0195136047.pdf

13.2 INDUCTION MACHINES 565

and a magnetizing componentI ̄mlaggingE ̄ 1 by 90°. A shunt branch formed by the core-loss
conductancegcand magnetizing susceptancebmin parallel, connected acrossE ̄ 1 , will account for
the exciting current in the equivalent circuit, as shown in Figure 13.2.1, along with the positive
directions in a motor.
Thus far the equivalent circuit representing the stator phenomenon is exactly like that of the
transformer primary. Because of the air gap, however, the value of the magnetizing reactance
tends to be relatively low compared to that of a transformer, and the leakage reactance is larger
in proportion to the magnetizing reactance than it is in transformers. To complete the equivalent
circuit, the effects of the rotor must be incorporated, which we do by referring the rotor quantities
to the stator.
Because the frequency of the rotor voltages and currents is the slip frequency, the magnitude
of the voltage induced in the rotor circuit is proportional to the slip. Also, in terms of the standstill
per-phase rotor-leakage reactanceXl 2 , the leakage reactance at a slipSis given bySXl 2. WithR 2
as the per-phase resistance of the rotor, the slip-frequency equivalent circuit for a rotor phase is
shown in Figure 13.2.2, in whichE 2 is the per-phase voltage induced in the rotor at standstill. The
rotor currentI 2 is given by

I 2 =

SE 2

√

R^22 +(SXl 2 )^2

(13.2.2)

which may be rewritten as

I 2 =

E 2

√

(R 2 /S)^2 +Xl^22

(13.2.3)

resulting in the alternate form of the per-phase rotor equivalent circuit shown in Figure 13.2.3.
All rotor electrical phenomena, when viewed from the stator, become stator-frequency
phenomena because the stator winding sees the mmf and flux waves traveling at synchronous

+

−

E 2

jXl 2

I 2

R 2

S

Figure 13.2.3Alternate form of a per-phase rotor equivalent

circuit.

R 2

S

+

++

−−

−

V 1 E 1

R 1 jXl^1 jXl2

−jbm

E 2

Ic

gc

Im

I 1

I 0

I' 2 I 2

Figure 13.2.4Per-phase equivalent coupled circuit of a polyphase induction motor.