In this paper, the reduction approach based on the center manifold theory for parameter-dependent 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.
[1]
Eyad H. Abed,et al.
DYNAMIC BIFURCATIONS IN A POWER SYSTEM MODEL EXHIBITING VOLTAGE COLLAPSE
,
1993
.
[2]
S. Wiggins.
Introduction to Applied Nonlinear Dynamical Systems and Chaos
,
1989
.
[3]
Der-Cherng Liaw.
Feedback Stabilization via Center Manifold Reduction with Application to Tethered Satellites
,
1990
.
[4]
C. W. Taylor.
Power System Voltage Stability
,
1993
.
[5]
Guoxiang Gu,et al.
Bifurcation analysis and control for surge model via the projection method
,
1998,
Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).
[6]
V. Ajjarapu,et al.
Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system
,
1991
.
[7]
Ian Dobson,et al.
Towards a theory of voltage collapse in electric power systems
,
1989
.