A PSO based optimal switching technique for voltage harmonic reduction of multilevel inverter Rup Narayan Ray a , Debashis Chatterjee b, * , Swapan Kumar Goswami b a National Institute of Technology, Agartala, Tripura 799055, India b Jadavpur University, Kolkata 700032, India article info Keywords: Particle swarm optimization (PSO) Selected harmonic elimination (SHE) Multilevel inverter Total harmonic distortion (THD) abstract Selected lower order harmonics of multilevel inverter are eliminated while the overall voltage THD is optimized by computing the switching angles using particle swarm optimization (PSO) technique. The discontinuity in the solution of selected harmonic elimination (SHE) problem at certain modulation indi- ces is avoided by optimizing the individual harmonics to allowable limits. While choosing the set of solu- tion leading to minimum THD, the abrupt changes in the switching angles are discarded by limiting the voltage THD within allowable limits. Also the selected higher order harmonics are eliminated by addi- tional switching along with the lower order harmonics. In order to reduce the computational burden for online application, the switching angles computed by the proposed PSO technique for optimum THD at varying modulation indices are stored as a look-up table in the DSP memory. The simulated results are also validated through suitable experiments. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction A multilevel inverter is useful for high power application at higher voltage level by connecting different dc sources of lower voltage level (Menzies, Steimer, & Steinke, 1994; Tolbert, Peng, & Habetler, 1999). The desired ac voltage is synthesized from several dc sources by cascading individual inverters (Lai & Peng, 1996). Multilevel inverters can be used to interconnect several distributed generations (DG) like solar, fuel cell, rectified output of wind en- ergy with the ac grid. However, the main concern is eliminating the harmonics from the output voltage of multilevel inverter. The output voltage of the inverter must meet maximum THD limita- tions as specified in Duffey and Stratford, 1989. There are several methods used for harmonic elimination. Traditional SHE PWM method is widely used (Carrara, Gardella, Marchesoni, Salutari, & Sciutto, 1992; Enjeti, Ziogas, & Lindsay, 1990; Hammond, 1997; Loh, Holmes, & Lipo, 2005). Carrier based PWM technique is also reported (Tolbert & Habetler, 1999; Holmes & McGrath, 2001). But with these methods, higher order harmonics of the output voltage are not completely eliminated though the lower order har- monics are efficiently eliminated. To address the problem of higher order harmonics, an active harmonic elimination technique (Du, Tolbert, & Chiasson, 2006) has been proposed. In this method, the resultant theory (Chiasson, Tolbert, Mckenzie, & Du, 2003) is first applied to transcendental equations characterizing the har- monic contents to eliminate low order harmonics like 5th, 7th, 11th and 13th and to determine switching angles for the funda- mental frequency switching. Next, the residual higher order har- monics are eliminated by generating a square wave (one for each of these harmonics) with additional switching angles whose funda- mental is the opposite of the harmonic that is to be eliminated. Though the method is effective, the required number of switching is substantially high for the elimination of increased higher order harmonics. Moreover, at certain points of modulation indices, there are discontinuities in the solution. In Jiang and Lipo (2000) the dc link voltage of the multilevel inverter is optimized while a genetic algorithm is used for harmonic optimization in Ozpineci, Tolbert, and Chiasson (2004). Previously reported work (Chiasson et al., 2003) shows that the transcendental equations characterizing the SHE problem can be converted into polynomial equations that can be solved using the resultant theory. Further as degree of polynomials increases with the number of dc sources or order of harmonics to be eliminated, the theory of symmetric polynomials (Chiasson, Tolbert, Mckenzie, & Du, 2005) is exploited to reduce the degree of polynomial equa- tions that can reduce the computational burden. With reduced de- gree of polynomials, an online computation method for the switching angles has been proposed with all multiple solutions. But since the solutions are having discontinuity at certain points (Chiasson et al., 2005; Du et al., 2006), it is difficult for the control- ler to generate possible switching angles at those points. Moreover, 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.04.060 * Corresponding author. Tel.: +91 9433887966; fax: +91 3324132384. E-mail addresses: rupnarayan_r@yahoo.co.in (R.N. Ray), debashisju@yahoo.com (D. Chatterjee), skgoswami_ju@yahoo.co.in (S.K. Goswami). Expert Systems with Applications 37 (2010) 7796–7801 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa