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High-Feedback Operation of Power Electronic Converters
Department of Computer Science, South West State University, 50 Years of October Street, 94,Kursk 305040, Russia
Department of Physics, Technical University of Denmark, 2800 Lyngby, Denmark
Department of Electronics, Radioelectronic and Electrotechnical Systems, Bryansk State TechnicalUniversity, Bulvar 50 Letiya Oktyabrya, 7, Bryansk 241035, Russia
Department of Industrial Electronics, Tomsk State University of Control Systems andRadioelectronics, 40 Lenina Prospect, Tomsk 634050, Russia
* Author to whom correspondence should be addressed.
Received: 29 November 2012; in revised form: 4 February 2013 / Accepted: 11 February 2013 / Published: 27 March 2013
Abstract: The purpose of this review is to provide a survey of some of the most important bifurcation phenomena that one can observe in pulse-modulated converter systems when operating with high corrector gain factors. Like other systems with switching control, electronic converter systems belong to the class of piecewise-smooth dynamical systems. A characteristic feature of such systems is that the trajectory is “sewed” together from subsequent discrete parts. Moreover, the transitions between different modes of operation in response to a parameter variation are often qualitatively different from the bifurcations we know for smooth systems. The review starts with an introduction to the concept of border-collision bifurcations and also demonstrates the approach by which the full dynamics of the piecewise-linear, time-continuous system can be reduced to the dynamics of a piecewise-smooth map. We describe the main bifurcation structures that one observes in three different types of converter systems: (1) a DC/DC converter; (2) a multi-level DC/DC converter; and (3) a DC/AC converter. Our focus will be on the bifurcations by which the regular switching dynamics becomes unstable and is replaced by ergodic or resonant periodic dynamics on the surface of a two-dimensional torus. This transition occurs when the feedback gain is increased beyond a certain threshold, for instance in Electronics 2013, 2 114 order to improve the speed and accuracy of the output voltage regulation. For each of the three converter types, we discuss a number of additional bifurcation phenomena, including the formation and reconstruction of multi-layered tori and the appearance of phase-synchronized quasiperiodicity. Our numerical simulations are compared with experimentally observed waveforms.
Keywords: power electronic converters; DC/DC converter; DC/AC converter; pulse-width modulation; piecewise-smooth dynamical systems; border-collision bifurcations; torus birth; torus reconstruction; phase-synchronized quasiperiodicity
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Zhusubaliyev, Z.T.; Mosekilde, E.; Andriyanov, A.I.; Mikhal'chenko, G.Y. High-Feedback Operation of Power Electronic Converters. Electronics 2013, 2, 113-167.
Zhusubaliyev ZT, Mosekilde E, Andriyanov AI, Mikhal'chenko GY. High-Feedback Operation of Power Electronic Converters. Electronics. 2013; 2(2):113-167.
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Andriyanov, Alexey I.; Mikhal'chenko, Gennady Y. 2013. "High-Feedback Operation of Power Electronic Converters." Electronics 2, no. 2: 113-167.