Neutral Current Formula

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tkb

Senior Member
Location
MA
I am trying to calaulate neutral current on a 3 phase circuit but don't know the formula.

Is there a formula for neutral current when you know the voltage and amperage on the phases?

Assuming a pf of 1.0
 

charlie b

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Location
Lockport, IL
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Semi-Retired Electrical Engineer
You only need the phase currents.

Neutral current is the square root of the sum of the following things:
  • Phase A current squared, plus
  • Phase B current squared, plus
  • Phase C current squared, MINUS
  • Phase A current times Phase B current, MINUS
  • Phase A current times Phase C current, MINUS
  • Phase B current times Phase C current.
 

brian john

Senior Member
Location
Leesburg, VA
neutralcurrent1.jpg
 

roger

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Or, SQRT I?A + I?B + I?C - (IA x IB) - (IB x IC) - (IC x IA)

Roger
 

tkb

Senior Member
Location
MA
So...which formula is correct?

charlie b
√(A?+B?+C?)-(A*B-B*C-A*C)

brian john
√(A?+B?+C?)-(A*B+B*C+A*C)
 

tkb

Senior Member
Location
MA
When I input this formula in Excel I get a result of 400 amps on the neutral.

A1=200
B1=200
C1=200

N=400???

=SQRT(((A1*A1)+(B1*B1)+(C1*C1))-((A1*B1)-(B1*C1)-(A1*C1)))

Don't seem right.
Shouldn't the result be 0?
 

infinity

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Location
New Jersey
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Journeyman Electrician
40,000+40,000+40,000=120,000

120,000-(40,000-40,000-40,000)=0

SQ Root of 0=0

Charlie or Roger's formula
 

charlie b

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Location
Lockport, IL
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Semi-Retired Electrical Engineer
So...which formula is correct?
charlie b
√(A?+B?+C?)-(A*B-B*C-A*C)

You mis-represented my formula. Why did you put parentheses around any of my terms? I did not.

My formula, if translated from words into symbols, would be
√A?+B?+C?-A*B-B*C-A*C

This is the same as,
√(A?+B?+C?)-(A*B+B*C+A*C)

Thus, what I wrote in words, and what Brian showed with symbols, are the same thing.
 

tkb

Senior Member
Location
MA
Thanks for the algebra lesson. :grin:

Funny how the parentethis change the result.

I got it now.

Thanks
 

mull982

Senior Member
The nuetral current would also be a sum of all of the current phasors.

Ia + Ib + Ic = In

Ia, Ib, and Ic represent the current phasors which have a magnitude and phase angle.
 

charlie b

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Staff member
Location
Lockport, IL
Occupation
Semi-Retired Electrical Engineer
Not exactly, Brian's formula use *2 instead of squared.
Semantics. The asterisk character is often used to denote the square function. I think it's a leftover from early Basic or Fortran programming, but that memory has faded beyond recall.
 

don_resqcapt19

Moderator
Staff member
Location
Illinois
Occupation
retired electrician
very nice.:D cool tool.:D i am curious, what values would produce the largest current flow on a neutral ? i tried Ia=0,Ib=10,Ic=20, for a 20 amp circuit, just for fun and got 17.33 for In. just curious what max In could be?
The maximum neutral current is when you have one or two of the ungrounded conductors fully loaded. In both cases the neutral current will be the same as the ungrounded conductor current.
 

Smart $

Esteemed Member
Location
Ohio
In my original formula I used a squared symbol it did not transpose into Paint SORRY

Use the Print Screen key to copy an image of your screen to the Clipboard, or use Alt+Print Screen for an image of the active application. Paste into Paint and crop or otherwise modify to suit before saving to file.

If you are using Windows Vista, the Snipping Tool allows the user to capture any area of the screen. You can then Copy it to an image app or simply save it directly to an image file: PNG, JPEG, GIF, and/or a single file web page (*.MHT).

Additionally, Insert Equation or Insert Object > MS Equation in Office programs does a decent job of making formulas in true mathematical form...

NeutralCurrentFormula.gif
 
Last edited:

brian john

Senior Member
Location
Leesburg, VA
Use the Print Screen key to copy an image of your screen to the Clipboard, or use Alt+Print Screen for an image of the active application. Paste into Paint and crop or otherwise modify to suit before saving to file.

If you are using Windows Vista, the Snipping Tool allows the user to capture any area of the screen. You can then Copy it to an image app or simply save it directly to an image file: PNG, JPEG, GIF, and/or a single file web page (*.MHT).

Additionally, Insert Equation or Insert Object > MS Equation in Office programs does a decent job of making formulas in true mathematical form...

NeutralCurrentFormula.gif


I did this or tried to it did not transpose?????
 
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