Bifurcation analysis of 3D-PWS systems with two transversal switching boundaries: A case study in power electronics

This paper addresses the nonlinear analysis of PWS dynamical systems with two transverse switching boundaries through a real case study: a cascade of two buck converters connected to a common bus in a dc microgrid. Two-parameter bifurcation analysis is proposed to study local and global dynamics on a power electronic circuit feeding a constant power load and controlled by means of a sliding mode control. This electronic circuit is modeled as a 3D piecewise smooth dynamical system with two transversal switching boundaries, having sliding motion in just one of them. Complete characterization of phenomena associated with the bifurcations induced by two transversal switching boundaries is one of the main contributions of this work. Numerical continuation methods are employed to obtain bifurcation sets and bifurcation diagrams to understand the dynamic behavior of the study system and also to verify the analytical results.