This paper presents, in a tutorial manner, nonlinear phenomena such as bifurcations and chaotic behavior in DC-DC switching converters. Our purpose is to present the different modeling approaches, the main results found in the last years and some possible practical applications. A comparison of the different models is given and their accuracy in predicting nonlinear behavior is discussed. A general Poincaré map is considered to model any multiple configuration of DC-DC switching converters and its Jacobian matrix is derived for stability analysis. More emphasis is done in the discrete-time approach as it gives more accurate prediction of bifurcations. The results are reproduced for different examples of DC-DC switching converters studied in the literature. Some methods of controlling bifurcations are applied to stabilize Unstable Periodic Orbits (UPOs) embedded in the dynamics of the system. Statistical analysis of these systems working in the chaotic regime is discussed. An extensive list of references is included.
This paper is concerned with the study of nonlinear phenomena in a closed loop voltagecontrolled DC-DC Buck-Boost converter when suitable parameters are varied. The dynamics is analyzed using both the continuous-time model and the numerically computed stroboscopic map. The analysis of the one-dimensional bifurcation diagram shows that Neimarck-Sacker bifurcation occurs at certain values of the parameters. Phase-locking periodic windows, the period-adding sequence, and transition from quasiperiodicity to period-doubling via torus breakdown are also obtained. The two-dimensional bifurcation diagram is carefully computed. This shows that phase-locking orbits produce so-called Arnold tongues in the parameter space. It is shown that the winding number plotted as a function of the bifurcation parameter is a devil's staircase. As typically occurs in general circle maps, the fine structures of the Arnold tongues and the devil's staircase show self-similarity. *
In this paper, continuous conduction mode (CCM) operation of a class of single inductor multiple output dc-dc converters is proposed. The power stage combines boost and buck-boost structures loading non-inverted and inverted outputs. The control strategy is based on current mode control under an interleaving scheme, in which each output is controlled by a specific channel. These channels use different dynamic references, which are obtained from a set of proportional-integral (PI) controllers associated to the voltage outputs. The dynamical behaviour of this system is described by means of a large signal averaged model and direct simulations of the switched circuit-based model. Small signal stability analysis of the slow scale dynamics is also carried out by using the averaged model. Finally, some experimental results are provided to validate the theoretical predictions and the numerical simulations.Postprint (published version
Abstract-In this paper the nonlinear dynamics of interconnected power converters in an islanded direct current (DC) microgrid is analyzed. By using a simplified scheme based on two cascaded converters we analyze the dynamical behavior that can arise from the interconnection of these devices on a common DC bus. Furthermore, in order to address the bus voltage control problem, we propose a Sliding Mode Controller for a DC-DC bidirectional power converter to control the DC bus voltage under instantaneous Constant Power Loads (CPLs). This class of loads introduces a destabilizing nonlinear effect on the converter through an inverse voltage term that can lead to significant oscillations in the DC bus voltage. Simulation results are shown to illustrate the nonlinear analysis.
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