Analytical formula for leg voltage THD of a PWM mutli-level inverter

In this presentation, the derivation of an analytical formula for the leg-voltage total harmonic distortion (THD) is presented. The considered system is a leg of a multi-level pulse-width modulated (PWM) voltage source inverter (VSI). The solution is based on Parseval’s theorem. The assumption throughout the derivations is that the ratio of the switching to the fundamental frequency is high. Derivations are based on the integration of the power of the PWM signal in a single switching period over the fundamental period of the signal. Only an ideal sinusoidal reference leg voltage is analysed. An analytical expression for the leg-voltage THD is given for any number of levels. The validity of the derived analytical equations is confirmed by simulations and experiments.