Analytical Modelling of Voltage Balance Dynamics for a Flying Capacitor Multilevel Converter

This paper presents a strategy for the analytic determination of the natural voltage balancing dynamics of flying capacitor converters. The approach substitutes double Fourier series representations of the pulsewidth modulation (PWM) switching signals into a nonlinear dynamic circuit model of the converter. The result reduces to a linearized state-space model that can be readily solved, with the Fourier solution coefficients defining the state-space matrix terms. The solution can be readily developed for converters of any level, and allows rapid analytical investigation of the dynamic (and static) balancing behavior over a wide range of conditions. Furthermore, the approach allows powerful strategies such as root locus to be used to investigate the converter's performance as a function of changes in parameters such as modulation index and load. The analysis approach has been fully verified by comparing it against experimental results on a low voltage prototype converter.