Definition of Power Factor in Nonlinear Circuits

The term power factor originates from the basic AC circuit principle. When a sinusoidal AC power supply supplies power to an inductive or capacitive load, the load current is also sinusoidal, but it lags or leads the input voltage by an angle A. If the effective value of the input voltage is U and the effective value of the input current is F, the apparent power input by the power grid is J. However, the power actually transmitted to the load is only UIcosφ, and the input current component Icosφ that is in phase with the voltage of the load resistor provides power to the load. The current component Isin(a) that is perpendicular to the voltage of the load resistor does not provide power to the load. In electrical engineering, the ratio of the power U/cosφ actually transmitted to the load to the apparent power u input by the power grid is called the power factor (PF), and is expressed as cosφ, that is,

Where A is the phase difference between the sinusoidal voltage and the sinusoidal current.

Due to the nonlinearity of the diode in the rectifier circuit, although the mains input voltage is sinusoidal, the input current has a phase change and serious waveform distortion. Therefore, the power factor calculation method of the linear circuit is no longer applicable to the AC/DC rectifier-filter capacitor circuit, that is, cosφ can no longer be used to represent the power factor, but the waveform distortion factor should be added:

Assume that the input voltage of the rectifier-filter capacitor circuit is a sine wave (effective value is U), and the input current is a non-sinusoidal wave, its effective value is

Where I1 is the effective value of the fundamental wave of the input current;
IR is the effective value of the higher harmonics of the input current.

One point that must be explained here is that only the fundamental current in the input current has the same frequency as the input voltage and can deliver active power to the load. Its higher-order harmonic current has a different frequency from the input voltage and can only generate reactive power (higher-order harmonics do not do work and their average power is zero).

Assume that the fundamental current I1 lags behind the voltage U by a phase angle of A, as shown in Figure 1.

Figure 1 Phase difference between fundamental current 21 and voltage

Then the active power P delivered to the load by the mains grid is

P＝UI1cosφ

The apparent power Q input from the mains grid is:

Q＝U·I

According to the definition of power factor PF

Where kd is the distortion factor, which indicates the relative value of fundamental current (with the effective value of non-sinusoidal current I as the base value).
kφ is the displacement factor.

The power factor PF is equal to the product of the distortion factor kd and the displacement factor kφ.