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

Abstract

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 ofpower 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.

Additional information

Notes on contributors

John N. Chiasson

John Chiasson (S’82-M’84) received his Bachelor’s Degree in Mathematics from the University of Arizona, Tucson AZ, his Master’s Degree in Electrical Engineering from Washington State University, Pullman WA, and his PhD in Controls from the University of Minnesota, Minneapolis MN. He has worked in industry at Boeing Aerospace, Control Data, and ABB Daimler-Benz Transportation. Since 1999, has been on the faculty of Electrical and Computer Engineering at the University of Tennessee where his interests include the control of AC drives, multilevel converters and hybrid electric vehicles

Leon M. Tolbert

Keith J. McKenzie (S’01) received his B.S. degree in electrical engineering from The University of Tennessee (UT), Knoxville, in December 2001 and is currently pursuing the M.S. degree at the same university.

Zhong Du

Leon M. Tolbert (S 1989 – M 1991 – SM 1998) received the B.E.E., M.S., and Ph.D. in Electrical Engineering from the Georgia Institute of Technology, Atlanta, Georgia. He joined the Engineering Division of Lockheed Martin Energy Systems in 1991 and worked on several electrical distribution projects at the three U.S. Department of Energy plants in Oak Ridge, TN. In 1997, he became a research engineer in the Power Electronics and Electric Machinery Research Center at the Oak Ridge National Laboratory. In 1999, he was appointed as an assistant professor in the Department of Electrical and Computer Engineering at the University of Tennessee, Knoxville. He is an adjunct participant at the Oak Ridge National Laboratory and conducts joint research at the National Transportation Research Center (NTRC). He does research in the areas of electric power conversion for distributed energy sources, motor drives, multilevel converters, hybrid electric vehicles, and application of SiC power electronics. Dr. Tolbert is a registered Professional Engineer in the state of Tennessee. He is the recipient of a National Science Foundation CAREER Award and the 2001 IEEE Industry Applications Society Outstanding Young Member Award. He is an associate editor of the IEEE Power Electronics Letters.

Keith J. McKenzie

Zhong Du (S’01) received the B.S. degree in 1996 and the M.S. in 1999 from Tsinghua University, Bejing, China. He is pursuing the Ph.D. degree in Electrical and Computer Engineering at The University of Tennessee (UT), Knoxville. He has worked in the area of computer networks, both in academia as well as in industry. His research interests include power electronics and embedded control systems.