Determine Current Distribution in single conductor parallel runs

[majesus]

I have to install a 1600A feeder from a unit-sub to a 600V distribution switchgear. I can meet the free air ampacity @75C with 3x1c-#500MCM/PH. The problem is this configuration is unsymmetrical.
A-B-C
C-B-A A-B-C

I could run an extra conductor to make it a 4x1c-#500MCM/ph:
A-B-C C-B-A
A-B-C C-B-A


Since the impedance is a factor of conductor size, geometry, current and distance, I'm curious if the 3x1c-#500MCM/PH conductors will cause a significant imbalance at 1600A when the feeder length is only 15m. I looked up a few journals on IEEE but I did not find information relevant to short runs. I am trying to find information on the subject.

Regards,
Majesus

 

[PHovnanian]

A couple of questions:

What's your governing code (NEC, NESC, some EU regs)? What type of conductor (Al, Cu)?

What sort of margin do you have between the conductor ampacity and the calculated load?

While the lack of symmetry in conductor layout will affect the conductor's reactance, the resistance component will vary only with conductor length, so you should strive to keep all of the parallel runs to the same length. Unless your load is within a few percent of your feeder's rating, it's symmetry shouldn't be a problem. At any rate, with a 15m distance, a significant part of your feeder run will be near the equipment terminals where maintaining symmetry will be hopeless anyway.

 

[majesus]

The reactance also varies by distance as the units are ohms/distance.

I'm just curious to calculate the Impedance of different feeder configurations and observe how they vary by distance. I believe IEC 60287-1 has approximate equations where I can then proceed to hand calc a reactance value:

http://www.openelectrical.org/wiki/index.php?title=Cable_Impedance_Calculations

After that, I can model the cables at various distances and see how then current distribution changes in the parallel cables.

The feeders are copper (TECK) and all installation shall be in accordance with CEC. But not really relevant. This is more of a physics problem.

 

[PHovnanian]

There are two parameters that will result in an imbalance in the current distribution between the paralleled conductor sets.

The first is an inequality in lengths between the conductor sets. This results in unequal impedances, both the resistance(R) and reactance(X) components. Given an ohms per foot value for both R and X, you can figure out the current division due to length differences.

The second factor is the asymmetry of the phases in each conductor set. The formulas for cable reactances per foot that you posted make an assumption. That is: the reactances will be the same for each phase in each set due to physical transposition over the length of the sets. While it is a common practice in long lines to transpose phases to correct for this, it is rarely done for lengths as short as yours.

Between these two factors, unequal lengths will produce much larger imbalances than conductor asymmetry and the resulting reactance differences per phase. So the geometry factor is usually ignored.

 

[majesus]

Thanks PHovnanian,

Appreciate your help. I was trying to compute the Inductance tonight using the equations I posted in the link, but I got stuck, after digging in my Southwire Power Cable Manual and as you mentioned the assumption is that reactances will be the same for each phase. The equations are only valid for cable circuits having balanced current loadings. Which is... what I'm trying to calculate.

IEEE transaction IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-20, NO. 2, MARCH/APRIL 1984 "Single-Conductor Cables in Parallel" shows the proper method to calculate inductance for this problem.

 

[electricpete]

One general comment is that resistance tends to be important for small-diameter cables, but tends to be negligible for large cables such as 500MCM.

As I understand, there is no transposition involved, it is a 2-d problem. This could be modeled using FEMM free software.

=====================================
(2B)+(2B)' ?

 

[majesus]

Thanks Electricpete,

The FEMM program looks great. I took some time this morning to "test-drive" the software and review the documentation. It's a very powerful analysis tool, but I'm a little lost on how to apply it for this application. I did a google search on modeling conductors with FEMM to calculate Impedance and I found one of your previous posts:
"With free program FEMM, the question can probably answered in 10 minutes. (Allow 8 hours to learn the program first!)"

http://www.eng-tips.com/viewthread.cfm?qid=238383

I am trying to find a tutorial to show me how to model 3 phase current in 3x1c-#500MCM cable using the configuration in my original post. I was thinking I might be able to figure it out using the tutorial for Magnetics and the FAQ for Current Induced in a Steel Tube.

 

[electricpete]

Here is the file for the thread that you linked above.



=====================================
(2B)+(2B)' ?

 

[7anoter4]

For the proposed layout A B C
C B A A B C
The upper A will be 587 A [+10%] B 533 A and C 598 [+12%]
The lower layer will be up to 7% less.
But if you change the layout to A B C
A B C C B A all current will be o.k.[no imbalance].

 

[majesus]

For the proposed layout
A B C
C B A A B C
The upper A will be 587 A [+10%] B 533 A and C 598 [+12%]The lower layer will be up to 7% less.

But if you change the layout to
A B C
A B C C B A all current will be o.k.[no imbalance].

How did you figure that out 7Anoter4?

 

[7anoter4]

See:

http://www.eng-tips.com/viewthread.cfm?qid=238383

 

[7anoter4]

I have to apologize! I did a very big mistake introducing the data in my VB6 program. My solution is even worse than your.
The actual figures for your proposed lay-out are:
Upper row:
A 538.8+18.6i
B -326.7-492.8i
C -362.2+383.2i
Lower row:
C -354.8+409.9i
B -332-504.4i
A 504.6-35i
A 556.6+16.4i
B -141.2-388.2i
C -82.9+592.5i

 

[majesus]

No worries, I'm simulating them based on FEMM program. However, I am getting very marginal effects for a 15m run. Still work in progress thou.

Majesus

 

[majesus]

7Anoter4 are you numbers amps of voltage? You have "A" as units in your Oct 11 posting.

I modeled a few different configuration scenarios of 3x1c-#500/ph for 15m at 1600A in FEMM based on file Electricpete's upload file.

The simulations in FEMM calculate very small voltage drops. About 0.17% Vdrop for the 15m run on a 600V system. None of the different cable configurations I have modeled seem be problematic at this distance.

Electricpete, the FEMM program is very impressive. I modeled my cables in Autocad, imported the DXF and created my boundary conditions based on the setup of your file. Thanks for sharing the program.