MS#112. Attractor and Basin Portraits of a Double Swing Power System, 2002
With Yoshisuke Ueda, Makoto Hirano, and Hirofumi Ohta
Intl. J. Bifurcation and Chaos 14(9), Sept. 2004, 3135-3152.
Subjects: Electrical Engineering
Written: September 5, 2002
Abstract: In a normal power system, many generators are operating in synchrony. That is, they all have the same speed or frequency, the system frequency. In case some accident occurs, a situation might arise in which one or more generators are running at a different speed, much faster than the system frequency. They are said to be running away or stepping out, or in a state of accelerated stepping out. We have been engaged in a series of studies of this situation, and have found global attractor-basin portraits. In the course of this program, we have observed the phenomenon of decelerated stepping out, in which one or more generators deviate from the system frequency toward lower speeds. These kinds of behavior cannot be explained with the well-known model involving one generator operating on to an infinite bus. Rather, we require a model in which robust subsystems - for example, generator/motor combination, which we call swing pairs - are connected by interconnecting transmission lines. In this more general context, the deviant behaviors we are considering may be regarded as forms of desynchronization of subsystems. We therefore begin this paper with the derivation of a new mathematical model, in which there is no infinite bus nor fixed system frequency. In the simple case of two subsystems (each a swing pair) weakly coupled by an interconnecting transmission line, we develop a system of seven differential equations which include the variation of frequency in a fundamental way. We then go on to study the behavior of this model, using our usual methods of computer simulation to draw the attractor-basin portraits. We have succeeded in finding both accelerated and decelerated stepping out in this new model. In addition, we discovered an unexpected subharmonic swinging of the whole system.

Last revised by Ralph Abraham