What is the Correct definition of Power Factor?

Current and voltage directly decide the power consumption in DC as product of these two entities. However, in case of AC, the complex impedance comes into play, and power calculation becomes complex, since the impedance has both real and imaginary components. Similar to impedance, power also has real and imaginary components. Product of current and voltage (V x A), has three components, viz. (1) Apparent power VA, given by V x A, (2) Real (or active) power W, and imaginary power VAR. Out of the three, it is the real power which is useful for actually doing any physical work or producing heat. VAR component consists of inductive and capacitive currents, and does not take part in any useful work output.

Power Factor of an AC circuit or a system is defined as the ratio of active power (or real power) to apparent power. It is that fraction of total apparent power, which is consumed in doing a work, conversion into heat or some other form of energy.

In DC circuit, there is no concept of apparent power since there is no reactive power involved. In AC circuits having pure sine wave voltage and current, Power factor is easily calculated from current, voltage and phase angle, or apparent power and phase angle.

Real Power P = Apparent power x Cos φ

where φ is the phase angle between voltage and current waveforms. Hence Cos φ is the multiplication factor which gives real power from apparent power. This is therefore called Power Factor. Thus

P.F. =Cos φ, where φ is the phase angle between voltage and current waveforms.

This definition holds for pure sinewave quantities. In practice, there are waveform deformation and deviation from sine wave because of inherent properties of, say, diesel generators and inductive equipment. A diesel generator output is irregular, far from an ideal waveform, and it deviates significantly from sine wave in both directions (polarities) of reference time line. This deformed waveform does not obey the above equation for power factor. Further, most electronic circuits introduce their own harmonics due to rectification, chopping circuits, power electronic circuits and controls.

The irregular waveform generated by these circuits can be broken down into combination of several waves of different frequencies, called harmonics. Since there is no single defined frequency and waveform is not regular, above definition of power factor is no longer applicable.

Consider the waveforms, voltage, current and power in the above figure. The voltage is exactly ±1V, with same polarity as current (in phase with current), but a magnitude independent of current. Current is 1 A RMS, voltage is also 1 A RMS, giving an output of 1 VA. Average power is 0.9 W (1.414 x 2 π), giving a power factor of 0.9, yet there is no phase shift. Power factor is not unity, even though V and I are in phase.

The reason is the square shape of current wave. This shape can be broken down into combination of several sine waves, a sum of several harmonic frequency waves, each with its own magnitude. Harmonics do not fully contribute to power, but reduce the power factor to 0.9. This is an extreme case, but similar situations prevail in most practical circuits, and only pure resistive loads are really free from harmonics.

In such situations, improvement of power factor in supply system involves reduction or compensation of these harmonics by countering their effect.

Distortion Power Factor (DPF)

Basic definition of power factor as Cos φ does not apply in most cases due to harmonic components. A new type of power factor has emerged, called Distortion Power Factor (DPF), which takes into account the distortions caused by harmonics, THD being the total Harmonic Distortion.

It is assumed that voltage stays pure sinusoidal and undistorted, free from harmonics. This is a good approximation in practice (voltage stays almost sinusoidal). If I_1rms is fundamental frequency current, and I_rms is total RMS current, the overall power factor is given by

Conventional power factor correction systems measure and control basic power factor, which may not represent realistic situations. New generation advanced control systems aim at unity power factor, taking into account the distortion effects. Power factor is the true ratio between active power and overall apparent power, with all harmonics included.

Most conventional power factor instruments measure Cos φ, the phase angle between current and voltage of basic frequency, some using zero crossing detectors. This is not a true representation of power factor. Few expensive instruments like Fluke take into account harmonics as high as 31^st harmonic to calculate DPF and PF.