Time Scales, Coherency, and Weak Coupling.

Abstract : In this thesis the authors study a relation between time scales and structural properties of a class of spower 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 models 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. 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. (Author)