In this paper we discuss an application of the spectral decompositions of Gramians for the small-signal and transient stability analysis of electric power systems. Eigen-parts in these decompositions were named sub-Gramians. A theoretical comparison of the sub-Gramian method with other methods of modal analysis is provided. In order to demonstrate the potential of using the sub-Gramian method we apply it to the small-signal stability analysis of the IEEE 57-bus test model and compare it with the standard method of using eigenvalues.