Jeffrey Cheney

Interest

Three-phase power and power factor

Study notes. Jeffrey’s resume lists 277/480V systems as a skill. This page is the theory around that skill, not a log of services he has balanced.

Wye and delta

In a wye, each coil runs from a line to a common neutral. Line-to-line voltage is line-to-neutral voltage times the square root of three (about 1.732). That is why 208Y/120 and 480Y/277 are pairs: 120 × 1.732 ≈ 208, and 277 × 1.732 ≈ 480. Line current and coil current are the same in a wye.

In a delta, the coils sit between the lines and there is no neutral unless one is derived. Line voltage and coil voltage match. Line current is coil current times √3. A corner-grounded delta or a high-leg delta (120/240 with a wild leg near 208 volts to neutral) shows up in older buildings. The high leg is the one that must not be used as if it were 120.

Wye voltages Three coils meet at a neutral. Phase-to-neutral is 277 volts. Phase-to-phase is 480 volts. A B C 277 V to N 480 V line to line = 277 × √3
A 480Y/277 system. The neutral is the center. Line-to-line is the long way around.

Power triangle

Real power, kilowatts, does the work. Reactive power, kilovars, is the sloshing current that magnetizes motors and transformers. Apparent power, kilovolt-amperes, is what the wires and the transformer have to carry. They form a right triangle: kW on the adjacent side, kVAR on the opposite side, kVA on the hypotenuse. Power factor is kW ÷ kVA, which is the cosine of the angle between kW and kVA.

A 100 kW load at 0.78 power factor.

kVA = 100 / 0.78 ≈ 128.2 kVA.

kVAR = √(128.2² − 100²) ≈ 80.2 kVAR.

Current at 480 V, three phase: I = 100,000 / (1.732 × 480 × 0.78) ≈ 154 A.

The same 100 kW at unity power factor would be about 120 A. The wires feel the 154.

Power triangle A right triangle with kilowatts horizontal, kilovars vertical, and kilovolt-amperes on the hypotenuse. The angle is the power-factor angle. kW real kVAR kVA θ, PF = cos θ
Correcting power factor shortens the vertical side. The hypotenuse shrinks toward the real power.

Why utilities bill for a low power factor

The utility’s transformers and conductors carry kVA, while the energy meter mostly records kW. A low power factor means more current for the same work, more loss, and less room on the feeder for the next customer. Many tariffs add a charge, or a kVA demand ratchet, below a power-factor threshold. The threshold and the math are in that utility’s rate, not in the NEC. Eaton’s application note on power-factor capacitors says the local tariff is what decides whether a capacitor bank pays for itself.

Capacitor correction

Capacitors supply magnetizing current locally, so the utility does not have to. The kvar to add, to move from power factor PF1 to PF2, is kW times (tan of the first angle minus tan of the second).

Raise the 100 kW, 0.78 PF load to 0.95.

tan(arccos 0.78) ≈ 0.802. tan(arccos 0.95) ≈ 0.329.

Capacitor ≈ 100 × (0.802 − 0.329) ≈ 47 kVAR.

That size is a starting calculation. A bank that is too large can raise the voltage. A bank switched in with the motor, rather than left on an empty bus, avoids leading power factor when the load is off.

Harmonics

VFDs, rectifiers, and UPS inputs draw current in pulses. A 6-pulse drive is rich in 5th and 7th harmonics. Those currents distort the waveform. Displacement power factor (the fundamental angle) can look fine while true power factor, which includes distortion, is worse. Capacitors do not cancel harmonics. With the inductance of a transformer they can resonate near those harmonic orders and magnify the current. IEEE 519-2022 sets recommended limits on voltage and current distortion at the point of common coupling. It is a recommended practice, applied at the PCC, not a substitute for the NEC. Detuned reactors or active filters are the usual answer when a study says a plain capacitor bank would resonate.

Balancing phases

Single-phase loads on a three-phase panel — lighting at 277, receptacles on a 120-volt subpanel — should be spread across the phases. A heavy A phase and a light C phase waste capacity and heat the neutral when harmonics are present, because triplen harmonics add in the neutral instead of cancelling. The panel schedule is the place to see it. A clamp meter on each phase, with the building in a normal operating state, is the place to check it.

What's happening now

Code section numbers, energy-code rules, and utility practices change by edition and by city. The authority having jurisdiction, and the employer’s written program, decide what applies on a given job.