Power Triangle (S, P, Q)

Formula

Description

The power triangle relates the three types of power in an AC circuit: real power P (watts, the useful power that does work), reactive power Q (volt-amperes reactive, the power that oscillates between source and reactive components), and apparent power S (volt-amperes, the total power delivered by the source). Real and reactive power are orthogonal (90° apart), so they combine as a Pythagorean sum to give apparent power. The power factor is cos(φ) = P/S. Utilities charge industrial customers for low power factor because high reactive power increases the apparent power (and thus the current) that must be delivered.

Variables

• S — Apparent power (VA)
• P — Real (active) power (W)
• Q — Reactive power (VAR)

Practical Notes

The power factor is PF = P/S = cos(arctan(Q/P)). Capacitive loads have leading (negative) Q, inductive loads have lagging (positive) Q. A PF of 0.85 means 15% of the apparent power is reactive. To reduce Q and improve PF, add PFC capacitors (for inductive loads) or PFC inductors (for capacitive loads, rare). Most utility penalties begin below PF = 0.9. Unity PF (PF = 1.0) means S = P and Q = 0.