Power Systems & Protection ReferenceUpdated 2026-08-15

Power Factor in AC Circuits: Theory, Triangle & Correction

Complete guide to AC power factor, the power triangle (kW, kVA, kVAR), leading vs. lagging power factor, utility penalties, and power factor correction capacitors.

Key Formulas: PF = P / S = cos(θ) | S = √(P² + Q²) | Q_C = P × (tan θ_1 - tan θ_2)

The Power Triangle: Real, Apparent & Reactive Power

In AC circuits with inductive loads (motors, transformers, ballasts), magnetic fields continuously absorb and return energy to the grid. This creates three distinct forms of power forming a right-angled triangle:

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Real Power ( $P$ , kW): The working power converted into thermal, mechanical, or computational work.

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Reactive Power ( $Q$ , kVAR): The non-working power required to sustain magnetic and electric fields.

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Apparent Power ( $S$ , kVA): The total vector power supplied by the grid (

S = \sqrt{P^2 + Q^2}

Lagging vs. Leading Power Factor

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Lagging Power Factor: Current waveform lags behind the voltage waveform. Caused by inductive loads (AC induction motors, solenoids, transformers).

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Leading Power Factor: Current waveform leads voltage waveform. Caused by capacitive loads or over-excited synchronous motors.

Power Factor Correction (PFC)

To avoid costly utility low-power-factor surcharges, industrial facilities install shunt capacitor banks adjacent to large inductive loads. The capacitive reactive power ( $Q_C$ ) cancels out the inductive reactive power ( $Q_L$ ), bringing the overall power factor close to unity (0.95 to 0.98).

Frequently Asked Questions

What is an ideal power factor?

A power factor of 1.0 (unity) is ideal, indicating that all supplied apparent power (kVA) is converted directly into useful real power (kW) with zero reactive losses.

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