Handbook of Electrical Engineering

INDUCTION MOTORS 111

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

Zmc=

RcjXm

Rc+jXm

=

115. 0 ×j 17. 0

115. 0 +j 17. 0

= 2. 4593 +j 16 .6365 ohms

The total air-gap impedanceZm 22 is:-

Zm 22 =

ZmcZ 22

Zmc+Z 22

=

( 2. 4593 +j 16. 6365 )×( 6. 6747 +j 0. 8122 )

2. 4593 +j 16. 6365 + 6. 6747 +j 0. 8122

= 5. 1534 +j 2 .5313 ohms

The total motor impedanceZmotis:-

Zmot=R 1 +jX 1 +Zm 22 = 0. 179 +j 0. 438 + 5. 1534 +j 2. 5313

= 5. 3324 +j 2 .9693 ohms, which has a magnitude of 6.1033 ohms.

The stator current per phaseI 1 is:-

I 1 =

Vp

Zmot

=

239. 6 +j 0. 0

5. 3324 +j 2. 9693

= 34. 2982 −j 19 .0987 amps,

which has a magnitude of 39.257 amps.

The air-gap voltageVmis:-

Vm=Vp−I 1 Z 1 =( 239. 6 +j 0. 0 )−( 34. 2982 −j 19. 0987 )( 0. 179 +j 0. 438 )

= 225. 096 −j 11 .604 volts, which has a magnitude of 225.395 volts.

The rotor current per phaseI 2 is:-

I 2 =

Vm

Z 22

=

225. 06 −j 11. 604

6. 6747 +j 0. 8122

= 33. 0235 −j 5 .7569 amps,

Rc+jXm= 115. 0 +j 17. 0

which has a magnitude of 33.5215 amps.

The output powerPoutis:-

Pout= 3 ×I 22 ×Rout= 3 × 1123. 691 × 6. 5273 = 22 .004 kW

The magnetising current per phaseImis:-

Im=

Vm

jXm

=

225. 06 −j 11. 604

j 17. 0

= 0. 6826 −j 13 .241 amps