Application of catastrophe theory to power systems

In recent publications dealing with nonlinear systems, nonlinearities existing in the systems under study have drawn much attention. Studies on the effects of nonlinearities in power systems are becoming an increasingly important part of the research on system stability. It is probable that heretofore undiscovered phenomena caused by the nonlinearities involved in load flow equations, generator swing equations and characteristics of control equipments and loads, etc., may be found. This paper presents a new Catastrophe Theory application to nonlinear power systems. Making use of the concept of Duffing's equation, it is shown that a Catastrophe Theory analogy can be used to interpret unstable phenomena caused by system nonlinearities from the viewpoint of oscillations. When considering system nonlinearities due to poor combinations of system parameters and periodic disturbances, there may exist the characteristic 'jumps' in system rates that correspond to slow (quasi-dynamic) changes of the frequencies of periodic disturbances. With this Catastrophe Theory approach, a system bifurcation set can be identified to assess the unstable phenomena of power systems.