Mitigation of Complex Non-Linear Dynamic Effects in Multiple Output Cascaded DC-DC Converters

In this project, the cascaded DC-DC converters with multiple output configurations are contributing a dominant part in the DC distribution systems and DC micro-grids. An individual DC-DC converter of any configuration exhibits complex non-linear dynamic behavior resulting in instability. This paper presents a cascaded system with one source boost converter and three load converters including buck, Cuk, and Single-Ended Primary Inductance Converter (SEPIC) that are analyzed for the complex non-linear bifurcation phenomena. An outer voltage feedback loop along with an inner current feedback loop control strategy is used for all the sub-converters in the cascaded system. 

To explain the complex non-linear dynamic behavior, a discrete mapping model is developed for the proposed cascaded system and the Jacobian matrix’s eigenvalues are evaluated. For the simplification of the analysis, every load converter is regarded as a fixed power load (FPL) under reasonable assumptions such as fixed frequency and input voltage. The eigenvalues of period-1 and period-2 reveal that the source boost converter undergoes period-2 orbit and chaos whereas all the load converters operate in a stable period-1 orbit. The proposed configuration eliminates the period-2 and chaotic behavior from all the load converters and is also validated using simulation in MATLAB/Simulink

Keywords: Bifurcation, chaos, DC-DC power converters, non-linear dynamical systems.