A Generalized Time-Domain Framework For Modeling and Analysis of The Unbalanced Three-Phase Systems

This paper provides the theoretic foundation of a new time-domain modeling framework for three-phase unbalanced AC power systems. In particular, a generalized variant of the standard dq0 transformation termed as g-dq0 transform is derived. The proposed g-dq0 transform represents any phase and/or magnitude unbalanced three-phase quantity in a timeinvariant coordinates system, thus replicating the features of standard dq0 transform for balanced AC systems. Furthermore, underpinned by an invariance-preserving property, the g-dq0 transform projects impedance and admittance matrices onto an equivalent time-invariant representation regardless of the structural asymmetry or imbalances in time-domain quantities. Finally, we provide an example for the dynamic circuit modeling in g-dq0 coordinates, modeling details on different unbalanced load configurations, and simulation-based accuracy verification test cases.