This project presents a comprehensive investigation of various reference frames and their relative speeds in cascaded doubly-fed induction machines (CDFIMs). Then, a compact spacephasor model of CDFIMs in the natural and arbitrary reference frames is presented that is useful for performance analysis of CDFIMs based on rotating phasors. The merits of the proposed model compared with existing models are using a common (single) reference frame for all machines and parts of CDFIMs, and the model formulation is independent of the rotor angle position. The reference frames in the suggested model can be fixed on the common rotor of the CDFIM machines for dynamic analysis or it can be fixed on the stator/rotor flux of each cascaded machines useful for CDFIMs controller design. A two-axes equivalent circuit for a CDFIM is also presented, which enables analysis of CDFIMs in commercially available power circuit simulation software tools.This project also presents an instantaneous torque controlmethod for cascaded doubly-fed induction machines (CDFIMs)with a rated torque-sharing ratio feature under steady-stateoperation. The proposed methodis established based on transferring the torques equations of thetwo machines into the rotor-flux reference-frame of the auxiliarymachine. Then, by expressing the torque equations with respectto the current components of the stator of the auxiliary machine,the instantaneous torque control with the rated torque sharing isachieved.To verify the method and evaluate its capabilities, Thesuggested method is used for the speed control of a CDFIMexperimental setup. Further, a case study including 12-kW and 4-kWDFIMs is also simulated to evaluate the performance of thecontrol method for a CDFIM with different machine ratings. Thetest results confirm that the proposed control schemes achievethe desired performances without exceeding the ratings of themachines under various test scenarios. Key Words Brushless, doubly fed induction machines (DFIM), cascaded DFIM, dynamic model, equivalent circuit, reference frames, Rotor-Flux-Orientation, Instantaneous, Torque Control, Torque Sharing.
