1
Major Factors Affecting Cable Ampacity Francisco de León, Senior Member, IEEE
Abstract—This paper presents a parametric study of the major
II. UNDERGROUND CABLE INSTALLATIONS
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.
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.
Index Terms — Ampacity. Cable Rating. Underground Cables. Cables in Air. Cables in Riser Poles. IEC Standards. CYMCAP. Neher-McGrath.
The size of the cable has been varied from 250 MCM to 1500 MCM. Figure 1 shows the results for single-point and twopoint bonding.
A. Varying Conductor Caliber
600
I. INTRODUCTION
F. de León is with CYME International T&D, 1485 Roberval, Suite 104, StBruno, Quebec, Canada, J3V 3P8 (e-mail:
[email protected]).
1-4244-0493-2/06/$20.00 ©2006 IEEE.
Ampacity [A]
500
Single-Point Bonded
400
Two-Point Bonded
300 200 100 0 0
250
500
750
1000
1250
1500
1750
Conductor Size [MCM] Figure 1. Ampacity versus conductor size for two bonding types
600 500
Ampacity [A]
A
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 for underground 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 of solar 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.
Directly Buried
400
6% Duct Bank
300 200 100 0 0
250
500
750
1000
1250
1500
1750
Conductor Size [MCM] 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
2
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 thermal resistivity 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.
reductions. TABLE 1. VARIATION OF AMPACITY FOR TREFOILS WITH DIFFERENT BONDING
Bonding Arrangement Single-Point Two-Point Cross Bonding
Equal Section Lengths AM = 1.5 / AN = 1.25 AM = 2.0 / AN = 1.5 AM = 3.0 / AN = 2.0
464 455 441 416
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. 1000 Single P oint = Cros s Bo nded
800
800
Ampacity
Two P oint (trans po s ed)
600 Ampacity [A]
Ampacity [A] 464 394
400
600 Two P o int (no t trans po s ed)
400 200
1000 MCM
Standing Vo ltage / km
0 0
200 500 MCM 0 0
1
2
3
4
5
0.1
0.2 0.3 0.4 0.5 Distance be twe e n phase s [m]
0.6
Figure 4. Ampacity versus distance for different bonding arrangements (flat formation installation)
Soil Thermal Resistivity [°K-W/m]
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
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 is greater 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
3
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
1000 Steel
1000 MCM
1000 Single-Point Bonding
800
Two-Point Bonding
600 400 200 0 0
250
500
750
1000
1250
1500
1750
Conductor Size [MCM] Figure 7. Ampacity as a function of conduit diameter
B. Varying the Solar Radiation Intensity The effects of the variation of the intensity of solar radiation 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).
600 1200
400
500 MCM
200 0 0
100
200
300
400
0 .2 0.4 0 .6 0 .8
1000
PVC
500
600
Duct Internal Diameter [mm]
Ampacity [A]
Ampacity [A]
800
1200
Ampacity [A]
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.
800 600 400 200
Figure 6. Ampacity as a function of conduit diameter
0 0
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.
250
500
750
1000
1250
1500
Solar Radiation Inte nsity [W/m2] 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 noncontinuous 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.
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.
1200 Ampacity [A]
1000 800 600 400 200 0 Figure 9. Standardized arrangements for cables in air
0
0.1
TABLE 2. AMPACITY FOR CABLES IN AIR
1033 838 714 772 772 947 910 544
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 has the 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
0.5
0.6
0.5
0.6
Figure 10. Ampacity as function of separation
1000 Ampacity [A]
Ampacity [A]
800 600 400 200 0 0
0.1
0.2 0.3 0.4 Separation [m]
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. 1200 1000 Ampacity [A]
Arrangement Number 1 2 3 4 7 8 9 10
0.2 0.3 0.4 S eparation [m]
800
Vented Ends Vented Top
600 400
Not Vented
200 0 100
200 300 400 500 Inte rnal Diame te r of Duct [mm]
Figure 12. Varying the internal diameter of the conduit for different
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V. CONCLUSIONS
1400
Ampacity [A]
1200
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, a large 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).
1000 Vented Ends
800 600 Not Vented
400 200 0 0
0.2
0.4
0.6
0.8
1
Surface Absorption Coefficient Figure 13. Ampacity as function of the surface absorption coefficient of solar radiation
1400
Ampacity [A]
1200 1000 Vented Ends
800 600 400
NotVented
200
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).
0 0
500
1000
1500
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 the absorption 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.
2000 2
Intensity of Solar Radiation [W/m ] Figure 14. Ampacity as function of intensity of solar radiation
VI. REFERENCES 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). 800
Ampacity [A]
700 600 500 400 300 200 100 0 0
5
10 15 Wind Speed [m/s]
Figure 15. Ampacity as function wind speed
20
[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 25 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 0 Ambient temp = 25°C
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.
1 2 3 4 5 6
Native Soil = 1.00 °C-m/W
-6 Figure 16. Construction and dimensions of the concentric neutral cable used for most simulation
-4
-2
0
2
4
6
Figure 18. Four directly buried trefoils (distances in feet)
0 Ambient temp = 25°C 2
Voltage = 15.0 kV Cond. area = 0.7854 inch (1000 KCMIL)
1
Figure 16. Construction and dimensions of the concentric neutral cable used for most simulations
2
TABLE 3. CONDUCTOR SIZES 3 External Diameter of Layer [inch]
Size
[MCM]
Shield
Insulation
Screen
C. Wires
Jacket
250
Conductor 0.5748
0.6148
1.6384
1.7927
1.9541
2.1510
500
0.8129
0.8629
1.8866
2.0409
2.2023
2.3992
750
0.9980
1.0480
2.0716
2.2417
2.4448
2.6417
1000
1.1519
1.2119
2.2355
2.4056
2.6088
2.2805
1250
1.2889
1.3489
2.3726
2.5426
2.7458
2.9426
1500
1.4118
1.4718
2.4954
2.6655
2.8686
3.0655
Native Soil = 1.00 °C-m/W
-3
0
1
2
3
Figure 19. Flat formation for the parametric study of cable separation (distances in feet)
1 2 3 4 5 6 Native Soil = 1.00 °C-m/W
-4
-1
0
Ambient temp = 25°C
-6
-2
-2
0
2
4
6
Figure 17. Duct bank installation of a 2X2 duct bank with four trefoils (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.
