564 ROTATING MACHINES
flow of mechanical power. At standstill, however, the machine acts as a simple transformer with
an air gap and a short-circuited secondary winding. The frequency of the rotor-induced emf is
the same as the stator frequency at standstill. At any value of the slip under balanced steady-state
operation, the rotor current reacts on the stator winding at the stator frequency because the rotating
magnetic fields caused by the stator and rotor are stationary with respect to each other.
The induction machine may thus be viewed as a transformer with an air gap and variable
resistance in the secondary; the stator of the induction machine corresponds to the transformer
primary, and the rotor corresponds to the secondary. For analysis of the balanced steady state, it
is sufficient to proceed on aper-phase basiswith some phasor concepts; so we will now develop
an equivalent circuit on a per-phase basis. Only machines with symmetrical polyphase windings
excited by balanced polyphase voltages are considered. As in other discussions of polyphase
devices, let us think of three-phase machines as wye-connected, so that currents are always line
values and voltages are always line-to-neutral values (on a per-phase basis).
The resultant air-gap flux is produced by the combined mmfs of the stator and rotor currents.
For the sake of conceptual and analytical convenience, the total flux is divided into a mutual flux
(linking both the stator and the rotor) and leakage fluxes, represented by appropriate reactances.
Considering the conditions in the stator, the synchronously rotating air-gap wave generates
balanced polyphase counter emfs in the phases of the stator. The volt–ampere equation for the
phase under considerationin phasor notationis given by
V ̄ 1 =E ̄ 1 +I ̄ 1 (R 1 +jXl 1 ) (13.2.1)
whereV ̄ 1 is the stator terminal voltage,E ̄ 1 is the counter emf generated by the resultant air-gap
flux,I ̄ 1 is the stator current,R 1 is the stator effective resistance, andXl 1 is the stator-leakage
reactance.
As in a transformer, the stator (primary) current can be resolved into two components:
a load componentI ̄ 2 ′(which produces an mmf that exactly counteracts the mmf of the rotor
current) and an excitation componentI ̄ 0 (required to create the resultant air-gap flux). This
excitation component itself can be resolved into a core-loss componentI ̄cin phase withE ̄ 1+−+−V 1 E 1R 1 jXl^1−jbmIc
gcImI 1I 0I' 2 Figure 13.2.1Equivalent circuit for the stator
phase of a polyphase induction motor.SE 2+−R 2jSXl 2
I 2Figure 13.2.2Slip-frequency equivalent circuit for the rotor
phase of a polyphase induction motor.