In this article the mathematical model of complex regulated electric system in\nmatrix form is developed. This mathematical model makes it possible to study\nthe steady-state stability of a complex electrical system by determining the eigenvalues\nof the dynamics matrix. The model of an electrical system that reflects\ntransient processes for small deviations is convenient, both algorithmically\nand computationally, in particular, in cases of their joint solution with\nsteady-state equationsââ?¬â?the equations of nodal voltages. The obtained results\nin the form of the eigenvalues of the matrix spectrum are qualitatively the\nsame as the results of classical studies, which is a consequence of the adequacy\nof the proposed model and the correct reflection of the dynamic processes\noccurring in a real electrical system. In addition, the equations obtained are of\nindependent importance for the analysis of various modes, including transient,\nelectrical systems of any complexity.
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