Quaternion Analysis of a Direct Matrix Converter Based on Space-Vector Modulation

• NAKAMURA Kazuo

  Research Institute for Applied Mechanics, Kyushu University

• ZHANG Yifan

  Interdisciplinary Graduate School of Engineering Sciences, Kyushu University

• ONCHI Takumi

  Research Institute for Applied Mechanics, Kyushu University

• IDEI Hiroshi

  Research Institute for Applied Mechanics, Kyushu University

• HASEGAWA Makoto

  Research Institute for Applied Mechanics, Kyushu University

• TOKUNAGA Kazutoshi

  Research Institute for Applied Mechanics, Kyushu University

• HANADA Kazuaki

  Research Institute for Applied Mechanics, Kyushu University

• MITARAI Osamu

  Institute for Advanced Fusion & Physics Education

• KAWASAKI Shoji

  Research Institute for Applied Mechanics, Kyushu University

• HIGASHIJIMA Aki

  Research Institute for Applied Mechanics, Kyushu University

• NAGATA Takahiro

  Research Institute for Applied Mechanics, Kyushu University

• SHIMABUKURO Shun

  Research Institute for Applied Mechanics, Kyushu University

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.

Journal

• Plasma and Fusion Research

  Plasma and Fusion Research 16 (0), 2405037-2405037, 2021-03-12

  The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

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

Details

• CRID: 1390006144261995392
• NII Article ID: 130008022671
• DOI: 10.1585/pfr.16.2405037
• ISSN: 18806821
• Web Site: https://www.jstage.jst.go.jp/article/pfr/16/0/16_2405037/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed