Minimization of Voltage and Current Total Harmonic Distortion for a Single-Phase Multilevel Inverter Staircase Modulation

The paper addresses optimal voltage and current quality (minimal Total Harmonic Distortion - THD) for a single-phase multilevel inverter staircase modulation. The previous research mostly addressed optimal THD problem in frequency domain accounting for a limited harmonics count. The novelty of this research is that voltage and current minimal THD problems are formulated in time domain as a constrained optimization ones in order to find theoretically optimal switching angles accounting for all switching harmonics. The optimal switching angles and respective minimal THD values are obtained for different inverter level counts and the whole fundamental voltage (modulation index) range. Suggested are smooth ripple-free approximations for accurate voltage and current THD for arbitrary level counts and modulation indices. While these simple hyperbolic formulas accurately approximate the average trend, local maxima and minima of voltage and current THD may be considered on separate. In fact, the obtained current THD is frequency weighted THD that assumes inductance dominated RL-load. For grid-connected applications, normalized current fundamental harmonic is smaller than voltage modulation index and current THD is essentially larger than frequency weighted voltage one.