Figure 1 displays a power electronic converter connected to the mains. In general, a power electronic converter is an electrical power converter – controlled or uncontrolled rectifier, AC regulator, compensator of reactive power, converter of phase number, active power filter. The converter supplies a load with power Pout, and in the same time it loads the mains with active power P and total power S.
TopBasic Indicators In Respect To The Supply Network
Figure 1 displays a power electronic converter connected to the mains. In general, a power electronic converter is an electrical power converter – controlled or uncontrolled rectifier, AC regulator, compensator of reactive power, converter of phase number, active power filter. The converter supplies a load with power Pout, and in the same time it loads the mains with active power P and total power S.
Figure 1. Powers in conversion of AC electrical energy
Power factor is defined as a ratio of active power P to total apparent power S:
(4.1)If the voltage and current of the supply network are with non-sinusoidal waveform, they contain DC component and they can be presented in Fourier series, then the active power is given as:
(4.2) where in
Uk and
Ik are the effective values of the k
th harmonic of the voltage and current, respectively, and
is the displacement angle.
Total power is a product of the effective values of the source voltage U and the source current I:
(4.3) where in
and
(4.4)After substituting (4.4) in (4.1), it is found:
(4.5)The mains voltage is usually accepted to be of a pure sinusoidal waveform and it does not contain a DC component, and the source current is usually accepted to be of non-sinusoidal waveform. So, it is derived:
(4.6)From (4.6) it is seen, that the power factor is a product of two variables, the highest value of each of them can be equal to 1. The two variables are:
Besides the distortion factor, the current non-sinusoidal waveform is also characterized by harmonic distortion factor or a total harmonic distortion defined as:
(4.7)It is easy to find the relationship between the two coefficients:
(4.8) or
(4.9)