Multiple reference frame analysis of an unsymmetrical induction machine

Due to the asymmetry of the stator windings of an unsymmetrical induction motor, the equations which describe this device cannot be expressed in a frame of reference where the state variables are constant in the steady state. This prevents linearization and thereby places a stumbling block in the development of a transfer function which could be used in linear control analysis, as in servo applications. The work presented in this paper provides a means to accomplish this goal. This is achieved by eliminating the position-dependent terms brought about due to asymmetry by recognising a unique property of a combination of reference frames and by employing an averaging procedure. The resulting equations are shown to predict the performance of the unsymmetrical induction motor with the accuracy of the detailed equations. The stage is now set to develop accurate reduced-order models and linear transfer functions for unsymmetrical induction motors