ML17334A556

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Rev 0 to Calculation PS-CABLE-001, Thermo-Lag Ampacity Derating.
ML17334A556
Person / Time
Site: Cook  American Electric Power icon.png
Issue date: 10/23/1997
From:
INDIANA MICHIGAN POWER CO.
To:
Shared Package
ML17334A555 List:
References
PS-CABLE-001, PS-CABLE-001-R00, PS-CABLE-1, PS-CABLE-1-R, NUDOCS 9711280217
Download: ML17334A556 (39)
v • d • e


Text

'(IV97).NUCLEAR ENGINEERING DEPARTHENT Calculation Cover Sheet Cook Nuclear Plant SHEET I OF Q Electrical Systems/Com onents CALCULATION No.P5 C8 LE-OO SAFETY RELATED YES~NO SYSTEM 8"/TITLE 7brs~~a~r R~Pa~ry'ZRazuua RFC/MM/PM/PR/CR/TM No.FILE LOCATION INDIANA MICHIGAN POWER COMPANY UNIT No./~Z CALCULATED BY: VERIFIED BY: APPROVED BY: gD-/o-p DATE DATE DATE CALCULATION DESCRIPTION:

dvi'ern u'lare 4o e sN8/r ou M'ETHOO OF Yf RIFI CATION: ALTERNATE CALCULATION v REYIEW REVISION NO.REASON FOR CHANGE Calculated 8 Oate Veri fled 8 Oate Approved 8 Date 97ii2802i7 97ii24 PDR ADOCK Q50003i5 PDR

1.0 This calculation reviews the ampacity derating of all cables in power tray, protected with 1-hour Thermo-lag.

The ampacity derating is reviewed from two perspectives, development of correction factors and the comparison of tray loads to test results.The cables and their tray are identified in Attachment l.2.0 I F T The derating approach for analyzing the ampacity of cables in tray wrapped with Thermo-lag is two tiered.First, cables have been derated for placement in a tray with other cables, in accordance with a maintained spacing correction factor derived from IPCEA P-46-426, Table VII.This factor has been applied to the open air ampacity of the respective cables.Second, the Texas Utilities (TU)Thermo-lag derating factor of 32%has been conservatively applied to the respective derated cable ampacity to account for the Thermo-lag thermal barrier installed around the subject trays.This approach derates each cable first to account for its physical placement, and secondly to account for Thermo-lag.

3.0~A@3.1 Design Standard 1-2-EDS-642 directs that all power cables shall be configured in a single layer with maintained spacing when installed in a power tray.All cables in trays wrapped with Thermo-lag have been derated in accordance with IPCEA P-46-426 because of it'treatment of cables with maintained spacing.ICEA P-54-440 was not used because it was developed for fully loaded cables with no space between them.A correction factor of 0.8 has been derived from IPCEA P-46-426, Table VII to account for configurations of 12 or more horizontal cables in a single layer.This'correction factor has been applied to all cables in trays wrapped with one-hour Thermo-lag, except tray 1AI-P4 where an 0.87 correction factor has been used (only three cables present in tray).These derated ampacities are listed in Attachment 1.PS-CABLE-001 Rev.0 Page 2 of 6 In order to predict correction factors for fills greater than those discussed in IPCEA P-46-426 (up to 6 horizontal cables), it is necessary to determine the impact the neighboring cables will have on the cable of concern.The worst condition is when the cable of concern is in the center of the cable group.The correction factors for the cables are expected to be influenced by two factors, the change in the effective ambient temperature caused by the heat generated by the other cables in the tray and the changes in the thermal resistance from the center cable to the ambient due to the presence of the neighboring cables which impact thermal convection and radiation from the cable to the ambient.As noted in the IPCEA table, the cables directly adjacent to the cable of concern have the highest impact (a 13%reduction for the first two cables directly adjacent to the center cable).As the number of cables increase, the impact on the environment of the cable of concern is reduced due to the physical separation that exists, and therefore, the correction factor is reduced by only 1%for the addition of a flAh or sixth cable in the raceway.It is expected that there will be a point where the addition of cables in the horizontal plane will no longer influence the environment of the cable of concern and will result in no additional cable derating.Hence, the correction factor will reach a limit that it does'not fall below, regardless of the number of cables in the horizontal path.MATHCAD software was used to determine the correction factor of 0.8.First, a mathematical model was developed which represents the correction factors already identified in the IPCEA standard.The model consists of three components

.The first is an exponential term to reflect the effect of the increase in the cable thermal resistance due to adjoining cables, the second is also an exponential term that reflects the effect of additional heat generation in the raceway, and the third is a constant to represent the limiting value of the derating multiplier.

MATHCAD was then utilized to calibrate this model utilizing the known correction factors in the IPCEA standard and to calculate the correction factors for quantities of cables greater than the maximum value of 6.The result of this mathematical model determined that after 12 cables, the correction factor remained constant at 0.8.Therefore, a conservative derating factor of 0.8 can be used for fills greater than 6 cables.The MATHCAD file and results can be found in Attachment 2';This model assumes that all cables are carrying their respective rated ampacity.If a cable is carrying little or no current, then there is no significant increase in the ambient temperature.

Hence, the effect on the environment of the cable of concern is negligible, The majority of cables at D.C.Cook plant are lightly loaded and therefore the correction factor of 0.8 is conservative.

PS-CABLE-001 Rev.0 Page 3 of 6

3.2 The TU derating factor of 32%for cables in trays wrapped with 1-hour Thermo-lag has been applied to cables in trays wrapped with 1-hour Thermo-lag at DC Cook.The application of the TU 32%derating factor is considered appropriate and conservative for application at DC Cook for the following reasons:-The trays used for the TU testing and the trays used at DC Cook are both ventilated

'adder type, with no cover.-The TU testing was comprised of 126 3/C II6 CV cables energized at 15.9A in 24" x 4" tray.This configuration required the dissipation of 49W (126 x 3 x 15.9A2 x 5.14E-04Q) through 4.67ft of Thermo-lag that surrounds the tray.Therefore the ratio of unit heat generated to unit area of dissipation for the TU testing was 10.5W/ft.The bounding ratio of heat generated (25.18W)to area of dissipation (3ft)for DC Cook is 8.4W/ft (using the wattage of tray 1A-P20 as the bounding case).A comparison of the heat generated to area of dissipation ratios shows that applying the TU derating factor is conservative for DC Cook applications.

-The TU testing utilized pn additional thermal barrier, SilTemp cloth.This is not used at DC Cook (a source of conservatism when applying the TU derating factor to DC Cook).-The TU testing utilized 1/2" Thermo-lag panels, as does DC Cook.4.0 A review of Attachment 1 indicates that 2560G/1AI-P4 does not have a margin between its connected load and the available ampacity aAer being derated in accordance with sections 3.1 and 3.2.Tray 1AI-P4 contains just three cables, two of which have minor motor operated valve loads (<0.5A).Given the short operating time of these valves (<2 minutes), the cables powering them in effect contribute no heat to the steady state inner-tray environment.

Therefore these two cables may be disregarded with respect to the derating of the third cable, 2560G (i.e.-2560G need not be derated for placement in tray with other cables).This third cable supplies power to a welding receptacle rated for 60A.To justify the loading of this cable the nature of load must be considered.

The nature of the load is infrequent and intermittent, therefore the emergency overload rating of the cable should be considered.

For XLPE type insulation, the emergency overload rating is 130'C.PS-CABLE-001

'Rev.0 Page 4 of'6

This temperature rating of the cable is for those situations in which the load current is higher than normal but is not expected to last more than 100 hours0.00116 days <br />0.0278 hours <br />1.653439e-4 weeks <br />3.805e-5 months <br /> at any given time or more than a total of 500 hours0.00579 days <br />0.139 hours <br />8.267196e-4 weeks <br />1.9025e-4 months <br /> in the life of the cable (Reference 5).Adjusting for a change in heat rise of the cable (90'C to 130'C)in accordance with IPCEA-P-46-426 eq.5, a free air emergency overload ampacity of 87A is calculated.

Applying the 32%TU factor derates it to 59A.The portable welding equipment commonly used at DC Cook draws less than 50A.Also, it is expected that during the life of the welding receptacle it would be used within the time parameters associated with the emergency overload rating of the cable.Therefore this cable and its loading is considered acceptable.

5.0 As an alternate means of review of the loading of Thermo-lag wrapped trays listed in Attachment 1, direct comparisons and correlations between tests and actual configurations have been made in Attachment 3.This is highly relevant to the study of ampacity loading of Thermo-lag wrapped trays.In 1983, the Canton Test Lab performed Test CL-542 (Attachment 4)to simulate the effects of 1/2" Thermo-lag on conductor temperatures of spaced cables.These tests replicated actual installed raceway configurations, including the number and size of cables, loading and spacing.As an example, CL-542 Tests 1 and 3 were designed to replicate trays 1AZ-P8 and 1A-P20, respectively.

Direct comparison or correlation of data provided by these tests and trays under review, provides an excellent means of assurance that the temperature ratings of the spaced cables will not be exceeded at the stated loadings while the parent tray is wrapped in 1/2" Thermo-lag.

Attachment 3, Tables 1 and 2, provide a direct comparison between data from CL-542 test 1 and 3 and the cables contained in trays 1AZ-P8 and 1A-P20.The test currents used in the test were equal to or greater than the actual loading of the respective cables.A review of these tables shows that no cables exceed their temperture rating (90 C).while energized at their design loads, in fact, all conductor temperatures are less than 70'C.Attachment 3, Tables 3 through 8, provide correlations between data from CL-542 test 3 and other trays which are considered to be enveloped by this test.A review of these tables shows that tray 1A-P20 envelopes all other trays in both number of cables and loading.PS-CABLE-001 Rev.0 Page 5 of 6 l.IPCEA P-46-426 2.ICEA P-54-440 3.Texas Utilities Test Report 4.DC Cook Electrical Design Standard 1-2-EDS-642 5.EPRI Power Plant Reference Guide-Wire and Cable 6.DC Cook Tray Contents Listing 7.DC Cook Conduit and Cable Drawings H T 1.Derating tables 2.MATHCAD files 3.Test results applied to trays 4.CL-542 test report 5.Design Verification PS-CABLE-001 Rev.0 Page 6 of 6 0 0 TRAY¹TRAY SIZE FIRE BARRIER 1AI-Pl 12"W x6"D 1 HOUR RATED THERMO-LAG CABLE NO CABLE TYPE CBL OD OPEN AIR AMPACITY 80%OPEN 32%TSI AIR AMPACITY DERATING MARGIN 8255R 8174R 8177R 8113R 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 4.00 3TC¹12CU 0.32 4.00 3TC¹12CU 0.32 0.33 36 36 36 28.8 28.8 28.8 28.8 19.58 19.58 98.31 79.58 19.58 79.58 19.58 98.31 8119R 3TC¹12CU 0.32 0.33 36 28.8 19.58 98.31 8300R 8304R 8308R 8311R 8294R 8026R 8027R 1623R 1642R 2536R 9086R 9092R 9645R 8755RH 80083R 28765R 3TC¹12CU.0.32 0.33 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 2.10 3TC¹12CU 0.32 1.00 3TC¹12CU 0.32 1.60 3TC¹12CU 0.32 1.60 3TC¹12CU 0.32 2.90 3TC¹6AL 0.69 37.00 3TC¹12CU 0.32 3.48 SPARE 3 1/C 4/OCU 3TC¹12CU 0.32 2.00 4/C¹12CU 0.52 10.00 3TC¹8AL 0.60 25.00 36 36 36 36 36 36 36 36 36 36 36 69 36 28.8 28.8 28.8 28.8 28.8 28.8 28.8 28.8 28.8 41.6 28.8 28.8 28.8 55.2 28.8 19.58 98.31 19.58 98.31 19.58 98.31 19.58 98.31 28.29 11.62 19.58 91.83 19.58 91.83 19.58 85.19 37.54 1.43 19.58 82.23 19.58 98.31 19.58 89.28 19.58 94.89 19.58 89.79 19.58 48.94 Note: 4/C¹12CU ampacity Is derived from only 3 conductors utilized PS-CABLE-001 Rev.0 Attachment 1 Page1 of9

TRAY¹TRAY SIZE FIRE BARRIER 1AI-P2 12"W x6"D 1 HOUR RATED THERMO-LAG CABLE NO CABLE TYPE CBL OD OPEN AIR AMPACITY 80%OPEN 32%TSI AIR AMPACITY DERATING MARGIN 8116G 3TC¹12CU 0.32 0.33 36 28.8 19.58 98.31 8119G 8185G 8194G 8197G 8250G 8300G 8304G 8308G 8311G 8270G 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 3.20 3TC¹12CU 0.32 0.33 3TC¹1 2CU 0.32 0.33 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 0.33 3TC¹12CU 0.32 0.70 36 36 36 36 36 36 36 36 36 36 28.8 28.8 28.8 28.8 28.8 28.8 28.8 28.8 28.8 28.8 19.58 98.31 19.58 98.31 19.58 83.66 19.58 98.31 19.58 98.31 19.58 98.31 19.58 98.31 19.58 96.43 19.58 98.31 19.58 98.31 2978G 2559G 3TC¹6AL 3TC¹6AL SPARE SPARE 8756GH 3TC350MCM AL 1.9 150.80 397 317.6 215.97 30.17 8751 GH 8753GH 3TC¹GAL 0.69 15.50 3TC¹2AL 0.93 49.40 127 55.2 101.6 37.54 69.09 58.71 28.50 8755GH 1500G 3TC¹6AL 0.69 37.00 3TC 2lQ AL 1.27 50.30 206 164.8 112.06 55.11 55.2~37.54 1.43 PS-CABLE-001 Rev.0 Attachment 1 Page 2 of 9 TRAYS TRAY SIZE FIRE BARRIER 1AI-P4 12"W x6"D 1 HOUR RATED THERMO-LAG CABLE NO CABLE TYPE 8116G 3TC412CU 8119G 3TC412CU 2560G 3TCKAL CBL FLA OPEN AIR 87 lo OPEN 32fo TSI OD AMPACITY AIR AMPACITY DERATING MARGIN 0.32 0.40 36 31.32 21.30 98.12 0.32 0.40 36 31.32 2'I.30 98.12 0.69 60.00 69 60.03 40.82-46.99 Weiding recepticle sw.rating.I t'tt t tdl d.PS-CABLE-001 Rev.0 Attachment 1 Page 3 of 9 TRAY¹TRAY SIZE FIRE BARRIER 1A-P20 12"W x6"D 1 HOUR RATED THERMO-LAG CABLE NO CABLE TYPE CBL OD FLA OPEN AIR AMPACITY 80%OPEN AIR AMPACITY 32/o TSI DERATING MARGIN 8113R 8119R 1623R 1642R 3TC¹12CU 3TC¹12CU 3TC¹12CU 4/C¹12CU 0.32 0.71 0.32 0.71 0.32 2.60 0.54 6.40 36 36 36 36 28.8 28.8 28.8 28.8 19.58 96.37 19.58 96.37 86.72 19.58 19.58 67.32 8026R 3TC¹12CU 0.32 2.70 36 28.8 19.58 86.21 8027R 8294R 2349R 3249R 1509R 2353R 3TC¹12CU 3TC¹12CU 3TC¹12CU 3TC¹6AL 3TC¹12CU 4/C¹12CU 0.32 1.20 0.32 0.71 0.32 1.90 0.69 12.70 SPARE 0.52 16.00 36 36 36 36 28.8 28.8 28.8 55.2 28.8 19.58 93.87 19.58 96.37 19.58 90.30 37.54 66.17 19.58 18.30 2354R 4/C¹12CU 0.54 16.00 36 28.8 19.58 18.30 2355R 2356R 3TC¹12CU 3TC¹4AL 0.32 1.50 0.8 36.00 36 94 28,8 75.2 19.58 92.34 51.14 29.60 8984R 3TC¹12CU 0.32 15.60 36 28.8 19.58 20.34 8987R 1656R 9217R 3TC¹12CU 3TC¹2AL 3TC¹12CU 0.32 15.60 36 0.32 0.71 36 0.93 60.00 127 28.8 101.6 28.8 19.58 20.34 69.09 13.15 19.58 96.37 9221R 2348R 2962R 3TC¹12CU 3TC¹12CU 3TC¹12CU 0.32 0.71 0.32 6.80 0.32 6.80 36 36 36 28.8 28.8 28.8 19.58 96.37 19.58 65.28 19.58 65.28 2361R 1440R 8753RH 3TC¹6AL 3TC¹2AL 3TC¹4AL 0.69 31.40 69 0.8 49.00 94 0.93 60.00 127 55.2 101.6 75.2 37.54 16.35 51.14 4.18 69.09 13.15 Note: 4/C¹12CU ampacity is derived from only 3 conductors utilized PS-CABLE-001 Rev.0 Attachment.1 Page 4 of 9

TRAY¹TRAY SIZE FIRE BARRIER 1AZ-P8 12"W x6"D 1 HOUR RATED THERMO-LAG CABLE NO-1470R 1469R CABLE TYPE 3TC¹12CU 3TC¹12CU CBL OD 0.32 3.80 0.32 16.00 36 36 FLA OPEN AIR AMPACITY 80%OPEN AIR AMPACITY 28.8 80.60 19.58 19.58 18.30 32%TSI DERATING MARGIN 8067R 3TC¹12CU 0.32 1.20 36 28.8 19.58 93.87 8024R 8187R 8026R 3TC¹12CU 3TC¹12CU 3TC¹12CU 0.32 1.10 0.32 8.48 0.32 2.70 36 36 28.8 28.8 28.8 19.58 94.38 19.58'6.70 19.58 86.21 8027R 3TC¹12CU 0.32 1.20 36 28.8 1958 93.87 2349R 1476R 1488R 3TC¹12CU 3TC¹12CU 3TC¹12CU 0.32 1.90 SPARE 0.32 3.80 36 36 28.8 28.8 19.58 90.30 19.58 80.60 1991R 3TC¹2AL 0.93 60.00 127 101.6 69.09 13.15 6666R-3TC¹12CU 0.32 2.50 36 28.8 19.58 87.23 PS-CABLE-001 Rev.0 Attachment 1 Page 5of9

TRAY¹TRAY SIZE FIRE BARRIER 1AZ-P9 12"W x6"D 1 HOUR RATED THERMO-LAG CABLE NO CABLE TYPE CBL OD FLA OPEN AIR AMPACITY 80%OPEN AIR AMPACITY 32%TSI DERATING MARGIN 81,1 3R 8119R 1623R 3TC¹12CU 0.32 3TC¹12CU 0.32 3TC¹12CU 0.32 0.71 0.71 2.60 36 36 28.8 28.8 28.8 19.58 96.37 96.37 19.58 19.58 86.72 1642R 4/C¹12CU 0.52 6.40 36 28.8 19.58 67.32 8026R 3TC¹12CU 0.32 2.70 36 28.8 19.58 86.21 8027R 3TC¹12CU 0.32 1.20 36 28.8 19.58 93.87 2349R 9217R 9221R 3TC¹12CU 0.32 3TC¹12CU 0.32 3TC¹12CU 0;32 1.90 0.17 0.17-36-36 36 28.8 28.8 28.8 99.13 19.58 19.58 90.30 19.58 99.13 1440R 3TC¹2AL 0.93 60.00 127 101.6 69.09 13.15 8753RH 3TC¹4AL 0.8 49.00 94 75.2 51.14 4.18 Note: 4/C¹12CU ampacity is derived from only 3 conductors utilized PS-CABLE-001 Rev.0 Attachment 1 Page 6 of 9 TRAY¹TRAY SIZE FIRE BARRIER 2AI-P2 12"W x6"D 1 HOUR RATED THERMO-LAG CABLE NO CABLE TYPE CBL OD OPEN AIR 80%OPEN 32%TSI AMPACITY AIR AMPACITY DERATING MARGIN 3010G 3TC¹12CU 0.32 3012G 4/C¹12CU 0.52 3013G 4/C¹12CU 0.52 8987G 3TC¹12CU 0.32 9217G 3TC¹12CU 0.32 3014G 3TC¹6CU 0.85 8984G 3TC¹1 OCU 0.46 1.75 16.00 16.00 16.00 0.71 36.00 15.60 36 36 36 36 36 89 48 28.8 28.8 28.8 28.8 28.8 71.2 38.4 19.58 19.58 19.58 19.58 19.58 48.42 26.11 91.06 18.30 18.30 18.30 96.37 25.64 40.26 Note: 4/C¹12CU ampacity is derived from only 3 conductors utilized PS-CABLE-001 Rev.0 Attachment 1 Page7of9

TRAY¹.TRAY SIZE FIRE BARRIER 2AZ-P3 12"W x6"D 1 HOUR RATED THERMO-LAG CABLE NO CABLE TYPE CBL OD OPEN AIR 80%OPEN 32%TSI AMPACITY AIR AMPACITY DERATING MARGIN 8332G 96656 1970G 9696G 3001G 13945 G 3010G 3012G 3013G 8987G 3Q14G 9965G 9958G 8645G 8138G 3TC¹12CU 3TC¹12CU 4/C¹12CU 3TC¹12CU 3TC¹2CU 3TC¹2CU 3TC¹12CU 4/C¹12CU 4/C¹12CU 3TC¹12CU 3TC¹6AL 4/C¹12CU 3TC¹12CU 3TC¹12CU 3TC¹12CU 0.32 3.80 SPARE 0.52 6.70 SPARE 1.08 1.38 1.08 73.00 0.32'1.50 0.52 16.00 0.52 16.00 0.32 16.00 0.69 36.00 0.52 7.9 0.32 1.QQ 0.32 2.90 CO 36 162 36 36 36 36 69 36 36 NTROL 28.8 28.8 129.6 129.6 28.8 28.8 28.8 28.8 55.2 28.8 28.8 28.8 19.58 19.58 88.13 88.13 19.58 19.58 19.58 19.58 37.54 19.58 19.58 19.58 80.60 65.79 98.43 17.17 92.34 18.30 18.30 18.30 4.09 59.66 94.89 85.19 82046 3TC¹12CU 0.32 18.00 36 28.8 19.58 8.09 8317G 8756GH 8050GH 8053GH 3TC¹12CU 3TC¹2/QAL 7/C¹12CU 3TC¹8CU 0.32 3.80 1.27 96.40 36 206 CONTROL 0.72 12.89 66 28.8 164.8 52.8 19.58 112.06 35.90 80.6Q 13.98 64.10 Note: 4/C¹12CU ampacity is derived from only 3 conductors utilized PS-CABLE-001 Rev.0 Attachment 1 Page 8 of 9 TRAY¹TRAY SIZE FIRE BARRIER 2AZ-P10 12"W x6"D 1 HOUR RATED THERMO-LAG CABLE NO CABLE TYPE CBL OD FLA OPEN AIR 80%OPEN AMPACITY AIR AMPACITY 32%TSI DERATING MARGiN 8755RH 3TC¹2AL 8753 RH 3TC¹4AL 0.93 0.8 50.30 50.30 127 94 101.6 75.2 69.09 51.14 2?.19 1.63 8756RH 3TC 2/OAL 1500R 3TC¹2AL 1.27 0.93 100.50 206 50.30 127 164.8 101.6 112.06 69.09 10.32 27.19 8206R 3TC¹12CU 9962R 3TC¹12CU 9951R-3TC¹12CU 9901R 3TCN2CU 9908R 3TC¹12CU 16666R 3TC¹12CU 8327R 3TC¹12CU 8024R 3TC¹12CU 2481R 3TC¹2CU 8274R 3TC¹12CU 9221R 3TC¹12CU 9217R 3TC412CU 8030R 3TC¹12CU 8560R 3TC¹12CU 0.32 0.32 0.32 0.32 0.32 0.32 0.32 1.08 0.32 0.32 0.32 0.32 0.32 18.00 SPARE 0.80 2.99 2.99 2.14 2.99 1.00 1.38 2.20 0.71 0.71 1.34 3.29 36 36 36 36 36 162 36 36 36 28.8 28.8 28.8 28.8 28.8 28.8 28.8 129.6 28.8 28.8 28.8 28.8 28.8 19.58 19.58 19.58 19.58 19.58 19.58 19.58 88.13 19.58 19.58 19.58 19.58 19.58 8.09 95.92 84.73 84.73 89.07 84.73 94.89 98.43 88.77 96.37 96.37 93.16 83.20 PS-CABLE-001 Rev.0 Attachment 1 Page 9 of 9 The Mathcad software (version 6.0 by MathSoft Inc.)contains a function that allows the user to solve a system of simultaneous equations with an equal number of equations and unknowns (50 max.).This method returns numbers for the unknown variables.

There are four steps to solving a system of simultaneous equations.

These are: 1.)Provide an initial guess for the unknowns.Mathcad solves equations by making a series of guesses which ultimately converge on the correct answer.The initial guesses provide Mathcad with a place to start searching for solutions.

2.)The word Given is typed, followed by the series of equations.

3.)The series of equations and inequalities in any order below the word Given.4.)Type any equation that involves the Minen function.The Minerr function returns a vector of answers that solve the system of equations.

The equation used in this mathematical model is:.a+b e(tq/~q)+c e(t~/~~)=mf(t)where: a is a constant representing limiting value of derating factor b&~q are variables in an exponential to reflect the effect of the increase in cable thermal resistance due to adjoining cables c 8~2 are variables in an exponential to reflect the effect of additional heat generation in the raceway.Guesses a."-0.75 b:~0.15 c:-0.1 m:-2.2 n,'=1.7 Given a>bi c=1.0 (1)1 a.t b exp(--)~c cxp-=0.93 (m)"n'here t=0/2>2 as b exp~-)a c exp--=0.87 I m)n/3h 3 a i b cxp(-.)i c exp-=0.84 I)n a i b expI..<i c expt-=0.82 I)P5-CABLE-00l Rev.0 A8ndl eienk 2.'de I of3 aa'bb!j i cc t Minerr(a, b, c, m, n)i I mm r nn"'F::.1 0.93 0.87 0.84 0.83 0.82 MF is a vector of the data included in Table Vll of ICEA PR2-426.aa=0.8 bb~0.129 cc=0.073 mm~1.974 nn=1.991/tK tK mf(t)aa-bb exp~-j t cc exp-j t'=0,1..5 Ill tn nnj m/20)=0.8 l.05 1.03 0.98)0.95 0.93 MFt 0.9 0.88 0.85 0.83 0.8/mf(t)~MF, error(t),-

"-------MF terror:=g error(ti t terror 1.568 10 I3g t:ABLE'-OPJ gt.o.O 8gujh~f.'"~

~Pa~e 2 aP 3

0.98 0.96-~0.94 0.92-mgt)09 0.88 0.86~0,84~0,82-0.8 0..20 0 mft't)1.002

Comparison of CI 542 Test I Results fo Tray IAZ-P8 CABLE SIZE'TC¹12CU 3TC¹12CU 3TC¹2AL TEST CURRENT'.8 20.0 60.0 RUNS IN TRAY'IGHEST CONDUCTOR TEMP.('C)'5.6 59.7 55.7 CABLE(S)SIMULATED 1470R, 8067R, 8024R, 8026R, 8027R, 2349R, 16666 R-2 1469R, 8187R, 1488R 1991R YABLk 1 Comparison of CL-542 Test 3 Resulls fo Tray IA-P20 CABLE SIZE'TC¹12CU 3TC¹12CU 3TC¹12CU 3TC¹12CU 4/C¹12CU 4/C¹12CU 3TC¹6AL 3TCN6AL 3TC¹4AL 3TCN4AL 3TC¹2AL TEST CURRENT~0.71 6.8 16.0 6.8 16.0 16.0 36.0 36.0 53.0 60.0 RUNS IN HIGHEST CONDUCTOR TRAY~TEMP.('C)i 54.6 57.9 60.4 67.3 55.2 62.7 57.6 65.9 57.9 68.8 63.7 CABLE(S)SIMULATED 8113R,8119R 8294 R,9217R,9221R 1623 R,8026R, 8027R,2349R,2355R 2348 R,2962R 8984 R,8987R 1642R, 2353R,2354 R 3249R, 2361R 2356R, 8753 RH 1656R,1440R YABLC<2'est data conforms to the actual cables sizes, number of runs, loading and configuration of tray lAZ-P8.2 Test data conforms to the actual cables sizes, number of runs, loading and configuration of tray lA-P20.PS-CABLE-001 Rev.0 Attachment 3 Page 1 of 7 CABLE SIZE 3TC¹12CU 3TC¹12CU 3TC¹12CU 3TC¹12CU 4/C¹12CU 4/C¹12CU 3TC¹8AL 3TC¹6AL 3TC¹6AL 3TC¹4AL 3TC¹4AL 3TC¹2AL¹of energized cables¹of unused cables actual watts highest temperature Tray I A-P20¹of runs/loading (A)I 5/0.71 5/2.8 2/6.8 2/16.0 I/6.8 2/16.0 I/16.0 I/36.0 I/36.0 I/53.0 2/60.0 23 25.18 68.8'C Tray IAI-PI¹of runs/loading (A)8/0.33 5/2.10 4/4.0 I/10.0 1/25.0 I/37.0 20 7.17 TABLE 3 PS-CABLE-001 Rev.0 Attachment 3 Page2of7

CABLE SIZE 3TC¹12CU 3TC¹12CU 3TC¹12CU 3TC¹12CU 4/C¹12CU 4/C¹12CU 3TC¹6AL 3TC¹6AL 3TC¹4AL 3TC¹4AL 3TC¹2AL 3TC2/OAL 3TC 350MCM AL¹of energized cables¹of unused'cables actual watts highest temperature Tray I A-P20¹of runs/loading{A) 5/0.71 5/2.8 2/6.8 2/16.0 I/6.8 2/16.0 I/16.0~I/36.0 I/36.0 I/53.0 2/60.0 23 25.18 68.8'C Tray I Al-P2¹of runs/loading{A)10/1.0 I/3.2 I/15.5 I/37.0 I/50.0 I/51.0 I/151 16 12.4 TABLE 4 PS-CABLE-001 Rev.0 Attachment 3 Page3 of7 CABLE SIZE 3TC¹12CU 3TC¹12CU 3TC¹12CU 3TC¹12CU 4/C¹12CU 4/C¹12CU 3TC¹6AL 3TC¹6AL 3TC¹4AL 3TC¹4AL 3TC¹2AL¹of energized cables¹of unused cables actual watts highest temperature Tray IA-P20¹of runs/loading (A)5/0.71 5/2.8 2/6.8 2/16.0 I/6.8 2/16.0 I/16.0 I/36.0 I/36.0 I/53.0 2/60.0 23 25.18 68.8'C Tray I AZ-P9¹ofruns/loading (A)4/0.71 4/2.70 I/6.4 I/49.0 I/60.0 7.91 TABLE 5 PS-CABLE-001 Rev.0 Attachment 3 Page4of7 Oi CABLE SIZE 3TCII12CU 3TCI112CU 3TC012CU 3TC/I12CU 4/CP12CU 4/CP12CU 3TCI/10CU 3TCN6CU 3TCN6AL 3TC//6AL 3TCP4AL 3TC/I4AL 3TC02AL//of energized cables//ofunused cables actual watts highest temperature Tray 1A-P20 II of runs/loading (A)5/0.71 5/2.8 2/6.8 2/16.0 1/6.8 2/16.0 1/16.0 1/36.0 1/36.0 1/53.0 2/60.0 23 25.18 68.8'C Tray 2AI-P2 I/of runs/loading (A)2/2.0 1/16.0 2/16.0 1/16.0 1/36.0 7.82 TABLE 6 PS-CABLE-001 Rev.0 Attachment 3 Page 5 of7 CABLE SIZE 3TCN12CU 3TCN12CU 3TCN12CU 3TCN12CU 4/CN12CU 4/CN12CU 3TCN8CU 3TCN6AL 3TCN6AL 3TCN4AL 3TCN4AL 3TCN2AL 3TCN2CU 3TCN2CU 3TC2/OAL N of energized cables N of unused/control cables Actual Watts highest temperature Tray I A-P20 N of runs/loading(A) 5/0.71 5/2.8 2/6.8 2/16.0 I/6.8 2/16.0 I/16.0 I/36.0 I/36.0 I/53.0 2/60.0 23 25.18 68.8'C Tray 2AZ-P3 N of runs/loading (A)2/1.5 3/3.8 2/18.0 2/7.9 2/16.0 I/13.0 I/36.0 I/73.0 I/1.38 I/96.4 16 19.89 TABLE 7 PS-CABLE-001 Rev.0 Attachment 3 Page6of7

CABLE SIZE 3TCN12CU 3TCN12CU 3TCN12CU 3TCN12CU 4/CN12CU 4/CN12CU 3TCN6AL 3TCN6AL 3TCN4AL 3TCN4AL 3TCN2CU 3TCN2AL 3TC2/OAL Tray I A-P20 N of runs/loading(A) 5/0.71 5/2.8 2/6.8 2/16.0 I/6.8 2/16.0 I/16.0 I/36.0 I/36.0 I/53.0 2/60.0 Tray 2AZ-P10 N of runs/loading (A)3/0.8 4/2.2 4/3.3 I/18.0 I/51.0 1.38 2/51.0 I/101.0 N of energized cables N of unused cables actual watts highest temperature 23 25.18 68.8'C 17 16.95 TABLE<S PS-CABLE-001 Rev.0 Attachment 3 Page 7 of 7

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