe cable, oil may 53, the use of an average value as Iadicated be circulated through the pipe. Under in Table VIII will not introduce a serious 4T these conditions, the temperature rise is error, rs'W(total) not uniform dong the cable and increases By further restrictissg the range of D,'o I-I Inches ~, in the dir'ection of EIow of the cooling Eor cable in duct or coaduic and to 3"5 inches for pipe-type 15,8rs'r'K medium. The solution of this problem is AT/Dr') a+1.6e(I+0.0167') I cables, equation 53 is reduced to equation discussed in reference 21. 41. then'hm.feet (42) rs'A thcrmd ohm-Eeet If the cable h subjected to wind having Are a velocity of V>> miles pcr hour, the follow-Appendix I ing cxprcssiors derived from the work of (41) Schurig and Prick" should be substituted Development of Equations 41, 42, in which the values of the constants A, for the convectiors comyoricnt. and Table VIX B, arid C appear ln Table VII. Ia the case of oil.6Iled pipe cable, the rs'IV (coavectiors) ~0.286Dr'4Tv Theoretical 2nd semicmpiricd expressions Vu/De'atts for the thermal rcslstarice between cables analysis givers ia referesicc 10 gives the per foot (56A) surd als eaclosirsg pipe or duct wail are following expression Combining equations 55(A) arid 56(A) given in refercricc 10. Further data on the with T~~45 C thermal resistance between cables arid Sber and tnrssitc ducts are given in ref- rs'.60+0.025(Dr" T~'dT) 4T erericc 11. For purposes of cable cating, ohm-Eeet ~'hermal (54) 3.5rs's'IV(mlsl) it is desirable to develop staudardhcd D;(QV/D;+0.62e) expressions for these thermal resistances Assumiug aa avenge value of 4T~7 C thermal ehm-Eeet (42B) 760 iVeLer, yrlcGrc!r' Terr perafare and Load Capabilily o/ Cable Svs.'eras Ar-,nnm. 1057 g,g Appendix'l Table IX. Compadsoa of Values of go (+F) Da<<8.3 Inches. As indicated in the Chird for Sinusoidal Loss Cydes at 30$ paper of reference 3. however, theorcQcally Loss Factor D/c shouM vary as the square root of the Determination of the Geometric product of the dilfusivity and thc thne Factor Gi for Duct Eanld length of the loading cyde. Hence as thc Desccfpdou, li fddI diifusivity was taken as 2.?5 square inches Considering the surface of the duct bank to act as an isothermal cirde of Srst<<u laches Ifehec ShsakllaV/lseugea pel hour ia the above, radius ra, the thermal resistance between the duct bank and the earth's surface wUI IIloo ~~~~~~ 4 5 pipe.... 53/53... dl/d2...d3/dd Da << Ig02X be a logarithmh function of ri and Li the ~ ee 5 IIIoooooo 8 d pipe.....dd/dd... 50/57....53/50 5 pl pe..... 55/5... SO/58.. ~ .54/53 V acXlength of cyde in hours mches distance of the center'f the bank bdow Iveoooo ~ 10 d plpe. o ~ ..58/58... 5 l/50...55/53 (45) the surface. Using the long form of the Vo ~ ooo ~ ~ 0 d cable. \ ~ ~ ~ 80/80 Table IX presents a comparison of the ~e ~ Kennelly FonnuhLs we may deflne the VIe ~ ~~~ 1 5 ~le'....77j75. ~ '.77/75....77/77 geometric factor Gi as VII eeo ~ I ~ 0 cableo ~o oT1/71 values of per cent attainmcnt factor for VIII.... 2.0 cableoooo ~~~~~~~ 53/52 sinusoidal loss cydes at 30% loss factor as IXooo oo 3 0 cablcoo ~ . ~ ~ ~ ~ ~ ~ ~ o75/74 calculated by equations 45, 66, 62(A), and 63 Xo ~ ooo ~ 3 4 cable............77/Td log Li+O'Li'-ri'i<< Xa ~ roe 3 4 cable....83/80...83/81 and as they appear in Table II of the Grst ri XI ~ oooo 3 T cable....Td/74...74/173 paper of reference 3. XII eoo 4 2 cable....TO/55. ~ .To/5T ~og Igr/ro+O/(gr/ro)'-gl (gg> XIII 4.d cable.. ~ . d0/54. ~ . 55/54 ..51/53 In order to evaluate rb in"'terms of 'the a Dhduglelcy<<4.7 scuse>> lucha pcr hour. Appendix" IY.'Cafculaations for dimensions of a rectangular duct bank, let the snuiier dimension of the bank be x Representative Ca6le Systems and the larger dimension bP'y. The radius portion of the thermal circuit is reduced+ ~ of a cizde inscribed within the duct bank by a factor equal to the loss factor of the 15-Kv 350-NCN 3<<Conductor touching the sides is cydic Ioado The point at which this . Shielded Compact Sector Paper and reduction commences may be conveniently Lead Cable Suspended in Air fs <<x/2 (58) expressed in terms of a Gctitious diameter and the radius of a hrger cirde embracing Dao Thus D, <<0.618 (equivalent round); V<<gauge the four corners is depth <<0.539 inch Aca'<<Dec+(LF)/tcs thcrnul ohm-feet (42) / Dc <<2.129; T<<0.175 inch; l <<0.120 inch rr O/x'+g'r 2 For greater accuracy, it is desuable to establish the value of Dc empiricaily rather than to assume that Ds is equal to the cg ggcgg, 0250(234.5+75) ( 12.9 /234.5+SIN Lct us assume thaC the cirde of radius ri hich the earth i~con o lies between these circles and the nugnitude of ra Is such Chat it divides the thernul th~~1 cQcult co~I9SSSS3 <<37.6 microhms per foot (Eq. 10A) Equation 62 may be written in the form 2.009 inches (Eq. 12) resistance between rl and rs in direct Deca 2.129-0.120 8 '-8 +8 +(LFXd -8) rehtion to the portions of the heat Geld 37.9 between rs and rs occupied and unoccupied thernul ohmofeet (62A) C 'ggr roiororrroo by'he duct bank. Thus 2.009(0.120) In terms of the attainment factor (cf F), one pcr foot at 50 C (Eq. 11A) log- xy-~ n s r(log-) f rsN or may write kr <<0.6 (equivalent round) ~ ~**-.)( .) (AF)~ca (ci FXNcc+/t¹) kg <<1.0; (Table II) tog ~ 'xy/ rsN thernul ohmofect (63) lac/>c <<37.6g O.OM ri grss-r,s)((log -) Ycc r<) Equating equations 62(A) and 63 obtains (Eq. 21 and Fig. 1) from 'which Che rehtionship $ <<0.616+2(0.175+0.008) <<0.982 inches log fi<<( 2A~ <<) y) log (I+ ( xs) +log-2 Bcc<<(1-x)8¹-x/t<< thernul ohm.feet where (64) J4 Jkp <<62.6; F(xp') <<0.003 (Fig. 1) (40) Ycp <<4 0 003 <<0.002 It is desirable to derive ri hl terms of the x<< I-(cfF) (45) (Eq. 24A, and aote to Table II) perimeter P of the duct bank. Thus 1-(LF) P <<2(x+y) <<4- (1+y/x) . Since 1+ Yc <<1+0.008+0.002 <<1.010 2 8¹ <<0.012/s'p log Dc/Dc ~ s <<1.155(0. 175+0.OOS)+0.60(0.539) and therefore thermal ohm-feet (44) <<0.534 inch (Eq. 32) log-2 log P 4(1+y/x) (41) 83 log Dc/Dc << ,KI-x)/tca-x/eccl >>'/I (47) Yc<<Y¹<< 396 2(0.534)1 s 15?(3T.6) 2.009 J ( <<0.019 The curves of Fig. 2 have been developed Thc flrst paper of reference 3 presents (Eq. 31A) from equations 57, 60, and 81 for several the results of a study m which a number R/Rcc <<1.010+0.019 <<L029 (Eq. 14) values of the ratio y/x. 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. It should be 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 qg<<qc<<I+ 0.019 '<<1.019 1.010 (Eqs. 18-19) in all cases the sinusoidal loss cycle of the c,<<3.7(Table V); E<<15/Q<<S.T; same loss factor adequately expressed the maximum temperature rise which was cos y <<0.022 Appendix ill obtained with any of the actual loss cycles 0.00276 (8.7)'f3.7(0.022)i considered. An analysis by equations 65 and 6T of 2(Q. 175)+O.BSC Empirical Evaluation of D, the calcuhted values of attaiameot factors 0.681 In order to evaluate the effect of a cyclic for sinusoidal loss cycles given in Table II <<0.094 watt per coaductor foot load upon the maximum temperature rise and tile corresPoading cable systcra Pscamo (Eq. 36 and text) of a cable system simply, it is customary to etcrs given in Table I of the Grst papa'f assume chat the heat Gow in the Goal reference 3 yields a most probable value of (Vote: Ia computiag dielectric loss on %I,M.o~/l. g ~, ~ 4 r 4 / -a g/g.'r. C / :g. gir'a" <<t

• <<a 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 /'r ) images (Table VIII of reference 1) ~r 0.00522(700(0.45) } 1.64 thermal ohm-feet (Eq. 39) ~ s n'3; ~ ~0.41 (assumed) J 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 dg ~ 96/" thermal ohm-feet (Eq. 8) c 87.5" dt ~ dT<~0;094(0.82+7.18) ~0.75 C T, ~40 C (assumed) (Eq. 6) dg c96'e cc. 3e. 78 5. I 81-(40+0.8) cla" 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)( ) /5.59 i (3) 17.1 C L c4X5 I ~ 43.5 (Eq. 47A) b Te <<30 C (assumed) 5 I.O )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 will not always be true, and the procedure outlined above is~ preferable.'4 rcc 69-Kv Ir500-MEN Single-" 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 Fig. 3. Assumed duct bonk conR9uratlon for typical calculations on 69-lcv $ ,500.MCM shown in Fig. 3. De~0.600; De~ 1.543l Dr~2.113; tj 4. if oil@lied cable (Appendix lV) T O.N; D, 2.373; r 0.130 inches Te~75 Cl Rec~ 12.9 1.50 ~8.60 p, ci: pre/kc ~ ll 9r'cc ~0.075 (Eq. 21 and Fig. 1) 1+- '.006:"(Eq. 30A) microhms per foot (Eq. 10A) $ ~9.0 (Fig. 3) i Rec/4~ Rec/Rcr ~ ~ 1 082+0 006 1 088 (Eq 14) ~0.075 (Fig. 1) 10.75'(x~') 0.006 Dna ~2.373-0.)30~2.243 inches (Eq. 12) qc aqc w1+. 1.082 ~ ],006 (Eqs. 18-19) 37.9 ~ 130 microhms Ycrr 4((9.0)) 0075 . 0007 (Eq 24A) I ~ Rc (2 243)(0 30) cr ~ (Table V); 8 ~69.'y 3 ~40; 1+ Yc ~ 1+0.075+0.007 < li082 cos 4 ~0.005 per foot at 50 C (Eq. llA) 0.00276(40) r(3.5.'(0.005) Assuming the. sheaths to be openwircuited, ~0 1.543 -O.BOO(1.543+1.2003 1.543+0.600(1.543+0.600J c Yea log2.113 1.543 0.72; k~ O.S (Eq. 23 and Table il) 0.57 watt per cond ctor foot (Eq. 30) 7R'? rVchrr, N'd7rrrflr Trrrr 6crahurc and Load Caoabrvitv of Cable Svsfrrrrs QCTOBBR 1957 I 2 iv'h 2;( <<5.0 (Table VI) Pg 88<<0.012 550 log ~ 2.113 ~ aTc 0.57(0.45+1.75+0.24+4.63) Wc j > 45r (lr X8 BQX1.082) <<9 31 Ir ~ 4.0 C (Eq.~ 6) Ycp /1.632% <<4(( 2.76) 8 ) (0 035X1 7) 0 083 (Eq. 24A and text) <<0.90 thermal ohm-foot 6((Eq. 38) r watts per conductor foot (Eq. 1S) 1+ Yc <<1+0 088+0.083 <<1.1?1 4Trf6g <<(9.31Irr K I.QOBX0.80)+0.5?l)3.81 2.37+087 thermal ohm-feet (Eq. 41A) <<2>17'+28.5Irs degrees centigrade in circuit no. 2 (Eq. 48$ ' 52.9 leg (2.3X2.76) 2.66 irc<<480 (Table VI); 1<<0.25; Simihr calculations for the <<20.0 microhms per foot (Eq. 29A) second circuit cp ., Dc<<5.0+0.5<<5.50 for aber duct yield the foUowing values. Yg<<Ygc<<<<0011 (20.0) 2(1.7) 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 (Eq. 2?A and text) 120(asumed); jfc 85 (Table VI)'... ~  :.(9.31)(6.$ 5) 0.715-0.859I22 (Eq. 9A) Y (0 34X2.76)+(0.1?SX8.13) 6.35 ",* (Eq. 35) Rcc/Rcc <<1 171+0.011+0272 L554 (Eq. 14) -(-.)('-:)('=".)('-)("=) ';, ':-"'"..";".";;,",.... <<42,200 (Fig. 3 and Eq. 46) Solving simultaneously Ir <<0.714; Ir << ~ 0.011 1.171 '.171 I~ 0.011+0.372 (Eqs. 18-19) 1>(P 2(18+27) 0.483; ' hs: 0.487 kiloampere. 18 cr <<3.5 (Table V); .E <<138/Q3 <<80; 0> 0 87 (Ptg 2) 138-Kv 2000-2,102( 2(fgh-Pressure 5z~ cos p <<0.005 Oil-Filled Pipe-Type Cable 8.625-80% loss factor) (0.012)(85)(l)X Inch&utside-Diameter Pipe 'c'(at 0.00276(80)2(3.5X0.005) log 8.3 .+0.80log[~42~)J)+ I 4(43.5) The cable shielding will consist of an log2.642 1.632 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- <<1.48 watts per conductor foot (Eq. 3B) <<6.79 thermal ohm-feet (Eq. 44A,) shaped brass skid <<Ire LS-inch ly. The Ec'at unity loss th factor) <<8.44 hm.feet p (Eq. 44A) ~ cables will lie in cradled conBguration. Dc<<1.632; Dr<<2.642> T<<0.505; ') A<<550 (Table VI); 8r 0.012X 2.642( (550 log '.1.632) <<128 thermal 16 Egg. l2 (1.7k+0.24+6.79) R'gtg'0.90+1.00$ ohm-feet (Eq. 38) 72 ther<<) ehtu feet (Eu. 8) <. 8 (189)(234 5+70 ) 7 70 >>2<<3; Dc'.15(2.66) 5.72; 4'.57( 8M ~ 3(2.1) +L?4+0.24+8.44 625 microhms per foot (Eq. 10A) Ru 77 there.tet 5.72+2.45 <<6.2 C (Eq. B) ForshfeIdfngtape448<<7/8(0.003)<<0.00263l ohm-foot (Eq. 41A) Tc 25 C assumed), f<<I.Q; p<<23.8; 2 <<564 (Table 1) ptr<<100 (Table VI); t<<O.SO; 'er 75-(25+62) D, <<8.83+1.0 9.63 for 1/2-inch 23.8 ( (2.68 <<0.696 kiioampere (Eq. 9) 4(0.00263)$ 564+50) ( 1 j )',60(1.082)(9.72) 0.0104(100X3XQ.SO) wall of asphalt mastic To illustrate the case where the cable ) <<62,900 mlcrohms 9.63-0.50 'or 564+20'ircuits are not Identical, consider the foot at 50 C (Eq. 13) <<0.17 thermal ohm.foot (Eq. 40) second circuit to have ?50-MC'hf con-ductors. For the erst circuit . skid wiregg' r(Q 1)2 Q157 Assume pc<<80, I <<36 inches, (LF) <<0.85; Q II<<1, F 1 P <<3; (I F) <<0.80 (assumed); (8 F << <<92.4 (9 +0.80 log A(43.5) 8.3 9 (Eq. 46) r I R, 38E. l<<1.5; p<<38; r<<912 (Table I) 1+ (2.6Br)2 X <<11,100 microhms 88'(at 85% log loss factor) +0.85 log <<2.85 thermal ohm.feet 0.012(80)(3) (1) X (Eq. 44) t log S.S ( 8.3 92.4) J+ . )J per foot at 50 C (Eq. 13) 80'at unity loss factor) <<3.38 thermal obm.feet (Eq. 44) 0.012(120-8SX1X3)(0.80X0.87) <<3.74 thermal ohm-feet (Eq. 44A) l (62.9)(II.I)1 Pgcg<<1.38+1.M9(0.7?)+ 5 R, (net) <<L- L(62.9X11.1) JI>000 J ~ 1.327(0.17+2.85) <<6.1? thermal ohrn-feet (Eq. 8) ( <<9,435 microhms per foot at 50 C ~ 4Tc <<1.48(0.69+0.5 5 -,'0.17+3.3S) <<7.4 C 0.012(1) X k8<<0.435; kp <<0.35 (Table II) (Eq. B) (85 log 456-;3(120-85)(0.87)) Rcg/kg <<14.6l Ycg <<0.052(L7) <<0.088 Tc <<25 C (assumed); <<3.81 thermal ohrn feet. r (Eq, 49) (Eq. 21, Fig. I, and text) ls 70-(25'7.4) l4'.90+1.006(1."4+0.24+3.74) S 2.66+0.10 2. 6; Rc /k 17.2; 4 3 (6.35X1.171X6.17) <<6.65 therrrral ohm.feet (Eq. S) F(KP') <<0.035 (Fig. 1) <<0.905 ki!osmpere (Eq. 9) References >>mt Ssoxaxtaa Coxaactoks, AD1E Commiuee 17. h Stxrurtso M*tasxattcaL Paocsaaka ReyerL lbQ roL Tl> pt. ~ III,Ja>L 1952, pp. 30 roa Datsaxtxtxo tas Taaxatkxt Tsxrskataas 414. Rtssor Casut Svstsxs.J.H, Irchcr IbQ, vol.

1. Catcocattox or tna Euactstcu. Pooka,sxs AN Rsstataxcs or Coxrsuttoxar. Staaxo 72, pt. IILhug. 10$ 3, pp. 712-1S.

ar UNoskokoaNO Casass, D. )tL Shameae. Tbc Pa>>as Caucus nt Noxxstaaue Duct axo ue ~ IiL Tss Hsattxo or C>tacks Exroaso to tas Electric Iosraol, Bast Pittsburgh. Pa May Iaou Coxomt, R. W. Burteu> ItL Morda Ibid., Sax tx Raas, E>> B. Wedmere. leuc>>oL Iaatitu Nor. 1032. voL 74, pt. 111, Occ. 1055, yy. ION 23. ttoa at Electrical Eagloccra, vcL TS, 1034, pp. Loca Pactoa axo EttotvaLsxt Hoaas 10. Tas Tasaxu. Rsetstaxcs Batvrssx Cosc,ss 737&L tricot W'orld, Ncw York, pp. 50-60. ¹ Coxraaso, P. H. Buiier, C. A. Woodrau; Ztec. Y., vai. 02, ao. 2, 1028 axo a Saakoauonto Piro oa Duct Waar F> H>> Boiler, J. H. Zcher. IbQ., vaL dy, yt. I. 1050, pp. 34~9.

10. Loaaas La~russo tx hat>ossa Stxaas~xaactok>

h>>C Cast.ss, O. R. Schurig> H P. KuehuL F. H. Buuer. AIEE Trc>>roctk>ur> rai.

3. Stxroctatt ox Tsitrskatasa Rms or Casters, 11. Haav Ta*xsrsa Stout ox Po>>sa Casus 48, hpr. 1020, yp 417~.

vol. 72, yt. III, Juae 1053, pp. ~L AIRE Caauaittee Report. AIEE Tre>aroctio>tl>

4. h-C Rsarstaxcs or Ssoxaxraa Caucus nt Ducts axo Deer heaaxsc,tss, Paul Cceebicr, Ouy F. Baraett. Ibt>L, voL 69, pt. L 1050, pp. SST 57.

2tL CostaisotroN to tas Svaov or Loaass axo or Ssar4>ooottox or StuoasCoxuoctoa Ak xoaso Caaass, I Boaoae. Zt>ttrol>cairo, Miiaa, Srsst. Prrs. L Meycrhotr, O. S. Eager, Jr. Ibid., 12. Trts Tsxrseataas Rtss or Baatso Casuas Italy, 1931, y, 2. raL 68, pt. II, 1049, pp. 815-34. axttPtrss. J. K, Ireher, lbi>L, voL 68, pt. I. 1940, 2L hattnctaa, Coouxo or Poxsa Cast.s, F. H.

d. Pkorttxttv Enact ix Souo axo Hotaoer Romeo Coxooctoas, A, H. M. Araeid>> Ieur>tot, Iaaututioa ol Eicctticai Eagiacecs, Laodoa, yp. 9-21.

13. Tas Taurus*toss Ries or Case,ss nt a Doer Baxr, J. H. Neher>> Ibidpp. ~0.

19S2, pp. ~l. Bauer. ALEE Troarcctlear, vai. Tl, yt. 111, hug. , 22 Soar acs Hs*T TaaNSxiaaIQK>> R>> K, Henaiaa Eagiaad, vol. 88, pt. Il, Aug. 1941, pp. 340 59. Eaov&aaksxv Loaass nc Mattress Parka. INaotatso La*~russo Cast,aa, haxoaso o, -.14. Ott Faow axo Pasaaaas Caacouattoxs roa S~Ntatxso Ott> Fttuso Casas Svstaxs>> B. H. Bauer. J. H. Ifeher> P. O. Weutstoa>> lb>>d.> Bagiaecrv. Neer York, pp. 287~ ¹ Tio>t t>xticer, htacricaa Society at hf cchaoicci YroL 51, pt I, 1020. ar>o Uxakxokso, Cakavtxo Baaaxcsa 3-Prtaas vaL 75, yt. III, hpr. 1055, pp. ISHl4 23. Tss Caakaxt-CakkvLvo Caracttv or Ros Caaksxv, A. H. 5>L Arnot* Ibid., yt. I. Peb. ssa.INsuaatso Coxoacroaa. S. J. Roach. AIEE 1$ . Tasaxax. Tkaxarsuts oN Boktso Castaa, 1941, pp. 52-63. T. Ptrs Loecss M Norocaoxsttc Ptrs, F. P Bailer. IS@., vaL TO, yt. I, 10SI, pp. 4~. Trout>xrioor, raL ST, hyr. 1038, pp. 15~7. MeyerhotL AIEE Trouracliosr, vaL T2, yt. III, ld. Tas Dstsaxtxattox or Tsxrsaatoks 24. Hsatnto *No Coaksut~kttxo Car*cttv Taaxatsxts nt Cast,s Svatsxs sv Msaxs or ax 0' Baa' Couattctoks rok Oataooa Sskvics> Dcc. 1053, yp. 1260-T$ ,

8. A>>C Rsarstaxcs or Prrs-Casts Svatsxs ANaaooaa Coxrotak>> J. H. )Ichor. Ibid., yt. II, 1051, pp. 1361-T1. R>rserr, Scrtcaectady, ¹ O. R. Schurig, O. W. Prick. Ce>>>rot Zfcclric YvaL 33, 1930, y. 141.

issued in which a simple methad h yre- bash of the papu this ig'a logical approach Discussion gcnted for the rapid calcuhthn of cycHc but it appears ta dEer fiant the basis of ratings.'able computing ratings hitherto adopted in the C. C. Barnes (Central Electricity Authority, V giveg Specific inductive capaci- United States. An ampHGcatian of the Londan, Enghnd): This paper is an excel- tance values far yaper ast paper htguhtion autharg'iewpoint aa this important issue lent. and up-~te study of a most hnpar- (SOHd type), 3.7 (IPCEA value); paper wiH be >>deemed. tant subject. Par 25 yeirs D. M. inguhtian (Other type), 33-4A Is it pad- With reference ta the use af low-resittivity have been used for fundamental bttchfiH, recent Studies in Great Britain Simmons'rticled sible ta Hdt the other types and their Study on current rating problems, but the apyrapriate Specific inductive capacitance have Shown that the method of bachGHing numeraug cable deveiapmentg aud changes values or alternatively gunply use an cable trenches deserves careful cangideta in indtaihtian techniques introduced in average Specific htductive capacitance value thn as atteathn ta this point can result recent years have made a modern assess- af 3.7, far etample> for aH types af paper in incretset up ta 20% iu had currents. ment af this subject very neccsgary. The inguhthn? Equatha 43 gives the thettnal resistance essential duty af a power cable is that it Reference 15 made ta the adaption of the between any point in the etrth Surrounding should transmit the maximum current (ar hypothesis suggested by KenneHy as the a buried cable and ambient earth. It is power) far Specified instaihtian canditiang. There are three main factarg which deter-mine the safe continuous current that a Table X. Tempetblute Llmib for 8eHed; Screened- cnd HSL f'-Type Cebiet cable will carry.

1. The maximum yertnidgible temperature LaM Direct or la A)r Ia Ducts at which itg campanentg may be aperated Aiamiaum Atom)asm with a reaganable factor of safety. Sheathed Sheathed Lead Sheathed Lead Sheathed E. Thc heatMiggipathtg yrapertieg af the Armeured Armored cable. Syeteai Voltage aad Tyye Ua- or Ua- Ua er Ua ai Cable Armored armored armored Armored armored armored

3. The instalhtian canditians and ambient condithn5 obtaining.

1.1 kr In Great Britain the basic relerencc Stogie>cate.. F 80 ~~ ~~ ~ ~ 80 ~~ ~~~~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ 60>> ~ ~ ~ ~ ~ ~ ~ Ttria aad multicoce baited.>> ~~~ 80 ~ ~~~ SO>> ~ ~ ~ ~ ~ ~~ 80 ~~~~~ \ ~ 80 ~ \ >>60 ~ ~ ~ 80 document is ERA (The British Electthal and AHied Industries Regeirch Asgachtha) 2.3 kr aad 5.5 kr Siagtehae ~ ~ ~ ~ 80 ~ ~ ~ ~ ~ ~ ~ 80 ~~~~~~~~~ ~~~ ~ ~ ~ ~ ~ ~ 50 >> ~~ SO reyatt F/TI31t published in 1939, and in ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Thf~rc baited type ~ ~~ ~ ~~ ~ 80 ~>> ~ ~ ~ ~ >>80 ~~ ~~ ~~~ 80 ~ ~~ ~ ~~ SO ~ ~ ~ ~ ~ ~ >>60 ~ ~ ~ ~ ~ ~ ~ 80 1955 revised current tutiag tables for 11 kr solid-type cables up ta and including 33 kv Siagic~.. ~.......70.........70.....................50.........70 were pubHshed in ERA report F/TI83. Threncoee belted type....... ..SS.....,...5$ ...,.....65...,......5$ .........50.........d5 ~ A more detailed rcport sumtnarhing the Three>>care acrceacd type..~.....> 0..~......TO.........TO,........70.........50.....,...TO method of computing current ratings far 22 kv SOHd-type, ail GHed, and gas.preggure cables Static~re.. ..5$ .........6$ ............ ........$ ~ 0.... ~ . .5$ ~ ~ is naw being GnaHted and mn be published Three-care betted type..........SS.........SS,...........,........$ 5.....,...50 Threescore icrceocd type........6$ .........55.........5$ ..........5$ .........$ 0....... "5$ as ERA rcport F/TI87 satne time in 1958. Tht~c lSLI or Shl)........65................... A$ ..........65....................55 Until recent years currertt ratings in 33 kr (ccrccacd) eat Britain have usually bten considered Static~re.. .55. 50 . an a continuous basis, but the ltnpartance of taltittg into consideration cycHc ratings Three core HSL...............OS. .65 hag naw been eirefuny studied, since con- ~ Mccauccd ia degrcca ccatigrade. tinued high metal priced have forced cable t Hachttatcc separate lead. users to revietr carefully the effects of I Separate iced rheatbcd. cyclic laadings. A report has recently been 1 Separate alumtouaa sheathed. not clear, however, what value of soil recorded in an ERA reports deaHng with tained from Arnold'5 paper.s that where thermal resistivity is used in this expression continuous current ratings. and in two sheath and nonferrous reinforcement losses and information on this important point IEE (Institution of Electrical Engineers) occur a paraHel combination oE sheath and ls desirable. papersc> (based on ERA reports) deaHng reinforcement resistance permits the cal-In Great Britain a value of soil thermal with cycHc hacHng, but the majority of cuhtion of a single loss factor. that a simple resistivity (g) of 120 C cm/watg is generaHy this work ls in process of printing and formula has been derived for the external used but further test data are being slowly pub Hcation. thermal resistance of one of three cables acquired.'nd where tests have indicated An obvious dHEerence in British and in trefoil touching Eormation hid direct that a lower value, e.g90 C cm/watt, American technique is the method of cycHc in the ground,'nd that sector colrecriion is justified. this value is used. Current rating factor calculation. Mr. Neher and factors are often used ia British practice loading tables in ERA report F/T183 ~ Mr. McGrath'5 method is based on an for 3~re cable rating calcuhtions. provide data for soil thermal resistivity equivalence between typical daily loss values of 90 and 120 C an/watt, and cycles and sinusoidal loss cydes of the same REFEaasfcss correction factors for other values o! soil loss factor, while a method recently hftro-thermal resistivity are also provided. duced in Britain'4 takes full account 1. See ccfeceaee 1 of the paper. In the United States buried cables are of the form of a daily load cyde. Both 2. See cefeceaee 1 of bfc. Basses'fscossfoa. usually pulled into duct banks, but there methods are considerably shorter than Tss CAacoaano>> or Cosnsccoos RAnsos must be many cases where'irect burial, any that have been available'itherto. AND RAnND FActoas roa TRANacccsscoN AND as aormaHy,.used in Great Britain, wiH Nevertheless -,without further study I DistacsictioN CAaass. K Galdeabefg Rcpers result in lower'instaHation coits. Formulas would not feel certain that for British.type Rcfcnucr P/Tlry Elbl, Irsedea, Eoglaad, (ta be dealing with this instaHation technique published). cables, subject to their typical daily cycles, are a desirable addition. Permissible tem- the Eorm of the cycHc load can be ade- 4. Sce cefcccace 2 of Mr. Bacncs'fscossfoa. perature limits for the various types ot quately taken into account by use of the 5. Tss CAacoaanoN or Ctcccc RAnND PAccoas cables and instalhtion conditions used in AND EicsRDSNCT LDADcso roa ONR oa Moss loss factor independently of the cycHc CAscss LAiD DcRsct oa Dc Ducts, K, Gold enbecg. the United States will be a helpful ap- load wave form giving rise to it. In hct $ feeorrepA cco. 3$ l, fastftosfon ol Efcoscfcsf Engi-pendix, and it is suggested that this informa- the conclusion reached in my second IEE neers, July 1951. tion should be added to the paper. For 'paper,s is that a knowledge of the cyclic 8. Tss Esctsavao Tssauaa Rosie TANcs or comparison purposes, the limits recom- 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 Boacso CAai ss, E. Goldenbecg. Eceeccc Jeurccef, mended in Great Britain are summariged peak conductoi temperature, together with London, England, vof. $ 4, ao. 1, Fcb. 195T, p. 38. in Table X and in the foHowingl the loss factor, are adequate for cycHc T CQRRSNT RAIQcos roa PArsa ~ TNslKATRD Phstic-insuhted power cables............ rating hctor cdcuhtion. However, it C*sass To B.S.480, 1954; VARNcsssoCANsasc would be unhir to assess any of the rehtive INsccLATSD CAÃ.ss To B.S. $ 98, 1955. Rcport, Rc 70 C maximum conductor temperature fcnacc P/I'lpp, The British Efccccfcal and AQfcd merits of the two methods prior to the industries Research hssocfasfeo, Leachcchcad, Eag Gas-pressure and oH-HHed cable systems publication of one of them. lead. (<< types). The difference between Britbh and 8. See reference 5 of ihc papa. 85 C maxiniunl conductor temperature American cable rating technique is not so marked for continuous current rating cal-Finally, it will be helpEul to know if cuhtion as might appear to be the case Elwood A. Church (Boston Edison Com-adoption of the formulas in the paper wiH at Grst sight. In hct, such dilferences as pany, Bostoni Mass.): The authors present necessitate revision or ampliHcation of exist are principally due to the dHIerent a hrge amount of useful data and formulas existing rating tables and, iE so, when the types of cables employed on each side of for the calcuhtion of cable thermal con-revised tables will be published. the Athntic, and to the diiferent standard stants and suggest a new approach to the aw frequencies in use. Nevertheless a problem of calcuhtion of temperature rise REpERBBcas comparison o! the present paper with the for various loss factofs including steady-1~ CQRRRNT RATcvo or CAsass roa TRANS ERA report dealing with continuous current load or 100% loss hctor. Cable engineers sccsscoN *ND DcstacsonoN, S. Whitehead, E. E. ratingss gives rise to certain observations. usually agree on the hctors to be taken Huichfngs. Rcporh Rcfcrcrccr P/Pf Jl, The Bcfffsh The present paper fs principaHy.directed into account and the methods of calculation Efccccfcaf aad Allied fodusccfes Reseacch cfssocfa to the calcuhtion OE a single current rating, cion. Lcaihechesd. Eogtaad, 1939; also Jo rsel, for steady loads. However, there appears fastftutfoo of Elcetcfcal Baglaeecs, Loadon, but one use to which it might weH be put still to be disagreement on the problem o! Bagland, vol. 83, 1938, p. $ 1T. is the hrge-scale preparation of current cyclic loading.

2. Tss CAaeoaanoN or Ctcuc rating tables, with rating hctors for non- At the AIEE General Meethig in January RAToco PActoas roa Case,ss LAco Dcaact oa sN Doers, E Golden standard conditions. For such an applica- 1953, a group of papers'as presented berg. Precccdfacc, foscffusfon of Electrical Eagf tion it Is often preferable to introduce suggesting various approaches to the seers, Leaden, Eaglaod, TOL 104, pe. C, 195T, p. explicit formuhs for the rating factors, as problems of cycHc loading on buried cables 154.

these formulas might be independent oE and on pipe-type cable. Of the methods some of the thermal resistances or loss suggested in these papers, the one which factors involved, with a consequent saving appealed to the author the most was Mr. H. Goldenberg (Electrical Research Asso- in calculation time. Neher's methocl using sinusoidal loss cycles. chtion, Leathcrhead, England): The cal- The method employed for external ther- In his paper it was shoitn that this method cuhtion of cable ratings ls a subject of mal resistance calculation for grouped yields reasonably accurate results for the prime Importance to cable engineers. cables hid direct in the ground differs higher loss factors. For a low loss hctor Nevertheless, it seems that until recently somewhat from that.recolnmended in a sharply peaked cycle the results are not the American standard work on this subject recent paper of mine.c For the preparation a5 accllrate has been that of Simmons,'hile the OE group rating factors for the more com- A modification of this method would be corresponding British standard work has monly occurring groups of cables dealt to represent the load cyde more accurately been recorded by Whitehead and Hutch- with in an ERA report,s the combination lngs. by splitting it into harmonics and com-These papers have been supple- of certain simpli6ed external thermal puting the temperature rise Eor each mented by scattered pubHshed papers. formuhs and my recommended harmonic separately. This eatails more i 'esistance including developments deaHng with cyclic method has led to substantial saving In work. but with modern methods of machine loading. calculation time. I do not favor the calcuhtion it is cconocnical to use the The paper by 3fr. Neher and Mr. Mc- introduction cf a geometric mean distance, most accurate method available and let Grath records up to date American cable- or its equivalent, as it is inconvenient for the rnachine perforni the hborious cal-rating practice in a manner that will prove unequally loaded cables. culations. In fact, it takes very little invaluable to engineers for many years to A brief rcsucn6 of other points is that more time on the machine when the more cocne. It is a pleasing feature that the the thermal resistivity values given in rigorous methods are used instead of, any authors are espcciaHy competent to deal Table VI for thermal resistance calculation of the approximate methods which have with this subject in view of their valuable are generally somewhat lower than the been suggested. contributions to the cable-rating field corresponding British values, that the The author has invcsligslcd. the various over a number of years. Modern British proximity effect on cylindrical hoHoir methods of catculalioa of the cyclic com-cable rating prsctice has recently been conductors appears to mc to be best ob- ponecit of temperature rise of l,250-5ICM P 'i>P Pa v e C 4 ~ 1 4 Tab/c Xt. Thermal Impedance FuacQons Tab/e XIII. Maximum Temyctature R/ce for Cyclic Loading 1,250.MCM 115-Kv Csb/c Enclosed /n 6s)to-Inchucx/dc-I}/eactcr P/pc Coaductot P/pe Ts/C}o To/f)o I s/(/o yo/C}o Method Tempctacute, C 'armonic Tetapetacute, C of Ca)- oo............... 8.03/o'...........d.ss/o'...........s.pyio ca/ac/oa I Pfpe 2 Pipes .I P/pe 2 Pipes ......,.....9. 08/Oo ....,...... 8. $ 0/Oo ....,.......8.03/Oo ...........s.so/o't......,........lo. sdlos ~ For Loss Cyde I I............. 2.88/-30 ............1.57/ 43 ............1.24/-$ 4 ..~.........0.031-51 1.......39.1.....49.2......24.1 ....34.3 2.......30.8.....40.0......24.5 ....34.8 2 ~......,...... 2.20/<<38 ..........1,19/ 54 .....~......O.S2/-58 .... ~.... .O.ST/-77 > ~ ~ 3.......30.0.....$ 0.1......23.2e.. .33.4e ~ 3 "~ .. .~...... 1.94/ 43o............0.94/ ~ ~ dto............o.dl/ 79o............0.39/ /-87 For Loss Cyde 2 I ......30.0.....37.5...... 17. I .:..23.8 4 e ~ . ~ ~ .e" ~ ..... 1.58/ -50'............O.Td/ <<dyo............0.48/ 87'............0.20/ 95 ~ 2.......32.d.....30.2......18.2 ....24.9 ~ 3.......32.8.....39.5......15.xe....22.8e Steady.state componcaC for s/agic pipe f Steady.state compoaenc for c<<o pipes, 18 inches apart. These dgutcs do aoc iaciude the Ccmpctacute cise Qo<<<<acts copper ioss pct coaduccot pot foot due co die)acetic ioss, <<hfch would be added co the Ts<<'cctopctacute tise of conductor ~ ccady.state compoacaL 7's<<tcmpotaiute t(sa of shiddiag tape Ts<<cern pctacute tfse of oil ia pipe ~ These ste acetate ccmpctacutcs. It is aoc possible Co compute the maximum ccmpctaxute of 2'o<<Cetapctatute tise of pipe the pipe by this method. 115-kv cables enclosed in 6s/s-inchwutslde- ditferent sizes of cable (a total of 12 ma- pezatures, especially in summer when high dianxeter pipe buried in the earth. The trixes). The cost of pzogzanuning was earth temperatures prevail and where results of three such methods Eor two small since the generai program for solutioa higher daily loss hctozs arc more likely representative load cycles are presented of complex simultaneous equations was to be encountered: If the earth next to in this discussion for comparison. The already avaihble in the IBM library, and the pipe exceeds an avenge of 50 C, there three methods compared are: (1) the only a small amount of work was necessary is danger of drying out the soH causing Harmonic method using Bessel Eunctions to set up this particular problem. thezmal instability. Ca/culations ot cur-to compute the heat-Qow constants of the The components ot the loss cycles with rent~ying capability should take this cable for each harmonic of the temperature which the data in Table XI was multiplied liznit into account. cycle, (2) the sinusoidal method suggested to obtain thc tempezature cycles are given by'r. Ncher in his 1953 paper, and (3) in Table XII. These loss cycles are iHus- Rxcysaxcwcx the latest method suggested by Mr. Neher trated in Pigs. 4 and 5, with the cocre-and Mr. McOrath in their current paper. I. Sce tefcteacc 3 of the paper. syonding temperature cycles of the con-Space in this dhcussion does not permit a ductor and yiye, complete derivation of the heat-Bow equa; tions for the hazznonic components of the heat-Bow cycle, but only the results, as In aH future calcuhtions of this soct, it is planned to cany the programming stiH further and have the machine calculate K J. Passaic, conunended ¹ Wiseman (The Okonite Company, J.): The authors are to be for thh very Gne technical calculated by an IBM (Intenutlocul the temperature cycle for each size of cable paper. Thc nial for aa up-bxhtc com-. Business Machines) 550, are tabuhtecl in and detecznine its maximum value. Thh pihtioa ot engineering fonnuhs and con-Table XL It may be noted that the has been estimated to cost approxinutely stants for the calcuhtioa of current-znachine tiznc to solve the eight simul- $ 500 for programming and $ 15 extza per cacrylng capacities of cables has been of taneous equations necessary tor the solution size of cable to compute, increasing importance every year. When oE the tempecatures and heat Gows for each Usually only the temperature of the Dr. Simmons wrote his series of yayccs hazmonlc was approximately 5 minutes conductor and the pipe are signiGcant in about 25 years ago we might say the per znatrix, with a separate solution neces- calculation ot the current.carrying capa- electrical cable industry was young in sary for each harmonic. The whole cost bility but the electronic calcuhtor auto- engineering knowledge, the types of cable of the job m rental tinxe on the machine matlcaHy computes the other va/ucs'sted furnished were not too great in number, and punching the data oa the cards for in Table XI. and they are recozded Eor and the characteristics of the cables mere msertlon in the machine was $ 150 Eor three whatever use may be made of them. not too well known. Today our knowledge A tabu/ation of maximum temperatures of cable design, materials, ancl operating for the foregoing two load cycles and the conditions along with new types of cables Tab/c X/I. Hannon/c Componea/s of Loss three dHfecent. methods of calculation Hsced is hr ia advance ot 25 years ago. We have Cycles previously are tabulated in Table XIII been using the tonnuhs as they became in the same order. Examination of this knowa and it was desizable to bring theta table wHI reveal that the sinusoidal method together in one phce and, in addition, aH Loss Cyde I Loss Cyde 2 yields results which are nearer to the znore of us who have occasion to make these Hat Loss, Phase Loss, Phase accurate harmonic method tlun thc htest calculations wiH be using the same fozznuhs moa/c Watts hac(e, Waus Aag( ~, method proposed in thc paper. The and electrical and theznul constants. Desto so Decrees agreement between the various methods is Also, this paper <<iH be of great help to seen to be better at the higher loss factors. younger men coming into the cable in-I 2500231 0.......4.03...............2.54 It may be argued that the agrcemcnt is dustry. Although ic summarizes the ~~ ~ ~~ close enough between the three methods formulas, anyone stishing to get a dearer 2....... 1. 10..... +30......0.43...... +IS$ for aH practical purposes and that the appreciation of che text can refer to the 3.......0.20..... 00......0.do......+ ds 4.......0.$ 3..... +40......0.53...... 3$ accuzacy of the original thermal constants bibliograyhy and study che original papers. from which the computations were made To cnake any tare of this kind gencraHy Bxamp(e: The equation of loss cydc I using the fotegoiag data is as foiiooom (staximum Qo<<d.d does not warrant the extra work necessary useful, it is desirable that the procedure <<acts ptt toot ptt coaduccot} to use the harznonic method. However, be easy to follow sad the formulas readily Qo<<4.03+2.$ 0 sin oot+I.IO sin (sot+30o)+ the danger in using an approximate method applied. Theo recital fonnu/as involving 0."-0 sia (3ot-00o)+0.$ 3 sia (sc t+40o) <<ates is that someone unEacniliar with its deriva- higher mathematics can be used, but they Cottespoadiag ccmpttscute cycle fot cooduccot tion and its limitations wili use it where it take time, and vcr) .olccn it is not possible tempstacutc is ss folio<<s fot ~ siagie pipe: (I taxi. does not apply. The author does not con- to take the tune to stock up a case. Aga/n mum Ti <<35.lo) 7's<<32.4+7.24 sia (ut-30')+2.$ 7 sin (<<ot 8 )+ sider thc agrecznent close enough for 40 fo conditions ot inscsi/scion ate varlab/e 0.30 sia (3<<t 133') +0,80 sla (4a T') loss factor. daily, so if we atcczapc io mal'e a Geld check dcgttcs ccadgtsdc The computation ot the pipe Ietnpctature ot ca/cuhcions wc can Gad dL~ctcrtccs; Sere time<<5,00 a,cs. ia the fotegoiog expressions. is just as important as the conductor tcm- there/ore, cxaccnes) 'co 3 high degree is l l 5 ~ ~ t' 4 I 4 "~ ~ ~ ~ '1 J ~ r l II 3 100 100 ~do E ~ X X ~ ao >dO O O A ~ao l-ao z ux AVE.I CD rD co O. 20 O 20 ..,r..",, Xc- a ~ tiM A.M. Flg. 4. Loss and temperature cycles for 75%%uo load factor> Qlllullcf Ftg. 5. Loss and temperature cydes for 60%%uo load factor winter load cycle load cycle C4~coppcr toss cycle Values same as in F>g. 4 Tx~tcmpcraturc ol conductor Tc~tcmpcraturc of pipe Tcmpcrdturcs are ln per cent of copper tcmpcraturc corrcspond- tion of the cable having th>> highest thermal tng to steady load equal to the maximum. 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 not necessary. It has been suggested thaC the apparent thermal resistivity varied load exists and outside which the loss it is now possible to use computers on these due to the convection effects of the oil. factor of the load is taken into considera-problems. This is true for those who have IE we took the simple formula R>a~ tion. I have not been able to accepC this a computer, but here also time is taken for 1.60/D where D is the diameter over che assumption. It is an endeavor to obtain setting up the probtan for the computer. shielding tape we found we goC good a thermal cesistance for the soil that will Also we must show how to calcuhte the agreement with test. We neglected tan- ~ check with a study that Messcs. Neher, currents and in a Eorm thaC will be used. perature effects as the actual value of Butter, Shanklin and myselE made and is Vou will note thaC many of Che focmuhs Rra as coxnpaxed to thc thermal resistance referred to in reference 3 in the bibEography are new to mast ot you. These fonnuhs of the hsuhtion is very tow, many times of this paper. A study of the previous were developed to make the calculations in the order of one. tenth; therefore, papers will show thac the attahiment easily and quickly and yet do not cause a temperature effects are small. For a gas factor is not exactly the same for att types large error in the ttnat answer from the medium using 200 pounds per square inch of cables studied and all shapes of load highly theoretical formula. It is natural me use the equation 8>a 2.58/D. How curves, that the formulas may bc a compromise do these focmuhe cocnpase with equation The authors tabulate in Table IX a and some may feel that a particular formula 41(A) proposed by the authors) comparison of the attainment tactor for Chat they use may bc superior to that recom- Consider two cases, one having a diam- three methods of calcuhtion for a loss mended. Likewise the thermal constants eter over the shieiding tape of 1 inch and Eactor of 30% Eor several cable designs. may be a coxnpromisa This is true as another having a diameter ot 2.5 inches. Rather than give results for one loss factor far as I am concerned, yet we are witting The Eollowing table compares the two types only, it would have been betta'f they had to accept the recommendattons given in Che of equations. covered the cange of loss factors which were paper. The calcuhtion of the various studied in 1953. It these attainment fac-losses existing tn a cable systan and thc tors were plotted against loss factor as I location of these losses is well done and Dtameter ~ Diameter ~ did in my paper, it would have been noted 1 loch, XA laches, should bc carefully studied by all new Thermal Thermal that a straight line could be drawn giving engineers. OhmrPoot Ohm-Pool a good representation of how (>4F) varies The section dealing with the calculation with loss factor, naxnely, (>4F)~0.43+ of some of the thermal resistances need Ohoaite......t.do t.o.r....o.da t.o.f. 0.57 (t/) for my method. This equation careful study in order to appreciate than on..... Nehcr aad...1.3r ...0.80 follows the plot of (AF) and loss factor as they depart from the usual manna'n { vay well down to about 35% loss factor, which a thermal resistances are calculated. Ohoaite......2.5d Co.t.... 1.03 C.o.f. and in some cases, it gave a higher value Caa ~ ~~ Nehcr aad...2.22 ...1.04 For example: the thermal resistance htcCraxh and other cases a lower value than actually between a cable and a surrounding wall, calculatecL The (4F) values I reported such as a duct wall or a pipe; see equations are based on careful calculations from thc 41 and 41(A). Heretofore, we used 2>a~ Thc differences are not great and when exact load curve and no assumption that 0.00411 B/D, and referred to as thc IPCEA considered in relation to the total thecmal a single ine wave curve can be taken as method. This has been revised to take resistance, they are negligible. We can representuxg any load cucve. As it isa into consideration the condition existing accepC the authors'quations. rarity that cables are designed for loss and the materials. Equation 41(A) is a I am ghd to see the authors phce thc hctors as low as 30% (50% toad factor). general one, and by inserting the correct duct system in proper rehtionship to a my formula gives results as accurate as values of >4'nd B's given in Table I, buried cable system and that the same when using D, and easier to use. However, we can get R>. This is an example of how soil thermal resistivity will be used when for the sake of uaiforniity in methods of we can accept a compromise in order to making comparisons. This was the weak- calculation, we wilt accept the ness in the cluct heating constants originally authors'ethod. get agrecmcnc. We ac Okonite made tests years ago co determine the thermal set up by iVELA and hter known's In thh connection, I ivould like to raise constants for the oil or gas medium sur- IPCEA constants. Also a better under- a question which I hope will be taken up rounding cables in a pipe. Wc tried to standing of the effect of multiple cab'tcs in a by others interested in this subject. The use the cylindrical log fornxuta and found duct bank is obtainable, and th>> decermina- use of the equxciou involving Da is an Arrhrr fr/ rn>C n> ~ >rr n>>rf I'na:< I nnnVl~'t>> ~

,attesnpt to tn'crease the thernut resistance and have arrived at catatn condusions, been able to make the Neher-McGrath for the soil for cables or small pipe sixes; some of mhich are discussed in the following method tsack with the old and well proved hi other words, the computed value oE paragraph. NELA method is to reduce the soil thermal th emu! resistance is too Iow. Is it not The determination of thc losses m the resistivity to the order'of 40 C to 75 C IHldy that vre are leaving out of our equa-tion a term involving a surface contact between thc surface of the cable or pipe and the saiL This is term would be of the sasne fostn as we now use for the case of es in air, namely, 8~0.00411 B/D.

cables If we add this term to the log fortuna Eor soil thermal resistance, res we will get a higher of direct buried founded; althou h the bl d instalhtions appear to have'een well hod E 'l conductor, shield, sheath or pipe, and the dielectric have been weH estabHshcd by the authors and bear no further comment. Thc calculation of the thelmal resistances at the effect of cyclic loading scans to bc 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 total resistance and the Inliuence of the in question amottgst the various investiga- 10% of thc NELA method if a pa~75 C diameter of the cable or pipe willbe greater, toss (reference 3 of the paper). However, cm matt is used. the tower the diameter. It vriH be neces- as Ear as duct bank Instathttons are con- We have nude some calcutattons of the sary to determine the value of B. Thc cerned, the difference between the NELA thalnal resistance of cables in a duct bank idea of such a tenn is showa in the paper'r IPCEA current rating method and that from thc sheath to ground (or sink) using by Mr. Matha and his coauthors. In proposed by the authors is so grea t th a t the ¹her-McGrath method and the ~ Table I the y give same thermal data one cannot help but <<onder at the dearth average conditions on <<hich the NELA duct obtahtcd frotn tests made by them on a of practical data h the paper. constants were obtained. Thc average pipe-type cable. They give a value of ln reading references 10, 12, 13. 16. and conditions were: 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 not likely that wc have a surface resisttvity thecahleandthesoHmtmmedtate c, little data on cable 'temperature measurc-ments takal in th 6dd sQ ch as mas doric by the various utilities when the NELA I. Most of the measurements were taken tinder paved streets with the depth of pave-ment between 10 and 12 inches. values mere established. The work re- 2. Majority of ducts wac made of fibre. ported in these reEerences ts almost atl RBFEMtNCts theoretical, and laboratory measuranents 3. Avaage duct inner diasneter ~3.75 an,an~ogue mends u~ ~ ~ appr d inches.

1. Bottrtava.aa powaa ttotttrrtssa*norr Hton.

Voc TAOC Ciaoa SjtrotÃsy R Js MathafJ Pe Js I am

• Concrete spacer between ducts 2 MaCattoa, E. Dautlrtlatt. A IEE Traarrurtoas, gi to u dets t there inches, with duct..watt~1/4.tach, 3-inch a movement afoot to have this Neher- outer concrete sheIL Spacing between McGrath method accepted and to revise duct centres ~6t/t inches.

the IPCEA current rating tables accord- 5. Average depth of busial to top of duct E. K Thomas (ConsoHdated Edison Com- htgty. I am not sure that this is the case- bank ~30 inches. pany of New York, Inc., New York, N. Y.): The authors are tobe congratutated in setting 6. Most measurements with ~nductor up mathanatical equations to evaluate load lead sheathed cables fran 2 inches to 3 We have used the method given in thc inches outside diameter. Avaage diameter gret that no mention was made of the pio paper to compute the current sathtg of 2S inches. ncerworkbyWathceE.~ketnthemtddte quite a number of high-voltage cable cir- 7. AH Ioaded cables in outside ducts, all 1920's on the nthg of cables mstated m ~ts h a duct bank md 5 d complete dh- equaHy loaded. duct bank . Th work, I bdieve, f - agrcanent mith the NELA or IPCEA nicthod. In every case the Neher.McGrath 8. Soil thatnat resistivity (i>> situ) ~ ntshed thc b ~u of ~btc rating of thc method results in a hrger conductor stxe 120 C cm/watt. NELA and present IPCEA published rat-Ings of cable. The work of Zirke was pre- for a given current tathtg, m some cases Two cases mere studied and the results before thc AIEE anti pubHshcd in as much as 30% morc conductor metal is are summasixed in the foHomingl required by the Neher-McGtath method. Journal 1 The work on ratings of cabte by Ktrke. Ha h mhere our di a ~ begins. One Care I Thrcc cables in 2 by 2 duct bank 5dd m~ meats in the New Yorlc City area and tater of two things prevaHsl eitha Mr. ¹her and Mr. McGrath have cotstered the (onc of lourcr ducts crnpty). nonfcrroQs lnctat maske't or they arc . NELA Valtte (Le. 4.93/D,'+LrNH3 attanpting to make a pipe. type cable carry Loss factor........100%o..62.5%o..33% the same load as a dua-bank tnstaHatton. Rthc g thamal/ which lead to the NELAIPCEA satin ohns-feet.......5.09 ..3.92 ..3.00 Yet on the face of it, it is incomprehensible Qse of pipe-type cable. Zt should be hom anyone can conceive o! a ~nductor Neher-McGtath Value obvious that the answer obtained by high-voltage cable (and a Pipe-type cable Loss Eactor, 100%o 62,5%,33% mathenuttcai solution is never any better Upper cables assumptions ou which the equa colnpCtlng On a current sating basis with Rths s thalnal gona are dcvdoped and the constants used single.conductor high-voltage cables sePa- /ohms. feet... .6.68 ..5.02 ~ ~ ..3.71 vrith the equations. ratdy spaced in a duct bank where aw Lower cable I bdtcve the actual heat ttow in under losses are a minimum and heat dissipation ~m~ ~ot Rths.s" "" " "6-63 -.4-99 ..3.70 g d cable sy t~ h constd~bly mo~ complex than has been assumed in this a In either event we undastand why so much thne should bc Average values....6.66 ..6.01 ..3.71 ~ spent on devdoping a ncm method of cur- In order for Nehcr-McGlath values of paper and, therefore, actual ratings which therlnal resistances to be equal to NELA are obtained may be dHIcrcnt from those rent sating calculation for . duct-bank systelns without Gsst having at least values, soil resistivity would have to be; obtained by this calculation, obtained some actual In - service field measuranents to substantiate their At 100% loss tactor p, 65 C an/watt Rzt ttttstvcts At 62.5% loss factor p< ~60 C cm/watt fosmtttas.

l. ~iuu Caactraanorl or Caaaa Tattraaazoaas On thc other hand, we must sincerely At 33.0%o toss factor pa ~45 C an/watt commend the authors for attanpting to Case Six cables in 2 uridc by 3 dccp Il arrive at a realistic comparison between duct bank.

duct-bank and direct-buried systans. It NELA Value ts unfortunate, however, that in doing so D. Shortort (Canada Wire and Cable they have not based their formttta dcvdop- Loss factor...... 100% ..62.5% ..33.0% ompany, Toronto, Ont., Canada): Sevant ment on extensive 5dd survey data as was Rths-z thermal oE the engineer mho worL with me at Can- done at the time thc NELA duct constants /ohms-feet....6.89 ..5.05%..3.60 ada Wire have been studying the Neher. were established. ¹her-MCGrxth Value MCGrath P a P a over th e past few months, The only way in which we have as yet, Loss factor...... 100%..62.5%..33.0% Jt/cher, rtfcGrath Tcmpcratttrc and Load Capability rsf Cable Systcnls OCTOBER 1957 ~< k Lt ~ P I~ I'p per layer been'used extensively, but thc apparent formuh if the sink is the earth' Rths d ther-" thermal resistivity Inserte in the calcuh- surface. Why is thc euth's surface tem-mal/ohms- tions are based on that value obtained perature not the tzue ambient to use when feet..........10.23..7.24 ..4.88 irt ziltr, as measure4 in accordance with applying the Kennelly fozmuh? Is the Middle layer reconunended methods. To get a very British usc of a 2/3 factor in reaHty a Rths-d ther- accurate value of the apparent thczznal correction for the virtual sink temperature. mal/ohms- resistivity, it seems that the method to be or sink tenperatures if the deep Isothcmul feet..........10.95..7.69 ..5.12 used should exactly duplicate the cable and theory is valid. Lower layer its operating conditions; Le., thc same Rthc d ther- diameter as the cable, the same watts loss mal/ohms- dissipated, the same depth oE burial. and feet..........10.63,.7.49 ..5.02 L TssaxAL ANU MaatANTOAL PaoaLax oN at the titne when the thermal conditions 'enneHy 128 Kr Ptas CASLS TN Nsw Jaaaar, h. S. BrooLee, Average values.. 10.60..7.47 ..5.01 arc most onerous. Thus in the calcuhtion T. B. Starre. A188 'Frearerrioar, roL TC, pt. 111, Oat. LOST, pp. TT2%4 In order for Neher-McGrath values of of it thermal resistance Erom cable to ambient, that 2 AN AN otooos SoLUTIoN or CASLs Hsar thermal resistances to be equal to NELA appears the Kennelly fozmuh can be used to a high degree of accuracy if an PLow Paoatsaa, B. de Eaaa. P. J. Saadtford, values, soil resistivity would have to be: A, Vf. Vf. Caceeros ISfd., roL Td, pt. 111, Jaae apparent thermal resistivity of the soil in IOSS, pp. 215-22. At 100% loss hctor p,~53 C cm/watt situ is used. This measurement should At 62.5% loss factor pe~50 C cm/Iratt automatically take into account aH the At 33% loss factor p, 43 C cm/watt factors that otherwise limit thc KenneHy F. O. WoHaston (British Columbia Engi- ~< formula to a theoretical exercise. neering Company, Ltd., Vancouver, B. C., Other calcuhtions on slngle~nductor There has been a great deal"o!.investiga-high-voltage cables varying in conductor Canada): This discussion is confined to the tion into the infiuence of moisture on soil parts of the paper dealing with cables in size from 300 to 1,150 MCM instaHed in resistivity. However, as yet there seems outside ducts in a normal duct-bank systens ducts. The paper is in many respects to be no general agreement on another most adtnirable, notably the coverage of It was necessary to assutne a pe~75 C basic problen, and that is the direction of sLin dfect in conductors. of special types, cm/watt in order to make the Neher- the heat Qow. The authors and others and eddy current elfects, muttuI McGrath fozmuhs agree with the current proximity maintain that the heat Qow is to the surface heating effect oE multicable instalhtions, ratings calcuhted by the NELA method. o! the euth whereas other investigators The NELA method is of course strictly and the diect of extraneous heat sources. claim sotne heat Qow is downwards to a For the 6rst time these are aH adequately empirical and thc duct constants deter- deep isothermal, about 30 to 50 feet below mined from an average of a large number treated in onc paper. The methods of the earth's surhce. In reference 12 Mr. edculation must, however, be critically of 6eld surveys. It has been in use for well over 25 years; and there must of a Neher obtains the heat 6eld pattern by examined before being acceptecL I am superimposing the Geld based on the disturbed to Gnd that the methods given consequence be many thousands oE miles Kennelly fomtula on the temperature of cables operating at current ratings cal- for rating cables in ducts lead to sub-gradient. It is obvious from the Geld ~ stantially hrger conductor sizes than does culated by the use of these duct constants. patterns that in the summer the heat Qow So far as our experience in Canada is con- the IPCEA-NELA method. By thc is predominantly down, whereas in the. IPCEA-MELA method I mean the method cerned we know of no hot-spot failures with winter the heat Qow is to the surface. The high-voltage cables in duct-bank instalh- given in an Anaconda publication.t authors give no quantitative method of believe this method is identical to that tions. On the contrary one is led to read evaluating the cffect of the temperature with great interest the recent paper by used in preparing the existing IPCEA. cur-gradient on the apparent soil resistivity. rent mtings for cables. Brookes and Stazrs.t This could be one of the reasons foz'he Do the authors expect utility engineers The Neher-McGzath method leads to difference between the resistivity as meas- much higher values for the duct heating operating duct-bank instaHations to adopt ured in the laboratory and h the field. constant (the thezznaI resistance from the method put forward in the paper and An indication of the effect of change of duct. bank to eazth ambient) than does the forthwith reduce their loads accordingly! apparent thcrnul resistivity h shown in IPCEA-NELA method, when the thezznal This is a question of great importance, a paper by de Haas, SandiEord, and resistivity of the euth is taken as 120 C and we should have a categorical statement Camezon,t wherein the dfect oE introducing from the authors in this speci6c regard. an/watt in the Neher-McGrath calcuh-a deep isothcmzal (ground water) in combi- tion. The value to bc used for earth In Appendh IV the authors give a speci- nation with the euth's surface as the sink theznul resistivity is of paramount izn-men calcuhtion for a typical duct-bank has a theznul resistance oE approximately portance and wiH be discussed in more htstaHation and also a similar calcuhtion 25% less than iE the earth's surface was detail later. A few Qlustrations of the for a pipe-type instaHation. In the one the o=ly sink, This would indicate that differenc between the two methods wQI they use a pe of 120 and in the other a the thermal resistivity of the medium is Gzst be given. pe of 80. Would the authors enlighten changed whereas the change in tempera-me on the significance of these two different The Gzst application of the Neher-ture cHstributlon due to the temperature McGrath method which we made was to values for p,. On this point Dr. Wiseman gradient should be investigated. detezznine the conductor size for a pro-stated in his discussion of the paper that he was glad to leam that. we can now base It should be enphasized that the Ken- posed 230-Lw cable instaHation. The cal-nelly formula is applicable to steady-state culated conductor size was 1,500 MCM, the duct-bank calcuhtions on the same basis conditions only. The authors redize this, whereas by the IPCEA-NELA method the of pe as pipe-type cable, but the authors of course, and attempt to ccnnpcnsate for calcuhted size was 1,150 MCM. Some have not done this in their Appendhc IV. this shortmming by applying a cydical 42 mQes of cable were involved in the The use of the Kennelly fozmuh in the loading factor to the external thermal path. proposed project, so the Neher-McGrath practical case of cablet buried in the earth The factor they usc h based upon measured result would have meant substantial extra is at best an approximation. For'the values obtained on direct buried and/or cost for the cable compared to the IPCEA-theoretical case of a heat source in a medium pipe-type cables. Since thc thezznal cucuit NELA zcstdt. that is homogeneous, of uniform resistivity of a duct bank is quite dHferent from that In another tnztazcc, thc Ncbcr MCGzath and temperature, the formula would apply. of direct buried cables, we do not agree method was used to determine the required However, for the practinl case of cables that thh satne cyclical Ioadhg factor (as size of cable leads for a 75.mva trans-in the euth, there is considerable deviation'rom measured on direct buried cables) can be forzner. The calculated size was so large the ideal case such as honunifozzn applied to a duct. bank instalhtioa. as to be considered physicaffy Impractlad, medium, seasonal variation of temperature FinaHy it is pertinent to point out that whereas by the IPCEA.NELA method the gradient in the earth. nonuniform distribu- thc KenncHy formuh is premised upon aH calcuhted size was pzactied. Rather than tion of. moisture in the earth, moisture the heat energy Qowing to the earth' risL possible trouble H the IPCEA-NELA migration, and other factors, which render surface. One must thea ask the authors result were adopted, it was decided to the Kennelly formula more or less inac- what they mean by ambient soil tempera- use aerial bus instead of cable for these curate. Thus in its use one must bear in ture. Theoretiedly at least the tempera- leuis. mind these limitations. of the earth at the cable depth of 'ure In a third case, the cable leads of a 50-In Europe the Kennelly formula has burial is not thc ambient to be used in the mva 13.S-L>'enerator were to be changed OCTOBER 1967 %cher, iVcGraffs 'Tcrrt pcrafurc at:d Load Capabtl Ey of Cable Sys.'crtts 769 < l'~l- 1 $l h C l ~ r' Table XIV. It was necessary to measure Table XY. ThcrnNl Resistances Pertaining the air temperature in an occupied duct. to Test since there werc no empty ducts. The loading on the machine vras recorded and So s>> Eeshsaaee, lfehet 'hermal IPCEh Ezperi-Iz ss ~l2 us,g the current division between the six C pcr Watsrryoos Mcarash Tfgch mensal i cables was detcsmhscd. The maximum departure from equal loading of the two cables on each phase was only 2%. After Znsuiasioa...~........0.73 ..".O.TS 5 days the duct air temperature was 43 C. Shesih so dues....'....1,52,....1.82 Duct wall.............0.13 cn rrs. The ambient ground temperature was 19.5 Duce wall io carsh '1 .'.Qi..'.QI C at the same depth as the center of thc ~ mblen!............8.7$ >>.~...4.0 duct bank, Dividing thc temperature rise Occupied duce air so ~ ~ by 1/6 of the total losses, a thermal re-earth ambient........ ..4.51 sistance of 4.6 ohms is obtained. Table >> Calculased from criuasfoa44(hj usiag p>>~120 C 5 sr ZRsrrzrff, OVCZ nr covcagrg. ZU shows the thermal resistances pertinent cmlwasz. to this case as dctesmincd by the Neher-Fig. 6. Cross section of duct bank McGrath method and the IPCEA-NELA znethod. The expcrisnental value (occuyied the earth resistbrity is taken as 55 C an/ because the associated ~o-Lw step-up duct air to earth ambient ot Table XV) is watt in equation 44(h). It does not sean transfosmcr was being rephccd with a in good agrcemcnc with the IPCEA- likely that the value of 55 is representative 345.kv unit. The existing leads consist NELA value given in "duct wall to earth of typical sail around duct banks. Many of two 2,500-MCM cables per phase ambient" of Table XV, while the ¹her- measurements in several laboratories have>-~- installed in a Mucc bank. hccording to .McGsath value is much higher. The consistently shown that the specific thczma1 1 the Neher;McGrath method, these cables ='-:Neher-McGrath *value should be ap- of earth varies frosn about r'esistivity should be approximately 3,500 MCM each proximatciy equal to the IPCEA-NELA 100 C cm/watt Eor a moisture content. of if thc AEIC allowable temperature of 'F6 C value i! the two methods arc to give the 15%, to about 300 or 400 C cm/watt for is not to be exceeded at full load in sununer same results, as is obvious by inspection of sero moisture content. A value of 180 C tiine. The unit has run at full load for Table XV. The Neher-McGrath value cm/watt seems fairly representative of long periods on many occasions since should be lower than our experimental average conditions. I conclude that the going into service in 1949. If our applica- value, since the fosmcr represents the validity of the ¹her.McGrath method of tion of the Neher-McGrath method is thczmd resistance from the outside surface cdcuhting the thcrznd resistance from duct correct, one'must conclude that the existing of the occupied duct wall to earth ambient, bank to earth. ambient should be desnon-cables have been severely overloaded many while the htter represents this same re- strated by tests whczchs the <<arth thermal times during their service period of 8 sistance plus the thcsmal resistance from resistivity is dcfinitcly known. Have the years. No evidence o! such overloading occupied duct air to the outside surface ot authozs verified their findings by such has been seen; the cables have been entirely the occupied duct wan. tests? trouble-Free. There are toro other units One is not entitled,to say that the dis-RETERENCE at this plant, identical in all respects to crepancy between the Nchcr-McGsath the one described above except that one of value and the IPCEA-NELA value is real t. Caaaaaz Raznros roa Baaczasoc Cosa than has been in service slightly longer, the other not quite as Iong. No trouble unless the value ot the specific thermal reshtivity of the earth ps is the same for nncroaL Anaconda Pssrrsstfen Hi0 BooL Com paar, Zoc Rew edlcfoa, Ocs. 1042. Yes ¹ C4t, McCcaw-Y., erst has occurred on the leads of these units. both. The ¹her-MCGsath value in the It was decided to make a temperature tabulation is obtained when a value ot survey to establish the correct facts. The earth thermal resistivity ps m 120 C cm/watt J. K, Ifcher and M. IL MCGratht We are unit was run at full load for 5 days. Test and thcsmal resistivity of concrete ps~85 indebted to Mr. Baznes and Mr. Golden-results showed that the duct structure are used m equation 44(A} ot the paper. berg for their dscuszions in which they atcaisscd equilibrisun temperature in 24 There has ncvcr bccn asly general agrec- summarize the present cable rating prac-hours.. The bulb of a recording thcsxnom- meat on what value of earth thcsmal tkcs in Great Britain and point out some cter was inserted 20 Eeet in the bottom resistivity is inherent in the IPCEA-NELA diifcrcnccs with hmczicxn practice. Prom xniddle duct. The details ot the duct duct constants. Several years ago Mr. this it would'ppeaz'hat in most respects bank and cable are, given in Pig. 6 and G. B. Shank!in and his coworkers in the the practices in the taro countries are General Electric Company investigated shnihr. While the method ot handhng Table XIY. Cable and l.oss Data this extensively and concluded that the group cable ratings developed by'x; value is about 180 C an/watt. If this Gold enberg may appear to difFer hoax the 2,500.MCM Scgiaentol Copper Condsrctorr conclusion is correct the discrepancy be- method ot the paper, actually both methods Pepcr inzuf4tcd.teed-Sheoshed Solid-Type, twom thc Nchcr-MCGzath result and the arc derived from the same basic prhxciplcs 13.8 Kv IPCEA-NELA duct heating constant is and should give identical results for the real and serious. Our test result cited sazne set of conditions. above does not give any information on To answer their questions with regard Curreas Wa Sic Loss this point because the earth thczsnal re- to tcsnpcrature lnnits and the relationship Cable Daring Teat, Per Boot sistivity was not measured, due to lack of zfo. hmpercs of Cable of this paper to the published rating tables, facilities. we may say that IPCEA, in collaboration If the discrcyaucy is real, one h led to with the AIEE, has under active con-question the soundness of the Kennelly sideration a xevision of the existing current 2.............. 0TS............... 5.13 formula used by thc authors. It is based rating tables based on the methods of cal-on the premise that all heat generated in cuhtion set !orth in this paper. The tem-the cable escapes to tbe surface of the earth. yerature limits wfii be those 5........... ..1,020............... ~ S.T3 Some ccnnpetent engineers have argued chat by IPCEA, AEIC, ctc.. in industry dready'dopted Total 30.50 Per cable average S. 1 part of the heat escapes by another path, spcclfications. namely to a sink deep in the earth. Mathe- Mr. Church has outlined a procedure for Roses: maticd development of this premise gives determining the effect of the loading cyme hmbleat earsh tom peraiure durlag teat was 10.5 C. a result for the thermal resistance between Cables are paired 2-3 for h-phase, CH for B-phase, on cable ratings which will be, we fear, 5-5 for C-phase. duct bank and earth that is only about an cnigsna to znost cable engineers despite D(ameser over <<oaductor, laches............2.000 two-thirds as large as the result by th the fact that ic represents a chdlenge Cotton tape shicxaess. laches...............0.01T Kennelly formula. hccording to this, we to those mathmssatically inc8ned. Mr. zasulssloa thichaess, laches................0.210 might expect the Nehcr.McGrath method Goldcnbcrg also has referred to a different 'lameser over insulation, laches............2.4S4 to agree with the NELA value iE the carch buc nevertheless machcsnatically involved sppcr tape shichaess, laches..............0.003 obeaib ihichaess, inches...................0.12$ thcrznd resistivity is taken equal to 2/3X procedure for doing this. For uorsnal cable Over.all diaescser. laches..................2.T10 180~120 C crn/watt in equation 44(A}. calcuhtions, the crcmmsdous asnount ot h< resissanee at 5$ C~$ .41 (Xo>>) ohms.face It turns out thac agreement occurs when computations required for each individual 7TO 1Vcher, McGrath Terrs perature and broad Capabihty of Cable Systerrss OCTOBER 1951 a a ~ ~ ee 1 ' 0 casi,'is simply not warranted <<ven iE a resultant thermal resistance from loaded 6eld meauraaents had not been carrie digital computer mere available to the cable duct mall to earth ambient of 9.0 for the to a steady state, and that laboratory engineer. worst soil in metropolitan New York and determinations of the earth resistivity were If the application of a particular load 6.00 for the best soiL These values, when not representative of thc soil in situ. cycle to a given cable system is to be compared with NELA constant of 4.9, Also, the appareqt discrepancy (which studied, we suggest that this may be done scarcely confirm Mr. Thomas'tatement to appears because thc direction oE heat Qow more siniply, morc rapidly, and more the effect that the present IPCEA-NELA implied in the Eozmu!a Is toward the surface economically by using an analog computer method is based on or is even closely whereas in summer the total heat Qow in designed for the purpose. We feel, how- rehted to Kirke's work, While Kirke the earth is obviausly in the reverse direc-ever, that the accuracy of thc method given made some attempt to take into account tion) is explained by the application of in the paper as compared to aB exact caI- the configuratioa o! the duct bank structure, the principle of superposition to the separate culations which we have examined, includ- he did not utilize resistivity as such, heat Gelds involved. As a result, cable ing those of Mr. Church, is suificient, par- and as previously indicated we believe that engmeezs, with very fem exceptions, have ticularly in view of the fact that any par- a knowledge of this and other parameters accepted the formula for cakulations in-ticular load cycle may never repeat itself. ignored by Kirke is essential to a realistic volving pipe-type and directly buried The method given in the paper is an method o! handling this problem, par- cable systems. The method of handling approximation, admittedly, but it has been tlcuhrly when one considers the problem cables in duct, given ia the paper, is a derived from the same fundamental prin- of comparison between different types o! logical extension of the priaciples under-ciples which underlie Mr. Church's method + steals. lying the Kennelly fozmuIa in order to through a series of careMIy considered hs Mr. Thomas has suggested, the heat include in the calculations tmo very im-simplifications. It should be understood Qom in a duct structure is complex, but this portant variables which are not a part of that there is nothing sacred about. the value complexity results from the superposition the NELA-IPCEA.method, namely the of 8.3 inches used for the fictitious diameter of a number of heat Bows any one of which, duct. configuration and the thermal Dc. This value happens to be the best due to a particular cable, is readily deter- sistivity of the surrounding soB. This single value to use based on the studies mined as indicated in reference 12. We are method is also not new. It mas Gzst described in reference 3. For Mr. Church's not interested in these heat Qoms frcr zc, described by N. P. BaBey ia a paper in case values of 7.1 for thc 75% load factor but only in the resulting temperature 1929'nd subsequently ia reference 13 of cycle, and of 5.1 for the 60% load factor difference betNreen a reference cable and our paper. cycle are indicated. The errors in using ambient and the corresponding thermal Mr. Short also mentions the two-thirds 8.3, however, amount to only 2 and 5% resistance which is fully expressed by the factor, another resurrected ghost of the high, respectively, m the conductor loss relatively simple equation given. True, past. Long'go the British established component of conductor temperature rise, the situation is complicated by the concrete that the two.thirds factor represents a which would be offset by a 10% error in envelope, but here extensive studies, both diffezence between laboratory and in cits the value of earth thermal resistivity ein- mathematical and on a Geld plotter, in- measurements of soil resistivity and that it ployed. dicate that the equation 44(A) is sufii~ does not stem from any lack of applicability Dr. Wiseman's conunents in this con- ciently accurate in view of the inherent of the Kennelly formula to the pzablezn. nection are most interesting since he has errors in Gxing the earth resistivity and Numerous British publications point out often expressed the opinion that, prac- loss factor in a particular situation. that the tmo-thirds factor is not to be used tically, it was sufiicient to consider Dc to Mr. Short, at the start of his discussion, where the resistivity is measured in sits be equal to Ds, or in other words to apply states in effect that he considers the method by buried sphere or by long or short cylinder. the loss factor to aB of the earth portion for determining the load capability .of In addition, in recent years the British oE the thezmal circuit. We can agree direct earth-buried or pipe-type cable to have developed a new laboratory sampling with this in respect to pipe-type cables, be "mell founded" for a 100% load factor procedure'hich checks not only with but, as he has indicated, we do not consider but, because of questions raised by various the buzied sphere, the buried cylhider, the this further simplification desirable in investigators in reference 3 of our paper. transient needle, but in addition also the case of small directly buried cables. does not seem to be too sure, that this is checks with results obtained on loaded Neither do we consider the forznuia which the case for other load and loss factors. cable installations. he gives for obtaining attainment factor hll four investigators mho undertooL to Another ghost mentioned by Mr. Short directly fram loss factor suitable in this itudy the problem for the Insuhted Con- is the deep isothermal approach (a proposal case. This is readBy apparent fram Fig. 2 ductor Comniittee, however, are on record which mas Grst suggested by Levy in af the Grst paper of reference 3 in our the de Kus, Sandiford, and Camezans 1930)'iting as recommending or agreeing to the method paper. Since the use of Dc has considerable given in the present paper. In accepting paper to give new life to this old suggestion. theoretical justification in our opinion, we the given method for buried and pipe-type However, in so doing Mr. Short faBs to feel that it should be made a part of the cable, Mr. Short does not seem to realize point out that the deep Isothermal in this general procedure Eor calcuhting the effect. that this method is based on the Kennelly case consists of a conducting paint electrode of the loading cycle. fozmula because in the latter portion of his of an analogue model connected electricaliy The introduction of an additional thermal discussion he questions thc applicability to another electrode representing the resistance to care for surface effects be- oE this premise to current rating determina- earth's surface and hence simulating a tween cable and earth is an entirely differ- tions for any type of underground instalh- lfrruiing (not stationary) ground water ent nutter since this will increase the tion, and proceeds to attempt to resurrect sink, a somewhat unusual condition that temperature rise both for steady and for a nuinber of the ghosts which plagued the is scaredy pertinent to the problem at cyclic loads, whereas the use of D> is Insuhted Conductor Committee some 10 I hand. Incidentally, Table of this paper intended to give the correct result for cyclic years ago when the latter started worL: an gives results of an excellent analog check loads on the assumption that the total a critical review of the basic parameters of the given method as applied to a duct thermal resistance in the circuit which is involved iu load capability calculation. bank. unchanged by the value of Dc is correct These ghosts were subsequently hid to We wish to assure Mr. Short that we for steady loading. It is quite possible rest, at least to the satisfaction of the vast have not cornered the nonferrous metal that such a surface effect term is present nujority of engineers in this country. market, nor are we saymg that three and that it may attain an appreciable Even at that time the Kennelly forznuh single~nductor cables of a given size magnitude in the case of small directly had been in existence for over 50 years. insuBed in a buried pipe must have the buried cables. We concur in the hope Despite the fact that this fozmuia is based same rating as three conductors of the same that this matter wBI be investigated further. on scientific principles found in most text size Installed in separate ducts. We Ivfr. Thomas has noted the pioneer work books on physics and electrical engineering, should point out, however, that this has of W. B. Kirke in connection with cable some cable engineers had misgivings as to been a rule af thumb for the past 10 years in duct and indicates that this worL: formed its applicability mainly because calculations or more and there are now many zniles af thc basis of the present NELA-IPCEA by it did not appear to checL with measure- high. voltage pipe cable in successful service method. Employing a duct bank con- znents in the Geld. This situation is dis. which are rated and are being operated at a Gguration such as shown by Wollaston and cussed in reference 12 of our paper wherein load capability level which Mr. Short utilizing equations 14 and 17 of the Kirke it is shown that the disagreement was not considers incomprehensible. article, we Gnd that Kiri:e would use a due to the fozznula but to the fact that the Mr. Short's dilemma results solely from OCTOBER 1957 Nchcr, hfcGratli T'crnpcraturc and Load Capabih.'.; of Cable Systcrnz 771 ~ - eat 'd'i lt o the Eact that he is attempting to compare account more properly the essential param- an unpublished 1947 memorandum by the r,cults of calcrdations made under a ~ eters which are pertineuC to the case aC G. B. Shanklin, that a resistivity of 180 is set of assumed conditions with the results hand. representative of average conditions; conse-of a procedure for which those same condi- With respect to Mr. Short's speciflc quently, the value of 55 which was obtained tions are not stated and in fact are unknown.~ ~ question, we hope that utility engineers by back calcuhtion from the given method ~ This Is a situation which existed imme- mill,adopt the proposed method but we do utIHzing his test results indicates a dis-cHately EoHowing the waz and is one of the not think that they will Gnd it necessary crepancy ia the method. We believe that ghosts previously nzentioned. Conductor to reduce loads unless they have very high if Mr. Wolhston wiH consult somcrs of size determinations for cable in duct values o! earth resistivity. Regarding the the many references which have appeared utHizfng the NELA constants require no need for reduction in loads on existing in the technical litemture over the past knowledge nor consideration o! soil re- drcuits, iC should be kept in mind that few years on determinations of soil re-sistivity as such. On the other hand. such it is only rehtively recently that AEIC sistivity h connection with experimental determinations for pipe-type cable systems spedflcatfons have made provision Eor duct bank, buried cable and pipe-type cable by any practical method require a speciflc Increased permissible temperature Hmits InstaHations, either alone or in conjunction numerica assumption to be made as to Eor emergency periods, and for the greater with buried cylinders, spheres or transient the value oE soil resistivity in order to anive portion of the period that these emergency needles, that he will Gnd that there is no at an answer. By taking the stand that limits have been in efect the nuznber of longer any justiflcatfon for an Inferred the concealed resistivity in thc NELA companies who have utiHzed them is resistivity oE the order of 120 in the NELA constants is 120 oz'ore, iC is thus possible relatively smaH. As a result, the greater constants or for his impression that a re-to obtain, an advantage in favor of duct-Iay portion oE the cables now in service have" o sistivity of 180 is representative of average cable. been sdected on the basis that normal conditions. Furthermore, because oE the use of cable ~ permissible copper temperature would not, In as much as no actual measurement was spacing factors and earth and concrete be exceeded under emergency conditions. made of soil resistivity at the sIte at which thermal resfstivltles in the proposed method, Moreover, in recent years a number of Mr. WOHaston obtained an indicated value it mill be obvious that calcuhtions by the ass zsfra measurements have been made with of 55, there are, of course, several possible given method will check with those of the the tzansient needle, the sphere, or the explanations that suggest themselves. As-IPCEA method only for certain combina- burie cylinder. Theoretical studies have suming the tern peratur'e measurements tions oE the variable parameters in the shown that measurement of ultimate soil werc made accurately. perhaps the soil methosL Since these parameters were not resistivity can be obtained readily vrith actually had a resistivity of this order of Gxed and in Fact are now'nknown as re- such devices. WhHe in many cases these magnitude. From recent studies on soils gards the NELA duct heating constants, have been made in connection with pipe- and the effects o! such matters as composi-it is obviously hnpossible to make a factual type cable instalhtions, they apply equaHy tion, density, compaction, particle size, comparison o! the results obtained by thc weH to duct bank instalhtions in so far etc., it Is evident that it is very difGcult two methods. Here again, by assuming as the resistivity o! the soil itself is con- to estimate the resistivity of a soil fronc earth resistivities oE 120 or 180 as both Mr. caned. The values in general range fronz appearance alone. Alternatively, it could Short and Mr. WoHaston have done, thc 50 to 100 with some higher values as the be that the measured value of resistivity given method wHI result in hrger conductor exception at certain times of the year. is not the ultimate value as a constant load sizes than the IPCEA method. Moreover, over the past decade a number applied for 5 days would not suflice to bring Despite the Fact that both Mr. Short oE pipe type InstaHatlons have been in- the duct structure to its ulthnate teznpera-and Mr. Thomas refer to the presumably staHed in this country with design re- ture rise over ambient, unless, o! course, large amounC of Factual data which underlie sistivities in the 70 to 90 range. Under it bad been canying substantially fuH load the NELA duct constants, we have been the circumstances, we do not believe that for some thne prior to the test in question. unable to ascertain the specfflc'conditions it will be found necessary in most cases Mr. Wolhston mentions that the tempera-on which these constants were based nor to reduce the loads on existing circuits. ture was measured 20 feet from the nzan-is there any indication Chat earth resistivity However. we do believe that engineers hole but does noC indicate the length of the mcaswements were taken as a part of the mill be well advised to take steps to ascer- duct zun orf which the test was conducted. data. About aH that can be done, there- tain the valuei o! thermal resistivity which This raises a question as to vrhether in his fore, Is to assume representative cable and are applicable for their conditions because particular case, there could have been any duct conflguzations and then to caIcuhte with the more liberal use of emergency aHeviatioa of temperature rise by longi-the earth resistiviCy required in the given temperature limits and the tendency for tudinal heat flow or, alternatively. by longi-method to match thc value calculated by shiEC in many areas in the load peaL from tudinal convection effects such as were the IPCEA method. We cannot agree winter to summer, the existing margin may Found in the tests made with ducts open to the values given as "the average condi- be reduced to a lovr level hc the not too and tions on which the NELA duct constants plugged.'s distant Euture. ~vere obtained" as stated by Mr. Short. The values of soil resistivity of 80 and Rather, vre believe that the conditions 120 used in the examples of Appendix IV psasscss assumed in reference 18 are much more were chosen merely Eor purposes of iHustra- 1. HsAT Paow roose UscosaoaoUND Etscralc representative, on'the basis of which an tion and the value of 120 rather than 80 Powso CAsass, Neil P Baser, AEEE Troar average earth resistivity of 75 was obtained ocrroer, voL 48. Jao. 1020. pp. 15&45. was used in thc duct Iay case in order to at 100% load Factor. emphasize the effect of a difference between 2. hN EvAAUAcrosc ov Two Rarro bfavsroos ov We take the position. therefore, that hsssssQco zsrs TosaMAl Rssrsrsvtvv or Soral the resistivity o! earth at 120 and concrete W. Marcosrsrd, E. blochrrar rcf. /o reer, the validity of the proposed method is not at 85. lascrcncroa ol Elcccri<<al Eazlacers. London. to be judged by whether or not the calcuh- Unlike Mr. Short, Mr. Wolhston is very Eacland. vol. 103, pt. h, no. CZ, Ocz. 103d, p. 433. tions made by it using parameters arbi- careful in his discussion to make it quite 3. CAsan Hoarrsco Uc Uscoeaoaoowo DUcrs. trarily picked by Mr. Short (or by Mr. dear that his comments relating to a R. D. Levy. Ccacrer Erccrrlc Ecvrcsc, Schcncccadrr Wolhston) agree with calculations made BL Y., hpr. 1030, p. 230. comparison of the results obtained by the by the IPCEA method. Rather we feel given method and the NELA-IPCEA 4. See reference 2 ol Mr. Shocc's drscnsslon. that the applicability of the IPCEA method is preznised on his own arbitrary S ToktoaAcnao Rrso Aoo CUaaoscv Ravnco method to a particular case depends upon assumption of a concealed soil resistivity or CAsass LArn'sc DocTsz E Bo Wedrnote> E Eo how well it checks with the method which Horchlass, Rcporr, Rr/rrcrrcc P/T los, The of 120 in the NELA constants and on bis Bclrlsh Electrical aod hrricd industries Research we have proposed, and which takes into impression, presumably based hrgcly on hssoelacloa, Loadoa, Eazla'ad, 1035. ""2 Ndhdr, sVcGraffi 7drrrsrrr!Urn Ter> Crrsntrr:rsr nr / nln Vvrlrmr r v n rs o cr 1 rr X 7 THXS PAGE XNTENTXONALLY LEFT BLANK 1 ~

• C i I 0 ~

e tive magnitudes of the terms, and the The Thermal Resistance Between Cables corresponding values finally employed <>. with suflicient accuracy over the entire sequent analysis and development i>>ill be ever, when calcuhting a cable rating, with working range. facilitated if this equation is written in a fixed copper temperature of the order of The theoretical relationship for the the equivalent form 70 degrees to SO degrees centigrade, th>> case of cables in duct was recently pre- 0.092 CsT'/sP range of this variable is very small, and Q sented in a paper by one of the an accuracy of the order of 3 per cent tn > Ds "/'(1.39+Dr'D4) /'s'aT authors.'n the present paper this rehitionship has per cent may be expected. 0.0213 been extended to cover oil and gas pipe , +0.102c(1+0.0167Tm) In the case of equation 2, the conduc. systems as tvell, and from the test data D,'og D4/Ds'atts presented the requisite working expres- per degree ccntigrad>> foot inch (1A) Paper 50 Sz, reeommcoded by the AiEE sions for thermal resistance or surface re- From the method of derivation which lated Cooductors Commsttce aad approved sistivity factors have been obtained. the Alas Tcchnical protram Committee ior assulnes a coaxial arrangement of the at tbc hlEE Winter Qcacrat hfcctinc. pres'otatioa cable within the duct or pipe, the numeri- He>> YoA, H. Y.. January 30.February 3. I93". Sfaauscript subcaitted October sl. t949: Theoretical Considerations cal constants of the first two terms oi available ior priories December y, 19t9. equations I, 1(A), and 2 must be con- F. H. Eot,tca is <<ith tbe General Electric Scbcoeetady. H. Yand J. H. Com'aay. The theoretical rckitionships given in sidered as being approximate only. They <<ith the philadelphia Elcetrie company. Appendix II of reference 1 for the case of will serve, however, to evaluate the rela- Fhna'elphi ~, Pa. Btdlcr, iVchcr Thcrnrcf Rcsislancc AIEE TEAishc TtoHs r Table l. Test Data on Gas-Riled Pip>> Type Cable Systems and the General Cable Corporation. These data are plotted in Figure 1 and the values al'/ 7'/ Teat Itumber Source D'r p Q a7 i' Q a'7 D,"I of a and b in equation 3 are established as a~0.0?0; baeOM. Table II presents similar data for I.....Detroit Bdlsota Compaay....3.42...8.07... I . ~ .23.4...20 ...$ 2....0.34......1.$ 8 cables in single dty fiber and Transite 7.8...27.3...15.8...$ 1....0.51......4.08 14.8...28.8...13.1...$ 1....0.84......5.34 ducts in concrete taken from the 28.9... 17.1...50....0.49......5.71 Barcnschera and Johns Manville tests dis-28.9... 14.4...$ L....0.59......$ .48 27.5...14.0...51....0.$ 8......$ .43 cussed in reference 1. These data also are 2.. .Ceoerai BieetrieCompsoy...3.92...8.07... 1,7... 7 3... 8.2 .,39.. 0.30... I.d4 plotted in Figure 1 where it will be seen ~ ~ Il.i" . 9.T...4$ ....0.30......1.83 IS.2... 12.4...50....0.31......1.73 that the Transite duct points fall on the 7.8... 8.8... 4.7...39....0.37......2.92 11.5... T.0...43....0.42......3.22 gas in pipe calve, but the fiber duct 14.9... 8.9. .4S....0.43... ~ ..3.42 ~ points result in a different curve having 11.2... 5:8...40...;0.49..'.::;4;22 "" the same value of a~0.07 but 5~0.10. 1$ .9. ~ 8.0...4$ . ,0.$ 1 . .4.$ S ~ ~ ~ ~ This difference may be explained by the 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 'able fact that the duct wall departs from an isothermal as a result of the relatively high thermal resistance of the materials 1L Test Data on Cables ln Rber and Trantlte Ducts Encased ln Concrete used, that of the dly fiber being consider-ably higher than that of the transite.'he test data for oil-filled pipe-type Test Itomber Source D l D,'Dr Q al','al'I Q a7'I 7'I cable systems from tests by The Detroit Edison Company,'he General Electric Company, and the Okonite Company are 5........Bareoseher........Fiber.......o.d9....3.S .... 1.0.... d.4.....0.228........1.T4 presented in Table III and plotted in 1.7....11.8.....0.203........2.03 2.5.. ~ .IS.L.....0.235........2. LT Figure 2. In this case, the analysis has 4.4.. .24.8.....0.25T...... .2.44 S.d....34.2.....0.281........2.SS beenmade by plotting the observed values 8.1.. .39.T.....0.295........2.78 of 12.3.. ~ .Sd.1.....0.318........3.00 .... 1.0....

1. 13....3.5 4.$ .. ~ ..0.20l 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 ~ .......1.41 y~ CDT 'itainst x~DQ"i'CaTi'Tea '5) 11.0.. .32.8.....0.300. .....2.32 ~ ~ ~ 14.8....48.S.....0.288........2.82 and results in the values of am0.026 18.8....$ 2.4.....0.28$ ........2.dl 18.4....S8.7.....0.278........2.89 b ~0.60 in equation 3. 3.13....3.5 .... 0.9.... I.d.....o. 194........0.S4 It will be seen from the analysis of the I.T.... 3.2.....0.173........1.00 2.4.... 3.8.....0.203........1.0$ test data that the agreement. between 4.5.... 7.7.....0. 188..... .1.75 ~ ~ theoretical and observed numerical con-8.1....12.1.....0.213..a.....1.40 )4.8....21.9.....0.217........1.53 stants of the simplified convection term is 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 ~ ~ ~ ~ ~ ~ extremely good in the case of oil as the LT.S....21.7.....0.238........1.$ 9 medium, but in the case of gas, the ob-T........Johns-MaosiILe.... Traosite....3.38....3.88....1d.T....18.9.....0.292........1.50 19.8, 19.4.....0,299.. .... 1.$ 5 served value of 0.07 is somewhat higher 23.3....22.0.....0.314........1.50 than the expected value of about 0.046. 2d.4....24.$ .....0.318...... . I.di This is rather surprising since tests num- ~ ber 2 (with gas) and number 9 (with oil) which are consistently dose to the es-tion term constitutes about 24 per cent of the numerical value of the denominator tablished curves in Figures 1 and 2 were the total for a typical oil pipe installation. omitted is in the order of two. ActuaUy made with the same physical setup which Variation is more important than is the the test datC was analyzed both with and remained unchanged throughout the case with the gas.pipe cable, but is still without this simplification, and no ap- tests except for the change in the media within tolerable limits. parent change in consistency in the re- employed. Therefore, we should expect One peculiar phenomenon has been ob- sults was observed. the ratio of values obtained to be the served. The ratio of DJDQ', which ap- same as the ratio of the numerical con-pears in the conduction term aIso, ap- Analysis of Test Data stants of the convection terms in equa-pears in the first {convection) tenn of tions 1 and 2. equations 1 and 2 but in such a way that It follows from the preceding discussion This discrepancy seems to be due to the a change in this ratio produces an oppo- that the test data for cables in duct and fact that in the case of several cables site, though lesser,'ffect on the total for gas filled pipe. type installations may within the pipe, a condition of the major-value of these equations. A minimum be analyzed by plotting the observed ity of test data, there is an additional cir-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 values of Q DD'II?" 'gainst . x~ CaT'I'pV'~ D ID/D (4) 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 procedure will simplify the convection The data given in Table I were compiled apparently not effective when a more tenn but it will have the effect of approxi- from tests on gas.fille pipe. type cable viscous medium such as oil is employed. mately halving its numerical constant as systems by The Detroit Edison Com- As indicated before, however, a high compared with equations 1 and'2 since pany,'he General Electric Company, degree of accuracy is not required, and it is 1960, VoLUME 69 Brtllcr, Nchcr Thcrrrral Rest'slancc 343 R, ~ 4 Table lll. Test Data on Oil Filled pipe Type Cabfc Sysleras p Fpa'(Gber) 0.00411 ,+0.33thernial ohm Tost lratabor Source D 'a 0 4T T 0 ol',/doT'/dT /i D,'eet (12) in which the second term represents the S.e" o .rietraiae ~ . e ~........ ~ ~e ~....4.83...8.07" 25.2.. 8.0....40....2.04. .~...e194 o ~ difference in thesmal resistance between a S.S.. 0.....o.Ceaerel Slleetrio CogaPsay...3.02...8.07 ll 4 3.0....37....2.19..eo.... ~ ~ ~ ~ e 4 5... 44.. .2.55. ~ ~ ~ ~ e ~ $5 50 4-inch fiber duct aad the corresponding lb.5... 6.8....48....2.88........ 70 section of concrete which it replaces. 10.......0boaire Cogapeay... .....4.50...5.13 0.4 '. 4.1... 2.$ ....25.... 1.55...... 43 4.4....31....2.14...,.. . 58 0.4 .. 5.4....21....1.75... ..., 53.$ Discussion of Values for Cables in ~

l. l... 7.$ ....38....2.81..... .. 70 ~

21.6... 8.8....41....2.45... .... 8$ .6 ~ Duct 3$ .2... 11.4....50....3.00........105 34.9...11.7....48....2.08. . .132 It wiH be seen that the method of de-termining the thermal resistance between felt that a working expression based on v ~ ~ L ~ a 'able an'd duct presented herein differs the foregoing analysis mill be sufficiently Ka'(QDg" Tm')'+24 somewhat from the method given in accurate. reference 1, although the results are sub-feet (ll) stantially the same for terra cotta and Worhing Ezpressions = - The value of p from equations 9 and 10 is fibre ducts. For Transite ducts, the -'n plotted in Figure" 3 as a function of values of thermal resistancI: derived in a formulating the thermal resistance (Q'P/Dg')' and the, value of Z,c from more fundamental manner in the present between cable and duct, it is customary to equation ll appears in Figure 4 as a paper, are slightly lower than those express this resistance in terms of an function on (QD,"T')'. Also indi- appearing in the reference, being equal to equivalent surface resistivity factor, as- cated on these figures are the values'f those assumed for terra cotta. suming that the entire resistance was these parameters for typical conditions. it will be reoaUed that the reasoniag concentrated at the cable surface, accord- In the case of cable in fiber duct, the used in developing eigebraio eapressions ing to the expression thermal resistance of the duct wall is for these, va ues assumes an isothermal appreciable and should be accounted for. duet wall. The test data presented in p This is most readily accomplished by Hgc 0.00411 , thermal ohm feet (6) Dg'n modifying equation 6 to include this re- Figurc 1~ Analysis of lest data for cables in which p is expressed in degrees centi- .sistance. Thus duct- and gas@lied pipes grade square centimeters per watt. Since a7 Hgc~ chT//Q it follows from equation 6 that p 243 Dg'chT Q degree centigrade centimeter 0 per watt (7) and 4T '~0.253 pl/tQI/d /, (degrees centigrade)'/'8) os It is thus possible to develop working ex-pressions in terms of p in the case of ~ 4 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 Os oT

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 oR p / / d e gre e s c e n 1 i p/e Q i g +$ 7 D,'rade square centimeters per walt (9) For cables in other types of single dry p p .,/,,/, /'11.3 13,700 degrees ccuti-0 0 D,'rade square cciitimclers per walt (10) ev'r" For cables in oil.filled pipe p,v Bullcr, Ãchcr Thermal Rcsisksncc A,l EE 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. ilia the 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. '.;.It follows therefore that a considerable tion in P for cables in single-fibre ..may be expected depending upon p 8 .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 0 ca foi single ducts to the case of cables Q.T .;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 ducts in concrete corre- 'riuitiple-fiber "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 limits under 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, 0 lo '0 so 40 so Co 70 eo 90 00 no lao l30 X": nclusioas 0','T~ T t":.~The theoretical relationships between 'various quaatities involved in the eQee- Appendix l. Theoretical Figuic 2. Anclysis of lest cfctc for cc6lcs in of Thermal Con- oil4lfccf pipe ,:thermal resistance between cables and 'evelopment

surrounding single duct or pipe have been ductivity 6etween Concentric

'eveloped ia a manner which properly The phenomenon of convection involves 'ts for 'the simultaneous modes ol heat Isothermal or Oil as Cyclinders with Gas the!ntervening Medium the conception of the temperature drop cr by convection, conduction, and being conccntratcd in two films, one at the tlon. surface of the cylindrical radiator of diame-ter substantially equal to the diameter of the I .'Ily means of these relationships certain The mechanism of heat transfer between a radiator D, in inches, and one at the surface test data on cables in duct and in gas- and cylindrical radiator and an enveloping iso- ol the enclosing isothermal surface which will 0:od.fiiled ~ . pipes have been analyted and work. thernial enclosure through an intervening be considered also being cylindrical of g,curves are'. presented for determining the Quid medium is such that a portion of the diameter Dc. The following formula based 'resistance lor any particular case ~ total heat Qow Q is carried by convection on McAdams'equation 42, page 251, 1st .. maY be encountered in practice. Q<<, a portion by conduction Qrc, and thc re- edition only) is applicable to either film. .~j'-'Under typical conditions representative mainder by radiarion Qi. ln fOrmuhting . es of the equivalent surface resistivity the components of thc thermal circuit. Q<< ~ 12"DI 'GATI'I'Kwatts pcr foot (14) 4 for use in equation B are 800 degree thcrcfore, it is morc convenient to <<ork in in which DI ic in inches, and ( ') ,.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-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 ~ /d'c gh -) i' watts pcr centimeter '~'c-at 200 pounds per square inch, and 350 across the circuit grees centigrade '~'15) Ies in oil fillcd pipe type installation. tative values of IS for cables in dry fiber ducts will vary from 850 to Q aT Qcr watts perdegrcccenti-Qcc aT + aT + aT Qi Thc significancc ol the components ol equation 15 and rcprcsentativc values lor 100. gas (air or nitrogen) and Suniso number B oil 'grade foot (13) are given in Table lv. ~..'Vot.vwit GO Bullcr, IVchcr Thcnnal Rcsisfancc 340 Mf J, ~,'\ gooo g Iaoo TYPICAL, OF CA81 E IN OUCT a IO P<<l u IL5 1100 BLE I N FIBRF OUC doe 243 Nsd Os ~ eeoO 4 I Ised/Og+.33 ~a CABLE IN PIPEs OF oa. FILLEO PIPE EAAA COTTA ANO 1w2$ cy <<4.$ T v'S 0 TAANSITE-OUCT aoo 20 40 40 oo goo uo lao goo goo goo rgo 240 Zoo taiy,s Ts>'A LE IN PIPE TYPICAL Of CAS FILLE PIPE AT 200 P. 5.1, Values ol p foc cables in dcy single dgccfs and gao-filled Figure 3 (left). 2S Os 4.$ pipe Rgure 4(above). Yafueo of Hga for cables in oif-flllecf pipe 0 Le x,a,o,a J.o xa 3.4 la aa L4 Ao aa 42 ~ 4.4 ~ ao Aa

• x 44 2 4 ao expressioa for the resistance between two 24 3.4 s ~ SO 4.2 fo"P/0; l'* concentric cylinders in terms of the dimen-sions of the cylinders and the thermal re-sistivity of che medium mill be used. Thus In the case of air or inert gas, these physi- The solution of equation 14 for the two

'aas ( 011CL4LC40gra cal propesties are substantially independent 6lms ia series and mith equation 16 or IS Q 0 0213 (gas) per degree of temperature over the working range but substituted therein is given with sufficient dT loggo Dc/Dc the density is a direct function of the accuracy by the expressions centigrade fooc (21) pressure. Thus, if P represents the prcssure in acmospheres, from equation 15 Qcr dT (gas) m0.092 Dc dT'/'P' watts pes de-Qcgr 'goal). 0.116 walls par degree Kcaa0.000755P'/'atts '/'l6) per centimeter centigrade '/'egrees 1.39+Dc/Dc grec centigrade foot (19) dT loggo Da/Dc centigrade foot (22) When oil Is employed as the medium thc The radiation component with gas as the physical constants are substantially inde- medium is given with sufficient accuracy by pendent of prcssure and tempesatures with the following expression based on McAdamss the exception of the viscosity which for the degree centigrade foot (20) equation 5, page 61, Gsst editioI), type of oil cornrnonly employed (Suniso I 0 cNIAc~~ number 6) may be taken as varying in-versely as th>> cube of the temperature ac-From a theoretical standpoint the ex. pression for the conduction component d1 (gas) aa0.102Dgc(1+0.0167Teg) watts cording to the rehtionship should take into account any eccentricity between the cyiindsical radiator and the per degree centigrade foot (23) 94,000 enveloping isothermal enclosure. In the in which e is the emissivity coefficient of the grams per ccncimetcr second (17) practical case of cables in duce or pipe the surface of the cable and T<< is the average cables will not rest uniformly on the bottom tenlperature of the medium. The radiation The value of K for oil thus becomes of the duct, and also in the case of a non- term is ineffective cohen oil is the medium. metallic duct the duct Ieafi is not strictly The over.all thermal conductivity is ob-K~ 0.000434Teg'/'accs per maintained as an Isothermal. Since these tained by substituting equations 19, 21, and centimeter'/'egrees centigrade '/'18) effects cannot be evaluated, the familiar 23 or equations 20 and 22 in equation 13. Table IV Appendix IL List of SymI3ots Q~totaf heat floggr from equivalent sheath Symbol Quaaiity Oaa al SO C OllalsOC to duct wall or pipe in watts per foot d7 aw temperature drop in degrees centigrade p........... Tbcrcasi resiscivicy...........,........C cm/<<atc....... 3 900.......... .TIS ~ ~ P aa prcssure in atmos pheres ga.......e...Average absolute viscogicy.............grains/cm scc....., 0.000l95........0.75 a ..~........ Deasicy.. .grams/cmg ......, .. 0.00l'lo P.......0.904 D, ~diameter of the sheath ininches Cr. ~ ~ ~ . ~ ~ ~ ~ ~ Specific bess ac coascaac pressure......,<<acc see/C....... ~ . 0.99S ~ ~ .. . ~....2.IO ~ Dc'<<equivalent diacnetcr of a group of graga cables in inches S........... Aeeeleratiaa due tO gravity.......... Cm/SCC1...........990. ~ ~ . ~ ~ ~ ~ ~ ~ .990 Da ~inside diameter of chc duct wall or pipe r.s......, .. TIgcrgnal eocil'ieicnt oi cpaasion........ I/C....... ~, ~ ~ ~ ~ ~ ~ ~ 0 OOSIO. ~ ~ ~ ~ ~ ~ ~ .0.00008 in inches Buflcr, /I/cIIcr Tr'crrnal Rcsisfancc 3, I EE TILAwsAcTIo85 T~'~averag>> t>>mperature of the medium in picture. the thermal circuit for a single- probable range of ig, for a particular case, degrees centigrade conductor cable in air is given in Figure 1 of will be better understood, Lh>>reby making coefficient of emissivity of the cable.sur- the discussion. possible more realistic comparisons. The face In this Ggure, iso, l,a, and ra are tempera- authors chrify our conception of the dfect r and y~rectanguhr coordinates tures of copper, sheath, and ambient. re- of the various parameters involved in the temperature drop between cable surface and a and b~>>xperim>>ntally determined con- spectively, 8 is insulation thickness, p is stants thermal resistivity of thc insuhting material, duct or pipe walL For a given system of H,a ~thermal resistance between equiva- sf z, is the log mean area of the fnsuhtion for cables in duct or pipe, the th>>rmaf resistance lent sheath and duct wall or pipe in ther- heat Gow, s(sa is sheath area, and fic and will decrease sensibly with increasing watts mal ohm fe>>t igs are the cabl>> engineers'erms for "sur- loss. Hsa'~equivalent thermal resistance be- face resistivity" for free convection and W. B. Kirk>>iintroduced this modiffcation tween equivalent sheath and Gbrc duct radiation. Each fraction in thc Figuri is which is taken into account in determining wall including the increased tb>>imal re. thc th>>rmal resistance; and when resist- cable ratings for the Consolidat>>d Edison sistivity of the duct wall over that of the ances and temperatures arc known, the heat systcfn surrounding mediuln in thermal ohm feet dissipation of the cable is known. But in As one follows the assumptions made in J)~equivalent surface resistivity factor in order for the resistances to be dimensionally this paper, there appear various points to degre>>s centigrade square centimeters per consistent, th>> dimensions of p must bediffer- which exception. might be taken .on the watt ent from thc dimensions of l), and therefore ground that they are not substantiated, sI ~ thermal resistivity in.degrc>>s centigrade p and ff should not be called by thc same for exampl>>l the assumption of the same cciltlnic'ters pcf wa'tt nanlc constant in the expression for the convection absolute viscosity in grams per 'verage Since the d>>Gnitlon of p as thermal resis- Ghn at (he cable surface and at the inner centimeters second tivity conforms to ASA standards, it might duct wall, the treatment of conduction on 8~density in grams per cubic centisneter bc better to denote ll as th>>rmal resistance thc basis of a concentric system, and the C~speciffc heat at constant pressure in of a unit surface. Its reciprocal h, is de6ncd arbitrary assumption of an cmlssivity co-watt seconds per degree centigrade gram as surface heat transfer coclffcient, or alter- >>fffcient of the cable surface of 1.0. Yet, g acceleration duc to gravity in centimeters natively as surface Ghn conductance. The the important point ls that putting all of per second squared concept of conductance is particuhrly ~ these various assumptions together in the c~ th>>rmal coefficient of expansion in centi- applicable here, as the total Glm conduct- particular form given in the paper, the over-meters per centimeter degree centigrade . ance is the sum of hr and hc. and therefore all end result does produce expressions which E~a factor dependent upon the physical numerically easier to handle. are reasonably satisfactory. constants of the medium in watts per The units of length used in the paper seem It is unfortunate that, while the basic c>>ntim>>t>>r'ia degrees centigrade'<<. to be a mixture of metric and engineering equations and the selection of parameters a units. A combination of square centi- hard a reasonably sound theoretical basis, meters with feet has no logical basis. If any the Gnal working expressions given are References cable dimensions were expr>>ss>>d in centi- essentially empirical and do not allow an meters, the mixture lvould bc logical al- accurate determination of the separate 1, TNR TaxtRRATVRR RIRR ot CARO'Rs IN A Dvcr BANC, J H. Licker. AlEE Transassions, volume though not standard; but since dimensions effect of the three modes of heat transfer. 08, part 1, 1049, pages 840-40. are not so expressed, it seems time to aban- On the average, the calcuhted values of

2. HRAT TRAicsaisstoN (book) W, H. Mchdams, don this practice and use the engineerin QfcaT for the oil-6lled pipes, gas-611>>d htcCsaas.Hill Book Company, )re>> York. Lc. Y., system of units throughout. pipes, and cable in duct are about 5 per cent dsst editloo, 1033. It is therefore proposed that the AIEE 15 per cent. and 55 per cent higher, respec

3. TIIRRNAI CRARAcraatsTIcsoF A 120 Vv Cominittee on Insuiat>>d Conductors take tively, than the measured vahtes given Gas.PIu.ao CARI R lnsTAt tATICN, HICII'aessvaa steps to p>>rsuade its adherents to become I, II. and IIIof the paper. Special- 'ables W. D. Sandcsson, J. Sticker, M. H. Mcasath. ists in the 6eld of cable heating would be AlEE 1 raasassiaas, volume dT, Psst 1, 1948, pages familiar with ASA standards and to use 487-08. them <<here they apply. interested in knowing which component or

4. A Srvor ot TKR TaiitaaATvae Dts'salsa components are responsible for these dis-Tio'I IN EI Rcsasc CARtas IN UaocacRovao crepancies so that >>xtrapoLttion into new Dvcrs, P. J. Baseacches. T'assis, Depastmeot ol IL W. Burrell (Consolidated Edison Com- Gelds could be Inade with conffdence.

Electsical Eagioecsing, Uaivessity ol Wisconsin (hfadlaon, Wis.), 192S. pany of Neir York, Inc., New YorL, N. Y.): It is stated in the paper that the agree-The authors have presented a desirable ment between theoretical and empirical S. CvaaRNT CARRTINo CAFAcITT oF LNtaao. NATRO PAFSR, RVS ~ RR ANO VARNISKRO CANRRIC elaboration of Appendix Il of a previous numerical constants of the simplified con-1Nsw.ATRo CAaaas. Pablisasion lruaIb<r P 2P. paper by Mr. N>>h>>r.'lthough the ap- vection term is dose for the case of an oil Cgd, lasulatcd Pores Cable Eagineess Association proach to the problem is uot changed, the medium, but is off appreciably for the case (Nciv York, H. Y.), dsst cditioa, 1043. lnaterial presented in the Appendix referred of a gas medium. It also can bc said that to is of sufficient importance to justify a the conduction.radLttion constant agrees more detailed presentation. lvith theory for the case of a gas medium; IL is apparent to those engaged in the 6eld however, for the case of an oil medium. the Discussion of cable heating that the Insulated Poirer constant theoretically app>>ars to range Cable Engineers Association recommended from 0.60, as given in the paper, to n>>arly R. H. Norris and Mrs. B. O. Buckhtnd value of l), while perhaps sufficiently conser- twice that value, depending upon the values (Gen>>ral Electric Company, Schenectady, vative for general design, lacks Lhc flexibility of D,'and Da involved. N. Y.): Eiftci>>nt work in the heat.transfer needed in comparing alternative construc- From the over-all standpoint, it neverthe-field on a variety of applications requires tions. Precise determinations of ig 'or less appears chat the expressions for J) and awareness of the definitions and units, in various types of inslalhtions may noL be H,a. as given in equations 9, 10, and 11 of order Lo avoid confusion and misunder- possible because of inherent variations in the paper are quite workable and agree with standing. In this paper and other papers the physical constants involved; however, test data as well as could reasonably be ex-written by cable engineers, confusion arises as additional test data are compiled. the pected. A high degree of accuracy in the as to th>>>>acct meaning of th>> expression calculation of allowable current ratings of "thermal resistivity." R>>sistivity as nor- cables is not yct to be expected but impor-mally deffncd (by the American Standards tant worL has been done in the past fcw Association (ASA) for cxasnple) is a prop- years in chrifying our understanding of heat erty of a substance and is not affected by flow through duct stluctur>>s and the earth, its geometry; for example, the resistivity of and this paper is an important contribution copper has a constant value at any spcciffed to such understanding. temperature, while its resistance dep<<nds on its site and shape. Then the us>> of thc n, RBFBRBNcas word "resistivity" for surface phenomena is Aw 1. See selcsence 1 ol the paper. a misuse of thc terra. 2. TK ~ Caacvaastoa ot Caata Tallteaafva ~s To show ho>> Lhc distinction between Flgvse l. 'hesincl circuit fos single conductor IN Svaw*r Ducts. W. B. Xlske. AlEE Joaraal. resistance and resistivity caters into lhc in ~ is volume 40, 1030, pace SSS. 1950, VOLUME G9 Bisllcr, iYchcr Ther>>tnf Rcsisfasscc 347 f' a>> lie I ~ I R. J. Wlseman (The Okonite Companyc in the paper, since this analysis gives the relative variations in the radiation and coti-Passaic, N. J.): I like thc author's paper very order of magnitude contributed by each of vection terms. much. It explains the three methods of the three mechanisms of heat transfer. The authors have neglected thc variation heat flow from a cable to a surrounding The authors have assumed for cable in in radiation component of conductivity with mediutn, nameiy, conduction, convection, duct that the component of the thermal con- tempenture, pointing ouC thac these varia-and radlaticn. Also, they give the various ductivity duc to radiation can be treated as a tions are quite smalL This is justlfiable i' parameters which influenec each factor constant in the range of normal operating from a practical stand point. However, the namely, cable diimeter, temperature, and temperatures. Only the component duc to variations in the convection component with temperature difference, and viscosity of the convection was considered as variable with temperature also should be neglected for medium. The various formulas look quite changing cable diameter and heat flow. practical considerations, since, as is shown "formidable when we note terms raised to This assumption does not lead to a true pic. in Table 1 of thc discussion this factor is fractional powers. It is not easy to obtain ture of the variation in thermal resis(ivity even smaller thart thc change in the radia- ~ I thc constants for each formuh as they are with heat flow, or more fundamen(ally, with tion tenn. This would considerably sirn-dependent on condicions not easily calcuhble cable tetnperature. Mr. Darnctt and 1 have plify the Bailer-Heber equations for the sur- r so it is necessary to gec test data and work stated in our papert that the decrease in face resistivity factor. ln their equations a back to nurnerics which will give the de- thertnal resistivity with increasing sheath 9 and 10, (he surface resistivity factor. f4 h sired results. It so happens that as all three temperature is caused primarily by varia- depends upon thc fourth root of the heac modes of heat transfer are funccioning at tion in the radiation component of heat flow. This does noc have much significancc che same time, a change in dimensioning transfer, and that the effect of temperature smce it is based upon the variation in thc tends to work in opposite directions, reduc- variations on convection are negligible over convection tenn, a second order elfccc com-ing thereby.chc,effect of diame(er. AIso the the normal operating range.. This state- pared with the radiation term. Similarly range in temperature is not great and as we menC is verified by calculations based upon the dependence of ti upon the square root of take the one. fourth power ot temperature equation 1A of the Huller-Ychcr paper, the sheath diameter is doubtful, since chc difference and three fourths power of which is repeated here: change from.a fourth root to a square rooc temperature, the variation with tempera. dependence in the convection term also was ture is not great. About two years ago we decided to re-q ( Di'ciTg i 0.0920,T'/P'i Da'(1 39+Dc /Dd) + (Ih) based on the very small change in convection conductivity with temperature. 0 study the thermal constants tre obtained (convection) The foregoing discussion tras confined to when we originally set up thc Oilostatic cable in duct with air as the intervening cable system. At that time we used the 0.0213 fluid. Its applicability to cable in gas-filled Di'og Dd/Dc'"d t+0.102c(l +00 167T>>t) cylindrical log forlnula of ra(io of internal ~ 'pipe at high pressures, where convection pipe diatneter to circumscribed circle over t. (radiation) becomes the principal mechanism of heat ri ) the assembled conductors, and also a con- transter, requires further study. L. stant which was a function of the tempera- in watts per degree centigrade toot inch. The authors have done an excellent job in ture. The emissivity factor, c, is assumed to be helping co establish the theoretical ground- ~ y Our more recent tests showed chat the unity at attnospheric pressure. work necessary to both encourage and guide thermal resistance was almost independent Table I of the discussion lists two repre- experimental workers in the duct heating ~ of temperature (a variation of abo'ut 10 per sentative sheath temperatures from our test problem. cent between 30 and 61 degrees centigrade) data on flber duct in concrete, and these i for an oil pressure zone and a very few per temperatures might very well be represent- RBFERENCE cent for a gas pressure zone at 200 pounds ative of the operating range of a cable. The per square inch. Wc also noted that

l. Hear TU*ttsrcx Srvov ott Powea Cast.a term (Q/D,'hT) evaluated in equation 1A Dvcts atto Dvcr Assctcstses. Pau( Gteeblcr, within the accuracy of testing we could is inversely proportional to the surface GU7 P. Batoctt. AlZZ 7 vaatoctioat, rolutoe 09, tc safely assume the thermal resistance to resistivity factor, tt. pan I, 1950, paces $$7-07.

vary as inversely as the diameter of the The three terms in the equation give thc shielding tape over the insulation. As a thermal conductivity components due to h. H. Kidder (Philadelphia Electric Com-result, we have sec up two simple formulas convection, conduction, and radiation respec- pany, Phihdelphia. Pa.): This paper by for the determination of the thermal resist- tively. As we increase the sheath tempera- Buller and Neher, together with two pre. ance of che pressure zone for three cables ture over the range showa, the increase in vious papers by Mr. Neher,4t completes in a pipe, namely, for oil pressure system the radiation tenn produced by substituting presentation of the steady-state considera-H~1.60/D thermal ohms per foot per con- our experimental data in the Buller-ocher tions involved in a project which was started ductor where, D is thc diameter in inches equation is five times grezCer than that of about four years ago when Philadelphia over the shielding tape; and H~2.58/D the convection term. This shows that the Electric Company interested Mr. archer in thermal ohms per foot per conductor for a experimentally obsetved decrease in tt over undertahng an investigation of funda-gas pressure zone operating at 200 pounds this range is due ahnost entirely to the in- mental relationships.'s necessary to dc(er-pcr square inch. You will flnd these values crease in the radiation tetm. These cal- mine approximately what pipe.cype cable of thermal resistance for the pressure zones culations are based, of course, on the rather circuit load ratings would be accurately amply accurate. large cable size that we employed in our comparable with thc load ratings of con-As the authors refer to the surface resis- tests. A smaller cable size will increase the ventional cable circuits in ducts. tivity factor P, the values of 4 comparable effect ot the convection term only slightly, The thermal resistance through the spaces to che above constants in H~0.00411 tt/D however, and not nearly enough to make its between the cable sheaths and the pipe or are IS 390 tor an oil.pressure system as cora- wall inclosures is an important link in f'uct variation with temperature equal to Chat of pared to 350 given by the authors and P~ the radhtion term. Identical calculations the thermal circuit. It had beenhoped that 827 for a gas pressure system at 200 pounds with our data on Transitc in concrete, a general rehtionship could be developed in i', per square inch as compared to 450 given by Transite in air, and fiber in air, show simihr such a form thac all of che differences bc-the authors. We are qutte confldent in our ' >> ~I values and have been'sin'g'theiii foi 'over a year. ts Table l. Gtecblet-Becne(( Da( ~ Pavl Greebler (Johns Manville Corpora- Gteeblet tion, Manville, N. J.): In this paper the Nehet Barnet t authors have contributed imrncnscly to-ward an understanding of the mechanistns Lead Sheath Temperature Temperatureullet Coclde Duct V/all Sot(ace Meso Temperature Temperature Drop ar Eeuatloo lA Cooccctlou Radlatloo Tctm Term tt lo Data 'C(cm)'/>> of heat transfer from (he cable to ics sur-rounding pipe or duct avail. The theoreti-cal analysis was necessarily based upon thc dd.2... ...40.$ ...........50.$ ... ~ ~ ~ ld. l. ~..., 0 0dx...o. Ipd.... .990 ~ ~ 77.2... ...5$ .0,....,.....0$ .4... ~ ..22.0.....,.0 005...0.2ls ...,..020 ~ simplifying assumption of a coaxial cable in loctcaac 0 00$ ...0.0l5,..., .. 00~ decrease duce arrangetnent. This does not, however, detract from thc value of the analysis given Temperatures acc lo dcrtccc ceodetadc. Thc latldc duct >>att cut(ace temperature lc au avctaee value. ,'34S Bttftcr, /V'cJtcr Thcrnaf Rest'stattcc AIEE TRANSACTIONS

~ ' ~ ' ~( ~ q, ~ ~

e Si 6 1~ s tween cables in air in ducts and cables in tween cable sheath and duct wall. 'lt is un- H,c (oil) ~0.70/De"/s thermal ohm teeL (I) high-pressure gas or oil-flied pipes could be fortunate that we do not have a more dis-explained in terms of the physical constants tinctive name for it. Hrc (gas at 200 psi) ~1.20/(Dr')'l thermal ich characterize the respective fiuids and Mr. Burrell has presented a thoughtfuldis- ohin feet (2) oertinent geomctricat relationships. cussion of the assumptions which we have The conesponding equations on a per

method presented by Buller and made in developing the theory used for cable basis and with three cables in thc pipe has approximately achieval this re- corrdating the test data. In this respect, a are sult, at least to the extent of permitting the book by Prof. McAdamst gives a constant correlation of data obtained by various in-vestigators at various tiines in various con-for the convection film on thc outside of a cylindrical surface in a free medium which is hrc ~= 1.44 Qp and hrc m 2.07 (D ) ~ s respectively

'structions. It does not disturb ine par- about 20 pcr cent lower than that for the in-ticularly to find that there is some apparent side of a pipe and which we have used for Figures 3 and 4 are intended to give prac-difference between the elects of Transite both films. Wc have not distinguishal be- tical working values ofhce or Hrd over a wide and fiber duct walls, respectively, under the tween the Lwo constants because no informa- range of operating conditions. Mr. Grecb-conditions which prevailed at the time the tion is given as to thc values of these can- ler is right in pointing out that the elect of tests were made. I think we should hesitate stants when the cylinder is placed within temperature variations upon the radiation to attach much significancc to these appar- the pipe. While a formula for the conduc. component is considerably greater than the ent differences because there was no attempt lion component in a nonwoncentric system effect of variations in the convection tenn to control the moisture content in thc fiber or is given by Whitehead and Hutchings't is which is the essential variant in Figure 3. the Transite, or even to make the tests far too complicated to use in this analysis, The inclusion of the temperature of thc under conditions comparable to those to bc 'and it reduces substantially to the concentric medium in thc ivorking expressions would expected in the usual exposures to natural formula which we have employed except for vastfy coinplicate them, however, and as a but variable moisture conditions to bc en- extremely small separations between the practical matter this is unnecessary. countered in underground structures. The cylinders at one point. Further there is In all of the Greebler.Barnett data't will significant point is that Buller and Neher considerable experimental evidence to sup- be observed that P varies inversely as Q'/< have obtained a correlation ivhich now per- port the assumption that the emissivity within the accuracy of measurement. The mits estimating the thermal resistance froin constant is substantially unity for the types dependence of P upon Dr cannot be evalu-cable to pipeor duct wall with sufficicut of cable surfaces employed. ated from this data since only a single value accuracy, so that little, if any, practical Discrepancies were expectal, because of of D, was employed, but since the convection iinprovement in cable load ratings can be the assumptions which had to be made, a'nd term theoretically varies directly as Q'/</D'/s gained by introducing furgher refinements in because the physical location of the cables we believe that the temperatssre variation in their analysis of this part of the thermal within the pipe cannot be controlled. We the radiation term which Greebler has men circuit. have used assumptions and theory only to tioned will be accounted for with su%cient obtain a sensible understanding of the accuracy by expressing the Greebler-Barnett RspsRBNcss problem with which we have to deal and to data for fiber and Transite ducts in the form I. Taa Tassraa*ruaa Rise or Bvaiao C*n,as determine ivhat simplifications can justifi-Auo Piras, J. H Neher. AlEE Troasersioar, ably be made in order to obtain practical Ji(fiber) <<1120Ds'/'/Q'/'egrees centi-olume il8, pact 1, 1040, pages 0-1T. worhng expressions. These working ex- grade square centimeters per watt (3) Sce relcreace 1 ol the paper. pressions were then developed directly from lf(Transite) m 990Dr'/'/Q'/'egrees centi-actual tests rather than from theory. We do not share Mr. Burrell's desire for working grade square centimeters per ivatt (4) F. H. Buller and J. H. Neher: Mr. Norris expressions of sufficient complexity to This will have the elect of changing the and Mrs. Bucldand have taken us somewhat identify the separate elects of the three slope of the curves <<hen plotted in ac-to task for our apparent'inconsistency in modes of heat transfer. cordance with Figure expressing our physical units in one system Dr. Wiseman's simplified formulas for 3.'he coiresponding values of Hrc assuming and our geometric units in another. For calculating her (on a per cable basis) for worhng value of Q m 10 watts per foot better or worse it has long been the custom three 'cables in an oil-flied pipe or in a gas-in cable rating procedure to express the filled pipe at 200 pounds per square inch are physical units involved in the watt-second- very intaesting and similar formulas may Hrc (Gber) m(2.59/Dr'/ )+0.33 thermal centimeter-gram system, and to express ~ be derived from Figures 3 and 4 of the paper ohm feet (5) length's in feet and diameters in inches. In assuming that Q, P, and T~ have Gxed developing our equations it would have been typical values. Unfortunately Dr. Wise- Hrc (Transite) 2M/D, I'hermal more consistent to have expressed the latter man's derivation of the equivalent P in his ohin feet (8) quantities also in centimeters, and thea to formulas gives values ivhich are not com- While further theoretical and experimen-have converted the final expressions to'he parable to P as defined in this paper. The tal work may well be undertaken in order to system of measurement used in practice. corresponding rehtionship for P as defined in clear up some of the apparent discrepancies Wc chose to use the mixed system through- the paper is between theory and practice and to yidd out, however, in order thag the reader might more factual data on thc pafonnancc of be able to use any equation in thc drvelop- hgc 0.004110 cables in duct; we agree with Mr. Kidder ment, directly, without encountering the 3 2.15DN that little of any practical improvement in uncertainty which inevitably arises as to cable load ratings will result. We do not whether you multiply or divide by the trans- and this yields P 290 for the oil.pressure wish to discourage further elorts in this formation constants. system and P ~ 450 for the gas-pressure sys- direction, but we feel that it is sufficient to The usc of the tarn "surface resistivity tem base cable ratings on Figures 3 and 4 of the factor" is a slightly different matter. and as We cannot accept his formula for the oil paper or more simply on equations (1, 2, 5, our sncntors have yoin]ed.out, it has dimen- system since its corresponding value on a and,8) just given. sions which are not those of true, or volu- total heat'iow basis is" Hrc" metric, "resistivity." Here again, this is equivalent to Q/dT ~ 3.9 for 1.15/Dr'hich nomenclature has been hallowed by tiinc Dr' 4.5. Noae of the tests cited in Table~ Rspsasscss and is thoroughly understood by cable engi ~ III of the paper give an('upport for so high 1 See ccfcreace 2 ol the paper. neers, for whom this paper was written. It a value. 2, Cvaaairr Rarsuo or C*ai,as roa TaaNsaus should be stressed, however, that this "sur- Dr. Wiseman also assumes that the over- siou auo Disraiavrsou, Se Whitehead, B. E rvce resistivity" is not a fundamental ~~ all thermal resistance varies inversely with Huichlags. sources lastliutioa ol Electrical Baciaecrs (toodoa, Eagieod), volume 83, 1038. rsical quantity, in the sense that volu- the diameter whereas we believe that a more cqueiioa 10.3, page 531. ..ctric resistivity is; but as pointed out, is representative variation may be deduced the resistance of a unit surface of a flin from the slope of the curves of Figures 3 and 3. Hear Taausraa Srvov oN Porvaa Caai.a Doers auo Doer Assausaas, Paul Greebler, Gus which, purely for purposes of convenience, 4 in the vicinity of the typical operatirg p. Beraeu. AIEE Trcareaioas, volume 80. pert is assumed arbitrarily to represent the entire points. Thus for Q 25 watts per foot and '1, 1030. paCes 337-5Z. thermal resistance of the composite heat T~ 50 degrees centigrade, we derive the C. 'Dlscussioa br J. H. Lleher ol cclcreace 3 transfer elects operating in the r'egion be- simplified expressions ~ bOve pegCs 385~ 1950, VOL.URIB 69 Bsdlcr. >Vchcr Thc.-nsal Ress'starve ATTACHMENT 3 TO AEP:NRC:0692DF CABLE TRAY ALLOWABLE FILL DESIGN STANDARD e ~l p ~ sir mao P ~J 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.

2. (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.

TRAY WIDTH ALLOVYABLE FII.I. 0 SPACING OISTAHCE 9 FOR KTWEEH CAMS 5EE HOTE5 I IZ.MLOW FIGURE f POWER CABLE SPACIAI6 TABLE I NOTES: POWER TRAY MA1IMUAI FILL

f. FOR CASLES OF EQIAL QL,SPACIH6 I& 0 EIL Z. FOR CAELES OF UHEOUAL CLL SPAQH& IS I/A clL 0F LARGER )casLE. ~

ALLOWASLE FIU. AI.I.OWAOLi FILI. TRAY Vj IOTN HI<& TRAY Ii. HIGH TRAY 26.8 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 cd =kA b,T X Where: q Conductive heat transfer. k Thermal conductivity A Area normal to heat transfer flow bT = Temperature difzerence X 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:q Convective heat transfer hcv Convective heat transfer coefficient A Surface area of the body Ts s Surface temperature of the body T a 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 The any body will absorb heat radiatec from any other heated body. net forth exchange of heat is proportional to the difference of the power of the'r absolute temperatures. The net transfer of energy by raciation from a body to ambient or from a body to a body separated by a nonabsorbing medium is given by surrounding (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 s Absoluter temperature of surface of radiator. a Absolute temperature of ambient 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 heat the governinc mechanism. If this is true, the allowable loss per linea" foot of cable trav will .be constant for a given total surface area of cables as per equations (2) and (3) the ~ Tne valica"ron of the above theory which is developed in 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 (4) s Where: As Total cable surface area P.U . n Number of 3 P cables per unit area d Diameter of each cable P.U. summation The percentage fill of the tray can of the per unit cable diameters or: be defined as the F = nd (5) Note tha" this differs from the industry standard of defining percentage sectional fillbased areas. on the summation of the cables cross-From examination that the surface area of equations will be (4) and (5) constant for a it is clear given percentage fillF. A The total heat generated per unit area by resistive heating of the cables is: Q = 3n I2 R (6) Where: Q Total heat generated per unit area. I Conductor current R ac a.c. resistance of conductor per unit length. Rearranging equation (5) n = F/d (7) Substituting in equation (6) Q = 3F d I2 R 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 l Therefore a plot of va ~dRac for a given percent fillfill . ahoulc 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 fill of 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 determined from the slope of the plots as shown below: fill may be (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 fill trays is dependent upon a uniform heat distribution per unit area of filled tray. FIGURE A-I ventilated tray with ventilated co 700 600 500 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 I 20 40 100 120 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 fill trays, 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 that: and rearranging equation,(8) it can be shown d 3I R = F Q (ll) or the heat produced by the resistive heating of one three phase cable is equal to the percentage of the total allo~able heat, Q, as determined by the area that cable occupies, d/F, in the cable trays. The allowable ampacity of any cable in tray can be calculated fill, if the allowable heat is known for from equation (9): a specified tray (9) The determination of allowable heat for various tray fills and Model. raceway configurations is discussed in Appendix B, Computer 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: T (T + ~Td) c a (12) Rd dc 1+7)c ca in equation (12) conductor current (kiloamps) conductor temperature 0 T ( C) c 0 ambient temperature ( C) 0 D Td dielectric losses in conductor ( C) dc D.C. resistance (microhms/f t. ) increment of ac/dc ratio R ca effective thermal resistance conductor to ambient (thermal ohms-ft.) 1cd 2cd R lcv R 2cv Ta R2 T c T.a = Q(R + R ) 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~ = [(r+ p< 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 c may be determine if the ac/dc ratio is known R /Rd= 1+I +Y+YP (14) where: Y s = increment of ac/dc ratio at shield Y = increment of ac/dc ratio at pipe or conduit Y will be zero provided shields are'pen-circuited and in a Y will be negligable in light of the fact that most cables tPay will be three phase twisted conductor. Therefore equation (14) reduces to ac dc 1+ Yc (14a) B.2.2 Determination of Thermal Resistance If shield and pipe losses are neglected as previously discussed, the total thermal resistance conductor to ambient, R ca 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. = 3. diameter over insulation (IN. ) D c = diameter of conductor (IN.) 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,> (16) 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 is simplier to take the inverse of the conductances added in series. it Using the equations developed in reference 4: C = lcd = 0.0213 (17) d aT lo~go /D'), D 'ET (18) DT Cr = '2r 0.102 D' (1 + 0.016 Tm) (19) AT where: C 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 0 T m = mean temperature of air space ( C) 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. ~ ~ ~ NI 4 The e ffective diameter o f 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 n' will be given by the expression. log D" D') 'he thermal resistance from the last surface to ambient, in still reference 3. air can be found from the following equation derived in 1 (21) [( ~ T/D"'" + 1.6 p (1 + 0.0167 Tm)] III where: D = outside diameter of outer surface conductor to ambient, R'ill As previously stated, the total thermal resistance thermal resistances thrSugh each medium. be the summation of the individual B.2.3 Determination of dielectric losses From reference 3: Td = Wd Rda (22) where: W. d = dielectric loss thermal resistivity based on da individual thermal resistivities at unity power factor. Wd 0.00276 E 2 $ cos g (23) log DE J where: E = phase to neutral voltage (KV) (r = specific inductive capacitance of insulatio.-. 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 insignificant was determined and could be that the thermal effects of the tray was 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 Data Input The data required for running the program is as follows: N The number of layers of material enclosing the cable. See B.3 D (I) The equivalent diameter of layer I in inches. T (I) The thickness of layer I in inches. (I) The dead air space outside of layer I in inches. S Enter "1" ~ if the air space is ambient air. Note: Enter '1" o~nl for ambient air. E (I) 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. 0 P (I) The thermal resistivity of layer I in C-cm/watt. Note: The variables D(I), T(I), S(I), E(I) and P(I) shall be entered for each layer input. ~ i A e J ~ w ' 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 under the access is stored in the Warner Computer System 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.

"Ampacities for Cables in Randomly Filled Trays," J. Stolpe. IEEE Transactions, Paper 70 TP 557 PWR.

3. "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. "Engineering Data for Copper and Aluminum Conductor Electrical Cables," The Okonite Company. Okonite Bulletin EHB-78. Pg. 5.

6. 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. Industrial Heat Transfer, Alfred Schack, Dr. Ing. John Wiley &

Sons, Inc. 1933. Pg. 18

9. 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 3 TC 412 CU 3.8 21.58 1469 R 3 TC 412 CU 16.0 21.58 8067 R 3 TC 412 CU 1.2 21.58 8024 R 3 TC 412 CU 1.1 21.58 8187 R 3 TC 412 CU 17.0 21.58 8026 R 3 TC 412 CU 2.7 21.58 8027 R 3 TC 412 CU 1.2 21.58 2349 R 3 TC 412 CU 1.9 21.58

• 1476 R 3 TC 412 CU 1488 R 3 TC 412 CU 20.0 21.58'0.67 1991 R 3 TC 42 AL 60.0 16666 R-2 3 TC 412 CU 2.5 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' /2 0 9g E /7' H R P /r-g BobT ~ 9 ci// C cr cl 092 R 0 1 COL, -2 / / iP ~Bo Z s8v' 9rc 9C <C /z 0 92 0 32 0 32 -2/ ge7 /7 // goZ6 N 3 c /2 O 3c . //P 2 gOZ 7 rZ c /z A/G u ~$ 2 0- 0/ //H / 234.5 3 c /z D4 G 03z Cu /)N // E' / / //P /- I 7@ 9 c / + 6')b 0 2- /H 7 u S C / acg u 092 w' sr P s P go / /c// /Z. C 2 'P2 DP P C) /c<c< ~-z C / 0 92 OT R CO Cy- R K 8P QI5 CONDUIT CONNECTED LOAD CALCULATED ALLOWABLE CABLE N a2KCI5X ESRZBLet +8003 R-1 4% ~ 3 TC 42 SH-AL 57.5 3.32 99.04 9.S6

• 8004 R-1 4N 3 TC 42 SH-AL 64.6 4.20 99 04 9.86

• S004 G-1 4H 3 TC 42 SH-AL 64.6 4-20 99 04 9.86 8026 R-1 0 3 TC 412 CU 2.7 .045 25. 85 4.14 8505 R-l 3 TC 412 CU 2.6 .042 25. S5 4.14 8506R-,1 3 TC 412 CU 2.6 042 25.85 4.14

<<8003 R-2 4N 3 TC f2 SH-AL 57.5 3 32 99 04 9.86 ~8004 R-2 4% 3 TC 42 SH-AL 64.6 4.20 99.04 9.86

• 8004 G-2 4N 3 TC 42 SH-AL 59 3-50 99 04 9.86 8154 G-2 1s 3 TC 412 CU 2.6 042 25. S5 4.14 8155 G-2 1 II 3 TC 412 CU 2.6 .042 25.85 4.14

+8744 R-2 4w 3 TC f2 SH-AT 71.9 5.20 99.04 9.86 +5ZV CABLE 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

~ ~ FZP c888E'YPE OiD FL8 >~asH, KV8 ~u gP HP ~P aB. Ml lM =L 2. XP P 2 2.d gP 9 ATTACHMENT 6 TO AEP:NRC:0692DF RESULTS FROM TEST REPORT gCL-542 4 ~, C e g TEST REPORT Page I of ~ American Electric Power Service Corp. Canton Laboratory P.O. Box 487 Canton, Ohio 44701 ltle: es t o. CL-542 December 16, 1983 AMPACITY TEST FOR POWER CABLES Test By: L.J. Balanti; J. P. McCallin blade For: AEPS Corp. Report By: L. J. Balanti Sponsor: W. F. Wilson - New York Approved By: - - A. P. Litsky Tes t Comp le ted,: November 18, 1983 g 0 I ZNTRODVCTZON C) Cl For compliance with 10CFR50, Appendix R at the D. C. 0 Cook Nuclear Plant, tests were conducted on power and control CL cables enclosed in a TSZ, Znc. one-hour fire barrier system. E The results of- the test will be compared to computer-generated Cl data to determine the validity of the computer model on heat run flow and cable ampacity. II. OBJECTIVE The test objective was to simulate as closely as possible the actual conditions of tray and conduit runs proposed for Cook g o Plant and determine the final conductor temperature for the specified ~ amperage and tray fill. ~ 4J E 0 g 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 4" I.D. Galvanized rigid steel. 1.2.2. 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. Prefabricated panels 6'-0" x 4.6 1.3.3. Prefabricated conduit sections. ': 1.3.4. Steel banding. 1.4. Cables The following cables were used for testing: 324 3TC 012 Cu 600 V 339 3TC N6 Al 600 V 344 3TC N4 Al 600 V 348 3TC 02 Al 600 V 3101 3TC 14 Al 5 kV shielded 3102 3TC N2 Al 5 kV shielded 3103 3TC '2/0 Al 5 kV shielded 3104 3TC N4/0 Al 5 kV shielded 3120 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. The conduits were encased in the prefabricated sections. 2.3 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. Heat generation is greatest. B~  :-: ar dissipation is the least (see Figure 3). 1 ~ t y, '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 3.8 324 'TCr12 Cu 20.0 348 3TC02 Al 60.0 324 3TC512 Cu 0 f 4 I H j tp 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 3.8 324 3TC~412 Cu 3 20.0 348 3TC~2 Al 1 60.0 324 3TC e~ l2 Cu 1 0 P 4.2 Test 02 Circuit No. Item No. Description Runs in Tray Ampacity 324 3TC512 Cu .17 324 3TCI12 Cu .71 324 3TC012 Cu 2.8 348 3TC$ 12 Cu 6.8 3120 4/C412 Cu 6.8 344 3TC54 Al 53.0 4.3 Test 43 Circuit No. Item No. Description Runs in Tray Ampacity 324 3TCf12 Cu 5 .71 324 3TC$ 12 Cu 5 2.8 3120 4/C012 CU 1 6.8 324 3TC012 CLI 2 6.8 3120 4/C012 Cu 2 16.0 324 3TC 12 Cu 2 16.0 339 3TC$ 6 Al 1 16.0 339 3TC56 Al 1 36.0 344 3TC54 Al 1 36.0 344 3TC54 Al 1 53.0 348 3TC02 Al 2 60.0 324 3TC012 Cu 1 0 4.4 Test N4 Cable Size: 3TCN12 Cu 600 V. Conduit Size: 1" I.D. EMI Ampacity: 2 amps. 4.5 Test 05 Cable Size: 3TC52 Al 5 kV shielded with one end grounded. Conduit Size: 4" I.D. Galv. rigid. Ampacity: 72 amps. 4.6 Test 56 Circuit No. Item No. 3101 3TCV4 Al Sh. 20 3102 3TCI2 Al Sh. 25 3103 3TC02/0 Al Sh. 40 3104 3TC54/0 Al Sh. 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: Ampacity Runs in Highest Conductor Test No. Cable (ampm) Tray Temperature (o C) 3TCC12 Cu 3.8 45.6 m 20.0 59.7 3TCC2 Al 60.0 55.7 3TC)12 Cu .17 42.6 m .71 42.7 2.8 45.1 6.8 44.4 4/C512 Cu 6.8 43.9 3TCT'4 53.0 58.3 3TCN12 Cu .71 54.6 2.8'.8 57.9 60.4 16.0 67.3 4/CR12 Cu 6.8 55.2* ~ I 16.0 62.7* 3TCe6 Al 16.0 57.6 36.0 65.9* 3TCt4 Al 36.0 57.9* m 53.0 68.8 3TC52 Al 60.0 63.7 3TCC12 CU 2.0 42.9 3TC02 Al 72.0 65.0 3TCS4 Al 20 45.6 3TC52 Al 25 45.4 3TCC2/0 Al 40 45.5 3TCm4/0 Al 50 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. J v f ~ ~ COMMENTS - TEST No. l l.) TEST ":. ) START 1 CL 6 ~ 11/Sl/8~ IME IS 4:29 A.M. A=. 785V B=. 798V C=. 81 BVi A' ~. 8 AMP

v. ) START A=. 7~2V B=.G57V C=i.82Vv ALL GG AMP Lc. ) START A='. 17V B=i. i4V C='.19V~ ALL 28 AMP

5. ) CHANNEL ~9= AMBIENT G. ) CHAN '=TRAY TOP~ "=TRAY BOTTQ,, 4=AIR N . RAY

7. ) CHANNEL, E, 7 .ARE ON SG AMP CIRCUIT Q ) CHANNEL 5~ 8 APE ON 28 AM. CIRCUIT

9. ) ALL OTHER CHANNELS ON . 8 AMP CIRCUIT

18. ) CURR END A 3. 9 B 3. 9 C ~. 9

11. 3 END A . 878 B . 805 C . 867

'OLT 1:". ) CURR END A 59. 2 B 59. 5 C 59. ~ 1 i, ) VOLT ~ END A .818 B .7',' 1 ~ 8"

14. ) CUP.R END A 28. 4 B 28.:" C 28. 2.

15. ) VOLT END A 1 ~ "'8 B f. 418 C l. 259 fE. ) END TEST Nf CL-542 ff/f/8Z CL-512

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44. " 8 87:45 rsn o &a s

4 8 48. 7 44. S 54. 9 59. 2 44. 4 4-V. J~ 8n ac ~

28. 7 41. e 41. 4 44a 8 Jv. S 59 44. 4 4:". S 4... r 8n o4c 41. 4 41. 9 45. 4 58. 9 c'4 59. 2 44. 7 4" 8 4~e J ~

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44. " 44.

42~ 59. S 59. 4 4c 1

41. S 45. 9 59. ~ 55. S 54a 5 45. ~ 44. 1 14 4l~ va. 1 41. 5 4r. " 45. 9 ca 7 c'5 54. S 59. S 4i 44. v 4". 9 ic ~

1 c v~a. 1 41. " 41. 9 45. 9 59. 4 c'J. S 54. S 59. 4 c'5. 4 44. 44. 1 15: 45 r 41. c'9 c' 45. 4 "-'4. 44. ~a ~ 9 4E 59. 5 55a 7 54 5 ~ 2 1 ~r7~ cia ~ ~ T<s lr= C ".17 CH~18 CHUB CH .5 CH CH .7 CH.:" CH".6 CH~'7 CH/s33. 84: r8 <<J ~ eJ rac <<Jo c e ecJo J ~

5. S <e C Rc' <<iJo n nc IJ r4.

84-45 c' ~9 4 .,8, 2 38. 1 ~8 .9. a  :"8. S  :"7. 9 8 "4. S ~5. S ~4. 7 o v5. 9 vS. 1 ~S v4. S sr 7 48. 8 8 c' 4 vS. F MSa 5 ~ rSo 7 ~9. 9 48. 1 48 -.n 41. 1 48. 4 8 c'S: 1.5 48. E 41a 4 41. 1 C'z. 4n c 48 4'". 4 GS-45 4s s 4"r. S 4 4..,4. 4". 9 42. 1 44. 8 48. 87- '5 42. 9 a 44 9 45. 5 ='8. 87:45 4<< 4 ~ .9 4 .1 44. 4 44i c'4. 8 4". '" 4c5. 4 fpn ~ 1 c'n 4n 4v. S 4v. ~ 44... 44. " 44. 7 4'. 4 S 41. ~~ a4c'9: 4 .1 4i o, ~ S 4... 5 44. E, 44. 4 n 45. 9 48. 8 15 4v 89 4C're' c'".8 4~. 4 4'. 7 4v. 5 4~. S 4lr.. 7 44i lr.4. S

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1 4s s ~ S 4i8 ~

48. S

48. 7 18o 15 4 ..4 4". 7 4 o c' 44o 8 44. 7 45. 4 4i, 7 'S..~

48. 7

'8 ~ ~ 45 4er o 4e ~ ~ 8 4:". 7 o ~ 5 44. 9 44. 8 4.. S 4E. 4 41 11: 15 4.... 4e s ~ n Cl 4,,7 4... 7 44. 8 44. 7 45. ~ n 4S 48. 9 11 c' 44 ~ 8 Q 44. a 44. 7 45. 44. 1 48. 7 ass ~ g 4 ., ~ 4sso 8 4e. ~ . ~ 7 44. E 44. 5 n 4S. .

48. 4 n 4...9 c'".

a ~ 4 c'o S 4.. 7 l. -..3 44. 7 4Jo 4F. 48. 4 lc 4.. S 4..9 44 n 45. S 4". 9 4 '8o

48. 8 4r. 7 4~. 9 n 44. 7 4ic'; 4v. 9 48. S r4 4~ 44, 1 4/s 4i 4 c'4. 44 48. 7 C ~ C c':.

4 ..9 / 7

44. 5 4c; c' 4. .9

~ 1 S ~ 8 7 ~ 4a.1 4 ~ C e 4 . E, 9 4. .::-: ~ l 4. 1 4i /. 4 /s le 4 48s CL-54". COl'll<<ENTS TEST No 2 1 ~ 3 THERM1 AMB-. Ek'T t'CH~9) a ~ THERMr".'OP TRAY ~ ~. ) ' Rl lvr 'OT Of1 TRAY 4, ) THE -4 AIR S ACE -. ) CURR STAR: A .2 8 ." C .2 C ) VOLT STAR.' ~ 815 8 ~ 81B C .82B 7 ~ ) CURR START A .9 B .9 C .9 B. ) VO' STAPT A .84B 8 .848 C .8 5 9.? CURR START A G. B 8 S. B C E.B ) VOLT START A . 471 8 . 478 C . 558 '1.) CURR S ART A ".B B 2.B C '.) VOLT START A . ~89 B . 1~,) CUR% START A 5~.8 8 5 .8 C 5~.8 '"7 ~ .B C .>8E 1 4 ) VQ: START A 1. 587 8 '. ~7B C . B86 '5. ) CL-54" TEST Fr'2 1'/~/B~ START 8515 1B. ) VOLT END A .8189 8 .8147 C. 8.48

7. ) CL'R END ALL . 28AMP 1B ) VOLT END A . 84BS 8 . 8496 C . 8559 CUR Q ) CUR END A .B8 B .88 C .B8 2i7i ~ ) 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 24, ) 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 '.'7 ~ ) CH ~ B ON 5" A:"lP CIPCUIT ~+I ) CH Bs 7 ON:-:' CABLE~ S. B AMP CIRCUIT "9. ) CH '8~ ' QN 4/C CABLE~ F. B AMP CIRCUIT a8. 3 CH 17i ~E ON .17 AMP CIPCU ~1. ) CH 11~ 28~ 25 QN .71 AMP CIRCUIT CL-542 r t ~s ~ a, ~ I t=* ~ . W j TEST No. ESTERLINE ANGUS DATA TT tlE CHUG CH CHir " CH 4 CH 5 CH"6 CH 7 CH - CH-9 CH" 18 CH << Gc ~ 4c .9. 6 re. 7 v .7 ~ 7 V>>J ~ 21. 4 2}. 8 err@ p 'e ~ ~ ~ >>rP ~ Gc-1 VG >>6 8 e>>9 4v. 6 r9, 1 4~o 8 v8 8. 4 vG 86:4 ~ vG. " v76. 4 'v. P\4 v4. 49o 4 o 4 5 "4. 6 4n. 9 v4>>. 9 iS. 6 a4. 7 87-}5 ='7 8 5 >>9 ~ 6 4~>> ~ .e. 4 C>> A~o e >> euo n >>euo V v7. 9 87- 45 v8. 8 >>,g 48 ':"9. 7 &So ~ 48. 5 48. 7 54 ~ 1 48 48. 5 'z9 88-1 V} 48 4}. " 48. 9 'ho

41. 9 41. 9 cc VSo c V 41 ~ 41. 6 48. 9 88-45 v1. "='i 48. 4 41. 7 41 8 ~ 9 '6.

8 c6 41. 8 4J ~ ~ 41. 6 GS 1 ~ 48. 5 4}. 4 4". 4 &7>> 4 ..4 4<. 4 56. v 4r. 4 4 ~ .7 e 89-45 V'}o 48. 5 41. "" 4 ~ c

57. 6 4v 4 4v. 6 c6 c 42. 6

}c ~}. 5 48. 7 4}. 4 4 ~ .9 57>> 7 4v. 9 , ~ 9 42. 4 18 4 "}. 5 48. 9 41. 7 4". 9 4'. 9 4",8 56. 9 4r. 9 4 ~ .4 42. 6 11:15 v}. 4 41 4r. 9 57o 7 4 .9 56. 9 4v. 1 4v. 4 42. 5 ii:45c o 1 4}. 1 41. 9 42. 9 ce ee 4>>4 44>> 1 42. 9 42. 6

1. ~ ~

~ o J 1 ~ 48. 8 41. 5 4v. 1 C ~ J8 44 44. 1 S6. 9 4V 1. 4v. 6 42. 5 +ro4c 4". 1

48. 9 4}o 6 1 Se 44. 1 44. 1 57o o 4 ~

.4 4' 6 vi ~ 4}. } 4>>+ 4V cw QGo 44 44. 1 57 4u 4m>> ~ 6 42. 4 1":45 41 ~ 1 4v. " Se. 1 44 44. 4 57. 1 4>o . 4v. 7 42. 6 '4:45 48. 8 41. 4 se. 44>> 4 44 57. 1 er 4v. 6 4r. 7 1c ~ ic 41. 2 >>J Vo 'n

44. 1 44. ~ S7, 1 4v. 7 42. 7 T1i1E CHO} CHN}7 CH~18 CH-..28 CH-.. 25 CH026 Chill l7 C."t02nv CHOZ6 CHOi7 CHN'9 85: 45 + P'e ~1 '7 o ~ ~ or o p V~ oo>>

4 Vdo u u c e QC ~ o vG. 7 ~ >>9 c 29. 4 ~ ~ "i. 5 :}. 4 ~ .0. 4 .9. 6 ~ ~> v~9. 6 '6:45 "6. 1', i4. 5 .4. 6 6. 7 "4. 6 a7. 4 87 v9 uo V7>> 5 '7. 6 "9. 5 =-e. ='7 7 48. F 48 87:45 48 8 v79. V 48. 6 v9. 4 41. 1, 48o 5 42. 5 48. 6 88: 15 41. 4 48 48. 4 42. 1 4ro 1 4a. S 48. 6 4.". 4 48. 7 88:45 48. 9 4( f ~ 4}o " 41. 1 4>>~r 7 42 7 ~ 41 ~ 2 44. 1 48. 8 89: 15 41. " 42. 4 41.. E 4}. n5 4v. 1 8 44. 4 48. 5 89: 45 4 ... 41. 5 4r. 4 41. 7 4.. 41. 9 48 ..i }8-}5 '" '='V. 4}. 7 42. 7 4>> e 4". 5 4". 4 44>> 7 48. 7 }8:45 41. 8 42. 7 4' ~ 1 4..4 .~ 1 4 ~

45. 1 48. 9 11: 'S Cl 42 9 4~>> ~ 4v 4 4v. 4>>r n 48. 7

':45 4 . 7~

42. 1 4r,7 42. 1 1

4:.. 6 4i. 5 4 1 45 48. 7 1 r-15 4v. 8 4...7 44. 9 48. 5 1.2: 45 4 c~~ ~ 4}o 9 4ro 8 4 ~ 4l>>7 4..., 7 4 er 4r. 4 44. 9 48. 7 }v:}5 4>> e ~ V 42. 1 4r. 4 n 4.~. 42. 4 n 48. 5 O ~ 4>> e ~ nV 4ro 9 4-'. 4 9 4u ~ 4>e ~ 42. 5 44. 8 48. 7 1 4 4c 4 ..6 4. 4-'. 4 4r. 4 4.'. 7 4r. 5 45. 1. 48. 7 15.15 4u. 9 42. 1 4 '. 42 4r. 4 n 4 c 45. 1 48 CL-542 r ~ ~ ' f.: .. ..',; - ' ',: . ~ ~ 4 ~ .: t' ~ sh, (L I i T P >. gt g ~ Q, P

5. ) HA 'MEL 4 Rc.Y P !ic.'A'E E.?

Ofl THE INSU'TION NQT THL CONDUCTOR 7 ) CURP, START A 5~. 8 8 5~~. 8 C 5". 8 VOLT STAR: A . 64' . 744 C . 697 C ) CURR STAR: A >E. 8 8 ~6.8 C ~6.8 VO'. T START A 1.5 8 1.45 C '.6

9. ) CURR START A 2.9 8 2. 9 C =.9 VOLT START A .~96 8 . ~99 C .426

18. ) CJRR START A 16.. 8 16. ~ C16.

START A 1.9-7 8 2. 8. C i. 'OLT 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 i~. ) CURR START A 56.8 8 57.=. e VOLT START A .64 8 . E4 C .67

14. ) . 7'MP CKT 512 CHAN'S iii17~25

15. ) 2. 8 AMP CKT ..12 CH'S 9. 18'1 26 27 26 m91 &7

16. ) 6. 8 AMP CKT 4/C CH' 18'2

6. 8 AMP CKT "-'= CH'S ~8

'7. ) 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 1 ~v'. ) :"6. 8 AiiP CKT N4 CH'S 28~ iB ==. e f.~P CKT ."6 CH S -.4, ~5 19 ) .:.. 8 ~MP CKT "4 CH' 5. 8

28. ) 68. 8 AMP CKT 12 CH'S 6~ 7

'r 1 ) 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 ~ 5o ) CURP. END A 2.9 8 ~ . "" C 2. 9 2h ) VQL T END A .416 8 .414 C .441

27. ) CUR.. END A 16. 2 8 '6. ~ C 16. 1 VOLT END A . 48 8 2. 84 C 2.26

~ ='9. ) CURR END A 6.7 8 6.8 C 7.8 ~3. ) VOLT END A .594 8 .628 C .6 7 '1. ) 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 24 ) VOLT END A . 6 "8 8 . 585 C .697 u5. ) END Q.= TEST R~ CL-542r '/1 'Sv 14 5 Y 'L s W ~ 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 <<ree I ~ Q u 24. v r4. 4 n4 2r4 86 ~ 1 C C' '1. 5 u4. 1 >>7o 5 48. 4 5. 4 e<<5a 7 48. 6 ~8, 29. 7 r9 86:45 ~ ~ <<J VE. 6 v9. 7 ~ J 1J ~ IJ C

58. 9 5}. 5 u'U ~ nu %7o 7 <<7o 87:15 9. " 4r. 4 c,'7 5n 5. ~ 1 CQI

44. 8 44 87-45 rB. 9 41. 1 4r. 7 47. 7 61. 4 56. 6 56. 7 62. ~

49 'r 48. 5 47. 5 8S:15 29. 1 4r. 6 4<< e ~ ld ~ r 59. 4 59. 4 F4 51. 8 58. 9 58. 2 8n c ' c' ~ () 6 44, 7 C'e ~ J 65. 5 68. 9 68. 9 EG. v IJ<< ~ ~ 5}. S 89: 15 29. 9 4...7 44. 5 54o 2 66. 7 Gr. 1 Er. 1 67. 6 54 ~ 5J 5v 5 ~ 5ra 6 89 45 44. C'C <<J IJ 67. 6 6" CC'5. 5 aJ 7~ }8-15 u8. 4 -'4... 8 C'C 67. 9 Ev. 4 6". 4 68. 8 4 c'4 5<<re 7 1,8- 45 "8. 7 44<< 4 44. 9 J ~ IJ GB. 4 Gu. 7 Gv. 6 69 55. 5 S4 v ~ J' ~ 0 u }1-15 V8. 7 44. 6 45. u 55. 8 67. 9 Gv. 4 E".4 GB. 7 55. 7 54o 4 11-45 >8. 8 44, 6 55. 6 67. 6 Ei. 1 Gv. 1 68. u 54 5 ~ 5~. 9 ier ~ u 8 'v ~ 44<< 5 4c sJsJ ~ 7 67 c Gc F .1 68. 4 55. 6 54o 5 5Z ~ '9 ic:r-45 <<8<<8 45. 6 5>>' 7 67. F 6 sr ~ <<J 6u ~ 68. 4 55. 6 54. 5 c'<< ~ 1 c >8. 6 44. ~ 44. 8 55o 7 67. 1 62. 9 Gu. 1 68. = 55. 6 54. 5 5u. 7 1=-.: 45 .:"8. 4 44. 6 45. 1 55. 8 F7 Gn 68. 1 55. 6 54o 5 T I tlE CHN}'Hn'15 CH=: 7 CHN}8 Cl-'-'28 CH-.. ri CIJI'P'e CH-.. 4 CHvr25 CHr. 25 CHc' 85-'45 24. 4 24 r4. 4 r4 ~

4. 4 24 u ~ 24. 4 'r4. u 86:15 29. 8 VG. 7 cSo c'1 1 ~

1 r9. 4 rt 86-45 VB 45. 4 l C'}. 7 48. 5 41. 4 <<rue u e'.IB<< 7 87e}5 51. 8 4 4c AG. 9 46. 8 48 47. 7 44. 4 45. 5 45. 5 87-45 48 9 c6 45 u 49. 7 c' <<J ~ e c1 ~ 52 51. 8 4IB. 4 49. 7 88:15 51. u 58. 4 47. 6 C'e ~ J e ~ <<J CJ<< e ~ ~ Il'<< 54 51 52a 5 c'n ~ <<J 8ne45 C'JI ' 68 49. ", 5>>I ~ 7 55 CC' <<J <<J ~ <<J 5. 9 55o 5='. 7 c4 54o 1 89:15 cc 6 8a:45 '8 1 W'4. 4 FG. 8 FJ8a

68. 5 a

49. 7 c8

54. 6 C'O';

<<J <<J >>' ~

55. 6

56. 9 57o>>

56. u 56.

56e 5 i rJ<<Jo ~ CC' <<J <<J ~ u u 5u 54 ~ N a

55. 1 5p. 5 SDo 8 54o 7 C'J sJ 5s/e 5

~ <<J 18- 45 C'/D u e C1 6 57 a 57. 6 56. 7 C'C <<Jm o C'/e C'J>> cE 11: 1,5 C'C <<J sJ ~ 'i. 1 C'1 <<e 55o 5 c7 4 57. 7 55. 9 cC 54. ~ 6 C6<< C'/5 11-45 C5 }.2 CC 57e 5 57. 4 c5 Q 54. 5 >><<J u '-15 sJ <<J a 1 6'8. 9 C' ~ <<J c'7 c7 J/ 57 5F. 1 54. 6 cC 1 cc <<J <<J ~ ~ n 12-45 5<<J ~ a 61. 2 51. "" 55. 6 c'7. 5 56. 9 uh 54. 5 5<<Je 9 }u:}5 55e 1. 68 uo C1 <<J 5/ ~ 4 57o<<e 57. 4 5F. 7 5c 54o 5 5 9 C'JQ s PS 1 4c C'C <<J <<J ~ ~e >>r 68. 8 c 1 55<< 4 57. 4 ~ J7<< ee 55. 7 54. 5 C <<J>> ~ Q V 7 CL-542 1 I ~ ~ 7 ~ ~ ~ ~ ~ Csgr ~ - C PL/!~, 1 s i <os Qglll >> CHN S PC' 4 C' 'r4. 4 r>>4 c 4 4 ~ r~ slIi o >>rg, ~ Ia ( ='9. 7 =:9. S .r'. 1 ~~7 1 C QPJe S 4i 1 ~ >> ~  % ~ ~ 8S:45 .n 4':.'. 5 41. 4 45 8 47. " 4S. 9 51. 41. 87:15 4c 4S 1

49. " '.:4.

47. 7 5'. 9 54e 1 4>>gl C'C rs ada>>

c C'C C'Je e! S e S

47. 47.

87:4c~ c'8 58a 5 51. C'Ca! ~ < sJ Aa DMe >>>> c9 c E='. 4 51. 9 51 8' 1 C'!>>>> ~ 7 e! ae>> ~ >>r i-'~. 9 c'7 4 S8 4i Ss ~ 1 Si. S E4. 9 54. Qi ' Oa S'. Sv. '" c'S-45 54 S 5S. 4 OsJe S F -'. 4, BS. 5 5S. C4e 89- 15 7 59. 'r 8 59 7 S:-'. 9 S~. S 67. 5 5S. Ql 55 a 89-45 18:'5 5S. 7 5S. 9 7~ 5Se cS c 1 e5>> S8. 1 ~ 7 55. 55 a S Fr 5S CCs &4l Ei. 9 ='t S4. S4. 5 r S5 S5. ~ SE. 7 S7 57e

57. b C'Pl C

57 57. a 18-4 sJ s r 5S. 7 S8, 4 O' rer S4. 8 Sc' S7 4Ga 57 a 11 ei5 57. 5S. 7 S8 5Ee 1 g r' 1 E4. 9 E5. 9 V7 ~ ~ C'Q Wva 57. 9 '1-45 ~ ~ 'J C'I <Ge s SQ..:. cS 58. u~ Sr. 1 E4.. 8 S5. 6 F7. 1 57a 57. 9 1": 1.5 57. ':: Cl SQ. ~ 55a 9 LQ E". S4. 7, S5. 7 P7 57. Pl CiP 57 5B, 7 S+ 5F. 1 64. 9 E5. 7 S7. 1 57. 9 57o Ql '-15 c'7 5Sa E S8. 56. 1 rr 5 >>L S4i ~ 7 S5. S Su. 9 57. 57. 1:": 45 c 7 56e 5 ='8. QSa 4 S4. S S5. 7 tS 7 57 7 a 57 a CHI:9 8C' ' '5 4C'S: ~S. S 85: 45 4>> Ql 87: 15 48o 4 87:45 48. 5 8G: '5 48. 7 8g e

48. 7 48.

4c'9et 5 7 ' 89: 45 48. 7 '8-15 48. 7 18-45 48. S ':15 48 '1-45 48. 9 4,1. 1 1 r 45 ~ 1 e ~ 1 C 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 c' QW ~ Pg "6. 6 oraJ 7~ ~ ..9. 4 2Q 7o M "S. 1 -6. 8 70 2".4 Se'9:88 <<'4 o Sl "B. 4 u5 4 ~5 34. 7 ~~So ~> 'p ~6. ~ g w<Mo ~o7 .9 \ ~7o N7 i7. 1 'V M o i6. 9 i5. 6 89 26. 6 ~9. 1 o 'Bo 4C .7 9 ~ 7 9 o,T 4 ~7. u ~6. 4 18:88 27, 6 ~9. 5 mq ~ ~ 48. 1  :"9. 4 <<>9o 5 "9. 7 "9. 1 v9. 1 m5o 7 18:>8 Clo 6 o,9 0 v9. 9 48. 5 48. ~ 48.; 48o 4 48 1 48o 2 11-88 v9. 9 v9. 9 48. 6 48. 4 48. 8 48. 5 48. 2 48. 5 ~~7. u~ 11:. 8 r9. E: ~9. 6 48. "-'8.

48. 6 48. 7 48. 5 48. 1 48. 6

~ 88 38 48 5 41 ~ 5 48 41 48. 7 48. 5 48. 6 ~ 8 Z8. ~ 48 48. 7 41. 9 48. 8 41. 2 48 48. 48. 5 1 i: 88 'i:~8 ~8. 4 'v,8 48, 1 48 48. 5 48. S 41 42. 9 48 48. 8 9 ~S. 4

48. 1 48 41 41 41. 1 48. 9 41. 7 48. 9 v9. 1 14:88 >8. 7 48. 2 48 Ql

41. 7 48. 8 48. 9 41 48. 41 ~ 1

'::"8 >8. 7 ~9. 8 48 ~ 41. 7 48. 5 4f. 1 48. 9 ~ 1

48. 6

~ 48o 8 "5. 7 COt"i."fENTS

i. ) TES! 4 f'9.5 i21. S

'.8119.4 ='. ) VOLT START A B C

s. ) Ql [RA START A 2.8 B C ~

.8

4. ) CHAN 9 NYALID CL 54'r TEST 4, C'

CURR 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 19 ~6. 7 'r o o 35. 6 .7. 7 "8. 1 '4 ~ 29e e 38. 2 31. 7 9o 8G 1 34. 7 37, 1 C .e 6 . c "5 7 37. 4 34. 6 8G:4 21. 9 39. 7 '7 e" v 7 3-. 5 45. 9 41. e 4 ~ .6 44. 5 4'. 5 89 ic ~ 'r3e 4 ie. 6 3e. 4 "9. 7 4r. 9 47. 4 51. 1 46e 7 4e. 1 58 46. e 8aeAc 39. 7 39. 3 48. 4. 46. ~

58. c5r rr 58. 6 cr, Vo' 54 58e e 18:15 48, 1 48, 2 48. e Ae. A.

7'3. 5 5~. C~ 44o 0 56. 9 18 45 .6. e 48 Ai 41. 5 58. 4 CC oi opere 59. 9 55e 3 57 58. 7 5ere 4 1> ~ 1 p AQ 51. e 56e 6 61. 9 56. 4 cn DGo ~ 68. 4 cS n 1 1 ~ 45 .e. F ~9 9 4'. 5 4r. 4 52e 7 57. e 57. 4 59. = 68. 9 57. e 12 ~ 48 41. e 42. 5 D~i C ~ 58. 6 63. 3 cn erGe u 68, 6' 5n c 1 ~:45 =9. 6 v9. un 41. 7 41. 9' 53o 7 63. e 58. 6 68. 5 62 5ee 9 1 ~:15 1':45 9 41. 4 i. 7 53. 9 Ca ~ U>> o 64. 5 68. 9 n 59. 4 38, 39. 7 41. 7 4: 53. 9 59. 5 64. 3 68. 9 62. 4 59o 5 14: 15 38. 4 39. 9 Are c 59. 7 64. 4 68. 6 9. 6 f3 erGe 9 9 ~o 14: 45 '8 7 ~9. 9 Arr 7 54 4 59. 9 64. S 59. 1 61. 2 6='. 7 59. 6 15: 15 38. 9 39. 6 41 6 Ai. 9 54. 3 68 64. e 59. 3 61. ~ 6=. 8 59. 7 I c5-.45 ~ i 48 54. 5 59'. 9 I I 68. 3 65 59. 5 61. 5 6 I~ COMMENTS 1 ~ ) 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 Ao ) CHN 1 " ON OUTSI DE h!SULATION

5. ) '-A.lBIENT 2-TOP CONDUIT

6. ) BOTTO!" CONDUIT 4-AI R SPACE

7. ) YOLT FINISH A . 631 B -997 C -S57 n CURR FIN1SH A 7 .8 B 7.. 1 C 71.9

9. ) END TEST 5 CL 54= 18/ r8/83 1545 C -542

CQ+gENTS - TEST NO. 6

1. ) CL- 4':: TEST 8 .ND RU" ll/18 8

) CHANNEL m9 AHBl+NT

v. ) CHANNEL " iRAY TOP

4. ) CHANN"L ~ TRAY BQ.TQl'i

) CHANNEL 4 AIR SPAC-E. ) 28 A."lP C!(7 CHANNELS 9

7. ) 25 AMP CKT CHANiNELS 8 18

8. ) 48 Ai~iP CKT CHANNELS 5~ 7

9. ) 58 AilP CKT CHANNELS 18~ 28~ ~S i8. ) CURR START A 28. ~ B 28. 4 C .8. ~

11. ) VOLT START A . 748 B . 769 C ..'SS 2 ~ CURR START A .5. 4 B 25. 8 C "5. i 1". ) VQl T S ART g j 88' 1 058 C 1, 59(

14. ) CURR START A 48. ~ 8 48. 8 C 48. Z

15. ) VOL. S ART A . 22K 8 . 214 C . 245 lbI ) CUR% SiAR: A 53.8 8 58.8 C 58.8

17. ) VOLT START A . "84 B . "89 C .287

18. ) END TEST S biD /18/8 Tl!CE 1545

19. ) CURR c'!>D A ""8. 5 B 21. 5 C ~i. 1 VOLT END A . 78c B. 8~8 C .8~7 28, ) 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

21. 5 i7. 7 c

.9 ore <<4 5o <<6o 8 o O7 o Joe ~ ~

24. 9 ore

<<do ~ 25. 6 +cuo c4 7 wz <<doc V

26. 7

'5. 6

26. 7 86-1 ~

o9. 7 ZS ~ So 8 , 29.S =-.8. 1 "r9. S ~r9 ~ 7 29. 6 29o 6 86:4u '49o u YQ u << ~,.u o'<<o J ,.:":". 9 g ~~a 2.'.,7, -vvo u ~ nu 87:15 48 Jg >9. 6 5 C'b/ ~ 4 ~ 'sJ ~ C' u o IIJo C> v5. 1 MMo 7 5 7 T5c 87:45 48. 6 48. 1 o6 5 u7. 4 u7. 8  :"7. 9 "7. S 37. 4 >7,9 u7 7 ~ 37. a 88-15 48. 7 48. 4 u8. 1 u9. 7 4 u9 6 v9. 1 59. 2 ~'3, 4 8S:45 "9. 4 48, 'r u9. 4 48. 6 41 41. 1 48. 9 48. 7 41 48. 4 48. 5 89:1 uSo 48. 7 48 or

41. 9 41. 8 4 +r 41. 6 41. 8 41. 5 41. 5 89:45 48. 1 41. u 41. 1 4r. 8 4Z. 1 4",4 4r.4 4r. 5 42 ~

18:15 48. 9 41. 5 41. 8 4 or ~ 4",4 4u. 4u. 4. 4u. 4 4 ~ .5 4r. 7 18:45 48, 41. " .6 4v. 8 4". 7 4r.9 ='u 2 4 Pg 4 4 44 7 '1:15 u9. 2 41. 1 44. 1 44. 1 44. 4 43. 9 44. " l-.. 1 4v. 5 48, 1 4r. 7 44. 6 44o 6 4u. 8 44 Qi 44. u~ 44o 5 4". 5 4u 8 12o 15 48. 9 41. 8 , ~ 1 44. 8 44. 8 44. 1 45 ~ 1

44. 6 44. 8 44 iso 4c 48. 7 41. 6 ..4v. r 4c 45. 1 44. 2 lc 44. 9 4",9 44. ~

15 >9. 4 41 2 4 44. 9 44o 9 44. 4 45 45. 1 4". 8 44. '-45 ~ ~ 4.8 41. 5 4...4 45. u 45. 1 44o 5 45o 5 4c 45. ~ 4~. 9 44. u 14:45 a9. 1 41. u 4u. 6 45. 4 45. 2 44. 6 45. 4 45o Z 4c 44. 1 44. 4 f.5- 15 <<8. 1 41 ~ 6 45. 4 44. 6 45. 45. 4 4c c 44. 4 1 c 4c ~ v9. 7 41. 5 4v. 5 4c c 45. u 44. 6 E'5. 6 45. 2 4c c 44. " 44. 5 TE IE CHOu6 CHOZS 85 '5 ac <<uo 5 Qc 4c~

6. 7 "6. 7 86: 15 Q9 Ql

'S. 5 86:45 v9. 9 87: 15 u5. 4 87: 45 8So 15 "7. Z9. u i 48. 48 48, 2 ~ BS: 45 48. 5 48. ~ 89: '5 48. 5 89:45 42. 1 48. 6 18o 18 '5 4u. 2 7 48. 48o 7 1 11 -15 48 11 -45 7 48. 5 12: 15 p 4$ 5o i or 4c 44 48. 5 1 1 49. 0 44... 48. 5 1 lL: 45 44. 4 40. 4 ico ic 44. 4 48. 7 I co45 44. " 48. 5 CL-542 Envelope Bottom for =fness Envelope Cover fahrica eQ

l<a PCS t Score Cut Steel B2JlQLng

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