Properties of Nonlinear Power System Models that are Symmetrically Configured in the Narrow Sense

Symmetry is a fundamental property of three-phase circuits and is widely used in the analysis of large-scale power systems. However, when the system is nonlinear or time-varying, classical symmetry generally does not provide sufficient information. Therefore, in this paper, we explore properties of three-phase circuits with dynamic models that are “simple” in some stronger sense. We define a circuit to be simple if its state and input matrices in the dq0 domain are constant, that is, independent of the reference angle, and show that this property leads to dynamic models which are linear and time-invariant, or at least suitable for low-complexity numerical analysis. We formally define circuits with this property to be Symmetrically Configured in the Narrow Sense (SCNS), and explore their properties. We show, for instance, that SCNS circuits must be symmetrically configured and that their state-space models have several interesting properties and structures. The overall aim is to develop a small toolbox, which may help identify and analyze SCNS circuits in the context of large-scale power systems. We believe this may contribute to the understanding of dynamic phenomena in large-scale systems which are too complex for direct simulation.