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Power supply for plasma control has been developed from condenser bank with ignitron for pulse tokamak plasma to PWM inverter with IGBT for steady tokamak plasma. Quaternion, four-dimensional hypercom...plex number is good at describing three-dimensional rotation. Utilizing the performance of the quaternion rotation,we analyze three-phase power electronic circuit for the tokamak plasma control of equilibrium and stability. By further introduction of biquaternion concept, we can deal with phasor of each phase of three-phase AC similarly. But, we have to multiply the rotation operator from the left-hand side and from the right-hand side by using the conjugation. We try to verify the merits beyond the multiplication inconvenience from both sides. Not only symmetrical three-phase AC (positive sequence) but also negative sequence and zero sequence can be dealt with. Concerning quaternion power of three-phase AC, we can obtain the similar result as the one in pq theory. Quaternion can divide three-dimensional vector. The capability is utilized to develop matrix converter strategy based not only on Venturini method but also on space vector method in more detail.show more
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