Calculation of current total harmonic distortion for a single-phase multilevel inverter with LCL-Filter

This paper addresses calculation of current Total Harmonic Distortion (THD) for a single-phase multilevel PWM inverter with LCL-filter. Analytical approach introduced in late 1980s for a 2-level inverter with inductance dominated load is generalized for a single-phase multilevel inverter with an arbitrary number of voltage levels accounting for the smoothing effect of LCL-filter. Though the obtained closed-form analytical solutions initially assume (infinitely) large ratio of switching and fundamental frequencies, they are practically accurate for the ratios of (apparent) switching and fundamental frequencies larger than 25-30. Also suggested are simple accurate Bessel function approximations. The formulas clearly reveal a single-phase PWM inverter current THD dependence on LCL-filter parameters and modulation index for an arbitrary level count and are easily modified to cover a grid-connected case.