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.