Three-phase variables in the induction motor can be represented by space vectors in the Cartesian coordinate set, dq, affixed to stator (stator reference frame). Space vectors of the stator voltage and current and magnetic fluxes (flux linkages) are commonly employed in the analysis and control of induction motor ASDs. The space vectors are obtained by an invertible, static, abc—>dq, transformation of phase variables. The vector notation is used in dynamic equations of the motor.
Space vectors in the stator reference frame are revolving, so that their d and q components are ac signals. A dynamic, dq—>DQ, transformation allows conversion of those signals to the dc form. The dq—>DQ transformation introduces a revolving frame of reference, in which, in the steady state, space vectors appear as stationary. The revolving frame is usually synchronized with a space vector of certain motor variable. Dynamic equations of the induction motor can easily be adapted to a revolving reference frame by substituting p + j(ae for p.
SUMMARY (Induction Motor)