How to Calculate Current in Parallel Feeders of Different Lengths

[Anachronite]

NEC 310-4c does not allow conductors to be different lengths in parallel installations. Obviously it is difficult to ensure the conductors are indeed the same length due to conduit routing, 90's, etc... Theory says if they are not the same length, current will be different in the conductors. Similar questions have been posed here before, but none of the answers I found here were in agreement with each other, and none seem very clear on how to calculated this.

We have a 3000 amp circuit being fed with (8) runs of 4x500 Kcmil in each conduit. This paraticular installation is such that it is impossible to complete this installation with all of the conductors the same length. So, we need to calculate the current in each conductor to see if the installation will work, or if we need to change the installation.

The longest run is 126 ft., and the shortest run is 119 ft. I need to calculate the maximum current in the conductors to make sure we do not exceed allowable ampacity.

Does anyone out there have a complete calculation to do this?

 

[weressl]

NEC 310-4c does not allow conductors to be different lengths in parallel installations. Obviously it is difficult to ensure the conductors are indeed the same length due to conduit routing, 90's, etc... Theory says if they are not the same length, current will be different in the conductors. Similar questions have been posed here before, but none of the answers I found here were in agreement with each other, and none seem very clear on how to calculated this.

We have a 3000 amp circuit being fed with (8) runs of 4x500 Kcmil in each conduit. This paraticular installation is such that it is impossible to complete this installation with all of the conductors the same length. So, we need to calculate the current in each conductor to see if the installation will work, or if we need to change the installation.

The longest run is 126 ft., and the shortest run is 119 ft. I need to calculate the maximum current in the conductors to make sure we do not exceed allowable ampacity.

Does anyone out there have a complete calculation to do this?

The specific wording is "(1) Be the same length". Obviously for practical reasons there always be difference between conductor lengths, the only question is how much is the difference? Fractions of inches? Inches? A couple of feet? Or is there a percentage of the total length? The Code stays silent on the issue. Even with identical length of conductors there will be a difference, since there is a manufacturing tolerance in the conductors which makes each of them potentially ever-so-slightly different resistance, and the current will be different accordingly.

Since it is an installation issue, the inspector - a reasonable one - would look at the installation and question if everything was done to assure that the conductors will be the same length? For example if you have numerous flat turns in the same direction, did you rotate the phases to compensate for the unequal lenghts?

The calculations can be complex or simple. You can take power factor, temperature rise and impedance into consideration for academic accuracy or just resistance for plan-Jane calcualtions. Herr Ohm and Kirchoff will help you out. The components divide the current according to their reciprocal resistances, so, in the case of two resistors, Ia/Ib=Rb/Ra.

 

[steve66]

You need to use the current divider formula:

http://www.allaboutcircuits.com/vol_1/chpt_6/3.html

Assume that each foot of cable is 1 ohm of resistance, and the currents reduce to cable lengths. (The actual resistances don't matter, just the ratios.)

So assume one cable is 119 ohms, and the other is 126 ohms. Rtotal would be:
1/(1/119 + 1/126) = 61.2 ohms.

The current through the 126' cable would be:
Itotal * 61.2/126 = Itotal * 0.485.

The current through the 119' cable would be:
Itotal * 61.2/119 = Itotal * 0.514.

So the longer cable will have 48.5% of the total current through it, and the shorter cable will have 51.4% of the total current flowing through it.

 

[Smart $]

...

Does anyone out there have a complete calculation to do this?

See http://forums.mikeholt.com/showthread.php/96501-parallel-wire-ampacity?p=807826#post807826

 

[don_resqcapt19]

Using just the resistance and assuming 1" succesive increases in length and a 3000 amp load I get 386 amps in the 119' one and 365 amps in the 126' one.
I attached the spread sheet that I used for the calculation. You will have to change the file extension back to .xls to use it.