Glossary term
Power Factor
The ratio of active power to apparent power in an AC circuit, measuring what fraction of the total current-voltage product performs useful work.
Definition
metricPower factor is the dimensionless ratio of active power to apparent power in an AC circuit; for sinusoidal voltage and current it equals the cosine of the phase angle between them.
Power factor indicates how effectively an AC electrical system converts current-voltage product into active power. With sinusoidal voltage and current, unity power factor means there is no reactive current component; with nonlinear loads, total power factor can still be reduced by harmonic distortion. Low power factor increases infrastructure costs, raises resistive losses, and complicates voltage regulation. Power factor correction is a standard practice in industrial electrical engineering.
In a sinusoidal AC circuit, if the voltage phasor and current phasor are separated by a phase angle \phi, the power factor is:
where P is the active power (watts) and S is the apparent power (volt-amperes). Power factor is dimensionless and lies in the interval [0, 1] when reported as a magnitude. A sinusoidal power factor of 1 means voltage and current are in phase and no reactive current component is present. A sinusoidal power factor of 0 means the phase angle is 90° and the average active power is zero.
Lagging and leading power factor
Power factor is described as lagging when the current lags the voltage (\phi > 0), which occurs with inductive loads — motors, transformers, solenoids. It is leading when the current leads the voltage (\phi < 0), which occurs with capacitive loads — capacitor banks, lightly loaded cables, some power electronic converters. In power systems, lagging power factor is far more common because most industrial and commercial loads are inductive.
Effect on current and losses
For a given active power P and voltage V, the current is:
As power factor decreases (larger \phi), the current increases for the same useful power delivered. This has two direct consequences. First, the I^2 R resistive losses in conductors and transformers increase with the square of the current — a load with power factor 0.7 causes twice the resistive losses of the same active load at unity power factor. Second, the equipment must be physically sized to carry the higher current — larger cable cross-sections, higher-rated transformers, and more robust switchgear — increasing capital cost even though the useful power is unchanged.
Displacement power factor and total power factor
In circuits with sinusoidal voltage and current, power factor equals \cos\phi — the displacement power factor. When current is non-sinusoidal (due to nonlinear loads such as variable speed drives, rectifiers, and switch-mode power supplies), harmonics are present and the total power factor is lower than the displacement power factor:
where D is the distortion power — the contribution of harmonic currents to the apparent power. Harmonic distortion reduces total power factor even when the fundamental displacement power factor is unity. This distinction matters in facilities with large variable-speed drives, UPS systems, and other power electronic equipment.
Power factor correction
Power factor correction (PFC) is the deliberate introduction of reactive elements to offset the reactive power demand of a load and bring the net power factor closer to unity. For inductive loads, capacitor banks are the standard solution: they supply the reactive current locally, so that the reactive current no longer needs to flow through upstream conductors and transformers. The required reactive compensation to correct from power factor \cos\phi_1 to \cos\phi_2 at active power P is:
After Q_C is known, capacitance depends on the connection and voltage. For a single-phase shunt capacitor at RMS voltage V, C = Q_C/(\omega V^2); for three-phase banks, use per-phase reactive power and the relevant phase voltage for the chosen connection.
Fixed capacitor banks are sized for average conditions; switched banks or static VAR compensators (SVCs) provide dynamic correction in response to varying loads. In many countries, utilities impose penalties on industrial consumers whose power factor falls below a contractual threshold (typically 0.90 or 0.95), making power factor correction economically mandatory in large industrial facilities.
Common mistakes
A common mistake is to assume power factor correction is always just adding capacitance. In networks with harmonic distortion, capacitor banks can resonate with system inductance and amplify harmonic currents unless detuned or filtered. Another mistake is confusing displacement power factor with total power factor when nonlinear loads dominate. A good electrical review states active, reactive, apparent, and distortion components, load profile, harmonic spectrum, utility requirement, correction equipment, switching strategy, and overcorrection risk under light load.