Parallel Conductors 1

[lannjenks]

I am researching the impact of using conductors in parallel that are not the same length.

Assuming everything is equal except length, and conductors are run in separate conduits with other phases (A-B-C-N), can I ignore inductance? These are 60Hz feeder conductors.

To calculate resistance of each conductor I use the formula R = k*L/A, where k is the specific resistance. This is my main question. The value of k is dependent on temperature. If one conductor is shorter than another, it will carry more current, therefore increasing the temperature of the conductor. Is this effect minimal enough that I can assume an equal k when calculating the resistance of each of my parallel wires? Is there an equation that shows how much a conductor heats up due to how much current it is drawing?

Thanks,

Laura Jenkins

 

[davidbeach]

If you are governed by the NEC, this is can only be a theoretical interest as the NEC requires matched length.

How much a conductor would heat up would depend on a variety of factors associated with the installation: above ground or below ground; proximity of other conduits; type of conduit; ambient air conditions if above ground; many others. I don't have any specific references, and given the wide variety of conditions there may not be a general formula or reference.

I doubt that you can ignore inductance unless you are doing your calculations at a unity power factor. The lower the power factor, the more that the inductance matters.

 

[PWR]

Actually, balanced inductive reactance (or the lack thereof )is usually what controls whether conductors in parallel equally share the load.

I have seen as much as six to one variation in the amount of amps in large (500 kcmil or larger) paralleled conductors on several installations. In all cases, the total length of the circuits was relatively short and the conductors were placed in tray where either phases were grouped together (very bad) or the conductors were haphazardly installed without any attention to placing phases (bad).

With regard to length, the big issue is not that all conductors be the same(code issues notwithstanding), but how much relative difference exists between them. If you have some that are 20 ft in total length and others that are 30 ft you will have problems that will not occur if you are at 100/110ft.

 

[jghrist]

I agree that inductance cannot be ignored except for small conductors where the resistance is much more than the inductance.

If you assume equal temperatures, you will be conservative in the current split. That is, you will calculate more current in the shorter conductor than will actually be the case. The shorter conductors will carry more current because the resistance and inductance will be less. With higher temperature, the resistance will increase, reducing the difference between the short and long conductors.

 

[lannjenks]

I would like to be able to assume equal temperatures, so that was part of my question - if I am able to do that even though the shorter conductor will be carrying more current.

Other than length, every other characteristic of the conductors are assumed equal - same conductor type, same conduit type, conduits are run parallel with one another, so they should experience the same ambient temperatures.

I am calculating that the percentage current difference between the two conductors in parallel is about equal to their percentage difference in length, but that was without taking inductance into effect. However, isn't the amount of inductance of each conductor also proportional to its length, thereby not changing the ratio for percentage current difference?

Thanks,

Laura Jenkins

 

[jghrist]

Yes, the inductance is proportional to length, so neglecting temperature differences, the total impedance is proportional to length and the current ratio I1/I2 would equal the length ratio L2/L1.

This also assumes that the resistance of the end connections, which would not vary with the conductor length, is small compared to the conductor resistance.

 

[jbartos]

Suggestion: It can be designed safe, if the current divider calculation is applied and the current for the longer cable is within its rated ampacity, and associated other parameters for the application.
The current divider relationships:
Itotal=Ishortcable+Ilongcable
Ilongcable=Itotal x Zlongcable/(Zlongcable+Zshortcable)
Zs can be obtain from
NFPA 70-2002 National Electric Code, Table 9 page 70-626

 

[lannjenks]

Jbartos - Thanks for the Table 9 reference. Just one correction

Ilongcable = Itotal x Zshortcable/(Zlongcable+Zshortcable)

I know that the code states that parallel cables must be equal length, but in reality, this does not always happen. There is usually a small amount of leeway on the inspectors part, and I wanted a way to judge when that leeway is reasonable and when it is not.

Laura Jenkins