TY - JOUR

T1 - Quaternion Analysis of a Direct Matrix Converter Based on Space-Vector Modulation

AU - Nakamura, Kazuo

AU - Zhang, Yifan

AU - Onchi, Takumi

AU - Idei, Hiroshi

AU - Hasegawa, Makoto

AU - Tokunaga, Kazutoshi

AU - Hanada, Kazuaki

AU - Mitarai, Osamu

AU - Kawasaki, Shoji

AU - Higashijima, Aki

AU - Nagata, Takahiro

AU - Shimabukuro, Shun

N1 - Funding Information:
This work was performed partly with the support and under the auspices of the NIFS Collaboration Research program (NIFS15KUTR111, NIFS17KERA013).
Publisher Copyright:
© 2021 The Japan Society of Plasma Science and Nuclear Fusion Research

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

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U2 - 10.1585/pfr.16.2405037

DO - 10.1585/pfr.16.2405037

M3 - Article

AN - SCOPUS:85112609080

VL - 16

SP - 1

EP - 5

JO - Plasma and Fusion Research

JF - Plasma and Fusion Research

SN - 1880-6821

ER -