Participation factor analysis method and device for linear periodic time-varying system

Abstract

The invention discloses a participation factor analysis method and device for a linear periodic time-varying system, and belongs to the field of dynamic analysis of the linear periodic time-varying system. The participation factor analysis method comprises the steps: for an n-dimensional linear periodic time-varying system, sequentially selecting row vectors or column vectors of an n-dimensional unit matrix as initial values of n state variables of the linear periodic time-varying system; sequentially calculating values of the linear periodic time-varying system at the T moment in different initial states by using a numerical integration method to obtain state responses x (T) of the n state variables at the T moment; taking the obtained n state responses as columns of an n * n matrix in sequence, and obtaining a numerical solution of the matrix phi (T, 0); calculating a matrix M formed by the feature roots of the matrix phi (T, 0), the right feature vectors and a matrix N formed by the left feature vectors, and defining a participation factor matrix by using the matrix M and the matrix N, so as to evaluate the relative influence of each state of the system on each feature root and further provide a theoretical basis for accurately positioning key links causing system instability when the system is unstable.

Description

technical field [0001] The invention belongs to the field of dynamic analysis of linear periodic time-varying systems, and more specifically relates to a method and device for analyzing participation factors of linear periodic time-varying systems. Background technique [0002] For practical systems, stable operation is the basic starting point for system analysis and control. Most of the actual systems are nonlinear systems, and it is difficult to directly analyze and control the nonlinear systems. Therefore, the existing research mainly studies the system stability within the neighborhood of the steady-state operating point of the system. In addition, the original characteristics of the actual system have time-varying characteristics. On the one hand, under certain assumptions, the time-varying system can be treated as time-invariant to obtain a linear time-invariant system; on the other hand, the original time-varying characteristics of the system can be preserved to obt...

AI Technical Summary

Problems solved by technology

Although the harmonic state space modeling realizes the time-invariant processing of the time-varying system, and thus can be analyzed by the participation factor analysis method of the complete linear time-invariant system, the theoretical harmonic state-space equation is an infinite-order state space Equations need to be truncated during analysis, but a reasonable truncation method still faces great challenges

In addition, for multi-machine large systems, harmonic state space modeling will lead to the problem of dimensionality disaster, which further limits the practical application of this method

[0028] It can be seen that the above-mentioned existing participation factor analysis methods for linear periodic time-varying systems have defects, and need to be further improved

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