Single-leg flying capacitor converter voltage balancing dynamics analysis accounting for PWM iron loss

Natural voltage balancing dynamics analysis for flying capacitor converter may be carried out in time domain using switched systems analysis technique based on stitching analytical solutions for consecutive switching subintervals. In conjunction with the small parameter assumption, it allows obtaining closed-form approximate analytical solutions. PWM induced eddy current iron core loss mechanism that is accounted for in equivalent scheme by a large parallel resistance speeds up natural voltage balancing dynamics. Presented simple analytical solutions for 3- and 4-level single-leg flying capacitor converter reveal the dependences on load parameters, carrier frequency, and normalized DC voltage command (AC modulation index).