Domain of stability of synchronous generators by a cell mapping approach

In this paper, the theory of simple cell mapping is applied to the determination of domains of stability of synchronous generators. The generators are represented by two-dimensional differential dynamical systems including the effects of variable damping and saliency. First, the differential equation governing the behaviour of a generator is reduced to a cell-to-cell mapping. A scheme of compactification is introduced in order to obtain a complete cell state space which consists of a finite number of cells. The methodology of the simple cell mapping is then used to prepare a computer program. Using the program, all the singularities of the cell mapping and the domain of stability can be determined readily. The method is particularly attractive because it can easily take care of any non-linearity. Different systems can be treated by the same program by simply changing the form of the differential equation in the program and/or changing the system parameters. Three kinds of synchronous machine are studied in this paper to show the applicability of this approach. The results are compared with the best of those obtained by the Lyapunov method. It is seen that almost the complete domains of stability are obtained by the new approach, including those portions which are not discovered by the Lyapunov method.