ML20107B942

Provides Suppl Response to NRC RAI Re Ampacity Derating Analysis.Procedure ESA 105 Encl.Procedure ESA 105 Withheld

ML20107B942
Person / Time
Site:	Byron, Braidwood
Issue date:	03/21/1996
From:	Saccomando D COMMONWEALTH EDISON CO.
To:	NRC (Affiliation Not Assigned), NRC OFFICE OF INFORMATION RESOURCES MANAGEMENT (IRM)
Shared Package
ML20013A486	List: ML20107B942
References
IEIN-94-022, IEIN-94-22, NUDOCS 9604170151
Download: ML20107B942 (69)

Text

{{#Wiki_filter:* i, Commonwealth IMison Company 14(X) Opus Place Downers Grove, IL 605155701 March 21,1996 Office of Nuclear Reactor Regulation U.S. Nuclear Regulatory Commission Washington, D.C. 20555 Attn: Document Control Desk

Subject:

Byron Station Units 1 and 2 Braidwood Station Units 1 and 2 Supplemental Response to the NRC Request for Additional Information Regarding Ampacity Derating Analyses NRC Docket Numbers 50-454/455: 50-456/457

Reference:

1) February 15,1995, M. J. Vonk letter to USNRC 2) March 28,1995, K. L. Kaup letter to USNRC j 3) March 29,1995, K. L. Graesser letter to USNRC 4) November 2,1995, R. R. Assa letter to D. L. Farrar 5) December 4,1995, G. F. Dick letter to D. L. Farrar 6) December 15,1995, D. Saccomando letter to USNRC Reference (1) provided the Commonwealth Edison Company (Comed) White Paper that compared the NRC fest results provided in Nuclear Regulatory Commission (NRC) Information Notice 94-22 for determining the ampacity derating factors for cable trays wrapped with three-hour rated Thermo-Lag 330-1 fire barriers with the Comed analytical techniques and results used to derate the ampacities of cables installed in wrapped trays. Reference (1) also provided the calculation that determined the ampacity derating factors for the potential Darmatt KM-1 Fire Barrier System to be installed at Braidwood Station. 9604170151 960321 PDR ADOCK 0500o454 i G PDR 146866 N 'll /h )? k:lic:ampacity7. doc g* gC / Mpu( j A Unicom Company 8

1 Document Control Desk March 21,1996 Reference (2) provided the response to the NRC Request For Additional Information, pursuant to 10CFR50.54(f), dated December 29,1994, for i Braidwood Station. Reference (3) provided the response to the NRC Request l For Additional Information(RAI), pursuant to 10CFR50.54(f), dated December 29,1994, for Byron Station. Reference (4) is the NRC Request For Additional Information regarding the ampacity derating analyses performed for Braidwood Station. Reference (5) is the NRC Request For Additional Information regarding the ampacity derating analyses performed for Byron Station. Reference 6 transmitted Comed's request to respond to the Braidwood and Byron RAls (references 4 and 5) concurrently because many of the issues discussed in the Braidwood RAI apply to Byron Station. The information being j transmitted in this letter is Comed's response to the RAls. The following provides some general clarification regarding the RAls transmitted in references 4 and 5 : l General: Though reference (1) was provided in response to phone l conversations between Comed and the NRC staff with respect to the planned Darmatt KM-1 installations at Braidwood, reference (2) subsequently notified the NRC staff that the re-routing of safe-shutdown cables to eliminate the need for installing fire-rated barriers had been chosen as the preferred option to achieve resolution of the Thermo-Lag 330-1 issues for Braidwood Station. Similarly, reference (3) notified the NRC staff that the re-routing of safe-shutdown cables to eliminate the need for installing additional fire-rated barriers had been chosen as the preferred option to achieve resolution of the Thermo-Lag 330-1 for Byron Station, for those applications that had not been previously protected with the Darmatt KM-1 fire barrier. At the Byron and Braidwood stations, the installed l Thermo-Lag 330-1 fire barriers are to be abandoned in place and no credit is being taken at either station for it as a fire barrier. With the selection and pursuit of the re-routing option, no Darmatt KM-1 fire l barrier is planned to be installed at Braidwood station and the cited Calculation l G-63, Revision 2 no longer applies to Braidwood. However, as noted above, some Darmatt KM-1 is installed at Byron Station and the NRC questions apply to these Byron installations. Therefore, the NRC questions have been answered i based on the Byron installation configurations. (Please note that the current revision of calculatien G-63 is Revision 2. Revision 3 of this calculation does not j exist, as cited in reference (4).] i k:hc:ampacity7. doe l

Document Control Desk March 21,1996 1 i Comed has been reevaluating the Byron and Braidwood Thermo-Lag 330-1 1 { ampacity analyses and has concluded that additional actions are necessary. This reevaluation has determined that the existing analyses may not completely ) envelope allinstalled configurations. Specifically, the as-installed Thermo-Lag ) 330-1 board thickness, in some cases, may be greater than the nominal value j supplied by TSI. This thicker Thermo-Lag 330-1 board value had not been used ) in prior ampacity derating calculations. Also, some installations may have an air gap between the Thermo-Lag panel and the cable tray that had not been modeled in the prior ampacity derating calculations. These identified conditions are being addressed at both stations and the appropriate calculations will be revised as necessary. During this reevaluation, Comed will compare the j analytical methodology to valid industry test data. Comed intends to utilize existing industry data that is readily available and has no plans to perform l additional ampacity derating tests. The following are the Comed responses to the specific NRC requests and j observations as presented in references (4) and (5). l A) From Reference (4): 1) . Request (Ref.: ltem 1, Pages 1 & 2): " Given that the referenced 1982 4 ampacity experiments were performed using solid bottom cable trays and i those experimental results are bases for determining the intemal resistance between cables and the surface of a covered tray, the subject l analysis must be considered to be limited to that application. In fact, the i 1982 American Power Conference paper, ' Tests At Braidwood Station on i the Effects of Fire Stops on Ampacity Rating of Power Cables', makes \\ note of the fact that the industry ampacity tables were found to be nonconservative for some of the tested configurations. l Based on the above discussion, the licensee is requested to confirm that all of the cable trays under consideration for Braidwood Station are solid bottom trays of the type used in the original tests performed for Braidwood Station as reportedin the aforementioned 1982 paper. If other types of cable trays are applicable for Braidwood Station, then a specific and detailedjustification for the applicability of the licensee's methodology should be submitted by the licensee." k:lic:ampacity7. doc

Document Control Desk March 21,1996 Answer: For Darmatt KM-1 Installations: All of the cable trays for Byron Station that are protected by the Darmatt KM-1 fire barrier are solid bottom trays of the type used in the original tests performed at Braidwood Station, and are governed by the methodology provided to the NRC staff in reference (1). As stated above, Braidwood Station currently has no plans to install any Darmatt KM-1 Gre barriers. Therefore, the question of cable tray wrapped with Darmatt KM-1 at Braidwood is not applicable. For Thermo-Lag 330-1 Installations: The existing Thermo-Lag 330-1 installations at the Byron and Braidwood Stations will be abandoned in place. Essentially all fire wrapped cables trays are solid bottom of the type used in the original tests performed at Braidwood Station. However, there is one 30 inch long section of ladderback tray, that provides a transition between two solid bottom cable tray sections, installed in Unit 2 at both stations. Because this section of ladderback cable tray, with respect to the total cable tray run, is a relatively small length, Comed believes its effect with respect to the ampacity derating values is insignificant. However, as stated above, Comed is reevaluating the ampacity calculations for the as-installed condition of the Thermo-Lag 330-1 installed at the Byron and Braidwood Stations, which will include an evaluation of this transition section. 2) ObservationlRecommendation(Ref.: Item 2, Page 3): "Although the licensee's methodology contains many conservative features, the staff questions whether the licensee's White Paperprovides an adequate basis for validation of the cable tray analysis method. Although the staff would not require a validation of the cable tray analysis assuming that the 1992 experiments performed for Braidwood station bound Thermo-Lag cable tray types, it is recommended that these calculations be revisited with valid industry test data. There are clearly more appropriate tests for which a more representative comparison and validation can be made (e.g., Comanche Peak Steam Electric Station, Unit 2. ampacity derating tests). It would cleady be desirable to see the licensee's analysis methodology validated against experimental data." k:lic:ampacity7. doc

1 4 Document Control Desk March 21,1996 Answer: Comed concurs that the methodology developed to calculate ampacity derating factors is conservative, however, concerns regarding the actual installed configurations have been identified. These identified concerns are being addressed at both stations and the appropriate - calculations will be revised as necessary. As previously stated, a comparison of the analytical methodology against valid industry test data will be made. Comed intends to utilize existing industry data that is readily available and has no plans to perform additional ampacity derating tests. 3) Observation / Request (Ref.: Item 3, Pages 3,4 & 5): "SNL noted an apparent error was made in the treatment of the air gap between the conduit and the fire bam*er system. The licensee's analysis utilizes a ' trick' which is commonly applied to steady state rectangularproblems. The ' trick' involves a mathematical manipulation where the air gap is converted \\ to an equivalent thickness of Dalmatt based on the ratio of their thermal conductivities."... "Unfortunately, this approach can not be applied j directly to annularregions.".. "Hence, the conversion of an annular gap of airinto an annular gap of Darmatt must be consistent with the above logarithmic form."... "SNL recalculated the values for the 1 hour and 3 hour barrier systems for a 3/4" conduit using the licensee provided data..." "The licensee is requested to address the above apparent discrepancy and to revise its analysis accordingly. " Answer: Comed acknowledges that the SNL derived equa!ien does provide a more accurate determination of the thermal resistance values of the conduit covered with the Darmatt KM-1 and will incorporate it into calculation G-63. In calculation G-63, Revision 2, the postulated il16" air gap was modeled as an assumed condition that is not expected to exist in the actual installation, since the Darmatt KM-1 is installed in direct contact with the conduit surface. This assumed value provides additional margin into the calculation and the simplified approach of converting the air gap to an equivalent thickness of Darmatt KM-1 was considered to be an appropriate model for calculating the total thermal resistance. The difference in the resultant thermal resistance between the model used and the calculation and the exact formula used by the NRC staff is 0.73 hr-ft *F/ BTU for a 3 hour Darmatt KM-1 barrier on a 3/4" conduit. However, it appears that the value of thermal conductivity used in the NRC staff calculation only accounted for heat transfer across the air gap k:he:ampacity7. doc w ..y m l

l Document Control Desk March 21,1996 by conduction. Heat will also be transferred across the air gap by radiation, which, based on the information provided, was not taken into account in the calculation. When the heat transfer by radiation is taken into account, the effective thermal resistance of the air gap will be decreased. This reduces the difference between the thermal resistance determined in Calculation G-63, Revision 2 and the thermal resistance calculated by the NRC staff. Therefore, since the SNL derived equation does provide a more accurate determination of the thermal resistance i values of the conduit covered with the Darmatt KM-1, Comed will incorporate this equation into calculation G-63. l 4) ObservationlQuestion(Ref.: Item 4, Page 5): "Given the information provided, the nature of the cable insulation andjacket resistance calculations are not clear. Specifically, th3 calculations presented as the top six lines ofpage 130 of Calculation G-63 require clarification. Although the calculations attempt to account for the cable insulation and jacket regions as annular regions, why are the multipliers of 2 and 3 applied to various parts of the resistance? How does the licenseejustify simply adding the vadous components without consideration of parallel path heat transfer and the fact that heat is not flowing from the center of each conductor radially through each individual conductor, but rather non-uniformly through the multi-conductor cable as a whole?" Answer: The first expression calculates the temperature drop between the conductor and the insulation and individual jacket surrounding each conductor:

• p,in gy

+ p, in -L rg V l 0.00522 x 2 t <d, d,, _ For a single conductor cable, the insulation and jacket would be concentric annular layers, and the thermal resistance in consistent units would be: 1

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4 s . 61 aJ a, u u.... u.. n u.., u u u a a u a u, u u n u u R.lt. Fig. 2-Geometric factors for single-conductor cable and multisooductor belted cable with round or sector conductors Geometric factors can be obtained by calculating the ratios (T + f)/4 and t/T (d beine denned for sector cables as the diameter of a round conductor of the same area as the sector), and then reading the required value of geometric factor from a curve above. The value thus obtained will be the correct geometric factor for a round-conductor cable. For sector con-ductors the values so obtained should be multiplied by the sector correction f actor. In cables of the non-type H form without belts, such as multi conductor rubber cables, the ratio becomes T/d, and t/T = o. a 13

I j 1 Document Control Desk March 21,1996 For the mixed units often used for cable calculations, the inclusion of the required unit conversion factors gives rise to the coefficient 0.00522. For a three conductor cable, the heat flow will not be uniform due to the proximity l of the other heated conductors, and the effective thermal resistance will be increased. The multiplier of 2 accounts for this increase. This factoris i based on formulations referenced in a 1957 paper by Neher and McGrath' The Neher-McGrath paper uses equations for this temperature drop of the form: 1-pG l-27r where, G is a geometric factor that takes the non-uniform heat flow into account. The expression 21n g > losely approximates the values of G, 1 c <d> as can be seen in the plot of G taken from Figure 2, page 13 of the D. M. Simmons paper. ' d'

• f d + 2t h 21n

- 21n I <d, d ) The second term accounts for the temperature drop of the three phase conductors passing through the overall Jacket: r g'#" 0.00522 x 3pj in < d,,,, i This resistance is applied to the heat generated by a single conductor. However, the overall jacket surrounds three heat generating conductors. Therefore, the factor of 3 is required to calculate the proper amount of heat flowing through the Jacket when the equation is multiplied by the heat generated by one conductor to obtain the temperature drop. l ' Neher,J. H. and McGrath, M. H.1957. "The Calculation of the Temperature Rise and Load Capability af Cable Systems". ALEE Transactions on Power Apparatus andSysterns 76 (October):752 72.

1. Donald M. Simmons, General Cable Corporation, " Calculation of the Electrical Problems of Underground Cables", reprinted from The Electric Journal, issues of May to November,1932, inclusive L:lic:ampacity7. doc

4 Document Control Desk March 21,1996 i 1 5) Observation (Ref.: Item 4, Page 5): "For this geometry, a cable reshng on the bottom inside of a conduit, treatment of the problem as one of purely annular regions, which apparently are cascaded one upon another, is not correct and appears to ignore the inherent 2-dimensionality of the problem." Answer: The expression used to calculate this temperature drop is equation 41A of the Neher-McGrath paper: R, =,' D, + B' 1 where D,' is the circumscribed diameter of the cables in the conduit and A' and B' are constants that depend on the conduit material. This equation has been in general use and is accepted industry practice. The derivation of the formula is given in Appendix l of the Neher-McGrath paper. As can be seen in this appendix, while the formula is partly derived from theoretical considerations, it is calibrated using experimental cata. Additional information that was used in the derivation of this formula is given by two other papers" 6) Request (Ref.: l tem 4, Page 5): " Based on the above discussion, the licensee is requested to submit a copy of Sargent & Lundy(S&L) Standard ESA -105. Further, the licensee should explain in greater detail, the full nature of the cable-to-conduit thermalresistance calculation process. This description should include a detailed explanation of both the basis. andintent of calculations (e.g., the first six lines on page 130 of the 1 i I i l l 8 Buller, F. H. And Neher,J. H.1950. The Thermal Resistance Between Cables and a Surrounding

• pe or Duct Wall. AIEE Transactions, VolumeI. 69:342-349 Pi Greebler, P. And Barnett, G. F.1950. Heat Transfer Study on Power Cable Ducts and Duct Assemblies. AIEE Transactions, Volume 1. 69:357-367.

k:lic:ampacity7. doc

Document Control Desk March 21,1996 Comed Calculation G-63) and an explanation andjustification for merging the two separate calculations into a single expression." Answer: Comed believes that the above answers and discussions address the cable-to-conduit thermal resistance calculation process. The relevant portions of S&L Standard ESA-105 have been addressed or summarized, along with justification for the formulae involved. However in response to the NRC Staff request, S&L Standard ESA-105 is provided in Attachment B. Comed is notifying the NRC Staff that S&L Standard ESA-105 is a proprietary document to S&L and requests that the staff control this document, accordingly. 7) Observation / Request (Ref.: ltem 5, Pages 5 & 6): "Another concem is the value assumed for the emissivity of the outer surface of the conduit. In both the cable tray and the conduit analyses, a lower bound value of 0.23 is used. In the casa of the cable tray analysis this was concluded to be a conservative approach. However, in the case of the conduit analysis, this appmach is aciuc!!y nonconservative."......"For conservatism, the conduit baseline case analyses should consider the maximum possible conduit surface emissivity rather than the minimum value." " Based on the above discussion, the licensee is requested to assess the impact on the calculated ampacity derating factors by using an upper bound emissivity value(i.e., 0.8 - 0.9) in its baseline conduit calculations." Answer: Comed acknowledges that utilizing an upper bound emissivity value (i.e., 0.8 - 0.9) would add conservatism to the conduit and cable tray analysis. However, postulating an emissivity value other than 0.23 is believed to add unnecessary conservatism to the calculation that does not properly represent the galvanized steel material from which the conduit and cable tray is fabricated. The cable tray and conduit emissivity value of 0.23 utilized in Calculation G-63, Revision 2 was taken from the, " Standard Handbook for Mechanical Engineers", Baumeister and Marks, Seventh Edition. This is listed as reference #7, on page 9 of 215 of the calculation. An emissivity value of 0.23 is applicable to the steel conduit modeled in the calculation and installed in the plant and is considered to be appropriate as utilized in the calculation. Uic:ampacity7. doc

Document Control Desk March 21,1996 8) Observation / Request (Ref.: ltem 6, Page 6): "The licensee did not provide any experimental validation of the analytical methodology for conduits based on actual test data. The licensee is requested to evaluate the validity of their analytical methodology using available industry test data. " Answer: The Neher-McGrath methodology used in Calculation G-63, Revision 2 and discussed above, has been used by the electricalindustry for calculating the ampacity of cables since the time it was derived. As mentioned in the papers referenced above, key parts of this methodology have been calibrated using test data. This methodology has been accepted in the Nationa/ Electrical Code [NFPA 70-1996, Clause B-310-15(b)(2)]. However, as previously stated, an attempt to validate the analytical methodology against valid industry test data will be made. Comed intends to utilize existing industry data that is readily available and has no plans to perform additional ampacity derating tests. B) From Reference (5): 1) Request (Ref.: Item 1, Page 2): "Please provide a copy of the typical calculation (s) depicting the use of the subject analytical methodology which were used to determine the ampacity derating parameters for the Thermo-Lag fire barriers that are installed at Byron Station." Answer: Though the methodology described above formed the basis for determining the ampacity derating parameters for the Thermo-Lag 330-1 fire barriers installed at the Byron and Braidwood Stations, a specific Byron and Braidwood calculation utilizing that methodology was not prepared. Rather the 33% derating factor for the Thermo-Lag 330-1 cited in the White Paper was determined by performing an independent evaluation of the raw data from an ampacity test, l.T.L. Report No. 82 555F, dated July,1982. This derating factor was compared to the calculated value of 32%, determined in the calculation (19-Al-8), referenced in the White Paper. Using the derating factor of 33%, detailed calculations for the cable routing points were then performed to confirm that the previously determined ampacities were still acceptable. L:lic:ampacity7. doc

a Document Control Desk March 21,1996 As previously stated, Comed is reevaluating the as-installed condition of the Thermo-Lag 330-1 installed at the Byron and Braidwood Stations, and concludes that additional actions are necessary. This reevaluation has determined that the existing analyses may not completely envelope all installed configurations. The identified conditions are being addressed at both stations and the appropriate calculationc will be revised as necessary. These will be made available for NRC Staff review. 2) Request (Ref.: ltem 2, Page 2): "/n its submittal of December 16,1994, the licensee referred to a site specific comparison regarding the acceptability ofplant ampacity derating parameters when compared to the test results citedin IN 94-22. The staff recognizes that most licensees may have excess ampacity margin using valid test data. However, those licensees who utilize industry test data must evaluate whetherinstalled configurations are representative of the tested configurations. The subject evaluations should also analyze any deviations of the installed configuration with respect to the test configuration. It should be noted that the methodology usedin the ampacity test differs significantly from the methodology utilized by the draft industry test procedure IEEE P848. In the event that the licensee wishes to use the test results citedin IN 94-22, the licensee must indicate whether the subject test configuration is representative of Thermo-Lag enclosed configurations which are installed at Byron Station." Answer: As previously stated, Comed is reevaluating the ampacity calculations for the as-installed condition of the Thermo-Lag 330-1 at the Byron and Braidwood Stations. During this reevaluation, a comparison of the analytical methodology against valid industry test data will be made. Comed intends to utilize existing industry data that is readily available and has no plans to perform additional tests. During this re-evaluation, any industry test data utilized for comparison, including the IN 94-22 data, will be evaluated for applicability to our analytical model. k:lic:ampacity7. doc

Document Control Desk March 21,1996 Please note Sargent & Lundy(S&L) Standard ESA -105 contains information proprietary to Sargent & Lundy, it is supported by an affidavit signed by Sargent & Lundy, the owner of the information (see Attachment B). The affidavit sets forth the basis on which the information may be withheld from public disclosure by the Commission and addresses with specificity the considerations listed in Paragraph (b)(4) of Section 2.790 of the Commission's regulations. Accordingly, it is respectfully requested that the information which is proprietary to Sargent & Lundy be withheld from public disclosure in accordance with 10 CFR 2.790 of the Commission's regulations. Correspondence with respect to the proprietary aspects of the items should be addressed to K. Kostal, Executive Vice President, Sargent and Lundy,55 East Monroe Street, Chicago, IL. 60603-5780. To the best of my knowledge and belief, the statements contained in this document are true and correct. In some respects these statements are not based on my personal knowledge, but on information furnished by other Comed employees, contractor employees, and/or consultants. Such information has been reviewed in accordance with company practice, and I believe it to be reliable. If there are any further questions concerning this matter, please contact this office. {[;;; OFFICIAL SEAL..:.. :.,..... Sincerely, 3 MARY JO YACK 3 h(NOT ARY PUBUC, STAT f I e, M N Denise Sbamando Senior Nuclear Licensing Administrator

• '7 O# 7/M M J2 %

b' l l Attachments: cc: H. Miller, Regional Administrator - Rlil G. Dick, Byron Project Manager-NRR R. Assa, Braidwood Project Manager-NRR l H. Peterson, Senior Resident Inspector-Byron C. Phillips, Senior Resident inspector-Braidwood i Office of Nuclear Facility Safety - IDNS i i k:lic:ampacity7. doc

I l i 4 I Attachment "A" Documents cited in the responses to items (10) and (11): 1) Neher, J. H. and McGrath, M. H.1957. The calculation of the Temperature Rise and Load Capability of Cable Systems. A/EE Transactions on Power Apparatus and Systems 76 (October):752-72. i 2) Donald M. Simmons, General Cable Corporation, " Calculation of the Electrical Problems of Underground Cables", reprinted from The Electric Journal, issues of May to November,1932, inclusive

3) Buller, F. H. And Neher, J. H.1950. The Thermal Resistance Between Cables and a Surrounding Pipe or Duct Wall. AIEE Transactions, Volume I.

69:342-349.

4) Greebler, P. And Barnett, G. F.1950. Heat Transfer Study on Power Cable Ducts and Duct Assemblies. AIEE Transactions, Volume I. 69:357-367.

l I l [ l i k:lic:ampacity7. doc

_, _ _ -, _. - - - - - - - " ' - ~ ' - - 'Ks H3 (%CICUlat.ien er{ tria Tamparatura Risa /' l l I du' ete =from image of cable no.1 to e -t rf-- { D = diameter, inches and Load Capability of Cable Systems D,=inside of annttlar conductor g :=:= d,t =:r, D,=outside of sheath J. H. NEHER M.H.McGRATH D, =mean diameter of sheath MEMBER AIEE D =outside of Jacket i MEMBER AIES D,' = eflective (circumscribing circle) of several cables in contact D,-inside of duct wall, pipe or conduit N 1932 D. M. Simmonsi published a sideration as being the most consistent , = dia er at s tot earth portion i series of articles entitled " Calculation of the Electrical Problemsof Underground and most readily handled over the full scope of the problem. D,= fictitious diameter at which the efect Cables." Over the intervening 25 years of loss factor commences this work has achieved the status of a All losses will be developed on the basis E=line to neutral voltage, kilovolts (ky) of watts per conductor foot. The heat , = coefficient f surface emissivity handbook on the subject. During this period, however, there have been numer-flows and temperature rises due to dielec.

• ~*"**kt"d"#*I"'**E*#I'*"#*I i"'"!*'

ous developments in the cable art, and. tric lossand tocurrent produced losses will much theoretical and experimental work be treated separately, and, in the latter f= frequency, cycles per second F, Fa,-products of ratios of distances han been % with c. vicw te ubLaining case, all heat flows will be expressed in F(x)= derived Bessel functinn nt.e (Table termsof the currentproducedlossoriginat. more accurate methods of evaluatm, g the ing in one foot of conductor by means of C =ceo et.e fa tor parameters involved. The advent of the C -applying to insulation resistance (Fig. 2 pipe-type cable system has emphasized multiplying factors which take into ac-i of reference 1) the desirability of a more rational method count the added losses in the sheath and Us= applying to dielectric loss (Fig. 2 of

conduit, of calculating the performance of cables reference 1)

In general, all thermal resistances will h'co*nd in duct m order that a realistic comparison be developed on the basis of the per con-eu en, kiloampe o may be made between the two systems. ductor heat flow through them. In the and segmental conductors k,= skin eHect correction factor for annular In this paper the authors have en. case of underground cable systems, it is deavored to extend the work of Simmons convenient to utilize an effective thermal kr= relative transverse conductivity f, actor by presenting under one cover the basic resistance for the earth portion of the[gr calculatmg conductor proximity principles involved, together with more thermal circuit which includes the effect!= lay of a shielding tape or skid wire, inches recently developed procedures for han. d1ing such problems as the eHect of the of the loading cycle and the mutual heat. L-depth of reference cable below earth's surface, laches loading cycle and the temperature rise ing effect of the other cable of the system. 16" depth to center of a duct bank (or of cables in various types of duct struc-All cables m. the system will be considered backfill), anches tures. Included as well are expressions to carry the same load currents and to be (if)= load factor, per unit required in the evaluation of the basic operating under the same load cycle, (1F)= loss factor, per unit n= number of conductors per cable The system of nomenclature employed n'= number of conductors within a stated parameters for certain specialized allied is in accordance with that adopted by the ,",'f eables or cable groups in a procedures. It is thought that a work of this type will be useful not only as a guide Insulated Conductor Committee as stand-y,,, to engineers entering the field and as a ard, and differs appreciably from that used system P= perimeter of a duet bank or backfill, in many of the references. This system inches reference to the more experienced, but particularly as a basis for setting up com. represents an attempt to utilize in so far es = er te of,the ins lon putation methods for the preparation of as possible the various symbols appearing 9 gg , 9 industry load capability and a-c/d-c ratio in the American Standards Associatiot* conductors and sheaths to the losses compilations. Standards for Electrical Quantities, Me-in the conductors chanics, Heat and Thermo Dynamics, g,= ratio of the sum of the losses in the conductors, sheath and conduit to The calculation of the temperature rise and liydraulics, when these symbols can of cable systems under essentially steady.. be used without ambiguity. Certam R = ele r cal resistance, ohms state conditions, which includes the effect symbols which have long been sned by Ru=d-c resistance of conductor of operation under a repetitive load cycle, cable engineers have been retained, even Ru= total a-c resistance per conductor as opposed to transient temperature rises though they are in direct conflict with R,=d c resistance of sheath or of the parallel paths in a shield skid wire due to the sudden application of large the above mentioned standardt amounts of load, is a relatively simple R = thermal tesistance (per conductor losses) procedure and involves only the applica. Nomenclate thermal ohm-feet tion of the thermal equivalents of Ohm's A, = of i,nsulation and Kirchoff's Laws to a relatively simple (A F)= attainment factor, per unit (pu) A,= cross-section area of a shielding tape n cable surface and surrounding etw thermal circuit. Because this circuit

• or skid wire, square inches enclosure usually has a number of parallel paths a-thermal diffusivity, square inches per hour with heat flows enterm.g at several pom. ts, however, care must be exercised in the CI-conductor area, circular inches Paper s7-66o, recommended by the AIER !asuisted tnethod used of expressing the heat flows d= distance, inches Conductors Committee and approved by the AIEE j

and thermal resistances involved, and a etc.= from center of cable no.1 to center[*$*daE E*[* m"e'r c7.'S*Yr'eIt7as"."Eo".'tr)d I n of cable no. 2 etc. o... c.anda. June 24-2s, 1937. Manuscript subay,t*d y *r[b g l'87; differing methods are used by various en-dn, etc.=from center of cable no. I to =*ds *'*ilabl* 'ar } gineers. The method employed in this image of cable no. 2 etc. J. H. Nsuss is with the PhnadelpHa Electrie . p per has been selected after careful con-da etc.=from center of cable no.1 to a 7"A"7db"d$$*'ca$ie cNUo$ PN point of interference Ambor, n. J. 732 Neher, McGrath-Teml>erature and Load Capability of Cable Systems Octoaan 1957

.O j h E I I l j80 --W /;ss [ // 8.o m% // d hs i x3 /[//,Q ao2s / /I/ V =$ \\ ',. "% $ ~b //A// ! =4,, i n i ///// A Q x U iw Eg ////[ !M R $5 l, hill W ///// l i @i,i, . i; i % "**"3 //////

• 2

,;y 2 2 2

.~

accas o 2s I I ' " // /// c Q-.. me 27l ! ! i j wf",s /'//'// s oas h aco ! i!$ l i ;I %4 l l l. l ///// i s':w wo, e,o 3 2 a.s 3 4 s 6 7 6 91D is 2o Jo do So 6o aoloo j // Rdc/h j f [f (([/[ Fi. 1 (*bove). F(x) and F(x,') es functions of R4./k ~ IIM n,. w,6o. as Io, e d.ct h.nu ,Ili// a .s .s a .s a 2 .s R4=of duct wall or asphalt mastic covering R.,= total between aheath and diameter 'P D, including Rj, R.4 and Rd RATIO Lb/ R =between condult and ambient R.'=efective between diameter D, and i ambient earth including the efects of loss factor and mutual heating by IVs" portion developed in the conductor Thus IVs" Portion developed in the sheath or other cables R '= effective between conductor and shield T.-T.= AT,+ AT4 degrees eentigrade ambient for conductor loss IFa" portion developed in the pipe or con. (g) duit R. '=efective transient thermal resistance IFd portion developed in the dielectric Each of these component temperature of cable system X."= mutual reactance, conductor to sheath rises may be considered as the result of a R4.'= effective between conductor and am. or shield, microhms per foot bient for dielectric loss rate of heat flow expressed in watts per Y=the increment of a-c/d c ratio, pu Ases-of the interference effect Y,=due to losses originating in the con-foot through a thermal resistance ex-R,.=between a steam pipe and ambient ductor, having components Y., due pressed in thermal ohm feet (degrees centi-earth t skin ef t and Y,, due to prox. grade feet per watt); in other words, the p = elec 1 resistivity, circular mil ohms radial rise in degrees centigrade for a heat A= thermal resistivity, degrees centigrade Ys-due to losses originating la the sheath or shield, having components Y., flow of one watt uniformly distnluted 4 centimeters per watt s= distance in a 3 conductor cable between due to circulating current effect and over a conductoriength of one foot. the effective current center of the Y,. due to eddy current effect Sm, ce the losses occur at several posi-conductor and the axis of the cable, Y,=due to losses originating in the pipe tions in the cable system, the heat flow in or conduit S= axial spacing between adjacent cables, Y.=due to losses originating h the armor the thermal circuit will increase in steps. inches It is convenient to express all heat flows in inches General Considerations of the termsof thelossperfootof conductor,and em ra re, de g d Thermal Circuit thus T.=of ambient air or earth 'I T,=of conductor T =mean temperature of medium Tus cat,Ctn.ATION OF TswPERArtras degrees centigrade (2) AT= temperature rise, degrees centigrade Risa AT,=of conductor due to current produced losses The temperature rise of the conductor in which IV, represents the losses in one f a cable above ambient temperature may conductor and Re is the thermal resistance {" Ij,d",C be considered as bemg composed of a of the insulation, g, is the ratio of the , ble due to extraneous eat r=lerred temperature of zero resistance, temperature rise due to its own losses, sum of the losses in the conductors and source degrees :ent grade (C) (used in which may be divided into a rise due to sheath to the losses in the conductors, correcting Ra, and R to tempera-current produced (PR) losses (hereinafter Ru is the total thermal resistance between n51ve ty idles per hour referred to merely as losses) in the conduc-sheath and conduit, g, is the ratio of the tor, sheath and conduit AT, and the rise sum of the losses in conductors,sneath and F. = conductor foot produced by Its dielectric loss AT4 conduit, to the conductor losses, and R. IV= tosses developed in a cable, watts per 753 Ocsoann 1957 Neher, McGrath-Temperature and Load Capability of Cable Systems

e, 4 la ths thermal resistance between the AT,= W,(R +g.Ru+g,[R$+(LF)X Tabis I. Electrical Resistivity of Writus conduit and ambient. (Ass)+(N-t)R,.)) (5) Materials ) is rarely constant and varies according to In practice, the load carried by a cable " We(A +feese +f*Ee') 8 degrees centigrade (5A) a daily load cycle having a load factor where the term in parentheses is indicated od'.$'r$ (lf). Hence, the losses in the cable will by the effective thermal resistance R.'. 38* '*1

• ao c

,, c vary according to the corresponding The temperature rise due to dielectric daily loss cycle having a loss From an examinatson of a larg, factor (LF). loss is a relatively small part of the total 1%j((p',^!A e number of temperature rise of cable systems op-commermi nross.C lord cycles and their corresponding load erating at the lower voltages, but at cgj^cS*'io za) (43.es.. sa.s...so4 and loss factors, the following general rela-higher voltages it constitutes an appre, ar= (sts% Acs).. as.o . 912 tiomhip between load factor and loss ciable part and must be considered. Al-IAt (SN.Ncs)... factor has been found to exist.8 though the dielectric losses are dis- .... 132.s ...saa (LF)=0.3 (I/)+0.7 (t/)* per unit (3) tributed throughout the insulation, it may .laternational Annented Copper Standard. be shown that for single conductor cable i In order to determine the maximum and multiconductor shielded cable with Calculation of Losses and Associated Parameters temperature rise attained by a buried round conductors the correct temperature cable system under a repeated daily load rise is obtained by considering for tran-CA1.cULAT10N OF D-C RESISTANCES cycle, the losses and rewltant hnt flows sient and steady state that all of the are calculated on the basis of the maxi. dielectric loss W, occurs at the middle The resistance of the conductor may be mum load (usually taken as the average of the thermal resistance between conduc. determined from the following expressions current for that hour of the daily load tor and sheath or alternately for steady. which melude a lay factor of 27o; see cycle during which the average current is state conditions alone that the tempera. Table I. the highest, i.e. the daily maximum one, ture rise between conductor and sheath for hour average load) on which the loss factor a given loss in the dielectric is half as R,, = 1.02a, microhms per foot at 20 C is based and the heat flow in the last part much as if that loss were in the conductor. of the earth portion of the thermal circuit In the case of multiconductor belted (to) t2.9 is reduced by the factor (LF). If this cables, however, the conductors are taken f 7f r 100% IACS copper reduction is considered to start at a point as the source of the dielectric loss.1 conductor at 75 C (10A) in the earth corresponding to the diameter The resulting temperature rise due to 21.2 D,,8 equation 2 becomes dielectric loss AT, may be expressed g for 01% IACS A T, = W,les +fsSu +9,( A,s +(LF)A,e)I AT,- W,R,.' degrees centigrade (6) aluc2inum at 75 C (10B) degrees centigrade (4) in which the effective thermal resistance In effect this means that the tempera. A,.'is based upon A,, R.,, and A,'(at unity where Cl represents the conductor size in ture nse from conductor to D, is made to loss factor) according to the particular circular inches and where p, represents depend on the heat loss c6rrespondmg to The temperature rise at points in the electrical resistivity in circular mil case. the maximum load whereas the tempera. the cable system other than at the cen. ohms per foot. To determine the value of ture rise from diameter D, to ambient is duetor may be determined readily from resistance at temperature T multiply the made to depend on the average loss over a the foregoing relationships. resistance at 20 C by (r+T)/(r+20) where r is the inferred temperature of 21 hour period. Studies indicate that the Tits cat. cut.ATton or LOAD CAPAmt.ITY 2em rebistance. procedure of assuming a fictitious en. ical In many cases the permissible maxs.- The resistance of the sheath is given i t diameter D, at which an abrupt change mum temperature of the conductor is by the expressions occurs in loss factor from 1007, to actual fixed and the magnitude of the conductor will give results which very closely R, =4D.: microhms per foot at 20 C (11) current (load capability) required to approximate those obtained by rigorous produce this temperature is desired. transient analysis. For cables or duct Equation 5(A) may be written in the form R. 37 9-- for lead at 50 C (11A) in air where the thermal storage capacity Da8 of the system is relatively small, the maxi-gggy ygp_, mum temperature nse is based upon the degrees centigrade (7) ,, 4;7,5 for 61% aluminum at 50 C heat flow corresponding to maximum load ' in which the quantity R,, (1+ Y,) which p,,3 without reduction of any part of the will be evaluated later represents the (1IB) th:rmaleircuit. effective electrical resistance of the con-where D. is the mean diameter of the When a number of cables are installed ductor in microhms per foot, and wh ch sheath and i is its thickness, both m close together in the earth or in a duct when multiplied by 18 (I in kiloampam) inches bank, each cable will have a heating effect will equal the loss W, in watts per conduc-upon all of the others. In calculating tur foot actually generated in the conduc-D.=D,-s inches (12) 4 the temperature rise of any one cable, it is to ; and R.' is the effective thermal The resistance of intercalated shields convenient to handle the heating effects of r;sistance of the thermal circuit. or skid wires may be determined from the the other cables of the system by suitably A, '=Ri+g,R,+g,A ' thermal ohm feet expression modifying the last term of equation 4. (8) j1+ ( p )\\n This is permissible since it is assumed /, From equation 1 it follows that R, (per path) =,,, thit til the cables are carrying equal cur-g rents, and are operating on the same load f T,-( T. + a T,) microhms per foot at 20 C (13) cycle. Thus for an N-cable system R,(1+ Y,)R c amperes where A, is the cross-section area of the 754 Neher, McGrath-Temperature and Load Capability of Cable Systems OcrOann 1957

? a The Tabl311. Recimataded Wlu;s cf k.ad k, ,J tipe or skid wire and I is its l' y. over all resistance of the shield and skid wire assembly, particularly for noninter. condacier cen irection coatins en strands Treatment k. !re calated shields, should be determined by electrical measurement when possible. Caac'atrie rouad.- Naa*..... . No**.. .3.0 -30 Io Concentrie round.. . Tin or alloy.. .. None.. .1.0 .0.80 Concentr6e round.. . None.. . Yes.. .t 0 C A!.Ctn,ATION OP l.,OSSES Compact round...... . None.. . Yes.. .1.0 .o6 Compact segmental., . None...... .. None.. .o.435. ..0.6 It is convenient to develop expressions Compact segmental.. . Tin or alloy.. . None.. . 0. 6 4.0. 7 - for the losses in the conductor, Sheath and Compact segmental.. . None.. . Yes.. .o.435. ... 0.37 Compact sector.. . None., , ) es.. .1. 0.. .(see note) pipe or conduit in terms of the components Norse: of the a.c/d.c ratio of the cable system 1. The term ** treated denotes a completed conductor wbich has been subjected to a drytag and impregnat-which may be expressed as follows i, p,,,,,,,i ii.,,, "s., e m pioy,d o, o.p,, p,..,,,3i.. 4 t R /R. = 1 + Y.+ Y, + Y, W L h*7*"***"""****""*FM***'8**Md**'****""" t8 4 having the same cross-sectional area and insulaQ a thickness. The a-c/d c ratio at conductor is 1+ Y, 3. proximity eseet on annular conductors may be approximated by using the vaive for a concestric round conductor of the same crosa. sectional area and spacing. The increased diameter of the annular type a Genew ImeaImm e untu eenaws t nun eSut but. for a sino asial spacing, unds end at Sheath or shieId Is IY YsY l#s to result in an increase in prosimity. 4. The valuu usted abon for compact wgmental nfu to four wgment constructions. The " uncoated. and at pipe or conduit is 1+ Y.+ Ya+ Y, treated" vslues may also be taken as applicable to four segment compact segemental with ballow core (ap-For unconted.t hollow core compact segmentallimited proximately 0.75 ineb elear).te.t data i.aates a, and a, vaine,"ef e.se an,reated", sit segment The cormpuuu..ms wa*s physically gen 9.33,,p ti.iy. er ted in the conductor, sheath, and pipe cre Table Ill. Skin E#ect in % in Solid Round Conductor and in Conventional Round Concentric IV,=l'R4,(1+ Y,) watts per conductor foot Strend Conductors (15) 100 F(x), Skin E#ect % IV, =18R4, Y, watts per conductor foot (16) 0 1 2 3 4 5 6 7 8 o TV, = I8R4, Y, watts per conductor foot (17) 0.3.. o.co... o.co.. o.oi... o.oi.. o.oi. 0.ot. 0.01, 0.oi.. o.01.. o.o1 This permits a ready determination of the 0 01 " 0.os m 0.02 m 0.02 m 0.02.. u 2.. o.03 m 0.03 - us lo6ses if the 8egregated a-c/d-c ratios are 0 4 '.. ". 03. " o5 0 0.04. o 04.. 0.04... 0.05.

0. 05..

0.05.. o.06.

0. 06..

o.06 known, and conversely, the a c/d-c rat,o 0.6.. o.07.. o.07.. o.08.. 0.08.. 0.09. 0.10. o.10. 0.11. o.18. 0.12 t o.12. 0.13.. 0.14.. o.t5.. o.16. o.17.. o.18. o.19.. 0.19. 0.20 is readil obtained after the values of Y8' 0 7 ",, Y o.8 0.21.. 0.22... o.24.. o.25.. 0.26. o.28. o.29.. o.30.. 0.31.. 0.33 Y, and Y, have been calculated. 0.9.. o.34.. 0.36. 0.38.. o.39.. o.41. 0.43. o.45.. o.47.. o.48.. o.s0 1.0.. o.82.. 0.54.. o.84. o.68... 0.61.. o.63.. o.65.. o 68.. 0.70... o.73 It follows from the definit. ions of g, and 1.1.. o.76. o.79. 0.81. o.84.. o.87. o.90.. o. 94.. o.97... 1.00.. 1.03 1.2.. 1 07.. 1.11.. 1.14.. 1.18.. 1.22. i.26.. 1.30.. 1.34. 1.38... 1.42 q that 1.3. 1.47... 1.62... 1.56.. l.61.. 1.66.. 1.71.. 1.76.. 1.81.. 1.86.. 1.92 1.4.. 1.07.. 2.02.. 2.08.. 2.14.. 2.20.. 2.26. 2.32. 2.39... 2.45, 2.62 (gg) 1.5.. 2.88..

2. 65..

2.72.. 2.79.. 2.86. 2.93. 3.01. 3.08.. 3.16... 3.24 y pyg y8.g4 +8 [V, 1 y, 1.6.. 3.32.. 3.40... 3.49.. 3.87.. 3.66.. 3.75.. 3.83. 3.92... 4.02.. 4.11 g,. 1.7.. 4.21, 4.30.. 4.40.. 4.80.. 4.60.. 4.70.. 4.81.. 4 91.. 6.02.. 8.13 1.8.. 6.24... 5.35.. 8.47.. 5.58.. 5.70.. 5.82. 5.94.. 6.06. 6.19.. 6.31 (gg) 1,0.. 6.44.. 6.57., 6.70.. 6.83.. 6.97. 7.11. 7.24... 7.38.. 7.53. 7.67 y 4 y8 gy84;y84;y8. g 4,4 7, }V, 1 2.o., 7.82..

7. 96..

8.11.. 8.26.. 8.42.. 8 67.. 8.73... 8.89... 9.05... 9.21 9,. 2.1., 9.38.. 9.54. 9.71... 9.88.. 10.05.. 10.22.. 1o.40.. 10.58.. 10.76.. 10.94

2. 2..

11.13.. 11.31. 11.80.. 11.69.. 11.88. 12.07.. 12.27 12.47 12.67.. 12.87 The factor Y, ts the sum of two compo-2.3. 13.07. 13.27.. 13.48.. 13.68.. 13.90.. 14.11.. 14.33.. 14.54.. 14.76. 14.98 Deuts, Yea due to Skin eHect and Y,, due 2.4. 15.21, 15.43.. 15.66.. 15.89. 16 12.. 16.35.. 16.58.. 16.82.. 17.16.. 17.30 2 6. 17.84. 17.78. 18.03. 18.27. 18.52.. 18.78.. 19.03.. 19.28.. 19.54.. 19.80 proxtmity eHect. 2.6.. 20.06. 20.32. 20.a8.. 20.85.. 21.12.. 21.38. 21.65.. 21.93. 22.20. 22.48 2.7.. 22.75.. 23.03.. 23.31, 23 60.. 23,88.. 24.17. 24,45.. 24 74.. 25.03. 26.83 IV =18R4,(1 + Y,,+ Y,,) 2.8.. 25 62.. 2s.92.. 26.21. 26.81.. 26.81.. 27.11.. 27.42. 27.72.. 28.03.. 28.34 2 9.. 28 65.. 28.96.. 29.27.. 29.88.. 29.90.. 30.21. 30.53.. 30.85.. 31.17. 31.49 watts per conductor foot (20) 3.0.. 31.81.. 32 13.. 32.45.. 32.78. > 33.11.. 33 14.. 33.77. 34.10.. 34.43.. 34.77 3.1., 35.10.. 35.44.. 35.78.. 36,11. 36.45.. 36.79.. 37.13.. 37.47.. 37.82.. 38.16 The skin effect may be determmed from 3.2.. 38.s0.. 38.85.. 39.20.. 39.ss.. 39.89.. 40.24.. 40.s9. 40 94. 41.29.. 41.6s 3.3.. 42 oo.. 42.35. 42.71. 43 06. 43.42. 43.78. 44.14. 44.49.. 44.85.. 45.21 the sk.in eHect function F(x) 3.4.. 45.s7.. 45.93.. 46.29.. 46.66.. 47.02.. 47.38.. 47.74.. 48.11.. 48.47. 48.84 3 8. 49.20.. 49.87.. 49.94. 60.30.. 50.67.. 61 o4.. 51.40. 51.77. 82.14, 52.81 . 83 99. 54.36. 54.73.. 68.10.. 55.48.. 55.85.. 56.22 E,s - I(Xs) (21) 3.6. 52 88.. 53.25 - 53 62.. 3.7.. 56.69. 56.96: 57.33.. 57.71 . 58.08. 58.45. 58.82.. 59.20. 59 87.. 59.94 l/k,- 0.80 3.8.. 60.3t.. 60.69.. 6t.06.. 61 44.. 61.81.. 62.18.. 62.56.. 62 93.. 63.30.. 63.68 3.9.. 64 os., 64.42.. 64.80., 65 17. 65.s5.., 65 92.. 66.29.. 66.67.. 67.04.. 67.41 x,=0.8754 - VR4,/h at 00 cycles 1 R4, 4.o.., 67.79.. 68.16.. 68.83.. 68.91.. 69.28.. 69.65.. 70 03.. 70 40.. 70.77., 71.14 (22) 4.1.. 71.82.. 71 89.. 72.26.. 72.63.. 73 00., 73 38.. 73.75.. 74.12.. 74.49.. 74.86 4.2.. 75.23. 75.60. 75.97. 76 34.. 76.71.. 77.08. 77.45.. 77.82. 78.19, 78.86 43. 78 93.. 79 30.. 70.67.. 80.04. 80.41.. 80.78.. 81.14. 81.81.. 81.88. 82 25 in which the factor k depends upon the 4.4.. 82.61. 82.98.. 83.33., 83 61. 84.08.., 84.4s. 84.8t. 83.18.. 85.ss. 8s.91 86 28. 86.64.. 87.01.. 87.37.. 87.73.. 88.10.. 88.46.. 88.82.. 89.19. 89.8s conductor construction. For solid or 4.s. 46. 89.91.. 90.28.. 90.64. 91.00.. 91.37.. 91.73.. 92.09.. 92.45.. 92 81., 93.17 convent. tonal conductors appropriate 4 7.. 93.83.. 93.89.. 94.25.. 94 61. 94.97.. 95.33.. 95.69.. 96.05.. 96.41.. 96.77 Values of k:Will be found in Table II. The 4.8.. 97.13.. 97 49.. 97.8s. 98 21.. 98.s7. 98.92.. 99.28.. 99.64..100.00.. 100.35 i

49..100.71.

101.07..101.42.. 101.78.. 102.14. 102.49..302.88..103.21.. 103.56..103.92 function f(x) may be obta.med from Table III or from the curves of Fig.1 in terms i of the ratio h/k at 60 cycles. For annual onductors and inner diameters of the annular con-annular conductor when computed by f ductor. In comparison with the rigorous equation 23 will not be in error by more k, p p, pg. p, i (23) Dessel function solution for the skin effect than 0.01 in absolute magnitude for j d* in an isolated tubular conductor, it has copper or aluminum IPCEA (Insulated 8 in which D, and D, represent the outer been found that the 60-cycle skin effect of Power Cable Engineers Association) filled 755 OCTODEn 1957 Neher, McGrath-Temperature and Load Capability of Cable Systems

l t Tabb IV. Mutual Reactanci at 60 Cydes, Crnductor te Shrth (rr Shidd) (2 S/Dm) as in the case of lead sh aths. l D /25 0 1 2 3 4 s 6 7 8 9 J yu " R, R,\\ 2S /.1 +- 4 12 \\ 2S /. I 04. .21 1. .20.5...19 9.. .19 4.. .18.9.. .18.3. .17.8. .17.4.. .16.9., .16.4 approximately at 60 cycles (30A) 0.3.. . 27. 7.. .26.9...26.2.. .25 6. . 24.8.. ,.24.1. . 23.6.,. 22 9.. .22.2.. .21.6 kI.' '.![I '.$$I. $$ '.$$ b $$I: '$$ I, '!2.$L $$. :N.j; ;M When the sheaths are short-circuited, the sheath eddy loss will be reduced and may be approximated by multiplying equations core conductors up through 5.0 CI and for also be estimated from equation 24 and 30 or 30(A) by the ratio 1 hollow core concentrically stranded copper 24(A). In such cases, S should be taken R,'/(R,'+X ') or aluminum oil. filled cable conductors as the axial spacing between adjacent up th. " gh 4.0 CI. conductors. In c mputing average eddy current for For va.s.es of x, below 3.5, a range The factor Y,is the sum of two factors, cradled con 6guration, S should be taken which appear to cover most cases of prac-Yu due to circulating current effect and equal to the axial spacing and not to the tical interest at power frequencies, the Y, due to eddy current effects. geometric-mean spacmg. Equations 30 conductor proximity effect for cables in and 30(A) may be used to compute the R ;( Yu+ Yu) equilateral triangular formation in the s" d eddy-current effect for single conductor same or in separate ducts may be cal-watts per e nductor foot (26) cables installed in separate ducts. culited from the following equation based Because of the large sheath losses which btrictly speakmg, these equations apply on an approximate expression given by result from short-circuited sheath opera-only to three cables in equilateral con-j Arnold * (equation 7) for a system of tion with appreciable separation between 6guration but can be used to estimate j three homogeneous, straight, parallel, metallic sheathed single conductor cables, losses sa large cable groups when latter are solid conductors of circular cross section this mode of operation is usually restricted so oriented as to approximate a regular arranged in equilateral formation and to triplex cable or three single-conductor I P ygon. carrying balanced 3 phase current remote cables contained in the same duct. The The eddy current effect for a 3-conduc. from all other conductors or conducting circulating current effect in three metallic tor cable is given by Arnold.' material. The empirical transverse con-sheathed single-conductor cables arranged ductance factor k, is introduced to make in equilateral configuration is given by Yu = 3R,~ (2s/Dm)' (2s/D,.)4 + + the expression applicable to stranded R /R,, +1 +1 conductors. Experimental results sug-Yu (27) - f f m gest the values of k, shown in Table II.

1. '!'Y"U (22/Dm)'

~ (33) en (R,/X.)8 is large with respect t 16[.2R,y+l Y,,= F(x,)(D,, X 7 unity as usually is the case of shielded non. \\// 1.18 leaded cables, equation 27 reduces to (24) When (5.2R,/f)' is large with respect to .F(x,) +0.27 +0.312\\S/. X. y,g#'# ' approximately (27A)

unity, 0.80 d

396[2s}s x, = /Ra,/k, * 'Y' E""M flog 2 /D,. Yn?p,gd, \\p, \\ microhms per foot (28) When the second term in the brackets approximately at 60 cycles (31A) -52.9 log 2S/D. is small with respect to the first term as it microhms per foot at 60 cycles (28A) s=1.155T+0.60Xthe V gauge depth for usually is, equation 24 may be written conapact sectors where S is the axial spacing of adjacent .0.295(D,/S)',

1.155T+0.58 D, for round conductors y,,q(y) cables. For a cradled configuration X

(32) . F(r,) +0.27 may be approximated from =4(g,\\S D and Tis the insulation thickness,includ-F(x,') (24A) 2.52 S [1,[ S }8 ing thickness of shielding tapes, if any. D. \\D,-S/ While equation 31(A) will suffice for lead where the function F(x,') is shown in microhms per foot at 60 cycles (29) sheath cables, equation 31 should be used E' I' The average proximity effect for con- =52.9 log 2.3 S/D,. for aluminum sheaths. ductors in cradle configuration to the approx mately (29A) On 3-conductor shielded paper lead same duct or in separate ducts in a forma-Table IV provides a convenient means for cable it is customary to employ a 3 or 5-tson approximating a regular polygon may deternunmg X. for cables in equilateral mil copper tape or bronze tape inter. e n6guration. calated with a paper tape for shielding and binder purposes. The lineal d c resist. The eddy-current effect for single-Tabb V. Specific Inductive Capultance of conductor cables in equilateral configura-ance of a copper tape 5 mils by 0.75 inch Insulations tron with open.ctreutted sheaths is is about 2,200 microhms per foot of tape at 20 C. The d-c resistance per foot 3 R, /R,, of cable will be equal to the lineal resist. ""A I" " X +g[ 2S \\) correction factor as given by the expres-1 ance of the tape multiplied by the lay 5.2 R, 8 Potrethylene................. s. s y P:pa lasulation (solia trpe).. 3.7 UPCB A value) /D 8 -1 + 5 /Dm\\ s-sion under the square-root sign in equation Paper tosulados (otha types). 3.3-4. s (30)

13. In practice the lay correction factor

.'4.7.. 'I. .I 7. 8 ~ ~ may vary from 4 to 12 or more resulting UPCEA value) varsi.hea cambrie..........a uPCa A valug) when (5.2 Rdf)'is large in respect to 1/5 in shielding and binder assembly resist-750 Neher, McGrath-Temperature and Load Capability of Cable Systems OCrossn 1957

ances of cpproximately 10,000 or more and for 3-conductor belted cable by Tabla VI. Tittmal Resistivity of Verish.t a ah microhms per fcot of cable. Even on 0.019Es., cos 6 the assumption that the assembly resist-We= watts per 0 ' matortat A.ccm/ watt ence is halved because of contact with ad- 'Y* ' IU jacent conductors and the lead sheath computations made using equations 27 where E is the phase to neutral voltage Paper insulation (solid type).. 700 (IPCE A value) ' cEA nin) and 30 show that the resulting circulating in kilovolts, e, is the specific inductive P'M",*d l'$E/,4N6[o ui t, Rubber and rubber like...... 500 (IPCE A value) and eddy current losses are a fraction of capacitance of the insulation (Table V) T 1% on sizes of practicalinterest. For this is its thickness and cos c is its power factor. "Uns.'""' " " ".500 reason it is customary to assume that the The geometric factor Ce may be found Qd,"j*gg;, j losses in the shielding and binder tapes from Fig. 2 of reference 1. Tran.ite dues. .200 of 3-conductor shielded paper lead cable Fcr compact sector conductors the di-c > r.'I ' are negligible. 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 frequently employed, tube same cross-sectional area and insulation THERMAL RESISTANCE OP J ACKETs, Dcct tapes are effects may be present and may materially thickness. WALLS, AND SOMAsTIc COATINGS lower the resistance of the shielding assem. bly and hence increase the losses to a Calculation of Thennal Resistance The equivalent thermal resistance of pomt where they are of practical s,igmfi-relatively thin cylindrical sections such as InsRuAL Rn:mTANCE OF THE I:CULATIOM jackets and ha duct walb may b* cance. An exact detenninat,on of the p,pe loss For a single conductor cable, determined from the expression i i effect Y, an the case of single-conductor thermalohm feet \\ cables installed in nonmagnetic conduit R,=0.012h tog D./D, R =0.01044,s'/ g } thermal ohm feet (38) or pipe is a rather involved procedure 60) as indicated in reference 7. Equation 31 where h s the thermal resistivity of the i may be used to obtam a rough esttmate insulation (Table VI) and De is its with appropriate subscr. ts applied to ip of Y, for cables in cradled formation on diameter. In multiconductor cables Y the bottom of a nonmagnetic pipe, how. there is a multipath heat flow between the outside diameter of the section and iits ever by taking the average of the results thickness, n'is the number of conductors obtained for wide triangular spacing P'***I " P'***"t8 "" '9"IV"I'"I '"I"' contained with the section contributing with s=(D,-D )/2 and for close tri. which, when multiplied by the heat flow th" Ihi angle spacing at the center of the pipe from one conductor, will produce the with =0.578 D.. The mean diameter of O THERMAL RESISTANCE BETWEEN CABLE

• • E*'* "#*

the pipe and its resistance per foot should nductor abow the sheath. SURFACE AND SURROUNDING PIPE, be substituted for D,. and R, respectively. CONI)UIT, OR DUCT WALL, For magnetic pipes or conduit the R, = 0.00522AC thermal ohm-feet (30) i Theoretical expressions for the thermal following empirical relationships' may be Values of the geometric factor Ci for 3 resistance between a cable surface and a employed conductor belted and shielded cables are surrounding enclosure are given in refer-given in Fig. 2 and Table VIII respec. As indicated in Appendix I, 1,, = 1.54s -0.115D, tively of reference 1. On large size sec. ence 10. these have been simplified to the general R,, (33) tor conductors with relatively thin in. IO N sdaen ds (i.e. ratios of insulation 0.89S-0.111D,(single-conductor, thickness to conductor diameter of the n'A Y, = order of 0.2 or less); values of Ci for 3 Asd " l +(B + CT.)D,' close triangular) (34) conductor shielded cable as detertnined (41) Y, = ' (single-conductor, by back calculation, on the basis of an in which A, B, and C are constants, D ' R4, assumed insulation resistivity, from lab-cradled) (35) oratory heat run temperature rise data, represents the equivalent diameter of the have not always confirmed theoretical cable or group of cables and n' the neuber These expressions apply to steel pipe' values, and, in some cases. have yielded of conductors contained within D,'. T. and should be multiplied by 0.8 for iron Ci values which approach those for a is the mean temperature of the interven. nonshitlded, nonbelted construction. ing medium. The constants A, B, and C conduit.' The expressions given for Y, and Y, above should be multiplied by 1.7 to find (.onstants fer Use in Equtions 41 and 41(A) Table Vil the corresponding in pipe effects for mag-netic pipe or conduit for both triangular Cesdition A B C A' B' and cradled configurations. CALCULATION OF DtELEcTRIC 1 oss to metanie conduit.. .17 .3 o . 0 029. .3.2.. . 0.19 to 6ber duct in air.m. .17 ,.2.1 . 0 016 .s.6. . 0 3s The dielectric loss lY, for 3-conductor la Aber duet in concrete.. 17 .2.3. . 0.024. .4.6.. . 0.27 shielded and single-conductor cable is 'l l,'*"$1"c'l ll 'I'Jfrete., j jj.1 N. jI N2 Can-6Hed pipe cable at 200 pai.- .3I. ..l.16., ,.0.0053. .2.1. . 0.68 given by th4 expression Oil-Alted pipe cable.. . 0.s4. .0 . 0.006s. .2.1. .2.45 0.00'36E'e, cos # p,. i.00x diameter or cable tor one cable gratts per 1.65 x diameter of cable fer two cables E,d "10E (2 T+D.)/D8 2.15 x diameter of cable for three cables i conductor foot at 60 cycles (36) 2.s0xdiameter or cable for tour cable. 1 757 Neher, McGrath-Temperature and Load Capability of Cable Systems Ocroosn 1957

g

• given in Table VII have been determined heiting effects of the other cables of the mum. N refers to the number of cables or from the experimental dita given in reftr.

system. In the case of cables in a con-pipes, and Fis equal to unity when N= 1. , j ences 10 u a1, crete duct bank, it is desirable to further When the cable system is contained i If representative values of T.=60 C recognize a difference between the thermal within a concrete envelope such as a are assumed, equation 41 reduces to resistivity of the concrete A, and the duct bank, the effect of the differing. ,,j, thermal resistivity of the surrounding thermal resistivity of the concrete en. R.4 =O',+0, thermal ohm feet (41A) earthA,. velope is conveniently handled by first as-Tbe thermal resistance between any suming that the thermal resistivity of the It should be noted that in the case of point in the earth surrounding a buried medium is that of concrete 7, through. j ducts, R., 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 8 ing beyond the concrete envelope to the t the duct wall should be added to obtain R,.=0.0124, log d'/d thermal ohm-feet therrnal resistivity of the earth 4.. Thus S**- (43) R,'=0.0124 m'X THEaMAL RES! STANCE FROM CABLES, in which 4. is the thermal resistivity of the [og 84(47) jog \\D,/ y,, i 4 CONDtHTS, On Ducts SUSPENDED IN earth, d' is the distance from the image De Ata of the cable to the point P, and d is the 0.012(A,-AJ 'N(LF)Cs The thermal resistance R, between distance from the cable center to P, thermal ohm-feet (44A) cables, conduits,or ducts suspended in still From this equation and the principles t.ir mIy be determined from the following discussed in references 3,12, and 13, the '"**""'."'"""N" expression which is developed in Ap-following expressions may be developed, in Appendix II is a function of the depth to the center of the concrete enclosure pendix I. applicable to directly buried cables and La and its perimeter P, and may be found to pipe-type cables. 15.6s, convemently from Fig. 2 in terms of the g*, D,'[(a T/D,')d* + 1.6e(1 + 0.0167 T.)] R,' = 0.0124 n' X ratio Is/P and the ratio of the longest to thermal ohm-feet (42) p, r short dimension of the enclosure. 4 In this equation AT represents the differ. De 5/. For buried cable systems T. should be ence between the cable surface tempera. thermal ohm-feet (44) taken as the ambient temperature at the ture T, and ambient air temperature T. in depth of the hottest cable. As indicated zu which D,is the diameter at which the in reference 12, the expressions used degrees centigrade, T. the average of these temperatures and a the coeflicient of earth portion of the thermal circuit com. throughout this paper for the thermal rnences and n' is the number of conduc. reststance and temperature rise of buried emissivity of the cable surface. Assum. tors contam, ed within D The fictitious cable systems are based on the hypothe. ing representative values of T,=60 and T.=30 C, and a range in D,' of from 2 diameter D, at which the effect of loss sis suggested by Kennelly applied m ) factor commences is a functson of the accordance w,th the principle of super-i to 10 inches, equation 42 may be simplified diffusm,ty of the medium a and thelength position. According to this hypothests, to of the loss cycle.s the isothermal-heat flow field and tem. 9.5s' perature rise at any point in the soil sur-1 + 1.7D.'(e +0.41) D, =1.02Va(length of cycle in hours) founding a buried cable can be represented (42A) inches (45) by the steady-state solution for the heat fbw between two parallel cylinders The value of a may be taken as equal The empirical development of this equa-8a rec to 0.95 for pipes, conduits or ducts, and tion is discussed in Appendix III. For a g te a, } in a in6 planted or braided surfaces, and from 0.2 daily loss cycle and a representative value medium of uniform temperature and to 0.5 for lead and aluminum sheaths, of a=2.75 square mehes 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 interestmg to be noted that the value of D, obtamed depth of burial and with source and sink note that equation 42(A) checks the from equation 45 is applicable for pipe respectively generating and absorbing IPCEA method of determining R. very diameters exceedmg D,, in which case the heat at identical rates, thereby resulting closely with e=0.41 for diameters up to first term of equation 44 as negative. in the temperature of the horizontal mid. 3.5 inches. In the IPCEA method R,= The factor F accounts for the mutual plane between cylinders (i.e., correspond. 0.00411 n'B/D/ where B-G50+314 D,' heatmg effect of the other cables of the ing to the surface of the earth) remaining, for cable system, and consists of the product by symmetry, undisturbed. i the ratios of the distance from the D,'-0-1.75 inches and B -1.200 for targer The principle of superposition, as values of D,, reference cable to the image of each applied to the case at hand, can be stated of the other cables to the distance to that in thermal terms as follows: If the ther. ErrscTrva THERMAL REs! STANCE cable. Thus' mal network has more than one source of BETWEEN CADLES, Dt' cts. OR PIPES, /g\\/g\\ / r\\ temperature rise, the heat that flows at r s AND AnotENT EARTit F-p. g }(N-1 terms) any point, or the temperature drop be. As previously indicated, an effective (g) tween any two points, is the sum of the thermal resistance R,' may be employed to heat flows and temperature drops at represent the earth portion of the thertnal It will be noted that the value of F will these points which would exist if each circuit in the case of buried cable systems. vary depending upon which cable is source of temperature rise were considered This effective thermal resistance includes selected as the reference, and the maxi-separately. In the case at hand, the the effect of loss factor and,in the case of mum conductor temperature will occur sources of heat flow and temperature rise a multicable installation, also the mutual in the cable for which 4LF/D, is a maxi-to be superimposed are, namely, the heat 758 Neher,.1fcGrath-Temperature and Load Capability of Cable Systems. Octoann 1957 ~

- - - - - - -. -.. - - - - ~ _ _ _ - _ ,t from the cable, the outward flow of heat IT,'-PW Y,)(R.'- Ru')-(T@T ) kiloampetes (47) I' " from the core of the earth, and the in-yg, ward heat flow solar radiation, and, when present, the heat flow from interfering in which Ru' is the effective transient i sources. By employing as the ambient thermal resistance of the cable system for where A,. is the thermal resistance be. temperature in the calculations the tem-the stated period of time. Procedures tween the steam pipe and ambient earth, perature at the depth of burial of the for calculating Ru' for times up to several hottest cable, the combined heat flow hours are given in reference 14, and for AERIAL CABLES from earth core and solarradiation sources longer times in references 15-17. In the case of aerial cables it may be desirable to consider both the efects of is superimposed upon that produced at HE ErrEcr or EXTRANEOUS IIEAT the surface of the hottest cable by th solar radiation which increases the tem-heat flow from that cable and interfenng perature rise and the effect of the wind OURCES sources which are calculated separately In the case of multicable installations which decreases it." Under maximum with all other heat flows absent. The the assumption has been made that all sunlight conditions, a lead-sheathed cable combined heat flow from earth core and cables are of the same size and are sim-will absorb about 4.3 watts per foot per solar sources results in an earth tempera-ilarly loaded. When this is not the case inch of profile" which must be returned ture which decreases with depth in summer ; the temperature rise or load capability to the atmosphere through the thermal increases with depth in winter; remains of one particular equal cable group may be resistance A,/n', This effect is con-about constant at any given depth on the determmed by treatmg the heating effect veniently treated as an interference average over a year; approximates con. of other calde pwps sc;:aratdy, mtro' temperaime 16 according to the rela. stancy at all depths at midseason, and ducing an interference temperature nse tionship in turn results in flow of heat from cable AT., in equations 1 and 9. Thus AT,. - 4.3D.'R,/n' sources to earth's surface, directly to sur.

• ~#'+

face in midseason and winter and in- ,,,,,," centigrade (IA) For black surfaces this value should be directly to surface in summer. /T (T.+ aT4+aTi. ) g,g gg gg Factors which tend to invalidate the f, k, Ru(1+ Y,)Ra' As indicated in Appendix II, the follow-combined Kennelly-superposition princi. kiloamperes (9A) ing expression for R, may be used where pie method are departure of the tempera. F. is the velocity of the wind in miles per ture of the surface of earth from a true in which ATs,,, represents the sum of a hour isothermal (as evidenced by meltmg of number of interference eHects, for each snow m wmter directly over a buned f which 3.5n' steam main) and nonuniformity of thermal resistivity (due to such phe-aT. = [W,q,(l F)+ WalRt., D,'(V V /D,'+0.62,) degrees centigrade (48) thermal ohm-feet (42B) l nomena as radial and vertical migration of moisture). The extent to which the A s. -0.0124,n' log Fs.: thermal ohm-feet USE Or Low REsistivtTV BACKFILL Kennelly-superposition pnnenple method (49) In cases where the thermal resistivity is invalidated, however, is not of practical importance provided that an over all or ym.fd'8')(d"')(du')..dn' (N terms) of the earth is excessively high, the value (du)(du)(du).. dye of R,' may be reduced by backfilling the effective thermal resistivity is employed in (50) trench with soil or sand having a lower the Kennelly equation. value of thermal resistivity. Equation where the parameters apply to each sys. Special Conditions tem which may be considered as a unit. 44(A) may be used for this case if Af, the thermal resistivity of the backfill is sub-For cables in duct stituted for A., and C. applies to the Although the majority of cable tem. Re., =0.012n'[A, log Fe.,+ N(A - A,)Cel zone having the backfillin place of the I perature calculations may be made by thennd ohm cet (MA) zone occupied by the concrete. the foregoing procedure, conditions fre'- quently arise which require somewhat Because of the mutual heating between SINcLE-CONDUCTOR CA. LEs IN Duct 9 specialized treatment. Some of these cable groups, the temperature rise of the wrrn sot.mtv BONDED SHEATHS are covered herein. interfering groups should be rechecked. If all the cable groups are to be given The relatively large and unequal sheath EnsacENCY RATINos mutually compatible ratings, it is neces-locses in the three phases which may result sary to evaluate IV, for each group by from this type of operation may be deter-Under emergency conditions it is fre-successive approximations, or by setting mined from Table VI of reference 1. It quently necessary to exceed the stated up a system of simultaneous equations, will be noted that nonnat temperature limit of the conductor substituting for IV,its value by equati R, I,. 8 / R, In' T, and to set an emergency temperature 15 and solv, g for I, y,,,.

y,n. (R*

R* I* I, m timit T,'. If the duration of the emer. In case ATs. or a component of it is y,[\\Ro/ \\ I' /'R'YIts'h p gency is long enough for steady-state con-produced by an adjacent steam main, the k@ ditiIns to obtain, then the emergency temperature of the steam T rather than / i rating I' may be found by equation 9 the heat flow from it is usually given. where expressions for In'/I8 etc., appear Thus in the table. The resulting unequalvalues substituting T.' for T, and correcting Re for the increased conductor temperature. of Y,in the three phases will yield unequal j If the duration of the emergency is less a T,, values of g,, and equation 5 becomes for than that required for steady-state con.

• T, -- T. ~ S

ditions to obtain, the emergency rating R,. phase no.1, the instance given as equa. of the line may be detennined from degrees centigrade (51) tion 5(A) on the following page. 759 Neher..WGrath-Temperature and Load Capability of Cable Systems ( OctonEn 1957 i

J. 4T.i-W.[h +9nl Au +R..+(LF)A,al + Tabl[ Vill. Constats for Use in E(uetion 53 t i Ng,,(L F)R,e] thIrmalohm-feet (5A) ) l ' *i trheregu.is the average of gn, gn, and go. Average l conditten a b s at I Anuonzo CADI.ES i CaMe in metsilic condult.. .. 0. 07.... . 0.121.. . 0.0017... .20 l In mult:. conductor armored cables a Cable in Aber duct to air...... . 0.07.. . 0.036........ 0.0009.. .20 c.bie in aber duct to concrete.. . 0. 07... . 0.043.... . 0 0014.. .20 loss occu.s in the armor which may be cable in transite duct in air.......... 0. 07..... .. 0.088....... . 0.000s.. ... 20 j considered as an alternate to the conduit Cable to transite duct la concrete....... 0.07.. . 0.079.. . 0.0016.... .20 o.,4 i,4 pipe. type cable at 200 psi.. . 0. 07.. .0.121. . 0.0017. .10 i i or pipe lass. If the armor is nonmag-i netic, tFe cornponent of armor loss P. to be used instead of Y, in equations 14 based upon all of the data available and and a range of 150-350 for D,'T., equation cnd 19 may be calculated by the equa* including the effect of the temperature of 54 reduces to equation 41 with the values tions fc' sheath loss substituting the the intervening medium. of A, B, and C given in Table VII. resistan'e and rnean diameter of the The theoretical erpression for the case In the case of cables or pipes suspended armor ior those of the sheath. In cal-where the intervering medium is air or gas in still air, the heat loss by radiation may culitit 8 the armor resistance, account as presented in reference 10 may be general. be determined by the Stefan Bolzmann ized in the following form: formula should be taken of the spiralling effect for which equation 13 suitably modined n' n'W(radiation) may b used. If the armor is mag ~ [aTP jt/s -0.1%D,* i(T,+mP-(T.+mWO 8 net}c, one would expect an increase in D,' \\ ,) % T",, watts per foot (55) the factors Y, and Y. In equation 14 "h *'* sinei this occurs in the case of magnetic

• b

' I' th' * *III*I*"* I **I'*I"I*# conduit. Unfortunately, no simple prn-Ra=the effective thermal resistance be* of the cable or pipe surface. Over the i cedure is available for calculating these tween cable and enclosure in thermal limited temperature range in which we are interested, equation 55 may be simplified effects. A rough estimate of the induc. p,,- t he ble diameter or equivalent tive effects may be made by using the pro

• diameter of three cables in inches n'W(radiation)=0.102D.'ATeX cedure given above for magnetic conduit.

aT= the temperature differential in degrees (1 +0.0167 T.) watts per foot (55A) l A simple method of approximating the centigrade losses in single conductor cables with steel-P=the pressure in atmospheres Over the same temperature range the T.=mean temperature of the medium in heat loss by convection from horizontal wire armor at spacings ordm.artly em-degrees centigrade cables or pipes is given with sufficient ployed in submarine installations is to as-n'= number of conductors involved accuracy by the expression i sume that the combined sheath and armor current is equal to the conductor current.t The constants a, b, and,c in this equation n ' W(con vection ) = 0.064 D,'A T( A T/D,') d8 The effective a c resistance of the armor have been established empirically as follows: watts per foot (56) Considering b+cT. as a constant for the miy be taken as 30 to 60% greater than moment, the analysis given in reference in which the numtrical 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 fit with the dicated above. Il more accurate calcula. thus established, the data given in reference carefully determined test results reported ions are des. d references 19 and 20 10 for cable in pipe, and in reference 11 by IIcilman'8 on 1.3, 3.5 and 10.8-inch t. tre will be found useful. for cable in fiber and transite ducts were diameter black pipes (s = 0.95). Incl. j analyzed in situllar manner to give the dentally, this value also represents the values of b and c which are shown in Table best fit with the test data on 1.9-4.5 inch ErscCT OF FoncED COOUNO VIII. diameter black pipes reported by Rosch.sa in order to avoid a reiterative calculation For vertical cables or pipes the value of The temperature rise of cables in pipes procedure, it is desirable to assume a value this numerical constant may be increased i or tunnels may be reduced by forcing air for aT since its actual value will depend by 22%88 axially along the system. Similarly, in up n ha and the heat flow. Fortunately, Combining equations 55(A) and 56 we the c:.se of oil-filled pipe cable, oil may as aT occurs to the 1/4 power in equation obtain the relationship 53, the use of an average value as indicated be circulated through the pipe. Under in Table VIII will not introduce a serious AT p'~ 'W(total) these conditions, the temperature rise is error. n not uniform along the cable and increases By further restricting the range of in the direction of flow of the cooling D,' to 1-1 inches for cable in duct or 15.6s' medium. The solution of this problem is a T/D,')W+1Es(1 +0.0lW.H es. equati n is edu e o eq t discussed in reference 21. 41, thermal ohm feet (42) n'A If the cable is subjected to wind having Appendix I "'I +(8 + cr.)D., thermal hm-feet a velocity of F. miles per hour, the follow- ) ing expression derived from the work of Schurig and Frick84 should be substituted Development of Equations 41,42, l and Table VII in which the values of the constants A, f r the convection component. B, and C appear in Table VII. Thtorttical and semiempirical expressions In the case of oil tilled pipe cable, the n'W(c avcetion)=0.286D,'ATVV,/D ' for the thermal resistance between cables analysis given in reference 10 gives the cnd an enclosing pipe or duet wall are watts per foot (56A) given in reference 10. Further data on the Combining equations 55(A) and 50(A) w th T.= 45 C thermil resistance betw een cables and 6ber and transite ducts are given in ref. Rg = 0.60+0.025(D,'8T.'AT)i/* AT 3.5n' crrnee 11. For purposes of cable rating, thermal ohm-feet (54) O' " n'W (total) it is desirable to develop standardized D,'( V I /D.'+0.62,) expr:ssions for these thermal resistances Assuming an average value of AT=7 C thermal ohm-feet (42B) 760 Neher, McGrath-Temperature and Load Capability of Cable Systems Ocionen 1957

Appendix ll TM IX. Cows,ison of Values of % (AF) D, = 8.3 inches. As indicated in the third ' .t paper of refIrence 3. howevtr. thlorttically for Sinusoidal Loss Cycles at 30% D, should very as the square root of the L*" Feeto, D: termination of the Geometric pr duct f the diffusivity and thi time length of the loading cycle. Hence as the Factor Go for Duct Bank 5 gy> diffusivity was taken as 2.75 square inches Considering the surface of the duct Deartetten. sietosa lachu Nebu ShandaMeernaa per hour in the above. bank to act as an isothermal circle of O*"I D r:dius re. the thermal resistance between 4.5 pipe.... 63/63.. 61/82....es/es Va,XIength of cycle in hours inches I.. the duct bank and the carth's surface will 33".".,".. 6.e pipeo n.se/so..,60/af....sa/co (45) be a logarithmic function of re and Le the y,,,,t /, distLnce of the center of the bank below lt1 .m o the surface. Using the long form of the V....... o.s emble........... 80/s0 Table IX presents a comparison of the VI. o n. 1.5 cable... 77/76.. 77/76... 77/77 values of per cent attainment factor fo' is we may deAne the VII.... 1.s emble... 71/71 Kennelly Formula geometric factor Ce as V111... 2.0 embts.......... 63/as sinusoidal loss cycles at 30% loss factor as [ N Ne""(([M calculated by equations 45. 66. 62(A), and 63 and as they appear in Table II of the first t t x Le*+ Vie -re xa..... s.4 cabie....s3/so...s3/st e Ce=los XI...... s.7 cable... 76/74.. 74/7s paper of reference 3. re = log [Le/r6+V(Le/re)8-1) (57) $! "" O N'aT,$fh,',NfE....et/es [ppggdlg ly, (glgglgglggg (gg Ic order to evaluate re in terms of the

• DIEusivity = 4.7 square inches per hour.

dimtnsions of a rectangular duct bank. let Represent tive Ceble Systems thi smaller dimension of the bank be z r.nd the larger dimensiou 1,y y. The radic portlen of *he %=al circuit is reduced of a circle inscribed within the duct bank by a factor equal to the loss factor of the 15-i.y 350.MCM-3-Conductor Shielded Compact Sector Pape? and touching the sides is cyclic load. The point at which this reduction commences may be conveniently Lead Cable Suspended in Air ri = x/2 (58) expressed in terms of a fictitious diameter D, = 0.616 equ. ent round); V = gauge D,. Thus rnd the radius of a larger circle embracing the four corners is R '=R +(LF)R,e thermalohm-feet (62) D, = 2.129 ; T = 0.175 inch ; i = 0.120 inch For greater accuracy. It is desirable to Vx +y8 59 8 r8 " establish the value of D, empirically rather T,=81 C; R4 =0.350\\234.5+75/ 2 than to assume that D, is equal to the Let us assume that the circle of radius to diameter D. at which the carth portion of =37.6 microhms per foot (Eq.10A) lies between these circles and the magnitude the thermal circuit commences. of re is such that it divides the thermal Equation 62 may be written in the form D,.-2.129-0.120 = 2.009 faches.(Eq.12) resistance between ri and rs in direct Aa'"Au+Am+(UFXAm-S**) 37.9, r;lation to the portions of the heat field thermal ohm-feet (62A) R =2.000(0.120) between ri and rs occupied and unoccupied by the duct bank. Thus In terms of the attainment factor (A F), one per foot at 50 C (Eq.11 A) logU="~ {lo '\\ or k,=1.0; k,=0.6 (equivalent round) r(r '~ri')\\ g 5/ R.' a( A F)R =(A F)(Ru+R.) (Table II) rs s thermal ohm-feet (63) R4./k,= 37.6; Yu = 0.008 er:8-sy [ re re I 4' r(r '-ri')\\ I Equating equations 62(A) and 63 obtains ~~ s 8/ re the relationship S = 0.616 +2(0.175 +0.008) = 0.982 inches from which A.e =(1 -x) Am -x Au thermal ohm. feet (64) Ra./k,=62.6; F(x,')=0.003 (Fig.1) 8 1x 4 x x log rs =- - - - log 1+ +1og 2 - 0.616 8" 2ya y where 1-4 0.003 =0.002 (60) y,, = 2 - 0.982 1 -( A F) (65) (Eq. 241, and note to Table II) It is desirable to derive re in terms of the xqq perimeter P of the duct bank. Thus 1 + Y. = 1 +0.008 +0.002 -1.010 Since P = 2(x+y)= 4 f (1+y/x) s = 1.155(0.175 +0.008)+0.60(0.539) R.,=0.012n's log D,/D. =0.534 inch (Eq. 32) thermal ohm. feet (66) and therefore J 2(0.534)p =0.019 396 " # (1~8)Aa-xR ] (67) y, y,,.157(37,6){ 2.000 J I ICE 0 /U*" log = log (61) 8 2 4(1+y/x) (Eq.31A) The first paper of reference 3 presents The curves of Fig. 2 have been developed the results of a study in which a number R,,/R,, = 1.010 +0.019 = 1.029 (Eq.14) from equations 57. 60. and 61 for several i typical daily loss cycles and also sinu. values of the ratio y/x. It should be soldal loss cycles of the same loss factor q,=g.=1+0.019 - 1.019 (Eqs.18-19) noted in passing that the value of rs= were applied to a number of typical buried 1.010 0.112P used in reference 13 spplies to a cable systems. The results indicated that y/x ratio of about 2/1 only. m all cases the sinusoidal loss cycle of the e,= 3.7 (Table V); E = 15/V5 = 8.7; same loss factor adequately expressed the cos = 0.022 maximum temperature rise which was Appendix Ill obtained with any of the actual loss cycles W =0.00276 (8.7):[3.7(0.022)] considered. 4 An analysis by equations 65 and 67 of 3,, 2(0.175) +0.681 Empirical Evaluation of D, the calculated values of attainment factors 0.681 In order to evaluate the effect of a cyclic for sinusoidalloss cycles given in Table II =0.094 watt per conductor foot load upon the maximum temperature rise and the corresponding cable system param* (Eq. 36 and text) of a cable system simply,it is customary to eters given in Table I of the first paper of assume that the heat dow in the final reference 3 yields a most probable value of (Note: In computing dielectric loss on 761 OcTousn 1957 Neher, McGrath-Temperature and Load Capability of Cable Systems

I l f. {,a sector conductors, thi equiv;1 tnt diamet:r of the conductor is tak:n aqual to that of a (h I p; e e s concentric round conductor, i.e., 0.681 v s inch for 350 MCM.) = h =700 (Table VI); Ci =0.45 f7% h (Table Vl!! of reference 1) (/ [Q,/ Images A: = 0.00522l700(0.45)l = 1.64 thermal ohm-feet (Eq.33) s'=3; e =0.41(assumed) 3 (a\\ s\\ I 9.5(3) [ 1+1.7[2.129(0.41 +0.41)] l -7.18 thermal obm-feet (Eq. 42A) j An = 1.64 + 1.019(7.18) = 8.96 l l thermal ohm. feet (Eq. 8) d'2 is 96.5* d'G 896* dd

• 8 7' 5,,

4 T4 = 0.094(0.82 +7.18) = 0.75 C (Eq.6) j d'3;= 78.5, i r T. -40 C (assumed) I= df'sfe* 37.6[1.010(8.96)] l L =0.344 kiloarnpere (Eq.9) l If the cable is outdoors in sunlight and ij subjected to an 0.84 mile per hour wind q,g m y yp, rag g y gypygg g p,,, 3.5(3) I Re = { 2.129W0.84/2.129+0.62(0.41)) e 7 =5.59 thermal ohm feet (Eq.42B) fJ A,.' = 1.64 + 1.019(5.59) = 7.34 { thermal ohm-feet (Eq. 8) 3o* aTs.s =(4.3)(2.129) = 17.1 C f (Eq.47A) L * *3 8" b T.=30 C (assumed) g._ j81-(30 +0.6 +17.1) I801 i

f. T 1 (37.6)(1.010)(7.34)

.U =0.346 kiloampere (Eq.9) g In this particular case the net effect of i colar radiation and an 0.84 mile per hour d er d3t= 2.'?..;- wind is to effectively raise the ambient e 3 trmperature by 10 degrees, which is a

---

+

rough estimating value commonly used. 27* It should be noted, however, that this d will not always be true, and the procedure eer 9. - 21.s 2.7*. d outlined above is preferable.] ,al. 69-Kv 1,500-MCM-Single ' ,.j,,. g Conductor Oil-Filled Cable in Duct Two identical cable circuits will be la* considered in a 2 by 3 fiber and concrete duct structure having the dimensions shown in Fig. 3. Fig. 3. Assumed duct bank conAguration for typical calculations on 69-hv 1,500-MCM 4AN dh M D,=0.600; D,= 1.543; Da =2.113 T=0.285; D, = 2.373; 1-0.130 inches R s/la"1191 Yes =0.075 T, =75 C; R,, 12 9g = 8.00 (Eq. 21 and Fig.1) ~ IY ~[\\2(0.0)/,,2.243 js-5 d i2 ~ microhms per foot (Eq.10A) S= 9.0 (Fig. 3); R4,/k, = 10.75; R.,/R,, = 1.082 +0.006 = 1.088 (Eq.14) F(x,') = 0.075 (Fig.1) Dm = 2.373 -0.130 - 2.243 inches (Eq.12) 37.9 Y,, = 4 1.412 '0.075=0.007 g, = g, = 1 +1.082= 1.006 (Eqs.18-19) (Eq.24A) (2.243)(0.130) " e = (Table V) E=69/d=40; r 1 + Y, = 1 +.075 +0.007 = 1.082 per foot at 50 C (Eq.11A) co 4 0.005 Assuming the sheaths to be open-circuited.

1. " 0.00276(40)8(3.5)(0.005)

,1.543 -0.600[1.543 +1.200} 8 Y,,=0 d 2.113 l 1.543 +0.600\\1.543 +0.000/ 396 2.243 8 I E 1 Y, = Y,, = x 1.543 = 0.72; k, =0.8 (Eq. 23 and Table II) 130(8.60) 2(9.0) =0.57 watt per conductor foot (Eq.36) 763 Neher, McGrath-Temperature and Load Capability of Cable Systems Octoann 1957 l

1 i A,= 550 (Table VI) A T4 = 0.87 (0.45 + 1.75 +0.24 + 4.63 ) = 4.0 C 1.632}8 ( 2.113j (Eq.6) \\ 2.78 / (0.035XI.7)=0.083 'g 7 ~ 1.543/ lp.(7,sX8.60X1.082)=9.31 li, (Eq. 24A and text) g =0.90 thermal ohm-foot (Eq. 38) watts per conductor foot (Eq.15) 1 + 1*, = l +0.088 +0.083 = 1.171 i 1((6) a Tu, = (0.31/M(1,000X0.80)+0.57])3.81 n'= 1; A,4 =2.37+0.27 = 2.17+28.51,s degrees centigrade in 3 c 52.9 Iq(2.3)(2.76) . g,74 thermal ohm-feet (Eq.41A) circuit no. 2 (Eq. 48) 2.66 = OD mbbmsper foot (Eq M A4-480 (Table V1); i=0.25; Similar calculations.for the second circuit D, = 5.0 +0.5 - 5.50 for fiber duct yield the following values. 1., = 1,u =((9.435X6.35) 20.0)*(1.7) = 0.011 0.0104(480X0.25) A,.'=7.18; aT4 =3.4; 10,3-17.44l 8; 5.50 - 0.25 aTas = 1.71+53.2138 in circuit no.1 (Eq. 27A and text) 4 ~ d~ , ~ 75 -(25 + 4.0 + 1.71 + 53.21,8)X y,.(0.34X2.76)+(0.175X8.13) thermal ohm-foot (Eq.40) = 0.372 6.35 A,=120(asumed); A,=85 (Table VI); (9.31X6.65) L = Le = 43.51 aches (Fig. 3) = 0.715 -0.8591:8 (Eq.9A) R.,/R4, = 1.171 +0.011 +0.372 = 1.554 N= 6; (LF)=0.80 (assumed); (Eq.14) (90 78' [96.5} [87.5} [78.5} I:8=' X 9/\\ \\12.7/ \\ 9 / \\12.7/ 3 .2281.8 (Eq.9A) g,=1 + #.1,oog; g.1 + E D E = 42,200 (Fig. 3 and Eq. 46) 1.171 1.171 Solving simultaneously li = 0.714; Is " =1.327 (Eqs.18-19) =0.483

• E = 1.5 0.487 kiloampere.

Le/P = (18+27) ' 18 er=3.5(Table V); E=138/Va =80; 2 Ce = 0.87 (Fig. 2) 138-Kv 2,000-MCM High-Pressure cos + =0.005 Oil-Filled Pipe-Type Cable 8.625-R,' (at 80% 1oss factor) =(0.012X85X1)X Inch-Outside. Diameter Pipe

y,.E N W M @ M 2.642 (log 8.8+0.80 log

~ (43.5)(42,200)- 308 4 + The cable shielding will consist of an g 5.5 8.3 Intercalated 7/8(0.003)-inch bronse tape--- 0.012(120-85X1X6X0.80X0.87) 1 inch lay, and a single 0.1(0.2)-inch D. =1.48 watts per conductor foot (Eq. 36) =0.79 thermal ohm-feet (Eq. 44A) shaped brass skid wire-1.5-inch lay. The A -550(Table VI); As=0.012X cables will lie in cradled configuration. [550 los E633 ) =1.38 the 2.642 \\ A,' (at unity loss f actor)= 8.44 ( thermal ohm-feet (Eq. 44A) D,=1.632; De=2.642; T=0.505; , =. , = 8.125 ohm-feet (Eq. 38) A.' = 0.90 + 1.006 (1.74 +0.24 +6.79) ) s'-3; D,'- 2.15(2.66) = 5.72; 4+ =9.72 thermal ohm-feet (Eq. 8) T, = 70 C; Ra, -..: \\ ,2.00f,234.5+75/ 3(2.1) AT4 -0.57(0.90 +1.74 +0.24 +8.44) 7 =6.35 microhms per foot (Eq.10A) R.4 = 5.72 +2.45 " ohm-foot (Eq.41A) =6.2 C (Eq.6) For shleiding tape A, = 7/8(0.003) = 0.00263;

1. ~

I*~ T. = 25 C (assumed); p4 = 100 (Table VI); i=0.50; D =8.63+1.0=9.63 for 1/2-inch J 2.66r 75-(25 +6.2) 23.8r - 8.60(1.082X9.72)

1. ~ 4(0.00263) Y 1

0.0104(100X3X0.50)

0.696 kiloampere (Eq. 9) 564 + 50 pd

-62,900 microhms 20 9.63 - 0.50 To illustrate the case where the cable circuits are not identical, consider the per foot at 50 C (Eq.13) =0.17 thermal ohm-foot. (Eq. 40) second circuit to have,750-MCM con. 1 Assume A,=80, L-36 inches, (LF)=0.85; ductors. For t e 6rst circuit, For skid wire An g r(0.1)8=0.0157; y.1,p.1 N = 3; (4 F) = 0.80 (assumed); y, ~ S F= - 92.4 (Eq.46) R,= (0.0157) 1+ X -go,9.63+0.85 log \\ 8.3 (1)/- 38r 2.66r e 4 1.5 R.' = 0.012(85X1)X =11,100 microhms log +0.80 log 92.4 + g,(at unity loss factor) =3.38 thermal ohm-feet (Eq. 44) ~ Per foot at 50 C (Eq.13) 0.012(120-85)(IX3X0.80X0.87) " 62.9)(11.1)- A ' = 1.38 +1.000(0.77)+ =3.74 thermal ohm feet (Eq.44A) R (net)= ((62.9X11.1) 1,000 1.327(0.17+2.85) p,.[96.4}[87.5}[78.5j, = 6.17 thermal ohm-feet (Eq. 8) \\12.7/ \\ 9 / \\12.7/ =9,435 microhms per foot at 50 C g AT4 -1.48(0.69 +0.77+0.17 +3.38) = 7.4 C (Eq. 50) k, = 0.435; k, = 0.37 (Table 11) (Eq. 6) Ran = 0.012(1)X 6 [85 los 456+3(120-85)(0.87)) R4,/k, = 14.6; ru = 0.052(1.7) = 0.088 T.=25 C (assumed); = 3.81 thermal ohm feet (Eq.49) (Eq. 21. Fig.1, and text) 70 -(25 +7.4) A.' = 0.90 + 1.006(1.74 +0.24 +3.74) s = 2.66 +0.10 = 2.76; R4,/k, = 17.2; Y (6.35X1.171X6.17) =6.65 thermal ohm-feet (Eq.8) F(x,') = 0.035 (Fig.1) = 0.905 kiloampere (Eq.9) Oc70 ann 1957 Neher, McGrath-Temperature and Lead Capability of Cable Systems 763

- ~ s g IIrM bM.WNTE CoNouevols AIEE C mmittee

17. A SurLart:0 MArazzaticAL P&ocInuss g

Report. 16M. vol. 71, pt. I!!, Jas.1953. pp. 393 rom Darnauswtmo tus ToAwaisut Tsursaarvas 414. R ess or CAsLa SYor# Ns. J. H. Neher. l6id. vol. 1. CALcVLartoM or tas ELacts: CAL Paost. sus 9. A C Resisrawes or CowyswisoMAL SrsaNo 72, pt. !!!. Aug.1953, pp. 712-18. or Unostomouwo CAsLas. D. M. Simmeas. The Powan Castas tw NowusrALLic Duct Amo in

18. Tus Heatino or CAstas Exposso To tus Ehrtric Journal, East Pittsburgh, Pa.,

May, laon Cowoorr, R. W. Burrell. M. Morris. 1644..

Box en Racas. E. B. Wedmore. /omissf. Institu. Nsv. 1932. vol. 74, pt. I!!, Oct.1955. pp.1014-23. tios of Electrical Esgiseers, vol. 75,1934. pp. 2. Loap Faeron ano Equiv Atsnt Hooms

10. Tao Tassun Resisrawes Batwasu CasLas 8'

Csarasso. F. H. Buller. C. A. Woodrow. Ele amo a Sommoonotwo Pres on Duct WALs., F. H.

19. Loesse in Anuouso Suroca-Comoveton.

frics! World, New York. N. Y., vol. 92, no. 2,1928, Butler, J. H. Neher. I6id., vol. 69, pt. I,1950 Laao Corusso A.C CAstas. O. R. Scharig H. P. pp. 89-60. pp. 343-49. Enehal, F. H. Baller. AIEE Trassections, vol. 3. Svurostuu on Tsursaarvsa Riss or Castas, !!. Heat TaAnaras Srvor on Powns Casta 48, Apr.1929, pp. 417-35. AIRE Comunittee Report. AIEE Treesschoes, DocTs Ano DocT Assoustras. Past Greebler, Guy

20. Courassetton to tas Brooy or Loessa ano vol. 72 pt. !!!, June 1953. pp. 630-62.

F. Bersett. 16sd., vol. 69. pt. I,1950, pp. 357-or 8ste-Iwoccitou or S nots Conoccrom As. 4. A-C Ras stawes or Saousarat Casses in 67. monso CAntas. I. Bosome. EleurWusica. Mas. SftsiL Poa, L. MeForhof, G. 8. Eager, Jr. 16id.,

12. Tao Taurosatuas Rise or Buasso CAsLas Ital,1931. p. 2.

vol. 68. pt. II.1949. pp. 416-34. Amo Pirus. J. H. Neher. 16id., vol. 68. pt. I,1949, 21. Aartric AL CooLNO or Powna CAsLs. F. H. 8. Paouutty ErraCT iM EoLlo AND Hollow pp. 9'-21. Beller. AIEE Tressectiosa vol. 71. pt. !!!. Aug. Rouzo Comouctoas, A. H. M. Arnold. Josrael.

13. Tsu Toursaarvas R:ss or Castes im A 1952, pp. 634-41.

Institutlos of Electrical Est seers. Londos. Doct Daws, J. H. Neher. 16i4.. pp. 640-49,

22. Soaraca H sat Ts ANsuissioN, R. H. Hellmas.

i Ergized. vol. 88. Pt. II. Aug.1941 pp. 84b39.

14. Ott Plow Ano Passavas CAtevLarrows ros Destacess. AmMcas Mey M h ban d 6.

Epov.Cuasswt Lossas aw Mutts.C6as Pares. Bete Courasmso 0L-FLLao CasLa SysTsMs, Engineers. New York. Pf. Y vol. 51, pt. I,1929, Insutatso Laap-Covasso Ca stss, Aamosso F. H. Buller. J. H. Neher. F. O. Wollastos. 16dd., pp. 287-302. ago 11wAsmosso, Cassrswo BALAmeso 8.Psass vol. 78, pt. !!!, Apr.1966. pp.180-94. ^*

23. Tas Cranswt-CAasvano CArActTT or Rus.

1941,"pp.' 82-63.

18. TuseuAL TsaNorswTo oM bus so CAsLas ass-INsDLaTso CoNocctoas, 8. J. Reech. AIEE F. H. Butler. 1644.. vol. 70. pt. I,1981. pp. 45-68, TressecJions, vol. 67, Apr.1938, pp.185-67.

tyerbod. AIEE ras e n, to 72 t.' 11

16. Two Datas uinarson or Tsurmaatvas

24. HeartNo ANo CUnasNT-CassY1No CarACrTv Dec.1933, pp. 1260-75' TaANs sNTs N CasLa SVsTsMs af MsANs or AN or Baas CoNouCToms com Outooon Seavics, AmALoous CourvTsa. J. H. Neher. 16i4.. pt. II, O. R. Schurig, G. W. Frick. Cessrel Elusric 8.

AC Resistance or Pres. Casts, Srstaus 1961, pp.136e71. Rsview, Schenectadr. N. Y., vol. 33,1930, p.141. + Discussiofg ssued in wh ch a simple method is pre. basis of the paper-this is a logical approach sented for the rapid calculation of cyclic but it appears to differ from the basis of ratings.s computing ratings hitherto adopted in the C. C. Bernes (Central Electricity Authority. Table V gives specific Inductive capaci. United States. An amplification of the London, England): This paper is an excel. tance values for paper as: paper insulation authors' viewpoint on this important issue lent and up-to-date study of a most impor. (solid type), 3.7 (IPCEA value); paper will be welcomed. t nt subject. For 25 years D. M, Simmons' insulation (other type),3.3 4.2. Is it pos. With reference to the use of low. resistivity uticles have been used for fundamental sible to list the other types and their backfill, recent studies in Great Britain study on current rating problems, but the appropriate speelfic inductive capacitance have shown that the method of backfilling numerous cable developments and changes values or alternatively simply use an cable trenches deserves careful considera. In installation techniques introduced in average specific inductive capacitance value tion as attertion to this point can result rectut years have made a modern assess. of 3.7, for example, for all types of paper in increases up to 207o in load currents. ment of this subject very necessary. The insulation? Equation 43 gives the ther.nal resistance essential duty of a power cable is that it Reference is made to the adoption of the between suy point in the earth surrounding should transmit the maximum current (or hypothesis suggested by Kennelly as the a buried cable and ambient earth. It is power) for specified installation conditions. There are three main factors which deter. mine the safe continuous current that a Table X. Temperature Limits' for Belted., Screened. and HSLt Type C Wes cable will carry, 1. The maximum permissible temperature L*1d Direct or is Air la Docts tt which its components may be operated Alamissa Alamissa with a reasonable factor of safety. 8huthed Sheathed Lead Sheathed Lead Sheathed 2. The heat. dissipating properties of the Armoured Armored cable. system vettaes and Type Us. or Us. Ua. er Ua. of Cable Armored armored armored Armored armored armored 3. The installation conditions and ambient conditions obtaining. 1.1 kr In Great Britain the basic reference Sissie.cono m m o. m m m o o som, o so .em .so omo. mo. document is ERA (The British Electrical us and mume n bened-o m som om-o som mm..som Em E and Allied Industries Research Association) 8 8 ['g**d 6 6 kv,. 3 report F/T1316 published in 1939, and in ..som .mm ... ~ E. . 80 Thru. core belted-tree... . 80.. .so., .80.. .80.. . 60.. .so 1955 revised current rating tables for u he solid-type cables up to and including 33 kv sissi.. core......... were published in ERA report f/T183. Three-core betted. type.. . 70... . 70.. .50.. .70 .65.. .65.. . 65. .65., .50.. .63 g A more detailed report summarizing the Thrw.co e scrased type.. . 70..,. 70.. .70... .70., .60... .70 mtthod of computing current ratings for 22 kv solid type, oil.611cd, and gaopressure cables sissie-core......... .65.. .65., ..to.. .65 s Q," *",l $ld '.$e.'.' ' ". $".,. '. $ '.. .....$2.'.'.50... is now being 6nalized and will be published ,,d ld 5., ' .. 65 ts ERA report F/T187 some time in 1958. Three-con (s1.t or sal).. .63 .65. .65., . 65 Until recent years current rstings in 33 kw Scr m ed) Grest Britain have usually been considered sissie. core.. .63.. .50 on a continuous basis, but the importance Three. core......... .....65.. .65.. .65.. . 50 of taking into consideration cyclic ratings Thrw<on HSL o . 65 m .65 bas now been carefully studied, since con.

• Measured in degrees cestisrade.

tlnued high metal prices have forced cable t Ilochstater separate lead. users to review carefully the effects of t separate tend sheathed. cyclic loadings. A report has recently been I separate aluminum shuthed. t 764 Neher, McGrath-Temperature and Loaa Capability of Cable Systems OCroann 1957 \\ t

o y 4 not clear, b wIver, what v lue of soll recorded in en ERA report 8 dealing with tained from Arnold's paper,' 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 parallel combination of sheath and is desirable. papers ** (based on ERA reports) dealing reinforcement resistance permits the cal. In Great Britain a value of soil thermal with cyclic loading, but the majority of culation of a single loss factor, that a simple resistivity (g) of 120 C cm/ watt is generally this work is in process of printing and formula has been derived for the etternal used but further test data are being slowly publication. thermal resistance of one of three cables acquired, and where tests have indicated An obvious diference in British and in trefoil touching formation laid direct that a lower value, e g., 90 C em/ watt, American technique is the method of cyclic in the ground,' and that sector correction is justified, this value is used. Current rating factor calculation. Mr. Neher and factors are often used in British practice loading tables in ERA repert F/T183 Mr. McGrath's method is based on an for 3-core cable rating calculations. provide data for soil thermal resistivity equivalence between typical daily loss values of 90 and 120 C cm/ watt, and cycles and sinusoidalloss cycles of the same REFERENCES correction factors for other values of soil loss factor, while a method recently intro-3- 8" "'"ence 1 of the paper. thermal resistivity are also provided. duced in Britaint' takes full account In the United States buried cables are of the form of a daily load cycle. Both 2. see reference 1 of str. Barnes' discussion. usually pulled into duct banks, but there methods are considerably shorter than 3. Tus CAtevtAttoN or CowTtwoova RAttuos must be many cases where direct burial, any that have been available hitherto. Amo R Artwo Facross rom TaAnnutsarow Awo as normally used in Great Britain, will Nevertheless without further study I Dismatmow Canons. H. Goldenberg. Aspo*f, ^ ' ' " result in lower installation costs. Formulas would not feel certalu that for Dritish-type ,l@,he dealing with this installation technique cables, subject to their typical daily cycles, ( su nrnence 2 of Mr. Barnes' discussa. are a desirable addition. Permissible tem-the form of the cycile load can be ade. padmu LA fer thc. var!cus types of quately taken into c.ccount by une of the 5. Tus CALem.Arion or Cvcue RArtuo FActons cables and installation conditions used in loss factor independently of the cyclic '",",g,","g',*[,' o,"',",p' e s. H".'0ollen ^ rg. 4 the United States will be a helpful ap-load wave form giving rise to it. In fact no.orrap4 251, insutution of Electrical Engi-pendix, and it is suggested that this informa-the conclusion reached in my second IEE neers. Jutr 1951. tion should be added to the paper. For papes,8 is that a knowledge of the cyclic 6. Tum ExTsswAL Tuna u AL RastarANCS Or comparison purposes, the limits recom-load wave form for the 6 hours prior to somruo CAsLas, u. condenberg. ses=a Journal. mended in Great Britain are summarized peak conductor temperature, together with Load **. England, vct. 64. no.1. Feb.1957, p. 36. in Table X and in the following: the loss factor, are adequate for cyclic 7. Cuanswr R ATINos rom PArsa.InsutArso rating factor calculation. However, it Castas to a s 4so,1954: VAnnauso-Causaic. I"sm.Arno CAstas to B.s. sos.1955. R,pors. Rs. Plastic-insulated power cables. would be unfair to assess any of the relative hE a 70 C maximum conductor temperature merits of the two methods prior to the fl7[,'t,7,TiU, ge

yltios, g,

t thead, g Gas-pressure and oil-filled cable systems publication of one of them. tand. 1 (all types). The diference between Dritish and

s. See reference 5 of the paper, 85 C maximum conductor temperature American cable rating technique is not so marked for continuous current rating cal-g Finally, it will be helpful to know if culation as might appear to be the case Elwood A. Church (Boston Edison Com-adoption of the formulas in the paper will at first sight. In fact, such diHerences as pany, Boston, Mass.): The authors present necessitate revision or amplification of exist are principally due to the diferent a large amount of useful data and formulas existing rating tables and, if so, when the types of cables employed on each side of for the calculation of cable thermal con-revised tables will be published.

the Atlantic, and to the diHerent standard stants and suggest a new approach to the a< frequencies in use. Nevertheless a problem of calculation of temperature rise RanaENcas comparison of the present paper with the for various loss factors including steady-ER A report dealing with continuous current load or 100% loss factw. Cable engineers hissfow'*[Mo D$s'r*a's"sur o'n, S.Shitehead EIE. ratingts gives rise to certain observations. usually agree on the fMtors to be taken IIntshings. Rsport. Referents F/TiJi, The Bntish The present paper is principally directed into account and the methods of calculation g Electrical and Aihed Industries Research Associa, to the calculation of a single current rating, for steady loads. However, there appears NtuNa r c71 but one use to which it might well be put stiti to be, disagreement on the problem of of El ng ee s odo I England, vot 83,1938 p. 817. ts the large-scale preparation of current cyclic loading. 1 i rating tables, with rating factors for non-At the AIEE General Meeting in January be EsosILA o$m"scr'on* wiveYs'*1Yo'oEd/*qandard conditions. For such an applica-1953, a group of papers 8 was presented berg. Procedens. Institution of Electrical Eng,, tion it is often preferable to introduce suggesting vanous approaches to the meers. London, Eastand. vol,1o4, pt. C,1957, p. explicit formulas for the rating factors, as problems of cyclic loading on buried cables 154-these formulas might be independent of and on pipe-type cable. Of the methods j some of the thermal resistances or loss suggested in these papers, the one which q factors involved, with a consequent saving appealed to the author the most was Mr. H. Goldenberg (Electrical Research Asso-H calculation time. Neher's method using sinusoidal loss cycles. ciation, Leatherhead England): The cal-The method employed for external ther-In his paper it was shown that this method culation of cable ratings is a subject of mal resistance calculation for grouped yields reasonably accurate results for the prime importance to cable engineers. cables laid direct in the ground diners higher loss factors. For a low loss factor Nevertheless, it seems that until recently somewhat from that recommended in a sharply peaked cycle, the results are not the American standard work on this subject recent paper of mine.e For the preparation as accurate, has been that of Simmons,8 while the of 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 lead cycle more accurately been recorded by Whitehead and Hutch-with in an ERA report,' the combination by splitting it into harmonies and com. ings.8 These papers have been supple-of certain simplified external thermal puting the temperature rise for each mented by scattered published papers, resistance formulas and my recommended harmonic separately. This entails more including developments dealing with cyclic method has led to a substantial saving in work, but with modern methods of machine h loading. calculation time. I do not favor the calculation it is economical to use the The paper by Mr. Neher and Mr. Mc-introduction of 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 machine perform the laborious cal. i rating practice in a manner that will prove unequally loaded cables. culations. In fact, it takes very little f invaluable to engineers for many years to A brief resum6 of other points is that more time on the machine when the more 4 come. It is a pleasing feature that the the thermal resistivity values given in rigorous methods are used instead of any h authors are especially competent to deal Table VI for thermal resistance calculation of the approximate methods which have J 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 investigated the various over a number of years. Modern British proximity effect on cylindrical hollow methods of calculation of the cyclic com-cable rating practice has recently been conductors appears to me to be best ob-ponent of temperature rise of 1,250-MCM Octonen 1957 Neher, McGrath-Temperature and Load Capability of Cable Systems 765

1 l 4 I 7 i l Table XI. Thermal lmpedene2 Functions Tebb Xill. Masimum T:mperature Rise for e 4che ns 1,250-MCM 115.Kv Cable Enclosed in 68/ cinch-Outside-Diemeter Pipe T /Q. Ts/Qe Ta/Qe T4/Qe Method To p at e, C Tempe s'ture, C Harmonic i l of Cal-colauen i No 2 Nes 1 Mpe 2 Mpq l 0 8.. 8.03 _l0' .6.5510'- . 5.9710_' .5.60l0 \\ Ot.. .10.5610' .9.0810' .8 50l0' .8.0310' N C@1 1 2.881 - 30'. .1. 67 l - 43*.. .1. 2 41 - 54'.. .0.931 - 61' 1.. .39.1.. .49.2.. .24.1.. 34.3 2. .39.8.. .49.9.. .24.6.. 34.8 2... 2.291 - 38'.. .1.191 - 84'.. . 0. 821 - 68*.. . 0.571 - 77' 8.. .39.9.. .50.I. .23.2*... 33.4' i 8. 1.94 l - 43*.. . 0. 941 - 61'.. . 0. 611 - 79'.. . 0.891 - 87' For Loss Crcle 2 4, 1.681 - 50'.. .... 0. 76 l - 67 *.. . 0. 4 8 l - 87 *........ 0. 29 l - 95' l ' fg;f; lIIgg ', 3. . 32.8.. .39.5.. .16.1*... 22.8' ' Steady state component for single pipe. t Steady. state component for two pipes.18 inches apart. Theu oswes da not include the temperature rise Qem watts copper loss per conductor per foot due to dielectrie toes. which would be added to the i i Te = t:mperature rise of conductor steady state component. I Te=t:mperature rise of shielding tape

• These are average t emperatures. It is not l

Ts=t:n.perature rise of oilin pipe poss ble to compute the manimum temperature of l Ta = temperature rise of pipe the pipe by this method. ( I15-kv cables enclosed in 0%-inch-outside-different sizes of cable (a total of 12 ma-peratures, especially in summer when high diameter pipe buried in the earth. The trizes). The cost of programming was carth temperatures prevail and where results of three such methods for two small since the general program for solution higher daily loss factors are more likely l representative load cycles are presented of complex simultaneous equations was to be encountered. If the earth next to i in this discussion for comparison. The already available in the IBM library, and the pipe exceeds an average of 50 C, there three methods compared are: (1) the only a small amount of work was necessary is danger of drying out the soil causing IIarmonic method using Bessel functions to set up this particular problem. thermal instability. Calculations of cur-g to compute the heat-flow constants of the The components of the loss cycles with rent carrying capability should take this cable for each harmonic of the temperature which the data in Table XI was mtatiplied limit into account. eycle. (2) the sim'soidal method suggested to obtain the temperature cycles are given 1 by Mr. Neher in his 1953 paper, and (3) in Table XII. These loss cycles are illus-Rsrsaacs i the latest method suggested by Mr. Neher trated in Figs. 4 and 5 with the corre-1. su nfennu 8 et m papen and Mr. McGrath in their current paper. sponding temperature cycles of the com j Space in this discussion does not permit a duetor and pipe. I complete derivation of the heat Sow equa. In all future calculations of this sort. R. J. Wiseman (The Okonite Company, tions for the harmonic components of the it is planned to carry the programming Passaic, N. J.): The authors are to be heatJ1ow cycle, but only the results, as still further and trave the machine calculate commended for this very fine technical calculated by an IBM (International the temperature cycle for each size of cable paper. The need for an up-to-date com I Business Machines) 650, are tabulated in and determine its maximum value. This pilation of engineering formulas and <ca-i' Tc ble XI. It may be noted that the has been estimated to cost approximately stants for the calculation of current-machine time to solve the eight simul-8500 for programming and $15 extra per carrying capacities of ables has been of t'.n ous equations necessary for the solution size of cable to compute. increasing importance every year. When j of the temperatures and heat flows for each Usually only the temperature of the Dr. Simmons wrote his series of papers harmonic was approximately 5 minutes conductor and the pipe are significant in about 25 years ago we might say the per matrix, with a separate solution neces-calculation of the current carrying capa* electrical cable industry was young in t sary for each harmonic. The whole cost bility but the electronic calculator auto-engineering knowledge, the types of cable of the job in rental time on the machine matically computes the other values listed furnished were not too great in number, cad punching the data on the cards for in Table XI, and they are recorded for and the characteristics of the cables were insertion in the machine was 3150 for three whatever use may be made of them. not too well known. Today our knowledge A tabulation of maximum temperatures of cable design, materials, and operating for the foregoing two load cycles and the conditions along with new types of cables Tals Xil. Humonic Components of Loss three different methods of calculation listed is far in advance of 25 years ago. We have j Cycles previously are tabulated in Table XIII been using the formulas as they became in the same order. Examination of this known and it was desirable to bring them { table will reveal that the sinusoidal method together in one place and, in addition, all Less Cycle 1 Len Cycle 2 yields results which are nearer to the more of us who have occasion to make these H a.

Lees, Phase

toss, Phase accurate harmonic method than the latest calculations will be using the same formulas 7

meele Watts

Angle, Watts

Angle, method proposed in the paper. The and electrical and thermal coruitants.

Degren Degrees agreement between the various methods is Also, this paper will be of great help to seen to be better at the higher loss factors. younger men coming into the cable in-

0...

.4 03., .2.64 It may be argued that the agreement is dustry. Although it summarizes the 1.. .2.60.. 0.. . 2 31... - 20 close enough between the three methods formulas, anyone wishing to get a clearer N: + 5 f r all practical purposes and that the appreciation of the text can refer to the l

4..

.0.63.. . + 40... 0. 83... - 35 accuracy of the original thermal constants bibliography and study the origmal papers. from which the computations were made To make any text of this kind generally b BCuplo The equation of loss cycle t using the does not warrant the extra work necessary useful, it is desirable that the procedure wa ts f condu or) to use the harmonic method. However, be easy to follow and the formulas readily O. = 4 03 + 2.60 sia i + 1.10 min (2.i + 30*) + the danger in using an approximate method applied. Theoretical formulas involving 0.20 sin (bi-90*) + 0 53 sin (4.d + 40*) watts is that someone unfamiliar with its deriva-higher mathematics can be used, but they Carresponding temperature cycle for conductor tion and its limitations will use it where it take time, and very often it is not possible p temperature 6s as follows for a single pipe (hai. does not apply. The author does not con-to take the time to work up a case. Again sider the agreement close enough for 407, conditions of installation are variable 32 + 7 24 sin (.# - 30') + 2 57 sin (2.#- 8 *) + o 39 sin (3.d - t33*) +0 s9 sin (4.# - 7 *) loss factor. daily, so if we attempt to make a 6 eld check j degrees centigrade The computation of the pipe temperature of calculations we can find differences; j 2ero time-9 00 a m. la the foreroing empressions. is just as important as the conductor tem-therefore, exactness to a high degree is l 766 Neher, McGrath-Temperature and Load Capability of Cable Systems OcToasn 1957 l

1 f ( N l l l l nI / \\ l l / & = E,a / rm eA .r_ l l I /I l\\ l a j" _qML F..lIA -{----- - -l - - l l / l 1 R 1 \\ l l xUiR

1.,

m [" ( % d --4 --h -j-7 AWW Y,*.P ~~~~ Q~ i

• W" f "f ~~h ~

6 / J M_ _. _... [. AVE lOF Qo) _p - \\ / gto. / 1 i rto v x s 0 0 13 4 12 6 12 12 6 12 4 12 AM RM A.M. RM. Fig. 4. Loss and temperetwe cycles for 75% load lector, sum,ner Fig. 5. Loss and temperetwe cycles for 60% load factor winter toed cycle loed cycle O = copper loss cycle Values same es in Fig. 4 Ti-temperature of conductor Te= temperature of pipe Temperatures are in per cent of copper temperature correspond-tion of the cable having the highest thermal ing to steady load equel to the maximum. resistance is possible. Appendix III discusses the* derivation of D,, a fictitious diameter in the soil up to which it is assumed that a steady heat not necessary. It has been suggested that 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 If we took the simple formula Rw= tion. I have not been able to accept this a computer, but here also time is taken for 1.60/D where D is the diameter over the assumption. It is an endeavor to obtain setting up the problem for the computer. shielding tape we found we got good a thermal resistance for the soil that will Also we must show how to calculate the agreement with test. We neglected tem. check with a study that Messrs. Neher, currents and in a form that will be used. perature effects as the actual value of Butler, Shanklin and myself made and is You will note that many of the formulas Ru as compared to the thermal resistance referred to in reference 3 in the bibliography are new to most of you. These formulas of the insulation is very low, many tunes of this paper. A study of the previous were developed to make the calculations in the order of one-tenth; therefore. papers will show that the attainment easily and quickly and yet do not cause a temperature effects are small. For a gas factor is not exactly the same for all types large error in the final answer from the medium using 200 pounds per square inch of cables studied and all shapes of load highly theoretical formula. It is natural we use the equation Rw =2.58/D. IIow curves. that the formulas may be a compromise do these formulae compare 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 factor for that they use may be superior to that recom-Consider two cases, one having a diam-three methods of calculation for a loss mended. Likewise the thermal constants eter over the shielding tape of 1 inch and factor of 30% for several cable designs. may be a compromise. This is true as another having a diameter of 2.5 inches. Rather than give results for one loss factor far as I am concerned, yet we are willing The following table compares the two types only, it would have been better if they had to accept the recommendations given in the of equations. covered the range of loss factors which were paper. The calculation of the various studied in 1953. If these attainment fac-losses existing in a cable system and the tors were plotted against loss factor as ! location of these losses is well done and Diameter = Diameter = did in my paper, it would have been noted should be carefully studied by all new 7d**Ai $8M that a straight line could be drawn giving 1 engineers. Medium Ohm-Foot Ohm Foot a good representation of how (AF) varies with loss factor, namely, ( A F) = 0.43 + The section dealing with the calculation 0.57 (If) for my method. This equation of some of the thermal resistances need okonite.... 1.60 t o L. 0. 64 t o.f. careful study in order to appreciate them Oil.,. Neher and,,.1. 37 .0 80 follows the plot of (A F) and loss factor hicGrath very well down to about 35% loss factor, I as they depart from the usual ma'nner in [ which a thermal resistances are calculated. y,7,,g,.] M ] t ol and in some cases, it gave a higher value g,,,, For example: the thermal resistance

hicorath, and other cases a lower value than actually j

between a cable and a surrounding wall, calculated. The (AF) values I reported such as a duct u all or a pipe; see equations are based on careful calculations from the 41 and 41(A). IIeretofore, we used Aw = The differences are not great and when exact load curve and no assumption that 0.00411 B/D. and referred to as the IPCEA considered in relation to the total thermal a single sine wave curve can be taken as method. This has been revised to take resistance, they are negligible. We can representing any load curve. As it is a I h into consideration the condition existing accept the authors' equations. rarity that cables are designed for loss l and the materials. Equation 41(A) is a I am glad to see the authors place the factors as low as 30% (50% load factor), i general one, and by inserting the currect duct system in proper relationship to a my formula gives results as accurate as values of A' and B' as given in Table I, buried cable system and that the same when using D, and easier to use. Ilowever, we can get R,. This is an example of how soil thermal resistivity will be used when for the sake of uniformity in methods of we can accept a compromise in order to making comparisons. This was the weak-calculation, we will accept the authors' l get agreement. We at Okonite made ness in the duct heating constants originally method. ( }l tests years ago to determine the thermal set up by NELA and later known as In this connection, I would 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. We tried to standing of the effect of multiple cables in a by others interested in this subject. The j use the cylindrical log formula and found duct bank is obtainable, and the determina-use of the equation involving Ds is na 1 l Octoaan 1957 Neher, McGrath-Temf>erature and Load Capability of Cable Systems 767 L

. --...------___--_~ j

• attempt ta increase the th:rmal resistanca and have arrivo:1 at cittain conclusions, been able to mzks ths Nehtr-McGrtth o for th3 soil for cables or small pipe sizest samt of which tre discussed in the following method track with the old t.nd well proved g in other words, the computed value of paragraph.

NELA method is to reduce the soil thermal thermal resistance is too low. Is it not The determination of the losses in the resistivity to the order of 40 C to 75 C likely thi.t we are leaving out of our equa-conductor, shield, sheath or pipe, and the em/ watt. The actual value which one tion a term involving a surface contact dielectric have been well established by would use to arrive at the same conductor between the surface of the cable or pipe the authors and bear no further comment, size as determined by the NELA method t.nd the soil. This term would be of the The calculation of the thermal resistances appears to depend upon the number of samt form as we now use for the case of of direct buried cable and pipe cable cables in the duct bank and the value of the cc.bles in air, namely A=0.00411 B/D. Installations appear to have been well daily load factor chosen. In contradis-i If we add this term to the log formula for founded; although the method of arriving tinction Mr. Neher in reference 13 of the sou thermal resistance, we will get a higher at the effect of cyclic loading seems to be paper states that his method agrees within total resistance and the in8uence of the in question amongst the various investiga. 10% of the NELA method if a pe=75 C diameter of the cable or pipe will be greater, tors (reference 3 of the paper). However, em watt is used. the lower the diameter. It wu! be neces. as far as duct bank installations are con-We have made some calculations of the sary to determine the value of 5. The corned, the difference between the NELA thermal resistance of cables in a duct bank idea of such a term is shown in the papert or IPCEA carent rating method and that from the sheath to ground (or sink) using by Mr. Mather and his coauthors. In proposed by the authors is so great that the Neher-McGrath method and the Tcbie I they give some thermal data one cannot help but wonder at the dearth average conditions on which the NELA duct obtained from tests made by them on a of practical data in the paper, constants were obtained. The average pipe-type cable. They give a vahne of In reading references 10,12,13,16, and conditions were: 3 for surface of Somastic to water of 218 17 of the paper, there seems to be very thermal ahms per em'. I like this. Is it little data on cable temperature measure.

1. Most of the measurements were taken t

not likely that we have a surface resistivity ments taken in the 6 eld, such as was done unoer pavec streets with the cepth of pave- ' between the cable and the soil in immediate by the various utilities when the NELA ment between 10 and 12 inches. contact? values were established. The work re-2. Majority of ducts were made of Abre. l ported in these relerences is almost all 3. Average duct inner diameter = 3.75 Rarsaswcm theoretical, and laboratory measurements an ana@ methods used are aH appmai. i 1. Bounvn.La Pows Anamneraarton Haos. l vests.sa cason aroeses, n. J. asather, F. J. mations. 4.. Concrete spacer between ducts 2 asecans, s. Demarinna. Nas Treasusions. I am given to understand that there is inches, with duct wall =1/4-inch, 3-inch vol. 70, pt. !!!.1967 (Peter so. 57 rJ#h a movement afoot to have this Neher. outer concrete shell. Spacing between McGrath method accepted and to revise duct centres =6% inches. I the IPCEA current rating tables accord-5. Average depth of burial to top of duct E. R. Thomas (Consolidated Edison Com. ingly. I am not sure that this is the case-bank =30 inches. pany of New York Inc., New York, N.Y.): but if it is, then perhaps the authors can The authors are tobe congratulated in setting teu us upon what factual data their method

6. Most measurements with 3-conductor is based.

lead sheathed cables from 2 inches to 3 up mathematical equations to evaluate load g carrying capabuities of cable systems. I re-We have used the method given in the , inches outside diameter. Average diameter gret that no mention was made of the plo. Paper to compute the current rating of . 5 inches, neer work by Wallace B. Kirke in the middle quite a number of high voltage cable cir*

7. All loaded cables la outside ducts, all 1920's on the rating of cables installed in cults in a duct bank and and complete dis

• equally loaded.

is I bel f agreement with the NELA or IPCEA n hed th of le ratin of t rnethod. In emy case the Neher McGrath 8. Soil thermal resistivity (in siim) = NELA t.nd present IPCEA published rat. method results in a larger conductor size 130 C cm/ watt. ings of c;ble. The work of Kirke was pre. for a given current rating, in some cases Two cases were studied and the results as m as % in Qn uc or are summarized in the following: j a sent bel the AIEE and pub!!shed in p} The work on ratings of cable by Kirke Here is where our duemma begins. One Case I-Three cables is 2 by 3 duci bank was based on thousands of Seld measure. of two things prevails: either Mr. Neher (oss of lower ducts empty), i and Mr. McGrath have cornered the I ments in the New York City area and later NELA Value (i.e. 4.93/D,'+LfNN) - nonferrous metal market or they are 6 eld measurements furnished by utuities throughout the country furnished data attempting to make a pipe-type cable carry Loss fact or....... 100 %. 62.5 %. 33% Rths a thermal / 8 ***' th ace o

t. It is sid hms feet...... 5.00. 3.92. 3.00 which lead to the NELA.lPCEA rating how anyone can conceive of a 3 conductor Neher.McGrath Value use f Ipe-I obvious that the answer obtained by high voltage cable (and a pipe-type cable Loss factor.......100%. 62.5%. 33%

g mathem tical solution is never any better is in fact a direct. buried 3-conductor cab,le) Upper cables than the assumptions on which the equa. competing on a current rating bas,s with Rths. thermal i tions are developed and the constants used single c nductor high voltage cables sepa. / ohms-feet..... 6.68. 5.02. 3.71 j with the equations' rately spaced in a duct bank where a c Lower cable I believe the actual heat Sow in under. losses are a minimum and heat dissipation Rths 4......... 6.63. 4.99. 3.70 1 a maximum. In e ther event we cannot Average values.. 6.66. 5.01. 3.71 d ground cable systems is considerably more rsta"d why so mucli time d counplex than has been assumed in this In order for Neher.McGrath values of ,n d eur paper rnd, therefore, actual ratings which rent rating calculation for duct-bank thermal resistances to be equal to NELA are rbtained may be different from those obtained by this calculation. systems without first having at least values, soll resistivity would have to be: M b. 6M At We loss factw n=65 C cm/ watt measurements to substantiate their RarsanNCE At 62.5% loss factor n = 60 C cm/ watt At 33.0% loss factor p,=45 C cm/ watt t !~

1. Tes Caocutarios or cason Tsuessavnene On e other hand, we must sincerely

'y*f*RDyy'***&E*** MER '** commend the authors for attempting to Case Il-Six cables is 2 wide by 3 deep arrive at a realistsc comparison between ducibank. 4 }- duct-bank and direct-buried systems. It NELA Value is unfortunate, however, that in doing so b ** I"**"" " " #%* ' ' 62 ' 5%"' ' 33 ' 0% I IL D. Short (f'anada Wire and Cable they have not based their formula develop. Rthc i Compa:y, Toronto. Ont., t'a==Aa ): Several ment on extensive 8 eld survey data as was joh f " ' '6.89. 5.05%. 3.00 of the engineers who work with sne at Can. done at the time the NELA duct constants ada Wire have been studying the Neher. were established. Neber McGrath Value McGrath paper over the past few months. The only w'ay in which we have as yet Loas factor.....100%.,62.5%. 33.0% 768 Neher, McGrath-Temperature and Load Capabslity of Cable Sytems Ocyosan 1967

..-.- _.-~.- _.-_-.- -~._ --.-_.---. -, t Upper layer been used extensively, but the apparmt Kennelly formula if the sink is the er.rth's Rths.a ther, thermal resistivity inserted in the calcula-surface. Why is the carth's surface tem. e mal / ohms. tions are based on that value obtained perature not the true ambient to use when feet......... 10.23. 7.24. 4.88 is siin, as messured in accordance with applying the Kennelly formulaf is the Middle layer recommended methods. To get a very British use of a 2/3 factor in reality a Rths.a ther. accurate value of the apparent thermal correction for the virtual sink temperature, mal / ohms. resistivity, it seems that the method to be or sink temperatures if the deep isothermal feet........ 10.05. 7.69. 5.12 used should exactly duplicate the cable and theory is valid. Lower layer its operating conditions; i.e., the same Rthn ther. diameter as the cable, the same watts loss RapsaENCE mal / ohms. dissipated, the same depth of burial, and t. rmammac ano M nemanners. Paostou ou feet......... 10.63. 7. 49. 5.02 at the time when the thermal conditions tas.'x, Pies Cason in New Junssy, A. 8. Brookes. Average values.10.60. 7.47. 5.01 are most onerous. Thus in the calculation T. E. starrs. AIRE TreasMooms, vol. 70, pt. !!!. of thermal resistance from cable to ambient. Det.1957, pp. 773-84. In order for Neher.McGrath values of it appears that the Kennelly formula can 2. An Anatows Sa m n or Cast.s Hear thermal resistances to be equal to NELA be used to a high degree of accuracy if an f{ Q'C,'l,,8' NN Mt. N values, sod resistivity would have to be: apparent thermal resistivity of the soil in 1965 pp. 315-22. At 100% loss factor n=53 C cm/ watt situ is used. This measurement should At 62.5% loss factor p =50 C cm/ watt automatically take into account all the factors that otherwise limit the Kennelly F. O. Wollaston (British Columbia Engl. 1 At 33% loss factor p,=43 C.cm/ watt formula to a theoretical exercise. neering Company, Ltd, Vancouver, B. C., Other calculations on single. conductor There has been a great deal of investiga. Canadah This discussion is conaned to the l high voltage esbles varying h candnetnr tl~ !* +9 HfW af mnkwa em anil parts of the paper dealing with cables in ) sise from 300 to 1,150 MCM installed in resistivity. However, as yet there seems ducts. The paper is in many respects j outside ducts in a normal duct-bank systems to be no general agreement on another most admirable, notably the coverage of it was necessary to assume a p =75 C basic problem, and that is the direction of skin efect in conductors of special types, em/wstt in order to make the Neher. the heat Bow. The authors and others proximity and eddy current efects, mutual i McGrath formulas agree with the current maintain that the heat Sow is to the surface heating efect of multicable installations, ratings calculated by the NEI.A method, of the earth whereas other investigators and the efect of extraneous heat sources. The NELA method is of course strictly claim some heat Bow is downwards to a For the first time these are all adequately empirical and the duct constants deter. deep isothermal, about 30 to 50 feet below treated in one paper. The methods of mined from an average of a large number the earth's surface. In reference 12 Mr. calculation must, however, be critically l of field surveys. It has been in use for Neher obtains the heat 6 eld pattern by examined before being accepted. I am well over 25 yearsl and there must of a superimposing the Seld based on the disturbed to $nd that the methods given consequence be many thousands of miles Kennelly formula on the temperature for rating cables in ducts lead to sub. of cables operating at current ratings cal. gradient. It is obvious from the 6 eld stantially larger conductor sizes than does l culated by the use of these duct constants, patterns that in the summer the heat flow the IPCEA.NELA method. By the l So far as our experience in Canada is con. is predominantly down, whereas in the IPCEA.NELA method I mean the method l cerned we know of no bot spot failures with winter the heat Sow is to the surface. The given in an Anaconda publication.8 I high voltage cables in duct-bank installa. authors give no quantitative method of^ believe this method is identical to that tions. On the contrary one is led to read evaluating the efect of the temperature used in preparing the esisting IPCEA cur. with great interest the recent paper by gradient on the apparent soil resistivity. rent ratings for cables. Brookes and Starts.' This could be one of the reasons for the The Neher.McGrath method leads to Do the authors expect utility engineers diference between the resistivity as mess. much higher values for the duct heating operating duct. bank installations to adopt ured in the laboratory and in the 6 eld. constant (the thermal resistance from the method put forward in the paper and An indication of the eMect of change of duct. bank to earth ambient) than does the forthwith reduce their loads accordingly? apparent thermal resistivity is shown in IPCEA.NELA method, when the thermal l This is a question of great importance, a paper by de Haas, Sandiford, and resistivity of the earth is taken as 120 C l and we should have a categorical statement Cameron,8 wherein the efect ofintroducing cm/ watt in the Neher McGrath calcula. from the authors in this specific regard, a deep isothermal (ground water)in combl* tion. The value to be used for earth In Appendix IV the authors give a speci. nation with the earth's surface as the sink thermal resistivity is of ' paramount im. I men calculation for a typical duct. bank has a thermal resistance of approximatelY portance and will be discussed in more [ installation and also a similar calculation 25% less than if the earth's surface was detail later. A few illustrations of the for a pipe. type installation. In the one the only sink. This would indicate that diference between the two methods will l' they use a n of 120 and in the other a the thermal resistivity of the medium is first be given. l u of 80. Would the authors enlighten changed whereas the change in tempera. The 6rst application of the Neher. L me on the signi6cance of these two di6erent ture distribution due to the temperature McGrath method which we made was to values for n. On this point Dr. Wiseman gradient should be investigated. determine the conductor size for a pro. stated in his discussion of the paper that It should be emphasized that the Ken. posed 230.kv cable installation. The cal. he was glad to learn that we can now base nelly formula is applicable to steady. state culated conductor size was 1,500 MCM, the duct. bank calculations on the same basis conditions only. The authors realize this, whereas by the IPCEA.NELA method the of n as pipe type cable, but the authors of course, and attempt to compensate for calculated size was 1,150 MCM. Some l have not done this in their Appendix IV, this short. coming by applying a cyclical 42 miles of cable were involved in the 1 The use of the Kennelly formula in the loading factor to the external thermal path, proposed project, so the Neher.McGrath practical case of cablen buried in the earth The factor they use is 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 sourca in a medium pipe-type cables. Since the thermal circuit NELA result. that is homogeneous, of uniform resistivity of a duct bank is quite diferent from that In another instance, the Neber McGrath S and temperature, the formula would apply. of direct buried cables, we do not agree method was used to determine the required 4 However, for the practical case of cables that this same cyclical loading factor (as size of cable leads for a 75-ava trans. In the earth, there is considerable deviation measured on direct buried cables) can be former. The calculated size was so large from the ideal case such as nonuniform applied to a duct. bank installation. as to be considered physically impractical, medium, seasonal variation of temperature Finally it is pertinent to point out that whereas by the IPCEA.NELA method the gradient in the earth, nonuniform distribu. the Kennelly formula is premised upon all calculated size was practical. Rather than L tion of moisture in the earth, moisture the heat energy flowing to the earth's risk possible trouble if the IPCEA.NELA migration, and other factors, which render surface. One must then 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 serial bus instead of cable for these curate. Thus in its use one must bear in ture. Theoretically at least the tempera. leads. l mind these limitations, ture of the earth at the cable depth of In a third case, the cable leads of a 50 In Europe the Kennelly formula has burial is not the ambient to be used in the mva 13.8.kv generator were to be changed OcToven 1957 Neher, McGrath-Temperature and I.oad Capability of Cable Systems 769

s. enou* " Table XIV. It we.s necessary to measure TsW2 XV. Thermel Resistences Pertaining _W///dW//dY///MF/M thi sir tempersture in e.n cecupied duct. ts Test smee there were no empty ducts. The loading on the machine was recorded and i . I the current division between the six Thwmal Ruistem. Nebw-I M A. gami-as, I "'I'* ""**I cables was determined. The maximum f ..

• p *. l ',

departure from equal loading of the two

• h'h
• lw cables on each phase was only 25 After 3**"38tl**

0 78. 0 73 i 5 days the duct air temperature was 43 C. Sbes,th .j. .,132 duum r I g{ oue n es m. The ambient ground temperature was 19.5 Duet wau to earth i ~ .Q*.e C at the same depth as the center of the antent........ s 7s *.. .4.9 R L.. duct bank. Dividing the temperature rise O*M d *** ** ** by 1/6 of the total losses, a thennal re-La a na.esne ouet sistance of 4.6 ohms is obtained. Table

• Calculated from equation 44(A) usins ji.= 120 C XV shows the thermal resistances pertinent

'"/"*"* = conca m to this case as determined by the Neher. Fis. 6. Cross section of duct bank McGrath method and the IPCEA NELA method. The experimental value (occupied the earth resistivity is taken as 55 C cm/ i watt in equation 44(A). I likely that the value of 55 a,t does not seem ] bee use.the associated 234kv step-up duct air to earth arabient of Table XV) is s representative j transformer was being. replaced with a in good agreement with the IPCEA-345-kv unit. The existing leads consist NELA value given in " duct wall to earth I typical soil around duct banks. Many i of two 2.500-MCM cables per phase ambient" of Table XV, while the Neher-measurements in several laboratories have inMaded in a 6 duct bank. According to McGrath value is much higher. The e nsistently shown that the specific thermal i res stivity of earth varies from about thi Neher-McGrath method, these cables Neher-McGrath value shouM be ap-should be approximately 3,500 MCM cach proximately equal to the IPCEA-NELA 100 C cm/ watt for a moisture content of if thi AEIC allowable temperature of 76 C value if the two methods are to give the 15% to about 300 or 400 C cm/ watt for la not to be exceeded at fullload in summer same results, as is obvious by inspection of zero moisture content. A value of 180 C em/ watt seems fairly representative of thn2. The unit has run at full load for Table XV. The Neher.McGrath value lous 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 foamer represents the validity of the Neher McGrath method of tion of the Neher.McGrath method is thennal resistance from the outside sur' ace calculatm, g the thermal resistance from duct torrect. one must conclude that the existing of the occupied dact wall to earth ambient, bank to carth ambten,t should be demon-eables have been severely overloaded many while the latter represents this same re-strated by tests wherem the earth thermal times during their service period of 8 sistance plus the thermal resistance from resistivity is definitel,y known. Have the years. No evidence of such overloading occupied duct air to the outside surface of authors verified their findings by such has been seen; the cables have been entirely the occupied duct wall. tests? trouble-free. There are two other units One is not entitled to say that the dis-Rarman cs ct th's plant. Identical in all respects to crepancy between the Neher McGrath the one described above except that one of value and the IPCEA-NELA value is real 1. Cyamant RArtmos rom ELacrasCAL CON-them has been in service slightly longer, unless the value of the specific thermal Eg7"O [",'(*",I 3D,Nfg7C the other not qaite as long. No trouble resistivity of the earth p, is the same for edioon, oes.1942. has occurred on the leads of these units. both. The Neher-McGrath value in the It was decided to make a temperature tabulation is obtaine:1 when a value of survey to establish the correct facts. The earth thermal resistivity p,= 120 C cm/ watt J. H. Neher and M. H. McGrath: We are unit was run at fullload for 5 days. Test and thermal resistivity of concrete p.=85 indebted to Mr. Barnes and Mr. Golden-results showed that the duct structure are used in equation 44(A) of the paper, berg for their discussions in which they tttalci equilibrium temperature in 24 There has never been any general agree-summarize the present cable rating prac. hours. The bulb of a recording thermom. ment on what value of carth thermal tices in Great Britain and point out some eter was inserted 20 feet in the bottom resistivity is inherent in the IPCEA NELA diHerences with American practice. From middle duct. The details of the duct duct constants. Several years ego Mr. this it would appear that in most respects bank and cable are given in Fig. 6 and G. B. Shanklin and his coworkers in the the practices in the two countries are General Electric Company investigated similar. While the method of handling TaWe XIV. CaWe and Lose Dets this extensively and c neluded that the group cable ratings developed by Mr. value is about 180 C cm/ watt. If this Goldenberg may appear to diHer from the 2,500-MCM Segmental Copper Conductor, e nelusion is correct the discrepancy be-method of the paper, actually both methods Paper Insulated. Lead-Sheathed Solid-Type' tween the Neher-McGrath, result and the are derived from the same basic principles 13'8 Kv IPCEA-NELA duet heating constant is and should give identical results for the real and serious. Our test result cited same set of conditions. above does not give any information on To answer their questions with regard corrent Watta tan this point because the earth thermal re-to temperature limits and the relationship Cable During Test, Per Feet sistivity was not measured, due to lack of of this paper to the published rating tables, m. Ampen of cable facilities, we may say that IPCEA, in collaboration If the discrepancy is real. one is led to with the AIEE, has under active con-r.. .1.035.. s.79 question the soundness of the Kennelly sideration a revision of the existing current {," Q 8 $ formula used by the authors. It is based rating tables based on the methods of cal-4.. 90s.. 4.4a on the premise that all heat generated in culation set forth in this paper. The tem-

s..

911.. 4.4e the cable escapes to the surface of the earth, perature limits will be those already .1.02L 7 em Some competent engineers have argued that adopted by IPCEA, AEIC, dc.,in industry. Par emble average s.: part of the heat escapes by another path, specifications. namely to a sink deep in the earth. Mathe. Mr. Church has outlined a procedure for Note matical development of this premise gives determining the eHect of the loading cycle Ambirt earth temperature during test was 19.s C. A result for the thermal resistance between on cable ratings which will be, we fear, C 1ee we pa 2-3 for A. phase,1-4 for B-phase' duct bank and earth that is only about an enigma to most cable engineers despite two-thirds as large as the result by the the fact that it represents a challenge tN17h ckne s Kennelly formula. According to this, we to those mathematically inclined. Mr. C c la uttion thickans. tache.... .....o.210 might expect the Neher-McGrath method Goldenberg also has referred to a diHerent j Diametw ovw insulatsa. laches... . 2.454 to agree with the NELA value if the earth but nevertheless mathematically involved thiUkaeYfI ..N thermal resistivity is taken equal to 2/3X procedure for doing this. For normal cable o,w 11 diameter. inches................. 2.7 0 180 -120 C cm/ watt in equation 44(A). calculations, the tremendous amount of A-C ruistance st os C = s 41 :10-9 ehmeteet It turns out that agreement occurs when computations required for each individual 770 Neher, McGrath-Temperature and Load Capability of Cable Systems Octonen 1957

e cose is simply not warmuted even if a resultant thermal resistr.nce from loaded 6 eld measurements had not been carried ,i digital computer were e,vrilable to the cabla duct well 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 the soil su siJ u.

cycle to a given cable system is to be compared with NELA constant of 4.9, Also, the apparent discrepancy (which studied, we suggest that this may be done scarcely confirm Mr. Thomas' statement to appears because the direction of heat flow more simply, more rapidly, and more the effect that the present IPCEA.NELA implied in the formula is toward the surface economically by using an analog computer method is based on or is even closely whereas in summer the total beat flow in designed for the purpose. We feel, how-related to Kirke's work. While Kirke the earth is obviously in the reverse direc-ever, that the accuracy of the method given made some attempt to take into account tion) is explained by the application of in the paper as compared to all exact cal-the con 6guration of the duct bank structure, the principle of superposition to the separate culations which we have examined, includ-he did not utilize resistivity as such, beat 6 elds involved. As a result, cable ing those of Mr. Church, is sufficient, par-and as previously indicated we believe that engineers, with very few exceptions, have ticularly in view of the fact that any par-a knowledge of this and other parameters accepted the formula for calculations 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 of handling this problem, par-cable systems. The method of handling approximation, admittedly, but it has been ticularly when one considers the problem cables ir, duct, given in the paper, is a derived from the same fundamental prin-of comparison between different types of logical extension of the principles under-ciples which underlic Mr Church's method systems. lying the Kennelly formula in order to through a series of ca.efully considered As Mr. Thomas has suggested, the heat include in the calculations two very im-simplifications. It should be understood flow 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 flows any one of which, duct con 6guration and the thermal re-D,. ' Ibis value happens tu l e the but due to a prti:uhr =ble, b redily Ster-cittidy of tb==rmmding soil. This single value to use based on the studies mined as indicated in reference 12. We are method is also not new. It was first described in reference 3. For Mr. Church's not interested in these heat Bows per se, described by N. P. Bailey in a paper in case values of 7.1 for the 75% load factor but only in the resulting temperature 19298 and subsequently in reference 13 of cycle, and of 5.1 for the 60% load factor difference between 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, in the conductor loss relatively simple equation given. True, past. Long ago 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 differpace between laboratory and is sita the value of earth thermal resistivity em-mathematical and on a field plotter, in-measurements of soil resistivity and that it played. dicate that the equation 44(A) is suffi-does not stem from any lack of applicability Dr. Wiseman's comments in this con-ciently accurate in view of the inherent of the Kennelly formula to the problem, nection are :nost interesting since he has errors in fixing the earth resistivity and Numerous British publications point out often expressed the opinion that, prac-loss factor in a particular situation. that the two-thirds factor is not to be used tically, it was suflicient to consider D, to Mr. Short, at the start of his discussion, where the resistivity is measured iss situ be equal to D,, 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 all of the earth portion for determining the load capability of In addition, in recent years the British of the thermal circuit. We can agree direct earth buried or pipe type cable to have developed a new laboratory sampling s which checks not only with with this in respect to pipe-type cables. be "well founded" for a 1007, load factor procedure but, as he has indicated, we do not consider but, because of questions raised by various the buried sphere, the buried cylinder, the this further simplification desirable in investigators in reference 3 of our paper, transient needic, 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 formula which the case for other load and loss factors. cable installations. he gives for obtaining attainment factor All four investigators who undertook to Another ghost mentioned by Mr. Short directly from loss factor suitable in this study the problem for the Insulated Con-is the deep isothermal approach (a proposal case. This is readily apparent from Fig. 2 duetor Committee, however, are on record which was first suggested by Levy in 1930)8 of the first paper of reference 3 in our as recommending or agreeing to the method citing the de Haas, Sandiford, and Cameron 8 paper. Since the use of D, 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 fails 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 for calculating the effect that this method is based on the Kennelly case consists of a conducting paint electrode of the loading cycle. formula because in the latter portion of his of an analogue model connected electrically The introduction of an additional thermal discussion he questions the applicability to another electrode representing the resistance to care for surface effects be-of 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 installa-flowing (not stationary) ground water ent matter 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 nwr.ber of the ghosts which plagued the is scarcely pertinent to the proi,lem at cyclic loads, whereas the use of D, is Insulated Conductor Committee some 10 hand. Incidentally, Table I of this paper intended to give the correct result for cyclic years ago when the latter started work on 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 in load capability calculations. bank. unchanged by the value of D, is correct These ghosts were subsequently laid 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 majority of engineers in this country. market, nor are we saying that three i l and that it may attain an appreciable Even at that time the Kennelly formula single conductor cables of a given size magnitude in the case of small directly had been in existence for over 50 years. installed in a buried pipe must have the buried cables. We concur in the hope Despite the fact that this formula is based same rating as three conductors of the same i l that this matter will be investigated further. on scientific principles found in most text size installed in separate ducts. We Mr. 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 of thumb for the past 10 years in duct and indicates that this work formed its applicability mainly because calculations or more and there are now many miles of l the basis of the present NELA-IPCEA by it did not appen to check with measure-high voltage pipe cable in successful service method. Employing a duet bank con-ments in the field. This situation is dis-which are rated and are being operated at a j figuration such as shown by Wollaston and cussed in reference 12 of our paper wherein load capability level which Mr. Short utilizing equations 14 and I" of the Kirke it is shown that the disagreement was not considers incomprehensible. article, we find that Kirke would use a due to the formula but to the fact that the Mr. Short's dilemma results solely from Ocioann 1957 Neher, McGrath-Temperature and Load Capability of Cable Systems 771

e Thi fact that h1 is ettempting to compare account more properly thi essential param. an unpublished 1947 memor tndum by

• the results of cdculations made under a eters which en pertinant to thi ccse c.t G. B. Shanklin, that a resistivity of IfJ is g 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 speciSc 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 calculation from the given method This is a situation which existed imme-will adopt the proposed method but we do utilizing his test results indicates a dis-diatily following the war and is one of the not think that they will find it necessary crepancy in the method. We believe that ghosts previously mentioned. Conductor to reduce loads unless they have very high if hit. Wollaston will consult some8 8 of size determinations for cable in duct values of earth resistivity. Regarding the the many references which have appeared utilizing the NELA constants require no need for reduction in loads on existing in the technical literature over the past knowledge nor consideration of soil re-circuits, it should be kept in mind that few years on determinations of soil re. sistivity as such. On the other hand, such it is only relatively recently that AEIC sistivity in connection with experimental determinations for pipe-type cable systems specifications have made provision for duct bank, buried cable and pipe-type cable by any practical method require a speci6c increased permissible temperature limits installations, either alone or in conjunction numwical assumption to be made as to for emergency periods, and for the greater with buried cylinders, spheres or transient thi value of soil resistivity in order to arrive portion of the period that these emergency needles, that he will find that there is no at en answer. By taking the stand that limits have been in eHect the number of longer any justi6 cation for an inferred the concealed resistivity in the NELA companies who have utilized them is resistivity of the order of 120 in the NELA constrats is 120 or more, it is thus possible relatively small. As a result, the greater constants or for his impression that a re-to obtain an advantage in favor of duct-lay portion of the cables now in service have sistivity of 180 is representative of average c2ble. been selected on the basis that normal conditions. Furthermore, because of 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 .2L

• thermd resistivities in the proposed method, Moreover, in recent years shamber of Mr. Wollaston obtained an indicated value
• it will be obvious that calculations by the in sits measurements have been made with of 55, there are, of course, several possible given method will check with those of the the transient needle, the sphere, or the explanations that suggest themnives. As-IPCEA method only for certain combina-buried cylinder. Theoretical studies have suming the temperature measurements tions of the variable parameters in the shown that measurement of ultimate soil were made accurately, perhaps the soil method. Since these parameters were not resistivity can be obtained readily with actually had a resistivity of this order of fixed and in fact are now unknown as re-such devices. While in many cases these inagnitude. From recent studies on soils gards the NELA duct heating constants, have been made in connection with pipe-and the cHects of such matters as composi-it is obviously impossible to make a factual type cable installations, they apply equally tion, density, compaction, particle size, comparison of the results obtained by the well to duct bank installations in so far etc., it is evident that it is very di5 cult two methods. Here again, by assuming as the resistivity of the soil itself is con.

to estimate the resistivity of a soil from carth resistivities of 1ll0 or 180 as both hir. cerned. The values in general range from appearance alone. Alternatively, it could Short tnd hit. Wollaston have done, the 50 to 100 with some higher values as the be that the measured value of resistivity given method will result in larger conductor exception at certain times of the year. is not the ultimate value as a constant load sizes than the IPCEAemethod. Moreover, over the past decade a number applied for 5 days would sot sumee to bring Derpite the fact that both Mr. Short of pipe. type installations have been in. the duct structure to its ultimate tempera. and Mr. Thomas refer to the presumably stalled in this country with design re-ture rise over ambient, unless, of course, large unount of factual data which underlie sistivities in the 70 to 90 range. Under it had been carrying substantially fullload thi NELA duct constants, we have been the circumstances, we do not believe that for some time prior to the test in question. untble to ascertain the specific conditions it will be found necessary in most cases Mr. Wollaston mentions that the tempera-on which these constants were based nor to reduce the loads on existiag circuits. ture was measured 20 feet from the man-is there any indication that earth resistivity However, we do believe that engineers hole but does not indicate the length of the measurements were taken as a part of the will be well advised to take steps to ascer. duct run on which the test was conducted. data. About all that can be done, there-tain the values of thermal resistivity which This raises a question as to whether in his fore, is to assume representative cable and are applicable for their conditions because particular case there could have been any duct configurations and then to calculate with the more liberal use of emergency alleviation of temperature rise by longi. the earth resistivity required in the given temperature limits and the tendency for tudinal heat flow or, alternatively, by longi-method to match the value calculated by shift in many areas in the load peak from tudinal convection efects 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 low level in the not too and plugged? tions on which the NELA duct constants distant future, were obtained" as stated by Mr. Short. The values of soil resistivity of 80 and Rarsanxess Rtther, we believe that the conditions 120 used in the examples of Appendix IV assumed in reference 13 are much more were chosen merely for purposes of illustra. 1. Hsar Ft.ow raou Unosmonovno ELaerare representative, on the basis of which an tion and the value of 120 rather than 80 P a Can s. eu B EE Dess. ej av; rage earth resistivity of 75 was obtamed was used m the duct lay case m order to et 100% load factor. emphasize the effect of a difference between 2. An EVALUATION or Two Rapto Marmons or Asas991xo TRs TRaRuAL R as:strirrTT or Son., We take the position, therefore, that the resistivity of earth at 120 and concrete M. W, mkowsid, K. WehHniskL heral, the validity of the proposed method is not at 85. Institution of Electrical Engineers. London, to be judged by whether or not the calcula-Unlike Mr. Short, Mr. Wollaston is very England, vol.103, pt. A, no.11. Oct.1956, p. 453. tions made by it using parameters arbi. careful in his discussion to make it quite 3. CasLa Hsavino rw Unnssonouwo Docrs, R. D. Luy. Gewal Elutru Rnww, Scbeautadt. trarily picked by Mr. Short (or by Mr. clear that his comments relating to a "* Y" ^P I' * ' P' * ' Wollaston) agree with calculations made comparison of the results obtained by the by the IPCEA method. Rather we feel given method and the NELA.IPCEA ( su nfenna 2 of & Shon's discussion. that the applicability of the IPCEA method is premised on his own arbitrary 5. Tsursaareas RIss Ano ComaswT Ravino method to a particular case depends upon assumption of a concealed soil resistivity L',C s as Io sn, Degs;,E;,B dinf e, E,E. ,, p how well it checks with the method which of 120 in the NELA constants and on his British Electrical and Allied Industries Research %ft have proposed, and which takes into impression, presumably based largely on Association. London. England,1936. 772 Neher, McGrath-Temperature and Load Capability of Cable Systems OcToneR 1957

'V ~& m i e, S* 1 ll$p \\ l1 f t Heat Transfer Study On power (ab!C Since the geometry of the duct assembly is not radially symmetric, it was realized 1 Ducts and Duct Assemblies

• "e m-carly in the study of this problem that, in perature around a duct surface,it would be necessary to use a large number of PAUL GREEBLER GUY F. BARNETT therm e uples spaced circumferentially NONMEMBER AIEE ASSOCIATE AIEI around the surface. Furthermore, it was recognized that the temperature distribu-tion along the length of the duct would be STUDIES of heat transfer on power ture of the iron pipe in the Tratuite was nonuniform due to the irregular contact cable in duct have indicated the need sufficiently different from that in the fiber between the inner duct wall surface and for more experimental data to establish duct, both measured under conditions of the lead sheath; and so it was necessary thermal resistivity values for several com-equal heater load, to justify further study to space the thermocouples along the duct ponents of the duct system, particularly of the effects of the thermal resistivity of length as well. A 2-foot length of duct, that portion of the heat flow path from the duct upon the thermal resistance from placed in the center of the 8 foot as-the cable sheath to the outer duct wall sheath to outer duct wall surface in a sembly, was employed for the measure-surface. Theoretical considerations of cable system.

ments. Thus 3-foot sections of duct on hest transfer from the cable to the outer After about two years, during which each side of this test length served as duct wall surface have treated the duct time tests and procedures were estab. guards, reducing end effects and thereby I wall as an isothermal surface; and, gen. lished, the control apparatus was de. allowing the test area to more closely rep-erally, no consideration has been given to signed and assembled; and work was resent a small section of a long duct, the effect of the thermal resistivity of the started on the first stage of the 2-stage A preliminary survey of the tempera-duct material upon the heat flow from the program, which was planned to include ture distribution around the duct surfaces cable. These approximations are made investigation of (1) ducts in air: (2) single showed that 4S thermocouples along the necessary in theoretical studies of cable duct encased in concrete. This paper 2-foot length placed in a 3-turn helix of systems by the complex geometry of the contains a description of the tests cover-10 couples per turn would provide enough duct assembly, the cable sheath resting ing this program, and the application of temperature readings to yield a true nonuniformly at the l>ottom of the duct. the test results is indicated to the solu-While such studies, supported by the ex. tion of heat flow problems in duct banks, perimental evidence available, yield rea. "*"""m Conductors t.I,cmmmmended by the AIEE Insulated bonably accurate thermal resistivity Thermocouple Assembly Tuhatc0 Prwam Committee for presentatmn at ittee and approved by the A!! E vahleb, the eIIcCts of a nonisothermal duct the AIEH Winter General Meeting. New York, wall and of the thermal resistivity of the Eight foot lengths of Transite and N. y, January so-rehru.ry 3. 9.o w aiiu.cript ""h"''d J ", 8. ' "4 8 - duct material can be taken m, to account fiber duct were employed for the tests in ="d' a vailab '"' 'r'at-ing December 8 194 a ' by 1*Tforming measurements on a duct Mir. The main Components for this test pmg,,,,,,,,,,,,,,,,,,, ,,,,,,,y,,,,, Maevule Research Center. Manville, N J.and essembly. are the duet, the lead sheath restinE on "" E """sn i. Eletronics Enginur with the In 19h a study of heat flow in duet the bottom of the duct and containing a National Bureau of btandards. R ashington D. C.. formerly with Johns Manydle Research Center, s,htem9 was begun at the Johnotanville calrod heater along its axis, and the ap-The authors wish to acknowledge the helpful sur-Nehearch Center to determine the thermalparatus for regulating the power supply E',$"J3,"d *","'d'",",',",'i $/,"[',,",'j,', h',

• I resistance of the components of the heat and measuring the thermocouple elec.

Bradley of the Johno Manville Corporatson. and g"W path m, a duet awembly.,l~ransit e tromotive forces. also to Mr. Ddion, Mr. O'Donnell, Mr. W. Guin L. and fiber duct, the latter pmessmg the and t, members i.f the Physica section hkher thermal resistan e, were telected for the tests

• Preliminary experiments

[' were performed with each type of duct '] tlacawd in concrete and buried in earth,

• n iron pipe enclosin: a heater resting on the bottom of cath duct. The tempera-MM m

D' rentaret,ve ducts referred to " '"% ^ [ bestm ari 13 i e 1 l r eunduit eovered ic t eder.i nnerincatu.n ll - C-

• Aurunt 1. W3C and anheatoa rement conduit enoeOuple essem.

[*tu.n nif.371. At.ril 3, II*Ucoverrn in Federal Stier"f bly oft Outside ' t* I (J M Kordert t lot h dutte are o 9 Murh wall thsch ness. duet surface .f, 1

• 9..4. Ve sLt Ml: M (s'rerMon, ihtrnrll-lient Transfer Study 337 i

.Jl ,;,r;.;m cm d '> D, Figura 2 (I(ft). Front view ol ' T"' gg,,,2,,,,_,g 3 je ~ 1< -y

i.,;t- - 7Q contral boud. Power end

_ _ a, m g [r " n,g yh thermocoeple circuit ecmpo. l* {M r,: nents are numbered as follows: .,Is 1 ~ 3 (1) fuse bones and transtats, b-M arst.gr J. - !7 'T'. (2) ammeter, (3) integrating

f

~ wattmeters, (4) colectray tem. aan W 'W perature controller (5) pilot 4 4 lights (6) type K 2 Leeds and I)~ ej Northrup potentiometer (7) q g selvenometer spot reference = glass (8) type R Leeds and j ~ -.a Northrup galvanometer end [ t i, optical system, and (9) thermo. j couple selector switches @ pl } >W ~ .. ? ..Q L f average surface temperature. Fi;ure i number 30 Brown and Sharpe gauge con. h] shows the assembly of the temperature stantan wires is equal to that of a single measuring thermocouples on a test length 10-gauge wire, it was concluded that this j of fiber duct. The constantan wires are quantity of wire has negligible etTect upon lud sheaths are seen protruding from the rig,,e 4, Ducts encased in concrete. The j soldered to a narrow strip of thin copper the heat flow. duct awembila. The ducts are not clurly foil, which is cemented to the outside I The Transite and fiber ducts employed visible since their ends have been packed with surface of the duct. An identical thermo-in the tests each had a 4-inch inside diam. rock ***l. Aa *"p*ri"*"t*l **"duit l' 8h'** d couple assembly is employed on the inside eter and 0.31-inch wall thickness. 3"'"i Pition in addition to the Transite and 'f surface. As can be seen in Figure 1, the Aber duct usemblia ] constantan wires on the outside surface The Heating Unit helix are run about two inches along the l surface and then inserted into holes taking The lead sheath used in the duct as-and held in place by thin Transite disk i them inside the duct. sembly was cut from a lead pipe of 3%- spacers. The shield was used as the re-7 All of the constantan leads were car-inch outside diameter and 1/8-ibch wall turn current lead to eliminate the possi-ried inside the duct to reduce the possi-thickness. The pipe was stored in the bility of inducing potentials in the ther-g bility of abrasion when set in concrete. laboratory for over a year before the mocouple leads. The resistance of the , O Also. the leads were run along the duct tests were begun, and so the lead surface Calrod heater was measured as approxi-E surface for at least two inches to avoid had Sutlicient time to attain a high emis-mately 3.4 ohms per foot with ten watts { change in the junction temperature by sivity oxide coating. A 7.75 foot length per foot heat flow in the assembled duct. g conduction along the wire. In order to Calrod heater, consisting of a coaxial After some investigation, sand was r permit the measurement of the average nichrome wire and metallic shield sep-found to be a suitable medium with [ surface temperature of a duct by con-arated by a refractory material, was which to surround the Calrod heater in-necting the couples on that surface in placed along the axis of the lead sheath side the lead sheath. Five copper con-parallel, the constantan leads were all cut to lengths of equal resistance. Con- [ sideration was given to the effect the mass Figure 3 (left). Rue $4 of wires inside the duct might have un the Wew of control og, e, l l 'k [ _ ] a surface temperature of the lead sheath board. Numbered and of the inner duct surface. Since the 'NUM r total cross sectional area of the 96,

• ,5.'coNCne tt,(,;

I thermocouple ter.

• @k minal board (t) the
• MW g

survey couple selec. i! tot switch essembly, ?s t ' ~ and (3) the power lh. eg *'* ( Duc7 7^* circuit relays 9 e ' p-a

2,

J j ~ Figure 5 (right).

IEg7,

/ i l Cross-section detail /4 d ,'y \\ * "((" *= of duct encased in s A l, ,g concrete for Test l} U l j $eria 1." A 12 seneuir couetse e, 'l U h, acouse cincuarsunca e J inch concrete casing Ea's,' [Ne7e* o'c" M

}

L.? was employed in 808't s : Pes e rt.tsst ( " Test Seria 2." The ]y k ($ lud shuth encloses n -~'~ ^ wW] L L e centered Calrod I N F,, 7 concaste sunracs 4 heeter I b countas 358 Greebler, Barnett-Heat Transfer Study AIEE TRANSACT 10N' lt 1:

1 Nintan thermocouples made from numk r test period of three to six hours by con. The concrete casings were aged before 24 !!rown and Sharpe gauge wire were trolling the temperatme of the lead placed in a helical arrangement along a sheath and that of ambient air. tests were started until the electrical re-e sistance of wood blocks containing metal Sfoot length in the middle of the lead The ends of the duct were packed with electrodes, which were cast in the con-pipe. The duct assembiv us then com. rock wool to cut down convection, con. crete, reached an equilibrium condition. pleted by placing the sheath inside the tributing to the erTectiveness of the guard The aging period, as judged by this duct, the lead pipe resting on the bottom sections in elimmating end effects. Tem-and ferming an air crescent with the inner metled, was approximately four months. perature measurements along the test Seven thermocouples were piaced wall surrace, length of the lead sheath during the test around the surface of the concrete en-period showed variations from the mean velopes to obtain surface temperatures. Apparatus temperature of about one per cent. With the additional observation of out. Figures 2 and 3 show the front and rear These temperature variations were ran-side concrete surface temperature, the test dom along the test length of the sheath, method was identical with that described respectively of the control board. Tne with no indication of a maximum tem-for ducts in air, power circuit controls and the thermo-coupic circuit instruments are numbered perature near the center, indicating that Figure 4 shows the concrete encased to simplify their identification. the guard sections were effective in elim-ducts in test position behind the panel inating end effects. Along the top of board. The concrete envelopes are spaced The lead sheath temperature was main-the duct, the temperature was nearly ten inches apart, and the temperature in tained constant during a test run by means of the Celectray temperatue con. constant along the 2. foot test length. the air space midway between the en-Appreciable temperature differences were troller, which surveyed the control cased ducts exceeded room temperature couples of each duct assembly once a - measured along the length on the bottom by less than 1 degree centigrade. A duct i of the duct, but these differences were bank of experimental conduit is shown in minu te. The control couples w(re random and can be attributed to the non-addition to the Transite and fiber duct mounted on the lead sheath, and the con-troller functioned to reduce the current uniform contact between lead sheath and assemblies. Figure 5 shows a cross-sec-j duct wall. through the Calrod heater when the lead tion detail of ducts in concrete. Three " points" each at four different A second series of tests was conducted sheath temperature exceeded the set sheath temperatures were obtained for vzlue and to increase it w hen the tempera-on Transite and fiber duct, using two each duct. Transite and fiber, after ther-additional samples, to add weight to the ture fell below the setting. Pilot lights mal equilibrium had been obtained. A original data obtained. The test as-on the control board showed which duct e;sembly was being surveyed by the con-point consisted of obtaining a record, by sembly in air was identical with that de-means of theintegrating wattmeter.of the scribed before except that the length of troller at any given time. Although the power dissipated in each duct throughout the duct assembly was reduced to six controller has a sensitivity of 0.1 degree the test period, recording the surface feet and the number of lead sheath ther-centigrade, the temperature variations of temperatures of the sheath and duct wall mocouples was increased to seven. An the sheath exceeded this quantity be-at intervals during the test period, and additional change made for the tests on ecuse of the appreciable thermal capacity noting the ambient air temperature. The ducts in concrete was to increase the size of the duet system. The deviation from the set value was held, however, within tests were run in a constant temperature of the concrete envelope so that the total room (34 degrees centigrade) so that cross-section of the duct bank was a 12-1 per cent of the sheath temperature little change was noted in the ambient air inch square. It is believed that this setting, varying periodically between temperature. high and low values. larger concrete envelope more closely rep-Energy dissipation in a duct heater resents a single-duct be. h buried under-during a test interval was measured with Test Assembly ground. The metnod of test employed in integrating wattmeters, and the average the second test series was identical'with power was computed from the time in. The assembled ducts were suspended that of the first series except that " points" terval of the test run. Thermocouple side by side in air, widi a separation of were taken at a larger number of lead sheath temperatures with only one electromotive forces were measured with one foot, behind Ge control board. a type 102 Leeds and Northrup potenti. Temperature measurements in the air " point" for each temperature. Also the ~ ometer, and thermocouple switches were space between the Transite and fiber tests were run in a lower ambient room connected so that the electromotive ducts shued that their mutual heatmg temperature (about 26 degrees centi-grade). Data pertaining to the first and forces of each couple could be measuted effects were negligible. Thermocouple separately or an averan surface tempera leads were carried through the inside of second series of tests will be designated ture reading be made by connecting in each duct and connected to the terminal respectively as Series 1 and Series 2. parallel the coupks on that surface. board. The second stage of the investigation, Results Method of Test namely the study of single duet encased m a concrete envelope, was carried out Table I contains typical observations H All temperature measurements w ere employin;; the following concrete mix: and calculations from the tests on ducts made under steady stete conditions of 440 pounds cement; 1,295 pounds sand; in air and in. concrete. Although this { heat flow. Ther nal equilibrium u as and 2.100 pounds 3 <4-inch stone. table contains only a small number of the 2enerally attained about 72 hours after This is approximately a 1:3:5 mix, total test points employed in the investi-the initial setting of the controller and based upon the fullowing densities: sand gation,it shows the method of calculation Dower transtats. minor power adjust-IN pounds per cubic foot, stone 100 used to obtain the values of thermal re-f t ments being made during the first 4s pounds per cubic foot, and cement 94 sistance and resistivity employed in the { hours of this period. This steady-state pounds per cubic foot. No allowance was illustrations. j condition was inaintained throuebout the made for moisture content of the sand. 4 Values of thermal resistance are plotted i 1%6. Vot.t'Mc w Greener. Barnett-ilrat Trwfer %dy 3% H

r c -M ~, - '3' ' !" 'cA T E 7 Q' [...T ~ l _~ ~ = 1 .m_ . _. ~. 4 w.. _ ,o., as -s-.: a - " ' - ' ~ ' - ' - ~ ' ~ ~ ~; O O O k o e6 a: at j s.e j g3._ 5 N s <n i .... n.. n. a. N N 0.4 d0-e u N N .N " in N__.a e.,e,,, e w w g3 o u g3 g riesa-sem,gg g ,4 z g en u realTE-ste, a N = ._ o re g a en 0.2 -- th - - --s. t 1 1 manse it.stners a n_ y u l c3 s A E J j

• TnanssTI'.sEntES I 4 y 2

I g a 5 Nx o-x e- ,k

• • b

- ~ -so e5 To 75 to SS to SS h SHEATH TEMPERATURE C

1. 8 Fis w 6.

Thermal mistance frose lead sheath to inside duct swface versus lead sheath tempe,.. SHEATH TEMPERATURE C. l two for Transite and Aber ducts in air Fisme 8. Thermal resistance of the duct well versus lead sheath temperatwe for Transite and D b-8 o Aber ducts in air 2 9 a h $c 80.0 E i T = D >e+ g d 4 .reen-adnies e $o N e. c.an-. .. e y d.3 - - - - N t p u a_______ La Y O N N 5 2 E 0.2 E 8.1 N* m reat Ms, = Taans TE.-sta gs a _ _ h r Tnans:TE-v[ntre ~- ~' g g; e ~ m~- r,. a 41m Q 00 se so. _ _ _ _ _ N .= m o es To 75 so es so 50 56 so M 70 ' 75 m 46 $n SHEATH TEMPERATURE C 2 SHEATH TEMPERATURE C ~. - 9, lism e 1. Theemal mistance from lead sheath to inside duct swface versus lead sheath tempe,a-Fiswe 9. Thermal resistance of the duct wall versus lead sheath temperatwe for Trannies and twe foi Teensite and Aber ducts encased in concrete Aber ducts encased in concrete u. 4

1 ,n T W l. Typical Esperimental Data e Teinterature. *C lasid el.Etande ~ Thermal Resistance. 'C Po, Thermal Restatmty'* Watt Per Lanear Ft Duct Doct Doct Getside Sheath Earlate Watta histernal* Wall Wall Concrete Doct Vetene Per Ft Sheath to Dust R esistmty Res.stasty $urface Surface Eurface Ambient to Concrete C cm8/ watt Duet Wall AAF Ratelope pe Ae C em/ watt es av hher a ls. Dseta ia Air f%er (Is .10.6 .6.14 47 4 45.1. .33.9. .l.83. hher (11 .13 2 70 6 .31 1. 47 9. . 0 22...l.07... IS 3 .sJ 7, .57.4 .52 6 .35 0. 1 48.. 0.24.. 0.98.. 1%er (fly. .t.300..1.200 ,.300 hber tib. .12.6.. .no 7. 42.4.. 37 2, . 34 4. .l.38 .0.26... 0.99., .l.260 .l.100. . 320 .13 8. tal 3 .43.9. .37.7.. . 25 6 .l.47. . 0.41. ..0.93. hur (II:.. 21.9 .8) 6 .53 6. .44 2. 1.170 .t.110. .350 't ranute (l * . 25 0. ,1.81.. 0 46.. 0.94. 1.250..1.050. . 650 12 6. El 4. .48 2. .46 3 . 25 1. .1.28 1ranute flJ . 0.43.. 0 87. 1.280..l.060.. . 620 .56 3 70 1. .58.6.. .49 1. . 33.9. .l.14.. 0.15.. 0.93. .33 9 .l.21.. 0.18.. 0 98.. . 9s0. . Sito Tranute (IL .l.090 .19.1. .76 2. .54.7.. .51.7.

• l ransite (!!,

.l.030...l.100. 14 0 .54 2. 40 7. .38 6. . 83 9. .l.12. .0.16.. 0 93. 970...1.050. .300 Transite 1111 .18 8 .67 6. 45 3 .42 3 ,,25 9. .I.25.. 0.15... 0.90.. . 950 .1.050.. . 220 . 200 Trannste (I h. _ .24 0 .79 7. .61.7. .45.2 .28 3. .27 6. .1.22.. 0.17... 0.80.. 1.060...1.010 .200 .1.17. 1.040 900. .0.16...0.83. .230 bber fin .1,000. 930, .200 Ducts in Concrete hher i t i .32 4 .64 9 48 3 .43 0... 37.3.. 33 5. 14 9 71 1. .51 8 45.6 .38 8 .33.8. .3.30.. 0 42.. . 0 46. .1,180. .1.35. . 0.43. bber fli. hber fils. .19 9...88 9. .57 6. . 49 3...40.3. .33.5. .1.22.. 0.42. l .1.000..580. ,.81 .16 7.. 66 2. .46 8 .40 0 .30.6.. 26.1. .t.16.. 0.41. .D.48. .l.110. hber (IlL. .0.45. .1.040. .1.100... 560...87 .21 6 .77 2. .53 6 .45 2. . 33 0... 26.1. .l.09... 0.89.. . 0.66. 990. hber (lle. .1.110. .860... 81 .23.6. . 82 8. .57 3 .47.6. .34.4.. 27.2. .l.07. . 0.41. 1 ransite f fi. .1.000... 650.. 90 .la 7. 65 3.. 49 2. .46 t. .39.7... 33.8.. 1.02.. 0.12. 910.. . 0.56. 930. Transite (fl., . 1 56 .1,180...620... 90 .19 9. .71.1. .61.6. .49.1. Trans>te ili .1.130,.650.. 90 . 41. 2.. 33. 6... 0. 97. .26.3 .51.7. 57 3 .53.7. .0.39., 870.. 1 rana 4e <lli. .0.14.. .1.210...160... 7) 43 6... 33.6... 0 93.. 0.14 . 0.89. 830., .19 5. t 5 1, 44 3 .41 7. 30 6 Trana<te flh .1,260...190... 71 .25 2..77 0 .51 A 48 1.. 33.8. 26.1.. 1,01.. 0.13.. . 0.39.. 790.. . 26.1. .1.07.. 0.13.. Tsanutefilj. 1,240...190.. 71 . 27. 0. 60 7. .64.1. .50 8. .34.7. 27.2. .0.99.. 0.14. . 0.67 910.. . 0.57. 860.. . 860.. 180..92

• Numiserin parenthe eg repreunts ttie test series from which th d

.1.130.. 180. .92 . 0.88.. 340.. e ata was taken. .1,030.. 190.. 93

• • #. de and 8, are surf act reustivd y factor 6 respectively f c, are volume remitwitws of duct and concrete respectuely.

rom sheath to duct wall, from duct wall to ambient air These t hermal resist wity values are eumputed from the follow, and from concrete to am k) adand ins equations l' I*" 032 to. Dd/6/ " Y012 los a D,/D duct wan. and the concrete envelope.where he, ha. be'. hd. and he are the respective ther 4 and D., D., D. and D. are an isches the respectne diameters of abeathmal resistanc oqun aleta concrete diameter d o air, concrete to air, of the , inner duct wau surlace outer duct wall surface, and against lead sheath temperature for the components of the heat flow path in the tween these surfaces. the thermal re-sistance values decrease with increasing thermal resistance values from the lead ducts, Firures 6 through 9. Figures G It was not ex-sheath to the inside duct surface. For a lead sheath temperature. end 7 show the variation with sheath tem-perature of the thermal resistance from pected that the heat transfer due to con-given sheath temperature, the thermal sheath to inside duct wall for ducts in air vection would increase so rapidly with in-resistance is consistently higher for ducts and ducts in concrete respectively. Since creasing sheath temperature as that due in air than in concrete. Also the fiber radiation through the air crescent between to radiation, the former varying nearly duct consistently gives a higher resistance sheath and inside duct surface is an im-lineariy with the temperature difference from sheath to inside duct wall than does portant factor in the heat transfer be. of the two surfaces, the latter with the the Transite duct. The influence of the difference in the fourth powers of the concrete casing can be attributed to its surface temperatures.' etiectiveness in producing more uniform- '"4 Two general conclusions can be drawn ity of the heat flow lines in the entire duet from these curves regarding the relative assembly, since its thermal resisthity is relatively low. Differences between the / fiber and Transite assemblies can be at-p/ tributed to the heat transfer from sheath to duct by direct conduction. The lead t sheath " snakes" throughout the bottom 7 s /!,\\'/ of the duct. making a nonuniform contact with it. The duct material of lower i E Figure 10 (left). Temperature dis-thermal resistivity more readily conducts l t i {J' T n. A j p heat away from the lead sheath. tribution around (; j the br duct eur-The difference in the thermal resistance

• u y

faces at 82 de-from lead sheath to inside duct wall as grees centistede between the Transite and fiber ducts is \\ f had sheath tem. considerably greater in Series 1 tests than / O D 8 E \\/ O perature. The d -M p'N solid lines repre. values for the fiber duct assembly is / s .,,,s. f sent the duct en. about 15 per cent of the resistance from emd in concrete, sheath to duet wall, and we attribute it to i 9 the dotted lines the variable factor of contact area be-la ett ] % wtur m tween lead sheath and the duct containing cmwr. sar, leu-m rra,qer sua, 3 w

4 Fisres 11 (Idt). Icad sheath dc<s net rest umfntmly on the' .w- '~~ itmuraturs 6 bottom ut' the duet, the heat duw is nqt j tribution eroend entirely symmetncal about the vertical y[. / the Transite duct 4 surfaces et 82 de-axis. Thetemperaturedistnbutionaround the duct walls for ducts in air at the same / / g,"[,, sheath temperature is similar to that in [\\' p.,.iv,,,. The e nerete, except that a higher percentage [ N solid lines repre, of the total heat flow occurs near the l,l f' '\\gj ' sent the duct on. bottom. wl / \\ sm_ casedin concrete, Figures 12 and 13 show reduced scale i ' '( !] the dotted lines drawings of the fiber and Transite ducts j in air with their lead cheaths. The tempera. s o

/.

\\' tures on the duct wn;1s at each 30 degree radial position viere taken from the solid i ^ d h/ line polar graphs, Figures 10 and 11, rep. resenting ducts encased in concrete, and i / N,'-t-N recorded on the drawings. The tempera-g ture falls off rapidly on the bottom half of perature of the ambient surroundings as the duct from the region of contact with r well as that of the outside duct surface. the lead sheath, and it remains nearly The resistance of the concrete envelope constant on the top half. The direction it. This deviation is not unreasonably completes the thermal circuit for ducts in of the temperature gradient through the high, since considerations of the heat concrete in the laboratory instanation, duct is indicated by the arrows. transfer from sheath to duct by White-although the thermal resistance of the Calculations of thermal resistance for head and liutchings8 indicate that vana-surrounding earth would also be con-the heat tiow components of a duct sys-tions in spacing between the sheath and sidered in an underground duct bank. tem are usually based upon accepted the bottom of the duct produce consider-Table I also contains the thermal re-values of thermal surface or volume re-able efect upon the thermal resistance of sistance values for the concrete envelopes, sistivity. Resistivity values are more this component of the heat flow path. the values for the Series 2 tests being useful to the cable engineer than are re-Figures 8 and 9 show the thermal re-greater since the larger concrete envelope sistance values since the former are inde. sistance of the duct itself as a function of was employed for these tests. pendent of the dimensions of the com-i lead sheath temperature for ducts in air Figures 10 and 11 are polar graphs ponents of the duct system. The thermal and ducts in concrete respectively. This showing the temperature distribution resistance values obtained from the tests factor as small compared with the total around the duct walls respectively for have been employed to calculate surface resistance of the heat flow path from the fiber and Transite ducts at a sheath tem-resistivity of the lead sheath, volume re-sheath to ambient surroundings, but it perature of 82 degrees centigrade. The sistivity of the duct material and of the j serves to measure the effect of the thermal solid lines represent ducts in concrete, concrete, and surface resistivity of the resistance of the duct upon the over-all dotted lines, ducts iu air. The average outer duct wallin air. These values are heat flow through the duct assembly, temperature of the three thermocouples shown in Table I, and since there is some { The Transite duct possesses a lower re-at each 22.5 degre e radial position interest in the surface resistivity of the h ststance in concrete than in air, possibly (corresponding to ep.h turn of the three-outside of the concrete casing in air, these ) due to the reduction m its outside surface turn helix cf con %es) was employed to latter values are also given. Lead sheath resistance when in contact with the con. obtain the points for these curves. The surface resistivity values in fiber and cre te envelope, Transite and concrete both departure from uniform radial heat flow being cement products. An anomalous in the duct is shown by the large tem. curve in the set shown m Figures 8 and 9 perature digerence between the top and is that for the Series 1 tests on nber duct bottom of the duct wall. Also since the i in air, Sfoisture content, among other factors, was considered as an explanation l for this anomaly, but it was discounted \\ / x since the Transite and fiber ducts were s exposed to identical environments before figure it (right). and during the tests. Since the fiber duct j Reduced scele, y/. samples employed in the two tests were diesrani of deeth s / identically assembled, no satisfactory ex-and duct showins 38 -M. S planation for the anomalous curve has the ternperature 7(M)s been found. distribution \\, / / The thermal circuit for ducts in air is '"ad O' n / completed with the outside due; wall sur-duct encased in face resistance, typical values for which are shown in Table I. These values give ds / the order of marnitude of the outside ,,g,,3,,g M ,,,,,,,,,g,,,,, n surface resistance of the duct wall, and in dow the direc-I an actual installation, the exact value of tion of the tem. / \\ this resistance will depend upon the tem-peneture predient i 4 363 Greebler, Barnett-Heat Transfer Study ALEE TarusscrIONS u F

n' l Figurs 13 (l;ft). Tebb ll. Thermal Resistivity Factore-10 l 1 tar ' R;due:d scale Wetts Per Frot Heat Fl w \\,, diestem of sheeth 4 and duct showing Thermal Component Srm bol Resistwitr the temperature l / '/ dlattibWlion Lead sheath in 6ber duct. { j eround the Irene-surhee nmmmty.... .A. .t.200 C em / watt \\ [ / s J lte duct encased Lead ebeath in Tranerte \\ 7 x N \\ / o,,et.., r.,,,,,,,,,,, y.. s. 1,02o C em'/wat s \\ \\ / In concrets at 33 Duct as mir, surface re degree conti-matmt y. .80. 1.1 C emVwau s, sM //./ Concrete in air, surface dN8 g 3rede sheath tem- --o-.- 80 ' resstivit y....., ..s,..,1,120 C em8/ watt perature. Arrows Fiber duet, volume re. A 7~

• N show the direc-sist mt y........

, es.. 480 C em/ watt jg Transite duct. nleme re- \\ tion of the tem-

• "it y....

.... ed., 200 C em/ watt j perature gradient ty 64 C em/ watt / variable in the heat transfer from sheath to duct, this assumption probably does / To s not introduce an appreciable error in j g cable calculations. In temperature meas-j dra \\ urements on a cable sheath and the in-side of an enclosing fiber duct encased in concrete, Barenscher obtained data indi-8 cating the correctness of the inverse re-Traasite ducts are computed, as is custom-per foot, and the values thus obtained lationship between sheath diameter and ary in cable calculations, by formulating may be used conveniently as duct con-thermal resistance from sheath to duct the thermal resistance from sheath to stants in cable calculations. These wall. The temperature rise of a given inner duct wall in terms of the sheath values, along with the volume resistivities cable in a buried duct bank above am-surf ace resistivity. The surface resistivity of duct wall and concrete obtained from bient earth is obtained by replacing the of the concrete envelope in air, and also the tests, are contained in Table II-fourth term in the equation with the ex-its volume resistivity, is calculated by em-The temperature rise of a cable in a pression derived by Neherd, the latter ploying a diameter of a circle whose perim-duct in airis given by the equation eter is equal to that of the square con-taking into consideration the thermal re- / g sistance of concrete and surrounding crete casing. The concrete surface re-T,= (Rm+0.00411 g'+0.0t2ae X earth and the heating produced by the sistivity values are computed from the other icaded cables in the duct bank, letst precise of all the temperature log, d+ 0.00411 Further tests on various duct materials

1. d meesurements made on the duct assem-8 Ud blits, and the data should be weighted should be of great value to cable engi-where the four terms in parentheses rep-neers in establishing duct constants for ecemdingly.

resent the thermal resistances respec-these materials, and should add weight to Figure 14 shows thermal surface re-tivelv from copper to lead, lead sheath to the data submitted here on Transite and sistivity values for various duct assembly insid'e duct wall, across the duct wall, and fiber duct. A more complete investiga-components versus heat flow in watts per outer duet wall to ambient air; and O is tion is needed of the thermal resistance of foot of duct. Curves of lead sheath sur-the heat flow in watts per foot of cable. the heat flow path from the cable sheath free resistivity in fiber and Transite duct The symbols employed in the last three to the outside of the duct wall, including are based upon average values from the terms in the parentheses are defined in experimental data on the effect of varia-four sets of tests; that is, Series I and 2 Table I, and the resistivity values are tions in lead sheath and duct diameters for ducts in air and in concrete. The contained in Table II. The equation as-and in thermal resistivity of the duct wall curves of outside surface resistivity of the sumes that the sheath to duct resistance material. Tests on groups of ducts in a duet wall and the concrete envelope are is independent of the duct diameter; duct bank would also be of considerable each based upon average values from four and since theoretical considerations show interest, although the heat flow path out-sets of tests on both Transite and fiber. For a given value of sheath temperature, that the sheath diameter is the primary side the duct wall can be treated, with the outer duct wall surface resistivity i, g isoc l lower for Transite than for fiber since d greater heat flow occurs in the assembly i,,,, l of the former, giving its outer d.act wall j l l surface a hi her temperature. Ilowever. R A-co=caete a aia F since resistivity values in Figure 14 are l1800" ,,%. " a Plotted against heat flow in watts per foot of duct, the outside duct wall surface re-Fisure 14. Thermal l l w' ee, -re Sistivities for Transite and fiber duct in air "N 4 N' at i are nearly equal and are represented by a [d she e in Tren Smgle curve. It is mterestmg to note that u, t ite duet, lead sheath the surface resistivity valuu of the vari-e N In Aber duct, outer ous components are of the same order of duct surfece in air, J 70 l Mynitude. The curves in Figure 14 are end outer concrete 8 80 extrapolated to a heat flow of ten watts surface in air nur roow-warts m roer or euct 1H.%, ht ur (,o Greebler, Barnett-11 eat Transfer Study 363

8 mnsiderable degree of accuray, with con. a here T, and T. are the temperatures in Tase Maruous ventionti rnethods of heat flow calcula- 'legrees Kelvin f the sheath and duct wall The authors < tate that tN power mout

• respectively, se that 4 T T, - T. and was controlled to keep the u.uh tem.

a ) = ( Te - T. )( To r-T. ) ( Te' + perature constant and that botn the sheath } References We see then that Ra, is a function of "*""'"""**'*'"'"*"*""""d 7 to maintain steady state heat-flow condi. ] f 1. Its At Ta muiswum muukt W. fl. !dcAdams. ( A T[" + k(Te t I.)( Ts'f Tie ) tion t The actual power input was ob. 8 j hicGraw-Hill 0%k Compeay, New Y,rir, N. L tained by measurmg the euergy inDut over a j second,dition.1942. where & = k /k. period of three to six hours. If the rate of i i n 2. Cuessur RArince or CAntse rua T a Ak s. In plotting their Values for Ra, against heat transfer were accurately proportional j uinnom ou Disreisurion. J. B. whitehead. sheath temperature, the authors have to the temperature ditTerences, this would uU[. bA d".med that the duct wall temperature be an entirely justidable metho,l. Ilowever, esten v e j T. is constant and that the convection term due to the nonlinear relations myolved, the aYe$AsLasi Duc$s". is negligibly small. To see how these quan-vahdity of an anthmetic average for the in-w I Uxoan au o P. J. Barenscher. TAeses. Unneruty of Wisconsin titles affect the appearance of the curves, put power is questionable. Moreover, it t.\\tadison. Wie s,1928. Figures 1 to 4 of the discussion have been would have been far simpler to keep the in-4 Tue TEuPER Arves Rssm or C ARLRs (N A DuCr prepared from the complete test records put power and the ambient temperature B An s, J. H. Neher. A/EE Dmmson, volume which Mr. Greebler very kindly made avail. constant for a given run and to let the sheath 08 part 1,1949, pages 644-49 able for this purpose. Ra, is plotted against temperature fall where it would. { (a T/" in Figures 1 and 3 and against ( T, + T.)( T ' + T.8) in Figures 2 and 4. Figures 1 and 2 are for liber while Figures 3 Disensiori and 4 are for Transite-curves for duct in n w. autreli f con otidated Edison com-l air and in concrete are given in each illus-pany of New York, Inc., New York, N. Y.): V. V. Mason (The tfydro-Electric Power tration because, for the purpose of this dis-The data presented by the authors are of .d Commission of Ontario, Toronto, Ontario, cussion, it is of most interest to compare all considerable interest to cable engineers, and l Canada): This discussion deals with two the values for a given kind of duct. Figures the Johns-Manville Company and the points which may not bear greatly on the I and 3, Ra, versus (a T/", would 1.011 if authors are to be congratulated for the practical value of the results attained by Mr. the heat transfer due to radie tion were si. dl v.entation of this data. The painstaking Greebler and Mr. Barnett but which are of compared to that by convec ion, while Fig-care used in making these tests is com-some importance as regards the experimental ures 2 and 4 would hold for negligible con-mendat>le. The results would have been of method and the presentation of the results. vection. That is, these figu~es represent still greater value if the tests could have extremes; any practical case will be some been carried out on more than one cable size PmESCNTAT!oN oF Rast t.rs combination of the two, obtained by assign-or at least on a more representative com. The authors present their results for the ing a suitable value to k. bination than a 3'/rinch cable in 4-inch sheath to-duct thermai resistance, Ra,,as a Examination of these figures indicates duct. The data presented contribute sis-graph with the sheath temperature as the in. that for tiber ducts, the agreement between nificantly to our understanding of the ther-dependent variable, and express some con-S: ries I and II in both air and concrete is mal drop from cable sheath to duct w dl. cern over the lack of agreement of these considerably better when plotted against Of particular interest are the polar irraphs of curves for the Series I and Series !! tests. ( ATf" than when plotted against T or Figures 10 to 11 of the paper showing the To find a more suitable quantity against ( T. + T. X T,' + T.8). Transite, on the temperature distribution around lo.Wed duct which to plot Ra, consider that the rate at other hand, exhibits the most reasonable be-walls. A need for further exploration of this which heat is transferred from sheath to haviour when ( T, + T.) ( T,' + T.') is phenomenon a indicated when the4e data duct, being partly by conduction, partly by used for the abscissa. This would seem to are compared with the values shown in Fig-convection, and partly by radiation, may be indicate that with the tiber duct a large part ure 1 of Mr. F. V. Smithi discunion of a written thus of the heat transfer is due to convection, paper by J. !!. Lher presented in 19M t while with Transite, radiation is the more im-it should be noted that the temperatures P = k a T+ k:( a T) + kaa( T*) (1) portant mechanism. This difference may be given in Mr. Smith's di3cussion are outside i i ascribed to the difference in the thermal duet wall values, but these show little de-where k, km, km are constants, and T is the emissivities of the Transite and fiber sur-parture from an isothermal *urface in con. absolute temperature m degrees Kelvm. faces. trast with the vaiuus for outside wall shown The exponent of the temperature ditierence The agreement between the two series of in Figures 10 and 11 of the paper by Mr. for the convection term actually may vary runs is still far from perfect, but does ap-Greebler and Mr. Barnett. L'nfortunately, from 1 to l.5, but 1.25 ts probably fairly near pear to be considersbly improved. Another in the ca.>e of Mr. Smith's data, the heat the true value. poss ble point of difference between the ton per foot of cable. 3.0 watts, is relatively The thermal tesistance Rae, then,.is given various tests not considered by the authors low for an average cable of a diameter of by is the presence of the thermocouple leads 2 52 inches. The comparison is also ob-1 p with regard to their effect on the convection scured by the possible variations as between - - = k + k:( ATf"+k ( Ts + Te)X currents. Small changes in their position single and multiduct structures. i Ra, aT could affect materially the magnitude of the There are a number of etiects indicated in ( T,8 + T.8) (2) convection component of heat transfer. the data presented by the author

• whirb Figure 1 (left). Thermal E

resistance versus ATS" 1E l .. e se_ I' i N= l e-. uses t for Aber duct i s %l l, l l m.a uns.: {t l u. l = =a =u x t-e . %.d l 1 l' l IMi"I" concu to aconeners 1 " "'"g j I l 1 g { 1,.. K.M (y I W I Ai 4 LI N I "i I i I &II o Figure 2 (risht). Ther.

t.,

l K l mel resistance versus l (T. + T XT ' + T.') X H l l l l .le 7 s.e s. sa (*fr s.a s.. a.s s ie i.e 10" for Aber ducts t s.r.u r,s.,,an.-e 3M Greebler, Barnnt-lhat Transfer Study ALEE TnausAcTson

v t ss this is the range of temperature octually i: el

• l

'l l.T311LL j l obtain:d m practice, and not the 82 degrees l TRANsrtt j j n-g e M ^ g gy centigrade reported in the paper. We then H l i l acomarn a would have obtamed thermal constants l m,g g i a canceg n 1 t e paper the authors give [ f 5 g i i thermal resistivity values. The value of surface resistivity for the lead sheath should g l q a 4 j g#l,j D4).,, be qualified that it is for a sheath diameter l.Q%, n i e. ^ e i r} j '

• .%l actually a function of diameter. In the l

] ~ of 3.5 inches. Past tests indicate that it is H 'A N= Insulated Power Cable Engmeers Assocta' s, u ss sa s. l ta rt ** is a u u u tion we take cognizance of thit by assuming t,..r g e.a.,,ews g that it increases from #=660 ohms per i Fisure 3. Thermal resistance versus.iT'a for per square centimeter for 'D=lJ'2UO. hms Figure 4. Thermd ruistence versus (T + T ) '9"*" C'"'I**'" I ' O " O

• I

) 5 mehes (T,s+Tr')X10-s for Transite ducts j Transite ducts and constar t thereafter. According to l Table 11, these values may apply to fiber i duct. l possibly may be talien as random deviation For Transite duct perhaps we should duct wall while affecting the Transite duct rather than true effect. In Figure ti of the have a reduction of 15 to 20 per cent. The wall comparatively little. paper, the indicated change in thermal re-v lume resistivity values f r fiber duct, Next. consider the question of plugging up sistance from sheath to duet wall, for the Transite duct, and concrete are very wel-the duct ends. case of fiber ducts in air, as between Series I c me. e have been takig a value of 100 edly justified m, The, authors were undoubt-this procedure, since on and Series II, indicates the need for tests thermal ohms per centimeter for concrete, such a short length of duct any appreciable l on a representative number of samples be. s were n the conservative side. longitudinal flow of air probably would 8 fore firm conclusions can be drawn, although have distorted observed results to a point RsraanNcs there is no doubt that the thermal resistance where they became meaningless. Ifow-is higher in the case of dry fiber ducts as t. see retenuce 4 of the paper, ever, it is not customary to seal up duct against Transite ducts m n e, a d h is sornethnes The data on the volume thermal done. Hence, in service, we may expect resistivity of Transite and fiber material are a me 1 ngitudinal movement of air, which of interest. The average value for Transite F. H. Buller (General Electric Company, would tend to reduce the value of # below is less than that formerly used by the Con-Schenectady, N. Y.): There are two points what was observed by the authors. Pipe solidated Edison Company m rating cal-in connection with this paper which are par-cables, on the other hand, are necessarily culations, and we have ado,ited the lower ticularly worthy of notice. All tests were sealed in service, since they operate under value since these data were first released by taken on ducts in air, or encased in a con-

pressure, crete envelope situated in air, and the ends These facts may explain, at least in part, the Johns-Manville Company some few years ago. The value for fiber is higher than of the ducts were plugged up to prevent the difference between the # values ob-our normal standard, and it is to be noted longitudinal convection. These statements tained by the authors and the lower ones that the values derived from these tests are also apply to the Barenscher investigation) observed in field tests on cable-installed for the dry condition and may be appreci.

Let us examine the significance of these underground in multiple duct banks, no-ably lower when wet. points. Mr. Greebler and Mr. Barnett tably those reported by Mr. Halperin.8 Considering the various values of d pre have presented eurves (Series 2 tests) which To sum the matter up, while it would sented so far from different sources, appar.' show the effect of increasing the mass of appear that these tests were very carefully concrete around the duct with the thought made, and while the technique used can ently for the present we must accept a possible 10- to 20-per cent plus or rninus that the heavier mass of material simulated probably be properly taken as a model for somewhat more closely the effect of under-any future tests made on ductsin air, the re-variation in a for a given installation. Ad' ditional test data of the detailed type pre-ground burial of the duct bank. In this suits are not necessarily representative f or the sented by the authors, on single and mutta' thought they are probably correct, and it case of duct banks buried in the ground and duct structures, in air and especially in will be noted from Figure 2 of the paper operated under service conditions. They earth, with cables of representative size and that the surface thermal resistance of the migh* possibly approximate more closely loadmg, are required before positive con-cable falls off materially in the case of the to the case r4 duct banks in air as sornetimes clusions can be drawn, fiber duct and increases slightly in the case used indoors in powrr stations and elsewhere. of the Transite duct, thus bringing these RsrERENcs thennal properties. Presumably, burial in 1 Dncusen by Frsak V, $mith of Tus Tsun". 1. See reference 8 el the paper. I arth would exaggerate this effect further; e.t is quite possible, however, that such burial areas R sa or Casi.ss tw a Duct Bawau J. H 2. Loan RarrNos' w CAS-mmud Eu.=,, y as' a, Herman Halperin. Nein. AIEE 7eausaiou, volume 68. part 1 I 7,e mmoan,voiume nu, p.gn 54Ns. might ultimately reduce the values of sur-as. October 1939, pares $35-66. face thermal resistance in both cases below those given here for ducts in air. Further R. J. Wiseman (The Okonite Company, research is needed along these lines. J. H. Neher (Philadelphia Electric Com-Passaic, N. J.): This paper is a welcome Moreover, it is noted that these tests pany, Philadelphia, Pa.): This paper de-i addition to the investigation which has were made on an isolated duct. There is scribes the procedure employed in obtaining been going on in recent years as to the ther-reason to believe that in a multiple-duct the test results on cables in fiber and Tran-mal resntance of duct systems. It, along bank, the value of $ may be materially site ducts which I cited in my recent paper,' with Mr. J.11. Scher's paper,5 can well be aficcted by the modi 6 cation of the heat and which also appears in a paper by F. IL studied for more exact thermal constants field in the duet structure by the presence Butler and J. If. Neher 8 I wish to compli-for ductt Today there is a desire to obtain of additional loaded ducts in close proxim-ment the authors of this paper on the every ampere possible out of a cable. As sty, so that a test in air on a single duet is thoroughness with which they have worked the physical structure of the duct bank is not necessarily representative of a multiple-out this procedure, w hich may well serve as a important in determming the total thermal duct bank buried in the ground. model for future work along these lines. resistance of the duet bank, better knowledge The authors also have shown clearly that Unfortunately, the tests were conducted l of the inthnce of the kind of duct is desir. the drop through the fiber duct wall is with a single, and lager than average, cable b .ble. The paper by Mr. Greebler and Mr. greater than that through the Transite duct size so that some extrapolation is necessary barnett furnishes this information to us. wall. Ilowever, these tests were taken on to convert the results to normal practice. I wish the authors had used a beating dry ducts. Presumably water saturation. The authors have attempted to do this in 1%d which would have given a sheath which frequently occurs in the field, would Figure 14 of the paper by expressing # as a temperature of 40 to 45 degrees centigrade, tend to reduce the drop through the 6ber function of the heat flow, but completely t 1D'oO, %Ltatt t;n 1 Grcchier 13arnett-11 eat Tran.tfer Study 365 1

l i isoo A wa 5. CamMmsa of al teametnal vanabb t!ut bect t i g \\ l j i tsa data ca M et ud cable to duct resistance, a 1 it would t the' ',, Il N j Tra mt) ducts is concrets influenced by the mutual hwme erfects in af p'g g i i multiduct struc ture. It is espected that N s N l l con 3iderab!e departure from isntnermalmfuct i t surfaces necurs in any practical duct instal. [ N vela gN scwg' m n mying an apprecuye had and 1 00 's negn employing nonmetallic ducts with the cables [ ). y' l s rening on or near the bottom of their re. d Viegn

• I.\\'

h!r. Buller has pointed out several factor < spective duct walls. q 3000 in field install.itions, which we could nor ! l i g I!,; /3 4 '3 duplicate in our laboratory tests, that would 'j

1. 00 g (*

modify the heat deld and, therefore, influ. ence the value of the cable thermal surface 8 Nf E,T,NEME" % \\, " '3 resistivity 3. These factors tend, in 8 # g l general.,to lower the value of d, and so the N % TR AN stT g 43

1. 8I"*8 83Ven in ur paper are slightly on the N

t t p l, 8 conservative stde when applied to current w s.r e - 'l ,%mansivgu rating calculations in buried duct strue. .m tures. ^ Both hir. Burrell and Mr. Buller have discussed the influence of moisture on the 4 .9 8.0 f.4 f.2 1.3 IA / thermal resistivity of the duct materials in Q{/0,g the field. It is true that the presence of moisture would produce a decrease in the thermal resistivity of the duct wall. How. tver, for design purposes it would appear disregarding the etTect of the cabic diameter installation in the field, but it is larger than advisable to base calculations on the limiting uport d. 31r. Buller and I have shown in that commonly employed in a 4-inch duct. case of dry ducts because it is not uncom. s our paper that as a best approximation J is The earlier experimental work by P. J, dependent upon the fourth root of the heat Barenscher,' as well as the more recent mon to encounter such conditions in prac. tice, particularly for extended periods dur-Bow and the square root of the cable diam. theoretical study by F. H. Butler and J. H. ing the summer months. For continuously

eter, Neher.8 indicates that the inverse relation.

Figure 5 of the discussion shows the data ship between the sheath diameter and the submerged ducts, special experimental deter-minations may be justified and may be ex. of hir. Greebler and Sir, Barnett plotted thermal resistance from the sheath to the pected to show a significant reduction in the as a function of the parameter QW/D.'NQ duct is valid, as a gomi approximation, over magnitude of the thermal resistance com-in watts per foot; De in inches) together an appreciable range of cable diameters. ponent from sheath to duct wall. with t he Bart tscher data for Eber ducts and Additional tests ort Transite and Eber ducts. The tests described in our paper cover the a time curve for cable in pipe given in the using several smaller cable diameters, would range of cable sheath temperatures from 50 y Butler and Neher paper.s add greatly to the value of these experi-to 80 degrees centigtade for duct in air and It should be noted that the Buller and mental and theoretical investigations. Neher curve for 6ber duct is based on the .\\fr. Liason has presented data in his plots 60 to 80 degrees centigrade for duct encased in concrete. Dr. Wiseman has pointed out Barenscher data with which the fiber Series t of he versus variables in the convection that temperatures for cable sheaths ob-test data of Str. Greebler and hir. Barnett and radiation terms that are very helpful tained in practice are normally below the is in fairly good agreement. Similarly, the toward understanding the mechanisms of Greebler and Barnett Transite Series 1 test beat transfer from the cable to the duct. range of temperatures covered in our tests. It is pertinent to point out that more and data is so close to the cable in pipe curve We have not anumed in our paper, how-more emphasis is being placed on emergency that a distinction between the two is ever, that the duct wall temperature is con-loading at allowable copper temperatures scarcely warranted. Only the Series I stant nor that the convectiott term is negli-that, for example, may be as high as 96 Greebler and Barnett tests were available to gibly small. It was stated in the paper that degrees centigrade at 15 ky (Association of hit. Buller and myself when our paper was variations in the convection term were small Edison Illuminating Companies). Under prepared. compared with those in the radiation term. such conditions a sheath temperature of the i The second set of tests by the authors. This statement is verified by calculations order of 80 degrees centigrade would not falling as they do between the first tests on carried out by Sir. Greebler in his discussion appear to be unduly high. The thermal Figure 5 of the discussion, would seem to of a paper by Butler and Neher.8 Values volume resistivity values given in Table II indicate that in the case of both tiber and for Ria. were plotted against sheath tem. of the paper are essentially independent of Transite duct,4is a not too definite quan, perature since this temperature is the prin-temperature over the entire operating range, g tity ranging from 900 to 1,100 degrees cen-cipal variable in the thermal resistance from but the surface resistivitics increase as the tigrade square centimeters per watt for a the cable to the duct for a given cable in duct cable temperature is lowered. The surf 2ce typical cable installation in fiber duct and geometry. Str. htason is entirely correct in resistivity values given in Table II of the from 750 to 850 with a Transite duct. pointing out that the arithmetic average of a I heartily indorse the authors' concluding periodically varying power input does not paper were obtained by extrapolating the paragraph to the etTect that further tests necessardy give the same results as an curves of Figure 14 of the paper to a heat flow of ten watts per foot The d values along these lines would be valuable, equivalent constant power input, since the thus obtained represent a sheath tempera-relationship between thermal resistance ture near 70 degrees centigrade for ducts in RsFERENCBs from cable to duct and power input is not air and below 50 degrees centigrade for 1. See reference 4 et tbe peper. linear, in our tests, however, the periodic ducts in concrete. Extrapolation of these 2. Tan Tassmat Rssisrawcs Barwasw Cantse power fluctuations were very small com. values to lower sheath temperatures, as-wo a Scssorworwo Prra on Doer WALL. F. H. pared with the average input power, justify. suming a linear relationship over the operat-Baller, J. H. Neher, AIER Trearemoss, volume ing the use of the latter as a highly accurate ing range, is justifiable as a go,od approxi-69, part I,1950, pages J42-49. first-order approximation. mation. The departure from a linear rela-3. See reference 3 of the paper. Sir. Burrell has discussed the polar graphs tionship when extrapolating to a lower f of Figures 10 and 11 of the paper showing temperature should yield resistivity values the temperature distribution around loaded slightly on the conservative side, since it is Paul Greebler and Guy F, Barnett: Prob-duct walls, and has compared these wieh expected from theoretical considerations i ably the most common criticism of the test similar data presented by hir. F. V, Smith that the slope of a J versus sheath tempera-procedure arises frons the fact that the sheath in a discussion of a paper by hir. Neher.' diameter employed was somewhat large. The temperature distribution around the ture curve would approach zero as the k This cable size was taken from an actual duct wall depends upon all of the thermal Sir. Neher has pointed out that Figure temperature is lowered. .386 Greebler, Barnett-Heat Transfer Study AIEE TarusacTioNs i

_h.* I itbli 1. Thsrmit Raletivity Facttr S As a Functism of sh:.th Texerature and cal. Diametzt d in Degrers Centiorde Same Cewmeter Per Watt r Tem perature, Fiber is Alri transite ha Airt Fiber la Coacrete; Trasa4te la Concrete: l I, Degrees Cable Diameter. loches Cable Diameter. Inches Cable Diameter,laches Cable Diameter, lacses Cestiera de 1.5 20 28 40 3s 15 20 2.5 3.0 a.5 '5 2.0 2.5 3.0 3.5 1.5 2.0 2.5 3.0 3.s 40, .l.160.l.230.l.290 1.320. l.3.M. 970.1,0M. l.070.. I,110. l.130.. l 030.. i.090. 1,140.. l.180.1,200. 840. 890. 920. 950. 970

41..

,1.140. ).210.1,270. l.310. l.33u. Wo. l.010. l.060. l.090. 1,110.. l.020. 1,070.. l.120.. ),160.1, l M. 820.,840. 910. 930. 950 54. . I,I29.. I,l A0.1,2 40.. l.270. l.3fio. 956 1,rno,1.050...,040..),100 990. 1,040..l.090. 1,130,1,150.. 810.850 890. 920. 940 55. .l.100.1,160.l.220.l.250.l.240. 930 980.l.030.1,060. 1.090.. 960..l.020..l.0*0..l.100..! 120. 790. 840. 870. 900. 920 tu. .l.Ok0.l.140.l.190..l "30 l.230. 91o. M u.l.010.I,040, 1,060. 940.. 990..l.040.l.070.1,090. 780. 820.b60. 880. 900 65.. .l.060.l.120.l.170 1.200 l.23u..wou. 950. kie0.l.020.1,040... 920. 970. 1.020..l.050. 1,070.. 770.810. 840.870. 890 70.....1,030.l.000..l.140..I.160.l.20u. 870. 9Jo. MO. 2'M.1,010.. 900., 950, 990.,1,020..l.040. 750. 790.820. 850. 870 7!.. 1,010.. l.060. l. Ilo.. l.150. I.170.. &SO. 900.. 940-. 970., 990.. 880.. 930.. 970..l.000. 1,020.. 730. 770. 800. 820. 840 l

60..

990. 1,040.. ).0!*0.. l.130.. l.150.. hJO 870.. 910.. 940.. 960.. 850.. 900., 940.. 970.. 990.. 710 750. 780. 800. 520 1 l 14 of the paper does not give a complete inches. Four cases are' considered sepa-I of the discussion shows that a decrease in picture of the variation in # since the effect rately, namely. 6ber duct in air, Transite the sheath temperature of 20 degrees centi. I of the rable di.tmeter is not included. It is duct in air, fiber duct m concrete, and grade coupled with a 100 per centincrease in unforsunately true that a varies in a rather Transite duct in concrete. Thermal sur. cable diameter produces an increase in d of comp.icated manner with sheath tempera. face resistivity values shown in the table the order of magnitude of 20 per cent for ture, uble diameter, and the many other for a 3.5 inch diameter cable are the aver-each of the four cases considered. These factors in the over all heat flow path from ages of the two series of tests, with the ar,. data substantiate the previous statement conductor to ambient that affect the heat sumption that linear extrapolation to 40 that for most practical calculations o may field and, therefore, determine the tempera. degrees centigrade is justifiable. Approxi. be considered as a constant for a given duct ture drop from the sheath to the duct. On mate values of B for cable diameters smaller material in air or in concrete over the normal the fortunate side, however, all of thue than 3.5 inches were obtained by assuming operating range of sheath temperatures. variables produce only small changes in d that convection contributes 30 per cent of The values given in Table I of the discus-i i over normal operating rangen; and so S the total heat transfer from the cable to the sion indicate, however, that averaging # can be treated asaconstant for a given duct duct and that variations in the cable diam. values for duct in air and duct in concrete, material or pipe ior most practical thermal eter produce an appreciable effect only upon as was done in Figure 14 and Table II of the calculations. the convection component of the thermal paper,is not entirely justifiable. l The authors of this paper do not agree conductivity of the air space from the cable The various discussions indicate that with h!r, Neher that as a best approxima. to the duet. These calculations are based in more experimental data are desired for a i tion d is dependent upon the fourth root of principle upon an analysis given by Mr. more complete investigation of the duet the heat flow, and this divergence has been huller and h!r. Neher'in which the convec. heating problem, and the authors heartily elaborated upon by h!r. Greebler in his dis-tion component of thermal conductivity is concur in this opinion. If our paper encour. j cusuon of a paper by h!r. Buller and h!r. shown to vary inversely with the square ages additional experitnental investigations Neher 8 The value of 6 is determined by root of the cable diameter. The thermal and serves as a guide toward obtaining re-the temperature distribution in the air conductivity is just the reciprocal of the liable data from such further work, it will (' space between the cable and the duct, and in resistwity factor d, and the resistivity have succeeded in its major objective. relationship to the duct variables, this is v.alue for a cable diameter D, is computed most intimately associated with the sheath from that experimentally determined for a Rarrancas ~ temperature. The cable diameter is prob. 3.5-inch diameter da.a employing formula 1. Su nfuence 3 of the papu. ably the second most important of the vari-2. Ten TBERMA RERIM ANCS BMWEEN CAKH o iu da s ables that affect the value of 6 In order Amo A StrasovuotNo Pas on Doct WALL, F. H.

1. =0 70+0 50D#

q 4 Bauu J,H. bhu. NEE Tnuunm, nium to take into consideration variations in 4

69. Part I.1980, peges 342-49.

j with sheath temperature and cable diam. This formula is consistent with the assump. 8. Discussma by Paul Greebler of reference 2. eter, values of d are tabulated in Table I tion mentioned earlier in this paragraph, p se a4s. of the discussion for sheath temperatures and the value of 3 thus obtained is associ. C heu'aion by Frank V. Santh of Tas Tsurra. ranging from 40 to 80 degrees centigrade sted with the same sheath temperature as febe. l'EE h Ns"if" sis' fE[m os'

• ar's and for cable diameter from 1.5 to 3.5 the d3. that is used in the formula. Table 1949. p.ses 547-4s.

p l I\\ a !i

4

i a

b.~,6, \\*01.t'Mr no Greebier Barnett-Heaf Transfer Study 367 ? -l i

t 4.. p i y v I ne nermal Resistance Between Cables tive magnitudes of the terms and the c -sWu values dnany employed will be based on test data. and a burroundinS Pi e or Duct Wall ^"r7"-a~ ^ hd- ' P accuracy,s not required since the thermal resistivity between cable and duct or pipe F. H BULLER J. H. NEHER "P"*" * . lad ely small Part of the f MEM8ERAIEE MEMBER Alff total thermal circuit, and we are justified } in materially simplifying these equations. From the standpoint of analysis of the ONE step in the calculation of under-cables in duct have been expressed more test data and the subsequent develop-ground cable coeratures involv"s completely to account for the physical nent of working expressions, it is desir-the determination c the tenacerature rise characteristics of the media involved in able to utilize the simple linear relation. of the cable surface above the iramediately Appendix I of this paper. The resulting ship I surrounding inclosure such as a duct strue. equations for the the thermalconductiv-ture or a gas-or oil filled pipe. Since the ity between cable and duct or pipe with pg g intervening medium is a fluid, the mode air or gas as the intervening medium are where y and z are variables and a and 5 of heat transfer simultaneously involves Q 0.092 D,#NT*Pw are constants. Equations 1 and 2 are of convection, conduction, and radiation. -(sas) = + this form provided that the second (con-The semiempirical methods now in use aT 1.39 + D,'/D4 duction) and third (radiation) terms may j for this detennination in the case of cables 0.0213 be considered as constants within the de-in duct are not entirely sat,isfactory, and tosaD4/D/ sired accuracy of the final result. Con. 02D,Wm6U ) with the advent of gas-6 oil filled pipe. watts per degree centigrade foot (1) sidering equation I A the conduction term type cables there has arisen a definite need for a method of evaluation for these and with oil as the medium constitutes about 14 per cent of the total cable types as well. in the case of a typical cable in duct in-Q Because of the complex nature of the Tr( II)"0.053D,%T T 0.116 stallation, and about 8 per cent for a 1.39+ D//D4 +1 egad /D,, typical gas filled pipe type installation at problem and the nu*.nber of independent 4 variables which art. present, it is imprac-watts per degree centigrade foot (2) 200 pounds per square inch. The corre-sponding values for the radiation term are tical to cover compt tely all possible com-For a single cable D/ = D,, the diameter 63 and 43 per cent. binations which raa; be met within prac-of the cable. For three cables in the pipe Normal variations in D//D, may pro-tice solely by tests. By developing a or duct it is customary to base D/ on the duce' considerable variation in the con-theoretical relationship between the vari, circumscribing circle of the cables in tri-duction term, but the erfect on the over. ables, however, it is possible to develop angula configuration, D/=2.15 D,. For all picture is small, because conduction is procedures by which the test data avail. two tables the relationship D/=1.65 D, able may be analyzed in such a way that s satisfactory. such a small part of the total heat flow. Variations of T.,. can affect the radiation relatively simple working expressions It will be noted that the primary vari. term by as much as 20 per cent over a may be derived which may be applied able in equation 1 is D/. As a result, sub-sufficieritly wide operating range; how-with sufficient accuracy over the entire sequent analysts and development will be working range. facilitated if this equation is written in ever, when calculating a cable rating, with a fixed copper temperature of the order of The theoretical relationship for the the equivalent form case of cables in duct was recently pre-70 degrees to 60 degrees centigrade, the sented in a paper by one of the authors.' Q 0.092 AT Pw range of this variable is very small, and In the present paper this relationship has g,g gjw(g,gg+g,,g]+ an accuracy of the order of 3 per cent to 5 been extended to cover oil and gas pipe 0.0213 per ent may be expected. systems as well, and from the test data D,, log D4/D,,+0.102e(1 +0 0167T,,,) In the case of equation 2, the conduc-presented the requisite working expres, watts per degree centigrade foot inch (IA) sions for thermal resistance or surface re-Paper so-s2, recommended by the AIEE tosis-sistivity factors have been obtained. From the method of derivauon which lated co auctor. committee.4 ap assumes a coaxial arranEement of the ' b' ^' ' 8 T"""**' *** * """'"" proved er estation at the AtEE Winter General Steetics. cable within the duct or pipe, the numeri. New York. N Y. Muary 30-February *.1950. Theoretical Considerations ca! constants of the first two terms of U*.M.I', ?,,""",*d ",'O/r 'if f 0 e equations 1,1(A), and 2 must be con-The theoretical relationships given in sidered as being approximate only. They puy, Schenutady. N. Y4 dad L H. Nsasa se F. H. svu.se is with the cenerst Etectrie com-Appendix II of referenci: 1 for the case o.' will serve, however, to evaluate the rela. 4,7p"h i."*p.$" d'** "'"*"* """" 312 Buller, Neher--Thermal Resistance ALEE TnwsrcnoNs L

T: bis 1. Test Dete on Gee. Fill;d Pipe.Tras Cebli Systems and the General Cable Corporation. These

• c t e,,

data are plotted in Figure I and the values namner some p.* Da r o at 7 D.'a r D*"' ' _o_ a r%r_.

• of a and b in equation 3 are established as a = 0.070; b = 0.20.
• t.

, Detroit Edison Crimpany.. 3.42. 6 07. 1 Table 11 presents similar data for { .. 23.4.. 20.. 82... 0.84.... 1.86 7.8. 4f.3...ls.6.. 61... 0.81. Cables in single dry 6ber and Transite . 4.08 14 6.. 28 6.. 13.1.. 61.,.,0.64. ..$.84 ducts in concrete taken from the N.:!I :.:$$" $2.'. f Barenscher* and Johns h!anville tests dis-2 .nener i nuectric Compaar..s.92...e.07. 2 s.. i7...ja.34.0...a1...068...0a0.....if plotted in Figure I where it will be seen .a m cussed in reference 1. These data also are 9 is. 2.. 12. 4.. 60... 0.ai. ..i 1 "'t$:b: $ :U:li N:. * [ that the Transite duct points fall on the 14,9. 8 9.. 45.. 0.43.. gas in pipe curve, but the 6ber duet . 3.44 14.6.. 6.s.. 3.7.. 35.. 0.46. . 3.7? 11.2... s.s.. 40....e.49.. points result in a different curve having ., General Cat,4 Corporatica.. 4 90.. 6.07.. 14. 6.. 23. 9..

9. 2.. 86.15.9.. 8.0.. 45~. 0.81.the same value of a=0.07 but b=0.10.

3. . 4.22 ,.4.8' 4.. . General klectrie Compaor.. This difference may be explained by the . 0 5?... 4.47 4 90.. 6.07.. 14.6.,.23.1. 31.8.. 44. .0.40.. . 4.7? fact that the duct wall departs from an isothermal as a result of the relatively Table 11. Teet Date on Cables in Fiber and Tiensite Ducts Encased in Concrete high thermal resistance of the materials used, that of the dry Eber being consider. ably higher than that of the transite.3 7.e: ._2 a r'4f The test data for oil-filled pipe-type

n. ber s.orce Duci o.'

p, o ar v.'a r p.W. cable systems from tests by The Detroit Edison Company,8 the General Electric

a..

.mareenber.,... riber.. .0.69...s.s. Company, and the Okonite Company are . [0...;typ,,g2$: presented in Table III and plotted in 2 a... 14.1. . 0.233.. .. 2.17 Figure 2. In this case, the analysis has 44 24 6 0.257 2 44 ele.' *:34:2'..':0.2s17. T2:6s been inade by plotting the observed values 8.1.. 39.7,.. 0.299. . 2.76 12.8... 66.t.... 0.318... of 1.13.. 8.8.. 1.0... 4.5....o.204.. .l.41 .. 3.00 l i.:: J i ::: i N:: :. : i it >- 6.: araimt -o.wr^rm'^ m 8 0... 30.4..,.0.233... . 2.18 11.0... 32.8... 0.300...... 2.3: 24.e...es.s.,. 0.268...... 3.re 16.8....s2.4. and results in the values of a=0.025 . 0.285.. . 2. rli 28 4....s8.7... 0.27s... b = 0.60 in equation 3. 3.18... 3.8. .2y . 0.9.,. 1.6... 0.194... .09 1.7..

3. 2... 0.173..

.t.. 11 will be Seen front the analysis of the 2.4. , 3.8... 0.20s.. test data that the agreement between ...es 2 b * *.'!"f theoretical and observed numerical con. 8 1 o....... Johns-Me e viHe.... Fiber... .8.88... 3.ss...n.s.. 21.9... 0.2 7.. 14.s. 6 ..e3 stants of the simplified convection term is .3.a8....s.s8...to 7. 16 9.. 017. a... 21. 7.... 0.23s... extremely good in the case of oil as the 7.... .. Jones-u. viue... 71...iee., ...69 medium, but in the case of gas, the ob. 0 g gggg ,.g gg 23.a.. 22.0... 0. ate... .,t.a0 26.4.. 24.8.. .0.318.. .1.64 than the expected value of about 0.046. This is rather surprising since tests num. tion term constitutes about 24 per cent of ber 2 (with gas) and nutuber 9 (with oil) the total for a typical oil pipe installation. the numerical value of the denomint. tor which are consistently close to the es. Variation is more important than is the omitted is in the order of two. Actually tablished curves in Figures 1 and 2 were case with the gas. pipe cable, but is still the test data was analyzed both witt. - nd made with the same physical setup which remained unchanged throughout the trithin tolerable limits. without this simpli6 cation, and no Ap-parent change in consistency in the re. tests emept for the change in the media One peculiar phenomenon has been ob-sults was observed. employed. Therefore, we should expect served. The ratio of D,/D,', which ap. the ratio of values obtained to be the pe'trs in the conduction term also, ap. Analysis of Test Data same as the ratio of the numerical con. pears in the 6rst (convection) term of stants of the convection terms in equa-equ'ations 1 and 2 but in such a way that It follows from the preceding discussion tions 1 and 2. a change in this ratio produces an oppo. that the test data for cables in duct This discrepancy seems to be due to the site, though lesser, effect on the total and for gas-filled pipe-type installations :nayfact that in the case of several cables v lue of these equations. A minimum a be analyzed by plotting the obsaved within the pipe, a condition of the major. mor should. therefore, prevail when the values of ity of test data, there is an additional cir-conductica term is treated as a constant culation of the gas between the cables i If the ueaominator of the convectiony =p,,p 3phpw themselves which is not ) terrn a T "#* " *~ properly ac. alsc is treated as a constant. This D,'S (4) e unted for by the use of an equivalent procedure will simplify the convection term but it will have the effect of approxi. The data given in Table I were compiled diameter for the three cables, but which is j niately halving its numerical constant as from tests on gas-filled pipe-type cable apparently not effective when a more Nmp'. red with equations I and 2 since systems by The Detroit Edison Com. viscous medium such as oilis employed. g pany,8 the General Electric Conmany, As indicated before, however, a hich 1950, \\'ot.true 69 degree of accuracy is not required, and it is i Bsdier, Neher-Thermal Resistence a 343 L

M -. r<: r. :ar.J; - a m 5k h l s. Tabis til. Tso Det4 en OilJilled Pix. Type C.Ws Syste.ie 'k

/}s T=

Nrmb.e s.ene ila'?6berl = 0 W411 3 o.' 04 0 ar r. at .2 O.;+0 33 thermal ohm j }1 s.......o.i,.ac.. o.%s r% r.% feet (12) .4.ssm.eo7..:oa...s o. 4o.2et......ios in which the second term repres

e.......c.

i si.an. co.n.r...a on.e or. j ii. 4.. I. e e... a o.. 27.. is.... diiference in thermal resista .. s. 44. . ss ... u.. j $$E. $ $1 :$$E $ !$[.'2 s i...... se$ **I" # * "crett "hich it repla 4.m. a io..... oto.it. co.n.r.. 9..44. at.

4 E.

.4 so...e is. U: 8j, 725 ;g8;; 58 8

21. 8.. 4 8...,4 t... 2. 45..... ;. s5 sDiscussion of Values for C

34. 9... ll. r.. 30.. 3 09...

3S 2. 11.4 Duct .30s 44.. 3 94.. .i33 felt that a working expression based on It will be seen that the meth the foregoing analysis will be sufficiently "" "N,4%(QD/sF.)W+i4 th*' mal hm cable and duct presented herein dif termining the thermal resistance be 40 accurate. somewhat from the method given in Worldng Erpressions feet (11) reference 1. although the results are s The value of a from equations 9 and 10 is stantially the same for terra cotta and plotted in Figure 3 as a function of fibre ducts. In formulating the thermal resistance For Transite ducts, the W (Q P/D/)% and the value of H.4 from values of thermal resistance d between cable and duct, it is customary t equation 11 appears in Fi more fundamental manner in the presen express this resistance m terms of an function on (QD/*T.8)%.gure 4 as a s Also indi-paper, are slightly lower than those equivalent surface resistivity factor, as-sunung that the entire resistance was cated on these figures are the values of appearing in the reference, being equal i concentrated at the cable surface, accord-these parameters for typical conditions those assumed for terra cotta, In the case of cable in fiber duct, theIt will be recalled that the reasonin mg to the expression thennal resistance of the duct wall is used in developing algebraic expression H 4 = 0.00411 a appreciable and should be accounted for, for these values assumes an is g ; thermal ohm feet This is most readily accomplished by The test data presented in duct waII. (6) modifying equation 6 to include this re-in whi:h 4 is expressed in degrees centsistance. Thus Fiswe 1. grade square centimeters per watt. t Anetysis of test dets for embles in Hu= AT/G it fo!!ows from equation 6 Since duct and sen-Alfed pipes ,y 7 that } i DjaT l l l J = 243 degree centigrade centimeter ) i L l I l 1 e} l per watt t ?) l 4 / AT% = 0353# (degrees [ centigrade)w l l l l l I I I' \\ .s (8) It is thus possible to develop working ex-e pressions in terms of 3 in the case of cables in duct or gas filled pipe by sub-A ( -s ( k stituting equations 7 and 8 in equations 3 {' g and 4 with the appropriate values of a and g

6. In the crae of oil filled pipe a simpler f

expression is obtained in terms of Hu. 7 /i f s 3 - A' k 1 For cables in single dry fiber ducts y /lo.s

1. =

13.700 / s l - degrees centi-lf d bfg + 5 L grade square centimeters per watt { l e ,s l l l (9) / For cables in other types of single dry t I / ducts and in gas-filled pipe /- l f 1 A=- 13.700 i %[ - degrees centi-l + A \\ Dj / + 11.3 t ( l k grade square centimeters per watt oL l i t (10) L ( ( j (, For cables in oil filled pipe g % p,' I ip tt tc 344 De

• R si:

Buller, Neher-ThermalResistance 1

.-=w Table 11 cod plotted in Figure 1, how. u ever, indica.te a good correl 2 tion even j l

• e where there is substantial deviation from the assumed isothermal as indicated by thi basic data on which the table is based.

u Within the range covered by the data,in. creasing the departure from the isother-u msl changes the resulting constants some- %8 a what but does not invalidate the method u of enalysis. It follows therefore that a considerable variation in a for cables in single fibre og ducts may be expected depending upon lg the relative thermal resistivities of the 14 duct uall and the surrounding medium, g / I and other data which has come to the u authors' attention confirms this. Thus the curve of Figure 3 for fibre duct should a be considered as an upper limit. Similarly, the application of the values l a a given for single ducts to the case of cables a Se in a multiduct structure, depends upon i ic the eficct which the total heat field has in further changing the temperature gradi- ) ents around the individual duet walls. The data given by Smith in his discussion j of reference 1 indicates a value of fi for '2 multiple. fiber ducts in concrete corre-sponding closely to the curve for cable to in pipe. ) As indicated in reference 1, addi. .s tional test data taken on multiple-duct assembliet are desirable to definitely ) establish the lirr:its under these conditions. j l ] For reasons also indicated in reference 1 l these values are not directly comparable to the values adopted by the Insulated Power Cable Engineers Association and 8 j are not directly adaptable to their calcula-l, tion prondure. o io ao w ao no so m so so co no iao no Dh ATA T\\ l Conclusions 1. The theoretical relationships between 8ppendiX !. Ibeoretical Fisure 2, Analysis of test date for ceWes in the various quantities involved in the eflee-tive thermal resistance between cables and Development of Therrnal Con-

• **d p '

a surroundmg single duct or pipe have been ductivity between (oncentric aeveloped in a manner which properly l$0 thermal ( Clinders with Gas The phenomenon of convection involves accounts for the simultaneous modes of heat the conceptio, of the temperature erop transfer by convection, conduction, and or Ci! es the nterYening Medium being concentrated in two films, one at the radiation. surface of the cylindrical radiator of diame-ter substantially equal to the diameter of the 1 Ly 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 cyhndrical radiator and an enveloping iso. of the enclosing isothermal surface which vill oil 411ed pipn have been analyzed and work-thermal enclosure through an intervening be considered also being cylindrical of tr4 curves are presented for deterrnming the fluid medium is such that a portion of the diameter Dg. The following formula based tiiertual resistanet for any particular case total heat flow Q is carried by convection on McAdams8 (equation 42, page 251,1st abich may be encountered in practice. Q,,, a portion by conduction Qu,and the re. edition only) is applicable to either film. B Under typcal conditions representative mainder by radiation Q,. In formulating ) values of the equivalent surface renistivity the components of the thermal circuit, factor o for use m equation 6 are p degree therefore, it is more convenient to work m in which D is in inches, and centigrade square centimeters per watt for terms of thermal conductances rather than f tabl9 in pipe, single dry terra cotta or thermal resistances since the former quanti-h A" 68C,g c gnMte ducts Lt atmospheric prenure,450 ties are directly addit.ive. Thus,if ATis the watts per centimeter ^ de-s r cable in gas-fdled pipc type installa-tem rature op m degrees centigrade p p ens at 310 pounds per square inch, and 350 ,g lj<'eprr cables in oil 411cd pipe type installations. p -- + pg+- watts per degree centi-The significance of the components of p, p, esentativt values of 6 for cables in AT AT AT equation 15 and representative values for % 1e dry fiber ducts ws;l vary from h50 to aT 5 bl% gas (air or nitrogen) and Suniso number 6 oil grade foot (13) are given in Table IV. l b, Yot. tuts: w Buller, Neher-Thermal Resistance 345 J

j I I h l l H,' l l\\ l l l l t I \\lI!Ii i I ! I~ e 1 l I i\\ t i =~ I 1II i F \\1 1 s i r.. m n....o, .u, ~ ~c, 1 s \\! i.lII .,0.,. i h. NI \\ l 1 ~ t \\ l Ii il l l i\\ ~, 1 \\ l t 1 \\l!II II 1 .s

3 n, m,N,,... ~c 1, i

s e 8000 s \\ i,l l l ......,s 0...u l\\ ~ \\ l l hsj l t Il \\ l \\' 1 Il;l l NI ~ i s N x. l i

w. ~

\\ N \\ l i s t l N ~ I N s cAsce in eiac. N I 3 (TCARA COTTA ANO g l vvpa At or o,e ruco piec ' NTR ANSITg DUCTN

4. 2$

o;. 4 6 T.. So 1 1 ' s toe l i N N N L _d: N l i N I eo 4 .o .o .oo iso o o. aoo mao a o.. N I %cAsLg fN PIPC (Q 0;* T ')'d' &fYPICAL or cAS FucC g s.,. c Ar o NJ,, g';, " n,u.. w.m. w..s of, fo, e.w.s a d,y sa,i. a-ts.a,.soa t aiae y n,,. u.so..). woes of s., fo, c.w.s in oira a pi,. ~. a s.. ao s.: t4 a. ss 4.. 4.s 4.4 u 44 a4 s.: 4 gg pg 3% expression for the resistance between two concentric cylinders in terms of the dimen-In the case of air or inert gas, these physi-sions of the cylinders and the thermal re. cal properties are substantially independent The solution of equation 14 for tue two sistivity of the medium will be used. Thus of temperature over the working range but films in suies and with equation 16 or 18 Od 0.0213 f the density is a direct function of the substituted therein ts given with sufficient ),logi Dg/D. AT pressure. Thus, if P represents the pressure accuracy by the expressions in atmospheres, from equation 15 centigrade foot (21) Q.(gas) =0.002.% %W D AT P K, = 0.000755PW watts per de. Qa.(o;g). 0 !!6 watts per centimeter % AT 1.39 + D./Dd watts per degree degrees centigrade % (16) gree centigrade foot (19) JT logie Ds/D, When oil is employed as the medium the centigrade foot (22) Q,, D T physical constants are substanti.dly inde. {7(oil)=0.053,%A TW The radiation component with gas as the pendent of pressure and temperatures with watts per 1.39+ D,/Da medium is given with sutficient accuracy by the exception of the viscosity which for the the following expression based on McAdams' type of oil commonly employed (Suniso degree centigrade foot (20) equation 5. page 61, first edition nurnber 6) may be taken as varying in. From a theoretical standpoint the ex. versely as the cube of the temperature ac-pression for the conduction component Q, cording to the relationship should take into account any eccentricity {7 (gas) =0.102D,.(1+0.0167T,,,) watts 94.000 between the cylindrical radiator and the per dtgree centigrade foot (23) T., grams per centimeter second (17) enveloping isothermal enclosure. In the u= practical case of cables in duct or pipe the 'I ' b* The value of K for oil thus becomes cables will not rest uniformly on the bottom surface of the cable and J',, is the average of the duct, and also m the case of a non' temperature of the medium. The radiation K, = 0.000434 2,. watts per centsmeter metalh,c duct the duct wall is not strictly term is inetfective when od is the medium. degrees centigrade ;

• maintamed as an tsothermal. Since these The over-all thermal conductivity is ob-(18) etfects cannot be evaluated, the famihar tained by substituting equations 19,21. and 23 or equations 20 and 22 in equation 13 T.ble IV Appenclix 11. List of* Symbols simbot Quantity Units on. at 50 C ou at 50 c Q= total heat riow from equivalent sheath

. Thermal resistivit r.. to duct wall or pipe in watts per foot s.. i . Average absolute viscosity.. .C em/ watt.. .J.900........ .715 a T = ternperature drop in degrees centigrade

4..

. Dew e r...... . grams /em see.. 0.000104... . 0,75 P = pressure an atmogheres C,.. .Speci8c heat at constaat pressure.. . grammi ems.. 0 00110 P., . 0.006 De = diameter of the sheath m. inches . watt sec/ C.. 0.998.. .2.to De' = equivalent diameter of a group oI stam g.. . Accelerstlos due to gravity.. .cen/sec, .930.. .ggo cables in mehes a a. . Thermal coet5cient of expansiue. . t /C.. , 0 00310.. .0.00068 D,g minside diameter of the duct wall or pip # In inches 346 Butler, Neher-Thermal Resistance ALEE TaansActioNS <u

b = average temperature of the medium in picture, the thermal circuit for a sing!c. probable range of S. for a particular eue degrees centigradt conductor cabie in air is given in Figure 1 of ,=coerficient of crnissivity of the cable sur. the discussion. will be better understood, thereby makmg possible more realistic comparisons. The face in this figure, f,.. to, and is are tempera. authors clattfy our conception of the effect s and y= rectangular coordinates tures of copper, sheath, and ambient, re-of the vanous parameters involved in the a and b= experimentally deterinined con-spectively, e is insulation thickness. p is temperature drop between cable surface and stants thermal tesistivity of the insulating material, duct or pipe wall. For a given system of H.,-thermal resistance between equive-A t. is the log mean area of the insulation for cables in duct or pipe, the thermalresistance lent sheath and duct wallor pipe in ther-heat flow, Aa is sheath area, and 6, and will decrease sensibly with increasing watts mal ohm feet 8, are the cable engineers' terms for sur-loss. H./ = equivalent thermal resistance be-face resistivity" for free convection and W. D. Kirke introduced this modification 8 tween eqmvalent sheath and fibre duct radiation. Each fraction in the Figure is which is taken into account in determining wai' includmg the increased thermal re. the thermal resatance; and when resist. cable ratings for the Consolidated Edison sistivity o(the duct wall over that of the ances and temperatures are known, the heat system. surrounding mediuni in thermal ohm feet dissipation of the cable is known. But in As one follows the assumptions made in ts = equivalent surface resistivity factor in order for the resistances to be dimensionally this paper, there appear various points to degreen centigrade square centimeters per consistent, the dimensions of a must be differ-which exception might be taken on the ustt ent from the dimensions of d. and therefore ground that they are no: substantiated, a= thermal resistivity in degrees centigrade a and 3 should not be called by the same for example: the assumption of the same centimeters per watt name. constant in the expression for the convection p= average abwfute viscosity in grams per Since the definition of a as thermal resis-fdm at the cable surface and at the inner centimeters second tivity conforms to ASA standards,it might a = density in grams per cubic centimeter be better to denote o as thermal resistance duct wall, the treatment of conduction on the basis of a concentric system, and the C, = specific heat at constant pressure in of a unit surface. Its reciprocal h,is defined arbitrary assumption of an emissivity co-watt rieconds per degree centirrade gram as surface heat transfer coefficient, or alter-efficient of the cable surface of 1.0.

Yet, g = acceleration due to gravity in centimeters natively as surface film conductance. The the important point is that putting all of per second squared concept of conductance is particularly these various assumptions together in the r = thermal coefficient of expansion in centi-applicable here, as the total film conduct-particular form given in the paper, the over-meters per centameter degree centigrade ance is the sum of h, and h,, and therefore all end result does produce expressions which K=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 centtructeth degrees centigrade'h. to be a mixtt're of metric and engineering equations and the selection of parameters units. A corabination of square centi-have a reasonably sound theoretical basis, Rereretices meters with feet has no logical basis. Ifany the final working expressions given are e c,bi, dim,n, ion,,,,, ,xp,,,,,d in,,nti. ,,,coti,ii,,,,i,ic,1,nd d,,,,,13,,,, 4 1 Tze Tsurasarcas Rise or Castss su a Dect meters, the mixture would be logical al-accurate determination of the separate kawa J. H. Fieber. AIEE Transastmas. volum, though not standard; but since dimensions effect of the three modes of heat transfer.

68. put I,1949, poses 544 49 are not so expressed,it seems tinv to aban-On the average, the calculated values of 2 Haa? TsawsMressON mouk) W. H. nicAdams, don this practice and use the engineering Q/.i T for the oil-filled pipes, gas-filled bicGraw. Hall Book Company. New York. N. Y.,

system of units throughout. pipes, and cable in duct are about 5 per cent, first edition.1933. It is therefore proposed that the AIEE 15 per cent, and 55 per cent higher, respec-1 Tasswat Cmasactsarstres or a 120.Kv Hron-Committee on Insulated Conductors take tively, than the measured values given in Pszzaces Gas Fri. Lao Casta lustaLLa rto"a sitps to persuade its adherents to become Tables I, !!, and III of the paper. Special-IEifrYe 's!v'o I. P

p. e\\

familiar with ASA standards and to use ists in the field of cable heating would be me to es7 93 them where they apply. interested in knowing which cornponent or 4 A STcow or tus Tsuras4Tess Distsise-components are responsible for these dis-tion in Etnersic Castes sw LNossosoewo crepancies so that extrapolation into new Dvcts. P. J. Barenscher. Thesis. Departenent of R. W. Burrell(Consolidated Edison Com. fields could be inade with confidence, Electrical Engineenna, l'nwersay of hconsin Gladison, Was 1,1925 pany of New York, Inc., New York, N. Y.) It is stated in the paper that the agree-g g g

• ((r"ss.St(([ss a!aYa Esm[o N7s elaboration of Appendix 11 of a previous numerical constants of the simplified con-ais twwtarsu casts: r.waria xan r-n.

paper by Mr. Neher.8 Although the ap-vection term is close for the case of an oil Ud. Insulated Power Cable Engineers Association proach to the problem is Dot Changed, the medium, but is off appreciably for the case Wew York, N va. 6rst edition.1943-material presented in the Appendix referred of a gas medium, it also can be said that to is of sufficient importance to justify a the conduction-radiation constant agrees more detailed presentation. It is apparent to those engaged in the field with theory for the case of a gas medium; Discussiorg of cable heating that the Insulated Power however, for the case of an oil medium, the constant theoretically appears to range Cable Engineers Association recommended from 0.60, as given in the paper, to nearly R. H. Norris and Mrs. B. O. Buckland value of B, while perhaps sufficiently conser-twice that value, depending upon the values (General Electric Cornpany, Schenectady, vative for general design, lacks the flexibility of Ds' and De involved. K Y.): Eflicient 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 $ for less appears that the expressions for # and aw reness of the definitions and units, in various types of installations may not be H,,, as given in equations 9,10, and 11 of a (stder to 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 engmeers, confusion arises ns additional test data are compiled, the peeted. A high degree of accuracy in the as to the exact meaning of the expression ' therm.1 resistivity. ' Resi*tivity as nor-calculation of allowable current ratings of rnally defined (by the American Standards g* g, cables is not yet to be expected but impor-l A5weiation ( ASA) for example) is a prop-tant work has been done in the past few erty of a substance and is not affected by { years in clarifying our understanding of heat 4, flow through duct structures and the earth, its geometry; for example, the resistivity of 4 and this paper is an important contribution cupper has a constant value at any speenfied if j 9fnperaturt, w hile its resistance depends on to such understandmg. d' "8 tize and shape. Then the use of the 'i' j REFERENCES word " resistivity" for surface phenomena is 4 4 thisuse of the term. a. 3, 9,,,,,,,,,, j or m, p. p,,, To show how the distinction between Figure 1. Nrrul cirevit for single conducto# ( ] ',C^{Clg "y { Q^,",',' T'yg"j^[,"'" ,C5istance and resistivity enters into the in air , aume o.19w p.se us %, Yott.ste m Buller. Neher-Thermal Resistance 347

l R. J. Wiseman (Tha Okonite Cunnp.ny, in the paper, since this analysis gives tha relative vanations in the radbtien in<t sum ,) ' Passate, N. J.): Iide thiauthor's paper very order of magnitudi contributed by each of vection terms. ] w much. It caplains the three methods of the three mechanisms of hett transfer. The authors have neglected the v.triation , }a N heat dow from a cable to a surrounding The authors have assumed for cable in in radiation component of conttuettvtty wnh medium, namely, conduction, convection, duct that the component of the thermalcon-temperature. pomting out that these vart.a. and radiaticn. Also, they give the various ductivity due to radiation can be treated as a tions are quite small. This is justifiable 3 a parameters which influence each factor constant in the range of normal operatmg from a practical standpoint. Ilowever, the namel,, cable diameter, temperature, and temperatures. Only the component due to variations m the convection component with j temperature diderence, 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 I of the discussion this factor is !I fractional powers. It is not easy to obtain ture of the variation in thermal resistivity even *maller than the change in the radia. ): the constants for each formula as they are with heat tiow, or more fundamentally, with tion term. This would considerably sim. dependent on conditions not easily calculable cable temperature. Afr. Barnett and I have plify the Buller. Neher equations for the sur-so it is necessary to get test data and work stated in our papert that the '-crease in face resistivity factor. In their equations { back to numerics which will give the d - thermal resistivity with iner sheath 9 and 10, the surface resistivity factor, d, }7 sired results. It so happens that as all thi, temperature is caused primai

• ia +

depends upon the fourth root of the heat hj modes of heat transfer are functioning at tion in the radiation compcao. at flow. This does not have much signi6cance l lj the same time, a change in dimensionmg transfer, and that the effect if te since it is based upors the variation in the e J tends to work in opposite directions, reduc-variations on convection are egh .a :r convection term, a second order efect com. l]1 ing thereby the efect of diameter. Also the the normal operatint range. ' ns sts e-pared with the radiation term. Similarly range in temperature is not great and as we ment is verified by calculation

• ased ' en the dependence of # upon the square root of i 'r take the one. fourth power of temperature equation l A of the Buller &her Wper, the sheath diameter is doubtful, since the

! ) difference and three. fourths power of which is repeated here: change from a fourth root to a square root temperature, the variation with tempera- ~ { ture is not great. [ O h,, 0.092aT%,l' dependence in the consection term also was About two years ago we decided to re- \\ D.' AT/ D.'*(1.39 + D.'/Dd) + (1A) based on the very small change in convection conductivity with temperature. T study the thermal constants we obtained The when we originally set up the Oilostatic (convection) cable m, foregoing discussion was confined duct with air as the intervening i cable system. At that time we used the 0.0213 fluid. Its applicability to cable in gas-fdled cylindrical log formula of ratio of internal D,' log DdD,' +0.102s (! + 0.0107T.) pipe at high pressures, where convection pipe diameter to circumscribed circle over (conduction) (radiation) s becomes the principal mechauism of heat 'l the assembled conductors, and also a con-transfer, requires further study. stant which was a function of the tempera-in watts per degree centigrade foot inch. The authors have done an excellent job in p ture. The emissivity factor, t, is assumed to be helping to establish the theoretical ground-Our more recent tests showed that the unity at atmospheric pressure, work necessary to both encourage and guide o thermal resistance was ahnost independent Table I of the discussion lists two repre-experimental workers in the duct heating 1b. of temperature (a variation of about 10 per sentative sheath temperatures from our test problem. 3 h cent between 30 and 61 degrees centigrade) data on fiber duct in concrete, and these f for an oil pressure zone and a very few per temperatures might very well be represent-Rartaases cent for a gas pressure zone at 200 pounds ative of the operating range of a cable. The 1. Haar TaANWER SrUDY ON Powns C a et. ) per square inch. We also noted that term (Q/D,'aT) evaluated in equation IA DUCT 9 AND DUc7 AssS usust. Paul Greebier. within the accuracy of testing we could is inversely proportional to the surface Guy F. Barnett. AIEE Tunsaamas, volume b. [ safely assume the thermal resistance to resistivity factor, S. P'" 3 " W " " M 7-vary as inversely as the diameter of the The three terms in the equation give the f shielding tape over the insulation. As a thermal conductivity components due to A. H. Kidder (Philadelphia Electric Com. ] P result, we have set up two simple formulas convection, conduction, and radiation respec-pany, Philadelphia, Pa.): This paper by i for the determination of the thermal resist-tively. As we increase the sheath tempera-Buller and Neher, together with two pre-l ance of the pressure zone for three cables ture over the range shown, the increase in vious papers hy hfr. Neher,5 8 completes l in a pipe, namely, for oil pressure system the radiation term produced by substituting presentation e, the steady-state considera-H= 1.tiO/D thermal ohms per foot per con-our experimental data in the Butler Neher tions involved in a project which was started ductor where, D is the diarneter in inches equation is 6ve times greater than that of about four years ago when Philadelpbia { over the shielding tape; and H=2 58/D the convection term. This shows that the Electric Company interested Str. Neher in

g thermal ohms per foct per conductor for a experimentally observed decrease in # over undertaking an investigation of funda-gas pressure sone operating at 200 pounds this range is due almost entirely to the in.

mental relationships, as necessary to deter-j per square inch. You will find these values crease in the radiation term. These cal-mine approximately what pipe-type cable of thermal resistance for the prenure zones culations are based, of course, on the rather circuit load ratings would be accurately j amply accurate. large cable size that we employed in our comparable with the load ratings of con-l As the authors refer to the surface resis-tests. A smaller cable size willincrease the ventional cable circuits in ducts. {" tivity factor 6, the values of d comparable effect of the convection term only slightly, The thermal resistance through the spaces to the above constants in H-0 0mit S/D however, and not nearly enough to make its between the cable sheaths and the pipe or i f are # = %0 for an oil-pressure system as com-variation with temperature equal to that of duct wall inclosures is an important link in ~ pared to 350 given by the authors and d= the radiation term. Identical calculations the thermal circuit.. It had been hoped that H27 for a gas-pressure system at 200 pounds with our data on Transite in concrete, a general relationship could be developed in per square inch as compared to 450 given by Transite in air, and fiber in air, show similar such a form that all of the differences be-j the authors. We are quite confident in our values and have been using them for over a i j Y'*'- Table 1. Greebler Bamett Data i Paul Greebler (Johns-Manville Corpora-i o,uvier. tion Enville, N. J h In this paper the suuer-Neher garnet authors have contributed immenselv to-Inside Duct Mean Temperature Eaustion I A Data I Lud Shead Wan Sudace Temperature Drop Commuon Radtauon din Wmg ward an understandmg of the mechanisms Temperature Temperstare, T. AT Terin Terra 1 y of heat transfer from the cable to its sur-r rounding pipe or duct wall. The theortti-cal analysis was necessarily based upon the Q y; { jQ 5. simplifying assumption of a coaxial cable m ,, _ g , gn,,,,,,,,,,,,e duct arrangement. This does not, however. detract from the value of the analysis given

• Temperaturn are in desrees ceausrade. Tt6e inside due it aurt.ce temperature is sa averase enlu'-

348 Butler, Neher-Thermal Resistance ALEE TnrusseTIOM r

l.2 1 iweco cables in air in ducts and cables in hign pressure gas or oil.611cd pipee could be tween cable sheath and duct wall. It is un-explamed in terms of the phy*ical constants fortunate that wa do not have a more dis-H,4 (oil) = 0.70/D,/8thermalohm feet (1) tinctive name for it. Hu (g:s at 200 psi) = 1.20/(D ')" th rmsl e which characterire the respective fluids and Mr. Burrell has presented a thoughtful dis. j the pertinent geometncal selationships. cussion of the assumptions which we have ohm feet (2) The method presented by bulkt and Neher has approximately achwved thn re-ruade in developing the theory used for The corresponding equations on a per correlating the test data. In this respect. a cable basis and with three cablesin the pipe sult at least to the extent of pernutttng the correlation of data obtained by varmus in. book by Prof. LicAdamst gives a constant for the convection nlm on the outside of a vestigators at various times in various con-cylindrical surface in a free medium which is ha = 1.44a and Au = 2.07 structione. It don not disturb me par-about 20 per cent lower than that for the in-respectively g ticularly to nnd that there is some apparent difference between the effects of Trausite side of a pipe and which we have used for both 61ms. Figures 3 and 4 are intended to give prac-and 6ber dutt walls, respectively, under the We have not distmguished be-tical working values of 6 or Hu over a wide conditions which prevailed at the tirne the tween the two constants because no irdorma-tion is given as to the values of these con-range of operating conditions. Mr. Greeb- -{ to attach much significanec to tne e appar-stants when the cylinder is placed within ler is right in pointing out that the effect of tests were marte. I think ur should he>itate the pipe. While a formula for the conduc. temperature variations upon the radiation ) ent differences because there w as no attempt tion component in a non concentric system component is considerably greater than the l6 to control the moisture content m the fiber or the Transite, or even to rnde the tests is given by Whitehead and Hutchings* it is effect of variations in the convection term 'I under conditions pomparable to thow to be far too compbcated to use in this analysis. which is the essential variant in Figure 3. expected m the usual exposures to natural and it reduces substantially to the concentric The inclusion of the temperature of the medium in the working expressions would i but variable moisture conditions to be en-formula which we have employed except for vastly complicate them, however, and as a extremely small separations between the countered in underground structures. The cylinders at one point. Further there is In all of the Greebler Barnett data it will practical matter this is unnecessary, significant point is that Buller and Neher 8 have obtained a correlation which now per-considerable experimental evidence to sup-be observed that d varies inversely as QW port the assumption that the emissivity within the accuracy of measurement. The mits estimatmg the thermal resistance from cable to pipe or duct wall with sufficient constant is substantially unity for the types dependence of $ upon D, cannot be evalu-of cable surfaces employed. ated from this data since only a single value accuracy, so that littie, if any, practical Discrepancies were expected, because of of D, was employed, but since the convection improvement in cable load ratings can be gained by introducing further re6nements in the assumptions which had to be made, and their analysis of this part of the thermal because the physical location of the cables term theoretically varies directly as Q%/DW we believe that the temperature variation in

etreuit, within the pipe cannot be controlled. We the radiation term which Greebler has men-have used assumptions and theory only to tioned will be accounted for with sufficient R uraaNCE6 obtain a sensible understanding of the problem with which we have to deal and to accuracy by expressing the Greebler Barnett 1.

Ter Tsursaartian Ress or Iwasso Canaa determine what simph6 cations can justi6 data for 6ber and Transite ducts in the form an hran. J. IL Nebw. A/EE 7 tauasmu. ably be made m order to obtam, practical B(6ber) = 1120D,g/Q egrees cent - volutna 64, part I.194W. pace. 9-17 working expressions. These working ex-grade square centimeters per watt (3) l 2. See rerwenee 1 et the papu. pressions were then developed directly from actual tests rather than from theory. Wedo

1. (Transite) = 990D,g/Q.3 degrees cents.-

not share Mr. burrell's desire for working grade square centimeters per watt (4) F. H. Buller and J. H. Neher: Mr. Norris czpressions of sufficient complexity to and Mrs. Buckland have taken us sornewhat identify the separate effects of the three This will have the eHect of changing the to task for our apparent inconsistency in modes of heat transfer. slo e of the curves when plotted in ac. l expressing our physical units in one system Dr. Wiseman a simplined formulas for cordance with Figure 33 j and our geometric units in another. For calculating h,, (on a per cable basis) for The correspondingvalues of Hu assuming l better of worse it has long been the custom three cables in an oil-611ed pipe or in a gas-a working value of Q = 10 watts per foot l in cable rating procedure to express the Alled pipe at 200 pounds per square inch are l physical units involved in the watt second-very mteresting and similar formulas may centimeter. gram system, and to express be derived from Figures 3 and 4 of the paper Hu (6ber) = (2.59/D,'h)+0.33 thermal lengths in feet and diameters in inches. In assuming that O P, and T. have 6xed ohm feet (5) developing our equations it would have been typical values. Unfortunately Dr. Wise. Nu (Transite) = 2.29/D.'hthermal inure consistent to have expressed the latter man's derivation of the equivalent $ in his quantities also m centimeters, and then to formulas gives values which are not com-ohm feet (6) have converted the 6nal expressions to the parable to d as de6ned in this paper. The While further theoretical and experimen-

• ystem of measurement used in practice.

corresponding rela tionship for $ as de6ned in tal work may well be undertaken in order to We chose to use the mixed system through. the paper is clear up some of the apparent discrepancies out, however, m order that the reader might between theory and practice and to yield be able to use any equation in the develop. h,, 0.004113 more factual data on the performance of ment, directly, without encounterms the 3 2.15Da cables in duct; we agree with Mr. Kidder uncertainty which inevitably arises as t that little of any practicalimprovementin whether you multiply or divide by the trans-formation constants. and this yields d = 290 for the od. cable load ratings will result. We do not -pressure ,1 Tne use of the term " surface resistivity system and $ = 450 for the gas pressure sys-wish to discourage further eHorts in this tem. direction, but we feel that it is sufficient to I4etor"is a shghtly ditlerent matter, and as our mentors have pomted out. it has dtmen-We cannot accept his formula for the ott base cable ratings on Figures 3 and 4 of the

• )ns which are not those of true, or volu-system smee its correspondmg nlue on a, paper or more simply on equations (1,2,5.

t total heat flow basis is Hu " 1.15/D, and 6)just given, hw trie. " resistivity." llere again, this which is equivalent to Q41T = 3.9 for tunneuelature has been h41 owed by time D,' = 4.5 None of the tests c.ted in Table Rarsassess ahd i> thoroughly understood by cable engi-111 of the paper give s9y mpport for so high hetts, for whom this paper was written. It a value. 1. See reference 2 of the paper. %uM bt stressed, how ever, that this "sur-Dr. Wiseman also assumes that the over-2. Cuanswt EartNo OF Ca3LRS FOR ira,f 8 Mis be" t e sistivit y" is not a fundamental mon ano Distnisenon. s. Whitehead, E, E. Mydeal quar:tity, in the sense that volu-all thermal resistance varies inversely with listemass. Jamai, lutituuon of Electncal the diameter whereas we believe that a more thetric resistivit v is, but as pointed out, is representative variation may be deduced ee neeri a nynelands. volume sa,1938. g } N reente i f a urut surface of a film f rom the slope of the curves of Figures 3 and Y h. puttly for purpo*t s of convetuence, saSrnvgw_Pwas 3 Isar aau Ca a 4awumed arbitrarniv to represent the enttre 4 in the vicinity of the typical operating F. Barnett. AIEE Transmou, volume 69. part poin ts. Thus for Q = :5 watts per foot and 3,1930 pages a57-e7. Strmal resistance of the composite heat T - 50 degrees centigrade, we derive the Ddh5ftr effects operating m the region be-simpli6ed expressions 4 ancu.sme by J. H. Naber of reference 3 b ateove, pages 36546. % %txn @ 1Mer, Neher-Thermal Resistance 349

i Calculation of the E:ectrica Problems g of Uncerground Cab es J,.a u aa c 1 4 1 y O Hy Donalil M. Simenon GENERAL CABLE CORPORATION 420 Lexington Ave., New York, N. Y. O Reprinted frem The Electric Journal, issues of May to November,1932, inc.

Calculation of the Electrical Problems of Uncerarounc. Cales q b 1 J DONALD M. Simross Chief Consulting Engineer, General Cable Corporation Fundamental Circuit Constants 1 IIE calculation of the core has a thin layer of t 7 subject was printed m, article metallic tape or metallized Q EVEN years ago an on this same performance of an Tut ELLeinic Joca. underground c a b i e-p t.. Since that time the art of manufacture paper immediately surround-such as regulation at full of underground cables has. moved steadily for-ing the individual conduc-ward; the type H construction for high voltage, load and no load, is not es* multi-conductor cables has been generally tor insulation. The three sentially different from that adopted, the oil-filled cable has been introduced. cores are cabled together I theoretical investigations and experimental stud-for overhead transmission ies of many cable problems have been made. and rounded out with fillers when certain constants are To bnng this subject up to date and to collect as in the belted type but the the mathematical data and equations relating to known. For underground the electrical problems of underground cables belt msulat on is omitted. transmission the simpler scattered throughout the literature this group of For multi-conductor type H articles is presented. The data is assembled in methods are usually apph.* a somewhat more limited way but in the general or smgle-conductor cable, l cable, as the lines are rela-f ashion of that in the, masterly series of articles there is of course only one I on overhead transmission hne problems by Nes. tively shorter, though, for bit', s.) as to assist in calculating any of the thickness of m.sulation to be j any given length of line the ordinary electrical problems in undergroun' considered. l transmission. Equations are included which J distributed capacity and its considered best adapted to the practical cah. There is no general agree-The den,the problems met in cable engineering. ment on exactly what thick-effects are greater in an in. tions of y vat ons of the various formulas and i sg sulated cable than m. a bare treatment of certain problems which occur but ness should be used for a wire line. The calculation inf,requently are not discussed. Slany of the re-given voltage, since there finements meluded here, but not present in the t of some of the line con-original article, need not be worked out fully are so many factors in-as the simpler formulas still apply in many volved. In most cases, con-stants is, however, diff erent. cases; thus some of the comph, cations are more Moreover, a fundamental apparent than real. Specifically these articles tinuity of service. the is difference between the two discuss. nrst, the fundamental constants of the most important considera-circuit, and, second, the question of current-cases is that for cables, the carrying capacity as limited by temperature rist. tion, and relatively con-allowable current is more The problems of feeder sizes as affected by eco-servative thicknesses are n mies will n t be discussed. often limited by the permis-g ,g sible temperature of the in-sacrifice has been made in sulating material. the factor of assurance by using thinner layers

sulation so that there will be Insulation Thickness room for more cop; m a given diameter of cable.

Knowledge of the usual insulation thicknesses may Another case in point is in Europe where, in general, be helpful in some cases, especially in preliminary cal-slightly less insulation is used than in this country. culations where definite dimensions of cables are not This is due chiefly to the lower permissible operating available. In multi-conductor belted cables, there are temperature allowed, the practice of basing cable rat-two thicknesses to be considered, as shown by the cable ings on 1009o load-factor, and the fact that cahles cross-sections in Fig. 2: each conductor is insulated abroad are usually buried in the ground without being separately with a thickness T; and after the conductors subjected to the strains involved in pulling a cable into l have been twisted or cabled together and the interstices a duct. Furthermore, while in this country, most com-rounded out with the fillers. the group is insulated as panies make temperature measurements in idle ducts 1 a whole with insulation called the " belt", of thickness and regulate cable loadings by actual conditions, in

t. The insulation thicknesses may be given in terms of Europe usually no such provisions are made for meas-the conductor insulation thickness and the belt (T and uring temperatures, so that with ordinary load-factors

[) t), or in terms of total thickness of insulation between even the low permissible temperature values are not l~ conductors and between conductors and ground (2T approached. It is not to be expected, therefore. that l and T + t). In the multi-conductor type H cable each there are or will be any hard and fast rules for insula-l conductor is separately insulated as before but each tion thickness. The recommended thicknesses of insu-l l 1

e e TABLE l-RECOMMENDED b!!NIMUM MERAGE Yl!!CENESS OF INSULAft0N8 F0ft SINGLE-CONDUCTOR CABLE AND TilRELC07tDUCT0ft TYPE il CABLE g g( Pa per Varn phed Cambrw7 H ubbers Conductor terounced + ( nerou ioed i teruvuoed r t, narounoeo oroundeu 1., na rounoeu i i Ibted I W ii humtwr N eutr al N eutt.tl heutral Neutr.H N eutrA Neutra . ) oitaget n ot luull Cir M da - 64t he Mile 1 64tl.a M ale i 64uis hida I 64the M ds a 64tha h4ils 64the Alsle i 14-v J 47 I J 17 4 4' J 4. I j 4 4 63 4 61 3 47 3 47 4 b3 4 hi 7-2 4 h3 4 bl 4 61 4 le l 4 bl 4 61 W10, 225-5dM) 4 6J 4 63 4 94 6 b4 6 94 6 94 I - 4 10 4 64 4 bl 5 74 5 74 5 74 5 7s i l t 525 1000 5 74 5 TN 7 lW 7 109 I IW. 4 115 I lud ' Over itNIO ri 94 b

1. 4 4

125 4 115 4 115 i [ j 14 -e i s,' i

• 3 4

b.) 4 65 ' 4 64 ' 4 bJ ' 4 6J f t 1000 ' 7-2 4 13 4 t.3 4 til 4 61 5 78 5 is f i l-4 /0 4 nJ 4 61 5 74 5 78 225 500 4 65 4 tLJ 6 94 6 b4. 6 64 6 94 i 7 IW I 7 109 SJ5-I th)0 5 79 5 78 7 109 7 low b 125 t h 124 Over 1000 h b4 ' n WI is 125 t 125 9 til 9 141 14-s (5# 5 79 4 79 %5 is 5 Ta 5 is 7-2 A 78 5 78 5 78 5 78 6 94 5 se l 6 b4 I j 225-50'V 5 74 5 N 6 b4 6 94 8 125 i h lJ5 2000 ' I -4 5 74 5 7a 6 94 6 94 7 109 i 7 109 0 l 525-1u00 l 6 bl l 6 kl 7 109 1 7 IOW 9 Ill ] 9 141 i Over ImM) l 7 109 l 10W 4 125 l A 125 9 141 I 9 141 l i 14-4 \\6) 5 Iii 79 (B) i 109 l 109 l 7 IW ! 109 7-4.0 5 74 5 74 7 109 i 7 109. 9 141 l 9 141 A 125 i t 125 i 3000 j 225-5u0 5 74 5 ?# A 125 1 4 125 l 525-1000 4 18 4 6 b4 H 125 i s I?5 r 9 14l j 9 let J I Over itMio ~ 109 7 109 9 141 9 141 ' 10 156. 10 156 i 14 -4 + (6) h 94 ts 94 al a 125 i n 125 W 14Il V 141 4000 225 1000 h h4 6 94 9 141 9 141 i 10 156 I 10 156 i Over 1000 109 1 109 l 10 156 10 156 Il 172 1 11 172 14-4 4# its b 96 i ti 94

8) 9 141 10 156 10 156 l 10 156 5000 225 1000 6

94 l 6 94. 10 156 11 172 11 172 l 12 ll 172 I 14-4 tu __ 7 104 l 7 109 l 10 156 18 172 1 12 IN8 Over itMX) tilA i 109 luu h 81tu 156 11 !!2 i 10 150 } 12 len (*) 6000 225-1000 7 103 I 7 109 - 10 156 1 12 1% l 11 !!2 i 12 148 Over itMio 9 125 i 7u00 m-l u ni 4 1.5 ' n 125 l 10 156 i 12 19R l 12 144 13 203 w 141 l 11 172. 14 203 ' Over 1000 8 125 u til l 11 I ?2 l 13 203 'h 7111 172 14 219 12 IMI 15 2.14 8000 7-luta) 161 9 141 to 156 it6112 in 14 219 14 las I 16 150 14 219 { 13 203 l 17 266 i Over 1000 9 141 10 156 i 12 144 i vouu 7-1000 [ W b lil 14 171 nilj 203 r Ib 250 t IJ 204 17 2b6 ' Over 1000 1 9 141 11 17J 13 203 i 16 250 i 14 219 14 2'il l l 16)* 10 156 JJ lH l(6)l4 219 l 19 2Al 1 14 219 15 2hl ' 10000* i 7-4000 Over 1000 10 156 12 IP9 e 14 219 l 14 251 1' 15 2.t4 19 297 ! i 7-1000 th) 10 L5e 12 l'a '(0 15 2J4 IV 297 15 234 20 JtJ f' il000 Over 1000 10 156 12 169 15 234 19 297 10 250 21 32il i 12000 i e -1000 Il 171 13 20 1 (4816 250 20 3IJ tt)l0 250 22 344 l l Over 1000 11 172 13 203 16 250 20 313 17 266 23 3 59 I IJoud I 6-10u0 11 172 14 219 (4117 2no JJ 344 (!)l7 266 23 359 Over 1000 ll 17? 14 219 17 266 22 344 18 2Al 24 375 14000 0-1000-I B* 15 234 (411s 2sl 24 375 (1)l5 2'11 25 396 Over 1000 12 188 15 234 la 241 24 375 19 297 es 406 150uu O-1000 IJ 20J la 250 (4119 297 26 406 (1)lv 297 J7 422 Over 1000 13 203 16 250 19 297 26 406 20 313 24 438 1000u 4 and larger 13 20-1 17 166 20 313 27 422 17000 4 and narrer 14 219 18 2RI 21 328 28 438 18000 t and larger 15 234 1,

sl 22 344 19000 4 and larger 15 234 l9 297 23 359 20000 2 and larser le 250 19 297 (4)24 375 21000 2 and larger 16 250 20 313 25 39) 22000 2 and larger 17 266 21 328 26 406 23000 2 and larger 17 766 22 344 27 422 24000 2 and larger 18 281 2?

344 28 434 25tMN) 2 and larger 19 2RI

3 351 29 453 2emo 2 and larser 19 297 24 375 30 469 27000 2 and latter 19 297 25 3WI 280tm) l and larger 20 313 76 406 29000 I and larger 21 318 27 422 30000 I and larger 21 318 27 421 a 3l000 I /0 and larrer 21 344 28 434 1 32000 t /C and larrer 22 344 2g 43g i 33000 I to and larger 23 359 29 433 l 340u0 1/0 and larger 24 375 30 469 l 35000*

1,0 and larger

• 24 375 31 4 g4 1 36000 210 and larger 25 391

} 370t10 2 @ and larger 26 406 1 38000 2 <0 and larger 2ti 406 1 39000 2 'O and larger 27 422 iThe insulation thicknemes for paper and warn shed cambr e are I.P.C. l 40lNMP 2 /0 and larger 27 422 E.A. Standards. ' The rubber wa:Is, thouub not 1.P.C.E. A. btandards, j 410F)

11) and larger 24 4M are believed to be representauve of modere practsee irnder average con-l 42000 3.0 and larger 28 431 diuona.

l 43000 l 3 /D and larger 29 453 8All cables are rated on conduetor to conductor basis for three-3 40 and larger 24 453 phase circuits. il emb6es have an operauna amerance of V~e above the 1 44(x10 1 i 45000 3,0 and larger [; 30 4 *i9 rated voltage enrept those rated at 15 000 votu and below, wbich have no 4 WmM) i 3 ;0 and 6areer 30 4w operating toserance. 4 7fm0 ! 4,U and larrer 31 4d4 8For miermediate voltases take the wall for the nest hirber lated 4 mou0 # 4 0 and larrer 32 500 voitare. Mmimum round condurtar siar i AWG1 indicated in parenthesee 49000 l 10 and larger, 32 Sm i under respecove insulauon u hen dJIerirs from size snown under "Bise l 500tio i 4 0andlarrer r 33 516 l of Conductor". 510 N) 4 U and larger i 34 511 PAPER i 52tM)0 i 4 c and largre ! 34 531 eFor voltares 10 000 to 35 000 the thicknemace riven apply to both 53000 1 250 and larrer I 35 547 sinsie conductor and inree-camductor type il cable 54000 ; Do and larrer I h Stil 4nt vettages 40 000 and higher, type 11 single-conductor cable it recom-55000 1 250 and iarrer 34 563 mended. 5a0110 250 and larrer 37 578

• ltecornmended minimum acetor ronductor aises for inree ennductor l 250 and larger

( 57000 37 57a tvne l{ cabic are i S. 2 U. 3 U. and 4 H a WGi correrpond ne to voltm 5's000 I 3m) and inraer ! 31 594 ranrea of lotMio to20000, 21000 to J5000, 26 000 to 3000u und 31000 1 i 59000 l 3uu ard sarrer 34 514 to 35000 respectively. [ i 60000 j 300 and larrer 39 609 i 61000 l 300 and lererr 39 639 V ARNISilED CAMBl. 'C f 62000 I 300 an.4 larger 40 625 i 63000 1 3u0 and larece 40 625 'For braided or special denians consult 1.P.CJ. A. specificauons or manu-facturer. l 64000 300 and larser 41 641 t 65000 350 and hars r 42 656 f 66000 350 and larrer 42 656 RUBBER I 67000 350 ard larger i 41 672 'Theae thicaneesen also appir to multi-conductor cables. For multi-1 6*m0 350 and narrer l 44 tW4 conductor lead envered eshire for voltases it isou and bisher, shieldmg i i 69000 350 and larger j 44 658 u advisabie For braideo or enecial densna consult the manufacturer. l f'i

..~_ 1 TABLE Il-RECOMMENDED MINIMUM AVERAGE THICENESS or INstTLATioN rott THREE c0NCtl0TOH BELTED CABLES Recommended la tae lasulated Pe=er Cabie Ensinnes Association Standarde P4PER l V 4RN14HED ClMBRIN i Conductor I Belt l Conduetar Bett Sue of I 'nerounded Conductor Grounded Unrrounded I ' Grounded L Rated AWo N4 stier Neutral. Neutrar i Neutra Neutral n oitage3 ne l000 Cir. Mile 44the Miss 64tha Mas 64tba Mils ( 64tha Mi's 164dia M d4 1 64tne Mas i 14 4 i 8 e3 4 43 2 31 2 3B 3 47 i' 0 0 0 0 i 72 4 63 2 31 2 38 4 63 i O o 6 0 600 l l-40 4 63 2 31 2 al 8 is l 0 0 0 0 223-500 8 78 2 31 7 31 6 94 i 0 0 0 0 625-1000 8 79 2 31 2 31 o 94 ! 2 31 2 31 Over 1000 76 2 31 2 31 7 109 I 2 31 2 31 14-2 18) 4 61 2 31 2 al 4 61 0 0 0 0 1-40 4 61 2 31 2 31 3 74 0 0 0 0 4000 224-500 8 79 2 31 2 31 6 94 0 0 0 0 i 424 1000 5 76 2 31 2 31 6 94 2 al 2 31 1 l over 1000 8 74 2 al 2 31 7 1 011 l 2 31 2 al 4-2 4 71 2 31 2 31

• 8 fil i 0

0 0 0 1 140 4 Ti 2 31 2, 31 6 94 I O O O O 2000 2' 4-S M 78 1 3 47 3 47 6 to ' n 0 o n ,t 4 8 sino 3 79 J-47 3 47 6 14 2 al 2 31 i Over 1000 4 76 3 47 3 47 7 109 I 2 31 2 31 l 2 3 ft 3 47 3 47 l 5 73 I 2 31 2 31 l g.600 i 1 4 Til - 3 47 3 47 ; -6 94 2 31 2 31 3000 l 323-10uo 8 78 l 3 47 3 47 6 94 f 3 47 3 47 Over 1000 3 79 i 3 47 3 47 7 109 l 3 47 3 47 i n-800 6 64 3 47 3 !? 6 94 l 3 47 3 47 4000 - 823-lou 0 6 94 3 4t 3 47 6 94 ' 4 63 4 61

• l Over 1000 e

to 3 47 3 47 7 109 4 61 4 61 s f 8-40 6 94 4 63 4 63 1 6 94 ' 4 61 l l 4 61 j 4 61 4 63 ? ? 109 I 4 63 $000 223-1000 6 14 4 63 , Over 1000 6 be 4 el 4 64 7 10J, 5 74 5 78 j l .i + i -t-e 6-40 6 94 4 63 4 61 1 6 94 5 is i 5 is 6300 225 4 000 n 94 4 63 4 66 i 7 109 4 74 i 8 79 3 Over 1000 6 54 4 63 4 61 i 7 109 4 78 l 6 94 7000 6 and latter 7 109 4 61 6 94 7 109 8 78 6 94 8000 6 and la'ser ? 109 4 61 7 M9 7 109 6 94 7 109 9000 i S and larger 4 1: 8 4 63 8 1:4 8 125 6 94 8 123 10000s 6 and larger 8 125 4 63 8 I?S 9 141 6 94 9 141 11000 6 and larter 1 8 175 5 79 a l'8 10 156 6 94 to 156 12000 6 and Isrser ; 9 let 8 78 9 148 (4110 186 7 109 10 136 13000 6 and latser 9 141 8 78 9 14l still 112 7 109 11 172 14000 o and larger 10 I$6 4 76 10 184 itit! 194 7 109 12 IF6 13000s 6 and larger 10 146 4 78 10 164 (4:13 203 7 109 13 203 i 16100 4 and larser 14 219 7 109 14 219 O 17000 4 and lareer - 14 219 7 109 14 219 NUrES osasaar.: AAll catnes for three phase circutta are rated on eonductor to conductor basis. All embles have an operstma tolersnee of 5". etaept those rated at la 000 wasta sad below wheeb have no operating tolerance. For intermediate voitase take well for nest hieber hited voltase. 3 Minimum round conduttor sise ( AWO) indicated in parentbenes under terpective insulation when d4rru r fra m rise shown under"staa of Conductor". Minimum sector conductor sine for paper embles of all voitases listed at i10 AWG. Paren: 8For voltages to 000 to 13 000 type H Cable is recommended where appliesble. for voltases is 000 and bisher type H esbie only is recommended. Vannianso CAMBale!

• For bradsd or rpecial designa consult I.P.C.E. A. Speci6 cations or manufacturer.

Reuman: For e shh-r multbeonductor lead. covered embles u*e thicknesses riven in Table 1. lation adopted by the Insulated Power Cable Engineers Cable Diameters Association for paper and varnished cambric are given If the number of conductors in a cable, the diam-in Tables I and 11. The thicknesses listed are generally eter of the conductor (given in Table IV), and insu-considered as representative minimums for modern lation thicknesses are known, it is possible to calculate cables in this country installed and operated under aver-the core diameter and outside diameter by elementary age conditions. geometry. For convenience, however, the following The ungrounded neutral thicknesses listed. in formulas are given : Tables I and II are intended to apply to systems in D.- - 4 + 27 for one-conductor cables. (1) which the neutral is ungrounded or grounded through D. - 2(d + 27) + 2t (-r two-conductor cables a resistance which has a value in excess of the criterion (' ""d dimiex) 42) proposed by the American Standards Association:- D. - ( 1 + -- (d + 27) + 2t (or three-con- "An underground cable system is classified as hav. ductor cables.. (3) ing the neutral grounded when resistance in the neutral D. - (1 + d) (4 + 2T) + 2t for four conductor cables.- (4) ground (or grounds) is of such value that the lagging in which I), is the inside character of the lead sheath, d the component of short-circuit current is always equal to conductor diameter, T the conductor insulation thickness, i the belt thickness-all in inches. or greater than the total charging current of the system at the point of fault. When the neutral resistance These formulas refer to cables with round conduc-exceeds this value, the system should be classified as tors. For the case of sector cables, there is no hard being ungrounded, since the conditions are such that and fast rule, because the term " sector" is not a mathe-cumulative oscillation may be caused during a failure." matical description of shape, and there is a large variety 3

=. 4' the shape of the sector. For the case of two-conductor j sector cables. the manufacturers have information avail-3 able for the usual sizes, or close results can be obtained i by laying off the cable graphically. j TABLE !!!-T!!!CKNESS OF 1.EAD EllE%T!! l i Recommended by The lasutaed Poser OL,le Enaineers' Amoeisuon ] l s Paper led Power Cable j } [ lt 64the M ds 0 - 400 3 78 401 - 11 % 6 94 e j 1001 - 1800 7 109 4 1901-7WO g 1 *$ i l 2 mil-3200 9 141 j 320s and over l 10 t$s varnehed Cambne'imad Power Cables J J core D me t'nder Lead Thicanes b-425 3 47 1 420 - 700 4 63 j 701 - 1050 6 78 1051 - 1500 6 94 1 2l:= l e 4 3001 and over g til I Three-conductor type H cable 'Usually sonsidered representative for rubber lead power cables also. l of sector shapes. In general, the saving in cable diam-The diameter over the lead sheath is figured by eter is approximately proportional to the size of con-adding twice the lead thickness to the core diameter. { ductor and thus the saving relative to the diameter of The lead thickness in general varies with the core diam-the cable is less with thick insulation. The reduction i l in diameter due to sector conductors also diminishes as the. number of conductors increases. In other words, G it is a maximum for two-conductor cables, with the [ so-called D-shaped sector, E-essary to know the diameter of a cable in order to I , M,h...[p h From a practical point of view, it is of course nec-Ne' - ks l determine whether or not it can be installed in a given / T duct line. For the purpose of calculating cable char-l acteristics, however, great accuracy in calculating the b j diameter is not of real importance. Most transmission j l problems with multi-conductor cables deal with three-conductor cables. A close approximation to the core Segmental conductor 4 diameter of a sector three-conductor cable can be obtained by calculating the diameter by eq. (3) as if eter, the larger cables having thicker lead. The thick-the conductors were round, and then subtracting 0..t ness of the lead sheath varies somewhat with conditions, to 0.4 times the conductor diameter d, depending on but in general will be close to that given in Table III: 0 4

Resistance and Reactance O permit bending the cable, and especially because of the large conductors now ordinarily used in $@%~ T '

[.

] ) underground transmission, only stranded con. ag 7 y-r _~ I ductors are used, and only such will be considered here. ~ {Y_I i --.fj ? The dimensions and resistance of the usual sizes of con-ductor are shown in Table IV. The values of resistance g are based on the International Annealed Copper Stand- $6 i h'( s ard 0.15328 ohms (meter-gram) at 20 C. which figure y"'#. v 4 D ll 4 - I is increased two percent to allow for the effect of W M( stranding. .F 8f y} l ^ These figures can be used directly for single con-r

f. "1 s

ductor cables. For multi-conductor cables, where the --d l * 'NQ~ y 'y.j j conductors are twisted around each other, there will be an additional increase of resistance. This will vary sJ e { increase of two percent above the values in Table IV ~ j.. j with the makeup of the cable, but can be taken as an [1 } _. l} t 4 I ) for most practical purposes. The dimensions and resistance of stranded alumi- 'I num conductors can also be readily determined from .t j Table IV with the aid of the following ratios: ,f I al cu. Relative conductance for equal volume.... . o.63 1.00 i Relative volume for equal conductance 1 59 1.00 l Relative diameter for equal conductance . 1.26 1.00 f j Relative weight for equal volume 1.00 3 29 Relative weight for equal conductance [jy $ It is necessary to correct the resistance for tem-O perature in most problems. The resistance of copper Applying paper tapes to cables. This machine applies 192 tapes simultaneously, making it possible to insulate is Prop rtional to 234 + T where T is in deE. C., and cable for voltages up to 220-kv service in one operation. i the resistance at any temperature T can therefore be calculated from the 25o C. value in Table IV by the fol-case of tubular conductors. The temperature is taken as 65* C., which is an average value of maximum permis-lowing equation: sible operating temperature. To find the alternating-234 + 7 Rr = X Ra. (5) current resistance, multiply the direct-current resist-259 R. is the table value, the number in the denominator being ance by the skin effect." '9"* '34 " #5 The skin effect or ratio of alternating to direct-The skin eficct, or ratio of alternating to direct-current resistance varies with temperature. However, current resistance, is quite appreciable even at 60 cycles, if the skin effect at 65 C. is used, no very large error t l especially for conductors larger than 1 000 000 circular will be introduced in an ordinary problem, especially 4 mils. A novel method for reducing the skin effect of with the sizes of conductor usual in three-conductor l large sizes of single-conductor cable, which avoids the cables. For instance, the change in skin effect between j usual rope core construction and resultant diameter in-20 and 65 C. for 1000000 c.m. conductors is only l crease, has been recently developed. The construction 2.7(/c, the change being less for the smaller sizes. For f is illustrated on p. 4. It will be seen that the "conduc-large conductors, such as in single-conductor cables, tor" consists of four sectors, which are separately it may be necessary to calculate the skin effect at the stranded and then cabled together to form a round con-operating temperature if a high degree of accuracy is ductor with a layer of insulation between sectors. The "The skin effect in the usual form of strand has been reduction in skin effect is due to the equalized reactance calculated by the 13essel f unction f ormula which can be con-j of the various layers, resultmg from the transposition venientiv obtained f rom Table XX11 of reference 2 of the n The skin etTect of the stranded conductors is of the individual strands. By this means. the total skin bibliography.,f for solid conductors of the same cross-section, calculated as i I I effect of the conductor can be reduced to a value ap-which is the proper procedure both theoretically :tnd experi-mentally, as shown in reference 3 For the case of tubular I1roximately that of one round conductor, with one third conductors, the calculations have been based on Dwight,s work, O the cross-section of the segmental conductor. reference.t. For this case the actual inside and outside dimen-i sions of the stranded tube have been taken. but the fact that The values of skin etiect ratio at 60 cycles s it is a stranded conductor and not a solid tube has been taken i l tabulated in Table V for the ordinary range of size of care of by using an equivalent resistivity calculated from the di urrent resistance and the actual cross-se%al i l conductor, both in the usual form of strand and for the je,""g i['e y*b l j 5

desired, as the change with temperature is greater the cable sheath and the losses due to them can be though such precision is rarely required. most conveniently considered mathematically by assum-The skin effect is a measure of the increase in ing that there is an additional effective conductor resist-l resistance because there is a tendency for the current ance of such value that when this resistance is multi-density to decrease toward the center or axis of the con-plied by the square of the actual current flowing through a ductor and for the phase of the current in the different the conductor (and by the number of conductors for g layers to change, due to an increase of inductance to-multi-conductor cables), the loss in the sheath will be wards the center. The skin effect assumes an isolated obtained. The ratio of the conductor loss plus the conductor; that is, it is an increase of resistance due sheath loss to the conductor loss is then given by: to what takes place in the conductor itself. If two con-Coedwor Lon + S4mA Lou R+R. ~ ductors are close together, however, there will be a Comfw0r Lo" R tendene7 for an increase in current density at the where R = actual conductor resistance in ohms per looo feet at a given temperature and frequency. R. Is the added effec-points where the two conductors are dosest together, tive resistance due to sheath losses and might be greater than which is another cause of increase in resistance. This the conductor resistance itself for larger sizes of single-con-ductor cables. is called the proximity effect. For the case of stranded For two single-conductor cables in a single-phase conductors it is not only a function of the spacing, but circuit or three single-conductor cables in a three phase is greatly influenced by the strand lay, cable lay, and circuit with equilatral spacing and with negligible contact resistance between strands. In general it is con-sheath proximity emct (which is usually the case siderably less than indicated by theoretical considera-except for very close spacings) Ro is accurately given tions* * * ' based on solid conductors. Tests made in by the following: the laboratories of the company with which the writer yy g, " w + p, ohms per 1000 feet. (7) is associated, on its standard stranded sector cables Ra show the value of the combined skin and proximity where Xu is equal to 2r/M in which M is mutual inductance effect at 60 cycles to be aIiProximately 1.35* times th'e i e nduct r and she th of a single-conductor cable obtained by eq. (13), and R. Is the sheath resistance and is given in eq. theoretical skin effect for a round isolated single-con- (to). ductor of the same size. For the other usual arrangements of one and two Several other features must be considered in calcu-circuits of single-conductor cables, Halperin and Miller

• lating conductor resistance. Any induced currents in in their admirable work on sheath losses have given readily applicable formulas for the sheath losses, cur-TABLE IV-RESISTANCE or STRANDED COPPER CoNDt'CToRS**

rents, and Voltages in the individual sheaths' 8' 88 taw gs tab hedy hm M wd a nme si or C.w. o6m. 0.r iOOO r t stand.rd Co sin. Str=*s cal magmtudes substituted for the vector ratios. From g, cir.ular AWQ. 25* C. 65* C. NO "f k' 5)?.ide Table VI, Ro for the individual sheaths of the different o m, no. <-77 ra (- 14r ra r.et or to m. io wii. arrangements may be found by multiplying eqs. (4), IEE SE $E E! !!I jg (5), (6), (7) (Table VI) by R.. lgg != l= in jijj jd For the case of multi-conductor cables, the induced 1 000 000 0.00674 0.00778 4940 127 112 2 1459 1 800 000 0 00719 0 00830 4630 91 128 4 1412 TABLE V-DIMENSIONS AND 60 CYCLE SKIX EFFECT RAT!o oF 1 400 000 0 00770 0 00889 4120 91 124 0 1364 STRANDED COPPER CONDUCTORS AT 65* C. I 300 000 0 00430 0 00058 4010 91 119 8 1318 1 000 0. 84 Aise 0 0 25 0.50 O.75 1 000 0 0 0108 0 0124 3090 61 123 0 1152 Caremar 950 0 0 0114 0 0131 2930 61 124 8 1123 W8 900 000 0 0120 0 0138 2780 61 121.8 1093 850 000 0 0127 0 0146 2620 Si 118 0 1062 d Ratio d Ratio d htio d Ratio j$$ lQ ] ] 0 66 2 000 000 1 633 1.239 1 67 20 1 72 1.17 1.80

1. !2 700 000 0 0154 0 0178 2160 61 107.1 964 I 500 000 1 412 1.145 1.45 12

'. 82 1 09 1 63 1 06 650 000 0 0166 0 0192 2010 61 103 2 929 600 000

0. 01 A0 0 0207 1e50 61 99 2 893 1 600 000 1.152 1 069 1.19 05

.25 1.03 1 39 1.02 8 h lN N l'28 l'ol 850 000 0 0196 0 0226 1700 61 95.0 855 6 800 M0 0 0216 0 0249 1540 37 116 2 814 500 000 0 914 1 018 0 26 01 0 97 1 01 M 000 0 724 1 012 0 78 1.01 450 900 0 0240 0 0277 1390 37 110 3 772 300 000 0 630 1.006 400 000 0 0270 0 0311 1240 37 104 0 728 350 000 0 0303 0 0356 10e0 37 97 3 691 ew 4 TuWe Mnar k W 25 0 3 0 f he 1.00 1.25 1 50 2 00 212 000 0000 0 0509 0 0547 653 19 105 5 529 Careular 164 000 000 0 0642 0 0741 518 19 94 0 4 70 0 5 d Ratio d Ratio d Ratio d Ratio 83 700 1 0 129 0 149 258 19 66 4 332 3 000 000 2 27 1 23 2 39 1.19 2 54 1.15 2 117 1 04 2 500 000 2 12 1 16 2 23 1.12 2 4r 1 09 2 75 1 05 64 C 2 0 162 0.147 205 7 97 4 292 2 000 000 1.94 1 09 2 09 1 06 2 "i 1 05 2 61 1 02 - 1 600 3 0 205 0 237 161 A6 7 260 1 M 000 1.75 1 04 1 91 1.01

• 07 1 02 2.47 1.01 41 700 4

0 259 0 299 129 7 77 2 +32 1.72 1.01 j 1gg 33 100 5 0 326 0 376 102 7 68.8 206 M 000 26 300 6 0 410 0 473 81 7 61.2 1:4 20 800 7 0 819 0 599 64 3 7 54 & 164 16 500 8 0 654 0 755 51 7 44 6 148 'On a type of very compact sector, developed since the writing of this article, this value becomes o oo. Thi, table ema the conductor dameter in inche. 4. and the 60 eveie ak diameter = 0,to direct. current rectance, tmth for the ordmarv form of.in eneet or r of alteenatme trandms On.ide

• • Taken from Table XII of Bullet:n 31 of the bureau of Standards.

and for submar conductors. Imaed on reference, a and 4 6

- - -.. - ~ ~ _ ~... - - ,e e TABLE VI-FORMUL at FOR $HE ATM VOLTAGEE CURRENrR, AND LO9SES FOR $1NGa.E. CONDUCTOR C ARIEM 1 la til IV V VI Cable Osse Ptiase Equdateral Rectangular Flat Two Circuit Two Circuit !{ ^'iT;*"' r@ r l @@*4*.*S-I acd i=- 6 a==-8

=

1@ @ ts -u. ~. Sheaths Open Cargutted C 8 3Y8+(XM 8+(Xu-h)# 1Y a + t X M - s )3 3Y +(XM-f) I ,a XM XM 3Y j' = Xu Xu XM XM (XM t h) (XM + {} 2 hiv,(xu.j)8 3ya, txu.a ): 3ys +(xy. g y qiya,(xy.g h= a 3 XM l Sheaths Solidly Honded 2 (p2,3Q : + 24(P Q)

• 4

], W.i a 10 _ g _ Xut XM2 3 4 J 2 I a, R. g,4 + Xua g,a. xgt e (p4 + i) (9 + 3 j l ta Re2 XM2 xgt l.28 W.s = 103 I

• ~IC
• R.8 + Xua g,a, xus (q4 + i) 7 21 R.

3 2 (P + 3Q,. 2 A (P.Q) + 4 g W.,aso3, g Xut [ 13 l'R. 8% R.3 + Xua 4(p2+i)(q2+i) W.T u 303 8 2 Re aver. Xul P+Q+2 31 g, " gs R.,xus 3(pd+3)(q1,3) 2 i Where va XM (XM + ) (XM + a) (XM+s+ ) (XM + a- ) (XM-f) (Xu *p) (Xue ) (XM d-f) Psh Qsh 2n Xu .a ohms to neutral per 1000 feet Xy a r7ff(0.140s legio )ltrW am 2Tft0.1404 logie2i10-3J,,.s 2Tff 01404 lostal)10* la ohms to neutral per 1000 feet at 60 cycles,Xu a 0.0$292 logigh a s 0.01593; b a 0.03e99 All cases It to VI. Inclusive, are three phase, phase rotation A, B, C. Subscripts 1, e, 8 correspond to phases A, B, C, respee-ho form the equations. set the quantitles la the vertical column headed " Cable Arrangement,... " equal to the quantitles under the column which is headed by the arrangement being ineestigated. ] sheath currents are usually small, inasmuch as the tape on the individual conductors of type H cable, j sheath surrounds all the conductors and the inductive actual measurements indicate that for all practical pur-effects of the current in one conductor usually are poses these are negligible with slotted foil. The losses almost completely neutralized by the effect of the cur-that occur in the usual non-magnetic binders of brass rents in the other conductors. However, with large or bronze have also been found to be quite small, conductors and large currents, such neutralization is not although allowance can be made for these if desired complete and there is an appreciable loss in the sheath by assuming a portion of the tape to be in parallel with comparable in magnitude to the dielectric loss or skin the sheath. On type H cables having a magnetic binder effect. tape, the available test data appears to show that the Miller and Dwight have both published rigid the-distribution rather than the actual magnitude of the oretical equations

• involving convergent series for the losses is altered so that eq. (8) may be used at least sheath losses in round three-conductor cables. Fortun-for current-carrying capacity calculations with reason-ately, for practical cables at 60 cycles, the convergence able accuracy when no more accurate data is obtainable.

is so rapid that values of R. within a few percent of The apparent conductor resistance for a three-con-those given by the rigid equations may be obtained ductor cable, (also two single-conductor cables in a from the following approximate equation based on the single-phase line, or three single-conductor cables in a simplifying assumptions suggested by Atkinson, three-phase line with equilateral spacing, in which there 28 396 Si8 X 10-8 ohms txt 1000 feet per are induced sheath losses) is the actual conductor re-sistance R at a given temperature and frequency plus R. is given by eq. (to) and r. ste can sheath dius Si s the distance between the effective current cen-the added effective resistance R. from eq. (7) or (8). i in inches. ter of each conductor and the cable center, and is accurately For the other usual arrangements of single-conductor given for round conductors by cables that are not perfectly symmetrical, the apparent i (9) " f/ g, m

1. 5 3

conductor resistance when the sheaths are solidly For sector conductors an approximate value of S bonded and grounded at least at both ends is found i can be found by using eq. (9) but taking d from 0.82 from the master equations developed by Miller *

• and to 0.86 times the round conductor diameter depending tabulated for convenience in Table Vll.

on the shape of the sector, or by measurement from The added effective resistance given in Table VI the center of the sector to the center of the cable. should be carefully distinguished from the apparent con-While theoretically at least some allowance should ductor resistance. The added effective resistance, when be made for the losses which occur in the shielding added to the conductor resistance and multiplied by the ' Compare eq. (81) reference 9 and eq. (7) reference it. square of the conductor current, gives the actualloss dis-7 .~

sipated in heat in the conductor and sheath of the phase ity calculations to be able at least to estimate in advance considered. The apparent conductor resistance, when the armor loss to be expected. multiplied by the square of the conductor current, gives With three-conductor cables. the losses occasioned [ a fictitious loss representing that portion of the total by either type of armor are not of serious consequence, 7 conductor and sheath losses in all phases that are sup-being of the same order of magnitude as the sheath plied by the phase considered. While the respective losses. With single-conductor cables on alternating-sums of these loss values for all three phases are always current circuits, however, the armor loss is so pro-equal, the values for any one phase are not necessarily nounced that except for very small cables, such as those equal, the difference representing the power transferred used for series street lighting, steel-tape armor is im-between phases due to their mutual inductances. Fu r-practical. With steel-wire armor, the loss, while large, thermore, the apparent resistance when properly com-is not in most cases prohibitive. l bined with the apparent reactance to form an apparent An exceedingly simple method for approximating impedance and multiplied by the conductor current, the losses in single-conductor cables with steel-wire gives the voltage drop in the phase considered. The armor at spacings ordinarily employed in submarine in-added effective resistance is used in determining the stallations is to assume that the combined sheath and sheath losses and in all current-carrying capacity calcu-armor current is equal to the conductor current and is lations, while the apparent resistance along with the divided between the armor and sheath in proportion to TAliLE VII-EQUATIONS FOR LINE CONSTANTS OF SINGLE-CONDUCTOR CABLES (Sheaths Solidly Bonded) Apparent Resistance Apparent Reactance R. ' VI(VI + P) + (1 -Vf0) Phase 4 R+7 (p 4 g) (g 4 g) XI - Xu + 7R.' V.I(VIP-1) + (O + V3)' (p 4 g) (93 + j), R. R. O Phase B R + 9: 4 3 Xt - Xu + 9 4 g R. ' Vii VI-P) (1 + Vf 0) ' R. 'VI(VIP + 1) + (0-Vi) ' Phase C R+T (p + g) (93 + g) Xt - Xu + 7 (p + 3) (p + 33 + P8 + 0' + 2 ' O(P' + 1) + P (OS + li' Average R+R*

1. '~. +

• 2 (P8 + 1) (08 + 1),

2 (P8 + 1) (O' + 1) l Phase Rotation 4, B, C. R = actual conductor resistance at given temperature and t l Xt. - 2r/L where L is found from eg's. (11) or (12). freq uency. Xu = 2r/M where M is found from eq. (13). P and O are determined for given arrangement from Table VI. R. is given by eq. (10). All quantities are in ohms per 1000 feet. I apparent reactance as given in Table VII is employed their alternating-current conductances. The sheath re-in the calculation of line impedance, regulation, etc. See sistance is found from eq. (10), and the 60 cycle alter-example 5 for an illustration. nating-current resistance of the armor circuit may be The sheath resistance may be calculated by tlie estimated by increasing the direct-current resistance of following equation: all the armor wires in parallel (corrected for lay) by 1503 p. from 30 to 60%. The parallel combination of the R. = ri' - r., X 10-8 ohms per 1000 feet (10) sheath and armor resistance thus found represents ni s. Oic5 a*e'oN to tYe S c thso n hy cal a$1; directly the added effective resistance due to sheath and may be taken as 24 2 at 40*C., 25 2 at So', 26.1 at 6o', and armor losses, and if multiplied by the square of the con-37 1 at 70*, 25 2 being a,value correspondmg to an average ductor current, gives these losses. The method 'ust volue of maximum permissible currents.

r. and r. are the 3

inner and outer radii respectively of the lead sheath in inches. described is admittedly approximate, and may involve The denominator can be most conveniently calcu. errors as large as 20%, but the error in the fir al cur- . lated by writing this in the form (r. + r.) (r - r.), rent-carrying capacity will be much smaller than this. l noting that the second factor is equal to the lead thickness. Reactance Protective armor of steel wire or steel tape such As far as inductance and inductive reactance in j as employed on submarine or buried cables further multi-conductor cables are concerned, there is no essen-I modify conductor resistance calculations. When the tial difference between cables and overhead transmis-i magnetic characteristics of the steel used are known. sion lines, and the same equation

• applies, namely:

h is possible to calculate with a good degree of accuracy

• Equations (it) and (12) apply strictly to a straight solid I

the resistance and reactance effects". Although in round wire or tube and assume uniform current distribution preliminary work such data is usually not to be had, over the conductor area. The corrections in indnetance due ys$e*g"Ib"bIe rec $seIorI Nen v'e"fa# ** it is often important in making current-carrying capac-arc no at n ccu at 8

o X 10-8 hennes to neu-Equation (13) in efTect states that the mutual in-L= 0.1404 /ag n + 0.01525 ductance is closely dependent upon the average diameter i S being the distance bct veen centers o co due sa the radius of the conductor all in inches. of the lead sheath. S is actually the distance between i For sector-shaped conductors, complete data is not axes of adjacent conductors if the conductors are sym-h available; however, a reasonable approximation may metricaHy located in the vertices of an equilateral V be had if S in eg. (11) is taken as the distance between triangle. This will be the condition in three-conductor j the centers of the small diameters of the sectors. (Refer cables, and may be the condition in single-conductor j to sector correction given with eq. (9).) cables. If the configuration in a three-phase transmis-In three-conductor type H cables in which a mag-sion line is such that the conductors are not on the netic binder tape is employed, there is an appreciable vertices of an equilateral triangle, then as far as sheath increase over the theoretical reactance. A series of losses are concerned, there is no " effective spacing" in-j unpublished tests made by Electrical Testing Labora-dependent of sheath resistance. This will be apparent i tories working in collaboration with the Insulated if an attempt is made to solve for an " effective Xu" in Power Cable Engineers Association and the Association eq. (7) of Table VI. Ilowever, a geometric average i of Edison Illuminating Companies indicates that at 60 of the three distances between the three conductors cycles the steel binder will increase the reactance from taken pair by pair can usually be used with reasonable 10 to 209, depending on the steel. accuracy for the purpose of estimating current-carrying There are additional complications in the calcula-capacity and average temperature rise, in place of using tion of the reactance of cables not ordinarily found in the accurate equations given in Table VI. This is overhead cases. If a tubular conductor is used, such strictly true only for the impractical operating case in as Type H H cable, in the illustration below, that is, which the conductors and sheaths are transposed to-a conductor whose inner region is composed of non-gether, the sheaths being solidly bonded at the end J conducting materials, the following equation should be points only'. used for inductance, which reduces to eg. (11) if the For the case of single-conductor cables in a single-inner radius r. = zero: phase line or three-phase line with equilateral spacing and in which the sheaths are not interconnected at more i S 01404 r r L= 0.1404 lon. r + ( - r.')/, X logi 5 than one point, so that there are m. duced voltages along 'i + 0.01525 ((rt--3r,*). ,,_,,,)~ 10-* henries co neutral per the sheath but no flow of current, the field, exclus.ive 1000 feet (12) of a very slight effect of sheath proximity currents. is O There are stiii rn<ther censideratiens fer the case the same as in a# eve --ire itme er the s>=e size r i of single-conductor cables, inasmuch as the lead sheath conductor and the same separation. The self-induc-surrounds the conductor, and the effect of induced cur-tance is therefore the same as that given by eg. (11) rents in the sheath must be taken into consideration. the reactance being, of course, X. = 2rfL.* With j t The mutual inductance between conductor and sheath other configurations the equations given by many can be calculated by the following equation, Xu of authors for overhead lines may be used directly in j course being given by 2rfM, f being the frequency. obtaining either the apparent resistance or reactance. M = 0.1404 logi. h' 0 feet. (13) with equilateral spacing are interconnected at the two X 10-8 henries to neutral per If the sheaths of a single-phase or three-phase line 100 This equation for mutual inductance assumes that ends so that sheath currents.will circulate, there is an i the current is uniformly distributed around the lead apparent reduction of reactance according to: sheath, that is, that ther'e is no proximity effect in the Apparent Reactance = Xt-(14) sheath due to an adjacent cable. The error is a small . 'y, g ', one, though it is a maximum for the case of cables with The apparent reduction m reactance due to mduced sheaths touching. Miller and Dwight have worked out l l the ratio of sheath losses to conductor losses' 2'" in a rigid manner, so that the calculation can be made accu-rately, even if the sheaths are touching. For accurate work with sheaths in contact, the equations found in these references should be used. I Type H H hotlow-core transmission conductor values are required, as for example in connection with the paralleling of dissimilar cables, the formulas found in refer-ences 3, 4, ). and 16 should be consulted. In three-conductor

• For a complete investigation of the impedance charac-cables in which there are no magnetic materials, the reduction teristics of the individual sheaths of various arrangements, in reactance resulting from induced sheath losses may also be references 8. o. and 14 should be consulted. These references normally neglected. although at 60 cycles, this reduction may also discuss residual sheath voltage and related effects exist-be readily computed from the followmg approximate formula ing with asymmetr'eal arrangements. In the present article, i

obtained by adjusting the initial term of an unpublished con-in line with the field data and theoretical considerations dis-I vergent series formula developed by Miller (Compare formula cussed in 9, it has been assumed that with two or more (8) above). ground points. the residual voltage becomes zero without R.* r.,' X 10-s ohms per 1000 ft. appreciably altering sheath currents as computed for the ideal Reduction in reactance - per conductor case of a smgle ground point. 9

l 1 ) sheath currents is usually not great, by no means as shown in Table VI, the apparent conductor reactance j great as the apparent increase in resistance from the when the sheaths are solidly bonded and grounded at j same cause which is often of material amount. For the the end points is obtained from the equations given in j other usual configurations of single-conductor cable Table VII. j v, f' 4 i l Geometric Factor, Capacity, and Leakage 4 l i the electrical and thermal specific resistances of the material and log. (D /d). The dimensions of the cable i I j occur only in log (D /d) in these three expressions i j g and in the others derived from them, such as dielectric j P loss and charging current. Log. (D /d) therefore i plays the role of a geometric factor or shape modulus, i and has been defined as the " geometric factor". I For the case of multi-conductor type II cable with g j round conductors, it is apparent that as the layers of ] l conducting material are in contact with one another and i with the sheath, the electrical field within such a cable l (/ will be identical to that within a single-conductor cable. i Obviousiv, therefore, the calculation of the electrical l characteristics of each conductor such as capacity, elec-l trical resistance of the insulation, and the dependent quantities will be the same as for a single-conductor g 3 j - [ cable having the same dimensions at one of the indi-T l vidually-insulated conductors of the shielded cable. j While theoretically the single-conductor geometric fac-i tor does not strictly hold for sector shape, yet with ordinary practical sector shapes the difference is entirely negligible. If the metal layer which covers the surface of the l individual conductor i:.sulation is so thick that there is j no appreciable difference in temperature in this metal around the periphery, then the metal can be considered l .w h. i as an isothermal as well as an equipotential surface i Termination of 132-kv oil-filled cable line., Within the and the thermal Problem is also exactly the same as for porcelam bushing, a spun copper cone jomed to the sheath supports a series of concentric insulating tubes single-conductor cable. Actually, however, the metal foil around the insulation is so thin that there is a rise I n'HE equations thus far deal with the conductor i temperature in it. A mathematical solution to this ) and resistance and reactance, which are inde-pr blem has been presented elsewhere" and results m pendent of the shape and quality of the dielectric, the following equation for the reciprocal of the thermal except as they affect separation between conductors. resistance (i.e., thermal conductance) between crmduc. k There is a series of other characteristics of cables which rs and lead of a three-conductor type Il cable with t tw nuls r m te copper foil: { depend upon the shape and specific qualities of the i dielectric. These are primarilv the capacity, the thermal [\\I p,(d + 27) *#} 2,, l resistance, and the electrical' resistance of the insula K ~ I83 kep G(d+ 27) * \\ 2pic / j tion, and the dependent quantities, chargine current. , 183 h' 0 thermal mhos per foot.(15) temperature rise, dielectric loss. etc. ] For the case of single-conductor cables the capacity From this equation the following expression for h l is proportional to the permittivity or specific inductive G, (i.e., the geometric factor to be used in determinin l eapacity and inversely proportional to log. (D fd). The the thermal characteristics of three-conductor type H i i electrical and thermal resistances are proportional to cable) is readily obtained. l 10 i

/ 2 [f } 31ie is much more accurate, though this has errors likely a C' " " X "d 'ja/og,a O 2a tor,d X*/ to exceed ten percent

• There have been, however,

-i two experimental and two graphical determinations of + tor,4 ~ the geometric factor, and, subsequently, Dwight and his and0=(I+ associates have worked out rigid equations for the " ',O where a = v Table VIII gives the geometric factors for a large geometric factors of two and three-conductor belted y g;g g g range of conductor sizes and voltages calculated trom '9'(I0)' can be computed to even a higher degree of accuracy than is warranted by the facts, since there is an essen-Equation (16) shows that C for a type 11 cable tial non uniformitv of cables in view of their construc-3 is not strictly a shape modulus. It is dependent upon tion with conductor insulation, fillers, and belt. For all two parameters, namely a and #. The former includes the ratio of the thermal resistivities of the foil and practical purposes. however, the graphical and experi-s mental solutions are in such close agreement that our insulation. It would be possible to plot G much the data will be based on them. i same as has been done in Fig. 2 for multi-conductor belted cables using a in place of t/T. This has not The geometric factors of a single-cono,uctor cable been done because the above equation, neglecting. as ",nd a multl-conductor type H cable have been defined. Fr multi-c nductor belted cable such as a three-con-it does heat conduction through the filler spaces, is sub-ject to some error in cases of very thin foils or metal-ductor cable, capacity, insulation resistance, etc., are not lized papers. Dr. Konstantinowskv and his associ-definite qu ntities characteristic of a cable, but are ~ ates""'* have already published results of an experi-quantities which depend on the connections. For three-mental determination of G by an electrolytic method C nductor belted cables there are nine different capaci-i for round conductors and have well under way similar ties depending on how the measurement is made, and experiments on sector conductors. Using this data it the same with the other quantities, i.e., capacity of one will be possible to plot a family of curves covering the c nductor against the other two and the sheath, of three usual practical range of a and #. conductors versus the sheath, etc., etc. There will there-For the case of multi-conductor belted cables the fore be a geometric factor corresponding to each of these connections. The geometric factor for the quantities, capacity, and the electrical and thermal re-three conductors connected as one electrode and the sistance of the insulation can easily be expressed in accurate mathematical equations except for the element sheath as the other will be defined as G, and the geo-i introducing the dimensions of the cable, or, in other metric factor under normal three-phase working con-ditions will be indicated as G.. words, the geometric factor. There are two approxi- ~ All of these various mate equations for the geometric factor due to Russell, capacities and geometric factors for the other condi-tions, such as one conductor versus the other two and both of which, while applicable to many cables without large error, approach an infinite error for large con-the sheath, etc., are interrelated, however, and may be ductors and thin insulation. An equation developed by

• see references 21 and :2 for a full discussion of these features.

"I ' g .p g y t .t . N

• 4 4

.~

3, m_:._ Q %ee - - - ~. ~ T' - -

A *

\\ U%2h O e 4 d' 2 .J l, "pY ~: .s ~ _]f$Wj,s;yg A bank of impregnating tanks. A battery of carefully constructed and maintained tanks operated with strict temperature and electrical control during drying and impregnation is a vital factor in cable manufacture 11

i l i l a j expressed for three-conductor belted cables in terms of the sector correction factor is believed to be fairly satis-G, and G, as follows, A, B, and C representing the three factory, although there are wide differences in sector I conductors : shape. The original experimental data does not extend h Gi = cometric factor, d, B, and C vs. sheath, from below the ratio of 0.6; the extrapolation below is, how-6 is. 2 ever, justified by the fact that the theoretical maximum and minimum limits of geometric factor are not very Q G: m tric factor, three-phase operation, from = G = geometric factor,,1 vs. B (C and sheath floating or far apart, and the curve falls directly in the range. t connected to midpoint of transformer) = 2G' Having the geometric factors available from Fi. E t G. = geometric factor, d vs. R and C = 1.5 6 j Gi = geometric factor, d vs. sheath (B and Cinsulated) 2 and Table VIII, it is immediately possible to calculate l , 3Gi + 2G the various quantities referred to above by the following n, a ng m ne ur condue Ge = geometric factor, d vs B and sheath (Cinsulated) ((17) Gv (6Gi + Gd tors; 1 l j 3Gi + 2G 0 Ol69ak i G, = geometric factor, d vs. B, C and sheath Capacity, C = microfarads per 1000 feet.(18) g l 9Ci G' 0 00522pGi 1 6Gi + G, Thermal Resistance, Ra = thermal j G. = geometric factor,4 and B vs. sheath (Cinsulated) ohms per foot. (19) 6Gi + G' Insulation Resistance, R. 0 989;iG X in-* e l G, = geometric factor. 3 and B vs C and sheath j megohms per mil (20) 4 5 6'C' / 0 106Efnk i 3Gi + 2G Charging Current, I = milliamperes g f per 1000 feet. (21) Il Three-Phase Dielectric Loss, #h = watts per foot of cable. (22) i In these equations = is the number of conductors in a cable, .i j l-p is the thermal resistivity of the insulation in watt-cm. units, si 1 k is the specine inductive capacity of the insulation (see Appendix d), is the electrical resistivity of the insulation in megohm-cm. units, E and e are the voltages between conductors and to neutral in kilovolts s respectively, and m # is the power-factor of the insulation for a given temperature and frequency. In the above equations any of the quantities can r be found for ahy method of connection for three-con-ductor belted cables by substituting the correct G. The h dielectric loss has been shown for three-phase voltage j only, G, having been shown. The same equation, how-j ^ ever, can be used for calculating the losses in three-3 j g conductor belted cables in other connections if the V proper G is used and the constant is divided by 3. It Accurate measurement of dielectric loss on cable samples is important to note that in the above equations, if the from two or three inches long to full reellengths at power-constants under three-phase voltage are desired, G, factors as low as 0.017 and at voltages as high as 220-j kv are all within the range of this high-tension bridge being used, E must be the voltage c to neutral, and the j resistance capacity, etc., will be to neutral. In Fig. 2, C, is given for 1, 2, 3, and 4-conductor In using eqs. (18), (20), (21), (22), or (23) for cables, and G, for three-conductor belted cables. The handling three-conductor type H cable, the geometric { data for G are based on the graphical solution" of the factor for three conductors against the sheath is taken i j writer. The values of G, for three-conductor cables equal to C, and the geometric factor under three-phase are based on Atkinson's experiments, no corresponding voltage is taken equal to 3G where G is the geometric f values being available for two-conductor and four-con-factor for a single-tonductor cable of the same size of ductor cables. For the single-conductor cables there conductor and an insulation thickness equal to that on is only one geometric factor, namely G = log. (Di/d), each conductor of the type Il cable. This manner of j given for convenience in Fig. 2. dealing with type H cable avoids the necessity of inter-l The geometric factor for a three-conductor belted preting n for the connection employed and is readily l cable with sector conductors is smaller than the geome. shown to be identical to a single-conductor method of tric factor for a round-conductor cable with the same treatment. Equation (19) is used as given for type Il size of conductor and insulation thicknesses. The sec. three-conductor cable, the proper G, being obtained 3 tor geometric factor for multi-conductor belted cables directly from Table VIII. f can be obtained by finding the geometric factor for a It will be noted that the geometric factor G has f i cable with the same makeup with round conductors, and been used in the expression for thermal resistance. ) multiplying it by the ordinate obtained from the bottom This is the correct geometric factor to use because curve of Fig. 2", due to Atkinson. The accuracy of heat is generated in the three conductors and flows ) i 12

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c. Rate ^ Fig. 2-Geornetric factors for single. conductor cable and rnulti-conductor belted cable with round or sector conductors U Geometric f actors can be obtained by calculating the ratios (T + t)/d and t/T (d being defined for sector cables as the diameter of a round conductor of the same area as the sector), and then reading the required value of geometric factor from a curve above. The value thus obtained will be the correct geometric factor for a round-conductor cable. For sector con-ductors the values so obtained should be multiplied by the sector correction f actor. In cables of the non-type 11 form without belts, such as multi-conductor rubber cables, the ratio becomes T/d, and t/T = o. 13

,e TABI.E Vnt-GEOMETRIC FACTOR (Gi) BETWEEN CONDUCTORS AND SIIEATil 0F T!!REE-CONDUCTOR TYRE U CABLE Tms roometrie feetor is to be uwd in calculatma current-carryms espacity and is based on insuistion of thermal resistivity of 700* uats-em. units witn wrappmas oser the tuamation of copper tape a mus thn. EEcr0R CONDUCTORS t- { Insulauen Thickness in 3nd Inches I ' Ese of Cond. + AM G or C31. 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 1,0 0 54 0 61 0 72 0 El 0 88 0 96 1 03 1 09 1.15 1 21 1.26 1 31 1.36 1 40 1 45 1.49 1.53' 2 /0 0 50 0 54 0 67 0 75 0 82 0 89 0 to 1.02 1 07 1.13 1.15 1.23 12n n 32 1 37 1 41 1.45, 30 0 45 0 54 0 62 0 69 0 76 0 $3 0 89 0 95 1 00 1.05 1.10 1 15 1 20 1.24 1.29 1 33 1.36 49 0 41 0 49 0 57 0 63 0 70 0 76 0 82 0 87 0 93 0 94 1 03 1 04 1 12 l 16 1 20 l 24 l 28-250 000 0 39 0 46 0 53 0 60 0 66 0 72 0 78 0.83 0 89 0 93 0 94 1 04 1.07 1.11 1.15 1.19 1.23 300 000 0 37 0 44 0 50 0 56 0 62 0 69 0 73 0 78 0 84 0 88 0 93 0 97 t 01 1 05 1 09 1.13 1 17' 350 0ie 0 35 0 41 0 44 0 54 0 60 0 65 0 70 0 75 0 80 0 84 0 89 0 93 0 97 1 01 1 05 1 08 1.12 400 000 0 33 0 40 0 46 0 51 0 57 062 067 0 72 0 76 0 80 0 85 0 89 0 93 0 97 1 01 1 04 i On 450 000 0 38 0 39 0 44 0 49 0 55 0 60 0 64 0.69 0 74 0.78 0 82 0 86 0 90 0 94 0 97 1.0L i 04' 500 000 0 30 0 37 0 43 0 49 0 53 0 51 0 63 0 67 0 72 0 76 0 80 0 84 0 87 0 98 0 94 0 98 I Ol' 600 000 0 29 0 34 0 40 0 45 0 50 0 54 0 58 0 63 0 67 0.71 0 75 0.79 0 8J 0 86 0 89 0 93 0 96 l 700 000 0 27 0 32 0 37 0 42 0 47 0 51 0 55 0 60 0 64 0 68 0 72 0 75 0 79 0 82 0 85 0 88 0 91' i A00 000 0 26 0 31 0 36 0 41 0 45 0 49 0 53 0 57 0 61 0 65 0 69 0 72 0 75 0 79 0 82 0 AS 0 8a l RoUND CONDUCTORS Insulation Thicia-m 32nd loches bie of Cond. i AW U cr C.Al. 4 5 6 7 8 9 to !! 12 I' 14 15 16 17 15 19 20 i I I0 0 61 0 71 0 81 0 90 0 98 1 07 1.14 1.21 1 28 1.34 1 41 a 48 1 32 1 57 1 A3 1 67 1.78 ? !O O 57 0 67 0 *6 0 85 0 93 1 00 1 07 1.14 1.20 1.26 1.32 1 38 1.44 1.49 1.54 1.59 1.64 3 /0 0 53 0 63 0 71 0 79 0 87 0 94 1.01 1.08 1.14 1.20 1.25 1 38 1 36 1 41 1.46 1.51 1 56 6 49 0.50 0 59 0 67 0 74 0 82 0 s9 0 95 1.02 1 07 1 13 1.14 1.24 1 29 1.34 1M i 44 1.49 250 000 0 44 0 56 0 64 0 71 0 78 0 85 0 91 0 97 1.03 1.08 1.14 1.19 1.24 1.29 1.34 1 38 1.43 300 000 0 46 0 54 0 61 0 69 0 *5 0 81 0 87 0 93 0.94 1 04 1 09 1.14 1 19 1.24 1 29 1.3J l 3 81 350 000 0.44 0 52 0 59 0 65 0 72 0 78 0 84 0 90 0 95 t.0L 1.06 1.11 1 15 1 20 1.26 1.29 1.331 400 000 0 43 0 50 0 57 0 63 0 70 0 76 0.82 0 87 0 92 0 95 1 03 1 07 1 11 1.16 1.20 1.25 1 29 450 0U0 0 42 0 49 0 55 0 62 0 64 0.74 0.79 0 85 0 90 0 95 1 00 1 05 1 09 1.13 1.17 1.22 1.26, 500 000 0 41 0 48 0.54 060 066 0.72 0.78 0.83 0 88 0 93 0.93 1 02 1 06 !.!! 1.15 1.19 1.23) 6 MVhile not strictly sc. the therma! resntance of type 11 esbie is etosely proportior.al to the thermal resutmty, so that the above geometrie factors mey be used for otner remuvmes unh a reasonable degree of sceurso. formly cut toward the lea sheath, the lines of heat these four quantities have been determined, the cable flow being identical with the lines of current flow if problem is a straight transmission problem no different voltage is impressed between the three conductors as from that of an overhead line, Voltage drop, however, one electrode and the sheath as the other, for which is rarely a determining factor in limiting the allowable c6ndition G, has been defined as the geometric factor. current in cable circuits for transmission, though, of The other two of the four fundamental quantities, course, regulation is the important criterion in the case h namely, capacity and leakage, can now be calculated, of low-tension mains and feeders. For transmitting The capacity may be calculated directly by eq. (18), alternating current, a cable system has much better it being noteil that the 60-cycle capacity will vary only regulation than an open-wire circuit because the con- ) slightly with voltage or temperature and can practically ductors are so close together, as compared with an aerial j be considered as independent of both, line, that the reactive drop is much less. The insulation resistance is given by eq. (20). This, of course, means the insulation resistance as measured It is sometimes interesting to calculate the voltage rise of the cable system at no load, which can be done by direct-currcnt which is of such a high value that by using the above constants, though most cable lines leakage is ordinarily negligible. The alternating-cur-are so short that this effect is not great. As a matter rent conductance or leakage, however, is the quantity of fact, the ordinary transmission line calculation is g generally used in transmission-line calculations. This not the usual one made with cables. The above quanti-can be calculated by considering that the dielectric loss ties are used not so much in the normal way as in con-is due to a hypothetical resistance in parallel with the nection with the allowable current as limited by temper-capacity of the cable. It can be considered that in each ature rise. The capacity and charging current, how-phase there is a dielectric loss equal to the square of ever, are of ten of practical importance, not so much the voltage times the conductance. In the n phases, from their effect on the voltage characteristics of the there will be n times this loss, which will equal the cable itself as from the effect of the leading ky-a upon l dielectric loss, and from the above relationship the leak-the reactors, transformers, generators, and other station age can be determined: equipment. o lo@n m e, i Leakage r = X C nhs per m g, In addition, the apparent alternating current resist-feel to neutral (2n ance and reactance are of considerable importance in The calculation of resistance, inductance. capacity, determining whether the current will divide as expected and leakage has been shown. In calculating the per-between parallel cables of different types and sizes. It formance of a line, such as regulation and efficiency. is in this connection particularly that refinements in f and the usual problems of power transmission, af ter reactance calculations are justified. l 14 1}}