7.6 : Power Factor

The power factor is defined as the ratio of average (or active) power to apparent power, as illustrated by the relation

The term in bracket, (θ_v - θ_i), is referred to as the power factor angle, as it represents the angle whose cosine yields the power factor. If V represents the voltage across the load and Ⅰ signifies the current flowing through it, the power factor angle equates to the angle of the load impedance. Essentially, the power factor is the cosine of the phase difference between the voltage and current, as well as the cosine of the angle of the load impedance.

From the above equation, it can be inferred that the power factor is the multiplier for the apparent power to yield the real or average power. The power factor's value ranges between zero and one. When dealing with a purely resistive load, the voltage and current are in phase, resulting in a power factor angle (θ_v - θ_i) = 0 and a power factor = 1. This indicates that the apparent power equals the average power. For a purely reactive load, (θ_v - θ_i) = ±90^o and a power factor = 0, making the power zero. Between these two extremes, the power factor is said to be either leading or lagging. A leading power factor suggests that the current precedes the voltage, indicating a capacitive load, while a lagging power factor suggests that the current follows the voltage, indicating an inductive load. The power factor significantly impacts the electricity bills consumers pay to their utility companies.