Quaternion analysis of transient phenomena in matrix converter based on space-vector modulation

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. (author)