Frequency-domain transformation approaches to develop the d-q synchronous-frame models of three-phase symmetrical networks and applications in modeling of PWM power converters

Although state-space averaging small-signal modeling techniques are successfully established in DC-DC converters and three-phase sinusoidal PWM converters, these approaches are limited only to low-order systems, and the modeling process is very complex. This paper proposes two equivalent approaches in frequency domain to develop the d-q synchronous-frame models from stationary-frame models for arbitrary three-phase symmetrical circuits. The first modeling approach is illustrated with frequency transformation, by which the target synchronous-frame models could be easily obtained by frequency transformation of the prototype stationary-frame models. The second modeling approach is based on the reactive elements substitutions. These two approaches can be proven to be equivalent, and the first approach is suitable for input-output models, while the second approach is preferable for state-space models. As illustrative examples, these approaches are applied to develop the synchronous-frame models of large three-phase systems with PWM converters. They are proven valid with the comparison with current published models.