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https://hdl.handle.net/2142/66236
Description
Title
Time Scales, Coherency, and Weak Coupling
Author(s)
Avramovic, Bozidar
Issue Date
1980
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
In this thesis we study a relation between time scales and structural properties of a class of systems represented by power systems. First, the time scale decomposition of linear time invariant systems is studied. The properties of the time scale decomposition are shown to be defined by properties of solutions of a generalized matrix Riccati equation. Use of the Riccati equation formulation and a particular method for finding its solution led to the result which shows that the singular perturbation method and modal method for reduced order modeling are two extreme points of an iterative method for the time scale decomposition: singular perturbation is its first point and modal method is the limiting point. Convergence properties of a known class of iterative methods for the time scale decomposition are characterized. A method for the time scale decomposition of weakly nonlinear systems is proposed as an extension of linear system analysis to nonlinear systems. Then, for electromechanical model of power systems a connection between its time scales and structural properties is established by showing that the so-called slow coherency can be expressed in terms of the same Riccati equation used for the time scale decomposition. It is shown analytically and then conformed experimentally on a few realistic size systems, that in the case of slow coherency, the coherent areas are weakly coupled, and hence relatively independent on the fault location. By using the Riccati formulation of coherency, an efficient numerical algorithm for identifying coherent areas is obtained. Finally, a possibility of extending this study to the direct transient stability analysis of power systems is briefly discussed.
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