Based on the quadratic approximation of the stability region boundary,this paper proposes a transient voltage stability margin index,and analyzes the transient voltage stability of a one-machine and one-load system including an electromechanical transient model of induction motor.

This paper presents a new transient stability index based on the implicit expression for the stability region boundary and an approximation of the proposed index based on the quadratic approximation of the stability region.

The CCT is determined by the crossing point of the quadratic approximation surface and the continuous faulted trajectory.

Based on the first-order approximation method(FAM),a non-Cartesian variables and a Cartesian variable s and a Cartesian u_2,which denote the arc-length stretch and the transverse displacement respectively,are employed to describe the deformation of the beam.

By using the methods of root-analysis for the characteristic equation and first approximation etc, this paper provides criterions of the asymptotic stability for the zero solution of the above meutioued delay difference equations.

In this paper,firstly we have introduced nearly subconvexlike set vaklued map and obtained a series of characterizations about it,lastly we give the proof of the equivalence of subconvexlike set valued map and nearly subconvexlike set valued map in linear topological spaces.

The concept of nearly subconvexlike set-valued map is introduced and some important properties of the new concept are obtained in the linear space.