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UT Power Engineering Laboratory - "Powering the Future "

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, "Real-Time 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 9-12, 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 12-16, 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 2-4, 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 1-4, 2003, Madison, Wisconsin, pp. 663-669.

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. 345-354,

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 24-26, 2003, Palm Springs, California, pp. 284-289.

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 9-13, 2003, Miami, Florida, pp. 589-595.

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 9-13, 2003, Miami, Florida, pp. 596-602.

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 24-25, 2002, Auburn Hills, Michigan, pp. 135-142.

J. N. Chiasson, L. M. Tolbert, K. McKenzie, Z. Du, "Real-Time Computer Control of a Multilevel Converter Using the Mathematical Theory of Results," Proceedings of the Electrimacs ConferenceAugust 18-21, 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 23-27, 2002, Cairns, Australia, pp. 503-508.

Contact Information

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http://power.eecs.utk.edu/

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Email: jboles@utk.edu