An electric power system is a large-scale energy system composed of a lot of equipment such as power generating units, transmission lines, voltage transformers and power demand loads. It is also a very complex system including generator's electromagnetic dynamics and many control system's characteristics to maintain a constant level of voltage and systemfrequency. Eigenvalue analysis is one of the methods to handle a power system stability problem associated with the system dynamic perfomance. This paper describes mathematical models of power system components and also explains a calculation technique of eigenvalue analysis to evaluate a large -scale power system stability. Its application for improving stability enhancement using eigenvalue sensitivity is also described in this paper.

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We generate a sequence called Vander Corput's or integer bit reversal which distributes uniformly on the interval (0, 1). Using this sequence and the aid of Sunzi's theorem, we obtain an extended FFT of which length is arbitrary number. And then, we apply this to automatic approximation of function increasing the sample points more gradually than the case of common FFT. For example, we present the automatic Chebyshev expansion of function increasing the sample points as 3×2^l, 4×2^l, 5×2^l, l=0, 1, 2, …. As the automatic quadrature, this technique is efficiently applied to product type integration including typical several singular integrals.

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