Controlling Hopf bifurcation and chaos in a small power system. (English) Zbl 1074.93522

Summary: For the power systems, the stabilization and tracking of voltage collapse trajectory, which involves severe nonlinear and nonstationary (unstable) features, is somewhat difficult to achieve. In this paper, we choose a widely used three-bus power system to be our case study. The study shows that the system experiences a Hopf bifurcation point (subcritical point) leads to chaos throughout period-doubling route. A model-based control strategy based on global state feedback linearization (GLC) is applied to the power system to control the chaotic behavior. The performance of GLC is compared with that for a nonlinear state feedback control.


93C10 Nonlinear systems in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G99 Local and nonlocal bifurcation theory for dynamical systems
Full Text: DOI


[1] Kundur, P., Power system stability and control (1994), Electric Power Research Institute (McGraw-Hill Inc): Electric Power Research Institute (McGraw-Hill Inc) New York
[2] Kwatny, H. G.; Pasrija, A. K.; Bahar, L. Y., Static bifurcation in electric power networks: Loss of steady-state stability and voltage collapse, IEEE Trans. Circuit Syst., 33, 981-991 (1986) · Zbl 0621.94024
[5] Abed, E. H.; Varaiya, P. P., Nonlinear oscillations in power systems, Int. J. Electric Power Energy Syst., 6, 37-43 (1989)
[9] Nayfeh, A. H.; Harb, A. M.; Chin, C., Bifurcation in a power system model, Int. J. Bifurcation Chaos, 6, 3 (1996)
[10] Isidori, A., Nonlinear control systems (1989), Springer Verlag · Zbl 0714.93021
[11] Abed, E. H.; Fu, J. H., Local feedback stabilization and bifurcation control, I. Hopf bifurcation, Syst. Control Lett., 7, 11-17 (1986) · Zbl 0587.93049
[12] Abed, E. H.; Fu, J. H., Local feedback stabilization and bifurcation control, II. Stationary bifurcation, Syst. Control Lett., 8, 467-473 (1987) · Zbl 0626.93058
[14] Chiang, H.-D.; Dobson, I.; Thomas, R. J.; Thorp, J. S.; Fekih-Ahmed, L., On voltage collapse in electric power systems, IEEE Trans. Power Syst., 5, 601-611 (1990)
[15] Baillieul, J.; Brockett, R.; Washburn, R. B., Vaotic motion in nonlinear feedback systems, IEEE Trans. Circuit Syst., 27, 990-997 (1980) · Zbl 0499.93025
[16] Chang, H.-C.; Chen, L.-H., Bifurcation characteristics of nonlinear systems under conventional PID control, Chem. Eng. Sci., 39, 1127-1142 (1984)
[18] Harb, A. M.; Nayfeh, A. H.; Chin, C.; Mili, L., On the effects of machine saturation on subsynchronous oscillations in power systems, Electric Mach. Power Syst. J., 28, 11 (1999)
[19] Kravaris, C.; Chung, C., Nonlinear state feedback synthesis by global input/output linearization, AlChE J., 33, 4, 592-603 (1987)
[20] Henson, M.; Seborg, D., Input-output linearization of general nonlinear processes, AlChE J., 36, 11, 1753-1895 (1990)
[21] Kravaris, C.; Kantor, J., Geometric methods for nonlinear process control. 1. Background, I&EC Res., 29, 2295-2310 (1990)
[22] Kravaris, C.; Kantor, J., Geometric methods for nonlinear process control. 2. Controller synthesis, I&EC Res., 29, 2310-2323 (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.