Power factor (pf) is the ratio between real power (P) flowing to the load, and the apparent power (S) in the circuit: pf = P/S. It is a sinusoidal waveform and therefore expressed as a dimensionless number between -1 and 1.

Real power is measured in watts (W) and apparent power in volt-amps (VA). For a purely resistive load, the two power factors are identical; for a reactive load the arithmetic for the apparent power produces the same figure, that is, the product of the RMS values of voltage and current. However, to find the actual (real) power delivered to the load, the instantaneous product of voltage and current must be integrated over the complete sine-wave cycle.

When current is leading or lagging voltage, the value of that integral will always be less than the value for the in-phase case over the same interval. This reflects the attribute of an inductor or a capacitor to act as an energy store; at various points through the AC cycle the reactive component is either storing energy, or returning it to the system.

As shown in Fig. 1, the apparent power is the vector sum of the true power and the reactive power (Q), measured in reactive volt-amperes (VA); conventionally, this relationship is expressed as:

P = S cosƟ      or         P2+Q2=S2      (1)

 

The relationship is conventionally visualized in a right-angled triangle vector diagram:

This is a basic definition and works for pure sinusoids; non-sinusoidal waveforms are more complex, but can be represented by a series of harmonic sinusoids and therefore the same basic principles apply.