factors affecting cable ampacity

8/19/2019 Factors affecting cable ampacity

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Abstract—This paper presents a parametric study of the major

factors affecting cable ampacity calculations. The current

carrying capacity (or ampacity) of a cable depends on many of

the installation properties and conditions. In this paper the

effects on ampacity of conductor size, ambient temperature,

bonding arrangement, duct size, soil thermal resistivity,

resistivity and size of backfill (or duct bank) and depth of

installation for underground installations are presented. For

cables air the effects on ampacity of the intensity of solar

radiation, the spacing from the wall and the grouping of cables

are analyzed. For riser pole installations the effect of the solar

radiation, wind speed, ventilation and diameter of the duct are

shown.

Index Terms — Ampacity. Cable Rating. Underground

Cables. Cables in Air. Cables in Riser Poles. IEC Standards.

CYMCAP. Neher-McGrath.

I. INTRODUCTION

MPACITY (or current-carrying capacity) of a cable is

greatly affected by the installation conditions and

material properties. In this paper a parametric study of the

major factors affecting ampacity is presented. All simulations

were performed using the commercial ampacity program

CYMCAP, which works in accordance to the IEC standards;

see references [1] to [7]. The IEEE Standard 835-1994 [8]

gives very similar results to those of the IEC Standards forunderground cables. Differences are more noticeable for

cables in air. Both the IEC and IEEE Standards are based on

the Neher-McGrath method published in 1957 [9]. The

reader is referred to [10] for a thorough review the theory of

ampacity calculations, the historical developments and the

differences between the two methods.

For underground installations the effects on cable ampacity

due to the following parameters is studied: conductor size,

native soil thermal resistivity, bonding type, directly buried

versus duct bank installation and duct size.

For cables in air the effect on cable ampacity of the

following parameters is studied: conductor size, intensity ofsolar radiation, distance to the wall and cable grouping.

For cables installed in riser poles the effect on ampacity of

the following installation parameters is studied: conduit size,

surface absorption coefficient of solar radiation, wind speed,

type of ventilation, intensity of solar radiation and length of

the riser pole.

F. de León is with CYME International T&D, 1485 Roberval, Suite 104, St-

Bruno, Quebec, Canada, J3V 3P8 (e-mail: [email protected]).

II. UNDERGROUND CABLE INSTALLATIONS

Several installation features were varied to study their

effect in the ampacity. In the Appendix the reader can find the

data of cables and installations used to perform the parametric

studies. The ambient temperature was always 25°C while the

target temperature has been set to 90°C for all ampacity

calculations. The soil thermal resistivity is 1.0 [°K-W/m]

except when indicated. All cases are balanced with a unity

load factor.

A. Varying Conductor Caliber

The size of the cable has been varied from 250 MCM to 1500

MCM. Figure 1 shows the results for single-point and two-

point bonding.

0

100

200

300

400

500

600

0 250 500 750 1000 1250 1500 1750

Conductor Size [MCM]

A m p a c i t y [ A ]

Single-Point

Bonded

Two-Point

Bonded

Figure 1. Ampacity versus conductor size for two bonding types

0

100

200

300

400

500

600

0 250 500 750 1000 1250 1500 1750



Duct

Bank

Directly

Buried 6 %

Figure 2. Ampacity versus conductor size for directly buried and duct bank

installations (two-point bonding)

From the results presented in figures 1 and 2 one can

appreciate that doubling the conductor cross-sectional area

does not double the ampacity. Although the dc resistance of a

Major Factors Affecting Cable Ampacity Francisco de León, Senior Member, IEEE

A

1-4244-0493-2/06/$20.00 ©2006 IEEE.



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cable reduces in inverse proportion to the conductor area, for

ac excitation the skin and proximity effects play an important

role. The larger the cross sectional area of the conductor the

larger the effects of the induced eddy currents in single-point

bonded installations and the circulating currents in two-point

bonded installations.

Figure 2 shows that directly buried cables have a slightly

higher ampacity, about 6%, than cables installed in PVC

conduits. The reason is that the PVC has a higher thermalresistivity than the native soil.

B. Varying Soil Thermal Resistivity

The thermal resistivity of the native soil using 4-trefoils

(for 500 and 1000 MCM) directly buried cables was varied

from 0.4 to 4.0 [°K-W/m]; this covers the conditions for most

installations. The computed ampacities are presented in

Figure 3. One can note that the ampacity reduces as the

thermal resistivity of the soil increases and seems to follow a

hyperbolic function.

0

200

400

600

800

0 1 2 3 4 5

Soil Thermal Resistivity [°K-W/m]


1000 MCM

500 MCM

Figure 3. Ampacity as a function of soil thermal resistivity

C. Varying Bonding and Transposition

Figure 1 shows that two-point bonded cables have a smaller

ampacity than single-point bonded cables. This is due to the

large circulating currents in (sheaths or) concentric neutrals.

The ampacity reduction effect of the circulating currents

becomes more significant for larger cable sizes were larger

circulating currents are present in the sheaths or concentric

neutrals.Table 1 shows the calculated ampacity for several bonding

arrangements for the installation of the 4 trefoils specified in

the Appendix using 1000 MCM cables. The ampacity for a

two-point bonded installation is about 15% smaller than that

of the single-point bonded case. The circulating currents

cause this ampacity reduction. Cross bonding the cables with

equal section lengths completely eliminates the circulating

currents. However, in practice the lengths cannot be identical.

Table 1 shows how for different ratios AM (longest/shortest)

and AN (longer/shortest) one obtains different ampacity

reductions.

TABLE 1. VARIATION OF AMPACITY FOR TREFOILS WITH DIFFERENT BONDING

Bonding Arrangement Ampacity [A]

Single-Point 464

Two-Point 394

Equal Section Lengths 464

AM = 1.5 / AN = 1.25 455

AM = 2.0 / AN = 1.5 441Cross Bonding

AM = 3.0 / AN = 2.0 416

The same effects can be appreciated in flat formation

installations. Figure 4 summarizes the ampacity results for the

flat formation installation shown in the Appendix. Different

bonding arrangements were used and the distance between

cables was varied.

0

200

400

600

800

1000

0 0.1 0.2 0.3 0.4 0.5 0.6Distance between phases [m]

A m p a c i t y

Single P oint = Cross Bonded

Two P oint (transpos ed)

Two P oint (not transpos ed)

Standing Voltage / km

Figure 4. Ampacity versus distance for different bonding arrangements (flat

formation installation)

The ampacity for single-point bonding and cross bonding is

the highest and increases with the separation of phases. This

is due to a reduction in the induced heating between cables.

While cross bonding cables is more expensive, single-point

bonded cable installations produce standing voltages in the

ungrounded terminal. Those voltages increase with phase

separation (see the bottom curve in Figure 4).

Two-point bonded installations not only have reduced

ampacity as compared with single-point bonded installation,

but the ampacity has the initial tendency to reduce even

further as the separation between the phases increases. This

is because the effect of the larger circulating currents isgreater than the reduction of induced heating. There is a point,

however, where the effect of the increased circulating currents

is overcompensated by the reduction of mutual heating effects

and the ampacity augments slightly as the phases separate.

D. Varying the Number of Neighboring Circuits

Induced heating from neighboring cables produces

important reductions in cable ampacity. Consider the duct

bank installation, with four trefoil circuits, shown in the



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Appendix. When only one trefoil circuit is present the

computed ampacity is 650 A. When a second trefoil is added

the ampacity reduces to 575 A while adding a third trefoil

reduces the ampacity to 512 A. When the last (fourth) circuit

is added the ampacity becomes only 464 A; this is about 70%

of the case with only one cable. Further reductions are

expected as the number of cables heating each other

increases. Frequently, there is the need to account for the

heating (or cooling) induced from neighboring heat sources(sinks) such as steam or water pipes running parallel to the

cable installation. It is not possible, however, to give rules of

thumb or to perform parametric studies because the

installation possibilities are infinite.

E. Varying the Conduit Size

The diameter of a PVC conduit buried in native soil was

varied from a very tight fit to very large size; see Figure 5.

The plot of Figure 6 shows that the ampacity increases

slightly as the diameter of the conduit increases. For steel

conduits the slope is even smaller than for PVC conduits.

Figure 5. Smallest versus largest conduit – 160 mm & 500 mm

0

200

400

600

800

1000

0 100 200 300 400 500 600Duct Internal Diameter [mm]


500 MCM

1000 MCMSteel

PVC

Figure 6. Ampacity as a function of conduit diameter

III. CABLES IN AIR

A. Varying Conductor Caliber

The conductor caliber has been varied from 250 MCM to

1500 MCM. Figure 7 shows the results for single-point and

two-point bonding for a solar radiation intensity of 1000

W/m2, which is typical for North America. One can

appreciate that the ampacity increases with the caliber of the

conductor at a larger rate that for underground cables;

compare the results of Figure 7 with those of Figure 1.

0

200

400

600

800

1000

1200

0 250 500 750 1000 1250 1500 1750


A m p a c i t y [ A ] Single-Point Bonding

Two-Point Bonding

Figure 7. Ampacity as a function of conduit diameter

B. Varying the Solar Radiation Intensity

The effects of the variation of the intensity of solarradiation on cable ampacity are shown in Figure 8. One can

appreciate, as expected, that the ampacity of the cable reduces

as the intensity of solar radiation increases. The behavior for

several surfaces having different coefficients of solar

absorption is also compared in the figure. As the surface

absorption coefficient increases a larger ampacity derate is

obtained for a given solar radiation intensity.

The solar radiation intensity, for not shaded installations,

depends on the geographical location of the installation

(latitude and altitude) and the day of the year and hour of the

day. The surface absorption coefficient depends on the

material type and color of the cable's external surface (the

surface exposed to the sun).

0

200

400

600

800

1000

1200

0 250 500 750 1000 1250 1500Solar Radiation Inten sity [W/m2]


0. 2

0.4

0. 6

0. 8

Figure 8. Variation of ampacity with solar radiation intensity for several surface

absorption coefficients

C. Varying the Distance to the Wall

In the IEC standard 287-2-1, reference [4], there are several

arrangements for cables in air installations using non-

continuous brackets, ladder supports or cleats; see Figure 9.

Table 2 shows the effect on ampacity of the distance from the

cable to the wall. The 1000 MCM concentric neutral cable,



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described in the Appendix, was used to compute the

ampacities.

Figure 9. Standardized arrangements for cables in air

TABLE 2. AMPACITY FOR CABLES IN AIR

Arrangement

Number

Ampacity [A]

1 1033

2 838

3 714

4 772

7 772

8 947

9 910

10 544

Comparing the ampacity of cases 1 with 9 and 3 with 10

one can see that cable installations near the wall show a

substantially smaller ampacity than those separated from the

wall. For the single-phase the obtained reduction is 12%,

while for the trefoil the reduction is 24%. One can also note

from cases 4 and 7 that there is no influence when installing

the cables vertically or horizontally. Grouping the cables hasthe effect, as expected, of reducing ampacity; compare cases

1, 2 and 4.

D. Groups of Cables

The effect of the separation between cables for groups of

cables was analyzed using the 1000 MCM cable (single-point

bonded) described in the Appendix. Figure 10 shows the

results for flat formations and Figure 11 the results for

trefoils. In both cases when the cables are grouped

horizontally there is a transition when (e / De) = 0.75. The

ampacity before and after the transition point is independent

of the separation between cables. When the cables are

grouped horizontally and vertically as well, one can see two

smoother transition points.

IV. CABLES IN RISER POLES

In Figure 12 the variation of ampacity as a function of the

internal diameter is presented. The variation is shown for

three different ventilation conditions. As expected, ventilation

on both-ends gives the greatest ampacity followed by the case

vented at the top. In all three cases the ampacity is highest

with very tight ducts, i.e. when the internal diameter of the

duct is equal to the minimum circumference that encloses the

trefoil formation. As the diameter of the ducts increases the

ampacity reduces reaching a minimum and then slowly rises.

Figure 10. Ampacity as function of separation

Figure 11. Ampacity as function of separation

Figure 13 shows the variation of ampacity with the surface

coefficient of solar absorption of the external surface of the

installation (cable or duct). One notices that the ampacity

reduces almost linearly with an increase of the surface

coefficient of solar absorption. Figure 14 shows the variation

of ampacity as a function of the intensity of solar radiation.

The ampacity reduces in a quasi-linear fashion from shaded

conditions as the intensity of solar radiation increases.

0

200

400

600

800

1000

1200

100 200 300 400 500

Internal Diamete r of Duct [mm]

A m p a c i t y [ A

]

Not Vented

Vented Ends

Vented

Top

Figure 12. Varying the internal diameter of the conduit for different

0

200

400

600

800

1000

1200

0 0.1 0.2 0.3 0.4 0.5 0.6Separation [m]


0

200

400

600

800

1000

0 0.1 0.2 0.3 0.4 0.5 0.6

Separation [m]




5

0

200

400

600

800

1000

1200

1400

0 0.2 0.4 0.6 0.8 1

Surface Absorption Coefficient


Vented Ends

Not Vented

Figure 13. Ampacity as function of the surface absorption coefficient of solar

radiation

0

200

400

600

800

1000

1200

1400

0 500 1000 1500 2000

Intensity of Solar Radiation [W/m2]


Vented Ends

NotVented

Figure 14. Ampacity as function of intensity of solar radiation

Figure 15 shows a plot of ampacity versus wind speed. The

ampacity increases with an increase of wind speed. However,the ampacity increase is larger at the lower end. Thus

increasing the wind speed form 0 to 5 m/s has a large effect

than increasing it from 15 o 20 m/s. The length of the riser

pole was varied from 1 to 20 meters and the ampacity did not

show any significant variation (results are not shown).

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25Wind Speed [m/s]

A m p a

c i t y [ A ]

Figure 15. Ampacity as function wind speed

V. CONCLUSIONS

A. Underground Cable Installations

The three major factors affecting ampacity in underground

cable installation are: cable caliber, soil thermal resistivity and

bonding method. Doubling the conductor cross-sectional area

does not double the ampacity; see Figures 1 and 2. The soil

thermal resistivity plays a very important role in the ampacity

of an installation. Keeping all other conditions unchanged, alarge variation on the soil thermal resistivity can affect the

ampacity in more than 50% (Figure 3). Depending on the

particularities of the installation, bonding type can also

account for up 50% of the ampacity (Figure 4).

B. Cables in Air

For cables in air the three major factors affecting cable

ampacity are: conductor size, the cable grouping and the

distance to the wall. Doubling the conductor cross-sectional

area does not double the ampacity, but the "reduction effect"

is smaller than that of underground cables. Ampacity is less

sensitive to the bonding type and somehow dependent on the

intensity of solar radiation especially for large values of theabsorption coefficient of solar radiation. However, ampacity

is very much dependent on the distance from the cable to the

wall and on cable groping; see table 2 and Figures 10 and 11.

C. Cables in Riser Poles

The ampacity of cables in riser poles greatly depends on the

diameter of the guard, the intensity of solar radiation and the

surface coefficient of solar absorption (Figures 12, 13 and

14). It is somehow dependent on the wind speed (Figure 15).

VI. REFERENCES

[1] Electric Cables – Calculation of the current rating – Part 1: Current rating

equations (100% load factor) and calculation of losses – Section 1:

General. IEC Standard 287-1-1 (1994-12).

[2] Electric Cables – Calculation of the current rating – Part 1: Current rating

equations (100% load factor) and calculation of losses – Section 2: Sheath

eddy current loss factors for two circuits in flat formation. IEC Standard

287-1-2 (1993-11).

[3] Electric Cables – Calculation of the current rating – Part 2: Thermal

resistance – Section 1: Calculation of the thermal resistance. IEC Standard

287-2-1 (1994-12).

[4] Electric Cables – Calculation of the current rating – Part 2: Thermal

resistance – Section 2A: A method for calculating reduction factors for

groups of cables in free air, protected from solar radiation. IEC Standard

287-2-2 (1995-05).

[5] Electric Cables – Calculation of the current rating – Part 3: Sections on

operating conditions – Section 1: Reference operating conditions and

selection of cable type. IEC Standard 287-3-1 (1995-07).

[6] Calculation of the cyclic and emergency current rating of cables – Part 1:

Cyclic rating factor for cables up to and including 18/30 (36) kV. IEC

Publication 853-1 (1985).

[7] Calculation of the cyclic and emergency current rating of cables – Part 2:

Cyclic rating of cables greater than 18/30 (36) kV and emergency ratings

for cables of all voltages. IEC Publication 853-2 (1989-07).

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

[9] J.H. Neher and M.H. McGrath, “The Calculation of the Temperature Rise

and Load Capability of Cable Systems”, AIEE Transactions Part III -

Power Apparatus and Systems, Vol. 76, October 1957, pp. 752-772.

[10] George J. Anders, " Rating of Electric Power Cables: Ampacity

Computations for Transmission, Distribution, and Industrial

Applications, IEEE Press / McGraw Hill, 1997.



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VII. APPENDIX: CABLE AND INSTALLATION DATA

Figure 16 describes the 15 kV, 1000 MCM, concentric neutral cable

used in this paper. The cables with different calibers used in the

parametric study have the same layers with different sizes; see

Table 3. Figure 17 illustrates the installation used in this paper with

four trefoil formations installed in a 2×2 duct bank. The directly

buried case is shown in Figure 18 and the flat formation is shown in

Figure 19.

Figure 16. Construction and dimensions of the concentric neutral

cable used for most simulation

Figure 16. Construction and dimensions of the concentric neutral cable used for

most simulations

TABLE 3. CONDUCTOR SIZES

External Diameter of Layer [inch]S i z e

[ M C M ] C o n d u c t o r S h i e l d I n s u l a t i o n S c r e e n C . W i r e s J a c k e t

2 5 0 0 . 5 7 4 8 0 . 6 1 4 8 1 . 6 3 8 4 1 . 7 9 2 7 1 . 9 5 4 1 2 . 1 5 1 0

5 0 0 0 . 8 1 2 9 0 . 8 6 2 9 1 . 8 8 6 6 2 . 0 4 0 9 2 . 2 0 2 3 2 . 3 9 9 2

7 5 0 0 . 9 9 8 0 1 . 0 4 8 0 2 . 0 7 1 6 2 . 2 4 1 7 2 . 4 4 4 8 2 . 6 4 1 7

1 0 0 0 1 . 1 5 1 9 1 . 2 1 1 9 2 . 2 3 5 5 2 . 4 0 5 6 2 . 6 0 8 8 2 . 2 8 0 5

1 2 5 0 1 . 2 8 8 9 1 . 3 4 8 9 2 . 3 7 2 6 2 . 5 4 2 6 2 . 7 4 5 8 2 . 9 4 2 6

1 5 0 0 1 . 4 1 1 8 1 . 4 7 1 8 2 . 4 9 5 4 2 . 6 6 5 5 2 . 8 6 8 6 3 . 0 6 5 5

Figure 17. Duct bank installation of a 2X2 duct bank with four trefoils (distances

in feet)

Figure 18. Four directly buried trefoils (distances in feet)

Figure 19. Flat formation for the parametric study of cable separation (distances

in feet)

VIII. BIOGRAPHY

Francisco de León (S’86, M’92, SM’02) was

born in Mexico City in 1959. He received the

B.Sc. and the M.Sc. (summa cum laude) degrees in

Electrical Engineering from the National

Polytechnic Institute (Mexico), in 1983 and 1986

respectively, and obtained his Ph.D. degree from

the University of Toronto, Canada, in 1992. He

has held several academic positions in Mexico and

has worked for the Canadian electric industry.Currently working with CYME International T&D

in St. Bruno (Quebec, Canada), he develops

professional grade software for power and

distribution systems and is the leading technical support of CYMCAP, CYME's

cable ampacity program. He has published over a dozen papers in refereed

journals (IEEE/IEE), which have been cited over 100 times in journals listed in

the Science Citation Index.

-6 -4 -2 0 2 4 6

0

1

2

3

4

5

6

Ambient temp = 25

C

Native Soil = 1.00 C-m/W

-3 -2 -1 0 1 2 3

Ambient temp = 25

C


0

1

2

3

Voltage = 15.0 kV Cond. area = 0.7854 inch2 (1000 KCMIL)

-6 -4 -2 0 2 4 6

0

1

2

3

4

5

6

Ambient temp = 25

C


factors affecting cable ampacity

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