Global Geometric Structure of the Transient Stability Regions of Power Systems

In this paper, a novel qualitative method is proposed to analyze the transient stability of power systems. Unlike the traditional methods, this method can illustrate the structural characteristics of the stability region and display the boundary on the global phase plane intuitively. Particularly, the stability boundary and phase portraits are investigated in three-dimensional space. Global phase portraits including the singularity at infinity (SAI) show the beginning and ending points of the portraits, and indicate the whole situation of an attractor's basin. To properly use the method to clarify the dynamic behavior at infinity, the multi-machine system is simplified by an equivalent method and the trajectories of the rotor angle near the unstable equilibrium point are projected into a closed ball based on the invariant submanifolds. The effects of damping coefficient, fault locations, and fault types on the transient stability region are discussed by the coordinate of the SAI, which are obtained based on the qualitative theory of differential equations. If the traditional generators are replaced with the distributed energy resources, the transient stability of the power system may be affected both positively and negatively. The simulation experiments of the IEEE 39-bus test system are carried out to validate the effectiveness of the proposed method.