I really need some help here.....Given two parallel copper conductors of different length - the shorter conductor will draw more current than the longer conductor. Will the increased current in the shorter conductor raise its resistivity, therefore decreasing the current?

The current will be proportioned between the parallel conductors in inverse proportion to the resistance of the conductors. So, for example, if I had to carry 300A of current, and one conductor had a resistance of 0.01 ohm, and the other conductor had a resistance of 0.02 ohm, the 0.01 ohm conductor would carry 200A, and the 0.02 ohm conductor would carry 100A.

Where temperature comes into play is that it changes the resistances that you need to use to calculate the proportioning of the current.

In your example, you have two very similar conductors, but with a length difference. In this particular case, the shorter conductor would run hotter, and this would tend to _reduce_ the resistance difference between the two conductors.

While the resistance difference will be reduced by the differential heating of the wires, it will _never_ be enough to cause the longer wire to carry more current than the shorter wire. This is because for the hotter wire to remain hotter, it _must_ be dissipating more power. But power dissipated is the product of the current flowing in the conductor and the voltage drop. For parallel conductors the voltage drop must be the same...so the conductor carrying more current will be dissipating more power, and this will have to be the hotter conductor.

(Note: The above argument presumes that the system has come to steady state equilibrium; I've not disproven the possibility of a system somehow oscillating, with one wire and then the other getting hotter...I'd have to think about this some more. )

-Jon

[This message has been edited by winnie (edited 12-05-2003).]

#128772 - 12/05/0304:00 PMRe: Conductor Temperature

Assuming this is a 60Hz NEC310-4 installation, the degree to which the shorter conductor raises its resistivity will likely be orders of magnitude too small to offset the impedance difference for conductor length.

#128773 - 12/05/0304:52 PMRe: Conductor Temperature

Bjarney, that's what I am thinking, but I'm not sure how to prove this.

This is a 310.4 issue that I am looking at. Even though the code book states that conductors must be the same length, there seems to be a small amount of leeway. I need to know the impact of unequal length parallel conductors.

If I calculate the resistance of conductors using R = k*l/A, wouldn't the value of k differ depending on the amount of current through each conductor (due to the heating effect). Or for small differences in length, let's say 5% or less, is the difference in k insignificant?

Is there an oscillating effect?

Thanks,

Laura Jenkins

#128774 - 12/05/0308:37 PMRe: Conductor Temperature

I don’t have a good answer on parallel-conductor lengths. Shorter runs likely are more critical in matching, and you can’t dismiss inductive reactance, where the cables may be of identical length, but may not share current exactly because of physical dissymmetry in cable routing. I don’t know about recent CMP activity, but I believe past proposals have requested clarification. Joe T — Do you know of any current work on this?

[This message has been edited by Bjarney (edited 12-05-2003).]

#128775 - 12/05/0311:15 PMRe: Conductor Temperature

6-6a Log #CP600 NEC-P06 (310-4) Final Action: Accept Submitter: Code-Making Panel 6 Recommendation: At the end of the existing first paragraph of 310.4, delete "(electrically joined at both ends to form a single conductor)". Substantiation: The parenthetical phrase does not provide clarity and is not necessary. Panel Meeting Action: Accept

COMMENT:

6 Log #1588 NEC-P06 (310- Submitter: Alan Manche, Schneider Electrc/Square D Co. Comment on Proposal Number: 6- Recommendation: The panel should reconsider and reject proposaI6-6a. Final Action: Substantiation: The parenthetical phrase "(electrcally joined at both ends to form a single conductor)" does provide clarity to this section. This wording was added to the 1971 NEC to enhance the clarity of parallel conductor installations. The removal of this wording wil likely be interpreted that parallel conductors are not required to be joined at both ends or at least create unecessary confusion. The panel should consider the wording in 230.2 which states: ... underground sets of conductors, 1/0 AWG and larger, ruing to the same location and connected together at their supply end but not connected together at their load end shall be considered to be supplying one service. The phrase in 310.4 provides a consistent and practical approach, as found in 230.2, in order to help the user of the code understand the requirement clearly.

Joe Tedesco, NEC Consultant

#128776 - 12/06/0310:22 PMRe: Conductor Temperature

Years ago I set up a simple demo of unequal cable lengths for discussing 310-4 with my students in a Code class. It used pairs of 3/0 THW aluminum in GRC at ~300 amperes. In that case, current division in each of two cables “per phase” was close to inversely proportional to conductor length.

#128777 - 12/07/0311:08 AMRe: Conductor Temperature

Laura Jenkins writes: > If I calculate the resistance of conductors using R = k*l/A, wouldn't > the value of k differ depending on the amount of current through each > conductor (due to the heating effect). Or for small differences in length, > let's say 5% or less, is the difference in k insignificant? > Is there an oscillating effect?

While I mentioned that I couldn't prove that there isn't an oscillating effect, I'm pretty certain that you won't have one in any normal situation, and I _think_ that one could prove that you wouldn't get one at all.

You are exactly right, you need to determine the resistance of the conductors using R=k*l/A, and conductors at different temperatures have different values of k. So to answer your question, you need to figure out what the difference in k will be.

The following short page on temperature coefficeint of resistance will help here. Very approximately, the value of k changes by about 0.4% per degree C. This means that a 12C difference in wire temperature will have about as much effect on the balance of current flow as a 5% difference in length. Thus I would say that the difference in k is potentially significant.

You now need to take the question further, and ask if there will be a temperature difference, and ask how much it will be. Remember that _both_ wires are carrying current, so both wires will heat up, and for short differences in length, the current will be pretty darn close to the same, so the temperature rise will be pretty darn close to the same, and the temperature difference pretty small. You also need to consider the environment that the wires are in. If they are well cooled, then the overall temperature rise will be pretty small, and the temperature difference smaller still. If they are well insulated but together (say two parallel conduits close together in thermal insulation) then there will be lots of temperature rise, but again the temperatures will be pretty similar. If you had two conduits separated by space, each buried in thermal insulation, then you could potentially get a large temperature difference, and the difference in k would be significant.

There is a very useful approximation for figuring out how hot something will get. It is called the 'lumped resistance' model, and basically you assume that conduction of heat acts just like conduction of electricity. You just use Ohms law, but interpret it differently: E=I * R, where E is the _temperature_ difference in degrees C, I is the _heat flow_ in watts, and R is the _thermal resistance_. You then calculate the heat being generated at the source, divide by the thermal resistance, and this gives you E, the temperature difference (or temperature rise). The higher the thermal resistance, the greater the temperature rise for the heat to be carried away.

I spent some time working backward from table B.310.16 (Ampacities of ...Conductors...In a raceway, cable or Earth), and figure that a resistance of about 4.5C/watt is about right for 4/0AWG wire (3 conductors in a cable). Each conductor would be dissipating about 4.3 watts per foot at the allowable current of 260A, and there are 3 conductors for a total of 12W per foot, and the allowed temperature rise is 60C. However I am not certain of the thermal conductivity number; I've just been playing with the tables and making some assumptions. I a resistance that I calculated at 90C from tables 8 and 9 in chapter 9, and these values don't quite agree with values from other sources. But this should give you an idea of a reasonable value for the thermal resistance to expect with cables.

This should give you an idea of what sort of temperature difference you might find in the situations that you are describing. 4/0 copper at full ampacity is carrying 260A (presuming 90C conductors, with 90C terminations, in a 30C ambient, everything else good for this use, blah blah blah), and dissipating 260^2 * 0.0000633 = 4.3 watts per foot. With three conductors in a raceway and a thermal resistance of 4.5C per watt, you get a temperature rise of 4.3*3 * 4.5 = 58 degrees. Now add a 5% current imbalance. You have 254A in one set of conductors and 266A in the other. The temperature rise for the low current set is 254^2*0.0000633 * 3 * 4.5= 55.1C, and for the high current set 266^2 * 0.0000633 * 3 * 4.5 = 60.4C (Note in this calculation I _presumed_ that k was the same in order to calculate the power dissipated in the wires. But the temperature is clearly different, so k _must_ be different...but this is a second order effect, and I've already mucked with this calculation for too long on a Sunday morning; you are welcome to refine the calculation...)

This 5C difference in temperature corresponds to about a 2% difference in length...so my rough estimate is that given this level of thermal resistance, the compensating effect of temperature change in coefficient of resistance would mean that a 5% difference in length would result in a 3-4% difference in current being carried by the two sets of conductors.

-Jon

#128778 - 12/08/0312:07 PMRe: Conductor Temperature

Winnie, that was very helpful. What it looks like it comes down to is this. If I want to be conservative in my calculations, I can ignore the temperature difference, which in the end is what I want to do. I'm looking for a worst case scenario kind of thing.

Thanks,

Laura Jenkins

#128779 - 12/11/0307:49 PMRe: Conductor Temperature