Simple analysis of a flying capacitor converter voltage balance dynamics for DC modulation

Flying capacitor multilevel PWM converter with a natural voltage balance is an attractive multilevel converter choice because it requires no voltage balance control effort. Flying capacitor converter practically does not suffer from voltage balance imposed performance limitations as opposed to multiple point clamped converter. Voltage balance dynamics analytical research methods reported to date deal mostly with an AC modulation case and are essentially based on a frequency domain analysis using double Fourier transform. Therefore, these methods require high mathematical skills, are not truly analytical and rather difficult to use in an everyday practice by electrical engineer. In this paper, we consider a DC modulation case to demonstrate that a straightforward time domain approach based on switching intervals piece-wise analytical solutions makes it easy to obtain time-averaged discrete and continuous models for voltage balance dynamics simulation. A primitive single-phase single-leg three-level converter analytical investigation yields a surprisingly simple accurate expression for capacitor charge / discharge related time constant revealing its dependence on inductive load parameters, carrier frequency, and duty ratio.