| Summary: | The article discusses the results of the analysis of the static stability of complex electrical systems. The efficiency of the combined application of the equations of nodal voltages (ENV) and the Lyapunov function in quadratic form for the analysis of small oscillations of the electrical system is shown in the literature, which is called the Allaev method. A joint solution of the equations of nodal voltages and the matrix Lyapunov equation is given, which makes it possible to determine the stability conditions for the electrical system and identify the generator first approaching the stability limit. A study of small oscillations of complex electrical systems, which can be performed in full on the basis of matrix methods, successfully developed in recent decades, is carried out, which is associated with a sharp increase in the speed of computation and the amount of memory of modern computers.
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