AC Power: Single and Balanced Three Phase

Method & assumptions

1. Sinusoidal steady-state AC power for a passive single-phase load or a balanced three-phase load. Enter RMS values and displacement power factor from 0 to 1.
2. Single phase: S = VI. Balanced three phase: S = √3 VL IL, where VL is line-to-line RMS voltage and IL is line RMS current. The latter applies to balanced wye or delta loads without substituting phase values for line values.
3. P = S cosφ = S PF. Q = ±S√(1 − PF²); positive for lagging inductive current and negative for leading capacitive current. Specified angle φ = ±acos(PF) is the per-phase impedance angle, not the angle between a line-to-line voltage and line current. At zero current, all powers are zero; the angle only reflects the specified input.
4. P is in watts, Q in var and S in volt-amperes. For balanced three phase, active power per phase is P/3. Unity power factor gives Q = 0.
5. Does not model harmonic distortion, unbalanced phases, exported active power, transients or motor efficiency. Displacement power factor need not equal true power factor for distorted waveforms. Results are not conductor ampacity, protection or equipment-rating selections.

Sources

• US DOE Electrical Science Volume 3, ES-09: power triangle and balanced three-phase loads ↗