ANALYSIS OF BIFURCATIONS IN A POWER SYSTEM MODEL WITH EXCITATION LIMITS

This paper studies bifurcations in a three node power system when excitation limits are considered. This is done by approximating the limiter by a smooth function to facilitate bifurcation analysis. Spectacular qualitative changes in the system behavior induced by the limiter are illustrated by two case studies. Period doubling bifurcations and multiple attractors are shown to result due to the limiter. Detailed numerical simulations are presented to verify the results and illustrate the nature of the attractors and solutions involved.

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DYNAMIC BIFURCATIONS IN A POWER SYSTEM MODEL EXHIBITING VOLTAGE COLLAPSE

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127493000969 ◽

1993 ◽

Vol 03 (05) ◽

pp. 1169-1176 ◽

Cited By ~ 41

Author(s):

E. H. ABED ◽

H. O. WANG ◽

J. C. ALEXANDER ◽

A. M. A. HAMDAN ◽

H.-C. LEE

Keyword(s):

Power System ◽

Reactive Power ◽

Period Doubling ◽

System Model ◽

Hopf Bifurcations ◽

Voltage Collapse ◽

Saddle Node ◽

Dynamic Bifurcations ◽

Period Doubling Bifurcations ◽

Power System Model

Dynamic bifurcations, including Hopf and period-doubling bifurcations, are found to occur in a power system dynamic model recently employed in voltage collapse studies. The occurrence of dynamic bifurcations is ascertained in a region of state and parameter space linked with the onset of voltage collapse. The work focuses on a power system model studied by Dobson & Chiang [1989]. The presence of the dynamic bifurcations, and the resulting implications for dynamic behavior, necessitate a re-examination of the role of saddle node bifurcations in the voltage collapse phenomenon. The bifurcation analysis is performed using the reactive power demand at a load bus as the bifurcation parameter. It is determined that the power system model under consideration exhibits two Hopf bifurcations in the vicinity of the saddle node bifurcation. Between the Hopf bifurcations, i.e., in the "Hopf window," period-doubling bifurcations are found to occur. Simulations are given to illustrate the various types of dynamic behaviors associated with voltage collapse for the model. In particular, it is seen that an oscillatory transient may play a role in the collapse.

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BIFURCATIONS IN A POWER SYSTEM MODEL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127496000217 ◽

1996 ◽

Vol 06 (03) ◽

pp. 497-512 ◽

Cited By ~ 48

Author(s):

ALI H. NAYFEH ◽

AHMAD M. HARB ◽

CHAR-MING CHIN

Keyword(s):

Power System ◽

Stable Manifold ◽

Reactive Power ◽

Period Doubling ◽

System Model ◽

Control Parameters ◽

Nonlinear Controller ◽

Basin Boundaries ◽

Period Doubling Bifurcations ◽

Power System Model

Bifurcations are performed for a power system model consisting of two generators feeding a load, which is represented by an induction motor in parallel with a capacitor and a combination of constant power and impedance PQ load. The constant reactive power and the coefficient of the reactive impedance load are used as the control parameters. The response of the system undergoes saddle-node, subcritical and supercritical Hopf, cyclic-fold, and period-doubling bifurcations. The latter culminate in chaos. The chaotic solutions undergo boundary crises. The basin boundaries of the chaotic solutions may consist of the stable manifold of a saddle or an unstable limit-cycle. A nonlinear controller is used to control the subcritical Hopf and the period-doubling bifurcations and hence mitigate voltage collapse.

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