Study on Application of Catastrophe Theory to Power Systems

Abstract

With rapid growth of the number of literatures on nonlinear systems, nonlinearities existing in the systems under study have drawn much attention. Studies on the effects of nonlinearities in power systems have been becoming an increasingly important part of researches for the investigation of system stability. It is probable that hidden phenomena may unexpectedly emerge due tc the nonlinearities that are involved in load flow equations, generator swing equations and characteristics of control equipments and loads, etc.
This paper presents a new Catastrophe Theory application to nonlinear power systems. Making use of the concept of Duffing's equation, we show that a Catastrophe Theory analogy can be used to interpret unstable phenomena caused by system nonlinearities from the viewpoint of oscillations. When considering the system nonlinearities, due to ill-combination of system parameters and periodic disturbances, there may exist the characteristic “jumps” in system states corresponding to slow (quasi-dynamic) changes of the frequencies of periodic disturbances. With this Catastrophe Theory approach, a system bifur-cation set can be identified to assess the unstable phenomena of power systems.