1 Harmonic Elimination in Multilevel Converters John Chiasson, Leon Tolbert, Keith McKenzie and Zhong Du ECE Department The University of Tennessee Knoxville, TN 37996-2100 chiasson@utk.edu, tolbert@utk.edu, kmc18@utk.edu, zdu1@utk.edu Abstract – A method is presented to compute the switch- ing angles in a multilevel converter so as to produce the re- quired fundamental voltage while at the same time not gen- erate higher order harmonics. Using a fundamental switch- ing scheme, previous work has shown that this is possible only for specific ranges of the modulation index. Here it is shown for a three DC source multilevel inverter that, by modifying the switching scheme, one can extend the range of modulation indices for which the switching angles exist to achieve the fundamental while eliminating the 5 th and 7 th harmonics. In contrast to numerical techniques, the ap- proach here produces all possible solutions. Keywords – Multilevel Converters, Harmonic Elimination, Resultants, Symmetric Polynomials I. Introduction Electric power production in the 21st Century will see dramatic changes in both the physical infrastructure and the control and information infrastructure. A shift will take place from a relatively few large, concentrated generation centers and the transmission of electricity over mostly a high voltage ac grid to a more diverse and dispersed gen- eration infrastructure that also has a higher percentage of dc transmission lines [1]. The general function of the multilevel inverter is to syn- thesize a desired ac voltage from several levels of dc volt- ages. For this reason, multilevel inverters are ideal for con- necting either in series or in parallel an ac grid with dis- tributed energy resources such as photovoltaics or fuel cells or with energy storage devices such as capacitors or batter- ies[2]. Additional applications of multilevel converters in- clude such uses as medium voltage adjustable speed motor drives, static var compensation, dynamic voltage restora- tion, harmonic filtering, or for a high voltage dc back-to- back intertie[3]. Transformerless multilevel inverters are uniquely suited for this application because of the high VA ratings possible with these inverters [4]. The multi- level voltage source inverter’s unique structure allows it to reach high voltages with low harmonics without the use of transformers or series-connected, synchronized-switching devices. A fundamental issue for a multilevel converter is to find the switching angles (times) so that the converter produces the required fundamental voltage and does not generate specific lower order dominant harmonics. In this work, a method is presented to compute the switching angles in a multilevel converter so as to achieve this goal. Using a fundamental switching scheme (see Figure 2), previous work in [5][6] has shown that this is possible only for specific ranges of the modulation index. Here it is shown that, by modifying the switching scheme, one can extend the lower range of modulation indices for which the switching angles exist. Further, in contrast with the PWM technique proposed in [7], the switching schemes proposed here are only slightly above the fundamental frequency. In contrast to numerical techniques such as used in [8], the approach here produces all possible solutions. II. Cascaded H-bridges The cascade multilevel inverter consists of a series of H- bridge (single-phase full-bridge) inverter units. The gen- eral function of this multilevel inverter is to synthesize a desired voltage from several separate dc sources (SDCSs), which may be obtained from solar cells, fuel cells, or ul- tracapacitors. Figure 1 shows a single-phase structure of a cascade inverter with SDCSs [4]. v a v [(m-1)/2] v [(m-1)/2-1] v 2 v 1 n S 1 S 3 S 2 V dc V dc V dc V dc S 4 + + + + - - - - SDCS SDCS SDCS SDCS S 1 S 2 S 3 S 4 S 1 S 1 S 2 S 4 S 3 S 3 S 2 S 4 Fig. 1. Single-phase structure of a multilevel cascaded H-bridges inverter. Each SDCS is connected to a single-phase full-bridge inverter. Each inverter level can generate three different voltage outputs, +V dc , 0 and −V dc by connecting the dc source to the ac output side by different combinations of the four switches, S 1 ,S 2 ,S 3 and S 4 . The ac output of each level’s full-bridge inverter is connected in series such that the synthesized voltage waveform is the sum of all of the individual inverter outputs. The number of output phase (line-neutral) voltage levels in a cascade mulitilevel inverter is then 2s + 1, where s is the number of dc sources.