INDUCTION MOTORS 113The 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 ohmsThe total air-gap impedanceZm 22 is:-
Zm 22 =ZmcZ 22
Zmc+Z 22= 0. 2437 +j 0 .3288 ohmsThe total motor impedanceZmotis:-
Zmot=R 1 +jX 1 +Zm 22 = 0. 4227 +j 0 .7668 ohmsThe stator current per phaseI 1 is:-
I 1 =
Vp
Zmot= 132. 124 −j 239 .64 amps,which has a magnitude of 273.65 amps, which is 6.97 times the full-load value.
The air-gap voltageVmis:-
Vm=Vp−I 1 Z 1
= 110. 988 −j 14 .9748 volts, which has a magnitude of 111.994 volts.The rotor current per phaseI 2 is:-
I 2 =
Vm
Z 22=
110. 988 −j 14. 9748
0. 253 +j 0. 333= 132. 039 −j 232 .98 amps,which has a magnitude of 267.795 amps.
The output powerPoutis zero.
The total shunt currentIoat the air gap is:-
Im=Vm
RcjXm
Rc+jXm= 0. 0842 −j 6 .6589 ampsThe input kVASinis:-
Sin=3 ×I 1 ∗×Vp
1000
= 94. 971 +j 172 .253 kVA, which has a magnitude of 196.699 kVA.Hence the input active powerPinin kW and input reactive powerQinin kVAr are:-
Pin1= 94 .971 kW andQin 1 = 172 .253 kVAr