IEC 287 calculations for three single-core cables in trefoil in 9 way (3 x 3) duct bank

[Adam1980]

Dear all,

concerning the current carrying capability of three-single core cables in trefoil in 9 way (3 x 3) duct bank and following the procedure in IEC 287 - 1 -1 and 287 - 2 - 1
when we are calculating T4 = T'4 + T"4 + T"' 4
T'4 is according to 287-2-1 2.2.7.1
T"4 is according to 287-2-1 2.2.7.2
T'" 4 is according to 287-2-1 2.2.7.3 and 2.2.3.2 considering the mutual effect of the other cables laid in the other ducts

The question is for T'"4 should we use 2.2.4.3.1 instead of 2.2.3.2?
that is use: (1.5/pi) x rho concrete x [ln(2u x (d'p/dp...)) - 0.630] instead of (1/(2 x pi)) x rho concrete x ln[(u - squareroot(u^2 - 1)) x (d'p/dp...)]

Thank you,
Adam

 

[7anoter4]

Since ch.2.2.4 is for “Groups of buried cables (touching) equally loaded calculation” you have to follow ch.2.2.3 solution for” Groups of buried cables (not touching)”.So you have to use 2.2.3.2 “Equally loaded identical cables” formula.

 

[Adam1980]

but we are considering in this case three single-core cables inside one duct, the other duct are not touching for sure. section 2.2.4.3.1 is for three singe-core cables in trefoil.
if we considered 2.2.3.2, which is a variance of the single isolated cable, how are we accounting for the mutual heat exchange between the three cables inside the duct itself. After all we are calculating the current carrying capabiltiy for one conductor of the three single-core conductors inside the PVC duct.

 

[7anoter4]

The three single-core cables current is supposed to be the same in all three. So the equivalent De diameter is the diameter of the circumcircle [De=2.15times the overall diameter of a cable].
It is indicated for pipe-type cable indeed, but it is employed for 3 single-core cables also.
The Neher and McGrath article indicated the same procedure [see D’s diameter formula 41].
In ch.1.4.1.1 formula you have to multiply this thermal resistance T4 by number of cables per duct[n].

 

[Adam1980]

how is the impact of the mutual heating inside the duct itself is accounted for in your opinion and in this case what is section 2.2.4.3.1 is used for!

 

[7anoter4]

All ch.2.2.4 is intended for touching cables [or ducts]. Ch.2.2.4.3.1 is for 3 metallic sheathed [covered] cable or metallic duct. You may put in each duct 1, 2, 3 or 4 single core cables.

 

[Adam1980]

so calculating for the case i am describing is it a combination of touching and not touching?
the 3 single-core cables are touching while the PVC ducts are not touching!

i am convinced that using the section with touching is not correct! but i cant find a clear argument that i can use section 2.2.3.2 for a three single-core cable. is there any literature or publication that can support that

 

[7anoter4]

1) First of all it's our experience for more than 30 years [and of other!].
2) The single-cores cables in a duct or pipe are always in "touching" position then you don't need to
add nothing to your calculation.
3) You could see also in IEEE-835/1994 [for instance]: in page Intro-23 A2-Calculation examples:
A.2.1 Example 1: 3-1/c 350 kcmil aluminum, 600 V cables installed in a 3 inch PVC conduit in the earth.
Cable Dimensions:
O.D. over conductor: 0.681 in ; O.D. over insulation: 0.871 in ; * Circumscribed diameter = 2.15 x 0.871 = 1.873 in
Cable to conduit:
Rsd=n'A/(1+ (B+CTm)Ds') TOF (Equation 41-Neher&McGrath)
Rsd=3 * 17/[1+ (2.3+0.024x70) (2.15 x 0.871)]= 6.033 TOF [Thermal Ohm-Feet].
4) You may try also Google "IEC 60287 Calculation Examples"

 

[Adam1980]

its great that you have time to respond, i appreciate it but unfortunately i dont have the experience that you have and would like to know how to explain the usage of the equations in the standard. I attached a calculation example here.

the challenge that i have is that i am getting a comment that for part 2 of T'"4 i should use 2.2.4.3.1 along with the FK muliplier in order to account for the single-core cable touching inside the PVC duct.

for me it is clear that this request is not clearly written in the standard, however having section 2.2.4.3.1 entitled "3-single-core cables in trefoil" is making my arguement weaker. I appreciate any advice!

Thanks

 

[7anoter4]

Very good calculation, Adam!

 

[Adam1980]

thank you, i had support from you to make that.

now for my understanding:
for singel-core conducter
T1 is the heat from the insulation
T3 is the the from the PVC jacket
T'4 is the heat from the inside ambient of the Duct
T"4 is the heat from the Duct thickness
T'" 4 is the mutual heat from the other cables in the duct bank (thats why we multiply by 3).

i fail to see here the effect of the other two cables within the PVC duct.

if we considered 2.2.4.3.1 in any of the above calculations i believe we shouldn't multiply by 3 which leads to very unrealistic results. however i still miss the arguement for not using a section which is called three single-core cables in trefoil

can you advice!

 

[7anoter4]

It is correct: multiplying by 3 you'll take the "other" two cables contribution to the "first" heating considering all three cables will be at the same temperature.
ch.2.2.4 it is for “Groups of BURIED cables (touching) equally loaded”. Your cables-if you agree-are in "air" in the duct. Then could be ch. 2.2.1.1 “Cables protected from direct solar radiation”.
In this case for I=203 A and 8.02E-5 ohm/m resistance you'll get 4.5 degrees drop for "free air" and 3.6 dgr. in duct [according to 2.2.7.1].

 

[Adam1980]

Hello, i agree with you that the cables inside the duct are in free air since IEC considers that when calculating T'4 by considering the temprature of the medium filling the duct.

However, i would like first to get your opinion that the standard is not very clear especially when it comes to single-core cables and thats why many interpertations could be possible.

as a result i would like to add to the calculation that i sent to you earlier an additional component to T4 and considering the worst case situation i will consider this component coming from 2.2.4.3.1.

in this case all the understanding we discussed before stay the same but for T4 i add a component from 2.2.4.3.1 which is accounting for three single-core cables which are touching.

in this case T4 = T'4 + T"4 + T'"4 (from earth) + T'"4 (from concrete and mutual effect of external not touching cables in other ducs) + T4new (mutual effect of cables touching within the duct).

the T4new is not multiplied by 3 since this is accounted for in transition from regular 1/(2 x pi) to 1,5/pi which is already multiplication by 3. this is case is very pessimistic since i am considering a rho of concrete where actually i am in free air inside the duct.

based on the above explanation for the calcualtion i sent to you earlier:
T4 becomes 5.062 and the current is 193 A

tell me your opinion!

 

[7anoter4]

I don’t think it is a reason to insert a temperature drop taking into account 3 cable touching in an earth medium since the soil is out of the duct bank, even. Maximum you may substitute the “cable to duct” part with “touching in free air “ taking the Z, E and g[or d] as in Table No.2 for 3 touching cables in trefoil [pos.3 or 10].You’ll get (DTs)^(1/4)=21.085 and T’4=0.1254.
Before, if you would introduce the calculated T1, T2 [actually your T3 is T2 as per 2.1.2.1 and T3=0] and T4 in formula 1.4.1.1:
Δθ = (I2R + ½ Wd) T1 + [I2R (1 + λ1) + Wd] n T2 + [I2R (1 + λ1 + λ2) + Wd] n (T3 + T4)
taking I=203 A- you would get Δθ=90-40=50 oC.
Now, if you will put instead of T4=4.586 the new T4 =4.586-0.361+0.1254=4.3504 then you’ll have to
enhance the current to 208.3 in order to keep the same 50 dgr.C.

 

[Adam1980]

Hello again,

is it possible to provide some links for examples that utilizes the approach we have here. you told me to go to google and search for IEC calcaution examples but i couldn't find much examples to support that this approach is the one practiced.

Thank you

 

[7anoter4]

Ok! The problem we are not agreeing with it is what D’e is in 2.2.7.1 formula.
If you’ll put D’e=overall diameter=39 mm you’ll get Ipermissible=187 A.
In my opinion it is a conservative value but I accept it.
In the formula 41 used in IEEE-835/1994 –it is a very close formula to 2.2.7.1-D’s=2.15*overall diameter-and it seems to me more realistic.
Good luck!