What a Phase Imbalance Does to a Motor

Why this matters

A motor sitting on an imbalanced supply is being heated by a current that appears nowhere on its nameplate, in a part of the machine its thermal protection may not be watching, and it will pass every bench test you can throw at it. Shops replace these motors twice, sometimes three times, before anyone reads all three legs at the same moment. The imbalance is usually small enough that the voltage readings look fine to the eye, which is exactly why the mechanism is worth understanding rather than memorising a threshold.

The mechanism: a field that turns the wrong way

Any unbalanced set of three-phase voltages can be decomposed into three balanced sets: a positive-sequence set rotating in the normal direction, a negative-sequence set rotating backwards, and a zero-sequence set which is in phase in all three legs and cannot reach a motor with no neutral connection. That decomposition is mathematics rather than a model, and it is what makes an imbalance predictable.

The positive-sequence set is what runs the motor. The negative-sequence set produces a magnetic field turning backwards at synchronous speed, and the rotor is turning forwards at close to synchronous speed, so relative to that backwards field the rotor is slipping at nearly twice synchronous speed. Two consequences fall straight out of that, and they are the two that matter:

• The rotor sees the negative-sequence field at roughly twice line frequency, near 120 Hz on a 60 Hz supply. Current at that frequency crowds toward the surface of the rotor bars and end ring, so the negative-sequence loss lands disproportionately in the rotor.
• The negative-sequence torque opposes rotation, and its interaction with the main field produces a torque pulsation at twice line frequency. Net output torque falls and the machine develops a 120 Hz vibration signature that was not there when the supply was balanced.

Why a small voltage imbalance makes a large current imbalance

At a slip near 2 the motor's impedance to the negative-sequence set is close to its locked-rotor impedance rather than its running impedance. For a general-purpose induction motor whose locked-rotor current is on the order of six times full-load current, that means the negative-sequence impedance is roughly a sixth of the positive-sequence impedance at rated load. The same percentage of voltage therefore drives roughly six times as much current.

That is where the field rule of thumb comes from: percent current unbalance typically runs about 6 to 10 times percent voltage unbalance, at or near rated load, on a general-purpose induction motor. The condition in that sentence is load-bearing in both directions. At rated load the ratio sits near the low end, because the positive-sequence current in the denominator is large. Lightly loaded, the positive-sequence current falls while the negative-sequence current barely moves, so the percentage climbs well past 10, and a percentage measured on an idling motor overstates the thermal problem rather than proving one.

Unbalance itself is defined as the maximum deviation of any one reading from the average of the three, divided by that average, expressed as a percentage. The same formula runs on volts or on amps, and you must say which one you measured, because the two numbers differ by that factor of six or more.

What the extra current does, and where the heat lands

Loss goes with the square of current, so the negative-sequence loss goes with the square of the voltage unbalance. The commonly cited approximation is that the percentage increase in temperature rise is about twice the square of the percent voltage unbalance: 2 percent unbalance costs roughly 8 percent extra rise, 3 percent costs roughly 18 percent, 5 percent costs roughly 50 percent. That is an approximation for general-purpose induction machines rather than a specification, and the manufacturer's own data governs a specific motor.

Where the heat lands is the part that defeats the protection. Thermal protection built into a motor most often sits in the stator winding, and a meaningful share of the negative-sequence loss is in the rotor, which nothing is watching. An overload relay in the starter is watching line current, and line current is inflated by the imbalance, which is the one piece of good news here: a sufficiently large imbalance eventually shows up as an overload trip. A modest one does not, and the motor simply runs hotter for the rest of its shortened life.

The derating the manufacturer expects you to apply

Motors built to NEMA MG 1, in the edition the manufacturer built to and reaching you through the motor's own literature rather than on its own authority, come with a derating curve for operation on an unbalanced supply. The curve begins at 1 percent unbalance and falls away steeply; the values commonly published on it are approximately:

Read the curve in the edition that applies rather than this table where the decision is close, and note the practical ceiling that accompanies it: continuous operation above 5 percent unbalance is not recommended at any derating. The factor multiplies the load the motor may carry, not the voltage and not the nameplate current directly.

Worked example: 2.6 percent that costs more than it looks like

A three-phase motor on a 208 V nominal supply, nameplate full-load current 22.0 A, driving a constant load. It has been replaced once already. Every reading below is taken with the machine running, which is energized work: 29 CFR 1910.333(a)(1) permits it only where the employer can demonstrate that de-energizing introduces additional or increased hazards or is infeasible due to equipment design or operational limitations, and an imbalance measurement is that case because the running condition is the thing being measured. Establish boundaries and select PPE on the basis in NFPA 70E-2021, 130.5 and 130.7, binding through your employer's electrical safety program or a contract rather than on its own; use a meter and clamp rated CAT III or better at or above the voltage present; keep hands and leads clear of the coupling and any exposed shaft while the machine turns. When you stop measuring and start working, open and lock the disconnect under 29 CFR 1910.333(b)(2) for the electrical exposure and under 29 CFR 1910.147 for the unexpected-startup hazard of the driven machine, prove dead with the live-dead-live sequence at NFPA 70E-2021, 120.5, and note that 1910.147 excludes the electrical exposure itself at (a)(1)(ii)(C), with 29 CFR 1926.417 as the construction counterpart.

Voltages, line to line, all three at the same moment: 212, 208 and 202 V.

Average = (212 + 208 + 202) / 3 = 207.3 V. Deviations are +4.7, +0.7 and -5.3, so the largest is 5.3 V and the voltage unbalance is 5.3 / 207.3 = 2.6 percent.

Currents, all three legs at the same moment: 24.8, 21.0 and 18.6 A.

Average = (24.8 + 21.0 + 18.6) / 3 = 21.5 A. Deviations are +3.3, -0.5 and -2.9, so the largest is 3.3 A and the current unbalance is 3.3 / 21.5 = 15.3 percent.

Check that against the rule stated above: 15.3 divided by 2.6 is a ratio of 5.9, just below the 6 to 10 band, which is what you expect on a machine loaded near its rating. Had the ratio come out at 20, the honest reading would have been that the motor is lightly loaded rather than that the supply is worse than the voltages say.

The heating cost: twice the square of 2.6 is 2 x 6.76 = 13.5 percent more temperature rise than the same motor would see on a balanced supply at the same load.

The derating, and the sting. At 2.6 percent, interpolating between the 0.95 at 2 percent and the 0.88 at 3 percent given above puts the factor near 0.90, and reading the published curve directly is better than interpolating where the decision is marginal. So this motor should be carrying no more than about 90 percent of its rating on this supply.

Now compare that against what it is actually carrying. Average line current 21.5 A against a 22.0 A nameplate is 98 percent of rating. The motor is under its nameplate current, which is why every previous tech signed it off, and it is roughly 8 percentage points above the ceiling its own manufacturer's derating curve sets for a 2.6 percent unbalanced supply. Being under nameplate current on an imbalanced supply is not the same as being within rating, and that gap is the entire reason this machine has been replaced once already.

The failure mode of missing this is specific and repeatable: the replacement motor is installed, runs, reads under nameplate on the one leg anybody clamps, and dies in the same season. The invoice says motor. The cause was 5.3 V.

Why the motor tests perfectly

Everything a tech does to a suspect motor is done with the supply removed, and the imbalance lives in the supply. Winding resistance measured leg to leg is balanced because the windings are fine. Insulation resistance is fine because the insulation has not failed yet. Spin it by hand and the bearings are fine. Put it on a balanced supply at the shop and it draws even current on all three legs.

That is not a bad test, it is a test of the wrong subject. The only test that reaches this fault is three simultaneous readings on the supply, taken with the motor loaded, which is the subject of a sibling article.

What to do with the finding

Establish which side the imbalance comes from before quoting anything. An imbalance measured at the motor terminals can originate in the utility supply, in a single-phase load distribution that is uneven across the three legs, or in a high-resistance connection somewhere in the run. Those three have entirely different owners and entirely different costs, and the diagnostic that separates them is a lead-rolling test at the motor, covered in the sibling article on measuring imbalance.

Do not treat a phase monitor as a fix. A voltage monitoring relay ahead of the starter protects the next motor by dropping the machine out when the imbalance exceeds its setting, which is worth having on any three-phase machine whose loss stops a process. It does not reduce the imbalance, and a monitor set loose enough to avoid nuisance trips can sit above the point where the derating curve has already taken meaningful life out of the winding. Set it against the derating the machine actually needs, not against the point where the machine will not run.

Correct the load distribution before you argue with the utility. Where single-phase loads in the building are spread unevenly across the three legs, the imbalance is generated on the customer's side and is correctable by moving circuits, which is ordinary work. Bring the utility a measurement taken at the service with the building's own single-phase distribution accounted for, or the first thing they will do is measure at the service and close the ticket.

Where the winding has already been cooked, replace the motor and the cause in the same visit. A motor that has run at 2.6 percent unbalance near full load for a season has spent insulation life you cannot get back, and a replacement into an uncorrected supply is a warranty claim waiting to be argued about.

References

• 29 CFR 1910.333(a)(1) and (b)(2) for energized work and de-energizing; 29 CFR 1910.147 for the unexpected-startup hazard of driven machinery, with the electrical carve-out at (a)(1)(ii)(C); 29 CFR 1926.417 for the construction counterpart
• NFPA 70E-2021, 120.5, 130.5 and 130.7, applied through an employer electrical safety program or contract
• NEMA MG 1 for the unbalanced-voltage derating curve and motor voltage tolerance, in the edition the motor manufacturer built to, reaching you through the motor's literature
• Manufacturer motor data for the specific machine, which owns its thermal protection arrangement and its permissible loading
• See related: How to Measure and Interpret Phase Imbalance; What Happens When a Phase Is Lost