Power factor describes how effectively an AC electrical system turns supplied electrical current into useful work. In factories, large motors often draw current that lags behind voltage, which increases the current needed for the same real power output. A low power factor wastes capacity in wires, transformers, and generators, even when the useful power in kilowatts has not changed.
Engineers monitor and correct power factor to reduce losses, avoid utility penalties, and improve system efficiency.
The power triangle connects real power P, reactive power Q, and apparent power S using right triangle geometry. Motor loads are usually inductive, so they consume positive reactive power measured in kVAR and create a lagging power factor. Capacitor banks supply leading reactive power that cancels part of the motor's inductive reactive demand.
This reduces apparent power and line current while keeping the real power delivered to the load nearly the same.
Key Facts
- Real power P is the useful power converted to work or heat, measured in watts or kilowatts.
- Reactive power Q is the power exchanged with magnetic or electric fields, measured in VAR or kVAR.
- Apparent power S is the total AC power capacity required, measured in VA or kVA.
- Power triangle relation: S^2 = P^2 + Q^2.
- Power factor: PF = P / S = cos(theta), where theta is the phase angle between voltage and current.
- Capacitor correction reduces inductive reactive power: Q_corrected = Q_load - Q_capacitor.
Vocabulary
- Real Power
- Real power is the average power that performs useful work in a circuit, such as turning a motor shaft or producing heat.
- Reactive Power
- Reactive power is power that moves back and forth between the source and reactive components without being permanently consumed.
- Apparent Power
- Apparent power is the product of RMS voltage and RMS current in an AC circuit and represents the total power capacity the source must provide.
- Lagging Power Factor
- A lagging power factor occurs when current lags voltage, usually because the load is inductive, such as a motor or transformer.
- Capacitor Bank
- A capacitor bank is a group of capacitors used to supply leading reactive power and improve the power factor of an AC system.
Common Mistakes to Avoid
- Confusing kW with kVA is wrong because kW measures useful real power while kVA measures total apparent power drawn from the supply.
- Assuming reactive power is wasted energy is wrong because reactive power is not consumed like heat, but it still increases current and equipment loading.
- Adding a capacitor that overcorrects the load is wrong because too much capacitive reactive power can create a leading power factor and cause voltage or resonance problems.
- Using PF = S / P is wrong because power factor is the ratio of useful real power to apparent power, so the correct formula is PF = P / S.
Practice Questions
- 1 A motor load uses P = 80 kW with a power factor of 0.80 lagging. Find the apparent power S and the reactive power Q.
- 2 An industrial load has P = 120 kW and Q = 90 kVAR lagging. A capacitor bank supplies 50 kVAR. Find the corrected Q, corrected S, and corrected power factor.
- 3 Explain why adding capacitors to an inductive motor load can reduce the current in the supply wires even though the motor's real power output stays approximately the same.