摘要：AbstractThe structure of the low-order model is characterized by the fact the eigenvalues of its dynamics matrix coincide with the weakly stable eigenvalues of the system, which are calculated using the spectrum of the system dynamics matrix and the method of the gramians spectral decompositions. The optimal synthesis of the simplified model parameters is based on the approximate solution of the matrix polynomial equation for the matrices of the numerator of the system matrix transfer function and its simplified model. The solution of the synthesis problem leads to the solution of the linear matrix algebraic equation formed by the adaptability matrices. The energy functionals of the system and its simplified model can be determined by means of spectral decompositions of the squared H2 -norm of the matrix transfer function of the system and its simplified model. When the system approaches to the stability boundary, the stability margins of the system and its simplified model determined by the dominant weakly stable eigenvalues coincide asymptotically. This makes it possible not only to guarantee the stability of the simplified model, but also to determine the stability margins of a high-order system with help of the stability margins of a low-order model. The method makes it possible to estimate the oscillational instability caused by the resonant interaction of intraregional and inter-area oscillations and also to evaluate the impact of the input and output system matrices on the system stability using input and output matrices of its simplified model.
关键词：KeywordsLyapunov direct methodsmall-signals stabilityenergy systemsmodel order reductionstructural propertiesspectral decompositions of gramians
