Local Reduction of Fold Bifurcation Relevant to Voltage Collapse in an Electric Power System

Abstract

In this paper, the reduction approach based on the center manifold theory for parameterdependent nonlinear dynamical systems is applied to simplify the analysis of the fold bifurcation relevant to voltage collapse in a simple electric power system. This technique enables us to obtain a lower-dimensional and topologically equivalent system in the neighborhood of the bifurcation value, which is a subset in the state-parameter space. Explicit formulas are presented for the computation of quadratic coefficients of the Taylor approximations to the center manifold for the fold bifurcation in parameter-dependent dynamical systems. It is demonstrated that it is the fold bifurcation but not other static bifurcations that occurs in the reduced power system, via validating the nondegenerate conditions for the fold bifurcation. The dynamics of the reduced system are visualized by two-and three-dimensional plots, which show that the reduction method is applicable and accurate to analyze local bifurcations in the power system. Furthermore, time domain simulation and modal analysis technique for linear systems are applied to distinguish the voltage stability from the rotor (angle) stability in the electric power system.

Structure-Induced Bifurcation in Large-Scale Electric Power Systems

“…Powerful computational tools for bifurcation analysis have been applied to study nonlinear problems arising in power systems, and in some cases, to relate this study to observed nonlinear phenomena in power systems, see for example [Abed & Varaiya, 1984;Abed et al, 1993;Ajjarapu & Lee, 1992;Cao & Chen, 2002;Chiang et al, 1990;Chiang et al, 1993;Dobson & Chiang, 1989;Kwatny et al, 1995;Makarov et al, 2000;Tan et al, 1995;Yorino et al, 1994]. Furthermore, some counter-measures to avoid bifurcations have been developed to design control schemes for prevention of power system instabilities.…”