The paper is devoted to the study of the static stability of complex electric power systems (EPS). The stability theory and and basic methods of its study are observed in the paper, from the method of Lyapunov to the most advanced methods, for instance, the method of gramians, pseudo-spectral analysis, artificial neuron networks etc. It is showed in the thesis that the static stability of small power systems can be studied with the help of a characteristic polynomial (CP) without finding the roots, but only with its localization on the plane. Also the modified method of rotation and decomposition method are suggested, which can be used while combining the systems. The last chapter is devoted to a detailed analysis of the static stability of the three machine system with using the classical approach (CP) and methods, proposed in the thesis. Also Latvian power system static stability is calculated.