Analytical Determination of the Capacitor Voltage Balancing Dynamics for Three Phase Flying Capacitor Converters

This paper presents a new strategy for the analytic determination of the natural voltage balancing dynamics of three phase flying capacitor converters. The approach substitutes Double Fourier series representations of the PWM switching signals into a non-linear transient circuit model of the three phase converter. This results in a linearised state space model with the Fourier coefficients of the modulation strategy defining the state space matrix terms. The state space model can be readily developed for converters of any level, and allows for the rapid analytical investigation of the dynamic (and static) balancing behaviour over a wide range of operating conditions. Furthermore, the approach allows powerful linear analysis strategies such as root locus methods to be used to investigate the converter performance as a function of changes in parameters such as modulation index and load. The analysis approach has been fully verified by comparison with experimental results obtained on a low voltage three phase prototype converter.