Unbalanced 3 phase neutrals

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Senior Member
The unbalanced 3-phase neutral on a 480/277 volt, 4 wire calculation is quite intimidating and requires alot of work to complete. Everytime I have made this calculation ,the result is always nearly close to just simply determining the greatest unbalanced load between any two phases. It is so close that it never requires an adjustment to conductor size. Maybe not for the classroom or an exam, but in the field, do you think that the second method is acceptable?

charlie b

Staff member
Seattle, WA
Electrical Engineer
Re: Unbalanced 3 phase neutrals

It depends on one thing only: the purpose of your performing the calculation. I did a quick (translate non-scientific) comparison of the two methods. I found that they gave answers that were generally within 15% of each other. The approximation becomes better when you are close to having two equal phase currents (with an imbalance on the third). So if that degree of accuracy is sufficient for your purposes, then go ahead.

The problem of course is that you cannot be sure how accurate the “easy method” will be on any specific calculation, unless you compare the results against the “harder method” calculation. But at that point, why bother?

By the way, jut to make sure we are talking about the same thing, here is how I calculated the imbalanced neutral current N, based on phase currents A, B, and C:
N = SQRT (A*A + B*B + C*C - A*B - A*C - B*C)


Re: Unbalanced 3 phase neutrals


There is a quick and accurate method to determine the neutral current in a wye system, assuming no harmonic loads.

This formula comes with the understanding of how the wye system works. The neutral conductor carries the combination of the phase currents.

Assuming that the power factor of each phase is the same, the phase currents are separated by 120 degrees of electrical time and only one phase is at maximum current at any given time.

If you drew a vertical line through a graph of a three phase sine wave, the combination of current values at the point of intersection would be the neutral current at that point in time. Bare in mind that you will most likely be combining postive and negative values.

The neutral current sine wave will have a different electrical time than any of the phase currents unless there is current in only one phase, then the neutral current will be in time with that phase.

In understanding the combination concept and equal phase currents result in 0 neutral current, we determine that the neutral current is balanced to the extent of the lowest phase current.

The formula Charlie submitted may be reduced to N = SQRT (A*A + B*B - A*B) when the lowest of the three phase currents is subtracted from the other two and the result are used in the formula.

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