AMApplied Mathematics2152-7385Scientific Research Publishing10.4236/am.2013.47139AM-34299ArticlesPhysics&Mathematics Total Harmonic Distortion Minimization of Multilevel Converters Using Genetic Algorithms .Salami1*B.Bayat1*Department of Electrical Engineering, Arak University of Technology, Arak, Iran* E-mail:a_salami@iust.ac.ir(.S);behnam_b60@yahoo.com(BB);28062013040710231027July 10, 2012January 5, 2013 January 18, 2013© Copyright 2014 by authors and Scientific Research Publishing Inc. 2014This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

This paper presents a genetic algorithm (GA) optimization technique to find the optimum switching angles of 11-level inverter with minimum number of dc sources and switches in comparison with the cascade multilevel inverter in order to minimize the total harmonic distortion (THD) of their output voltage waveform. Theoretical and simulation results for an 11-level converter show the efficiency of the proposed algorithm to determine the optimum angles in order to decrease the undesired harmonics and produce very high quality output voltage waveform.

Genetic Algorithm; Multilevel Converter Topologies; Multilevel Inverter1. Introduction

Multilevel inverters have become an effective and practical solution for increasing the power and reducing the harmonics of AC waveforms. Compared to the traditional two-level voltage source inverters, the stepwise output voltage is the major advantage of multilevel inverters. This advantage results in higher power quality, better electromagnetic compatibility, lower switching losses, higher voltage capability, and needlessness of a transformer at distribution voltage level, thereby reducing the costs [1].

Among The topologies for high power multilevel inverters, the cascaded inverter has the advantages that the DC-link voltage is balanced, the modularized circuit layout is possible, and it has the least components per phase. As the number of levels increases, multilevel inverters have low harmonic components and a low switching frequency, leading to the advent of step-pulse waves that switch once per fundamental cycle. Individual devices operate at high efficiencies because they can switch at a much lower frequency than PWM-controlled inverters [2]. For output step-pulse waveforms, it is necessary to obtain the conducting angles of switching devices. The predominant low-order harmonics can be eliminated. However, it has to solve conventional method has the merit that the simultaneous equations, which are the set of nonlinear transcendental equations for the fundamental component and the harmonic ones. It is difficult to obtain the conducting angles because the conventional method needs an iterative method such as the NewtonRaphson one. Additionally, the switching angles are obtained by means of an off-line calculation to minimize the harmonics for each modulation index, which leads to increased use of look-up tables.

The THD of the output voltage of the inverter is a measurement of the harmonic distortion, which is expected to be as small as possible in many applications of multilevel inverters. One popular example is the singlephase multilevel inverter for the photovoltaic power supply system, in which the THD of the output voltage of the inverter is regarded as a very important measurement of voltage quality [3].

This paper proposes a general genetic algorithm (GA) approach by which the switching angles can be calculated in the context of step modulation for multilevel inverters. This solves the same problem with a simpler formulation and with any number of levels without extensive derivation of analytical expressions. In this paper, the optimization aim of the proposed algorithm is the minimization of the voltage THD. Comparison with other methods also shows that the THD gained by the proposed method is the smallest. Simulation results are given to verify the performance of the proposed method.

2. The Circuit Topology

Figure 1 shows the circuit topology of the 11-level inverter. dc voltage sources are independent each other. Switches Ta, Tb and diode Da are the switches and the

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