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//Chapter 6:Induction Motor Drives
//Example 15
clc;
//Variable Initialization
//Ratings of the star connected Induction motor
f=50 // frequency in HZ
Vl=400 //line voltage in V
P=4 // number of poles
N=1370 //rated speed
//Parameters referred to the stator
Xr_=3.5 // rotor winding reactance in ohm
Xs=Xr_ // stator winding reactance in ohm
Rr_=3 // resistance of the rotor windings in ohm
Rs=2 // resistance of the stator windings in ohm
Xm=55 // magnetizing reactance in ohm
//Solution
Wms=4*%pi*f/P
Ns=120*f/P //synchronous speed in rpm
s=(Ns-N)/Ns //full load slip
x=%i*Xm*(Rr_/s+%i*Xr_)
y=Rr_/s+%i*(Xr_+Xm)
Z=Rs+%i*Xs+x/y //total motor impedance
Isf=(Vl/sqrt(3))/abs(Z) //full load stator current
Irf_=Isf*(%i*Xm)/(Rr_/s+%i*(Xr_+Xm)) //full load rotor current
Tf=(3/Wms)*abs(Irf_)**2*Rr_/s //full load torque
N1=Ns-N //full load slip speed
//(i) When the motor is operating at 30Hz
f1=30 //given frequency in Hz
//At rated slep speedvalue of torque and stator current is same as the rated value
T=Tf
Is=abs(Isf)
Ns1=f1/f*Ns //synchronous at f1=30Hz
N2=Ns1-N1 //required motor speed at 30Hz
//(ii)At a speed of 1200 rpm
N3=1200 //speed in rpm
Ns1=N3+N1 //required synchronous speed
f1=Ns1/Ns*f //required frequency at N2=1200rpm
//(iii)When speed-torque curves are assumed to be straight lines at 30Hz at half the rated motor torque
f2=30 //frequency in Hz
N1_=N1/2 //slip at half the rated torque
Ns1=f2/f*Ns //synchronous at f1=30Hz
N4=Ns1-N1_ //required motor speed
//(iv) When the motor is operating at 45hz and braking torque is equal to rated torque
f3=45 //given frequency in Hz
N1_=-N1 //slip speed when braking at rated torque
Ns1=f3/f*Ns //synchronous at f1=45Hz
N5=Ns1-N1_ //required motor speed
//results
mprintf("(i)At 30Hz the required value of Torque is T:%.2f N-m",T)
mprintf("\nStator current is Is:%.4f A",Is)
mprintf("\nMotor speed is :%d rpm",N2)
mprintf("\n(ii)Required inverter frequency is :%.2f Hz",f1)
mprintf("\n(iii)Required motor speed at 30Hz is:%d rpm",N4)
mprintf("\n(iv)Required motor speed at 45Hz is:%d rpm",N5)
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