Impedance/Admittance Modeling of Three-Phase AC Systems: A General Representation.

This paper establishes a general representation for impedance/admittance models in three-phase ac systems. It is pointed out that the rotating and complex transformations in the time domain are equivalent to similarity transformations on a harmonic transfer function (HTF) matrix in the frequency domain. Under certain conditions, such similarity transformations have a diagonalizing effect which essentially reduces the HTF matrix order from infinity to two or one, eliminating the infinite frequency-coupling effect and making it tractable mathematically. Furthermore, the paper makes the distinction between an internal and external frame and establishes their relationships, recognizing the small-signal perturbation of the reference frame itself. This turns out to be of significant importance in representing synchronizing dynamics, such as the swing dynamics of a synchronous generator and the phase-lock dynamics of an inverter. As a result, this work not only unifies different modeling methodologies, but also gives new insight into the properties of impedance/admittance models.