Abstract
This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.
Highlights
Power electronics converters have been widely used for industrial applications, such as motor speed variation, renewable energy technologies, and harmonic filtering [1,2,3], to adjust input voltages and currents to obtain regulated power supplies
First an accurate model has been used for numerically simulating the system behavior and predicting the nonlinear behavior of a three-cell flying capacitor buck converter under a discrete-time controller
We have illustrated the use of the theory by studying a three-cell flying capacitor buck converter under discrete-time controller
Summary
Power electronics converters have been widely used for industrial applications, such as motor speed variation, renewable energy technologies, and harmonic filtering [1,2,3], to adjust input voltages and currents to obtain regulated power supplies. A discrete-time digital predictive control for a three-level flying capacitor buck converter with voltage balancing is presented in [38]. Floquet theory has been successfully applied in the past to perform stability analysis of simple power electronics converters such as the conventional buck converter [25], cascaded converters [33] and interleaved converter [41] among others The application of this approach to multi-level flying capacitor converters has not been reported for the best knowledge of the authors. It is the aim of this paper to apply this theory to predict the nonlinear dynamics and to perform stability analysis of a three-cell flying capacitor DC-DC buck converter under discrete-time controller.
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