Development of tools for the study of chaotic behavior in power electronics

This paper describes the development of software tools for the analysis of chaos in power electronics systems. This project was motivated by potential contributions of chaos theory in the design, analysis and control of power electronics circuits. Nonlinear analysis software and computer programs were used for the detection and analysis of chaotic components. Simulations of power electronics devices were performed using commercially available circuit analysis packages. The voltage and current time series obtained from the circuit analysis were studied using the nonlinear analysis tools developed for this project as well as existing nonlinear analysis programs. The results of the nonlinear analysis can be used to design and implement better mitigating and control techniques for the circuits under study. Chaotic dynamics provide an alternate representation that can lead to better designs and new ways to explain nonlinear behavior in power electronics circuits. There is also a great pedagogical value in complementing the traditional representation of power electronic circuits with alternate models.

[1]  Peter Ashwin,et al.  Calculation of the periodic spectral components in a chaotic DC-DC converter , 1999 .

[2]  Chi K. Tse,et al.  Experimental confirmation of chaos in a current-programmed Cuk converter , 1996 .

[3]  H. Kantz.  A robust method to estimate the maximal Lyapunov exponent of a time series , 1994 .

[4]  L. Glielmo,et al.  Analysis of chaotic buck, boost and buck-boost converters through switching 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.

[5]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[6]  K. T. Chau,et al.  Chaotic behavior in a simple DC drive , 1997, Proceedings of Second International Conference on Power Electronics and Drive Systems.

[7]  Celso Grebogi,et al.  Robust chaos-the theoretical formulation and experimental evidence , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

[8]  D. C. Hamill,et al.  Problems of computing Lyapunov exponents in power electronics , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

[9]  Jonathan H. B. Deane,et al.  Some applications of chaos in power converters , 1997 .

[10]  S. Ben-Yaakov,et al.  A chaos model of subharmonic oscillations in current mode PWM boost converters , 1995, Proceedings of PESC '95 - Power Electronics Specialist Conference.

[11]  Soumitro Banerjee,et al.  Experimental control of chaotic behavior of buck converter , 1995 .

[12]  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).

[13]  J. R. Wood.  Chaos: a real phenomenon in power electronics , 1989, Proceedings, Fourth Annual IEEE Applied Power Electronics Conference and Exposition.

[14]  Neville R. Watson,et al.  Power System Quality Assessment , 2000 .

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

[16]  G.C. Verghese,et al.  Analysis of the chaotic regime for DC-DC converters under current-mode control , 1996, PESC Record. 27th Annual IEEE Power Electronics Specialists Conference.

[17]  Krishnendu Chakrabarty,et al.  Control of chaos in DC-DC converters , 1998 .

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

[19]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[20]  John Baillieul,et al.  Chaotic motion in nonlinear feedback systems , 1980 .

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

[22]  D. C. Hamill.  Learning about chaotic circuits with SPICE , 1993 .

[23]  George C. Verghese,et al.  Analysis and control of chaotic DC-DC switching power converters , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

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

[25]  R. Iravani,et al.  Guidelines for Modeling Power Electronics in Electric Power Engineering Applications , 1997, IEEE Power Engineering Review.