Quaternion Analysis of Transient Phenomena of Motor-Generator

A motor-generator slowly converts low electrical power to the large rotating energy of the induction motor, which is then converted to the higher electrical power of the synchronous generator through a pulse. Such a cycle is repeated in a tokamak plasma experiment. In the transient phase at the start of the synchronous generator, high transient voltage appears in the armature windings repeatedly. Due to the repeatability, it is imperative to estimate the high voltage and control it so that the maximum voltage is kept under a tolerable value. A quaternion is a four-dimensional hypercomplex number that is good at describing three-dimensional rotation. Utilizing the quaternion capability, a three-phase motor-generator is analyzed using three-dimensional rotation. The mechanical rotation was anlyzed by the rotation quaternion. The salient pole-type rotating field can be manipulated by direct-quadrature conversion even in quaternion analysis. The rotating dynamics and electrical phenomena of a motor-generator can be analyzed by considering the quaternion power from the motor-generator and the electrical load for plasma control.