A class of stability theory based on trajectories and its applications to power systems

On the basis of the existing electrical power engineering methods,a class of mathematical descriptions and the criterion of Lagrange stability based on trajectories are proposed.Firstly,the concept of trajectory stability and swing steadiness are defined.The sufficient conditions for the trajectory stability in terms of the geometric characteristics,called the dynamical saddle points,are then presented.Finally,the proposed methodology is verified by simulations of power systems.It provides a mathematical foundation for the emergency control in electrical power engineering and other fields.