Methods for Stability Analysis of Unbalanced Three-Phase Systems

This paper extends small-signal stability analysis methods developed for balanced three-phase systems to the more general unbalanced three-phase system. The impedance-based stability analysis method in the phase-domain is generalized to unbalanced systems characterized by coupled positive-sequence and negative-sequence impedance networks. Compared to balanced three-phase systems, modeling of unbalanced converter systems is more complicated due to the negative-sequence trajectory that is impressed on the ac system by the unbalanced condition. Small-signal models are developed to determine whether or not a small unbalance voltage condition introduces any significant change to the inverter impedance models of the perfectly balanced case. Simulation and experimental measurements are used for verification of the small-signal models and the proposed stability analysis method.