CHAOS, SOLITONS & FRACTALS, Vol. 9, No. 6, pp. 825-843 (1998)
Global Bifurcation Caused by Unstable Limit Cycle Leading to Voltage Collapse in an Electric Power System
HIROFUMI OHTA and YOSHISUKE UEDA
Abstract-It has been reported that a saddle node bifurcation or a blue sky bifurcation causes voltage collapse in an electric power system. In these references, computer simulations are carried out with the voltage magnitude of the generator bus terminal held constant. The generator model described by differential equations of internal flux linkages allows the voltage magnitude of the generator bus terminal to change. By using this model, we have carried out computer simulations of the power system to determine the possible steady states. A variety of nonlinear phenomena, including chaotic attractors and coexisting attractors, are observed. A number of bifurcations, including global bifurcation, are observed, and the involvement of unstable limit cycles is confirmed. It is an unstable period-2 orbit that causes the voltage collapse. This is very interesting from the point of view of a nonlinear problem. From the point of view of a power system, the power system will fluctuate in practice even in normal operation, and may sometimes operate beyond the limit of its stability in recent year. It is very important in this situation that we clarify bifurcations of limit cycles and chaotic attractors on the power system.
Department of Electrical Engineering, Kyoto University, Kyoto, 606-8501, Japan
2. POWER SYSTEM MODEL (digest)
2.1. Generator model (digest)
2.2. AVR model (digest)
2.3. Transmission lines model
2.4. Load model
3. RESULTS OF SIMULATION (digest)
3.1. Overview of bifurcations
3.2. Steady states and bifurcations
3.3. Voltage collapse and unstable limit cycles
APPENDIX: THE BASIC THEORY OF A GENERATOR [4-7]
A.1. Two-pole model of a generator
A.2. Park's transformation and voltage equations
A.3. Flux linkage equations
A.4. Per unit conversion
A.5. Swing equation
A.6. Conversion of manufacturer data
Figures 4 (b) and (c) are missing from the publication.
- Ohta and Ueda : "Unstable limit cycles in an electric power system and basin boundary of voltage collapse,"
Chaos, Solitons & Fractals, Vol. 12, No. 1, pp. 159-172 (2001)
- Ohta and Ueda : "Blue sky bifurcations caused by unstable limit cycle leading to voltage collapse in an electric power system,"
Chaos, Solitons & Fractals, Vol. 14, No. 11, pp. 1227-1237 (2002)