Bogdanov-Takens Bifurcation in a Bidirectional DC-DC Converter Supplying a Constant Power Load

Identifier:  imarina:9525574

Handle: https://hdl.handle.net/20.500.11797/imarina9525574

Authors:  Torres F; Freire E; Benadero L; Sebastia-Rullo M; Mandal K; El Aroudi A

Abstract:
Over the decades, bifurcation theory has emerged as a significant area of research, providing deep insights into the complex dynamics of systems across multiple disciplines. Moreover, it serves as a foundation for devising effective control methodologies aimed at avoiding or delaying undesirable dynamical transitions. This paper deals with both local and global dynamics of a bidirectional dc-dc boost converter supplying a constant power load (CPL) with a stabilizing resistor inserted in series with the main inductor. Numerical simulations performed on the averaged model of the system show interesting bifurcation phenomena explaining its local and global dynamical behavior. In particular, it is shown that in some parametric region, the system has two coexisting equilibria, one of them being a saddle and the other one an anti-saddle. The latter can be stable or unstable. An unstable limit cycle also coexists with the stable anti-saddle equilibrium. This limit cycle disappears through a homoclinic bifurcation. Moreover, a parameter space reduction is carried out by choosing suitable bifurcation parameters, and the normal form of the Bogdanov-Takens bifurcation is obtained hence mathematically demonstrating its existence. Finally, the analytical and simulation results on the switched model are partially validated by experimental measurements from a laboratory prototype.