The current work is dedicated to analytical and numerical methods of analyzing stability in electromagnetic and electromechanical processes of the electric power system (EPS). The EPS, considered in the present article, runs in the external network of infinite power. The algorithm of estimating the stability region's boundary was obtained using Lyapunov's Direct Method, and an analytical technique to study the system's stability was developed based on the algorithm. The suggested technique was used to study the EPS and the boundary of its stability region during the generator's frequency variation and various ratios of linear and nonlinear terms of the mathematical model of the studied system.