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diff --git a/3731/CH6/EX6.3/Ex6_3.sce b/3731/CH6/EX6.3/Ex6_3.sce new file mode 100644 index 000000000..c7b9ab538 --- /dev/null +++ b/3731/CH6/EX6.3/Ex6_3.sce @@ -0,0 +1,66 @@ +//Chapter 6:Induction Motor Drives +//Example 3 +clc; + +//Variable Initialization + +//Ratings of the star connected Induction motor +f=50 // frequency in HZ +Vl=400 // line voltage in V +P=6 // number of poles + +//Parameters referred to the stator +Xr_=2 // rotor winding reactance in ohm +Xs=Xr_ // stator winding reactance in ohm +Rr_=1 // resistance of the rotor windings in ohm +Rs=Rr_ // resistance of the stator windings in ohm + +//Solution +Ns=120*f/P //synchronous speed in rpm +Wms=2*%pi*Ns/60 + +//(i) +Sm=-Rr_/sqrt(Rs**2+(Xs+Xr_)**2) //slip at maximum torque +x=sqrt((Rs+Rr_/Sm)**2+(Xs+Xr_)**2) +Ir_=(Vl/sqrt(3))/x //current at maximum torque +Tmax=(1/Wms)*3*Ir_**2*Rr_/Sm //maximum torque +N=(1-Sm)*Ns //range of speed + +//(ii)an overhauling torque of 100Nm +Tl=100 //overhauling torque in Nm +// Tl=(3/Wms)*(Vl**2*Rr_/s)/y +// where y=(Rs+Rr_/s)**2+(Xs+Xr_)**2 +a=(1/Wms)*(Vl**2*Rr_)/(-Tl) //a=s*(Rs+Rr_/s)**2+(Xs+Xr_)**2 +a = 17 +b = 17.3 +c = 1 + +//Discriminant +d = (b**2) - (4*a*c) + +// find two solutions +s1 = (-b-sqrt(d))/(2*a) +s2 = (-b+sqrt(d))/(2*a) + +N2=(1-s2)*Ns //motor speed and we neglect s1 + +//slight difference in the answer due to accuracy + +//(iii)when a capacitive reactance of 2 ohm is inserted in each phase stator +Xc=2 //reactance of the capacitor in ohms +Sm=-Rr_/sqrt(Rs**2+(Xs+Xr_-Xc)**2) //slip at maximum torque +x=sqrt((Rs+Rr_/Sm)**2+(Xs+Xr_-Xc)**2) +Ir_=(Vl/sqrt(3))/x //current at maximum torque +Tmax_=(1/Wms)*3*Ir_**2*Rr_/Sm //maximum overhauling torque with capacitor +ratio=Tmax_/Tmax + + +//Results +mprintf("(i)Maximum overhauling torque that the motor can hold is:%.1f N-m",abs(Tmax)) +mprintf(" \nRange of speed is from %d to %d rpm\n",Ns,abs(N)) +mprintf("\n(ii)Now s*(1+1/s)**2+16s=%d",a) +mprintf("\n Or 17s**s+17.3s+1=0") +mprintf("\nThe solutions for s are %.3f and %.3f\n",s1,s2) +mprintf("\nTherefore Motor speed is:%d rpm\n",N2) +//Note :There is a slight difference in the answer due to the decimal place" +mprintf("\n(iii) Ratio of maximum torque with capacitor and to maximum torque without capacitor is:%.2f",ratio) |