Accurate THD Formulas for Multilevel Inverters with MILP Optimization

Mahmoud El-Bakry

doi:10.19026/rjaset.7.501

Abstract

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 %V HOrms 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.

Highlights

The Multilevel Inverter (MLI) has recently replaced the conventional inverter, due to its multilevel output voltage that can approach more closely a sine wave shape (Sing et al, 2012)
The author has introduced an optimization method based on applying a Mixed Integer Linear Programming (MILP) optimization model to determine the switching angles that minimize the values of any undesired harmonics (El-Bakry, 2009, 2010)
Due to the quarter wave symmetry of F, the value of Vrms could be obtained from the first quarter half cycle: The odd triplen harmonics, i.e., that correspond to 2m+1 = 3, 9, 15,.., ∞ are self cancelled and this distinguish the value of the Total Harmonic Distortion (THD) of the line voltage from that of the phase voltage

Summary

INTRODUCTION

The Multilevel Inverter (MLI) has recently replaced the conventional inverter, due to its multilevel output voltage that can approach more closely a sine wave shape (Sing et al, 2012). The author has introduced an optimization method based on applying a Mixed Integer Linear Programming (MILP) optimization model to determine the switching angles that minimize the values of any undesired harmonics (El-Bakry, 2009, 2010) In all these methods, low order harmonics are mainly considered and high order harmonics are not taken into consideration it may be not enough to consider eliminating or reducing low order harmonics. This idea depends on dividing the time interval of the output voltage into small equal subintervals such that a certain voltage level is associated with each subinterval. The values of the amplitudes of the main harmonic V1and the subsequent harmonics V2k+1 could be replaced by their route mean square (rms) values, getting:

OF A THREE PHASE MLI

The expression of the exact THD of the line

Findings

CONCLUSION