Towards development of generalized energy functions for electric power systems

Energy functions have been used in power systems for direct stability analysis, designs of control systems and stability analysis. The existing energy functions have been developed under the assumption that limit sets are composed exclusively of hyperbolic equilibrium points. However, the structure of limit sets for general power system dynamical models can be very complex; limit sets can be composed of equilibrium points, closed orbits, quasi-periodic solutions, or chaotic trajectories. The existing energy functions are not applicable to these general power system dynamical models. To this end, generalized energy functions are developed for these general dynamical models. In this paper, generalized energy function along with a comprehensive generalized energy function theory are developed. It will be shown that energy functions do not exist for some general power system dynamical models while generalized energy functions exist. With the developments of generalized energy functions, it is feasible to extend the existing energy-function-based tools to general power system dynamical models. In particular, it is feasible to perform direct stability analysis, designs of control systems and stability analysis of equilibrium points, closed orbits for extended transient stability models as well as mid-term stability models.