Entire stability region estimation using the invariant manifolds and singularities at infinity

This study provides a new perspective to study the formation and wholeness of the stability region of power systems. The main idea of the approach proposed in this study is to project the system into a closed area and then investigate the behaviours of the field in a neighbourhood of infinity on a sphere that is topologically equivalent to the original system. The invariant manifolds and singularities at infinity are described in detail to indicate the boundary of the entire stability region, based on the concept of the basin of attraction. The proposed method is applied to the single-machine model, two-machine model and multi-machine system to illustrate the complex geometry structure of the transient stability region. A singularity variation index is presented to estimate the size of the entire region and indicate the transient stability degree of the power system. Simulation results verify the correctness and effectiveness of the theoretical analysis.