560 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005

Ampacity Derating Factors for CablesBuried in Short Segments of Conduit

Pascal Vaucheret, R. A. Hartlein, Senior Member, IEEE, and W. Z. Black, Fellow, IEEE

Abstract—Buried cables are often routed through short seg-ments of conduit, and when this situation occurs, the ampacitymust be reduced or the cable will overheat as a result of thehigh thermal resistance created at the location of the conduit.This problem is examined for extruded cables by using a finiteelement heat transfer software program to determine the deratingin ampacity that cables in conduits must experience in order toremain below a maximum conductor temperature. The deratingfactors are provided as a function of conduit length, soil resistivity,burial depth and number of cables in the conduit. The resultsshow that once the length of conduit exceeds about 20 times itsouter diameter, then the ampacity of the circuit must be reducedto the value that it would have if the entire length were buried inthe conduit. Factors that result in lower cable ampacities, suchas high soil thermal resistivity and deeper burial depths lead tolarger derating factors.

Index Terms—Ampacity, cable in conduit, thermal ratings,underground cables.

NOMENCLATURE

outer diameter of cable [m]nominal diameter of conduit [m]

DF ampacity derating factorburial depth below the surface [m]current [A]length of conduit [m]heat generation per unit length of circuit [W/m]radial distance from center of cable [m]conduction shape factortemperature [ C]

Greek Symbolsthermal resistivity [cm C/W]

Subscriptsambient

air value that exists in the air layer inside the conduitconductor

cond value that exists when a conduit is presentdb value that exists when the cable is direct buriedequiv value for single cable that is thermally equivalent

to a triplexed cable

Manuscript received December 12, 2003; revised April 25, 2004. Paper no.TPWRD-00629-2003.

P. Vaucheret is with ECL-Pechiney-Alcan, Ronchin, France.R. A. Hartlein is with NEETRAC in the School of Electrical and Computer

Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA.W. Z. Black is with the George W. Woodruff School of Mechanical Engi-

neering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail:william.black@me.gatech.edu).

Digital Object Identifier 10.1109/TPWRD.2005.844358

equiv- conductor property of a single cable that is ther-mally equivalent to the conductor property of atriplexed cable

equiv-insul insulation property of a single cable that is ther-mally equivalent to the insulation property of atriplexed cable

insul value for cable insulation materialsoil value for surrounding soil.

I. INTRODUCTION

S INCE the mid 1900’s the accepted calculation of under-ground cable ampacities has been based on the model pro-

posed by Neher and McGrath [1]. Their thermal model is basedon a number of assumptions that greatly simplify the mathe-matical formulation. Perhaps the most significant assumptionwhich simplifies the approach is one which considers no vari-ation in any geometrical or thermal parameter along the lengthof the entire cable route. This assumption reduces the formu-lation from a three-dimensional analysis to one of two-dimen-sions. The two-dimensional formulation is then further reducedto a one-dimensional heat transfer problem by using the prin-ciple of superposition, which utilizes a fictitious heat sink ofequal strength above the cable at a distance above the earth sur-face equal to the burial depth. With the resulting one-dimen-sional model, solving for the ampacity of the cable is reduced toa straightforward solution of an algebraic equation. This math-ematical approach is the one used to provide values in the am-pacity tables [2] and those values are accepted as the standardthermal ratings of most underground cable systems.

If any changes in the thermal environment exist along thelength of a cable installation, the ampacity tables are unableto provide guidance for determining the ampacity of this morecomplex situation. If the thermal conditions exist for a rela-tively long segment of the route, it would be prudent, however,to rate the entire circuit on the basis of the worst combination ofthermal environment. When the poor thermal conditions existfor only a short length of the route, guidance as to the deratingthe cable must endure is less clear. Unfortunately this situationis often the case in the field where the cable will frequently berequired to share its underground space with other utilities orthe cable must be routed through a relatively short segment ofconduit or pipe. Any variation along the cable route that restrictsheat transfer to the earth will require a deviation from the am-pacity values provided by the ampacity tables [2].

One way to determine the ampacity of a cable route thatpasses through a region of high thermal resistance would be torate the circuit on the basis that the entire route is surroundedby the increased thermal resistance. This procedure is obviously

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VAUCHERET et al.: AMPACITY DERATING FACTORS FOR CABLES BURIED IN SHORT SEGMENTS OF CONDUIT 561

overly conservative and it will result in a severe penalty of re-duced ampacity. Another approach would be to ignore the re-gion of poor heat transfer and assume that the region of in-creased thermal resistance has a negligible effect on the cabletemperature. This method is a dangerous one, because even ashort length of poor soil or a short length of conduit can lead toa hot section of cable and the cable could ultimately fail fromunexpectedly high temperatures. Obviously there is some roomfor compromise between these two extreme approaches whenthe impediment to heat transfer occurs for only a short distancealong the cable route.

When the cable passes through a short segment of poorly con-ducting material, the calculation of the new, reduced ampacityis not a simple matter and the thermal model must account forthe fact that the heat transfer into the surrounding soil is com-plex and occurs in three dimensions. Therefore the analysis mustaccount for the increased complexity and the ampacity can nolonger be calculated from a simple algebraic expression that isoutlined in the Neher-McGrath model. The new approach nowrequires the solution of a complex set of differential equations,and in these cases it is prudent to use commercially availablethermal software to solve the complex three-dimensional heattransfer problem.

One of the most common situations that involve a change in thethermal environment along the cable route involves a cable that isinstalled in a short segment of conduit. This situation frequentlyoccurs when a cable route passes under a road crossing or passesclose to other pipelines or cables. If the conduit is only a short por-tion of the circuit length, the reduction in ampacity will be onlya fraction of that experienced when the conduit is long. The pur-pose of this paper is to provide guidance on the amount of reduc-tion in current that underground extruded cables must experiencewhen routed through a short segment of conduit. The results willalso quantify how the derating of the cable is influenced by sev-eral variables that are known to affect the cable ampacity, such asthe length of conduit , the value for the soil resistivity andthe cable burial depth as shown in Fig. 1.

The determination of cable derating factors that result whenthe cable route traverses a relative short section of unfavor-able thermal resistance has been addressed previously in [3],although the results reported here are more extensive than thoseappearing in [3]. In this previous paper the influence of a varyingambient soil temperature and presence of high resistivity blockof soil under a roadway are considered. The problem is ap-proached by using a thermal network and it considers heat flowin two dimensions. A network of thermal resistances is producedby discretizing the domain in both the radial and longitudinal di-rections and by replacing the continuous thermal regime with afinite number of discrete thermal resistors. An ampacity deratingfactor is defined which is identical to the one used here. Thederating factor is calculated for the situation where the lengthof high resistance soil layer is varied and the temperature andthermal resistivity of the soil layer is increased above the valuesfor the ambient soil layer. Derating factors as restrictive as about50 percent are suggested when the slice of soil is not conduciveto the transfer of heat from the cable and the region of high re-sistance extends more than about 4 m along the length of thecable [3].

Fig. 1. Geometry of cable domain.

The approach to the calculation of derating factors in thispaper differs in a number of respects from the one used in [3].The analysis presented here considers a single soil resistivityand a single ambient soil temperature that exists far from thecable. The factor that changes along the length of cable is thepresence of a short length of conduit that creates a region of ele-vated cable temperature. The penalty to be paid for the presenceof a short span of conduit is less severe than a change in the soilresistivity, because the presence of the conduit creates less of athermal burden than a change in thermal resistivity of the soilnext to the cable.

II. MATHEMATICAL MODEL

The calculation of the ampacity of a cable routed througha short section of conduit is very complex. The presence ofthe conduit compounds the mathematical analysis and createsa three-dimensional heat transfer problem for which the tem-perature distribution around the cable is a function of the axiallocation, distance from the cable and depth below the surface ofthe earth.

A. Assumptions

To transform the physical problem into one that is simpleenough to model mathematically, a number of simplifying as-sumptions were employed. They include:

— Steady state conditions exist.— Cable, soil and conduit properties are independent of tem-

perature and constant.— The cable shield is open-circuited.— All nonmetallic layers in the cable construction are

lumped into a single, thermally equivalent layer.— The conduit is thin and its thermal resistance is close to

that of the soil, so its thermal resistance is added to theresistance of the adjacent soil layer.

— The thermal resistance of the air layer in the conduit is afunction of temperature and is calculated from (41) in [1].The thermal resistance of the air layer is the only quantitythat varies with the temperature.

— The single, constant thermal resistance of the air layer isevaluated at highest cable temperature that exists in thecenter of the conduit length. This approximation is usedbecause (41) in [1] was developed for the two dimensionalcase where the temperatures are constant along the cableaxis.

562 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005

— The thermal resistivity of the soil is 90 cm C/W and theambient soil temperature is 25 C.

— The vertical plane through the cable centerline and thevertical plane perpendicular to the cable axis at the centerof the conduct are adiabatic planes.

— Regions of the soil that are far from the cable are main-tained at the ambient soil temperature.

— The cable is located concentrically within the conduit.This assumption is consistent with the assumption usedto develop (41) in [1].

— The cable installation geometry is identical both insideand outside the conduit. This assumption precludes con-sideration of parallel-spaced cable geometry outside theconduit with a triplexed geometry inside the conduit.

B. Finite Element Model

The finite element software package ANSYS [4] was usedto determine the derating factors. The fact that this programhas three-dimensional capabilities is important, because thederating factors must include the heat that is conducted alongthe axial direction of the cable. The axial conduction promotescooling of the cable segments inside the conduit and, if thisheat removal is ignored, the derating factors will be overly con-servative. Therefore when simplified two-dimensional modelsare used to calculate the derating factors, they would suggestthat the cable ampacity should be unnecessarily reduced.

Finite element software packages with thermal capabilitiesare able to solve heat transfer problems that typically consist ofcalculating the temperature field for given heat input rates. Todetermine the ampacity of a cable system, the inverse problemmust be solved: that is, the heat input rate (ampacity) must bedetermined for an assumed admissible temperature of the con-ductor. Therefore, the temperature distribution in entire domainmust be iteratively computed for a range of electrical currentsuntil the maximum cable temperature reaches the assumed ad-missible value. Between iterations, the temperature sensitive el-ements, such as the thermal resistance of the air layer within theconduit, must be continually corrected for the newly calculatedair temperature.

In order to model multiple cables in a conduit with the finiteelement program, the triplexed geometry had to be replaced bya single equivalent cable that has the same thermal resistance asthe three cables. In order for the single cable to have an equiva-lent conductor cross-sectional area as the three triplexed cables,the conductor must have a radius that is 1.732 times the radius ofthe conductor of a single cable. The diameter of a circle whichcircumscribes the three cables was used as the outside insula-tion diameter of the equivalent single cable in the finite elementprogram [1]. Therefore the outer radius of the insulation layeron the equivalent single cable is 2.16 times the outer radius ofone of the actual triplexed cables.

From [5] the thermal resistivity of the equivalent single insu-lation layer is established as a function of the thermal resistivityof the cable insulation. Two factors are involved. The first ac-counts for the fact that a cable in a triplexed configuration cannotdissipate heat around its entire circumference. The second is aresult of considering the heat transfer from the three cables to be

through an equivalent parallel thermal circuit. These two factorsprovide an equivalent single layer of insulation that has 0.390times the resistivity of a single triplexed cable. When this resultis combined with the expression for the thermal resistance of ahollow layer of insulation, the result is

(1)

This equation along with the dimensions of the insulation layerof a single equivalent cable in terms of the dimensions of thetriplexed cables permits calculation of the equivalent thermalresistivity of the insulation layer in terms of the dimensions andresistivity of a single cable. The equivalent thermal resistivity isthen used in the finite element program to simulate the heat thatis transferred through triplexed cable geometry.

III. MODEL VERIFICATION

The validity of the finite element program was verified bycomparing program results with simple cable installations thathave known heat transfer solutions. The first comparison in-volved a single, infinitely long cylindrical heat source directlyburied at a constant depth below the isothermal surface of theearth. For this situation, the relationship between the heat dis-sipation per unit length and the temperature rise of the cablesurface above the ambient temperature is given by

(2)

where the conduction shape factor [6] is

(3)

For this example case, the finite element model assumed a di-rect buried conductor without any insulation layers. The finiteelement program was used to calculate the temperature rise forseveral heat generation rates per unit length, soil resistivities andratios of burial depths to cable diameters. The calculated valueswere identical to those given by (2) and (3).

The second check of the validity of the finite element formu-lation involved comparing the program results with the softwareprogram CYMCAP [7]. The ampacity values were calculatedfor a 35 kV, 750 kcmil (380 mm ) aluminum conductor cable,soil resistivity of 90 cm C/W, a burial depth of 0.917 m anda conduit diameter of 152 mm. Several different installationswere used including a single, direct-buried cable and three, di-rect-buried cables. The ampacities were also calculated for thesame cable geometries when they were routed through a longconduit. The finite element values for the 90 C cable ampaci-ties are compared with the CYMCAP values in Table I.

The values in Table I show the differences that can be ex-pected to exist when comparing two programs, even though thegeometries are extremely complex and there are numerous inputvariables that cannot be exactly duplicated in both programs.Nevertheless, the two programs agree within 1.7 percent for theampacity values and within 4.1 percent for the heat generationrates.

VAUCHERET et al.: AMPACITY DERATING FACTORS FOR CABLES BURIED IN SHORT SEGMENTS OF CONDUIT 563

TABLE ICOMPARISON OF FINITE ELEMENT AMPACITY CALCULATION

WITH THE CYMCAP SOFTWARE PACKAGE

IV. RESULTS

The best way to display the ampacity results of the program isin the form of dimensionless groups. In this way the ampacity ofthe cables in the conduit can easily be calculated in terms of theampacity of the same cable and same geometry except directlyburied in the earth. The dimensionless ampacity value will be re-ferred to as a derating factor defined as the ratio of the ampacityof a cable routed through the short segment of conduit dividedby the ampacity of the same cable with an identical installationgeometry, but direct buried in the soil. The cable derating factoris then

(4)

This definition preserves the ampacity value that has been tra-ditionally provided in tables or calculated by accepted softwarepackages. Defined in this way, the derating factor can be inter-preted as a reduction in the cable ampacity due to the presence ofthe conduit. Since the medium in a conduit is usually air with anextremely high thermal resistivity ( – cm C/W),the ampacity of the conduit segment of the circuit will be lowerthan the ampacity value for the direct-buried portion of the cir-cuit. In this situation the derating factor will always be less thanone. However, if the conduit is filled with a fluidized grout orslurry that completely fills the conduit, remains in place and hasa thermal resistivity less than that of the ambient soil, the pres-ence of the conduit will result in a region of relatively good heattransfer. In this case the fluid-filled conduit could result in a der-ating factor which exceeds one, and the presence of the conduitdoes not represent a thermal bottleneck in the circuit. In this spe-cialized case, the terminology of a derating factor is perhaps in-appropriate and it would be more logical to refer to an ampacityenhancement factor applied to the location of the conduit.

A. Effect of Conduit Length

An important application of the finite element software is thedetermination of the effect of conduit length on the derating ofthe buried cable. Fig. 2 shows the trend in the cable derating fac-tors for a single cable and a triplexed cable geometry buried in a

Fig. 2. Cable derating factor as a function of dimensionless conduit length,L/D, for single and triplexed cables.

conduit with a variable length. The derating factor is plotted asa function of the dimensionless ratio of conduit length to meanconduit diameter. The specific values shown are for a 35 kVcable with a 750 kcmil (380 mm ) aluminum conductor buriedat a depth of 0.914 m in a soil with a thermal resistivity of90 cm C/W and an ambient temperature of 25 C. The der-ating factors in Fig. 2 show the steep decline in acceptable am-pacity as the length of the conduit is increased. However oncethe length of the conduit increases beyond about 20 times itsdiameter, the cable no longer needs to be further derated. Thisresult shows that once the conduit is longer than about 20 timesits diameter, the cable is fully derated and its ampacity shouldbe calculated on the basis of the entire cable route being insidea conduit.

B. Effect of Soil Resistivity

For buried cables the soil resistivity is the single most influen-tial factor that affects the cable ampacity, because the resistanceof the soil is the largest resistance in the thermal circuit. When acable is buried in a soil or thermal backfill that encourages heattransfer (that is, a low thermal resistivity material), the penaltythat is suffered when it is routed through a short segment of con-duit is more severe than when it is placed in a high resistivitysoil. In this situation the conduit replaces the good soil with alayer of high thermal resistance air, which hinders the transferof heat to the surrounding soil. On the other hand, if the cable isrouted through a thermally poor high resistivity soil, the reduc-tion in ampacity resulting from the presence of the conduit isless. This trend occurs because the presence of the conduit andair layer replaces a layer of soil that is already poorly conductingand causes a diminishing rating penalty. This expected trend inthe derating factor is illustrated in Fig. 3. In this figure the de-rating factor is plotted as a function of conduit length and soilresistivity, and all quantities are nondimensionalized. The con-duit length has been divided by the mean conduit diameter andthe dimensionless soil resistivity is determined by dividing thesoil resistivity by the equivalent thermal resistivity of the cableinsulation layers.

The curves in Fig. 3 assume a single 35 kV, 750 kcmil(380 mm ) aluminum conductor cable buried in 25 C soil to adepth of 0.914 m. The conduit is 152 mm in diameter and theequivalent thermal resistivity of the cable insulation layers is350 cm C/W. The trend in the derating factor is similar to the

564 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005

Fig. 3. Cable derating factor as a function of dimensionless conduit length,L/D, for several soil resistivities.

one shown in Fig. 2. The decrease in cable ampacity disappearswhen the ratio of conduit length to mean diameter exceedsabout 20 and the derating value asymptotically approaches therating for a cable in an infinitely long section of conduit. Theratings penalty paid by the cables in the lower resistivity soilis more significant than the reduction required when the soilresistivity is high. For example, the ampacity for a long lengthof conduit is only about 95 percent of its direct-buried valuewhen the soil resistivity is 160 cm C/W and it is about 87 and79 percent when the soil resistivity decreases to about 90 and50 cm C/W, respectively.

C. Effect of Cable Depth

As the burial depth increases, the effective thermal resistanceof the soil layer surrounding the cable also increases. Thereforethe ampacity of a cable decreases as the cable is buried moredeeply in the soil. If the presence of a short length of conduitis added to the thermal circuit, the ampacity of the cable mustbe further derated to account for the region of added thermalresistance that accompanies the presence of the air layer insidethe conduit. Cables that are buried at greater depths will be sub-jected to larger derating factors (smaller ampacity penalty) thanones buried at shallow depths. This trend in ampacity penalty isdue to the fact that any factor that reduces the thermal resistanceof the circuit (cables buried at shallow depths and cables buriedin low resistivity soil) will produce lower derating factors.

For reasonable cable depths, the computer results have shownthat the influence of the burial depth on the derating factor isnot significant. For example, decreasing the cable depth fromto 1.22 to 0.61 m creates a percentage decrease in the deratingfactor of less than 1.5 percent for the example case considered inthe previous section. Therefore the ampacity penalty that mustbe paid as the cable is buried shallower in the soil is relativelysmall and it is not greatly influenced by moderate changes in theburial depth of the cable.

D. Fluid-Filled Conduits

In practical installations buried conduits are often full ofwater. The finite element program was used to determinehow the presence of water might affect the cable ampacityderating factor for both a single and three cable fluid-filledconduit. The thermal resistance of the air layer was replacedwith a liquid layer by changing the empirical constants used

in (41) of [1]. The empirical constants for air were replacedby those for oil since no values were provided for water. Eventhough the thermal properties for water and oil are different,the computer results for the derating factor will give the correcttrend when water completely fills the void areas in the con-duit. It should be noted, however, that the thermal resistivityof oil ( – cm C/W) is higher than that of water( – cm C/W) so that conduction of heat throughan oil layer in a conduit is less than conduction of heat throughan identical water-filled conduit. In addition, the convection ofheat through a water layer is greater than through an equivalentoil layer, because the viscosity of water is less than that of oil.Therefore if a conduit can be filled with a fluid, water wouldbe a likely choice, because it would require a smaller deratingthan an oil-filled conduit. Since water is superior to oil as aheat transfer fluid, the computer results for oil will providederating factors that are larger than exist when the conduit iffilled with water. One caution should be noted if the deratingfactors for fluid-filled conduits are to be applied. The entirevoid space in the conduit must be filled with the fluid. If thefluid drains or seeps from the conduit, the derating of the circuitin the conduit must be increased to reflect the increase in localthermal resistance.

For fluid-filled conduits the derating factor approached anasymptotic value when the ratio of conduit length to mean con-duit diameter exceeded about 20. The derating factor is approx-imately one when a single cable was routed through an oil-filledconduit, because the thermal resistivity of the oil approaches theresistivity of the native soil that the conduit displaces. When theconduit is filled with water, the derating factor slightly exceedsone due to the superior heat transfer capabilities of water. Theseresults imply that the presence of the fluid-filled conduit doesnot require lowering the ampacity of the cable and the ampacityof the circuit is the same as the ampacity of a direct-buried cable,regardless of conduit length. However, for the case of a triplexedcable in a fluid-filled conduit, the ampacity should be reducedby up to about 3 percent when the conduit lengthratio exceeds 20. These results clearly indicate that the factorthat accounts for the derating of cables in conduit is the trappedair layer inside the conduit. Once the air layer is replaced bya better conducting medium, such as water, the reason for der-ating the cable is removed.

Even though the results presented here were calculated onthe basis of a single cable design buried in a soil with a singlevalue of thermal resistivity and ambient temperature, the useof dimensionless quantities would suggest that the magnitudeand trend of the derating factors would apply to other cable de-signs and other installations as well. In other words, the der-ating factors presented here can be used for a broad range ofcable designs and a wide variety of cable installations. Further-more, even though the analysis assumes the poor thermal envi-ronment is caused by a short segment of conduit, the trends inthe derating factors should apply to installations for which thethermal bottleneck is a result of a high resistivity slice of soil.This observation is supported by a comparison of the trend inderating factors presented here and the derating factors given in[3]. Both studies suggest that when a cable route passes througha segment of poor thermal conditions, the ampacity derating

VAUCHERET et al.: AMPACITY DERATING FACTORS FOR CABLES BURIED IN SHORT SEGMENTS OF CONDUIT 565

should be increased as the length of the thermal bottleneck isincreased. If the axial length of the poor region is more thanabout 20 times the diameter of the conduit (or diameter of thepipe in pipe-type installations), then the ampacity should be cal-culated on the basis of the entire cable route being buried in thepoor environment. This conclusion is the same regardless if thecable is in a short segment of conduit and the soil resistivity isunchanged or if the cable is routed through a dry section of soilthat exists under a roadway. When the poor thermal conditionsare limited to a shorter section of the cable route, the reductionin ampacity is less severe and it is a function of the axial lengthof the high resistance region.

The derating factors presented here also corroborate the mag-nitude of values presented in [3]. Since a change in soil resis-tivity or ambient temperature is a much more severe thermalbottleneck than experienced by a short span of conduit, their de-rating factors are more severe than the ones indicated in Figs. 2and 3. Their results indicate that a cable ampacity should be re-duced by as much as 50 percent when it is routed through a re-gion of higher resistivity soil with increased temperature. Whenthe installation includes a short segment of conduit, our resultswould require a reduction of less than 20 percentwhen the soil resistivity is low and the ambient temperature re-mains unchanged.

V. CONCLUSION

The ampacity of direct-buried cables must be reduced whenthey enter a segment of conduit, and the amount of derating de-pends on the cable geometry, cable construction, burial depthand thermal conditions of the soil. A derating factor is defined onthe basis of the rated ampacity of a direct-buried cable and thisfactor can be used to determine the reduction in ampacity thatmust be applied if the cable is to remain below acceptable tem-peratures inside the conduit. A finite element package is used todetermine derating factors for typical cable constructions andcommon installations. The results provided by the computermodel clarify the issue of how the length of conduit will in-fluence the ampacity of a buried cable system. The conduit isconsidered “short” if its length is less than 20 times its diam-eter. In this case the derating that must be applied to a cableampacity ranges between about 0.80 and 0.95 depending on thespecific installation. A length of conduit is said to be “long”from a thermal standpoint if its length is over 20 times its diam-eter. In this case the ampacity of the cable must be determinedon the basis of an infinitely long length of conduit. Conditionswhich result in lower ampacity (greater burial depths, higher soilresistivity) result in less derating of the ampacity or higher der-ating factors. Conduits filled with either water, oil or a materialthat has a resistivity similar to that of the ambient soil create acondition for which the derating factor approaches one.

ACKNOWLEDGMENT

This work originated as Georgia Tech NEETRAC BaselineProject 02-202. This support is gratefully acknowledged. Theauthors would also like to thank Dr. Ronald G. Harley ofGeorgia Institute of Technology School of Electrical and Com-puter Engineering and Mr. Thomas C. Champion of NEETRACfor their support of this work.

REFERENCES

[1] J. H. Neher and M. H. McGrath, “The calculation of the temperature riseand load capability of cable systems,” AIEE Trans. Power App. Syst., vol.76, pp. 752–772, Oct. 1957.

[2] IEEE Standard Power Cable Ampacity Tables, 1994. IEEE Std. 835-1994, NY.

[3] H. Brakelmann and G. Anders, “Ampacity reduction factors for cablescrossing thermally unfavorable regions,” IEEE Trans. Power Delivery,vol. 16, no. 4, pp. 444–448, Oct. 2001.

[4] ANSYS Finite Element Simulation Software, ANSYS Inc., Canonsburg,PA.

[5] R. A. Hartlein, “Heat Transfer from Electric Power Cables Enclosed inVertical Protective Shields,” M.S. Thesis, School of Mechanical Engi-neering, Georgia Institute of Technology, Mar. 1982.

[6] F. Kreith and W. Z. Black, “Basic Heat Transfer,” , N.Y.: Harper andRow, Publishers, 1980, p. 91.

[7] CYMCAP Power Cable Ampacity Program, CYME International, Inc.,St. Bruno, Quebec, Canada.

Pascal Vaucheret graduated in mechanical engineering from Ecole des Minesde Douai, France and Lille University of Science and Technology (DEA),France and in electrical and computer engineering from Supélec, France andthe Georgia Institute of Technology (MSECE).

His professional interests are applied R&D and project management for heavyindustry. He has worked in the energy field (EDF, NEETRAC) and for materialmanufacturers (Usinor, ECL-Pechiney-Alcan) in PR China, the USA, Europe,and Australia.

R. A. Hartlein (SM’02) is a mechanical engineering graduate of the GeorgiaInstitute of Technology.

He spent the first years of his career at the Georgia Power Research Center inAtlanta, Georgia. During that time he conducted research and test programs toevaluate the wide variety of materials used on electric utility transmission anddistribution systems. He came to Georgia Tech. in 1996 as the Underground Sys-tems Program Manager, where he develops and manages research and testingprojects related to electric utility underground cable systems. He actively par-ticipates in the development of industry standards and specifications for under-ground cable systems and has served as Chair of the IEEE Insulated Conduc-tors Committee. He has also authored a number of publications on the subjectof cable aging and operation.

W. Z. Black (M’77–S’94–F’96) received the B.S. and M.S. degrees in mechan-ical engineering from the University of Illinois, Urbana-Champaign, IL and thePh.D. from Purdue University, West Lafayette, IN.

His research area is heat transfer from electrical systems. He is currently Re-gents’ Professor Emeritus and he was previously a Georgia Power DistinguishedProfessor of ME at the Georgia Institute of Technology, Atlanta. Dr. Blackis active in IEEE ampacity committees and has published a number of IEEETRANSACTIONS papers in the ampacity area.