Analytical formula for leg voltage THD of a PWM multilevel inverter

In this paper derivation of an analytical formula for the leg voltage THD is presented. The considered system is a leg of a multilevel pulse width modulated (PWM) voltage source inverter (VSI). The solution is based on the 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. Analytical expression for the leg voltage THD is given for any number of levels. Validity of the derived analytical equations is confirmed by simulations and experiments.