In electrical engineering, the power factor of an AC power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit. Real power is the average of the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of root mean square (RMS) current and voltage. Apparent power is often higher than real power because energy is cyclically accumulated in the load and returned to the source or because a non-linear load distorts the wave shape of the current. Where apparent power exceeds real power, more current is flowing in the circuit than would be required to transfer real power. Where the power factor magnitude is less than one, the voltage and current are not in phase, which reduces the average product of the two. A negative power factor occurs when the device (normally the load) generates real power, which then flows back towards the source. In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The larger currents increase the energy lost in the distribution system and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers with a low power factor.
Power-factor correction (PFC) increases the power factor of a load, improving efficiency for the distribution system to which it is attached. Linear loads with a low power factor (such as induction motors) can be corrected with a passive network of capacitors or inductors. Non-linear loads, such as rectifiers, distort the current drawn from the system. In such cases, active or passive power factor correction may be used to counteract the distortion and raise the power factor. The devices for correction of the power factor may be at a central substation, spread out over a distribution system, or built into power-consuming equipment.
General case
The general expression for power factor is given by
power factor = P / P a {\displaystyle {\mbox{power factor}}=P/P_{a}}
P a = I r m s V r m s {\displaystyle P_{a}=I_{rms}V_{rms}}
where P {\displaystyle P} is the real power measured by an ideal wattmeter, I r m s {\displaystyle I_{rms}} is the rms current measured by an ideal ammeter, and V r m s {\displaystyle V_{rms}} is the rms voltage measured by an ideal voltmeter. Apparent power, P a {\displaystyle P_{a}} , is the product of the rms current and the rms voltage. If the load is sourcing power back toward the generator, then P {\displaystyle P} and power factor {\displaystyle {\mbox{power factor}}} will be negative. If the waveforms are periodic with the same fundamental period, then the power factor can be computed as follows:
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