Effects of Non-Smooth Phenomena on the Dynamics of DC-DC Converters

This paper shows the possibilities of applicability of novel approach for the global nonlinear analysis of dynamical systems, based on numerical path-following, to the widely used electronic circuits – switch–mode DC-DC converters. It has been proved, that the profound analysis of nonlinear phenomena in power electronics is profitable, as studying bifurcations and chaos can help engineers to understand the change of behavior in switching DC-DC converters when some parameters are varied. Nowadays the main tools for the investigation of the nonlinear dynamics of DC-DC, as one or more parameters are changed, are so called brute-force bifurcation diagrams. These diagrams give incomplete information about the possible types of nonlinear phenomena in the system, being not able to capture unstable periodic orbits as well as narrow stable regions (rare attractors). In order to overcome the mentioned drawbacks it is proposed to use the numerical path-following technique and appropriate data processing methods. Main results are illustrated on the current controlled boost converter, for which the complete one-parametric bifurcation diagrams are constructed and the possible interaction of period-doubling bifurcations and non-smooth border-collision phenomena are shown. The discrete time model is used, as this model enables one to avoid numerical computation of the phase space orbit from the continuous time model. The numerical results are verified by means of SIMULINK PowerSys Blockset model. The data verification allows concluding, that the results obtained on the basis of numerical path – following technique are very precise and the addition of real element nonidealities does not affect the global dynamics of the converter, causing just insignificant shifts of bifurcation points. Thus it has been proved that the complete bifurcational analysis could be efficiently applied to investigation of the dynamics of switching DC-DC converters in order to obtain information about the domains of existence and stability of desired period-1 operation as well as the appearance of smooth and various types of non-smooth bifurcations in this kind of circuits