Ampacity derating factors for cables buried in short segments of conduit

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560 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005 Ampacity Derating Factors for Cables Buried 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- equiv- conductor property of a single cable that is ther- ments of conduit, and when this situation occurs, the ampacity mally equivalent to the conductor property of a must be reduced or the cable will overheat as a result of the triplexed cable high thermal resistance created at the location of the conduit. equiv-insul insulation property of a single cable that is ther-This problem is examined for extruded cables by using a finite mally equivalent to the insulation property of aelement heat transfer software program to determine the derating in ampacity that cables in conduits must experience in order to triplexed cable remain below a maximum conductor temperature. The derating insul value for cable insulation material factors are provided as a function of conduit length, soil resistivity, soil value for surrounding soil. burial depth and number of cables in the conduit. The results show that once the length of conduit exceeds about 20 times its I. INTRODUCTIONouter diameter, then the ampacity of the circuit must be reduced to the value that it would have if the entire length were buried in INCE the mid 1900’s the accepted calculation of under- the conduit.

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• Publié par: pascalv
• Publié le: 22 septembre 2013
• Nombre de lectures: 340
• Langue: English

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560

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

Ampacity Derating Factors for Cables Buried 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 ampacity must be reduced or the cable will overheat as a result of the high thermal resistance created at the location of the conduit. This problem is examined for extruded cables by using a finite element heat transfer software program to determine the derating in ampacity that cables in conduits must experience in order to remain below a maximum conductor temperature. The derating factors are provided as a function of conduit length, soil resistivity, burial depth and number of cables in the conduit. The results show that once the length of conduit exceeds about 20 times its outer diameter, then the ampacity of the circuit must be reduced to the value that it would have if the entire length were buried in the conduit. Factors that result in lower cable ampacities, such as high soil thermal resistivity and deeper burial depths lead to larger derating factors.

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

N OMENCLATURE outer diameter of cable [m] nominal diameter of conduit [m] DF ampacity derating factor burial 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 factor temperature [ C] Greek Symbols thermal resistivity [cm C/W] Subscripts ambient air value that exists in the air layer inside the conduit conductor cond value that exists when a conduit is present db value that exists when the cable is direct buried equiv 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: [e-mail]). 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 a triplexed cable equiv-insul insulation property of a single cable that is ther- mally equivalent to the insulation property of a triplexed cable insul value for cable insulation material soil value for surrounding soil. I. I NTRODUCTION S ItECNimehd1900’stheacceptdeaccllutaoionuf ro - g ernd leabdcuniticapmaeebsahseedonnbasodelthemrp-o posed by Neher and McGrath [1]. Their thermal model is based on a number of assumptions that greatly simplify the mathe- matical formulation. Perhaps the most significant assumption which simplifies the approach is one which considers no vari- ation in any geometrical or thermal parameter along the length of 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 reduced to a one-dimensional heat transfer problem by using the prin- ciple of superposition, which utilizes a fictitious heat sink of equal 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 to a 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 standard thermal ratings of most underground cable systems. If any changes in the thermal environment exist along the length of a cable installation, the ampacity tables are unable to provide guidance for determining the ampacity of this more complex 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 of thermal environment. When the poor thermal conditions exist for only a short length of the route, guidance as to the derating the cable must endure is less clear. Unfortunately this situation is often the case in the field where the cable will frequently be required to share its underground space with other utilities or the cable must be routed through a relatively short segment of conduit or pipe. Any variation along the cable route that restricts heat 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 that passes through a region of high thermal resistance would be to rate the circuit on the basis that the entire route is surrounded by the increased thermal resistance. This procedure is obviously

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VAUCHERETet al.DERATING FACTORS FOR CABLES BURIED IN SHORT SEGMENTS OF CONDUIT: AMPACITY

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 cable temperature. This method is a dangerous one, because even a short length of poor soil or a short length of conduit can lead to a hot section of cable and the cable could ultimately fail from unexpectedly high temperatures. Obviously there is some room for compromise between these two extreme approaches when the impediment to heat transfer occurs for only a short distance along the cable route. When the cable passes through a short segment of poorly con- ducting material, the calculation of the new, reduced ampacity is not a simple matter and the thermal model must account for the fact that the heat transfer into the surrounding soil is com- plex and occurs in three dimensions. Therefore the analysis must account for the increased complexity and the ampacity can no longer be calculated from a simple algebraic expression that is outlined in the Neher-McGrath model. The new approach now requires the solution of a complex set of differential equations, and in these cases it is prudent to use commercially available thermal software to solve the complex three-dimensional heat transfer problem. One of the most common situations that involve a change in the thermal environment along the cable route involves a cable that is installed in a short segment of conduit. This situation frequently occurs when a cable route passes under a road crossing or passes close to other pipelines or cables. If the conduit is only a short por- tion of the circuit length, the reduction in ampacity will be only a 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 experience when routed through a short segment of conduit. The results will also quantify how the derating of the cable is influenced by sev- eral variables that are known to affect the cable ampacity, such as the length of conduit , the value for the soil resistivity and the cable burial depth as shown in Fig. 1. The determination of cable derating factors that result when the 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 those appearing in [3]. In this previous paper the influence of a varying ambient soil temperature and presence of high resistivity block of soil under a roadway are considered. The problem is ap- proached by using a thermal network and it considers heatflow in two dimensions. A network of thermal resistances is produced by discretizing the domain in both the radial and longitudinal di- rections and by replacing the continuous thermal regime with a finite number of discrete thermal resistors. An ampacity derating factor is defined which is identical to the one used here. The derating factor is calculated for the situation where the length of high resistance soil layer is varied and the temperature and thermal resistivity of the soil layer is increased above the values for the ambient soil layer. Derating factors as restrictive as about 50 percent are suggested when the slice of soil is not conducive to the transfer of heat from the cable and the region of high re- sistance extends more than about 4 m along the length of the cable [3].

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Fig. 1. Geometry of cable domain. The approach to the calculation of derating factors in this paper differs in a number of respects from the one used in [3]. The analysis presented here considers a single soil resistivity and a single ambient soil temperature that exists far from the cable. The factor that changes along the length of cable is the presence of a short length of conduit that creates a region of ele- vated cable temperature. The penalty to be paid for the presence of a short span of conduit is less severe than a change in the soil resistivity, because the presence of the conduit creates less of a thermal burden than a change in thermal resistivity of the soil next to the cable. II. M ATHEMATICAL M ODEL The calculation of the ampacity of a cable routed through a short section of conduit is very complex. The presence of the conduit compounds the mathematical analysis and creates a three-dimensional heat transfer problem for which the tem- perature distribution around the cable is a function of the axial location, distance from the cable and depth below the surface of the earth. A. Assumptions To transform the physical problem into one that is simple enough 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 the resistance of the adjacent soil layer. —The thermal resistance of the air layer in the conduit is a function of temperature and is calculated from (41) in [1]. The thermal resistance of the air layer is the only quantity that varies with the temperature. —The single, constant thermal resistance of the air layer is evaluated at highest cable temperature that exists in the center of the conduit length. This approximation is used because (41) in [1] was developed for the two dimensional case where the temperatures are constant along the cable axis.

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— C/WThe thermal resistivity of the soil is 90 cm and the ambient soil temperature is 25 C. —The vertical plane through the cable centerline and the vertical plane perpendicular to the cable axis at the center of 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 used to develop (41) in [1]. —The cable installation geometry is identical both inside and outside the conduit. This assumption precludes con- sideration of parallel-spaced cable geometry outside the conduit with a triplexed geometry inside the conduit. B. Finite Element Model Thefinite element software package ANSYS [4] was used to determine the derating factors. The fact that this program has three-dimensional capabilities is important, because the derating factors must include the heat that is conducted along the axial direction of the cable. The axial conduction promotes cooling of the cable segments inside the conduit and, if this heat removal is ignored, the derating factors will be overly con- servative. Therefore when simplified two-dimensional models are used to calculate the derating factors, they would suggest that the cable ampacity should be unnecessarily reduced. Finite element software packages with thermal capabilities are able to solve heat transfer problems that typically consist of calculating the temperaturefield for given heat input rates. To determine the ampacity of a cable system, the inverse problem must be solved: that is, the heat input rate (ampacity) must be determined for an assumed admissible temperature of the con- ductor. Therefore, the temperature distribution in entire domain must be iteratively computed for a range of electrical currents until 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 the conduit, must be continually corrected for the newly calculated air temperature. In order to model multiple cables in a conduit with thefinite element program, the triplexed geometry had to be replaced by a single equivalent cable that has the same thermal resistance as the 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 of the conductor of a single cable. The diameter of a circle which circumscribes the three cables was used as the outside insula- tion diameter of the equivalent single cable in thefinite element program [1]. Therefore the outer radius of the insulation layer on the equivalent single cable is 2.16 times the outer radius of one 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 resistivity of the cable insulation. Two factors are involved. Thefirst ac- counts for the fact that a cable in a triplexed configuration cannot dissipate heat around its entire circumference. The second is a result of considering the heat transfer from the three cables to be

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

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

(1)

This equation along with the dimensions of the insulation layer of a single equivalent cable in terms of the dimensions of the triplexed cables permits calculation of the equivalent thermal resistivity of the insulation layer in terms of the dimensions and resistivity of a single cable. The equivalent thermal resistivity is then used in thefiprogram to simulate the heat thatnite element is transferred through triplexed cable geometry.

III. M ODEL V ERIFICATION The validity of thefinite element program was verified by comparing program results with simple cable installations that have known heat transfer solutions. Thefirst comparison in- volved a single, infinitely long cylindrical heat source directly buried at a constant depth below the isothermal surface of the earth. For this situation, the relationship between the heat dis- sipation per unit length and the temperature rise of the cable surface above the ambient temperature is given by

where the conduction shape factor [6] is

(2)

(3)

For this example case, thefinite element model assumed a di- rect buried conductor without any insulation layers. Thefinite element program was used to calculate the temperature rise for several heat generation rates per unit length, soil resistivities and ratios of burial depths to cable diameters. The calculated values were identical to those given by (2) and (3). The second check of the validity of thefinite element formu- lation involved comparing the program results with the software program CYMCAP [7]. The ampacity values were calculated for a 35 kV, 750 kcmil (380 mm ) aluminum conductor cable, soil resistivity of 90 cm C/W, a burial depth of 0.917 m and a conduit diameter of 152 mm. Several different installations were used including a single, direct-buried cable and three, di- rect-buried cables. The ampacities were also calculated for the same cable geometries when they were routed through a long conduit Thefi cable ampaci- Cnite element values for the 90 . 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 the geometries are extremely complex and there are numerous input variables that cannot be exactly duplicated in both programs. Nevertheless, the two programs agree within 1.7 percent for the ampacity values and within 4.1 percent for the heat generation rates.

VAUCHERETet al.: AMPACITY DERATING FACTORS FOR CABLES BURIED IN SHORT SEGMENTS OF CONDUIT

TABLE I C OMPARISON OF F INITE E LEMENT A MPACITY C ALCULATION W ITH THE CYMCAP S OFTWARE P ACKAGE

IV. R ESULTS The best way to display the ampacity results of the program is in the form of dimensionless groups. In this way the ampacity of the cables in the conduit can easily be calculated in terms of the ampacity of the same cable and same geometry except directly buried in the earth. The dimensionless ampacity value will be re- ferred to as aderating factordefias the ratio of the ampacityned of a cable routed through the short segment of conduit divided by the ampacity of the same cable with an identical installation geometry, but direct buried in the soil. The cable derating factor is then

(4)

This definition preserves the ampacity value that has been tra- ditionally provided in tables or calculated by accepted software packages. Defined in this way, the derating factor can be inter- preted as a reduction in the cable ampacity due to the presence of the conduit. Since the medium in a conduit is usually air with an extremely high thermal resistivity (–cm C/W), the ampacity of the conduit segment of the circuit will be lower than the ampacity value for the direct-buried portion of the cir- cuit. In this situation the derating factor will always be less than one. However, if the conduit isfilled with afluidized grout or slurry that completelyfills the conduit, remains in place and has a thermal resistivity less than that of the ambient soil, the pres- ence of the conduit will result in a region of relatively good heat transfer. In this case thefluid-filled conduit could result in a der- ating factor which exceeds one, and the presence of the conduit does 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 ampacity enhancement factorapplied to the location of the conduit.

A. Effect of Conduit Length An important application of thefinite element software is the determination of the effect of conduit length on the derating of the 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

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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 as a function of the dimensionless ratio of conduit length to mean conduit diameter. The specific values shown are for a 35 kV cable with a 750 kcmil (380 mm ) aluminum conductor buried at a depth of 0.914 m in a soil with a thermal resistivity of 90 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 once the length of the conduit increases beyond about 20 times its diameter, the cable no longer needs to be further derated. This result shows that once the conduit is longer than about 20 times its diameter, the cable is fully derated and its ampacity should be calculated on the basis of the entire cable route being inside a 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 resistance of the soil is the largest resistance in the thermal circuit. When a cable is buried in a soil or thermal backfill that encourages heat transfer (that is, a low thermal resistivity material), the penalty that is suffered when it is routed through a short segment of con- duit is more severe than when it is placed in a high resistivity soil. In this situation the conduit replaces the good soil with a layer of high thermal resistance air, which hinders the transfer of heat to the surrounding soil. On the other hand, if the cable is routed through a thermally poor high resistivity soil, the reduc- tion in ampacity resulting from the presence of the conduit is less. This trend occurs because the presence of the conduit and air layer replaces a layer of soil that is already poorly conducting and causes a diminishing rating penalty. This expected trend in the derating factor is illustrated in Fig. 3. In thisfigure the de- rating factor is plotted as a function of conduit length and soil resistivity, and all quantities are nondimensionalized. The con- duit length has been divided by the mean conduit diameter and the dimensionless soil resistivity is determined by dividing the soil resistivity by the equivalent thermal resistivity of the cable insulation layers. The curves in Fig. 3 assume a single 35 kV, 750 kcmil (380 mm ) aluminum conductor cable buried in 25 C soil to a depth of 0.914 m. The conduit is 152 mm in diameter and the equivalent thermal resistivity of the cable insulation layers is 350 cm C/W. The trend in the derating factor is similar to the

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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 disappears when the ratio of conduit length to mean diameter exceeds about 20 and the derating value asymptotically approaches the rating for a cable in an infinitely long section of conduit. The ratings penalty paid by the cables in the lower resistivity soil is more significant than the reduction required when the soil resistivity is high. For example, the ampacity for a long length of conduit is only about 95 percent of its direct-buried value when the soil resistivity is 160 cm C/W and it is about 87 and 79 percent when the soil resistivity decreases to about 90 and 50 cm C/W, respectively.

C. Effect of Cable Depth As the burial depth increases, the effective thermal resistance of the soil layer surrounding the cable also increases. Therefore the ampacity of a cable decreases as the cable is buried more deeply in the soil. If the presence of a short length of conduit is added to the thermal circuit, the ampacity of the cable must be further derated to account for the region of added thermal resistance that accompanies the presence of the air layer inside the conduit. Cables that are buried at greater depths will be sub- jected to larger derating factors (smaller ampacity penalty) than ones buried at shallow depths. This trend in ampacity penalty is due to the fact that any factor that reduces the thermal resistance of the circuit (cables buried at shallow depths and cables buried in low resistivity soil) will produce lower derating factors. For reasonable cable depths, the computer results have shown that the influence of the burial depth on the derating factor is not significant. For example, decreasing the cable depth from to 1.22 to 0.61 m creates a percentage decrease in the derating factor of less than 1.5 percent for the example case considered in the previous section. Therefore the ampacity penalty that must be paid as the cable is buried shallower in the soil is relatively small and it is not greatly influenced by moderate changes in the burial depth of the cable.

D. Fluid-Filled Conduits In practical installations buried conduits are often full of water. Thefinite element program was used to determine how the presence of water might affect the cable ampacity derating factor for both a single and three cablefluid-filled conduit. The thermal resistance of the air layer was replaced with a liquid layer by changing the empirical constants used

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

in (41) of [1]. The empirical constants for air were replaced by those for oil since no values were provided for water. Even though the thermal properties for water and oil are different, the computer results for the derating factor will give the correct trend when water completelyfills the void areas in the con- duit. It should be noted, however, that the thermal resistivity of oil (–cm C/W) is higher than that of water (– so that conduction of heat throughcm C/W) an oil layer in a conduit is less than conduction of heat through an identical water-filled conduit. In addition, the convection of heat through a water layer is greater than through an equivalent oil layer, because the viscosity of water is less than that of oil. Therefore if a conduit can befilled with afluid, water would be a likely choice, because it would require a smaller derating than an oil-ficonduit. Since water is superior to oil as alled heat transferflthe computer results for oil will provideuid, derating factors that are larger than exist when the conduit if filled with water. One caution should be noted if the derating factors forfluid-filled conduits are to be applied. The entire void space in the conduit must befilled with thefluid. If the fluid drains or seeps from the conduit, the derating of the circuit in the conduit must be increased to reflect the increase in local thermal resistance. Forfluid-filled conduits the derating factor approached an asymptotic 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-filled conduit, because the thermal resistivity of the oil approaches the resistivity of the native soil that the conduit displaces. When the conduit isfilled with water, the derating factor slightly exceeds one due to the superior heat transfer capabilities of water. These results imply that the presence of thefluid-filled conduit does not require lowering the ampacity of the cable and the ampacity of the circuit is the same as the ampacity of a direct-buried cable, regardless of conduit length. However, for the case of a triplexed cable in afluid-filled conduit, the ampacity should be reduced by up to about 3 percent when the conduit length ratio exceeds 20. These results clearly indicate that the factor that accounts for the derating of cables in conduit is the trapped air layer inside the conduit. Once the air layer is replaced by a better conducting medium, such as water, the reason for der- ating the cable is removed. Even though the results presented here were calculated on the basis of a single cable design buried in a soil with a single value of thermal resistivity and ambient temperature, the use of dimensionless quantities would suggest that the magnitude and 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 of cable 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 in the derating factors should apply to installations for which the thermal bottleneck is a result of a high resistivity slice of soil. This observation is supported by a comparison of the trend in derating factors presented here and the derating factors given in [3]. Both studies suggest that when a cable route passes through a segment of poor thermal conditions, the ampacity derating

VAUCHERETet al.: AMPACITY DERATING FACTORS FOR CABLES BURIED IN SHORT SEGMENTS OF CONDUIT

should be increased as the length of the thermal bottleneck is increased. If the axial length of the poor region is more than about 20 times the diameter of the conduit (or diameter of the pipe in pipe-type installations), then the ampacity should be cal- culated on the basis of the entire cable route being buried in the poor environment. This conclusion is the same regardless if the cable is in a short segment of conduit and the soil resistivity is unchanged or if the cable is routed through a dry section of soil that exists under a roadway. When the poor thermal conditions are limited to a shorter section of the cable route, the reduction in ampacity is less severe and it is a function of the axial length of 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 thermal bottleneck than experienced by a short span of conduit, their de- rating factors are more severe than the ones indicated in Figs. 2 and 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. When the installation includes a short segment of conduit, our results would require a reduction of less than 20 percent when the soil resistivity is low and the ambient temperature re- mains unchanged.

V.C ONCLUSION The ampacity of direct-buried cables must be reduced when they enter a segment of conduit, and the amount of derating de- pends on the cable geometry, cable construction, burial depth and thermal conditions of the soil. A derating factor is defined on the basis of the rated ampacity of a direct-buried cable and this factor can be used to determine the reduction in ampacity that must be applied if the cable is to remain below acceptable tem- peratures inside the conduit. Afinite element package is used to determine derating factors for typical cable constructions and common installations. The results provided by the computer model clarify the issue of how the length of conduit will in- fluence the ampacity of a buried cable system. The conduit is considered“short”if its length is less than 20 times its diam- eter. In this case the derating that must be applied to a cable ampacity ranges between about 0.80 and 0.95 depending on the specific 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 determined on the basis of an infinitely long length of conduit. Conditions which result in lower ampacity (greater burial depths, higher soil resistivity) result in less derating of the ampacity or higher der- ating factors. Conduitsfilled with either water, oil or a material that has a resistivity similar to that of the ambient soil create a condition for which the derating factor approaches one.

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A CKNOWLEDGMENT This work originated as Georgia Tech NEETRAC Baseline Project 02-202. This support is gratefully acknowledged. The authors would also like to thank Dr. Ronald G. Harley of Georgia Institute of Technology School of Electrical and Com- puter Engineering and Mr. Thomas C. Champion of NEETRAC for their support of this work.

R EFERENCES [1] J. H. Neher and M. H. McGrath,“The calculation of the temperature rise and 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 cables crossing 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 in Vertical 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 and Row, Publishers, 1980, p. 91. [7]CYMCAP Power Cable Ampacity Program, CYME International, Inc., St. Bruno, Quebec, Canada.

Pascal Vaucheretgraduated in mechanical engineering from Ecole des Mines de Douai, France and Lille University of Science and Technology (DEA), France and in electrical and computer engineering from Supélec, France and the Georgia Institute of Technology (MSECE). His professional interests are applied R&D and project management for heavy industry. He has worked in the energyfield (EDF, NEETRAC) and for material manufacturers (Usinor, ECL-Pechiney-Alcan) in PR China, the USA, Europe, and Australia.

R. A. Hartlein(SM’02) is a mechanical engineering graduate of the Georgia Institute of Technology. He spent thefirst years of his career at the Georgia Power Research Center in Atlanta, Georgia. During that time he conducted research and test programs to evaluate the wide variety of materials used on electric utility transmission and distribution systems. He came to Georgia Tech. in 1996 as the Underground Sys- tems Program Manager, where he develops and manages research and testing projects 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 subject of 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 the Ph.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 Distinguished Professor of ME at the Georgia Institute of Technology, Atlanta. Dr. Black is active in IEEE ampacity committees and has published a number of IEEE T RANSACTIONS papers in the ampacity area.