Cable Ampacity Tables for Direct Current Traction Power Systems

R. W. Benjamin Stell, P.E. Parsons Brinckerhoff, Inc.

Boston, Massachusetts

ABSTRACT Feeder cables in direct current (dc) traction power systems carry load currents that vary greatly in magnitude and duration. These load currents change significantly with time of day in reasonably predictable, cyclical patterns. Traction power cables are often installed in underground duct banks that are either larger or configured differently than the duct banks included in available cable "ampacity" (rating) tables. In addition, the few commonly available cable ampacity tables were not developed for dc traction power application, and can provide overly conservative results when so applied. These reasons contribute to the difficulty of selecting the most cost-effective cable size and quantity for a traction application, or for determining the conditions under which existing cables will be overloaded. This paper contains underground cable ampacity tables developed specifically for dc traction power systems. The tables focus on the large cable sizes typically utilized for dc traction power systems, and include a wide variety of duct bank configurations. The calculation of daily load factor and daily load profile as applied to traction power systems is discussed and incorporated into the tables. Typical daily load factors derived from transit system train schedule and consist data are provided for reference. INTRODUCTION The value of current that a power cable can safely conduct under a specific set of conditions is known as its current-carrying capacity, also termed its "rating", or just "ampacity". The process of analytically determining the ampacity of multiple underground power cables is a challenging technical exercise involving the application of heat transfer theory. Considerable research performed during the past 100 years has resulted in the development of sophisticated techniques for calculating cable

ampacity [endnote 1]. These methods are exemplified by the International Electrotechnical Commission (IEC) Standards 287 and 853, and by their North American precursor, the Neher-McGrath Model [2]. To avoid the complex calculations associated with these methods, engineers often refer to published tables to obtain cable ampacities. The available tables, however, are based on installation and material assumptions which may not be readily apparent or even applicable to a given installation, particularly a dc traction power system duct bank. In addition, the available ampacity tables for underground installations were developed for application to balanced three-phase alternating current (ac) systems, and for a limited number of sizes and configurations more oriented to utility and industrial ac power systems. CABLE AMPACITY TABLE DEVELOPMENT CONSIDERATIONS In a 2003 APTA paper entitled “Cable Rating Considerations for Direct Current Traction Power Systems” [3], important issues involved with the rating of cables in underground duct banks were discussed. For the sake of brevity, these will not be repeated here, but the reader is encouraged to review them before making use of the tables presented in this paper. Additional considerations are addressed below. Earth Thermal Resistivity Current techniques for calculating the temperature rise of underground cables involves modeling the various cable layers, ducts, duct bank materials and backfill, and the surrounding earth by their equivalent “thermal resistances”. Earth thermal resistivity is the resistance of the earth surrounding a duct bank to heat transfer, somewhat analogous to insulation “R-value”. It is not related to earth electrical resistivity, although it also varies with moisture content, but to a much lesser extent. Earth thermal resistivity is typically expressed in units of

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°C-cm/Watt in the USA, which is frequently referred to as “RHO”, the Greek symbol normally used to represent resistivity, ρ. Available ampacity tables cite a typical value of 90 °C-cm/Watt (“RHO 90”) to be used when the actual value of earth thermal resistivity is not known; ampacities at higher and lower values of RHO 120 and RHO 60 are also provided for use where appropriate (NEC, ICEA Std. P-46-426, and IEEE Std. 835). Actual earth thermal resistivity may be determined from geotechnical soil borings or data from nearby projects. Field and laboratory measurements may also be made in accordance with IEEE Std. 442, IEEE Guide for Soil Thermal Resistivity Measurements. Determination and control of earth thermal resistivity is particularly important in the design of high voltage underground transmission circuits, which are often direct-buried (i.e., without concrete encasement). Considerable research has been performed in this area that may be of benefit to traction power system designers. Results of this research include the use of low-resistivity backfill materials to increase cable circuit ampacity, as well as the general recognition of concrete as an excellent low-resistivity, stable backfill/encasement material [4]. Load Factor Calculations

Load factor is defined as average load divided by peak load during a specific time interval which, for cables, is typically a 24 hour day. Daily load factors (DLF) are used in cable ampacity tables to account for the additional capacity that may be available when cables are not 100% loaded for an entire 24 hour period. Daily load factors for use in rating traction power cables can be derived from metered substation load data, or from load flow simulations. However, the author has found that daily load factors for specific locations may also be reasonably approximated from train schedule and consist data. This approach assumes that a substation’s load will change during the day in proportion to the number of MU cars that pass it each hour. Table 5 at the end of this paper includes a typical load factor calculation that employs this approach. A plot of the resulting “load shape” is shown in Figure 1 below; this shape is in good agreement with substation metered data shown in Figure 2. The load shape shown is typical for most transit systems, with AM and PM rush hour peak loads.

Figures 3 and 4 contains daily load factors similarly-calculated for a sampling of different rail systems. It can be seen that the heavy rail systems tend to have lower daily load factors than the light rail systems. This is particularly true for those systems that increase train lengths (consists) for peak service periods.

Figure 1

Figure 2

Daily Load Factors for Various Light Rail Systems (Calculated from Train Schedule Data)

System City Route/Station DLF MBTA Boston Boston College Line 0.60 MBTA Boston Riverside Line 0.54 MTA Baltimore Central Corridor/Lex. Market 0.70 MetroLink St. Louis Grand Station 0.70 Metro Houston METRORail 0.69 DART Dallas Red Line/Convention Center 0.45 DART Dallas Blue Line/Mockingbird Station 0.53 AVERAGE: 0.60

Figure 3

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Daily Load Factors for Various Heavy and

Commuter Rail Systems (Calculated from Train Schedule Data)

System City Route/Station DLF MBTA Boston Blue Line 0.51 MBTA Boston Orange Line 0.57 CTA Chicago Purple Line 0.49 CTA Chicago Ravenswood Line 0.45 CTA Chicago Orange Line 0.43 CTA Chicago Red Line/Dan Ryan 0.53 CTA Chicago Blue Line/Addison Station 0.55 Metro-North New York Harlem Line/White Plains 0.45 AVERAGE: 0.50

Figure 4 Ampacity Analysis Software The cable ampacities tabulated for this paper were calculated with CYMCAP Version 3.08.1 from CYME International T & D, Inc. [3]. CYMCAP provides the option of performing cable ampacity calculations using dc current (zero frequency). This is an important feature for dc cable ampacity calculations; calculations using 60 Hz alternating current include additional heating from losses that only occur in the presence of alternating current. Purpose of the Ampacity Tables The ampacity tables included in this paper were developed primarily as an aid to preliminary traction power system design. For this reason, they have incorporated some moderately conservative assumptions. It is recommended that installation-specific ampacity calculations be performed during the detailed design phase of a project. Such calculations are necessary to confirm the validity of the many assumptions on which these ampacities are based, as well as to optimize the design. Daily load factor is not always a good indicator of how traction load fluctuates during the day; this is better determined from a 24 hour load profile. Utilization of sophisticated cable ampacity analysis software such as CYMCAP for this task will also enable the designer to investigate the impact of dynamic cable ratings on the design. As noted in reference [3], distribution cable systems can be tailored to the daily load profile to which the cables will be subjected. End note [3] includes ampacity calculations using the CYMCAP program for several ICEA “Black Book” Std. P-46-426 duct bank configurations. The results of these calculations provide a confirmation of CYMCAP program results (Or quite possibly the reverse: the

CYMCAP program is much more highly developed than the programs that were used to develop the Black Book ampacity tables). ASSUMPTIONS INCORPORATED IN THE CABLE AMPACITY TABLES Ampacity tables have been prepared for single-core 1000, 1500 and 2000 kcmil cables, and triplexed 750 kcmil cables installed in concrete-encased duct banks. CYMCAP cable models are constructed layer-by-layer; the cables utilized for modeling purposes in these tables are based on the dimensions and materials of Okonite-Okoclear 2000V low smoke traction cable. Cables with similar components and dimensions will perform similarly. Other assumptions incorporated into the tables are as follows: 1. RHO for duct bank concrete and backfill The thermal resistivity of the duct bank concrete and

duct bank backfill have been set equal to the resistivity of the surrounding earth (CYMCAP allows different resistivity values to be used for each). This is a conservative assumption for the concrete as evidenced by the suggested RHO value of 55 for concrete bank thermal resistivity listed in NEC Appendix B. Ampacities have been provided for RHO 60, 90 and 120 earth resistivities.

2. Conduit Type Schedule 40 PVC has been used for all duct bank

models. This is a slightly conservative assumption, since schedule 40 is more thermally insulating than the thinner ducts often used for concrete-encasement (PVC actually has the highest thermal resistivity of all standard duct materials). Tables for 1000, 1500 and 2000 kcmil cables are based on 4” ducts, and the table for 3-750 kcmil triplexed cables is based on 5” ducts. As noted in reference [3], duct diameter by itself does not have a major impact on ampacity.

3. Maximum Cable Temperature

A maximum cable (conductor) temperature of 90 °C has been used for all ampacity calculations in accordance with modern traction power cable design. In other words, the temperature of the hottest cable in each duct bank will not exceed 90 °C. It should be noted that, particularly for the larger ducts banks, many of the cables are operating at much

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lower temperatures than the “hottest cable”, which is typically located in the middle of the duct bank (and on the bottom row for two-row duct banks).

4. Duct Bank Dimensions The tops of all duct banks are 30 inches below grade. The four sides of all duct banks have 3 inches of concrete cover over the outside ducts, and 2 inches of concrete between ducts. A 6-way duct bank with 2 rows and 3 columns of ducts is listed as a “2 x 3” duct bank.

5. Ambient Earth Temperature The temperature of the earth surrounding the duct bank is 20 °C.

6. Load Factors Ampacities have been calculated for 100%, 75% and 50% load factors. Intermediate ampacities can be approximated via interpolation (the relationship of ampacity to load factor is not precisely linear, but close enough for preliminary design purposes).

SUMMARY Ampacity tables for typical traction power cables and duct bank configurations have been provided as an aid to preliminary design. The following observations may be made from review of these tables: 1. Large duct banks, when filled with traction cables,

provide a large reduction in available ampacity. “Subdividing” a substation getaway duct bank may be advisable if the duct banks can be separated sufficiently to be out of each others’ thermal “area of influence” (CYMCAP provides a multiple duct bank modeling feature which can be used to determine this).

2. Horizontal duct bank configurations have similar ampacities as their corresponding vertical configurations. For example, the ampacity of a 2-row, 5-column duct bank is not much different from that of a 5-row, 2-column duct bank.

END NOTES 1. George C. Anders, “Rating of Electric Power

Cables”, IEEE Press, Piscataway, NJ, 1997, Chapter 1.

2. J. H. Neher and M. H. McGrath, “The Calculation

of the Temperature Rise and Load Capability of Cable Systems”, AIEE Transactions, Vol. 76, Part 3, October 1957, pp. 752-772.

3. R. W. Stell, “Current Rating Considerations for

Direct Current Traction Power Systems”, 2003 APTA Rail Transit Conference.

4. J. A. Williams, D. Parmar and M. Conroy,

Controlled Backfill Optimization to Achieve High Ampacities on Transmission Cables, IEEE Transactions on Power Delivery, Vol. 9, No. 1, January 1994. pp. 544-552.

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