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author | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
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committer | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
commit | 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 (patch) | |
tree | dbb9e3ddb5fc829e7c5c7e6be99b2c4ba356132c /3731/CH6 | |
parent | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (diff) | |
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Diffstat (limited to '3731/CH6')
-rw-r--r-- | 3731/CH6/EX6.1/Ex6_1.sce | 52 | ||||
-rw-r--r-- | 3731/CH6/EX6.10/Ex6_10.sce | 62 | ||||
-rw-r--r-- | 3731/CH6/EX6.11/Ex6_11.sce | 50 | ||||
-rw-r--r-- | 3731/CH6/EX6.12/Ex6_12.sce | 52 | ||||
-rw-r--r-- | 3731/CH6/EX6.13/Ex6_13.sce | 30 | ||||
-rw-r--r-- | 3731/CH6/EX6.14/Ex6_14.sce | 16 | ||||
-rw-r--r-- | 3731/CH6/EX6.15/Ex6_15.sce | 62 | ||||
-rw-r--r-- | 3731/CH6/EX6.16/Ex6_16.sce | 59 | ||||
-rw-r--r-- | 3731/CH6/EX6.17/Ex6_17.sce | 40 | ||||
-rw-r--r-- | 3731/CH6/EX6.18/Ex6_18.sce | 79 | ||||
-rw-r--r-- | 3731/CH6/EX6.19/Ex6_19.sce | 75 | ||||
-rw-r--r-- | 3731/CH6/EX6.2/Ex6_2.sce | 75 | ||||
-rw-r--r-- | 3731/CH6/EX6.20/Ex6_20.sce | 55 | ||||
-rw-r--r-- | 3731/CH6/EX6.3/Ex6_3.sce | 66 | ||||
-rw-r--r-- | 3731/CH6/EX6.4/Ex6_4.sce | 53 | ||||
-rw-r--r-- | 3731/CH6/EX6.5/Ex6_5.sce | 57 | ||||
-rw-r--r-- | 3731/CH6/EX6.6/Ex6_6.sce | 91 | ||||
-rw-r--r-- | 3731/CH6/EX6.7/Ex6_7.sce | 50 | ||||
-rw-r--r-- | 3731/CH6/EX6.8/Ex6_8.sce | 69 | ||||
-rw-r--r-- | 3731/CH6/EX6.9/Ex6_9.sce | 70 |
20 files changed, 1163 insertions, 0 deletions
diff --git a/3731/CH6/EX6.1/Ex6_1.sce b/3731/CH6/EX6.1/Ex6_1.sce new file mode 100644 index 000000000..989f15996 --- /dev/null +++ b/3731/CH6/EX6.1/Ex6_1.sce @@ -0,0 +1,52 @@ +//Chapter 6:Induction Motor Drives +//Example 1 +clc; + +//Variable Initialization + +//Ratings of the Y-connected induction motor +f=50 // frequency in HZ +Vl=440 //line voltage in V +P=6 // number of poles +N=950 //speed in rpm + +//Parameters referred to the stator +Xr_=1.2 // rotor winding reactance in ohm +Rr_=0.4 // resistance of the rotor windings in ohm +Rs=0.5 // resistance of the stator windings in ohm +Xs=Xr_ // stator winding reactance in ohm +Xm=50 // no load reactance in ohms + +//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 +Ir_=(Vl/sqrt(3))/x //full load rotor current +angle=-atan((Xs+Xr_)/(Rs+Rr_/s)) //angle in radian + +Ir_=Ir_*(cos(angle)+sin(angle)*%i) //full load rotor current in rectangular form +Im=Vl/sqrt(3)/Xm*(-%i) //magnetizing current +Is=Ir_+Im //full load current + +Zf=Rs+Xs*%i+%i*Xm*(Rr_/s+%i*Xr_)/(Rr_/s+%i*(Xr_+Xm)) +Zb=Rs+Xs*%i+%i*Xm*(Rr_/(2-s)+%i*Xr_)/(Rr_/(2-s)+%i*(Xr_+Xm)) +Z=Zf+Zb +I=(Vl/sqrt(3))/abs(Z) //motor current +Wms=2*%pi*Ns/60 + +//Torque due to positive sequence +Tp=(1/Wms)*(3*I**2*Xm**2*Rr_/s)/((Rr_/s)**2+(Xr_+Xm)**2) + +//Torque due to negative sequence +Tn=-(1/Wms)*(3*I**2*Xm**2*Rr_/(2-s))/((Rr_/(2-s))**2+(Xr_+Xm)**2) +T=Tp+Tn //net torque +Wm=Wms*(1-s) //rated speed in in rad/sec +Tl=0.0123*Wm**2 //required torque of the load + +//Results +var=phasemag(Is) +mprintf("Full load motor current Is:%.1f %.1f ° A",abs(Is),var) +mprintf("\nTp:%.2f N-m",Tp) +mprintf("\nTn:%.3f N-m",Tn) +mprintf("\n\nSince I:%.2f A and N:%d rpm",I,N) +mprintf("\nAnd I:%.2f A< Is %.2f A, the motor will run safely",I,abs(Is)) diff --git a/3731/CH6/EX6.10/Ex6_10.sce b/3731/CH6/EX6.10/Ex6_10.sce new file mode 100644 index 000000000..5c228cb9f --- /dev/null +++ b/3731/CH6/EX6.10/Ex6_10.sce @@ -0,0 +1,62 @@ +//Chapter 6:Induction Motor Drives +//Example 10 +clc; +clf(); +//Variable Initialization +//ratings of the star connected squirrel Induction motor is same as that of Ex-6.9 +f=50 // frequency in HZ +Vl=400 // line voltage in V +P=4 // number of poles +N=1370 // rated speed + +//the frequency variation is from 5 Hz to 50 Hz +fmin=5 +fmax=50 +//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 + +//calculation +Ns=120*f/P //synchronous speed +N1=Ns-N //increase in speed from no load to full torque rpm +Wms=2*%pi*Ns/60 +s=(Ns-N)/Ns //full load slip +Tmax=54.88 //maximum torque as obtain from Ex-6.9 + +//to obtain the plot between the voltage and the frequency +K=0 +k=[] +frequency=[] +line_voltage=[] +for i=0:9 +K=K+0.1 +f1=K*f +x=2*K*Wms*Tmax/3 +y=Rs+sqrt((Rs)**2+(K*(Xs+Xr_))**2) +Vl_square=3*x*y +Vl=sqrt(Vl_square) +k($+1)=K +frequency($+1)=f1 +line_voltage($+1)=Vl +end +disp(k,"K:") +disp(frequency,"f:in Hz") +disp(line_voltage,"Vl:in V") + +//Plotting the values of line voltage Vl vs f +plot(frequency,line_voltage,'b') +xlabel('f,Hz') +ylabel('Line voltage,volts') +xgrid(2) +title('Line voltage vs Frequency characteristic') +//for constant V/f ratio +x=[0,10,20,30,40,50] +y=[0,80,160,240,320,400] +plot(x,y,'--') +str=["$\underleftarrow{\huge{Constant V/f ratio}}$"] +xstring(21,160,str) + +mprintf("\nHence for a constant breakdown torque at all frequencies,") +mprintf("\nV/f ratio has to be progressively increased with increase in frequency") diff --git a/3731/CH6/EX6.11/Ex6_11.sce b/3731/CH6/EX6.11/Ex6_11.sce new file mode 100644 index 000000000..5a3b1ed97 --- /dev/null +++ b/3731/CH6/EX6.11/Ex6_11.sce @@ -0,0 +1,50 @@ +//Chapter 6:Induction Motor Drives +//Example 11 +clc; + +//Variable Initialization + +//Ratings of the star connected squirrel Induction motor are same as that of Ex-6.9 +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 + +//Solution +Ns=120*f/P //synchronous speed +N1=Ns-N //increase in speed from no load to full torque rpm +Wms=2*%pi*Ns/60 //synchronous speed +s=(Ns-N)/Ns //full load slip +D=Ns-N //drop in speed from no load to full load torque at 50 Hz + +//(i)When the frequency is 30 Hz and 80% of full load torque +f1=30 //given frequency in Hz +d=D*0.8 //drop in speed from no load to 80% full load torque +Ns1=120*f1/P //synchronous speed at the given frequency f1=30 Hz +N1=Ns1-d //required motor speed + +//(ii)When the speed is 1000 rpm for a full load torque +N2=1000 //given speed in rpm +Ns2=N2+D //synchronous speed +f2=P*Ns2/120 //required frequency + +//When the speed is 1100 rpm and the frequency is 40 Hz +N3=1100 //given speed in rpm +f3=40 //given frequency in Hz +Ns3=120*f3/P //synchronous speed at the given frequency f1=40 Hz +D1=Ns3-N3 //drop in speed from no load to N1=1100 rpm +x=(Rs+Rr_/s)**2+(Xs+Xr_)**2 +Tf=(3/Wms)*(Vl/sqrt(3))**2*(Rr_/s)/x //full load torque +T1=D1/D*Tf //required torque + + +//results +mprintf("(i)Hence the required motor speed is :%d rpm",N1) +mprintf("\n(ii)Hence the required frequency is :%.2f Hz",f2) +mprintf("\n(iii)Hence the required torque is :%.2f N-m",T1) diff --git a/3731/CH6/EX6.12/Ex6_12.sce b/3731/CH6/EX6.12/Ex6_12.sce new file mode 100644 index 000000000..c4bbd4eb9 --- /dev/null +++ b/3731/CH6/EX6.12/Ex6_12.sce @@ -0,0 +1,52 @@ +//Chapter 6:Induction Motor Drives +//Example 12 +clc; + +//Variable Initialization + +//Ratings of the star connected Induction motor are same as that of Ex-6.9 +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 + +//Solution +Ns=120*f/P //synchronous speed +N1=Ns-N //increase in speed from no load to full torque rpm + +//(i)When f1=30Hz and 80% of full load +Ns=120*f/P +f1=30 //frequency +N2=0.8*N1 //increase in speed from no load to 80% of full torque rpm +Ns1=f1/f*Ns +N=Ns1+N2 //machine speed + +//(ii)At a speed of 1000rpm +N2=1000 //given speed in rpm +N3=N2-N1 //synchronous speed +f3=P*N3/120 //required frequency + +//(iii)When frequency is 40Hz and speed is 1300 rpm +f4=40 //frequency in hz +N2=1300 //speed in rpm +Ns=120*f4/P //required synchronous speed in rpm +N4=N2-Ns //increase in speed from no load speed in rpm +Tf=25.37 //full load torque as calculated in Ex-6.11 +Tm=-N4/N1*Tf //motor torque + +//(iv) when the motor is under dynamic braking + + +//Results + +mprintf("(i)Required speed is :%d rpm",N) +mprintf("\n(ii)Required frequency is:%d Hz",f3) +mprintf("\n(iii)Required motor torque :%.2f N-m",Tm) +mprintf("\n(iv)The value of the frequency,speed and motor torque calculated in (i),(ii) and(iii)") +mprintf(" \nwill be the same when the motor is operated under dynamic braking") diff --git a/3731/CH6/EX6.13/Ex6_13.sce b/3731/CH6/EX6.13/Ex6_13.sce new file mode 100644 index 000000000..e2b1a1b86 --- /dev/null +++ b/3731/CH6/EX6.13/Ex6_13.sce @@ -0,0 +1,30 @@ +//Chapter 6:Induction Motor Drives +//Example 13 +clc; + +//Variable Initialization + +//Ratings of the star connected Induction motor are same as that of Ex-6.9 +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 + +//Solution +Wms=4*%pi*f/P +f1=60 //frequency in Hz during speed control of the motor +K=f1/f //the value of K at 60Hz +x=Rs+sqrt(Rs**2+K**2*(Xs+Xr_)**2) +Tmax_=3/(2*K*Wms)*(Vl/sqrt(3))**2/x //torque at 60 Hz frequency +z=Rs+sqrt(Rs**2+(Xs+Xr_)**2) +Tmax=3/(2*Wms)*(Vl/sqrt(3))**2/z //maximum torque +ratio=Tmax_/Tmax //ratio + +//Result +mprintf("Ratio of Motor breakdown torque at 60Hz to rated torque at 50Hz is:%.3f",ratio) diff --git a/3731/CH6/EX6.14/Ex6_14.sce b/3731/CH6/EX6.14/Ex6_14.sce new file mode 100644 index 000000000..292b73078 --- /dev/null +++ b/3731/CH6/EX6.14/Ex6_14.sce @@ -0,0 +1,16 @@ +//Chapter 6:Induction Motor Drives +//Example 14 +clc; + +mprintf("When operating at a frequency K times rated frequency f then") +mprintf("\nIm**2=[((Rr_/Ksf)**2+(2*pi*Lr_)**2)/((Rr_/Ksf)**2+(2*pi*Lm+2*Pi*Lr_)**2)]*Is**2----(1)") +mprintf("\nSince Im is constant for constant flux,") +mprintf("\nK*s*f=constant--------(2)") +mprintf("\nK*Wms*s=constant-------(3) which is the slip speed") +mprintf("\ns*K=constant----------(4)") +mprintf("\nThereofre for a frequency K*f") +mprintf("\nT=(3/K/Wms)*[(Is*K*Xm)**2*(Rr_/s)/((Rr_/s)**2+K**2*(Xm+Xr_)**2]") +mprintf("\nT=(3/K/Wms*s)*[(Is*Xm)**2*(Rr_)/((Rr_/s/K)**2+(Xm+Xr_)**2]-------(5)") +mprintf("\nHence for a given slip speed (K*Wms*s),K*s is constant and from (1) for a given K*s*f and constant flux") +mprintf("\noperation Is is fixed. Now from (5) T is also fixed. Thus, motor develps a constant torque and draws a") +mprintf("\nconstant current from the inverter at all frequencies for a given slip speed") diff --git a/3731/CH6/EX6.15/Ex6_15.sce b/3731/CH6/EX6.15/Ex6_15.sce new file mode 100644 index 000000000..55fb9a151 --- /dev/null +++ b/3731/CH6/EX6.15/Ex6_15.sce @@ -0,0 +1,62 @@ +//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) diff --git a/3731/CH6/EX6.16/Ex6_16.sce b/3731/CH6/EX6.16/Ex6_16.sce new file mode 100644 index 000000000..5767f58a4 --- /dev/null +++ b/3731/CH6/EX6.16/Ex6_16.sce @@ -0,0 +1,59 @@ +//Chapter 6:Induction Motor Drives +//Example 16 +clc; + +//Variable Initialization + +//Ratings of the Delta connected slipring Induction motor +f=50 // frequency in HZ +Vl=400 //line voltage in V +P=6 // number of poles +SR=2.2 //ratio of stator to rotor + +//Parameters referred to the stator +Xr_=1 // rotor winding reactance in ohm +Rr_=0.2 // resistance of the rotor windings in ohm +s=0.04 // given slip when motor runs at full load + +//Solution +Ns=120*f/P //synchronous speed +Wms=2*%pi*Ns/60 +x=(Rr_/s)**2+Xr_**2 +Tf=(3/Wms)*(Vl)**2*(Rr_/s)/x //full load torque +K=Tf/(Ns*(1-s))**2 +N=850 //speed of the motor in rpm +Tl=K*N**2 //torque at the given speed N +s=(Ns-N)/Ns //slip at the given speed N +y=Tl*(Wms/3)/Vl**2 //y=X/(X**2+Xr_**2) and X=(Re+Rr_)/s + +mprintf("\nThe torque at the given speed of 850rpm is:%d N-m",Tl) +mprintf("\nWith a slip of s:%.2f",s) +mprintf("\nTo find the external resistance connected the given quadratic equation is X**2-6.633X+1=0") +mprintf("\nWith X=(Re-Rr_)/s where Re is the required external resistance") + +a = 1 +b = -1/y +c = 1 + +//Discriminant +d = (b**2) - (4*a*c) + +X1 = (-b-sqrt(d))/(2*a) +X2 = (-b+sqrt(d))/(2*a) + +//Results +mprintf("\nThe solutions for X are %.4f and %.4f",X1,X2) +Re1=X1*s-Rr_ +Re2=X2*s-Rr_ + +if (Re1>0) then : +mprintf("\nThe number Re1:%.3f ohm is feasible",abs(Re1)) +R=Re1/SR**2 +mprintf("\nRotor referred value of the external resistance is:%.3f ohm",R) +end + +if (Re2>0) then +mprintf("\nThen Re2:%.3f ohm is feasible",abs(Re2)) +R=Re2/SR**2 +mprintf("\nHence Rotor referred value of the external resistance is:%.3f ohm",R) +end diff --git a/3731/CH6/EX6.17/Ex6_17.sce b/3731/CH6/EX6.17/Ex6_17.sce new file mode 100644 index 000000000..8aafafe27 --- /dev/null +++ b/3731/CH6/EX6.17/Ex6_17.sce @@ -0,0 +1,40 @@ +//Chapter 6:Induction Motor Drives +//Example 17 +clc; + +//Variable Initialization + +//Ratings of the star connected Induction motor +f=50 // frequency in HZ +Vl=440 //line voltage in V +P=6 // number of poles +Ns=120*f/P //synchronous speed + +//Parameters referred to the stator +Xr_=1.2 // rotor winding reactance in ohm +Xs=Xr_ // stator winding reactance in ohm +Rr_=0.4 // resistance of the rotor windings in ohm +Rs=0.5 // resistance of the stator windings in ohm +Xm=50 // magnetizing reatance +a=3.5 // stator to rotor turns ratio +delta=0 // duty ratio at the given breakdown torque +Sm=1 // slip at standstill + +//Solution + +//Slip at maximum torque without an external resistance is Sm=Rr_/sqrt(Rs**2+(Xs+Xr_)**2) +//When an external resistanc Re referred to the stator is connected +x=Sm*sqrt(Rs**2+(Xs+Xr_)**2) //x=Re+Rr_ +Re=x-Rr_ +y=0.5*a**2*(1-delta) // y=0.5*a**2*R*(1-delta) //y=Re +R=Re/y + +//(Ns-N)/Ns +//(Ns/Ns)-(N/Ns) +Sm=(Ns/Ns)-(1/Ns) +c=(x*Sm-Rr_)/(0.5*a**2*R) //c=(1-delta) +delta=1-c //given duty ratio + +//Results +mprintf("Variation of the duty ratio is:%.3f*N*10**(-3)",delta*1000) +mprintf("\nHence the duty ratio must change linearly with speed N") diff --git a/3731/CH6/EX6.18/Ex6_18.sce b/3731/CH6/EX6.18/Ex6_18.sce new file mode 100644 index 000000000..622d76165 --- /dev/null +++ b/3731/CH6/EX6.18/Ex6_18.sce @@ -0,0 +1,79 @@ +//Chapter 6:Induction Motor Drives +//Example 18 +clc; + +//Variable Initialization + +//Ratings of the star connected Induction motor +f=50 // frequency in HZ +Vl=440 // line voltage in V +P=6 // number of poles +N=970 // rated speed +n=2 // ratio of stator to rotor +Sm=0.25 // it is given the speed range is 25% below the synchronous speed which is proportional to the Slip + +//Parameters referred to the stator +Xr_=0.4 // rotor winding reactance in ohm +Xs=0.3 // stator winding reactance in ohm +Rr_=0.08 // resistance of the rotor windings in ohm +Rs=0.1 // resistance of the stator windings in ohm +alpha=165 // maximum value of the firing angle in degress + +//Solution +Ns=120*f/P // synchronous speed +Wms=2*%pi*Ns/60 +//(i) transformer turns ratio +al=alpha*(%pi/180) +a=-Sm/cos(al) //since Sm=a*math.cos(alpha) +m=n/a //since a=n/m where m is the transformer ratio + +//(ii)When speed is 780 rpm and firing angle is 140 degrees +N1=780 //given speed +alpha1=140 //given firing angle +s1=(Ns-N1)/Ns //slip at the given speed N1 +Vd1=(3*sqrt(6)/%pi)*s1*(Vl/sqrt(3))/n +al1=alpha1*(%pi/180) +Vd2=(3*sqrt(6)/%pi)*(Vl/sqrt(3))/m*cos(al1) +Rs_=Rs*(1/n)**2 //stator resistance referred to the rotor +Rr=Rr_*(1/n)**2 //rotor resistance referred to the rotor +Rd=0.01 //equivalent resistance of the DC link inductor +Id=(Vd1+Vd2)/(2*(s1*Rs_+Rr)+Rd) +T1=abs(Vd2)*Id/s1/Wms //required torque + +//(iii)when speed is 800rpm and firing angle is half the rated motor torque +N1=800 //given speed +s=(Ns-N)/Ns //rated slip +x=(Rs+Rr_/s)**2+(Xs+Xr_)**2 +Trated=(3/Wms)*(Vl/sqrt(3))**2*(Rr_/s)/x //rated torque +T_half=Trated/2 //half rated torque +s1=(Ns-N1)/Ns //given slip at speed N1=800rpm +Vd1=(3*sqrt(6)/%pi)*s1*(Vl/sqrt(3))/n +Vd2=(3*sqrt(6)/%pi)*(Vl/sqrt(3))/m +Id=(Vd1+Vd2)/(2*(s1*Rs_+Rr)+Rd) +T=abs(Vd2)*Id/s1/Wms //required torque + +//since the given torque is half of the rated value +//To find the find the firing angle we assumed cos(alpha1)=-X +//The given quadratic equation is X**2-0.772X+0.06425=0 +a = 1 +b = -0.772 +c = 0.06425 +//Discriminant +d = (b**2) - (4*a*c) + +X1 = (-b-sqrt(d))/(2*a) +X2 = (-b+sqrt(d))/(2*a) +alpha1=-acos(X2) //since cos(alpha1)=-X where alpha1 is radians +alpha1=alpha1*(180/%pi) +alpha1=180+alpha1 //required firing angle + + +//Results +mprintf("(i)Transformer ratio is:%.3f",m) +mprintf("\n(ii)Required torque is :%.2f N-m",T1) +//There is a slight difference in the answer for the torque due to accuracy +mprintf("\n(iii)The half rated torque at the given speed of %d rpm is:%.2f N-m",N1,T_half) +mprintf("\nWith a slip of s:%.1f",s1) +mprintf("\nThe solutions for X are %.4f and %.4f",X1,X2) +mprintf("\nFor X1:%.4f the motor is unstable so we use X2:%.4f",X1,X2) +mprintf("\nHence the required firing angle is :%.1f °",alpha1) diff --git a/3731/CH6/EX6.19/Ex6_19.sce b/3731/CH6/EX6.19/Ex6_19.sce new file mode 100644 index 000000000..3eaf445d3 --- /dev/null +++ b/3731/CH6/EX6.19/Ex6_19.sce @@ -0,0 +1,75 @@ +//Chapter 6:Induction Motor Drives +//Example 19 +clc; + +//Variable Initialization + +//Ratings of the star connected Induction motor is same as that of Ex-6.17 +f=50 // frequency in HZ +Vs=440 // line voltage in V +P=4 // number of poles +//Parameters referred to the stator +Xr_=1.2 // rotor winding reactance in ohm +Xs=Xr_ // stator winding reactance in ohm +Rr_=0.4 // resistance of the rotor windings in ohm +Rs=0.5 // resistance of the stator windings in ohm +Xm=50 // magnetizing reatance +a=3.5 // stator to rotor turns ratio + +//Solution +Ns=120*f/P // synchronous speed in rpm +Wms=2*%pi*Ns/60 // synchronous speed in rad/s + +//(i)When motor speed is 1200rpm with a voltage of 15+0j V + +V=15*(cos(0)+sin(0)*%i) +N1=1200 //speed in rpm +Vr_=a*V //rotor voltage +s1=(Ns-N1)/Ns //slip at the given speed N1=1200 rpm +Z=Rs+Rr_/s1+%i*(Xs+Xr_) //total impedance +Ir_=(Vs/sqrt(3)-Vr_/s1)/Z //rotor current +phi_r=atan(imag(Vr_),real(Vr_))-atan(imag(Ir_),real(Ir_))//angle between Vr_ and Ir_ +Pr=3*(abs(Ir_))**2*Rr_ //rotor copper loss +P1=3*abs(Vr_)*abs(Ir_)*cos(phi_r) //power absorbed by Vr_ +Pg=(Pr+P1)/s1 //gross power +T=Pg/Wms //required motor torque + +//(ii)when motor speed is 1200rpm with a unity power factor +N1=1200 //speed in rpm +Ir_=abs(Ir_) +Ir_=Ir_*(cos(0)+sin(0)*%i)//machine is operating at unity power factor +x=Ir_*Z //x=(Vs-Vr_/s1)*phi_r where phi_r is the angle between Vr_ and Ir_ + +//x=a+b +d=(Vs/sqrt(3)-Vr_/s1*cos(phi_r))**2 +e=(Vr_/s1*sin(phi_r))**2 +f=x/(d+e) +theta=atan(imag(f),real(f))//required angle in radian +theta=theta*180/%pi +//Now we should solve for the quadratice equation for the rotor current +// 0.9*Ir_**2 + 50.8*Ir_ + 90.12 = 0 +a1 = 0.9 +b1 = 50.8 +c1 = 90.12 + +//Discriminant +d = (b1**2) - (4*a1*c1) + +Ir_1 = (-b1-sqrt(d))/(2*a1) +Ir_2 = (-b1+sqrt(d))/(2*a1) + +Ir_=Ir_2 //Ir_2 is chosen because for Ir_1 the motor is unstable +Vr_sin_phi_r=abs(Ir_)/2.083 +Vr_cos_phi_r=s1*(Vs/sqrt(3)+2.5*Vr_sin_phi_r) +Vr_=Vr_cos_phi_r+%i*Vr_sin_phi_r //total rotor voltage referred to the stator +Vr_=Vr_/a //total rotor voltage referred to the rotor +var=atan(imag(Vr_),real(Vr_)) +phase=var*180/%pi + +//Results +mprintf("(i)The torque is :%.2f N-m and since it is negative the motor is operating in regenerative braking ",T) +mprintf("\n(ii)Now theta θ:%.2f ◦",theta) +mprintf("\nThe solution for Ir_ are %.3f and %.3f",Ir_1,Ir_2) +mprintf("\nWe choose Ir_:%.3f A since higher value corresponds to unstable region",Ir_2) +mprintf("\nHence the required voltage magnitude is Vr:%.2f V,phase:%.1f ◦",Vr_,phase) +//There is a slight difference in the answers due to accuracy diff --git a/3731/CH6/EX6.2/Ex6_2.sce b/3731/CH6/EX6.2/Ex6_2.sce new file mode 100644 index 000000000..9944263ea --- /dev/null +++ b/3731/CH6/EX6.2/Ex6_2.sce @@ -0,0 +1,75 @@ +//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) diff --git a/3731/CH6/EX6.20/Ex6_20.sce b/3731/CH6/EX6.20/Ex6_20.sce new file mode 100644 index 000000000..f9028a8ef --- /dev/null +++ b/3731/CH6/EX6.20/Ex6_20.sce @@ -0,0 +1,55 @@ +//Chapter 6:Induction Motor Drives +//Example 20 +clc; + +//Variable Initialization + +//Ratings of the single phase Induction motor +f=50 // frequency in HZ +Vs=220 // supply voltage in V +P=4 // number of poles +N=1425 // rated speed in rpm + +//Parameters referred to the stator +Xr_=6 // rotor winding reactance in ohm +Xs=Xr_ // stator winding reactance in ohm +Rr_=5 // resistance of the rotor windings in ohm +Rs=2 // resistance of the stator windings in ohm +Xm=60 // magnetizing reatance + +//Solution +N1=1200 //when the motor is operating at the given speed in rpm +Ns=120*f/P // synchronous speed +Wms=2*%pi*Ns/60 +s=(Ns-N)/Ns //rated slip + +Zf=%i*(Xm)*(Rr_/s+%i*Xr_)/2/(Rr_/s+%i*(Xr_+Xm)) +Rf=real(Zf) +Xf=imag(Zf) +Zb=%i*(Xm)*(Rr_/(2-s)+%i*Xr_)/2/(Rr_/(2-s)+%i*(Xr_+Xm)) +Rb=real(Zb) +Xb=imag(Zb) +Zs=Rs+%i*Xs +Z=Zs+Zf+Zb +Is=(Vs)/Z +T=(abs(Is))**2/Wms*(Rf-Rb) +Tl=T +K=Tl/N**2 + +//Therefore for a speed of of N1=1200 rpm we get +Tl=K*N1**2 //required load torque for the given speed N1 +s1=(Ns-N1)/Ns // slip for the given speed N1 + +Zf=%i*(Xm)*(Rr_/s1+%i*Xr_)/2/(Rr_/s1+%i*(Xm)) +Rf=real(Zf) +Xf=imag(Zf) +Zb=%i*(Xm)*(Rr_/(2-s1)+%i*Xr_)/2/(Rr_/(2-s1)+%i*(Xr_+Xm)) +Rb=real(Zb) +Xb=imag(Zb) +x=(Wms*Tl)/(Rf-Rb) //since Tl=(abs(Is))**2/Wms*(Rf-Rb) and x=Is**2 +Is=sqrt(x) +Z=Zs+Zf+Zb +V=Is*abs(Z) + +//Result +mprintf("Hence the motor terminal voltage at the speed of%d rpm is :%.1f V",N1,V) 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) diff --git a/3731/CH6/EX6.4/Ex6_4.sce b/3731/CH6/EX6.4/Ex6_4.sce new file mode 100644 index 000000000..7ec27cbb1 --- /dev/null +++ b/3731/CH6/EX6.4/Ex6_4.sce @@ -0,0 +1,53 @@ +//Chapter 6:Induction Motor Drives +//Example 4 +clc; + +//Variable Initialization + +//Ratings of the motor are same as that in Ex-6.3 +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 +N=950 //full load speed in rpm +SR=2.3 //stator to rotor turns ratio + +//Solution +Ns=120*f/P //synchronous speed in rpm +Wms=2*%pi*Ns/60 +s=(Ns-N)/Ns //full load slip +x=sqrt((Rs+Rr_/s)**2+(Xs+Xr_)**2) +Irf_=(Vl/sqrt(3))/x //full load current +Tf=(1/Wms)*3*Irf_**2*Rr_/s //full load torque + +//(i)initial braking current and torque +S=2-s //during plugging at 950rpm +y=sqrt((Rs+Rr_/S)**2+(Xs+Xr_)**2) +Ir_=(Vl/sqrt(3))/y //initial braking current +ratio1=Ir_/Irf_ +T=(1/Wms)*3*Ir_**2*Rr_/S //initial braking torque +ratio2=T/Tf + +//(ii)when an external resistance is connected such +//that maximum braking current is 1.5 times the full load current +Ir_=1.5*Irf_ +x=(Vl/sqrt(3))/Ir_ //x=sqrt((Rs+(Rr_+Re_)/S)**2+(Xs+Xr_)**2) +y=x**2 //y=(Rs+(Rr_+Re_)/S)**2+(Xs+Xr_)**2 +z=y-(Xs+Xr_)**2 //z=(Rs+(Rr_+Re_)/S)**2 +a=sqrt(z) //a=(Rs+(Rr_+Re_)/S) +b=(a-Rs)*S //b=(Rr_+Re_) +Re_=b-Rs +Re=Re_/SR**2 +T=(1/Wms)*3*Ir_**2*(Rr_+Re_)/S //initial braking torque +ratio=T/Tf + + +//Results +mprintf("(i)Ratio of initial braking current to full load current is:%.1f",ratio1) +mprintf("\nRatio of initial braking torque to full load torque is:%.2f\n",ratio2) +mprintf("\n(ii)Ratio of initial braking torque to full load torque when the resistance is added is:%.3f",ratio) diff --git a/3731/CH6/EX6.5/Ex6_5.sce b/3731/CH6/EX6.5/Ex6_5.sce new file mode 100644 index 000000000..72969a347 --- /dev/null +++ b/3731/CH6/EX6.5/Ex6_5.sce @@ -0,0 +1,57 @@ +//Chapter 6:Induction Motor Drives +//Example 4 +clc; + +//Variable Initialization + +//Ratings of the star connected Induction motor +f=50 // frequency in HZ +Vl=440 // line voltage in V +P=6 // number of poles +Vp=Vl/sqrt(3) //phase voltage in V + +//Parameters referred to the stator +Xr_=1.2 // rotor winding reactance in ohm +Xs=Xr_ // stator winding reactance in ohm +Rr_=0.4 // resistance of the rotor windings in ohm +Rs=0.5 // resistance of the stator windings in ohm +Xm=50 // no load reactance in ohms +N=950 // full load speed in rpm +Sm=2 // slip at maximum torque + +//Solution +Rr_=Sm*sqrt(Rs**2+(Xs+Xr_)**2) //Since Sm=Rr_/sqrt(Rs**2+(Xs+Xr_)**2) +Ns=120*f/P //synchronous speed in rpm +Wms=2*%pi*Ns/60 +s=(Ns-N)/Ns //slip at 950 rpm + +x=%i*Xm*(Rr_/s+%i*Xr_) +y=Rr_/s+%i*(Xr_+Xm) +Zp=Rs+%i*Xs+x/y +Ip=Vp/sqrt(3)/Zp +//The value of Ip is wrong which leads to other wrong answers + +Irp_=Ip*(%i*Xm)/(Rr_/s+%i*(Xr_+Xm)) +Tp=(1/Wms)*3*abs(Irp_)**2*Rr_/s +x=%i*Xm*(Rr_/(2-s)+%i*Xr_) +y=Rr_/(2-s)+%i*(Xr_+Xm) +Zn=Rs+%i*Xs+x/y +In=Vp/sqrt(3)/Zn +Irn_=In*(%i*Xm)/(Rr_/(2-s)+%i*(Xr_+Xm)) +Tn=-(1/Wms)*3*abs(Irn_)**2*Rr_/(2-s) +//The value of In is wrong + +T=Tp-Tn +I=abs(Ip)+abs(In) +Rr_=0.4 // from the parameters of the motor referred to the stator +x=sqrt((Rs+Rr_/s)**2+(Xs+Xr_)**2) +If=(Vl/sqrt(3))/x //full load current +Tf=(1/Wms)*3*If**2*Rr_/s //full load torque + +ratio1=I/If +ratio2=abs(T)/Tf + +//Results +mprintf("Ratio of braking current to full load current is:%.3f",ratio1) +mprintf("\nRatio of braking torque to full load torque is:%.3f",ratio2) +//Answer provided in the book is wrong diff --git a/3731/CH6/EX6.6/Ex6_6.sce b/3731/CH6/EX6.6/Ex6_6.sce new file mode 100644 index 000000000..9e1487acd --- /dev/null +++ b/3731/CH6/EX6.6/Ex6_6.sce @@ -0,0 +1,91 @@ + +//Chapter 6:Induction Motor Drives +//Example 6 +clc; + +//Variable Initialization + +//Ratings of the star connected Induction motor which operates under dynamic braking +f=50 // frequency in HZ +P=6 // number of poles + +//Parameters referred to the stator +Xr_=3.01 // rotor winding reactance in ohm +Xs=Xr_ // stator winding reactance in ohm +Rr_=4.575 // resistance of the rotor windings in ohm +Rs=1.9 // resistance of the stator windings in ohm +J=0.1 // moment of inertia of the motor load system in kg-m2 +Id=12 // given DC current + +N=1500 //given asynchronous speed +//magnetization chacrateristic at the given asynchronous speed +Im=[0.13,0.37,0.6,0.9,1.2,1.7,2.24,2.9,3.9,4.9,6,8,9,9.5] //magnetization current +E=[12.8,32,53.8,80,106,142,173,200,227,246,260,280,288,292] //back emf + +//Solution +Ns=120*f/P //synchronous speed in rpm +torque=[] +speed=[] +temp=[] +Is=sqrt(2/3)*Id //value of stator current for two lead connection +Wms=2*%pi*N/60 +for i=2:14 +x=(Is**2-Im(i)**2)/(1+2*Xr_*Im(i)/E(i)) //x=Ir_**2 +Ir_=sqrt(x) //required rotor current +y=(E(i)/Ir_)**2-Xr_**2 +S=Rr_/sqrt(y) //required slip +N=S*Ns //required speed +T=(3/Wms)*(Ir_)**2*Rr_/S //required torque +speed($+1)=N +torque($+1)=T +temp($+1)=T +end +mprintf("Hence the magnetization curve is") +disp(speed,"Speed:in rpm") +for i=1:13 +torque(i)=-1*torque(i) +end +disp(torque,"Braking torque :in N-m") + +//Results + +//Plot of of torque vs speed +subplot(2,1,1) +plot(torque,speed) +xlabel('Torque, N-m') +ylabel('Speed, rpm') +title('Torque vs Speed') +xgrid(2) + +//Plot of Wm vs J/T +inertia_over_torque=[] +for i=3:13 +J_T=1000*J/temp(i) +inertia_over_torque($+1)=J_T +end +disp(inertia_over_torque,"J/t :") + +Wm=[1,4,8,12,16,20,25,55,95,125,160] +//the values of Wm are taken for the angular frequency with maximum value of Wms=50*pi rad/s +subplot(2,1,2) +plot(Wm,inertia_over_torque) +xlabel('$Angular speed \omega_m$') +ylabel(' J/T,1*10e-2') +title('$J/T vs \omega_m$') +xgrid(2) +x=[6.5,6.5] +y=[2,4.5] +plot(x,y,'blue') +str=["${A}$"] +str1=["${B}$"] +str2=["${C}$"] +str3=["${D}$"] +str4=["${E}$"] +xstring(6,2,str) +xstring(6,4.5,str1) +xstring(80,3.4,str2) +xstring(156,8.3,str3) +xstring(156,2,str4) + +mprintf("Hence from the plot the area ABCDEA between the curve and the speed axis for speed change ") +mprintf("for synchronous to 0.02 times synchrnous speed is the stopping time which is equal to: 9.36 sec") diff --git a/3731/CH6/EX6.7/Ex6_7.sce b/3731/CH6/EX6.7/Ex6_7.sce new file mode 100644 index 000000000..234242390 --- /dev/null +++ b/3731/CH6/EX6.7/Ex6_7.sce @@ -0,0 +1,50 @@ +//Chapter 6:Induction Motor Drives +//Example 7 +clc; + +//Variable Initialization + +//Ratings of the Star connected Induction motor +f=50 // frequency in HZ +Vl=2200 // line voltage in V +P=6 // number of poles + +//Parameters referred to the stator +Xr_=0.5 // rotor winding reactance in ohm +Xs=Xr_ // stator winding reactance in ohm +Rr_=0.12 // resistance of the rotor windings in ohm +Rs=0.075 // resistance of the stator windings in ohm +J=100 // combine inertia of motor and load in kg-m2 + +//Solution + +//(i) During starting of the motor +Sm=Rr_/sqrt(Rs**2+(Xs+Xr_)**2) //slip at maximum torque +Wms=4*%pi*f/P //angular frequency +x=Rs+sqrt(Rs**2+(Xs+Xr_)**2) +Tmax=(3/2/Wms)*(Vl/sqrt(3))**2/x //maximum torque +tm=J*Wms/Tmax //mechanical time constant of the motor +ts=tm*(1/4/Sm+1.5*Sm) //time taken during starting +Es=1/2*J*Wms**2*(1+Rs/Rr_) //energy disspated during starting + +//(ii) When the motor is stopped by plugging method +tb=tm*(0.345*Sm+0.75/Sm) //time required to stop by plugging +Eb=3/2*J*Wms**2*(1+Rs/Rr_) //energy disspated during braking + +//(iii)Required resistance to be inserted during plugging +tb1=1.027*tm //minimum value of stopping time during braking +x=1.47*(Xs+Xr_) //x=Rr_+Re +Re=x-Rr_ //Re is the required external resistance to be connected +Ee=3/2*J*Wms**2*(Re/(Re+Rr_)) //energy disspated in the external resistor +Eb1=Eb-Ee //total energy disspated during braking + + +//Results + +mprintf("(i)Time taken during starting is ts:%.4f s",ts) +mprintf(" \nEnergy dissipated during starting is Es:%d kilo-watt-sec",Es/1000) +mprintf("\n\n(ii)Time taken to stop by plugging is tb:%.2f s",tb) +mprintf(" \nEnergy dissipated during braking is Eb:%d kilo-watt-sec",Eb/1000) +mprintf("\n\n(iii)Minimum Time taken to stop by plugging is tb:%.2f s",tb1) +mprintf(" \nRequired external resistance to be connected is Re:%.2f ohm",Re) +mprintf(" \nTotal Energy dissipated during braking is Eb:%.2f kilo-watt-sec",Eb1/1000) diff --git a/3731/CH6/EX6.8/Ex6_8.sce b/3731/CH6/EX6.8/Ex6_8.sce new file mode 100644 index 000000000..0499ed6ab --- /dev/null +++ b/3731/CH6/EX6.8/Ex6_8.sce @@ -0,0 +1,69 @@ +//Chapter 6:Induction Motor Drives +//Example 8 +clc; + +//Variable Initialization + +//Ratings of the delta connected Induction motor +f=50 // frequency in HZ +Vl=400 // line voltage in V +P=4 // number of poles +Pm=2.8*1000 // rated mechanical power developed in W +N=1370 // rated speed in rpm + +//Parameters referred to the stator +Xr_=5 // rotor winding reactance in ohm +Xs=Xr_ // stator winding reactance in ohm +Rr_=5 // resistance of the rotor windings in ohm +Rs=2 // resistance of the stator windings in ohm +Xm=80 // no load reactance in ohm + +//Solution +Ns=120*f/P //synchronous speed in rpm +Wms=2*%pi*Ns/60 //synchronous speed in rad/s +s=(Ns-N)/Ns //full load slip +x=(Rs+Rr_/s)**2+(Xs+Xr_)**2 //total impedance +T=(3/Wms)*(Vl**2*Rr_/s)/x //full load torque +Tl=T +K=Tl/(1-s)**2 //since Tl=K*(1-s)**2 + +//(i) When the motor is running at 1200 rpm +N1=1200 //speed in rpm +s1=(Ns-N1)/Ns //slip at the given speed N1 +Tl=K*(1-s1)**2 //torque at the given speed N1 + +y=(Rs+Rr_/s1)**2+(Xs+Xr_)**2 //total impedance +a=Tl*(Wms/3)*y*(s1/Rr_) //Since T=(3/Wms)*(Vl**2*Rr_/s)/x and a=V**2 +V=sqrt(a) //required voltage at the given speed N1 +Ir_=V/((Rs+Rr_/s1)+%i*(Xs+Xr_))//rotor current +Im=V/(%i*Xm) //magnetizing current +Is=Ir_+Im //total current +Il=abs(Is)*sqrt(3) //line current + +//(ii)When the terminal voltage is 300 V +V1=300 //terminal voltage in V +x=(Rs+Rr_)**2+(Xs+Xr_)**2 +T=(3/Wms)*(V1**2*Rr_)/x + +//Now we have to solve for the value of slip 's' from the given equation 104s**4- 188s**3 + 89s**2 - 179s + 25=0" +coeff = [104,-188,89,-179,25] //coeffcient of the polynomial equation +s=[] +s=roots(coeff) //roots of the polynomial equation + +T=K*(1-real(s(4)))**2 //torque at the given terminal voltage of 300 V +N=Ns*(1-real(s(4))) //speed at the given terminal voltage of 300 V +Ir_=V1/((Rs+Rr_/real(s(4)))+%i*(Xs+Xr_))//rotor current +Im=V1/(%i*Xm) //magnetizing current +Is=Ir_+Im //total current +Il1=abs(Is)*sqrt(3) //line current + + +//Results +mprintf("(i)Required torque is Tl:%.1f N-m",Tl) +mprintf("\nRequired motor terminal voltage is V: %.1f V",V) +mprintf("\nRequired line current is Il:%.2f A",Il) +mprintf("\n(ii)The roots of the polynomial equation are s1:%.3f s2:%.3f s3:%.3f s4:%.3f",real(s(1)),real(s(2)),real(s(3)),real(s(4))) +mprintf("\nHence Only s4: %.3f is valid",real(s(4))) +mprintf("\nRequired torque is Tl:%.2f N-m",T) +mprintf("\nRequired speed is N:%.1f rpm",N) +mprintf("\nRequired line current is Il:%.2f A",Il1) diff --git a/3731/CH6/EX6.9/Ex6_9.sce b/3731/CH6/EX6.9/Ex6_9.sce new file mode 100644 index 000000000..c478d4446 --- /dev/null +++ b/3731/CH6/EX6.9/Ex6_9.sce @@ -0,0 +1,70 @@ +//Chapter 6:Induction Motor Drives +//Example 9 +clc; +clf(); +//Variable Initialization + +//Ratings of the star connected squirrel Induction motor +f=50 // frequency in HZ +Vl=400 // line voltage in V +P=4 // number of poles +N=1370 // rated speed + +//Frequency variation is from 10 Hz to 50 Hz +fmin=10 +fmax=50 + +//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 + +//Solution +Ns=120*f/P //synchronous speed +N1=Ns-N //increase in speed from no load to full torque rpm +Wms=2*%pi*Ns/60 +s=(Ns-N)/Ns //full load slip + +//(i)to obtain the plot between the breakdown torque and the frequency +K=0.1 +k=[] +frequency=[] +torque=[] +for i=0:8 +K=K+0.1 +f1=K*f +x=Rs/K+sqrt((Rs/K)**2+(Xs+Xr_)**2) +Tmax=(3/2/Wms)*(Vl/sqrt(3))**2/x +k($+1)=K +frequency($+1)=f1 +torque($+1)=Tmax +end +disp(k,"K:") +disp(frequency,"f:in Hz") +disp(torque,"Tmax:in N-m") + +//Plotting the values of Tmax vs f +plot(frequency,torque) +xgrid(2) +xlabel('f,Hz') +ylabel('Tmax,N-m') +title('Torque vs frequency characteristic') + +//(ii) to obtain the starting torque and current at rated frequency and voltage +x=(Rs+Rr_)**2+(Xs+Xr_)**2 +Tst=(3/Wms)*(Vl/sqrt(3))**2*Rr_/x //starting torque at 50 Hz frequency +Ist=(Vl/sqrt(3))/sqrt(x) //starting current at 50 Hz frequency + +K=fmin/fmax //minimum is available at 10 Hz +y=((Rs+Rr_)/K)**2+(Xs+Xr_)**2 +Tst_=(3/Wms)*(Vl/sqrt(3))**2*Rr_/K/y //starting torque at 10 Hz frequency +Ist_=(Vl/sqrt(3))/sqrt(y) //starting current at 10 Hz frequency + +ratio1=Tst_/Tst //ratio of starting torque to the rated starting torque +ratio2=Ist_/Ist //ratio of starting current to the rated starting current + +//Results +mprintf("\n(i)Hence from the plot we can see that for a constant (V/f) ratio breakdown torque decreases with frequency") +mprintf("\n(ii)Hence the required ratio of starting torque to the rated starting torque is :%.3f",ratio1) +mprintf("\nHence the required ratio of starting current to the rated starting current is :%.2f",ratio2) |