The Equivalent Circuit of a Single Phase Induction Motor


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Before writing a set of expressions that will permit calculation of these
various currents, it is necessary to establish the frequencies of the two
traveling waves on the rotor. Keeping in mind that the angular coordinate _’ with respect to the rotor is



















Thus, if s is the conventionally defined slip, it is also the slip for the forward-going traveling wave, while 2–s is the slip for the reverse-going
wave. Now it is possible to cast the single-phase motor interaction in terms
which are already familiar. Currents are induced in the rotor in exactly
the same fashion for both forward and reverse traveling waves as they
are in the polyphase machine, taking note of the fact that the slips are
different. The voltage equation is






















These expressions correspond with the equivalent circuit shown in
Fig. 4.34.

Motor performance


The equivalent circuit of Fig. 4.34 may be used in a straightforward
fashion to find energy transfer through the machine. Time average power
across the air-gap is









 













  














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