Virtual orbits and two-parameter bifurcation analysis in power electronic converters
Tutor / director / evaluatorFossas Colet, Enric
Document typeMaster thesis
Rights accessOpen Access
When analytically investigating the 2-parameter bifurcation behaviour on a buck converter controlled by the ZAD strategy, the period doubling and corner collision curves in parameter space presented in  cross in four codimension two points presenting several properties. While two of them are given by the destruction of two bifurcation curves (period doubling and corner collision) at the boundaries of the feasible region in parameter space, a third one represents a change on the dynamics of the system and the fourth one is given by “appearance” of a saddle-node bifurcation curve. Using the concept of virtual and feasible orbits in the state space we will explain in this work how exactly this curve “appears” and we will add a fifth codimension two point where this saddle node bifurcation is destroyed and the corresponding curve “disappears”. We will also explain which are the changes on the dynamics of the system involved on the third codimension two point and we will give a partition of the parameter space so indicating where saturated and unsaturated T and 2T-periodic orbits exist. On the other hand, adding a third parameter representing a perturbation on the ZAD condition in one iteration of two periodic orbits, we will analytically show how some of the obtained phenomena are not possible to observe numerically due to the destruction of some of the previous structures for arbitrary small values of this parameter. At the same time, we will also justify why the numerical results when using an approximation of the ZAD condition (see ) contradict the analytical ones shown in .