Page 131 - Handbook of Electrical Engineering

INDUCTION MOTORS 113

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

115.0 × j17.0
R c jX m
Z mc = = = 2.4593 + j16.6365 ohms
R c + jX m 115.0 + j17.0
The total air-gap impedance Z m22 is:-

Z mc Z 22
Z m22 = = 0.2437 + j0.3288 ohms
Z mc + Z 22
The total motor impedance Z mot is:-

Z mot = R 1 + jX 1 + Z m22 = 0.4227 + j0.7668 ohms

The stator current per phase I 1 is:-

V p
I 1 = = 132.124 − j239.64 amps,
Z mot
which has a magnitude of 273.65 amps, which is 6.97 times the full-load value.
The air-gap voltage V m is:-

V m = V p − I 1 Z 1
= 110.988 − j14.9748 volts, which has a magnitude of 111.994 volts.
The rotor current per phase I 2 is:-

110.988 − j14.9748
V m
I 2 = = = 132.039 − j232.98 amps,
Z 22 0.253 + j0.333
which has a magnitude of 267.795 amps.
The output power P out is zero.
The total shunt current I o at the air gap is:-

V m
I m = = 0.0842 − j 6.6589 amps
R c jX m
R c + jX m

The input kVA S in is:-
∗
3 × I 1 × V p
S in =
1000
= 94.971 + j 172.253 kVA, which has a magnitude of 196.699 kVA.

Hence the input active power P in in kW and input reactive power Q in in kVAr are:-

P in1 = 94.971 kW and Q in1 = 172.253 kVAr