Basic sets and attractors of a double swing power system

In a normal power system, many generators are operating in synchrony. That is, they all have the same speed or frequency, a system frequency. In the case of an accident a situation might occur when one or more generators are running at a different speed, at much faster than the system frequency. They are said to be stepping out. We have been engaged in a series of studies of this situation, and have found global attractor-basin portraits. The electric power system involving one generator operating into an infinite bus is a well-established model with a long history of research. We, however, have derived 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 have developed 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 the straddle orbit method of computer simulation to find the basic set. We succeed in finding many basic sets in this new model. In addition, we consider unstable limit sets which have two- or three-dimensional outset.