Page 129 - Handbook of Electrical Engineering

INDUCTION MOTORS 111

The shunt components at the air gap are combined in parallel as:-

115.0 × j17.0
R c jX m
Z mc = =
R c + jX m 115.0 + j17.0
= 2.4593 + j16.6365 ohms

The total air-gap impedance Z m22 is:-

Z mc Z 22 (2.4593 + j16.6365) × (6.6747 + j0.8122)
Z m22 = =
Z mc + Z 22 2.4593 + j16.6365 + 6.6747 + j0.8122
= 5.1534 + j2.5313 ohms

The total motor impedance Z mot is:-

Z mot = R 1 + jX 1 + Z m22 = 0.179 + j0.438 + 5.1534 + j2.5313
= 5.3324 + j2.9693 ohms, which has a magnitude of 6.1033 ohms.

The stator current per phase I 1 is:-

V p 239.6 + j0.0
I 1 = = = 34.2982 − j19.0987 amps,
Z mot 5.3324 + j2.9693
which has a magnitude of 39.257 amps.
The air-gap voltage V m is:-

V m = V p − I 1 Z 1 = (239.6 + j0.0) − (34.2982 − j19.0987)(0.179 + j0.438)

= 225.096 − j11.604 volts, which has a magnitude of 225.395 volts.

The rotor current per phase I 2 is:-

225.06 − j11.604
V m
I 2 = = = 33.0235 − j5.7569 amps,
Z 22 6.6747 + j0.8122
R c + jX m = 115.0 + j17.0

which has a magnitude of 33.5215 amps.
The output power P out is:-

2
P out = 3 × I 2 × R out = 3 × 1123.691 × 6.5273 = 22.004 kW
The magnetising current per phase I m is:-

225.06 − j11.604
V m
I m = = = 0.6826 − j13.241 amps
jX m j17.0