Identification methods are presented for real-time development of discrete intelligent predictive models of dynamic processes for electric power systems. It is shown that digital models created at each time instant based on machine learning can effectively predict the possibility of stability loss for a wide class of nonlinear dynamic processes. The stability of discrete systems is studied on the basis of the Gramian method. In this paper, the stability indices of systems are determined using energy functional. Spectral expansions of functional are obtained, which makes it possible to reveal dominant modes that affect the energy of oscillations in the modes of operation of systems near the stability boundary.