Estimation of the Region of Attraction of Polynomial Swing Equation Using Sum of Squares Theory

Estimation of the region of attraction of the power system using sum of squares (SOS) programming theory is investigated in this paper. Firstly, the Taylor expansion formula is applied to explore the inherent polynomial structure of the swing equation. The single machine projection equation for a multi-machine system is proposed based on the amplitude characteristic of the rotor angle response in decoupled space. Secondly, the theory of SOS programming originating from the polynomial system is derived, and the theory about estimation of the region of attraction for the differential algebraic system is summarized. Thirdly, the method for estimating the region of attraction for the polynomial swing equation based on a V-S two-stage iterative procedure is proposed. Finally, a single machine infinite bus power system, an IEEE 3-machine power system, and an IEEE 4-machine power system are employed to validate the effectiveness and accuracy of the proposed method and analysis.