Methodology for Determining Stability of Power System

摘要

The article presents an algorithm for determining the modes with maximum power for long distance equivalent power systems in various configurations with a simplified representation of the excitation system of synchronous generators. Given the large volume of calculations and analytical transformations, a feature has been identified that allows one to determine the disturbance of static stability (out-of-step mode). The indicated sign is the extremum of the function of free term of the characteristic equation. A quantitative and qualitative analysis of the eigenvalues of the coefficient matrix of the system of linearized differential equations of electromechanical transients has been performed to confirm the proposed approach to determining stability. The dependence of the coefficients of the characteristic equation was studied in the course of the analysis with a change in the length of power lines and the power of the considered power units. The indicated coefficients were obtained after mathematical transformations of the system of linearized differential equations of electromechanical transients. According to the results of studies, it was found that among the roots of the characteristic equation that determine the electromechanical movement in the power system, there is a redistribution of material parts, while there is an increase in the attenuation of low-frequency oscillations. In the presence of excitation controllers using channels with respect to the derivative of the operating parameters, the redistribution of the material parts responsible for the attenuation of electromechanical vibrations is even more pronounced. Based on the results and conclusions, the authors proposed a generalized method for studying the stability of power system based on the appearance of low-frequency oscillations. This technique with simplified models allows you to evaluate the maximum transmitted power without the occurrence of electromechanical vibrations, i.e. while maintaining the static vibrational stability, which allows to reduce the volume of the considered design modes for power systems of very different structures.