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.
Highlights
The field of power electronics has undergone a dramatic evolution during the last few decades [1]
Between the resonance zones Π6,1 and Π7,1, for instance, we find a region where the system completes 13 switching cycles and 2 cycles of the slower oscillatory mode produced by the control loop before repeating its dynamics, and between Π6,1 and this region we find the resonance zone where the system performs 19 switching cycles and three slow cycles before repeating itself, etc
Over a few decades the use of DC/DC converters and other types of converter systems has spread from their initial application in space- and aircrafts [72] to the widespread use as power supplies in the industry and transportation sectors as well as in common household appliances
Summary
The field of power electronics has undergone a dramatic evolution during the last few decades [1]. The use of relatively high switching frequencies has reduced the requirements on the size of the output filter components, and together these developments have opened the way for a broad range of new applications [4,5,6], including applications in portable PCs and cellular phones [7], as backup systems for sensitive computer systems and hospital equipment, and as main electric power supplies at remote locations. Power electronic systems with switching operation are used in practically all sectors of our society. Examples from the industry and transportation sector are aircraft electronics, traction regulators in trains, and power supplies for electric vehicles [8]. An introduction to some of the complex nonlinear phenomena that one can observe in power electronics systems may be found in the book by Banerjee and Verghese [9]
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