A direct method to determine the stability of power systems during transients

During transients, the instability of the power system can attribute to the angle instability as well as the voltage instability. The angle and voltage stability are entangled with each other during transients. This paper proposed a direct approach to determine the types of instability of power systems during transients. Based on differential algebraic equations of the systems, the equilibriums and singular points of the system are defined. The singular surface consisting of singular points then divides the manifolds of the system trajectory into multiple algebraic manifolds, with each algebraic manifold containing one or more equilibriums. Three types of instability of the system are identified according to the distribution of equilibriums, i.e., the angle instability, voltage instability and angle-induced-voltage instability. The proposed method can easily determine the dominant instability mode of the system during transients and the case studies also demonstrate its effectiveness.