Hopf Bifurcation Control of Power System Nonlinear Dynamics via a Dynamic State Feedback Controller–Part I: Theory and Modeling

This two-part paper introduces a dynamic state feedback control law that guarantees the elimination of Hopf bifurcations (HB) before reaching the saddle-node bifurcations (SNB). Part I is devoted to the mathematical representation of the detailed system dynamics, investigation of HB and SNB theorems, and state feedback controller design. For purposes of dynamical analysis, the stable equilibria of the system is obtained. Then the control system is designed with the objective of preventing the voltage collapse before the SNB, such that the structural stability of the system is preserved in the stationary branch of the solutions. The controller aims to relocate Hopf bifurcations to the stationary branch of solutions located after SNB, eliminating the HB from normal operating region of the system. In order to evaluate the performance of the proposed controller, bifurcation analysis has been performed in Part II using single-machine and multi-machine test systems.

[1]  R. Sarpong,et al.  Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol , 2019, Chemical science.

[2]  M. Hadi Amini,et al.  Hopf Bifurcation Control of Power Systems Nonlinear Dynamics Via a Dynamic State Feedback Controller—Part II: Performance Evaluation , 2018, IEEE Transactions on Power Systems.

[3]  Pouya Mahdavipour Vahdati,et al.  Hopf Bifurcation Control of Power Systems Nonlinear Dynamics Via a Dynamic State Feedback Controller - Part II: Performance Evaluation , 2017, IEEE Power & Energy Society General Meeting.

[4]  S. Sitharama Iyengar,et al.  Smart Grids: Security and Privacy Issues , 2016 .

[5]  T. Sideris.  Ordinary Differential Equations and Dynamical Systems , 2013 .

[6]  Le Hoa Nguyen,et al.  Hopf bifurcation control via a dynamic state-feedback control , 2012 .

[7]  H. Henao,et al.  Modeling of synchronous machines with magnetic saturation , 2007 .

[8]  Guanrong Chen,et al.  Hopf bifurcation Control Using Nonlinear Feedback with Polynomial Functions , 2004, Int. J. Bifurc. Chaos.

[9]  Ahmad Harb,et al.  Controlling Hopf bifurcation and chaos in a small power system , 2003 .

[10]  Nadarajah Mithulananthan,et al.  Comparison of PSS, SVC, and STATCOM controllers for damping power system oscillations , 2003 .

[11]  Guanrong Chen,et al.  Anti-control of Hopf bifurcations , 2001 .

[12]  K. R. Padiyar,et al.  Bifurcation analysis of a three node power system with detailed models , 1999 .

[13]  M. A. Pai,et al.  Hopf bifurcation control in power systems with static var compensators , 1997 .

[14]  Hua O. Wang,et al.  Bifurcation control of a chaotic system , 1995, Autom..

[15]  H. Chiang,et al.  Bifurcations and chaos in electric power systems: Numerical studies , 1994 .

[16]  Wei-Min Liu,et al.  Criterion of Hopf Bifurcations without Using Eigenvalues , 1994 .

[17]  Felix F. Wu,et al.  Chaos in a simple power system , 1993 .

[18]  Felix F. Wu,et al.  Bifurcation and chaos in power systems , 1993 .

[19]  J. Alexander,et al.  Dynamic bifurcations in a power system model exhibiting voltage collapse , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[20]  Ian Dobson,et al.  Towards a theory of voltage collapse in electric power systems , 1989 .

[21]  E. Abed,et al.  Local feedback stabilization and bifurcation control, I. Hopf bifurcation , 1986 .

[22]  G. Shackshaft,et al.  Model of generator saturation for use in power-system studies , 1979 .

[23]  G. Sell,et al.  The Hopf Bifurcation and Its Applications , 1976 .

[24]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[25]  Anne Kuefer,et al.  Voltage Stability Of Electric Power Systems , 2016 .

[26]  M. Despalatovic,et al.  Modeling of Saturated Synchronous Generator Based on Steady-State Operating Data , 2012, IEEE Transactions on Industry Applications.

[27]  Daniel Liberzon,et al.  Common Lyapunov functions for families of commuting nonlinear systems , 2005, Syst. Control. Lett..

[28]  J. A. Kuznecov.  Elements of applied bifurcation theory , 1998 .

[29]  S. C. Srivastava,et al.  Elimination of dynamic bifurcation and chaos in power systems using FACTS devices , 1998 .