Re-visiting naturally balanced average capacitor voltages in multilevel DC-DC converters

Capacitor natural voltage balancing in multilevel converters is a potentially attractive feature because it does not require capacitor voltage measurement and balancing control effort. The paper addresses DC-DC step-down Flying Capacitor Converter average balanced capacitor voltages for inductance dominated LR-loads (or resistive LC-filtered ones). Capacitor voltage unbalances, or offsets compared to their expected theoretical balanced values, impose overstress on semiconductor devices and compromise output voltage quality. It is demonstrated that the unbalance problem may practically occur for 3 flying capacitor converters for relatively small resistance of inductance dominated LR-load when using modulation strategies different from classic carrier-based phase-shifted lead and lag ones. Motivation for such strategies may be improving natural balancing dynamics rate. Symbolic time domain analysis is carried out for a demo case of a three capacitor DC-DC step-down converter in a small parameter approximation. Average capacitor voltage offset expressions clearly demonstrate the dependences on load parameters and capacitances for different switching sequences.