The graphical D-Q transformation of general power switching converters

A novel circuit d-q transformation concept is introduced to analyze AC converters such as inverters, rectifiers and cycloconverters with ease. The equivalent linear time-invariant circuit is obtained by substituting switches with equivalent turn-ratio variable transformers and changing balanced AC reactors into equivalent DC reactors combined by gyrators. This circuit allows the utilization of power linear system analysis techniques such as Laplace transforms, which otherwise could not be applied to time-varying switching systems. The modeling procedure is shown for a controlled rectifier-inverter circuit. An analysis example is given for a buck-boost inverter, and the result is compared with that of the conventional approach. This approach is applicable to all AC converter families to determine the AC transfer function and the DC operating points. It is determined that the switching systems are equivalent to RLC filter circuits with transformers and gyrators.>