Symmetry in the Narrow Sense: On the Linearity and Time-Invariance of DQ0 Models
Elior Segev, Ron Ofir, Juri Belikov, Yoash Levron · IEEE Transactions on Power Systems · 2022
This paper presents necessary and sufficient conditions for a linear three-phase circuit to have a linear and time-invariant$dq0$model. More specifically, we show that a circuit with state and input matrices that can be partitioned into three-by-three circulant matrices at the$abc$frame of reference, can be transformed into a linear and time-invariant model in the$dq0$frame of reference. We also show that under this condition the circuit is symmetrically configured, in the sense that every three-phase balanced input results in a balanced state vector at steady-state. We explain that due to these properties, such circuits may be defined as “symmetrically configured in the narrow sense”.