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How this is calculated#

A three‑phase supply is balanced when its three line voltages are equal and 120° apart. Long rural lines, single‑phase loads spread unevenly and a failing connection all pull the three apart. The tool puts a number on how far apart they are, in the two ways the trade uses.

The deviation definition is the simple one. The tool takes the mean of the three readings and finds the reading furthest from it. The unbalance is that deviation over the mean, as a percent. This is the definition NEMA uses for motors.

The sequence definition comes from symmetrical components. Any three phasors split into a positive sequence, which turns a motor forward, and a negative sequence, which turns against it. The unbalance is the negative sequence over the positive sequence, as a percent. This is the IEC definition. The tool works it from the three magnitudes alone, with a closed formula that holds for line-to-line voltages. For a small unbalance the two definitions are close.

For voltages the tool also gives a motor heating figure. A widely published rule of thumb puts the percent increase in the winding temperature rise at twice the square of the percent unbalance. It is an estimate, not a standard's curve. AmpSize holds no standard for unbalance, so the tool cites none.

The same sums work on three line currents. Current unbalance is often several times the voltage unbalance behind it.

Worked examples#

• A motor starter reading 415, 402 and 409 V is 1.63 % out by the deviation definition and 1.84 % by the sequence definition.
• A rural supply at 400, 384 and 396 V is 2.37 % out by the deviation definition and 2.43 % by the sequence definition.
• A supply at 400, 388 and 412 V is 3 % out by the deviation definition and 3.47 % by the sequence definition. The rule of thumb puts the increase in the winding temperature rise at 18 %.
• A motor drawing 31, 27 and 29 A has a current unbalance of 6.9 % by the deviation definition and 7.99 % by the sequence definition.

Limits#

The tool takes three readings at one moment. A supply that swings through the day needs readings at its worst hour, or a logger.

It does not give a motor's rating at an unbalance. That curve is in NEMA MG 1 and in the maker's data, which AmpSize does not hold. Use the maker's figure for a motor that runs near its full load.

Phase-to-neutral readings can carry a zero sequence part that the sequence formula leaves out. Enter line-to-line voltages.

See also: Neutral current, Three phase power and Motor.