Global bifurcation caused by unstable limit cycle leading to voltage collapse in an electric power system [Chaos, Solitons & Fractals 9 (6) (1998) 825–843]

2000 ◽  
Vol 11 (4) ◽  
pp. 643
Author(s):  
Hirofumi Ohta ◽  
Yoshisuke Ueda
Keyword(s):  
Power System ◽  
Electric Power ◽  
Limit Cycle ◽  
Global Bifurcation ◽  
Electric Power System ◽  
Voltage Collapse ◽  
Unstable Limit Cycle

LOCAL REDUCTION OF FOLD BIFURCATION RELEVANT TO VOLTAGE COLLAPSE IN AN ELECTRIC POWER SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1039-1046 ◽  
Author(s):  
GUO-YUN CAO ◽  
CHEN CHEN
Keyword(s):  
Dynamical Systems ◽  
Power System ◽  
Electric Power ◽  
Center Manifold ◽  
Nonlinear Dynamical Systems ◽  
State Parameter ◽  
Electric Power System ◽  
Voltage Collapse ◽  
Fold Bifurcation ◽  
Parameter Dependent

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.

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