Determination of α, β and γ-components of a switching state without Clarke transformation

In three dimensional (3D) space vector pulse width modulation (SVPWM) applications, a defined overall 3D space is required within which the control signal vector has to be mapped. This overall space is called the active space and is obtained with vector representations of all valid switching states (SS) of the converter that has to be modulated. The vector representations of all valid SS are obtained from the Clarke transformation of terminal voltages obtained at ac terminals of the converter for respective switching states. In this paper simple alternative method has been presented to find α, β & γ components for a given SS. It can produce exactly same results as those computed by Clarke transformation. Application of the proposed formula does not need prior knowledge of Clarke transformation or converter's ac terminal voltages for different switching states.