16 Chaos in Power Electronics : An Overview

Power electronics is rich in nonlinear dynamics. Its operation is characterized by cyclic switching of circuit topologies, which gives rise to a variety of nonlinear behavior. This chapter provides an overview of the chaotic dynamics and bifurcation scenarios observed in power electronics circuits, emphasizing the salient features of the circuit operation and the modelling strategies. This chapter covers the modelling approaches, analysis methods, and a classification of the common types of bifurcations observed in power electronics. 1Financial support for C.K. Tse to undertake this work has been provided by the Hong Kong Research Grants Council under Grant PolyU-5131/99E.

[1]  D. C. Hamill POWER ELECTRONICS : A FIELD RICH IN NONLINEAR DYNAMICS , 1995 .

[2]  S.R. Sanders,et al.  Lyapunov-based control for switched power converters , 1990, 21st Annual IEEE Conference on Power Electronics Specialists.

[3]  P.T. Krein,et al.  Types of instability encountered in simple power electronic circuits: unboundedness, chattering, and chaos , 1990, Fifth Annual Proceedings on Applied Power Electronics Conference and Exposition.

[4]  Chi K. Tse,et al.  Instability and bifurcation in parallel-connected buck converters under a master-slave current sharing scheme , 2000, 2000 IEEE 31st Annual Power Electronics Specialists Conference. Conference Proceedings (Cat. No.00CH37018).

[5]  D. C. Hamill,et al.  Modeling of chaotic DC-DC converters by iterated nonlinear mappings , 1992 .

[6]  Mario di Bernardo,et al.  Corner collision implies Border Collision , 2001 .

[7]  J.H.B. Deane,et al.  Improvement of power supply EMC by chaos , 1996 .

[8]  M. Feigin,et al.  The increasingly complex structure of the bifurcation tree of a piecewise-smooth system☆☆☆ , 1995 .

[9]  H.H.C. Iu,et al.  Hopf bifurcation and chaos in a free-running current-controlled Cuk switching regulator , 2000 .

[10]  Enric Fossas,et al.  Study of chaos in the buck converter , 1996 .

[11]  Philip T. Krein,et al.  Elements of Power Electronics , 1997 .

[12]  David C. Hamill,et al.  Subharmonics and chaos in a controlled switched-mode power converter , 1988 .

[13]  M Di Bernardo The Complex Behaviour of Switching Devices , 2000 .

[14]  M. I. Feigin,et al.  On the structure of C-bifurcation boundaries of piecewise-continuous systems , 1978 .

[15]  Karl Henrik Johansson,et al.  Self-Oscillations in Relay Feedback Systems ; Symmetry and Bifurcations , 2000 .

[16]  James A. Yorke,et al.  Border-collision bifurcations including “period two to period three” for piecewise smooth systems , 1992 .

[17]  Mario di Bernardo,et al.  Grazing, skipping and sliding: Analysis of the non-smooth dynamics of the DC/DC buck converter , 1998 .

[18]  D. C. Hamill,et al.  Instability, subharmonics and chaos in power electronic systems , 1989 .

[19]  M. Bernardo,et al.  Discrete-time maps for the analysis of bifurcations and chaos in DC/DC converters , 2000 .

[20]  James A. Yorke,et al.  Anomalous bifurcations in DC-DC converters: borderline collisions in piecewise smooth maps , 1997, PESC97. Record 28th Annual IEEE Power Electronics Specialists Conference. Formerly Power Conditioning Specialists Conference 1970-71. Power Processing and Electronic Specialists Conference 1972.

[21]  Bimal K. Bose,et al.  Modern power electronics : evolution, technology and applications , 1992 .

[22]  Fred C. Lee,et al.  State-plane analysis of parallel resonant converter , 1985, 1985 IEEE Power Electronics Specialists Conference.

[23]  M. Abdelguerfi,et al.  Introduction 1.2 Parallel Database Systems 1.2.1 Computation Model 2 1.2 Parallel Database Systems Introduction Select * from Employee, Department Where (employee.dept_no @bullet Department.dept_no) and (employee.position = "manager") (a) Sql Request 1.2.2 Engineering Model , 2022 .

[24]  Jonathan H. B. Deane,et al.  Targeting in systems with discontinuities, with applications to power electronics , 1997 .

[25]  C. Tse Flip bifurcation and chaos in three-state boost switching regulators , 1994 .

[26]  C. K. Michael Tse,et al.  Chaos from a buck switching regulator operating in discontinuous mode , 1994, Int. J. Circuit Theory Appl..

[27]  Stephen John Hogan,et al.  Local Analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems , 1999 .

[28]  T. Ueta,et al.  Bifurcation of switched nonlinear dynamical systems , 1999 .

[29]  M. I. Feigin,et al.  Doubling of the oscillation period with C-bifurcations in piecewise-continuous systems: PMM vol. 34, n≗5, 1970, pp. 861–869 , 1970 .

[30]  J.H.B. Deane,et al.  Chaotic behaviour in current-mode controlled DC-DC convertor , 1991 .

[31]  Rudolf P. Severns,et al.  Modern DC-to-DC switchmode power converter circuits , 1985 .

[32]  T. Tsubone,et al.  Hyperchaos from a 4-D manifold piecewise-linear system , 1998 .

[33]  C. Hayashi,et al.  Nonlinear oscillations in physical systems , 1987 .

[34]  Arne Nordmark,et al.  Non-periodic motion caused by grazing incidence in an impact oscillator , 1991 .

[35]  Slobodan Cuk,et al.  A general unified approach to modelling switching-converter power stages , 1976, 1970 IEEE Power Electronics Specialists Conference.

[36]  Ian Dobson,et al.  Switching time bifurcations in a thyristor controlled reactor , 1996 .

[37]  T. Saito,et al.  On fundamental bifurcations from a hysteresis hyperchaos generator , 1994 .

[38]  Celso Grebogi,et al.  Border collision bifurcations in two-dimensional piecewise smooth maps , 1998, chao-dyn/9808016.

[39]  Yasuaki Kuroe,et al.  Analysis of bifurcation in power electronic induction motor drive systems , 1989, 20th Annual IEEE Power Electronics Specialists Conference.

[40]  C.K. Tse Chaos in power electronics , 2003, The IEEE International Symposium on Circuits and Systems, 2003. Tutorial Guide: ISCAS 2003..

[41]  C J Budd,et al.  Grazing and border-collision in piecewise-smooth systems: a unified analytical framework. , 2001, Physical review letters.

[42]  N. Inaba,et al.  A singular bifurcation into instant chaos in a piecewise-linear circuit , 1994 .

[43]  Eisuke Masada,et al.  Avoiding chaotic processes in current control of AC drive , 1998, PESC 98 Record. 29th Annual IEEE Power Electronics Specialists Conference (Cat. No.98CH36196).

[44]  Luigi Glielmo,et al.  Switchings, bifurcations, and chaos in DC/DC converters , 1998 .

[45]  Enric Fossas,et al.  Stabilization of periodic orbits of the buck converter by time‐delayed feedback , 1999, Int. J. Circuit Theory Appl..

[46]  S. Wiggins Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[47]  Ott,et al.  Border-collision bifurcations: An explanation for observed bifurcation phenomena. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[48]  James A. Yorke,et al.  BORDER-COLLISION BIFURCATIONS FOR PIECEWISE SMOOTH ONE-DIMENSIONAL MAPS , 1995 .