Elimination of harmonics in a multilevel converter using the theory of symmetric polynomials and resultants

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...

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Bibliographic Details
Published in:IEEE transactions on control systems technology 2005-03, Vol.13 (2), p.216-223
Main Authors: Chiasson, J.N., Tolbert, L.M., McKenzie, K.J., Zhong Du
Format: Article
Language:English
Subjects:
Applied sciences
Computation
Computer science
control theory
systems
Control theory. Systems
Converters
Electrical engineering. Electrical power engineering
Equations
Exact sciences and technology
Frequency
Fuel cells
Harmonics
Mathematical analysis
Mathematical models
Multilevel
Multilevel inverter
Photovoltaic cells
Polynomials
Power electronics
Power electronics, power supplies
Power grids
Pulse width modulation inverters
Resultants
Studies
Switches
symmetric polynomials
Voltage
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Summary: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. A difficulty with this approach is that when there are several dc sources, the degrees of the polynomials are quite large making the computational burden of their resultant polynomials (as required by elimination theory) quite high. Here, it is shown that the theory of symmetric polynomials can be exploited to reduce the degree of the polynomial equations that must be solved which in turn greatly reduces the computational burden. In contrast to results reported in the literature that use iterative numerical techniques to solve these equations, the approach here produces all possible solutions.
ISSN:1063-6536
1558-0865
DOI:10.1109/TCST.2004.839556