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Harmonic Elimination Technique and Multilevel Converters
Sponsored by Oak Ridge National
Laboratory and National Science Foundation
Team
Keith McKenzie
Zhong Du
Kaiyu Wang
Dr. John N. Chiasson
Dr. Leon M. Tolbert
Description
key issue in the design of a multilevel inverter is to determine the
switching angles (times) so as to produce the fundamental voltage and not generate specific higher
order harmonics. In this work, techniques are given that allow one to control a multilevel inverter
in such a way that it is an efficient, low total harmonic distortion (THD) inverter that can be used
to interface distributed dc energy sources to a main ac grid.
A procedure to eliminate harmonics in a multilevel inverter has been given which exploits the
properties of the transcendental equations that define the harmonic content of the converter output.
Specifically, it was shown that one can transform the transcendental equations into symmetric
polynomials which are then further transformed into another set of polynomials in terms of the
elementary symmetric functions.
This formulation resulted in a drastic reduction in the degrees of the polynomials that characterize
the solution. Consequently, the computation of solutions of this final set of polynomial
equations were easily carried out using elimination theory (resultants) as the required symbolic
computations were well within the capabilities of contemporary computer algebra software tools.
This methodology resulted in the complete characterization of the solutions to the harmonic elimination
problem. That is, for each m, it produces all possible solutions or it shows that no solution
exists. Experiments were performed and the data presented corresponded
well with the predicted results.
Related publications and presentations
John N. Chiasson, Leon M. Tolbert, Keith J. McKenzie, Zhong Du,
“A Complete Solution to the Harmonic Elimination Problem,”
IEEE Transactions on Power Electronics, 2004. (in press)
John Chiasson, Leon Tolbert, Keith McKenzie, Zhong Du,
"RealTime Computer Control of a Multilevel Converter
Using the Mathematical Theory of Results,"
Transactions of IMACS on Mathematics and Computers in Simulation, 2003. (in press)
J. N. Chiasson, L. M. Tolbert, K. J. McKenzie, Z. Du,
“Eliminating Harmonics in a Multilevel Inverter Using the Theory of Symmetric Polynomials and Resultants,”
IEEE Conference on Decision and Control,
December 912, 2003, Maui, Hawaii.
J. N. Chiasson, L. M. Tolbert, K. J. McKenzie, Z. Du,
“A New Approach to Solving the Harmonic Elimination Equations for a Multilevel Converter,”
IEEE Industry Applications Society Annual Meeting,
October 1216, 2003, Salt Lake City, Utah.
J. N. Chiasson, L. M. Tolbert, K. J. McKenzie, Z. Du,
"A New Approach to the Elimination of Harmonics in a Multilevel
Converter," 10th European Conference on Power Electronics and
Applications  EPE 2003, September 24, 2003, Toulouse, France.
J. N. Chiasson, L. M. Tolbert, K. J. McKenzie, Z. Du,
"Control of Cascaded Multilevel Converters with Unequal Voltage Sources for HEV,"
IEEE International Electric Machines and Drives Conference, June
14, 2003, Madison, Wisconsin, pp. 663669.
J. N. Chiasson, L. M. Tolbert, K. J. McKenzie, Z. Du, "Control
of a Multilevel Converter Using Resultant Theory," IEEE
Transactions on Control System Theory, vol. 11, no. 3, pp. 345354,
J. N. Chiasson, L. M. Tolbert, K. McKenzie, Z. Du,
"Harmonic Elimination in Multilevel Converters," IASTED International
Conference on Power and Energy Systems (PES 2003), February 2426,
2003, Palm Springs, California, pp. 284289.
L. M. Tolbert, J. N. Chiasson, K. McKenzie, Z. Du, "Elimination
of Harmonics in a Multilevel Converter with Non Equal DC Sources,"
IEEE Applied Power Electronics Conference (APEC 2003), February
913, 2003, Miami, Florida, pp. 589595.
J. N. Chiasson, L. M. Tolbert, K. McKenzie, Z. Du, "A
Complete Solution to the Harmonic Elimination Problem," IEEE
Applied Power Electronics Conference (APEC 2003), February 913,
2003, Miami, Florida, pp. 596602.
L. M. Tolbert, J. N. Chiasson, K. McKenzie, Z. Du,
"Elimination
of Harmonics in a Multilevel Converter for HEV Applications," The
7th IEEE Workshop on Power Electronics in Transportation, October
2425, 2002, Auburn Hills, Michigan, pp. 135142.
J. N. Chiasson, L. M. Tolbert, K. McKenzie, Z. Du,
"RealTime
Computer Control of a Multilevel Converter Using the Mathematical Theory
of Results," Proceedings of the Electrimacs ConferenceAugust
1821, 2002.
J. N. Chiasson, L. M. Tolbert, K. McKenzie, Z. Du,
"Eliminating
Harmonics in a Multilevel Converter using Resultant Theory," IEEE
Power Electronics Specialists Conference, June 2327, 2002, Cairns,
Australia, pp. 503508.
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