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#129843 - 09/20/05 08:57 PM 3 phase neutral current?  
bot540  Offline
Joined: Sep 2004
Posts: 174
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

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#129844 - 09/21/05 08:07 AM Re: 3 phase neutral current?  
winnie  Offline
Joined: Sep 2003
Posts: 649
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 08:16 AM Re: 3 phase neutral current?  
winnie  Offline
Joined: Sep 2003
Posts: 649
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 02:12 PM Re: 3 phase neutral current?  
JBD  Offline
Joined: Jul 2001
Posts: 599
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:

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