How to calculate the unbalanced neutral current in a 3 phase circuit

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rmann

Member
I was teaching a class in sharing the grounded conductor in a single phase circuit.
We only have 3 phase power in our class. I built a simple circuit with 2 equal loads on 2 seperate phases with a shared grounded conductor. I figured that the current in the grounded conductor in a three phase circuit would not be as low as in a single phase situation, but it would be significantly less than in the 2 hots.
When we measured the currents, the neutral was almost the same as the hots. what gives?
So does anyone know the formula for calculating the current in the grounded conductor in an unbalanced 3 phase circuit? I went over lots forums and archived forums and couldn't find any thing. I appreciate any help you can give.
 

480sparky

Senior Member
Location
Iowegia
WyeNeutralCalc.jpg
 

kwired

Electron manager
Location
NE Nebraska
Exactly the reason 310.15(B)(5)(b) exists.

(b)
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In a 3-wire circuit consisting of two phase conductors and the neutral conductor of a 4-wire, 3-phase, wye-connected system, a common conductor carries approximately the same current as the line-to-neutral load currents of the other conductors and shall be counted when applying the provisions of 310.15(B)(3)(a)
 

Rick Christopherson

Senior Member
Here is where vector mathematics comes in handy, and something you should be teaching to your students. Assuming resistive loads and all currents being equal in magnitude, you will have Ia = I∠120? and Ib = I∠240?. The sum of these two currents in the neutral will be found by adding the vectors. In this case, I chose to use the parallelogram method because it shows better in a single diagram. The other method is to redraw the vectors head-to-tail. (Don't ever let someone here tell you that tail-to-tail vectors means they should be subtracted. That is inappropriate vector math.)

Ia + Ib = I∠120? + I∠240? = I∠180?

In your example, you are missing the Ic = I∠0?. If Ic was present, then the total neutral current would be I∠180? + I∠0? = 0

2PhaseCurrents.jpg
 

charlie b

Moderator
Staff member
Location
Lockport, IL
Occupation
Retired Electrical Engineer
When we measured the currents, the neutral was almost the same as the hots. what gives?
That question has been answered. But let me suggest that you take the same two phase wires that you used for your experiment and connect them instead to the primary of a single phase transformer. The voltage ratio is not important, but for discussion sake let us say the secondary voltage is 120/240. Try your experiment again, this time using the transformer secondary as your voltage source.
 

iwire

Moderator
Staff member
Location
Massachusetts
That is fine where load power factor is identical on all three phases. But not if the power factors differ.

Neutralcurrent02.jpg

That is certainly a fact, but in any electricians training and testing I have seen they are looking for what 480 posted.

They don't usally consider PF in the questions involving neutral current.
 

Besoeker

Senior Member
Location
UK
That is certainly a fact, but in any electricians training and testing I have seen they are looking for what 480 posted.
They don't usally consider PF in the questions involving neutral current.

I'm sure what you say is correct. But it's a bit of a shame, I think. By all means give the expression that 480 posted but with the caveat that it applies to very specific circumstances, not all. Even not most.
Nah, on reflection, I don't think it should be taught to electricians. Is it of any practical use?
For the simple example I gave, the neutral current is nearly three times the magnitude that you would get by evaluating that expression.
 

jumper

Senior Member
I'm sure what you say is correct. But it's a bit of a shame, I think. By all means give the expression that 480 posted but with the caveat that it applies to very specific circumstances, not all. Even not most.
Nah, on reflection, I don't think it should be taught to electricians. Is it of any practical use?
For the simple example I gave, the neutral current is nearly three times the magnitude that you would get by evaluating that expression.

Do not confuse the situation with real life facts, we get flustered:)
 

rmann

Member
Big Thanks!

Big Thanks!

Thank you all for your great responses. I teach what's called a "pre apprentice" program at the san Diego Job Corps so a lot of your responses are way beyond my students( and me too). I think the Vector math that Rick submitted will be really helpful. somehow the visual really makes it clear. Thanks again. I'll be BACK!
 

kwired

Electron manager
Location
NE Nebraska
I have no problem with teaching someone the basic formulas, then also informing them that things like power factor and harmonic currents can complicate what is really there. For the average installer or basic troubleshooting person, that is what they need to know. If they get into a situation where that additional information they can turn to the books or places like this forum for help. Kind of what I do myself as I do not run into power factor or harmonic problems frequently enough to remember formulas, or even some of the technicalities that apply. Just knowing Ohms law, Kirchoff's laws gets most average installers and troubleshooters through what they run into the most. Knowing what else may be lurking and where to go for more help with it is important though.
 

rattus

Senior Member
To the mystery mod who deleted my posts, I was not bickering. I was correcting some misinformation in other posts.
 

mivey

Senior Member
To the mystery mod who deleted my posts, I was not bickering. I was correcting some misinformation in other posts.
Was the information related to the OP? If so, how about a re-post with just the facts? If not OP related, how about posting the information and correction (just the facts, of course) in a separate thread?
 
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