# Plasma and Fusion Research

## Volume 17, 2405025 (2022)

# Regular Articles

- 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)
- National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan
- 3)
- Institute for Advanced Fusion & Physics Education, 2-14-8 Tokuou, Kita-ku, Kumamoto 861-5525, Japan

### Abstract

The space vector of an output voltage can be rotated smoothly in a matrix converter. However, a zero-sequence component appears causing problems in the load, such as a motor. A quaternion is a four-dimensional hypercomplex number with an imaginary part that can simultaneously represent and deal with three-phase voltages. In addition, the quaternion is expressed in the exponential form; thus, it can easily represent the space vector rotation. Two zero configurations were used to optimize the ripple characteristics in fictitious pulse-width-modulated voltage-source inverter. The two zero configurations are used to remove the zero-sequence component from the matrix converter. The quaternion can be differentiated in time as well as rotate in space. Therefore, it is used to analyze transient phenomena in the matrix converter's rise-up and rise-down phases, and the switching's transition phase.

### Keywords

quaternion analysis, annihilation of zero-sequence component, transient phenomena, direct matrix converter, space-vector modulation, three-phase to three-phase

### Full Text

### References

- [1] J. Itoh, T. Iida and A. Odaka, “Realization of high efficiency AC link converter system based on AC/AC direct conversion techniques with RB-IGBT”, IECON 2006-32nd Annual Conference on IEEE Industrial Electronics (2006).
- [2] T. Takizuka, N. Oyama and T. Fukuda, “Resonant magnetic perturbation for ELM suppression with helical ferritic steel inserts in tokamak DEMO reactor”, Fusion Sci. Technol. 63, No. 1T, 64 (2013).
- [3] D. Casadei, A. Tani and L. Zarri, “Matrix Converter Modulation Strategies: A New General Approach Based on Space-Vector Representation of the Switch State”, IEEE Trans. Ind. Electron. 49, No. 2, 370 (2002).
- [4] J.H. Conway and D. Smith, On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry (A.K. Perters, Ltd, 2003).
- [5] J. Vince, Rotation Transforms for Computer Graphics (Springer-Verlag, 2011).
- [6] L. Huber and D. Borojevic, “Space Vector Modulated Three-Phase to Three-Phase Matrix Converter with Input Power Factor Correction”, IEEE Trans. Ind. Electron. 31, No. 6, 1234 (1995).
- [7] H. Pinheiro, F. Botteron, C. Rech, L. Schuch, R.F. Camargo, H.L. Hey, H.A. Grundling and J.R. Pinheiro, “Space Vector Modulation for Voltage-Source Inverters: A Unified Approach”, IEEE 2002 28th Annual Conference of the Industrial Electronics Society, ICON 02, 1 (2002) 23-29.
- [8] P. Kellan and P.G. Tait, Introduction to Quaternions (MacMillan and Co., Limited, 1904).
- [9] K. Nakamura, I. Jamil, X.L. Liu, O. Mitarai, M. Hasegawa, K. Tokunaga, K. Araki, H. Zushi, K. Hanada, A. Fujisawa, H. Idei, Y. Nagashima, S. Kawasaki, H. Nakashima and A. Higashijima, “Quaternion Analysis of Three-Phase Power Electronic Circuit by Using Conjugation, International Conference on Electrical Engineering”, ICEE 2015, 15A-476 (2015).
- [10] K. Nakamura, Y. Zhang, T. Onchi, H. Idei, M. Hasegawa, K. Tokunaga, K. Hanada, O. Mitarai, S. Kawasaki, A. Higashijima, T. Nagata and S. Shimabukuro, “Quaternion Analysis of a Direct Matrix Converter Based on Space-Vector Modulation”, Plasma Fusion Res. 16, 2405037 (2021).