Discrete Predictive Models for Stability Analysis of Power Supply Systems

Abstract

The paper offers an approach to the investigation of the dynamics of nonlinear non-stationary processes with the focus on the risk of dynamic system stability loss. The risk is assessed on the basis of the accumulated knowledge about power supply system operation. New methods for power supply modes analysis are developed and applied as follows: linear discrete point knowledge-based models are developed for nonlinear non-stationary objects; wavelet analysis is used for non-stationary processes; stability loss risks are analyzed through the investigation of spectral decompositions of Gramians of these linear predictive models. Case studies are included.

Spectral Decompositions of Gramians of Continuous Stationary Systems Given by Equations of State in Canonical Forms

“…The paper proposes to improve this approach by using spectral decompositions of the Gramians and the representation of the resolvent of the dynamics matrix by extending the scope to multivariable linear and bilinear control systems. [11,[26][27][28] In Section 3, we propose to use for Gramian decomposition the representation of the dynamics matrix resolvent of continuous linear stationary systems with many inputs and one output (MISO LTI) in the form of a Fadeev-Levereux series segment [29]. Conversion of the state equations to the canonical form of controllability allowed us to exclude the right part of the Lyapunov equations and the Fadeev matrix from the spectral expansions of the Gramians, This allowed us to further simplify the scalar part of the spectral expansions and to link the localization of the Gramian elements with the residues of the scalar transfer function of the linear system.…”