Voltage unbalance of a supply
Voltage or current unbalance from three line readings.
Try a job 4
Each job fills in example values. Replace them with your values.
- Check the voltage unbalance at a motorThe unbalance of 415, 402 and 409 V at a motor starter.
- Voltage unbalance of a rural supplyHow far out a long rural line is at 400, 384 and 396 V.
- Check the current unbalance of a motorThe current unbalance of a motor drawing 31, 27 and 29 A.
- Find the motor heating from unbalanceHow much a 3 % unbalance adds to the winding temperature rise, by the rule of thumb.
Inputs
Worked example with the default inputs. The live calculator replaces it when the page loads.
- Readings
- Line voltages
- Voltage A to B
- 405 V
- Voltage B to C
- 398 V
- Voltage C to A
- 411 V
Deviation unbalance
1.65%
- Sequence unbalance
- 1.86%
- Mean of the three
- 404.67V
- Largest deviation from the mean
- 6.67V
- Increase in winding temperature rise, rule of thumb
- 5.4%
This result is a design aid. Verify it against the current standard.
Calculation steps
- Mean of the three404.67V
- Largest deviation from the mean6.67V
- Deviation definition: 100 × 6.67 ÷ 404.67Result1.65%
- Sequence definition: 100 × negative ÷ positive sequence, from the three magnitudes1.86%
- Motor heating: 2 × 1.65²5.4%
About this calculator
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.
| Step | Table or clause | What it decides |
|---|---|---|
| Mean | The sum of the three readings over three | The reference the deviation is taken from |
| Deviation definition | Largest deviation over the mean | The NEMA style unbalance |
| Sequence definition | Negative over positive sequence, from the magnitudes | The IEC style unbalance |
| Motor heating | Twice the square of the unbalance | A rule of thumb for the increase in the winding temperature rise |
| A reading that cannot close | One reading larger than the other two together | No sequence figure, check the readings |
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.
Questions
Each answer describes what this tool calculates. The result is a design aid. Verify against the current standard.
How do you calculate voltage unbalance?
Take the mean of the three line voltages. Find the reading furthest from the mean. The unbalance is that deviation over the mean, in percent. 405, 398 and 411 V have a mean of 404.67 V and are 1.65 % out.
What is the difference between the deviation and the sequence definitions?
The deviation definition uses the largest deviation from the mean. The sequence definition divides the negative sequence voltage by the positive sequence voltage. For small unbalance the two are close. The tool gives both.
Why does voltage unbalance heat a motor?
The negative sequence voltage drives a current that turns against the rotor. It adds loss and heat for no work. A published rule of thumb puts the percent increase in the winding temperature rise at about 2 × the square of the percent unbalance.
Should I measure line or phase voltages?
Use the line-to-line voltages. The sequence formula needs three phasors that close a triangle, as line voltages do. Phase-to-neutral readings can carry a zero sequence part the formula leaves out.
Can it work current unbalance?
Yes. Pick line currents and enter the three readings. Current unbalance is often several times the voltage unbalance that causes it, so a small voltage unbalance can show as a large current unbalance on a motor.
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