The nonlinear dynamic characteristics of a simple three-bus power system mathematic model are studied, including phase diagrams and a bifurcation map. To control this undesirable chaos, sliding mode control law without buffeting is presented based on the LaSalle invariance principle, which considers the bounded disturbances. The theoretical analysis is in agreement with numerical simulation in that the designed controller could asymptotically stabilize the unstable power system to a typical steady-state. The research of this paper may help to maintain the power system's security operation.
ChenDYLiuYXMaXYZhangRF (2011a) Control of a class of fractional-order chaotic systems via sliding mode. Nonlinear Dynamics. doi: 10.1007/s11071–011–0002–x.
2.
ChenDYZhaoWLMaXYZhangRF (2011b) No-chattering sliding mode control chaos in Hindmarsh-Rose neurons with uncertain parameters. Computers and Mathematics with Applications61: 3161–3171.
3.
ChiangHDLiuCWVaraiyaPP (1993) Chaos in a simple power system. IEEE Transactions on Power Systems8: 1407–1417.
4.
De PaulaASSaviMA (2009) A multiparameter chaoscontrol method based on OGY approach. Chaos, Solitons & Fractals40: 1376–1390.
5.
HuangCFChengKHYanJJ (2009) Robust chaos synchronization of four-dimensional energy resource systems subject to unmatched uncertainties. Communications in Nonlinear Science and Numerical Simulation14: 2784–2792.
6.
HuangCHLinCHKuoCL (2011) Chaos synchronization-based detector for power-quality disturbances classification in a power system. IEEE Transactions on Power Delivery26: 944–953.
7.
KopellNWashburnRB (1982) Chaotic motions in two degrees of freedom swing equations. IEEE Transactions on Circuits and Systems29: 738–746.
8.
LaiDKSwarupKS (2011) Modeling and simulation of chaotic phenomena in electrical power systems. Applied Soft Computing11: 103–110.
9.
LoriaA (2010) Control of the new 4th-order hyper-chaotic system with one input. Communications in Nonlinear Science and Numerical Simulation15: 1621–1630.
10.
PaiNSYauHT (2011) Generalized projective synchronization for the horizontal platform systems via an integral-type sliding mode control. Journal of Vibration and Control17: 11–17.
11.
RevelGLeonAEAlonsoDM (2010) Bifurcation analysis on a multimachine power system model. IEEE Transactions on Circuits and Systems - Regular Papers57: 937–949.
ShiXRWangZL (2010) Robust chaos synchronization of four-dimensional energy resource system via adaptive feedback control. Nonlinear Dynamics60: 631–637.
14.
SudheerKSSabirM (2011) Adaptive modified function projective synchronization of multiple time-delayed chaotic Rossler system. Physics Letters A375: 1176–1178.
15.
SunMJiaQTianLX (2009a) A new four-dimensional energy resources system and its linear feedback control. Chaos, Solitons and Fractals39: 101–108.
16.
SunMTianLXZengCY (2009b) The energy resources system with parametric perturbations and its hyperchaos control. Nonlinear Analysis: Real World Applications10: 2620–2626.
17.
WeiDLuoXQinY (2011) Controlling bifurcation in power system based on LaSalle invariant principle. Nonlinear Dynamics63: 323–329.
18.
YeHPDingYS (2009) Nonlinear dynamics and chaos in a fractional-order HIV model. Mathematical Problems in Engineering. doi: 10.1155/2009/378614.
19.
YuYN (1983) Electric Power System Dynamics, New York: Academic Press.
20.
ZhangJSmallM (2006) Complex network from pseudoperiodic time series: topology vs dynamics. Physical Review Letters96: 238701–238701.
21.
ZhangJZhangKFengJFSmallM (2010) Rhythmic dynamics and synchronization via dimensionality reduction: application to human gait. Plos Computational Biology6: e10011033–e10011033.
