Plasma and Fusion Research

Volume 16, 2405037 (2021)

Regular Articles

Quaternion Analysis of a Direct Matrix Converter Based on Space-Vector Modulation
Kazuo NAKAMURA, Yifan ZHANG1), Takumi ONCHI, Hiroshi IDEI, Makoto HASEGAWA, Kazutoshi TOKUNAGA, Kazuaki HANADA, Osamu MITARAI2), Shoji KAWASAKI, Aki HIGASHIJIMA, Takahiro NAGATA and Shun SHIMABUKURO
Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasugakoen, Kasuga 816-8580, Japan
1)
Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasugakoen, Kasuga 816-8580, Japan
2)
Institute for Advanced Fusion & Physics Education, 2-14-8 Tokuou, Kita-ku, Kumamoto 861-5525, Japan
(Received 15 November 2020 / Accepted 26 January 2021 / Published 12 March 2021)

Abstract

In a three-phase matrix converter based on space-vector modulation (SVM), nine switches are controlled so that the instantaneous space vector of the line-to-line voltage rotates smoothly in two-dimensional space. The quaternion is a four-dimensional hypercomplex number that is good at describing three-dimensional rotation, such as that seen in three-dimensional game graphics programming theory. Utilizing the quaternion capability, we analyze a matrix converter by three-dimensional rotation instead of transforming to two-dimensional rotation in alpha-beta coordinates. It was clarified that the projection of the quaternion locus in three-dimensional space in the (1,1,1) direction is the same as an alpha-beta transformation locus in two-dimensional space. Concerning the direct matrix converter, we clarified that the (1,1,1)-directional superposition of three-fold higher harmonics cannot be eliminated. The quaternion can rotate and divide a three-dimensional vector. When the output voltage quaternion is divided by input one, the switching quaternion is obtained. The quaternion characteristics will be utilized to analyze a matrix converter based on direct SVM in more detail.

Keywords

circulant matrix, quaternion, direct matrix converter, space vector modulation, three-phase to three-phase

DOI: 10.1585/pfr.16.2405037

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