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

Kazuo Nakamura, Yifan Zhang, Takumi Onchi, Hiroshi Idei, Makoto Hasegawa, Kazutoshi Tokunaga, Kazuaki Hanada, Osamu Mitarai, Shoji Kawasaki, Aki Higashijima, Takahiro Nagata, Shun Shimabukuro

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1-5
Number of pages5
JournalPlasma and Fusion Research
Publication statusPublished - 2021

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics


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