Derivation of Induction Motor Equivalent Circuit Using Space-Phasor Concepts

The elements of space-phasor theory are discussed with application to the induction machine. The familiar derivation of resultant MMF for a three-phase winding is extended to give a definition of the current space-phasor. The ideas of space-phasor theory are used to derive the steady-state equivalent circuit for the induction machine. The properties of the space-phasor are used with alternate reference frames to justify the substitution of a line frequency rotor representation for the actual rotor having slip-frequency currents. The spacephasor method is thus shown to offer useful opportunities in the teaching ing of electrical machines. This paper is confined to steady-state analysis, but the method is also in use for the transient analysis of machines. By the use of this method, students may be given a single starting point for all aspects of machine analysis.