Analytical mapping of harmonics and impedance through phase-controlled converters

Mapping of the harmonics and the impedance in the line-commutated converters can be modeled using the so called mapping function method, which relates currents and voltages between dc and ac terminals of the converter. The frequency-domain analysis with double Fourier-series method has been used to derive the mapping function for uncontrolled line-frequency rectifiers. This paper presents a modeling method for phase-controlled converters. The mapping function is expressed in the frequency-domain by Fourier expansion and the effects of phase control and the phase lock loop are included in the model. The mapping relationship of the harmonics and impedance are calculated in an analytical form with the frequency-domain analysis of the mapping function.