Multilevel PWM Converter Voltage Quality Asymptotic Time Domain Evaluation

An on-going extensive research on multi-level and matrix converters requires physically meaningful easy-to-calculate criteria to compare numerous suggested converter topologies and voltage modulation strategies. Frequency domain voltage Total Harmonic Distortion (THD) criterion approach is too complicated and non-transparent as it involves multiple Fourier integral and results in multiple series with Bessel function coefficients. Our approach is to evaluate converter voltage quality in time domain using Normalized Ripple Voltage Mean Square (NRVMS) criterion that is about squared voltage THD. This is an asymptotic approach in the frequency domain sense meaning that PWM carrier to fundamental frequency ratio is supposed to be infinitely large C/F->oo. Or, alternatively, it is a quasi-static approach in the time domain sense meaning that the fundamental frequency signal is assumed constant on a single switching period. We present analytical NRVMS (THD) expressions that use elementary functions for an arbitrary number of levels N. NRVMS for multi-level DC/AC converter is obtained by double time integration – on PWM period and on output fundamental period (for matrix converter by triple integration – on PWM period, on input fundamental period and on output fundamental period). NRVMS criterion has a physical meaning of normalized PWM induced choke or electrical machine core loss that, under some realistic assumptions, is a major PWM loss mechanism dominating over PWM copper loss and PWM hysteresis core loss.