The Use of Power Sums to Solve the Harmonic Elimination Equations for Multilevel Converters

A method is presented to compute the switching angles in a multilevel converter so as to produce the required fundamental voltage while at the same time not generate higher order harmonics. Previous work has shown that the transcendental equations characterizing the harmonic content can be converted to polynomial equations which are then solved using the method of resultants from elimination theory. However, when there are several DC sources, the degree of the polynomials are quite large making the computational burden of their resultant polynomials via elimination theory quite high. Here, it is shown that by reformulating the problem in terms of power sums, the degree of the polynomial equations that must be solved are reduced significantly which in turn reduces the computational burden. In contrast to numerical techniques, the approach here produces all possible solutions. John N. Chiasson, Leon M. Tolbert, Zhong Du, Keith J. McKenzie cycles they are back to their original configuration (see [18-19] for details). For dealing with non equal DC sources, see [20]. Mathematical model of switching Following the development in [13] (see also [18]), the Fourier series expansion of the (staircase) output voltage waveform of the multilevel inverter as shown in Fig. 1 is