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diff --git a/3731/CH7/EX7.3/Ex7_3.sce b/3731/CH7/EX7.3/Ex7_3.sce new file mode 100644 index 000000000..66b494658 --- /dev/null +++ b/3731/CH7/EX7.3/Ex7_3.sce @@ -0,0 +1,105 @@ +//Chapter 7:Synchronous Motor and Brushless DC Motor Drives +//Example 3 +clc; + +//Variable Initialization + +//Ratings of the synchronous motor +Pm1=6*10**6 // power rating in W +f=50 // frequency in HZ +Vl=11*1000 // line voltage in V +pf=0.9 // power factor leading +P=6 // number of poles +I=10 // rated field current in A +Xs=9 // reactance of the windings in ohm +Rs=0 // resistance of the windings in ohm +N=120*f/P // synchronous speed + +//Solution +V=Vl/sqrt(3) //phase voltage +Is=Pm1/(sqrt(3)*Vl*pf) //rated current +rad=acos(pf) + +//(i)To find torque and field current at rated armature current +// at 750 rpm and 0.8 leading power factor +Is=Is * (cos(rad) + sin(rad)*%i) //rated current in vector form +V=V *(cos(0)+sin(0)*%i) +E=V-Is*%i*Xs //back emf + +N1=750 //speeed in rpm +pf1=0.8 //given leading power factor +f1=N1/N*f //required frequency +V1=abs(V)*f1/f //required voltage +Xs1=Xs*f1/f //required field resistance +E1=V1-Xs1*%i*(abs(Is) * (cos(acos(pf1))+sin(acos(pf1))*%i)) //rated back emf in complex form +E1_polar=abs(E1) //rated back emf in rectangular form + +//At rated field current and 750 rpm +E2=abs(E)*N1/N //back emf at the given speed N1 +If=abs(E1)/E2*f //field current at the given speed N1 +Pm=3*abs(V1)*abs(Is)*pf1 //power input at the given speed N1 +Wm1=2*%pi*N1/60 //angular motor speed in rad/s +T=Pm/Wm1 + +//(ii) At half the rated motor torque and 1500 rpm and rated field current +Pm=6*10**6 //rated power rating in W +N1=1500 //speeed in rpm +f1=N1/N*f //required frequency +Xs1=f1/f*Xs //required field resistance +E1=abs(E)*f1/f //back emf at rated field current + + +Wms=Pm +Wms_=N1/N*Wms +Pm_= (0.5)*Wms_ //required power developed at N1=1500 rpm + +sin_delta=Pm_*Xs1/(3*abs(V)*abs(E1)) //since Pm=3*abs(V)*abs(E1)*sin(delta)/Xs +delta=asin(sin_delta) //angle delta +Is=(abs(V)-(E1 * (cos(-delta)+sin(-delta)*%i)))/(%i*Xs1) //armature current +Is1=polar(Is) //aramture current in rectangular form +x1=phasemag(Is) +x1n=x1*%pi/180 +power_factor1=cos(x1n) //power factor + +//(iii) at 750 rpm and rated field current from part(i) +N1=750 //speeed in rpm +pf1=0.8 //given leading power factor +f1=N1/N*f //required frequency at N1=750 rpm +V1=abs(V)*f1/f //required voltage at N1=750 rpm +Xs1=Xs*f1/f //required field resistance +E2=abs(E)*N1/N + +Pm=-4.2*10**6 //braking power output +sin_delta=Pm*Xs1/(3*abs(V1)*abs(E2)) //since Pm=3*abs(V)*abs(E1)*math.sin(delta)/Xs +delta=asin(sin_delta) //angle delta +Is=(E2 * (cos(abs(delta))+sin(abs(delta))*%i)-V1)/(%i*Xs1) //armature current +Is2=polar(Is) //aramture current in rectangular form +x2=phasemag(Is) +x2n=x2*%pi/180 +power_factor2=cos(x2n) //power factor + +//(iv)from part (ii) at 1500 rpm and from part(iii) the armature current of 349.9 A is taken +Is=Pm1/(sqrt(3)*Vl*pf) //armature current as given from (i) +N1=1500 //speeed in rpm +f1=N1/N*f //required frequency at N1=1500 rpm +Xs1=f1/f*Xs //required field resistance +E1=abs(E)*f1/f //at rated field current +E2=V-%i*Xs1*Is +E2ph=abs(E2) +E2n=phasemag(E2) +E2na=E2n*%pi/180 +If1=abs(E2ph)/abs(E1)*f //required field current +Pm=3*abs(V)*(E2ph)*sin(abs(E2na))/Xs1 //power input +Wm1=2*%pi*N1/60 //motor speed in rad/sec +T1=Pm/Wm1 + +//Results +mprintf("\ni)Required torque is:%.1f N-m",T) +mprintf("\nField current :%.2f A",If) +mprintf("\nii)Armature current :%.1f %.2f ° A",abs(Is1),x1) +mprintf(" \nPower factor :%.1f leading",power_factor1) +mprintf("\niii)Armature current :%.2f %.2f ° A",abs(Is2),x2) +mprintf("\nPower factor :%.3f lagging",power_factor2) +mprintf("\niv)Field current :%.2f A",If1) +mprintf("\nRequired torque is:%.1f N-m",T1) +//There is a slight difference in the answers |