6.3 Voltage Unbalance

A three-phase motor is designed for three equal voltages 120° apart. When the three line-to-line voltages are not equal, the rotating field is distorted. Some windings carry more than their share of current, copper losses rise with the square of that current, and the stator and rotor run hotter than the nameplate temperature rise. The motor may still turn, the compressor may still make tons, and a single-amp clamp on one phase may even look “near FLA.” The damage is the hot phase you did not watch.

CIRO electricity items expect the NEMA MG-1 style definition, a calculator, and the judgment to derate or stop — not a vague sense that “unbalance is bad.”

The NEMA percent-unbalance formula

1. Measure the three line-to-line voltages at the motor terminals under load: V_AB, V_BC, V_CA.
2. Compute the average: V_avg = (V_AB + V_BC + V_CA) / 3.
3. Find the maximum deviation from that average (the largest of |V_AB − V_avg|, |V_BC − V_avg|, |V_CA − V_avg|).
4. Percent voltage unbalance = (maximum deviation / V_avg) × 100.

Use line-to-line voltages, not line-to-neutral, unless you are diagnosing a grounded-wye distribution problem. A motor does not run on phase-to-ground numbers. Measure under load; a loose lug often looks fine at no load and unbalances only when current produces a voltage drop.

NEMA MG-1 guidance is that voltage unbalance at the motor should not exceed about 1%. That is a tight number. Utility supplies, long feeders, and single-phase lighting on a shared transformer make 1% a maintenance target, not a decoration on a poster.

Worked example 1 — 480 V, 472 V, 488 V

A screw-compressor motor is running. Terminal voltages are 480 V, 472 V, and 488 V.

V_avg = (480 + 472 + 488) / 3 = 1440 / 3 = 480 V

Deviations from 480 V:

• |480 − 480| = 0 V
• |472 − 480| = 8 V
• |488 − 480| = 8 V

Maximum deviation = 8 V

Percent unbalance = (8 / 480) × 100 = 1.67%

That already exceeds the 1% NEMA preference. It is not a spectacular-looking set of voltages — 472 and 488 still “look like 480” if you only glance at one meter — but the formula does not care about glances.

Heating effect: about 2 × (unbalance %)²

A widely used NEMA-related rule of thumb is that the increase in temperature rise is approximately:

extra temperature-rise percent ≈ 2 × (percent voltage unbalance)²

For the 1.67% example:

(1.67)² ≈ 2.79

2 × 2.79 ≈ 5.6% extra temperature rise

That does not mean the winding is only 5.6% hotter than ambient. It means the motor’s temperature rise above its cooling baseline grows by about 5.6%. On a motor that was already near class limits because of a dirty TEFC fan, high machinery-room ambient, or operation in the service factor, 5.6% is enough to eat insulation life.

The square law is the operational point. Unbalance does not hurt in a straight line:

• 1% unbalance → 2 × 1 = 2% extra rise (near the NEMA target).
• 2% unbalance → 2 × 4 = 8% extra rise.
• 3% unbalance → 2 × 9 = 18% extra rise.
• 4% unbalance → 2 × 16 = 32% extra rise.
• 5% unbalance → 2 × 25 = 50% extra rise.

A motor that looked fine at 1% is not “twice as unhappy” at 2%; it is on a curve that gets steep quickly. Do not run with a large unbalance and hope FLA on the average of the three ammeters will save you.

Worked example 2 — a worse bus, same average

Same motor, voltages 468 V, 480 V, and 492 V.

V_avg = (468 + 480 + 492) / 3 = 480 V (the average still looks perfect).

Maximum deviation = |468 − 480| = 12 V (492 is also 12 V off).

Percent unbalance = (12 / 480) × 100 = 2.5%

Extra temperature rise ≈ 2 × (2.5)² = 2 × 6.25 = 12.5%

Push it further to 462 V, 480 V, and 498 V:

V_avg is still 480 V. Maximum deviation = 18 V. Percent unbalance = (18 / 480) × 100 = 3.75%. Extra rise ≈ 2 × (3.75)² = 2 × 14.06 = 28%. The average meter on the MCC could still be labeled 480 V. The windings would not agree.

Current unbalance and derating

Voltage unbalance of a few percent typically produces current unbalance several times larger — commonly on the order of 6 to 10 times the voltage-unbalance percentage, depending on motor design and load. A 2.5% voltage unbalance can mean on the order of 15% to 25% current unbalance. The hot winding’s I²R loss is then far above nameplate, while the average of the three clamp readings can still sit near FLA. Always record all three amperes, not one.

Current unbalance uses the same style of formula: (maximum deviation from average current / average current) × 100. If you find large current unbalance with small voltage unbalance, look for a motor-side problem (internal winding issue, high-resistance connection at T-leads). If both voltage and current are unbalanced, start on the supply: tap settings, a failing transformer, a high-resistance lug, a deteriorating fuse or starter pole, or heavy single-phase loads on one leg of the same bank.

NEMA MG-1 publishes a derating curve for unbalanced voltage. The allowed horsepower falls as unbalance rises; by several percent unbalance the motor is no longer a full-HP machine, and operation around 5% is not a normal running condition. A CIRO supervisor does not need to memorize every point on that curve. The field rule is:

• Stay near 1% or better at the motor.
• If unbalance is a few percent, reduce load (slide valve, number of fans, pump throttle) and fix the supply.
• If unbalance is large, stop the motor before you cook a 300 HP stator. Do not “watch it through the shift.”

Where unbalance comes from in a refrigeration plant

• Loose or corroded lugs on one phase at the disconnect, starter, or motor box (voltage drop on that conductor under load).
• A fuse or starter pole that is high resistance but not yet open (the next section’s single-phasing is the limit of this).
• Unbalanced utility or plant transformer taps; an open-delta bank that was never a good idea for motors.
• Large single-phase lighting or receptacles piled on one leg of a shared transformer.
• Long feeders of unequal length or a damaged conductor.

Operator sequence: clamp all three voltages at the motor under load, compute percent unbalance, clamp all three currents, then work upstream toward the MCC and the transformer. Tighten and infrared the connections. Do not pad overload settings to hide a hot phase. Unbalance protection on some electronic overloads will trip on current unbalance; older heater overloads may not, which is why the supervisor’s meter still matters.

A 300 HP screw at 93% efficiency is already turning roughly 241 kW of electrical input into heat plus shaft work. Extra I²R from unbalance is heat that the insulation and the oil-cooled package did not budget. Fix the bus; do not ask the windings to derate themselves in silence.