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This paper presents a comprehensive investigation of various reference frames and their relative speeds in cascaded doubly-fed induction machines (CDFIMs). Then, a compact space-phasor 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. The validity of the model is verified via the investigation of an experimental setup and consists of two mechanically coupled 4-kW DFIMs and a 4-kW dc machine as a load. The setup is investigated under various test scenarios, including free acceleration, load (torque) change, and frequency step change conditions. [ABSTRACT FROM AUTHOR]