The Electrical Contractor Network

ECN Electrical Forum
Discussion Forums for Electricians, Inspectors and Related Professionals

Books, Tools and Test Equipment for Electrical and Construction Trades

Register Now!

Register Now!

We want your input!


2017 NEC and Related
2017 NEC
Now Available!

Recent Posts
Parking lot pole light swap....
by ghost307
Today at 04:10 PM
International Wire Colour Codes
by Tjia1981
Today at 12:08 PM
Son of Sparky
by HotLine1
10/20/16 07:43 PM
Speaking of Plugmold ...
by gfretwell
10/17/16 02:37 PM
Broken battery charger? Check for cobwebs!
by gfretwell
10/17/16 02:30 PM
New in the Gallery:
12.5A through 0.75mm˛ flex (just out of curiosity)
Shout Box

Top Posters (30 Days)
gfretwell 12
HotLine1 7
ghost307 6
renosteinke 6
Potseal 4
Who's Online
1 registered (HotLine1), 162 Guests and 4 Spiders online.
Key: Admin, Global Mod, Mod
Topic Options
Rate This Topic
#129843 - 09/20/05 05:57 PM 3 phase neutral current?
bot540 Offline

Registered: 09/14/04
Posts: 177
Loc: Vernon Hills, IL
Is there a formula or a way for determining how much current will be coming back on the grounded conductor in a 3 phase network? IE: phase A is carring 10A, phase B 5a and phase C 15A. How much current is carried through the ungrounded conductor?
Jesus may have been a capenter,but God was an electrician.Genesis1:3

#129844 - 09/21/05 05:07 AM Re: 3 phase neutral current?
winnie Offline

Registered: 09/15/03
Posts: 652
Loc: boston, ma
The only absolutely correct way to do this is to sum the instantaneous current of all three ungrounded phases to get the instantaneous current in the neutral. However this is usually much more work than is necessary.

If the current flowing in each phase happens to be a perfect sine wave, then it can be completely _described_ by amplitude, frequency, and phase angle. Because frequency is a constant, all we are left with is amplitude (level of current flow) and phase angle. These two parameters can be represented as a vector, and vector math can be used to answer your question.

You simply represent the current flow in each phase by a vector, and add these vectors up. This will tell you the _net_ current flow from all the phases combined, and thus the current that the neutral must balance.

Remember that the vector representation is a vast simplification; you are using a single pair of numbers (magnitude and direction) to represent a continuously changing value (voltage over time), and this simplification requires a large number of assumptions. For example you are assuming that the current flow remains constant and is perfectly sinusoidal. This means that the equations themselves are mathematically exact, but that some of the input data has been thrown away, so your results may not agree with reality if reality doesn't agree with your input assumptions.

If the current flow is not sinusoidal, but includes _third harmonic_, then the answers that these equations give will be well off the mark.

As an even rougher (but faster) approximation, you assume that the phase angles are 0, 120, 240 degrees; in reality the phase angles will differ from this because of power factor issues.

Here is a reference for actually doing the vector math:


#129845 - 09/21/05 05:16 AM Re: 3 phase neutral current?
winnie Offline

Registered: 09/15/03
Posts: 652
Loc: boston, ma
P.S. When you work through the above link, you will be able to answer your own question (A=10A,B=5A,C=15A, what does N=?) After you do this, try answering the following:
Given a three wire feed from a 208V/120 wye connected supply, with phase A, phase B, and neutral (no phase C). 15A is flowing on phase A. What current flow on phase B will minimize the neutral current? What will this minimum neutral current be? Assume all resistive line to neutral loads (this lets you off the hook for phase angles, and lets you assume 0 and 120 degrees)


#129846 - 09/21/05 11:12 AM Re: 3 phase neutral current?
JBD Offline

Registered: 07/12/01
Posts: 599
Loc: WI, USA
Yes, there is a quick and dirty 3-phase formula. While it is only truly accurate for perfect sine waves with 0, 120, and 240 degree phase spacing, it can be used in most applications.

In = SQRT((Ia*Ia+Ib*Ib+Ic*Ic)-(Ia*Ib+Ib*Ic+Ic*Ia))

So in your example:


ECN Electrical Forums - sponsored by Electrical Contractor Network - Electrical and Code Related Discussion for Electrical Contractors, Electricians, Inspectors, Instructors, Engineers and other related Professionals