Accurate THD Formulas for Multilevel Inverters with MILP Optimization

This study aims to derive simple formulas for calculating the accurate Total Harmonic Distortion (THD) of Multilevel Inverter (MLIs), that considers all low and high order harmonics, for single phase and three phase MLIs., since the THD is a main criterion when judging the performance of a MLI. In addition, a formula for the percentage route mean square value of high order harmonics %VHOrms is derived. These formulas could be applied for all types of MLIs that use different switching techniques for harmonics elimination or reduction, so long as the switching angles of the phase voltage are known and it is specially suitable to be applied with the Mixed Integer Linear Programming (MILP) optimization model, which is constructed for determining the switching angles of the MLI that minimize the absolute values of any undesired harmonics. This study aims also to show that this MILP model can produce solutions that have low values of the accurate THD, by giving the detailed solutions of two cases taken from the references.