Asymptotic time domain evaluation of a single-phase multilevel PWM inverter current quality

This paper addresses theoretical calculation of a single-phase multilevel PWM inverter current Total Harmonic Distortion (THD). Analytical approach introduced in late 1980s for a 2-level inverter is generalized for an arbitrary level count for a single-phase inverter. Though the obtained closed-form piece-wise analytical solutions assume (infinitely) large ratio of switching and fundamental frequencies and pure inductive load, they are practically very accurate for the ratios of (apparent) switching and fundamental frequencies larger than 25-30 and inductance dominated loads. Along with strict mathematical solutions suggested are simple accurate Bessel function approximation and hyperbolic average trend one. The formulas clearly reveal a single-phase PWM inverter current THD dependence on modulation index for an arbitrary voltage level count and are easily modified to cover grid-connected cases.