Mathematical Relationships of Linearized Modeling Methods of AC Power Electronic Systems

The harmonic state-space, the dynamic phasor, and the generalized dq modeling are three methods developed for linearization of ac power electronic systems. This paper reveals explicitly mathematical relationships between the three modeling methods in both time and frequency domain. Representations of linearized models in different reference frames and from time domain to frequency domain, as well as their transformations are elaborated step by step. Case studies on a three-phase voltage-source converter that is connected to an unbalanced grid verify the theoretical findings.