Bifurcation Behavior of a Three Cell DC-DC Buck Converter

Most of nonlinear analysis techniques used for studying the stability of power electronics systems has been applied to particular cases such as the buck converter under voltage mode control, boost converter with current programmed control, etc. This is due to the inherent complexity of the mathematical description of such systems in spite of their topological simplicity. In this paper, we extend the use of these techniques for studying stability of periodic orbits of a three cell DC-DC buck converter. We begin by giving the state space description of the system dynamical behavior of the system. Then, a discrete time model in the form of a Poincaré map is described and used for stability analysis. The expressions of the fixed point and the Jacobian matrix of this map are given in closed form in terms of system matrices. Instabilities in the form of generic bifurcations like period doubling and Neimark-Sacker bifurcation can be be detected accurately. Numerical simulations confirms the theoretical predictions.