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//Chapter 6:Induction Motor Drives
//Example 2
clc;
//Variable Initialization
//Ratings of the Delta connected Induction motor
f=50 //frequency in HZ
Vl=2200 //line voltage in V
P=8 //number of poles
N=735 //rated speed in rpm
//Parameters referred to the stator
Xr_=0.55 // rotor winding reactance in ohm
Xs=0.45 // stator winding reactance in ohm
Rr_=0.1 // resistance of the rotor windings in ohm
Rs=0.075 // resistance of the stator windings in ohm
//Solution
Ns=120*f/P //synchronous speed in rpm
s=(Ns-N)/Ns //full load slip
x=sqrt((Rs+Rr_/s)**2+(Xs+Xr_)**2) //total impedance
Ip=(Vl)/x //full load phase current
Il=sqrt(3)*Ip //full load line current
Wms=2*%pi*Ns/60
Tl=(1/Wms)*(3*Ip**2*Rr_/s) //full load torque
//(i)if the motor is started by star-delta switching
y=sqrt((Rs+Rr_)**2+(Xs+Xr_)**2)
Ist=(Vl/sqrt(3))/y //Maximum line current during starting
Tst=(1/Wms)*(3*Ist**2*Rr_) //Starting torque
ratio1=Tst/Tl //ratio of starting torque to full load torque
z=Rs+sqrt(Rs**2+(Xs+Xr_)**2)
Tmax=3/(2*Wms)*(Vl/sqrt(3))**2/z //maximum torque
ratio2=Tmax/Tl //ratio of maximum torque to full load torque
//(ii) If the motor is started using auto transformer
y=sqrt((Rs+Rr_)**2+(Xs+Xr_)**2)
Ist1=Vl*sqrt(3)/y //starting current direct online
aT=sqrt(2*Il/Ist1) //transofrmation ratio
Ilst=2*Il/aT //starting motor line current
Ipst=Ilst/sqrt(3) //starting motor phase current
Tst1=(1/Wms)*(3*Ipst**2*Rr_) //starting torque
//(iii) If motor is started using part winding method
Rs_=2*Rs
Xs_=2*Xs
y=sqrt((Rs_+Rr_)**2+(Xs_+Xr_)**2)
Ist2=(Vl*sqrt(3))/y //starting line current
Ip=Ist2/sqrt(3) //starting phase current
Tst2=(1/Wms)*(3*Ip**2*Rr_) //starting torque
//(iv) motor is started using series reactors in line
Rs_=Rs/3 ; Rr_=Rr_/3
Xs_=Xs/3 ; Xr_=Xr_/3
Il=2*Il //line current at start
x=(Vl/sqrt(3))**2/(Il**2) //x=(Rs_+Rr_)**2+(Xs_+Xr_+Xe)**2
y=x-(Rs_+Rr_)**2 //y=(Xs_+Xr_+Xe)**2
z=sqrt(y) //z=(Xs_+Xr_+Xe)
Xe=z-Xs_-Xr_
//Results
mprintf("(i)Maximum value of line current during starting Ist:%d A",Ist)
mprintf("\nRatio of starting torque to full load torque :%.3f",ratio1)
mprintf("\nRatio of maximum torque to full load torque :%.2f\n",ratio2)
mprintf("\n(ii)Transformation ratio aT:%.3f",aT)
mprintf("\nStarting torque :%d N-m\n",Tst1)
//Answer for the starting torque in the book is wrong due to accuracy
mprintf("\n(iii)Maximum line current during starting :%d A",Ist2)
mprintf("\nStarting torque :%d N-m\n",Tst2)
//Answer for the starting torque in the book is wrong due to accuracy
mprintf("\n(iv)Value of the reactor Xe:%.3f ohm",Xe)
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