Ampacity Calculations for Deeply Installed Cables

IEEE TRANSACTIONS ON POWER DELIVERY

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Ampacity Calculations for Deeply Installed Cables Eric Dorison, George J. Anders, Fellow, IEEE, and Frederic Lesur

Abstract—In this paper, a new method is proposed for ampacity calculations of deeply installed cables. Two factors make these types of installations different from more common situations of cables located up to five meters underground. On the one hand, the time constant of the soil layer above the cable trench is very large, resulting in a very slow conductor temperature rise when the cable is first loaded, and, on the other hand, the weekly and yearly load-cycle variations can be taken into account to take the advantage of the greater laying depth. Both issues are explored in this paper. This paper introduces the concept of the equivalent laying depth which makes it possible to use the rating rules applicable to the steady-state conditions and avoid transient analysis. Index Terms—Ampacities, cable rating, direct drilling, load cycling, power cables.

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I. INTRODUCTION

NSTALLATION of new cable lines in large metropolitan areas in industrialized countries becomes more and more difficult. Obtaining necessary permissions is only one of the problems. From a technical point of view, most of the available right-of-ways are already occupied either by other power or communication circuits or by other infrastructures such as heating, sewage, and water pipes or underground transportation corridors. Therefore, burying cables at great depths is more and more frequent and, in spite of fairly high costs, laying of cables in deep tunnels become attractive; for instance, such tunnels were recently built in Toronto, Berlin or London, and several projects are under consideration in major European and North American cities. The most important are as follows. • The civil engineering work does not have to distract pedestrian or vehicular traffic. • The length of the cable route can be minimized. • Cables can be laid independently of the structure of the buildings above the right-of-way. • Access to the circuits is facilitated if they are laid in large tunnels. • The influence of electromagnetic fields at the earth surface is considerably diminished in comparison with the standard installations.

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• In case of large tunnels, additional circuits may be installed without a loss of existing rating capabilities by the introduction of forced air circulation. • An advantageous thermal environment is created, permitting improved heat dissipation. The last bullet is of particular interest in the context of cable rating calculations and will be explored in this paper. An advantageous thermal environment for deeply buried cables is a result of several factors. On the one hand, the soil tends to have higher moisture content at large depth due to the penetration of ground waters. On the other hand, daily, weekly, and even yearly load variations have a profound effect on the ratings of deeply buried cables. This effect is not so pronounced for cables buried at the usual depths. In addition, the large amount of soil above the cable trench results in the very large time constant of the thermal circuit and a slow heating of cable conductor. These facts, even though well recognized by the cable experts, have not been harnessed in practical mathematical formulae that could be included in the cable rating standards. Even though there are several publications dealing with ratings of cables in tunnels, a literature search conducted by the authors revealed that only one article has recently been published addressing the advantages of the deeply buried tunnels. The paper by Matsumura et al., [14] suggests the use of transient calculations to account for the very large thermal capacitance of the soil surrounding deep tunnels. This approach has been used successfully in the past by specialists in the field but it is cumbersome and requires significant skills and knowledge. The aim of this paper is to introduce a new simple method of cable ampacity calculations specifically taking advantage of the special heating regime of deeply buried cables, which could be incorporated into the next revision of the IEC standard dedicated to the calculation of the continuous current rating of cables [1]. The paper brings forward the definition of an equivalent depth, which allows using the rating rules applicable to the steady-state conditions, thus avoiding transient analysis. As the equivalent depth depends upon a limited number of parameters, charts may be developed to determine the value to be taken into account in an actual case. We will start by presenting mathematical formulae which take advantage of the high thermal constant of such installations as well as daily, weekly, and yearly load variations, and conclude by considering several practical examples.

Manuscript received May 12, 2009. E. Dorison is with Electricité de France

[Author: Please provide city and postal code] (e-mail: [email protected]). G.J. Anders is with the Technical University of Lodz [Author: Please provide city and postal code], (e-mail: [email protected]). F. Lesur is with RTE, the French TSO, Paris [Author: Please provide postal code], (e-mail: [email protected]). Digital Object Identifier 10.1109/TPWRD.2009.2033961

II. TEMPERATURE CHANGES FOR DEEPLY BURIED CABLES The time constants for deeply buried cables are very large. This can be illustrated using standard computational procedures for the steady state [1] and transient ratings [2], [3]. Table I summarizes the results of such analysis for a typical XLPE cable

0885-8977/$26.00 © 2009 IEEE

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(1)

TABLE I EXAMPLE OF AMPACITIES AND TEMPERATURES OF DEEPLY BURIED CABLES

where: a.c. resistance of the conductor (ohm/m); internal thermal resistance of the cable (K m/W); internal thermal resistance for dielectric losses (W/m); sheath and armor loss factors; attainment factor for the outer cable surface; external thermal resistance (K m/W); dielectric losses (W/m). and are functions of the cable diameter the laying depth (m), and are defined by

(m) and

(2)

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(3)

where

Fig. 1. Temperature profile for cables buried at various depth with an application of a step function at t = 0.

soil thermal resistivity (K m/W); exponential integral;

soil thermal diffusivity (in m /s).

circuit laid 10, 20, and 40 m deep with a step current applied at . As can be seen, after 40 years, the cable conductor has not reached its maximum allowable temperature of 90 C when the cable is buried at the depth greater than 20 m. This point is illustrated further in Fig. 1 by the temperature profiles of the same installations over a period of time. The temperature is computed with a standard equation for the external thermal resistance using an exponential integral [3]. In Fig. 1 the temperature rises quickly at first but then the growth is very slow. Analysis of these results suggests that applying the standard steady-state calculation algorithm would yield ampacities that are too small. A more appropriate approach would be to use the transient analysis algorithm and iteratively find out what value of the current would give the desired temperature at the end of the study period. This suggests that one can define an equivalent depth of the cable circuit that with the application of the steadystate algorithm would give the same value of current as obtained from the transient analysis. This approach is presented in the next section. III. EQUIVALENT DEPTH OF DEEPLY BURIED CABLES A. A Single Cable Let be the conductor temperature rise at time due to a current step , [3]:

For large , the first exponential integral in (3) can be approximated by [4] (4)

Combining (2)–(4), we have

(5)

Let be the external thermal resistance for the same cable, smaller than . Let be the maximum but with the depth permissible current for a continuous load, corresponding to the . maximum conductor temperature rise above ambient This temperature rise is obtained from the standard equation (6)

If after time , the steady-state allowable temperature is reached (7) Substituting (1) and (6) into (7), results in the following equation:

(8)

DORISON et al.: AMPACITY CALCULATIONS FOR DEEPLY INSTALLED CABLES

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Fig. 3. Relationship between the actual depth and an equivalent depth as a function of the soil thermal diffusivity for t 40 years.

=

Fig. 2. Relationship between actual depth L and an equivalent depth L as a function of the study period.

, which

In this section we will examine an implication of the fact that for deeply buried cables the presence of the adjacent cables may have a more profound effect on the rated cable than might be the case for cables buried at a normal depth. Considering a group of equally loaded cables (each with the ), the external thermal resistance of the hottest joule losses cable may be expressed as

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The equivalent depth is obtained assuming leads to

B. Multiple Cables

(9)

Substituting (5) for the left-hand side in (9) and using (2) for with replacing , we finally obtain

(11)

(10)

The equivalent depth is a function of the time and the soil thermal diffusivity . Fig. 2 illustrates the relation between the equivalent and actual depth for a typical value of soil thermal m /s. diffusivity of Fig. 2 indicates that the longer the study period the higher an equivalent depth will be. However, in all cases, the equivalent depth is much lower than the actual depth if the cable is laid at large depth. The equivalent depth is a function of the soil diffusivity as well. Fig. 3 shows this dependence for a typical value of the 40 years. time horizon, We can observe that the value of soil thermal diffusivity plays an important role in the definition of the equivalent depth. The equivalent depth more than doubles when we move for a soil m /s to the value that is four times with diffusivity of higher.

where is the spacing between cables and and is the spacing between cable and the image of cable . of the outer surface is The transient temperature rise shown in (12) at the bottom of the page. Since for deeply buried cables, we can assume for every cable

(13)

we have

(14)

and using an approximation of the exponential integral as in (4) , shown in (15) at with the assumption of low values of the bottom of the page. This gives the same equivalent depth as in the case of a single cable.

(12)

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IV. CASE OF DEEP TUNNELS

Fig. 4. Comparison of accurate and approximate formulae of equivalent depth. Tunnel diameter 8 m, depth 30 m. Soil diffusivity 0.5E-6 m /s.

Denoting by the calculated value of the right-hand-side of (18), the solution is given by

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Calculation of temperatures of cable tunnels, ventilated or not, may be complex because of the combination of heat transfers, (conduction, convection and radiation) between cables and tunnel wall, as well as longitudinal circulation of air [5]. We only focus here on the conductive heat transfer between the outer side of the tunnel wall and the ground surface. The case of deep tunnels involves special considerations as follows. • Depth value can easily reach hundreds of meters (tunnel between two valleys in a mountainous area). • The initial temperature of rocky soils at the core of mountains can reach unexpected temperature values (more than 50 C). • The heating source can be the combination of cable losses, other circulating fluids’ thermal effects (in multipurpose structures), but also water-cooling and forced ventilation with cold air renewal. The installation of cables in shared tunnels (e.g., railway tunnels) can lead to large diameters, because some tunnel-boring machines are capable of excavating a diameter greater than eight meters. Therefore, some of our assumptions in Chapter III regarding the depth and the diameter may no longer be valid and a more accurate, although somewhat more complex, solution may be required as shown below. We introduce new parameters

(19)

Finally, the equivalent depth of the tunnel is found from (17) (20)

The exact formula for the external thermal resistance of the round tunnel is given by (16)

where

(17)

When the value of exceeds 10, a good approximation (with the error smaller than 0.1%) is given by (2). However, as mentioned before, for large tunnels, (16) should be used. Using (16) in (9), we obtain

(18)

A question arises of when to use (10) and when to use the more complex equations (18)–(20). Fig. 4 shows that the approximation given by (10) is very good, even for deep tunnels. However, the approximation would not work for low values of the duration of the transient, because the equivalent depth would be smaller than the radius of the tunnel. is lower than We observe that the approximate value of the accurate one, which means that the value of the thermal reis not on the safe side sistance of the external environment when this approximation is used. However, investigations by the authors have shown that the error decreases rapidly with a decrease of the tunnel diameter and an increase of the depth of laying.

V. DAILY, WEEKLY, AND YEARLY LOAD VARIATIONS

When the cable circuit is located at large depths, for example, in a deeply buried tunnel, the heating time constant is very large, and in addition to daily load variations, the load changes over a week or a year could be considered. Representation of daily, weekly, and yearly load cycles is discussed next.

(15)


A. Daily Load Variations

The right-hand-side of (24) can be interpreted as follows. , the temperature changes acInside the circle of diameter cording to the peak value of the losses. Outside this circle, it changes with the average losses. at From (23), we observe that the fictitious diameter which the effect of loss factor commences is a function of the diffusivity of the medium and the length of the loss cycle. In the majority of cases, the soil diffusivity will not be known. m /s can be used. This In these cases, a value of value is based on a soil thermal resistivity of 1.0 K m/W and a moisture content of about 7% of dry weight [see Section 5.4 of for a load [4] for more details on this subject]. The value of cycle lasting 24 h and with a representative soil diffusivity of m /s is 212 mm (or 8.3 in.). Expressions equivalent to (23) can be developed based on methodology applied in the IEC standards (Appendix A) or through solving heat-transfer equations (Appendix B). The resulting characteristic diameter is given by (25) ranging from 0.97 to 1.37 for cable diameters of up to with 100 mm. Hence, the IEC and Neher–McGrath approach can be considered to be equivalent in this case. For larger diameters increases with the heating (ducts and tunnels), the value of source diameter and is given by (see Appendix B)

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Neher and McGrath [6] proposed a simple method to account for the cyclic loading of a cable. Their approach requires a modification of the external thermal resistance of the cable. The underlying principles are discussed below. In order to evaluate the effect of a cyclic load upon the maximum temperature rise of a cable system, Neher [7] observed that one can look upon a heating effect of a cyclical load as a wave front that progresses alternately outwardly and inwardly in respect to the conductor during the cycle. He further assumed that, with the total joule losses generated in the cable equal to (W/m), the heat flow during the loss cycle is represented by plus a transient compoa steady component of magnitude nent , which operates for a period of time during each cycle. The transient component of the heat flow will penetrate the earth only to a limited distance from the cable, thus will be smaller than the corresponding thermal resistance which pertains to steady-state conditions. its counterpart Assuming that the temperature rise over the internal thermal cable resistance is complete by the end of the transient period , the maximum temperature rise at the conductor may be expressed as

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(21)

where is the apparent internal thermal resistance of the cable, defined as

where is the external thermal resistance with constant load, is the effective transient thermal resistance in the earth, and is the temperature rise due to dielectric losses (we will omit them from now on). Further, Neher [7] assumed that the last thermal resistance in (21) may be represented with sufficient accuracy by an expression of the general form (22)

in which constants and were evaluated empirically to best fit the temperature rises calculated over a range of cable sizes. Using measured data, Neher obtained the following values for and when is expressed the constants: in hours and is expressed in m /s. Introducing the notation (23)

expressed in meters, the external thermal resistance in with (21) can be written as

(24) where

is the loss factor.

(26)

Alternative expressions for Heinhold [8]

(in millimeters) are given by

(27) (28) (29)

is the length of the period and where day. Heinhold assumes the following relationship:

Thus, when we take the recommended value of the soil thermal diffusivity of m/s (the corresponding value of the thermal resistivity equal to 1 K m/W), (27) is equivalent to the Neher’s expression. The choice of the method to compute the fictitious diameter depends partially on the analyst’s preferences and partially on the available information. If the daily load cycle variations are known, the IEC 60853 [2], [3] approach can be used. On the other hand, when a sinusoidal load shape can be assumed, either (23) or (25) or (27) can be applied. In other cases, IEC approach for load cycles where the shape is unknown and only the loss-load factor is known or (28) or (29) should be used, remembering that these are approximate equations. The following numerical example shows the results for all the formulae for sinusoidal load variations.

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TABLE II CABLE DIMENSIONS

TABLE III RESULTS ARE SUMMARIZED

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Consider three, single-core, 1000 mm Cu XLPE 123 kV cables with a PE jacket. Cables are in flat formation 1m underground spaced 0.2 m apart. Additional parameters are as follows: Soil thermal characteristics: ambient : 10 C-resistivity 1.0 m /s (for the Heinhold formula K m/W—diffusivity the value of 4.67 is used instead). For IEC calculations, the sinusoidal load curve is simulated by 24 steps as follows: with

The right-hand column “steps” in Table III is the result of 1-h steps superposition until convergence is reached. Hence, we can see that the approaches are really equivalent. Equations (27) to (29) are independent of the cable diameter. Investigations by Brakelmann [13] have shown that these equations are valid for cables with diameters between 5 and 150 mm. For larger ducts and tunnels, the expressions developed in Appendix B or discussed in the next section should be used.

Fig. 5. Characteristic diameter for cables in tunnel: the rows correspond to daily, weekly and yearly load cycles, respectively, and the columns to 0:4; 1:0 and 2.5 K1m/W, respectively. D is the tunnel diameter.

=

The external thermal resistance of the cable or tunnel located at large depth can be obtained from the following expression [8]–[11]:

B. Weekly and Yearly Load Variations

In the majority of practical cases, the load variations will exhibit a more complex pattern than the one described by a daily load cycle. For example, loading of cables is usually much lighter during the weekend than during the weekdays. For deeply buried cables, the yearly load variations will play a significant role because of the very long time constants at great depths. For cables in deep tunnels, the characteristic diameter can be obtained from the curves in Fig. 5 [9], [10]. Brakelmann used Fourier analysis to obtain those curves for tunnel diameters ranging from 2 m (the upper boundary of the region) to 5 m (lower boundary) for two shapes of the load cycle: sinusoidal (region bounded by straight lines) and rectilinear (region bounded by curved lines).

(30)

and correspond to daily, weekly and where subscripts yearly load variations and represent the external thermal resistances of the tunnel, daily, weekly, and yearly fictitious diameters, respectively. The characteristic diameters are given by (25)–(29) or (42) with the appropriate length of the period. VI. AMBIENT TEMPERATURE VARIATIONS

A sinusoidal variation of the air ambient temperature leads to a sinusoidal variation of the temperature in the ground, with a damping factor and a time delay, which both depend upon the soil diffusivity and the period.


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Fig. 6. Soil temperature daily variations for different depths.

The temperature at depth expressed as [12]

as a function of the time can be

(31)

Fig. 7. Installation of cables in tunnel.

A. Standard Computations The external thermal resistance of the tunnel is computed from the following expression [8]:

IE E Pr E oo f

where maximum ambient temperature, C;

duration of the cycle period (in seconds s); soil diffusivity, m /s.

day, C, and soil Fig. 6 illustrates (31) for m /s. It can be seen that for deeply buried diffusivity cables, the surrounding soil temperature is nearly constant. VII. EFFECT ON CABLE AMPACITY

The various approaches described in the previous chapters will be used to illustrate the effect of the depth of the cable on its rating. We will compute the ratings of six circuits, each in trefoil formation located in a horizontal tunnel as shown in Fig. 7. The 15-kV XLPE cables with concentric neutral wires bonded at both ends have the following parameters:

where:

height and width of the depth of soil above the tunnel plus the thickness of tunnel, the tunnel wall (it is assumed that the tunnel wall has the same thermal resistivity as the soil). K m/W and the ampacity of 258 A. This gives B. Equivalent Depth Scenario

Let us assume that the time horizon of interest is 40 years m /s. For the and soil thermal diffusivity equals to cable system considered here, the equivalent depth of the tunnel can be obtained by applying the approximation given by (10), yielding the equation shown at the bottom of the page. The external thermal resistance of the tunnel is equal to 0.607 K m/W, and the resulting ampacity is 267A.

C. Daily, Weekly, and Yearly Load Variations

The tunnel has a square cross section with a height of 2.0 m with 0.5 m concrete walls and 18 m of soil above the roof. The thermal resistivity of the soil is 1.0 K m/W and the ambient temperature is 15 C.

We will assume the following average loss factors for daily, weekly, and yearly load variations:

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Assuming rectilinear load shapes, the following characteristic diameters correspond to these values (see Fig. 5):

measure of the equivalent square current between and h prior to the expected time of maximum conductor temperature; iratio of the core temperature at time hours to the core temperature at steady state and is equal to [4]

The external thermal resistances between characteristic diameters and the earth surface are equal, respectively to

for (33) and (34)

Considering now daily, weekly, and yearly load cycles, from (30), we have

with the subscripts and corresponding to the core and the external cable surface, respectively. are the conductor losses and represents the total joule losses of the cable; cable attainment factors. For the long durations considered here, we can assume and is computed from (3).

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and

The cable rating corresponding to this value of the external thermal resistance of the tunnel is equal to 313 A, a 21% increase compared with the standard calculations.

and

Remembering that approximated by

VIII. CONCLUSION

(35)

The effect of laying cables at great depth has a profound influence on its rating. The influence depends to a large extent on the ratio of the depth of laying to the cable/duct/tunnel diameter and on the time horizon being considered. This paper presents several new developments on ampacity calculations of such cables. Fictitious diameters computed according to Heinhold’s or Brakelmann’s formulae for nonsinusoidal shapes are slightly higher than diameters resulting from the IEC formula. recommended for unknown load shape. The numerical examples presented in the paper show that the effect can be particularly significant if cyclic load variations over the week and the year are considered.

Introducing a notation into (35), we obtain

and substituting (33)

(36)

Because (6) representing

, (36) has the same form as (21) with and thus can be approximated by (37)

Using approximation with an exponential integral (valid for may also be written as an infinite thin wire), (38)

APPENDIX A CHARACTERISTIC DIAMETER—IEC STANDARD

Following the IEC approach and taking the six-hour-load variation before the maximum conductor temperature is obtained, the maximum cable temperature may be written as (see (5.25) in [4]):

Comparing the right-hand-sides of (37) and (38), we obtain (25). More generally, for a cycle of length hours, (39) which leads to (25) with

(32) where

, (32) can be

.

APPENDIX B CHARACTERISTIC DIAMETER FOR SINUSOIDAL LOAD AND LARGE TUNNEL DIAMETER


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IE E Pr E oo f

Fig.8. Relationship between fictitious and cable diameters.

The approximations considered above assumed that a cable is represented by an infinitely small wire. In the developments presented below, this assumption is dropped and, as a consequence, the cable diameter influences the diameter of the area affected by load variations. This is particularly important for cables in tunnels, where the tunnel diameter replaces the diameter of the cable. and period ), the For a sinusoidal load (with magnitude temperature around the cable/tunnel may be expressed, with the complex notation, as

Fig. 9. Relationship between fictitious and tunnel diameters for three values of soil diffusivity.

TABLE IV VALUE OF

K

(40)

with

where

Figs. 8 and 9 show the relationships between fictitious diameter and the cable/tunnel diameters. The relationships are almost linear with the fitting equations shown in the graphs. The following relationship can be applied to all curves:

cable/tunnel radius;

is the soil thermal resistivity, diffusivity; and

is the soil

are modified Bessel functions.

The maximum cable/tunnel surface temperature can be written as

(41)

(42)

up to 3 m, for This leads to an error less than 3% for every type of variations, with soil diffusivity ranging from to m /s. Equation (42) is the most general expression for fictitious diameter, covering virtually all practical cases. For tunnels with large diameters, daily and weekly variations lead to characteristic diameters close to the tunnel diameter.

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For cables directly buried,

can be approximated with

[14] M. Matsumura, K. Fukuda, E. Fujiwara, T. Shiro, M. Watanabe, Y. Sakaguchi, and T. Ooimo, “Transmission capacity design of underground power cables installed in deep tunnel,” presented at the Power Eng. Soc. General Meeting, Jun. 18–22, 2006.

(43) Eric Dorison is Design Engineer in the field of underground cables, within the Research and Development Department Electricité de France, where he has been since 1978. For several years, he has been Project Manager for technoeconomical optimization of bulk power transmission underground lines, using VHV synthetic cables. He is currently involved in cable thermal rating matters and development of a health index dedicated to underground links as an asset management tool. Mr. Dorison is a member of several IEC and

The is given in Table IV and is not far from the value of 1.02 given by Neher. REFERENCES

CIGRE working groups.

George J. Anders (M’74–SM’84–F’99) received the M.Sc. degree in electrical engineering from the Technical University of Lodz, Lodz, Poland, in 1973, and the M.Sc. degree in mathematics and Ph.D. degree in power system reliability from the University of Toronto, Toronto, ON, Canada, in 1977 and 1980, respectively. Since 1975, he has been with Ontario Hydro as a System Design Engineer in the Transmission System Design Department of the System Planning Division and as a Principal Engineer in Kinectrics, Inc., (a successor company to Ontario Hydro Technologies). Dr. Anders is the author of two books on power cables “Rating of Electric Power Cables,” (IEEE Press, 1997 and McGraw-Hill, 1998) and Rating of Electric Power Cables in Unfavorable Thermal Environment (IEEE Press/Wiley). He is a registered Professional Engineer in the Province of Ontario.

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[1] Calculation of the Continuous Current Rating of Cables (100% Load Factor), IEC Std. 60287 (1969, 1982, 1994), First edition 1969, Second edition 1982, Third edition 1994–1995. [2] Calculation of the Cyclic and Emergency Current Ratings of Cables. Part 1: Cyclic Rating Factor for Cables up to and Including 18/30 (36) kV, IEC Std., (1985), Publication 853-1. [3] Calculation of the Cyclic and Emergency Current Ratings of Cables. Part 2: Cyclic Rating Factor of Cables Greater Than 18/30 (36) kV and Emergency Ratings for Cables of All Voltages, IEC Std., (1989), Publ. 853-2. [4] G. J. Anders, Rating of Electric Power Cables. Ampacity Computations for Transmission, Distributions and Industrial Applications, ser. IEEE Press Power Eng. Ser.. New York: IEEE Press, , 1997. [5] Calculation of Temperatures in Ventilated Cable Tunnels CIGRÉ WG Rep. 21.08, Aug. 1992, Electra No. 143. [6] J. H. Neher and M. H. McGrath, “The calculation of the temperature rise and load capability of cable systems,” AIEE Trans., vol. 76, pt. 3, pp. 752–772, Oct. 1957, (1957). [7] J. H. Neher, “Procedures for calculating the temperature rise of pipe cable and buried cables for sinusoidal and rectangular loss cycles,” AIEE Trans., vol. 72, pt. III, pp. 541–545, June 1953, (1953). [8] L. Heinhold, Power Cables and Their Application. Part 1, 3rd ed. : Siemens Aktiengesellschaft, 1990

[Please provide location of publisher].

[9] H. Brakelmann, “Kabelbelastbarkeit bei Berücksichtigung von Tages und Wochenlastzyklen,” Elektrizitästwirtschaft, pp. 368–372, 1995a, Jg. 94, Heft 7. [10] H. Brakelmann, “Kabelbelastbarkeit im Unbelüfteten Tunnel,” Elektrizitästwirtschaft, pp. 368–372, 1995b, Jg. 94, Heft 26. [11] G. J. Anders, Rating of Electric Power Cables in Unfavourable Thermal Environment, ser. IEEE Press Power Eng. Ser.. New York: Wiley, 2005. [12] H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. Oxford, U.K.: Oxford . [13] H. Brakelmann, Balastbarkeiten der Energiekabel—Berechnungsmetoden und Parameteranalysen. Berlin/Offenburg: VDE-Verlag, 1989.

Frederic Lesur was a Research Engineer with Silec and was involved in the development of 400 kV underground lines in modeling and engineering tools design. He moved to EDF utility in 1999, and was responsible for the cable system testing facility of Les Renardières. He has been working in he engineering branch of RTE, the French Transmission System Operator, since 2007. Mr. Lesur is the Secretary of the technical committee of Jicable conference and is involved in various CIGRÉ activities.

Ampacity Calculations for Deeply Installed Cables

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