Torus-Bifurcation Mechanisms in a DC/DC Converter With Pulsewidth-Modulated Control

Pulse-modulated converter systems play an important role in modern power electronics. However, by virtue of the complex interplay between ordinary (smooth) and so-called border-collision bifurcations generated by the switching dynamics, the changes in behavior that can occur in multilevel converter systems under varying operational conditions still remain to be explored in full. Considering the dynamics of a three-level dc/dc-converter, we demonstrate a number of new scenarios for the birth or destruction of resonant and ergodic tori. One scenario involves the formation of a doubled-layered torus structure around a stable focus point through three subsequent border-collision fold bifurcations. Another scenario replaces one of the fold bifurcations by a global bifurcation. In both of these scenarios, the basic mode of the converter remains stable while other modes grow up and bifurcate around it. We also illustrate the subcritical birth of both an ergodic and a resonance torus from the basic operational mode.