diff options
Diffstat (limited to '3731/CH5')
-rw-r--r-- | 3731/CH5/EX5.1/Ex5_1.sce | 25 | ||||
-rw-r--r-- | 3731/CH5/EX5.10/Ex5_10.sce | 85 | ||||
-rw-r--r-- | 3731/CH5/EX5.11/Ex5_11.sce | 53 | ||||
-rw-r--r-- | 3731/CH5/EX5.12/Ex5_12.sce | 47 | ||||
-rw-r--r-- | 3731/CH5/EX5.13/Ex5_13.sce | 45 | ||||
-rw-r--r-- | 3731/CH5/EX5.14/Ex5_14.sce | 89 | ||||
-rw-r--r-- | 3731/CH5/EX5.15/Ex5_15.sce | 62 | ||||
-rw-r--r-- | 3731/CH5/EX5.16/Ex5_16.sce | 62 | ||||
-rw-r--r-- | 3731/CH5/EX5.17/Ex5_17.sce | 45 | ||||
-rw-r--r-- | 3731/CH5/EX5.18/Ex5_18.sce | 57 | ||||
-rw-r--r-- | 3731/CH5/EX5.19/Ex5_19.sce | 46 | ||||
-rw-r--r-- | 3731/CH5/EX5.2/Ex5_2.sce | 27 | ||||
-rw-r--r-- | 3731/CH5/EX5.20/Ex5_20.sce | 34 | ||||
-rw-r--r-- | 3731/CH5/EX5.21/Ex5_21.sce | 38 | ||||
-rw-r--r-- | 3731/CH5/EX5.22/Ex5_22.sce | 51 | ||||
-rw-r--r-- | 3731/CH5/EX5.23/Ex5_23.sce | 38 | ||||
-rw-r--r-- | 3731/CH5/EX5.3/Ex5_3.sce | 22 | ||||
-rw-r--r-- | 3731/CH5/EX5.4/Ex5_4.sce | 25 | ||||
-rw-r--r-- | 3731/CH5/EX5.5/Ex5_5.sce | 61 | ||||
-rw-r--r-- | 3731/CH5/EX5.6/Ex5_6.sce | 68 | ||||
-rw-r--r-- | 3731/CH5/EX5.7/Ex5_7.sce | 53 | ||||
-rw-r--r-- | 3731/CH5/EX5.8/Ex5_8.sce | 37 | ||||
-rw-r--r-- | 3731/CH5/EX5.9/Ex5_9.sce | 79 |
23 files changed, 1149 insertions, 0 deletions
diff --git a/3731/CH5/EX5.1/Ex5_1.sce b/3731/CH5/EX5.1/Ex5_1.sce new file mode 100644 index 000000000..ebc684a99 --- /dev/null +++ b/3731/CH5/EX5.1/Ex5_1.sce @@ -0,0 +1,25 @@ +//Chapter 5:DC Motor Drives +//Example 1 +clc; + +//Variable Initialization + +//Motor ratings +V1=200 //rated voltage in V +Ia1=10.5 //rated current in A +N1=2000 //speed in rpm +Ra=0.5 //armature resistance in ohms +Rs=400 //field resistance in ohms +V2=175 //drop in source voltage in V + +//Solution + +flux2=V2/V1 +Ia2=1/flux2*Ia1 //since load torque +E1=V1-Ia1*Ra +E2=V2-Ia2*Ra +N2=(E2/E1)*(1/flux2)*N1 + +//Result +mprintf("\nMotor speed is:%.1f rpm",N2) +//Answer provided in the book is incorrect diff --git a/3731/CH5/EX5.10/Ex5_10.sce b/3731/CH5/EX5.10/Ex5_10.sce new file mode 100644 index 000000000..ebe71b3aa --- /dev/null +++ b/3731/CH5/EX5.10/Ex5_10.sce @@ -0,0 +1,85 @@ +//Chapter 5:Dc Motor Drives +//Example 10 +clc; + +//Variable Initialization + + +V=220 // rated voltage in v +N=1000 // rated speed in rpm +Ia=175 // rated current in A +Ra=0.08 // armature resistance in ohms +N1=1050 // initial speed of the motor in rpm +J=8 // moment of inertia of the motor load system kg-m2 +La=0.12 // armature curcuit inductance in H + +//Solution +E=V-Ia*Ra +Wm=N*2*%pi/60 //rated speed in rad/s +//(a)When the braking current is twice the rated current +Ia1=2*Ia +E1=N1/N*E +x=(V+E1)/Ia1 //x=Rb+Ra +Rb=x-Ra //required braking resistance + +//(b)To obtain the expression for the transient value of speed and current including the effect of armature inductance +//The values given below are taken from Ex-5.9 +ta=0.194 //time constant in sec +B=0 +tm1= %inf //tm1=J/B and B=0 which is equal to infinity +tm2=1.274 +K=1.967 +Trated=E*Ia/Wm //rated torque +Tl=0.5*Trated //load torque is 50% of the rated torque +Ra=Rb +K1=N1*2*%pi/60 //initial speed in rad/s +//Values of the coefficient of the quadratic equation for Wm +x1=(1+ta/tm1)/ta +x2=1/tm2/ta +x3=-(K*V+Ra*Tl)/J/Ra/ta +//Values of the coefficient of the quadratic equation ia +y1=(1+ta/tm1)/ta +y2=1/tm2/ta +y3=-B*V/J/Ra/ta+K*Tl/J/Ra/ta + +//solving the quadratic equation +a = 1 +b = x1 +c = x2 +//Discriminant +d = (b**2) - (4*a*c) + +alpha1 = (-b+sqrt(d))/(2*a) +alpha2 = (-b-sqrt(d))/(2*a) + +K3=x3/x2 +K4=y3/y2 + +Wm_0=K1 ;ia_0=0 +d_Wm_dt_0=(K*ia_0-B*Wm-Tl)/J ;d_ia_dt_0=(-V-Ra*ia_0-K*K1)/La //Wm=K1 at t=0 and during braking rated voltage V is equal to -V + +a = [1,1;real(alpha1),real(alpha2)] +b = [Wm_0;d_Wm_dt_0] +x = inv(a)*b +c = [1,1;real(alpha1),real(alpha2)] +d = [-K4;d_ia_dt_0] +y = inv(c)*d + +//(c)To calculate the time taken for the speed to fall to zero value +a=-K3/x(1) //a=exp(-0.966*t1) +t1=alpha1*log(a) //take log base e on both sides + + +//Results +mprintf("(a)Hence the braking resistance is :%.3f ohm",Rb) +mprintf("\n(b)The solutions for alpha are %.3f and %.3f",real(alpha1),real(alpha2)) +mprintf("\nWm=%.2f + A*exp(%.3f*t) + B*exp(%.2f*t)",K3,real(alpha1),real(alpha2)) +mprintf("\nia=%.2f+ C*exp(%.3f*t) + D*exp(%.2f*t)",K4,real(alpha1),real(alpha2)) +mprintf("\nWe have to find the value of A,B,C and D in the linear equation using the initial condition") +mprintf("\nA=%.2f B=%.2f C=%.2f D=%.2f",x(1),x(2),y(1),y(2)) +mprintf("\nHence the expression for the transient value for the speed is") +mprintf("\nWm=%.2f+%.2f*exp(%.3f*t)%.2f*exp(%.2f*t)",K3,x(1),real(alpha1),x(2),real(alpha2)) +mprintf("\nHence the expression for the transient value for the current is") +mprintf("\nia=%.2f %.1f *exp(%.3f*t) +%.2f*exp(%.2f*t)",K4,y(1),real(alpha1),y(2),real(alpha2)) +mprintf("\n(c)Hence the time taken is :%.2f sec",real(t1)) +//There is slight difference in the answers due to accuracy diff --git a/3731/CH5/EX5.11/Ex5_11.sce b/3731/CH5/EX5.11/Ex5_11.sce new file mode 100644 index 000000000..b63945d9f --- /dev/null +++ b/3731/CH5/EX5.11/Ex5_11.sce @@ -0,0 +1,53 @@ + +//Chapter 5:Dc Motor Drives +//Example 11 +clc; + +//Variable Initialization + +//Ratings of the separately excited motor +V=220 // rated voltage in V +N=600 // rated speed in rpm +Ia=500 // rated current in A +Ra=0.02 // armature resistance in ohms +Rf=10 // field resistance in ohms + +//Solution +Ia1=2*Ia +E1=V-Ia*Ra //rated back emf at rated operation +Wm1=2*%pi*N/60 //angular speed +Trated=E1*Ia1/Wm1 //rated torque + +//(i) When the speed of the motor is 450rpm +N1=450 //given speed in rpm +Tl=2000-2*N1 //load torque is a function of the speed as given +Ia2=Tl/Trated*Ia1 //for a torque of Tl as a function of current +E2=N1/N*E1 //for a given speed of 450rpm +V2=E2+Ia2*Ra //terminal voltage for a given speed of 450 rpm + +//(ii) when the speed of the motor is 750rpm +N1=750 //given speed in rpm +Tl=2000-2*N1 //load torque is a function of the speed as given +Wm_=2*%pi*N1/60 +Ke_phi1=E1/Wm1 + +//Since we know that V=Ke*phi*Wm+Ia*Ra by solving we get that 0.02*(Ia_)**2 -220*Ia_ + 39270 = 0" +a = 0.02 +b = -220 +c = 39270 + +//Discriminant +d = (b**2) - (4*a*c) + +Ia_1 = (-b-sqrt(d))/(2*a) +Ia_2 = (-b+sqrt(d))/(2*a) + +Ke_phi=Tl/abs(Ia_1) +V1=V*Ke_phi/Ke_phi1 //required field voltage + +//Results +mprintf("(i)Hence motor terminal voltage is :%.1f V",V2) +mprintf("\nAnd the armature current is :%.1f A",Ia2) +mprintf("\n(ii)The solutions for Ia_ are %.1f A and %.1f A",abs(Ia_1),abs(Ia_2)) +mprintf("\nWe ignore %d A since it is infeasible,\n Hence armature current is :%.1f A",abs(Ia_2),abs(Ia_1)) +mprintf("\nHence the required field voltage is :%.1f V",V1) diff --git a/3731/CH5/EX5.12/Ex5_12.sce b/3731/CH5/EX5.12/Ex5_12.sce new file mode 100644 index 000000000..5e410cde3 --- /dev/null +++ b/3731/CH5/EX5.12/Ex5_12.sce @@ -0,0 +1,47 @@ + +//Chapter 5:Dc Motor Drives +//Example 12 +clc; + +//Variable Initialization + +//Ratings of the 2-pole separately excited DC motor with the fields coils connected in parallel +V=220 // rated voltage in V +N=750 // rated speed in rpm +Ia1=100 // rated current in A +Ra=0.1 // armature resistance in ohms + +//Solution +E1=V-Ia1*Ra //rated back emf at rated operation +Wm1=2*%pi*N/60 //angular speed +Trated=E1*Ia1/Wm1 //rated torque +Ke_phi1=E1/Wm1 + +//(i) When the armature voltage is reduced to 110V +Wm2=2*%pi*N/60 //angular speed +E2=Ke_phi1*Wm2 +//Now there are two linear equations...that we have to solve +//They are given by 0.3*N2+2.674*Ia2=500 and 0.28*N2+0.1*Ia2=110 +a = [0.3,2.674;0.28,0.1] +b = [500;110] +x = inv(a)*b +N2=x(1) //let the motor speed be N2 +Ia2=x(2) //let the motor current be Ia2 + +//(ii)When the field coils are connected in series +K=Ke_phi1/2 +Wm3=2*%pi*N/60 //angular speed +E3=K*Wm3 +//Now there are two linear equations...that we have to solve" +//They are given by 0.3*N3+1.337*Ia3=500 and 0.14*N3+0.1*Ia3=220" +a = [0.3,1.337;0.14,0.1] +b = [500;220] +x = inv(a)*b +N3=x(1) //let the motor speed be N3 +Ia3=x(2) //let the motor current be Ia3 + +//Results +mprintf("(i)Hence the motor armature current is Ia2 :%.1f A",Ia2) +mprintf("\nAnd the required speed is N2 :%.1f rpm",N2) +mprintf("\n(ii)Hence the motor armature current is Ia3 :%.1f A",Ia3) +mprintf("\nAnd the required speed is N3 :%.1f rpm",N3) diff --git a/3731/CH5/EX5.13/Ex5_13.sce b/3731/CH5/EX5.13/Ex5_13.sce new file mode 100644 index 000000000..aa644aa15 --- /dev/null +++ b/3731/CH5/EX5.13/Ex5_13.sce @@ -0,0 +1,45 @@ +//Chapter 5:Dc Motor Drives +//Example 13 +clc; + +//Variable Initialization + +//Ratings of the separately excited motor +V=200 // rated voltage in V +N=875 // rated speed in rpm +Ia=150 // rated current in A +Ra=0.06 // armature resistance in ohms +Vs=220 // source voltage in V +f=50 // frequency of the source voltage in Hz + +//Solution +E=V-Ia*Ra //back emf +Vm=sqrt(2)*Vs //peak voltage + +//(i)When the speed is 750 rpm and at rated torque +N1=750 //given speed in rpm +E1=N1/N*E //back emf at the given speed N1 +Va=E1+Ia*Ra //terminal voltage +cos_alpha=Va*%pi/2/Vm +alpha=acos(cos_alpha) //required firing angle in radian +alpha1=alpha*180/%pi //required firing angle in degrees + +//(ii)When the speed is -500rpm and at rated torque +N1=-500 //given speed in rpm +E1=N1/N*E //back emf at the given speed N1 +Va=E1+Ia*Ra //terminal voltage +cos_alpha=Va*%pi/2/Vm +alpha=acos(cos_alpha) //required firing angle in radian +alpha2=alpha*180/%pi //required firing angle in degrees + +//(iii)When the firing angle is 160 degrees +alpha=160 //firing angle in degrees +alpha=alpha*%pi/180 +Va=2*Vm/%pi*cos(alpha) +E1=Va-Ia*Ra //since Va=E1+Ia*Ra +N1=E1/E*N //the required speed at the given firing angle + +//Results +mprintf("(i)Hence the required firing angle is :%.1f °",alpha1) +mprintf("\n(ii)Hence the required firing angle is :%.1f °",alpha2) +mprintf("\n(iii)Hence the required speed is :%.1f rpm",N1) diff --git a/3731/CH5/EX5.14/Ex5_14.sce b/3731/CH5/EX5.14/Ex5_14.sce new file mode 100644 index 000000000..4b499ef77 --- /dev/null +++ b/3731/CH5/EX5.14/Ex5_14.sce @@ -0,0 +1,89 @@ +//Chapter 5:Dc Motor Drives +//Example 14 +clc; + +//Variable Initialization + +//Ratings of the separately excited motor is same as that of Ex-5.13 +V=200 // rated voltage in v +N=875 // rated speed in rpm +Ia=150 // rated current in A +Ra=0.06 // armature resistance in ohms +Vs=220 // source voltage in v +f=50 //frequency of the source voltage in hz +La=0.85e-3 // armature curcuit inductance in H + +//Solution +E=V-Ia*Ra //back emf +Vm=sqrt(2)*Vs //peak voltage +Wm=2*%pi*N/60 //synchronous angular speed + +//(i)When the speed is 400 rpm and firing angle is 60 degrees +N1=400 //given speed in rpm +alpha=60 //firing angle in degrees +W=2*%pi*f +x=W*La/Ra +phi=atan(x) +cot_phi=1/tan(phi) +Z=sqrt(Ra**2+(W*La)**2) +K=E/Wm + +y=Ra*Vm/Z/K +a=(1+exp(-(%pi*cot_phi)))/(exp(-(%pi*cot_phi))-1) +alpha=alpha*%pi/180 +Wmc=y*sin(alpha-phi)*a //required angular speed in rps +Nmc=Wmc*60/2/%pi //required angular speed in rpm + +E1=N1/N*E + +//The equation Vm/Z*sin(beta-phi)-E/Ra+(E/Ra-Vm/Z*sin(alpha-phi))*exp(-(beta-alpha)*cot_phi)=0 +//can be solved using trial method such that beta=230 degrees +beta=230 //in degrees +beta=beta*%pi/180//in radians + +Va=(Vm*(cos(alpha)-cos(beta))+(%pi+alpha-beta)*E1)/%pi +Ia=(Va-E1)/Ra +T1=K*Ia + +//(ii)When the speed is -400 rpm and firing angle is 120 degrees +Le=2e-3 //external inductance added to the armature +L=La+Le +N2=-400 //given speed in rpm +alpha=120 //firing angle in degrees +x=W*L/Ra +phi=atan(x) +cot_phi=1/tan(phi) +Z=sqrt(Ra**2+(W*L)**2) +K=E/Wm + +y=Ra*Vm/Z/K +alpha=alpha*%pi/180 +a=(1+exp(-(%pi*cot_phi)))/(exp(-(%pi*cot_phi))-1) +Wmc=y*sin(alpha-phi)*a //required angular speed in rps +Nmc1=Wmc*60/2/%pi //required angular speed in rpm +//The motor is operating under discontinous condition" +E2=N2/N*E + +//The equation Vm/Z*sin(beta-phi)-E/Ra+(E/Ra-Vm/Z*sin(alpha-phi))*exp(-(beta-alpha)*cot_phi)=0 +//can be solved using trial method such that beta=281 degrees +beta=281 //in degrees +beta=beta*%pi/180//in radians + +Va=(Vm*(cos(alpha)-cos(beta))+(%pi+alpha-beta)*E2)/%pi +Ia=(Va-E2)/Ra +T2=K*Ia + +//(iii)When the speed is -600 rpm and firing angle is 120 degrees +N3=-600 //speed in rpm +alpha=120 //firing angle in degrees +alpha=alpha*%pi/180 +Va=2*Vm/%pi*cos(alpha) +E3=N3/N*E //since Va=E1+Ia*Ra +Ia=(Va-E3)/Ra +T3=K*Ia + +//Results +mprintf("(i)Hence the required torque is :%.2f N-m",T1) +mprintf("\n(ii)Hence the required torque is :%.1f N-m",T2) +mprintf("\n(iii)Hence the required torque is :%.1f N-m",T3) +//There is a minor difference in the answers because of accuracy diff --git a/3731/CH5/EX5.15/Ex5_15.sce b/3731/CH5/EX5.15/Ex5_15.sce new file mode 100644 index 000000000..9e719a1ed --- /dev/null +++ b/3731/CH5/EX5.15/Ex5_15.sce @@ -0,0 +1,62 @@ +//Chapter 5:Dc Motor Drives +//Example 15 +clc; + +//Variable Initialization + +V=200 // rated voltage in v +N=875 // rated speed in rpm +Ia=150 // rated current in A +Ra=0.06 // armature resistance in ohms +Vs=220 // source voltage in v +f=50 //frequency of the source voltage in hz +La=2.85e-3 // armature curcuit inductance in H + +//Solution +E=V-Ia*Ra //back emf +Vm=sqrt(2)*Vs //peak voltage +Wm=2*%pi*N/60 //angular speed +W=2*%pi*f + +alpha=120 //firing angle in degrees +x=W*La/Ra +phi=atan(x) +cot_phi=1/tan(phi) +Z=sqrt(Ra**2+(W*La)**2) +K=E/Wm + +y=Ra*Vm/Z/K +a=(1+exp(-(%pi*cot_phi)))/(exp(-(%pi*cot_phi))-1) +alpha=alpha*%pi/180 +Wmc=y*sin(alpha-phi)*a //required angular speed in rps +Nmc=Wmc*60/2/%pi //required angular speed in rpm + +Va=2*Vm/%pi*cos(alpha) +E1=Nmc/N*E //value of back emf at the critical speed of Nmc +Ia=(Va-E1)/Ra +Tc=K*Ia + +//(i)When the torque is 1200 N-m and firing angle is 120 degrees +T2=1200 //given torque in N-m +Ia2=T2/K //given terminal current for the given torque and the answer in the book is wrong +E2=Va-Ia*Ra +N2=E2/E*N + +//(ii)When the torque is 300 N-m and firing angle is 120 degrees +T=300 //required torque in N-m +beta=233.492 //required angle in degrees +beta=beta*%pi/180 //in radians +x=beta-alpha +E1=(Vm*(cos(alpha)-cos(beta)))/x-(%pi*Ra*T)/(K*x) +N1=E1/E*N //required speed + + +//Results +mprintf("\nThe motor is operating under continuous condition") +mprintf("\nThe torque Tc is :%.2f N-m",Tc) +//The answer for torque Tc in the book is wrong due to accuracy which leads to other incorrect answers +mprintf("\n(i)Hence the required speed is :%.1f rpm",N2) +mprintf("\n(ii)The equation Vm/Z*sin(beta-phi)-sin(alpha-phi))*exp(-(beta-alpha)*cot_phi)=") +mprintf("\n(Vm*(cos(alpha)-cos(beta))/Ra/(beta-alpha)-pi*T/K/(beta-alpha) )*(1-exp(-(beta-alpha)*cot_phi)") +mprintf("\ncan be solved using trial method such that beta=233.492 degrees") +mprintf("\n Hence the required speed is :%.1f rpm",N1) diff --git a/3731/CH5/EX5.16/Ex5_16.sce b/3731/CH5/EX5.16/Ex5_16.sce new file mode 100644 index 000000000..3e7e9948f --- /dev/null +++ b/3731/CH5/EX5.16/Ex5_16.sce @@ -0,0 +1,62 @@ +//Chapter 5:Dc Motor Drives +//Example 16 +clc; + +//Variable Initialization + +//Ratings of the separately excited motor +V=220 // rated voltage in v +N=960 // rated speed in rpm +Ia=12.8 // rated current in A +Ra=2 // armature resistance in ohms +Vs=230 // source voltage in v +f=50 //frequency of the source voltage in hz +La=150e-3 // armature curcuit inductance in H + +//Solution +E=V-Ia*Ra //back emf +Vm=sqrt(2)*Vs //peak voltage +Wm=2*%pi*N/60 //angular speed +W=2*%pi*f + +//(i)When speed is 600rpm and the firing angle is 60 degrees +alpha=60 //firing angle in degrees +N1=600 //motor speed in rpm +x=W*La/Ra +phi=atan(x) +cot_phi=1/tan(phi) +Z=sqrt(Ra**2+(W*La)**2) +K=E/Wm + +y=Ra*Vm/Z/K +alpha=alpha*%pi/180 +b=sin(phi)*exp(-(alpha*cot_phi)) +c=sin(alpha-phi)*exp(-(%pi*cot_phi)) +a=1-exp(-(%pi*cot_phi)) +Wmc=y*(b-c)/a //required angular speed in rps +Nmc=Wmc*60/2/%pi //required angular speed in rpm + +Va=Vm/%pi*(1+cos(alpha)) +E1=N1/N*E //value of back emf at the speed of N1 +Ia=(Va-E1)/Ra +T=K*Ia + +//(ii)When the torque is 20 N-m and firing angle is 60 degrees +T1=20 //required torque in N-m +alpha=60 //required firing angle in degrees +Ec=Nmc/N*E //motor back emf at critical speed of Nmc +Tc=K*(Va-Ec)/Ra //torque at the critical speed + +Ia=T1/K +E1=Va-Ia*Ra +N1=E1/E*N //required speed + +//Results +//if N1<Nmc then +mprintf("(i)The motor is operating under continuous condition") +mprintf("\nHence the required torque is :%.2f N-m",T) +//end +//if Tc<T1 then +mprintf("\n(ii)The motor is operating under continuous condition") +mprintf("\nHence the required speed is :%.1f rpm",N1) +//end diff --git a/3731/CH5/EX5.17/Ex5_17.sce b/3731/CH5/EX5.17/Ex5_17.sce new file mode 100644 index 000000000..c07442049 --- /dev/null +++ b/3731/CH5/EX5.17/Ex5_17.sce @@ -0,0 +1,45 @@ +//Chapter 5:Dc Motor Drives +//Example 17 +clc; + +//Variable Initialization + +//Ratings of the separately excited motor +V=220 // rated voltage in V +N=1500 // rated speed in rpm +Ia=50 // rated current in A +Ra=0.5 // armature resistance in ohms +Vl=440 // line voltage inV with 3-phase ac supply +f=50 //frequency of the source voltage in Hz + +//Solution +//(i) Tranformer ratio +alpha=0 //firing angle in degrees +Va=V //motor terminal voltage is equal to the rated voltage when the firing angle is 0 degrees +Vm=%pi/3*Va/cos(alpha) +Vrms=Vm/sqrt(2) //rms value of the converter input voltage +a=(Vl/sqrt(3))/Vrms //required transformer ratio + +//(ii)Value of the firing angle +E=V-Ia*Ra //back emf at the rated speed + +//(a)When the speed of the motor is 1200 rpm and rated torque +N1=1200 //speed of the motor i rpm +E1=N1/N*E //back emf at the given speed N1 +Va=E1+Ia*Ra //terminal voltage at the given speed N1 +alpha=acos(%pi/3*Va/Vm) //required firing angle in radians +alpha1=alpha*180/%pi //required firing angle in degrees + +//(b)When the speed of the motor is -800 rpm and twice the rated torque +N1=-800 //speed of the motor in rpm +E1=N1/N*E //back emf at the given speed N1 +Ia=2*Ia //torque is directly proportional to the current hence twice the rated current +Va=E1+Ia*Ra //terminal voltage at the given speed N1 +alpha=acos(%pi/3*Va/Vm) //required firing angle in radians +alpha2=alpha*180/%pi //required firing angle in degrees + + +//Results +mprintf("(i)Hence the required transformer ratio is :%.3f",a) +mprintf("\n(ii)(a)Hence the required firing angle is :%.2f °",alpha1) +mprintf("\n(b)Hence the required firing angle is :%.2f °",alpha2) diff --git a/3731/CH5/EX5.18/Ex5_18.sce b/3731/CH5/EX5.18/Ex5_18.sce new file mode 100644 index 000000000..342b13451 --- /dev/null +++ b/3731/CH5/EX5.18/Ex5_18.sce @@ -0,0 +1,57 @@ +//Chapter 5:Dc Motor Drives +//Example 18 +clc; + +//Variable Initialization + +//The separately excited motor is fed from a circulating dual converter +V=220 // rated voltage in V +N=1500 // rated speed in rpm +Ia=50 // rated current in A +Ra=0.5 // armature resistance in ohms +Vl=165 // line voltage in V +f=50 // frequency of the source voltage in Hz + +//Solution +E=V-Ia*Ra //back emf at the rated speed +Vm=Vl*sqrt(2) //peak voltage + +//(i)During motoring operation when the speed is 1000 rpm and at rated torque +N1=1000 //speed of the motor in rpm +E1=N1/N*E //back emf at the given speed N1 +Va=E1+Ia*Ra //terminal voltage at the given speed N1 +alpha_A=acos(%pi/3*Va/Vm) +alpha_A=alpha_A*180/%pi//required converter firing angle in degrees +alpha_B=180-alpha_A + +//(ii)During braking operation when the speed is 1000 rpm and at rated torque +N1=1000 //speed of the motor in the book is given as 100 rpm which is wrong +E1=N1/N*E //back emf at the given speed N1 +Va=E1-Ia*Ra //terminal voltage at the given speed N1 +alpha_A1=acos(%pi/3*Va/Vm) +alpha_A1=alpha_A1*180/%pi//required converter firing angle in degrees +alpha_B1=180-alpha_A1 + +//(iii)During motoring operation when the speed is -1000 rpm and at rated torque +N1=-1000 //speed of the motor in rpm +E1=N1/N*E //back emf at the given speed N1 +Va=E1-Ia*Ra //terminal voltage at the given speed N1 +alpha_A2=acos(%pi/3*Va/Vm) +alpha_A2=alpha_A2*180/%pi//required converter firing angle in degrees +alpha_B2=180-alpha_A2 + +//(iv)During braking operation when the speed is -1000 rpm and at rated torque +N1=-1000 //speed of the motor in the book it is given as 100 rpm which is wrong +E1=N1/N*E //back emf at the given speed N1 +Va=E1+Ia*Ra //terminal voltage at the given speed N1 +alpha_A3=acos(%pi/3*Va/Vm) +alpha_A3=alpha_A3*180/%pi//required converter firing angle in degrees +alpha_B3=180-alpha_A3 + +//Results +mprintf("\n(i)Hence the required firing angle is :%.1f °",alpha_B) +mprintf("\n(ii)Hence the required firing angle is :%.1f °",alpha_B1) +mprintf("\n(iii)Hence for negative speed during motoring operation the required firing angles are :") +mprintf("\nalpha_A :%.1f ° and alpha_B :%.1f °",alpha_A2,alpha_B2) +mprintf("\n(iv)Hence for negative speed during braking operation the required firing angles are :") +mprintf("\nalpha_A :%.1f ° and alpha_B :%.1f °",alpha_A3,alpha_B3) diff --git a/3731/CH5/EX5.19/Ex5_19.sce b/3731/CH5/EX5.19/Ex5_19.sce new file mode 100644 index 000000000..aff7bfc47 --- /dev/null +++ b/3731/CH5/EX5.19/Ex5_19.sce @@ -0,0 +1,46 @@ +//Chapter 5:Dc Motor Drives +//Example 19 +clc; + +//Variable Initialization + +//Ratings of the separately excited motor +V=230 // rated voltage in V +N=960 // rated speed in rpm +Ia=200 // rated current in A +Ra=0.02 // armature resistance in ohms +Vs=230 // source voltage in V + +//Solution +E=V-Ia*Ra //back emf + +//(i) When the speed of motor is 350 rpm with the rated torque during motoring operation +N1=350 //given speed in rpm +E1=N1/N*E //given back emf at N1 +Va=E1+Ia*Ra //motor terminal voltage +delta=Va/V //duty ratio + +//(ii) When the speed of motor is 350 rpm with the rated torque during braking operation +Va=E1-Ia*Ra //motor terminal voltage +delta1=Va/V //duty ratio + +//(iii)Maximum duty ratio is 0.95 +delta2=0.95 //maximum duty ratio +Va=delta2*V //terminal voltage +Ia1=2*Ia //maximum permissable current +E1=Va+Ia1*Ra //back emf +N1=E1/E*N //maximum permissible speed +Pa=Va*Ia1 //power fed to the source + +//(iv) If the speed of the motor is 1200 rpm and the field of the motor is also controlled +N2=1200 //given speed in rpm +//Now the field current is directly proportional to the speed of the motor +If=N/N2 //field current as a ratio of the rated current + + +//Results +mprintf("(i) Duty ratio is :%.3f",delta) +mprintf("\n(ii)Duty ratio is :%.2f",delta1) +mprintf("\n(iii)Maximum permissible speed is :%d rpm",N1) +mprintf("\nPower fed to the source is :%.1f kW",Pa/1000) +mprintf("\n(iv)Field current as a ratio of the rated current is :%.1f",If) diff --git a/3731/CH5/EX5.2/Ex5_2.sce b/3731/CH5/EX5.2/Ex5_2.sce new file mode 100644 index 000000000..6bb6466c9 --- /dev/null +++ b/3731/CH5/EX5.2/Ex5_2.sce @@ -0,0 +1,27 @@ +//Chapter 5:DC Motor Drives +//Example 2 +clc; + +//Variable Initialization + +V1=220 //rated voltage in V +Ia1=100 //rated current in A +N1=1000 //rated speed in rpm clockwise +Ra=0.05 //armature resistance in ohms +Rs=0.05 //field resistance in ohms + +//Solution +//Turns is reduced to 80% then flux is also reduced by the same value and hence current is also reduced +T1=Ia1**2 //flux is directly proportional to current Ia +T2=0.8*1**2 //flux is directly proportional to current Ia +Ia2=-Ia1/sqrt(0.8) //since T1=T2 and the direction is opposite + +E1=V1-Ia1*(Ra+Rs) + +Rs=.8*Rs //Rs=80% of the field resistance 0.05ohm since the flux is reduced to 80% +E2=-(V1+Ia2*(Ra+Rs)) + +N2=(E2/E1)*(Ia1/Ia2)*(N1/0.8) //since E=Kn*flux*N + +//Result +mprintf("\nMotor speed is:N2=%.1f rpm",N2) diff --git a/3731/CH5/EX5.20/Ex5_20.sce b/3731/CH5/EX5.20/Ex5_20.sce new file mode 100644 index 000000000..f3e6054c5 --- /dev/null +++ b/3731/CH5/EX5.20/Ex5_20.sce @@ -0,0 +1,34 @@ +//Chapter 5:Dc Motor Drives +//Example 20 +clc; + +//Variable Initialization + +//Ratings of the separately excited motor when it is operated in dynamic breaking +V=230 // rated voltage in V +N=960 // rated speed in rpm +Ia=200 // rated current in A +Ra=0.02 // armature resistance in ohms +Vs=230 // source voltage in V +Rb=2 // braking resistance in ohm + +//Solution +//When the motor speed is 600 rpm and the braking torque is twice the rated value +Ia1=2*Ia //torque is directly proportional to current +N1=600 //speed of the motor in rpm +E=V-Ia*Ra //back emf +E1=N1/N*E +x=E1/Ia1-Ra //x=(1-delta)*Rb +y=x/Rb //y=1-delta +delta=1-y //duty ratio + +//(ii)If the duty ratio is 0.6 and and the braking torque is twice the rated value +delta1=0.6 //duty ratio +Ia1=2*Ia //torque is directly proportional to current +E1=Ia1*((1-delta1)*Rb+Ra) //back emf +N1=E1/E*N + + +//Results +mprintf("(i)Duty ratio is :%.2f",delta) +mprintf("\n(ii)Hence the motor speed is :%.1f rpm",N1) diff --git a/3731/CH5/EX5.21/Ex5_21.sce b/3731/CH5/EX5.21/Ex5_21.sce new file mode 100644 index 000000000..eede688eb --- /dev/null +++ b/3731/CH5/EX5.21/Ex5_21.sce @@ -0,0 +1,38 @@ +//Chapter 5:Dc Motor Drives +//Example 21 +clc; + +//Variable Initialization + +//Ratings of the series motor +N=600 //speed in rpm +Vs=220 //source voltage in V +Ra_Rf=0.12 //combine armature resistance field resistance + +//Magnetisation curve at N +If=[10, 20,30, 40, 50, 60, 70, 80] //field current in A +E =[64,118,150,170,184,194,202,210] //terminal voltage in V + +//Solution +//(i)When the duty ratio is 0.6 and motor current is 60 A +delta=0.6 //duty ratio +Ia1=60 //motor current in A +Va1=delta*Vs //terminal voltage for the given duty ratio +E1=Va1-Ia1*Ra_Rf //back emf for the given duty ratio + +//For Ia1=60 A the terminal voltage is 194 V as given in the magnetization curve +N1=E1/E(6)*N //motor speed for the given duty ratio + +//(ii)When the speed is 400rpm and the duty ratio is 0.65 +delta=0.65 //duty ratio +N2=400 //speed in rpm +Va1=delta*Vs //terminal voltage for the given duty ratio + +//From the magnetization characteristic for the speed of 400rpm the current Ia=70 A +E1=Va1-If(7)*Ra_Rf //back emf for the given duty ratio +T=(E1*If(7))/N2/(2*%pi/60) //required torque + + +//Results +mprintf("(i)Hence the motor speed is :%.1f rpm",N1) +mprintf("\n(ii)Hence the required torque is :%.1f N-m",T) diff --git a/3731/CH5/EX5.22/Ex5_22.sce b/3731/CH5/EX5.22/Ex5_22.sce new file mode 100644 index 000000000..45a1f3d02 --- /dev/null +++ b/3731/CH5/EX5.22/Ex5_22.sce @@ -0,0 +1,51 @@ +//Chapter 5:Dc Motor Drives +//Example 22 +clc; + +//Variable Initialization + +//The motor is operated using regenarative braking method +N=600 //speed in rpm +Vs=220 //source voltage in V +Ra_Rf=0.12 //combine armature resistance field resistance + +//Magnetisation curve at N +If=[10, 20,30, 40, 50, 60, 70, 80] //field current in A +E =[64,118,150,170,184,194,202,210] //terminal voltage in V + +//Solution +//(i)When the duty ratio is 0.5 and the braking torque is equal to the motor torque +delta=0.5 //duty ratio +Va1=delta*Vs //terminal voltage +Ia1=If(7) //current at rated motor torque +E1=Va1+Ia1*Ra_Rf //back emf for the given duty ratio +N1=E1/E(7)*N //for a current of 70 A E=202 V from the magnetization curve + +//(ii)When maximum permisssible duty ratio is 0.95 and current is 70A +delta_max=0.95 //maximum duty ratio +Va1=delta_max*Vs //terminal voltage +Ia1=70 //maximum permissible current in A +E2=Va1+Ia1*Ra_Rf //back emf for the given duty ratio +N2=E2/E(7)*N //for a current of 70 A E=202 V + +//(iii)When the motor speed is 1000rpm and maximum current is 70A with duty ratio in the range of 0.05 to 0.95 +Ia1=70 //maximum permissible current in A +N3=1000 //given speed in rpm +delta_max=0.95 //maximum duty ratio +E3=N3/N*E(7) //terminal voltage +x=(E3-delta_max*Vs)/Ia1 //x=R+Ra_Rf where R is the required external resistance +R=x-Ra_Rf //external resistance + +//(iv)when the motor is running at 1000rpm with current at 70 +Ia1=70 //maximum permissible current in A +N4=1000 //given speed in rpm +Ra=Ra_Rf //total value of armature resistance is assumed to be the same +E4=Va1+Ia1*Ra //back emf for the given speed N4 +E_=N/N4*E4 +ratio=E_/E(7) //fraction of the requuired number of turns to be reduced + +//Results +mprintf("(i)Hence the motor speed is :%.1f rpm",N1) +mprintf("\n(ii)Hence the motor speed is :%.1f rpm",N2) +mprintf("\n(iii)Hence the required external resistance is :%.1f ohm",R) +mprintf("\n(iv)Hence fraction of the number of turns to be reduced is :%.3f",ratio) diff --git a/3731/CH5/EX5.23/Ex5_23.sce b/3731/CH5/EX5.23/Ex5_23.sce new file mode 100644 index 000000000..b6ec994f6 --- /dev/null +++ b/3731/CH5/EX5.23/Ex5_23.sce @@ -0,0 +1,38 @@ +//Chapter 5:Dc Motor Drives +//Example 23 +clc; + +//Variable Initialization + +//The motor is operated using dynamic braking method +N=600 //speed in rpm +Vs=220 //source voltage in v +Ra=0.12 // armature resistance in ohms +delta_min=0.1 //manimum value of duty ratio +delta_max=0.9 //maximum value of duty ratio + +//Magnetisation curve at N +If=[10, 20,30, 40, 50, 60, 70, 80] //field current in A +E =[64,118,150,170,184,194,202,210] //terminal voltage in V + +//Solution +//(i) Maximum braking speed is 800rpm with armature current of 70 A +N1=800 //maximum braking speed in rpm +Ia=70 //armature current in A +E1=N1/N*E(7) //at 70A motor back emf is 202V +Rbe=E1/Ia-Ra //effective value of braking resistance +Rb=Rbe/(1-delta_min) //required braking resistance + +//(ii)When the speed of the motor is 87 rpm +//now torque is maximum when the duty ratio is maximum +N1=87 //speed in rpm +R=Rb*(1-delta_max)+Ra + +Ia=If(5) //value of armature current for the given value of E=184V +Ke_phi=E(5)/(2*%pi*N)*60 +T=Ke_phi*Ia //required torque + + +//Results +mprintf("(i)Hence braking resistance is:%.2f ohm",Rb) +mprintf("\n(ii)Hence the required torque is :%.1f N-m",T) diff --git a/3731/CH5/EX5.3/Ex5_3.sce b/3731/CH5/EX5.3/Ex5_3.sce new file mode 100644 index 000000000..79a209292 --- /dev/null +++ b/3731/CH5/EX5.3/Ex5_3.sce @@ -0,0 +1,22 @@ +//Chapter 5:Dc Motor Drives +//Example 3 +clc; + +//Variable Initialization + +//Motor ratings +V1=220 //rated voltage in V +Ia1=200 //rated current in A +Ra=0.06 //armature resistance in ohms +Rb=0.04 //internal resistance of the variable source in ohms +N1=800 //speed in rpm +N2=600 //speed when motor is operatingin regenerative braking in rpm + +//Solution +Ia2=0.8*Ia1 //motor is opereting in regenerative braking at 80% of Ia1 +E1=V1-Ia1*Ra //back emf at rated operation +E2=(N2/N1)*E1 //back emf at the given speed N2 +V2=E2-Ia2*(Ra+Rb) //internal voltage of thevariable source + +//Results +mprintf("\n Internal voltage of the variable source:%.1f V",V2) diff --git a/3731/CH5/EX5.4/Ex5_4.sce b/3731/CH5/EX5.4/Ex5_4.sce new file mode 100644 index 000000000..0774feecb --- /dev/null +++ b/3731/CH5/EX5.4/Ex5_4.sce @@ -0,0 +1,25 @@ +//Chapter 5:DC Motor Drives +//Example 4 +clc; + +//Variable Initialization + +//The ratings of the motor are same as that of Ex-5.2 +V1=220 //rated voltage in V +Ia1=100 //rated current in A +N1=1000 //speed in rpm clockwise +N2=800 //given speed during the dynamic braking in rpm +Ra=0.05 //armature resistance in ohms +Rs=0.05 //field resistance in ohms + +//Solution + +T2 = 2 //dynamic torque is twice the rated torque +Ia2=Ia1*sqrt(T2) //since T=Kf*Ia**2 +E1=V1-Ia1*(Ra+Rs) +E2=(Ia2/Ia1)*(N2/N1)*E1 //since E=Ke*Ia*N +Rb=E2/Ia2-(Ra+Rs) //since E2=Ia2(Rb+Ra+Rs) during braking + +//Results +mprintf("\n Braking current Ia2: %.1f A",Ia2) +mprintf("\n Required braking resistance Rb: %.2f ohm",Rb) diff --git a/3731/CH5/EX5.5/Ex5_5.sce b/3731/CH5/EX5.5/Ex5_5.sce new file mode 100644 index 000000000..168a12d7e --- /dev/null +++ b/3731/CH5/EX5.5/Ex5_5.sce @@ -0,0 +1,61 @@ +//Chapter 5:Dc Motor Drives +//Example 5 +clc; + +//Variable Initialization + +//Ratings of the DC shunt motor which operated under dynamic braking +Rb=1 //braking resisance in ohms +Ra=0.04 //armature resistance in ohms +Rf=10 //field resistance in ohms +T=400 //load torque in N-m + +//Magnetisation curve at N1 +N1=600 //speed in rpm +If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25] //field current in A +E =[25,50,73.5,90,102.5,110,116,121,125,129] //back emf in V + +//Solution +disp(If,"Field current If:in A") +x=(Rb+Rf)/Rb +Ia = If * x //armature current +Wm=2*%pi*N1/60 +Ke_flux=E / Wm //Ke*flux=constant +T=[] +for i=1:10 +T($+1)=(Ke_flux(i))*(Ia(i)) //torque +end +disp(Ke_flux,"Ke_flux :") +disp(T,"Torque :in N-m") + + +//Results + +//Plotting the values of Ke*flux vs If +If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25] //field current in A +subplot(2,1,1) +plot(If,Ke_flux,'y') +xlabel('field current I_f') +ylabel('Ke*flux') +title('If vs Ke*flux') +xgrid(2) + +//Plotting the values of T vs If +If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25] //field current in A +subplot(2,1,2) +plot(T,If) +xlabel('Torque T') +ylabel('field current I_f') +title('T vs If') +xgrid(2) + + +mprintf("\nFrom the plot we can see that when the torque is 400 N-m, ") +mprintf("\nthe field current is If=19.3 A, and Ke*flux=1.898 when If=19.3 A") +T=400 // braking torque in N-m +If=19.13 // field current in A +Ke_flux=1.898 // Ke*flux +Ia=x*If +E=If*Rf+Ia*Ra //since E=V+Ia*Ra +N2=(E/Ke_flux)*(60/(2*%pi)) //required speed +mprintf("\nHence the required speed in is :%.1f rpm",N2) diff --git a/3731/CH5/EX5.6/Ex5_6.sce b/3731/CH5/EX5.6/Ex5_6.sce new file mode 100644 index 000000000..7240174df --- /dev/null +++ b/3731/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,68 @@ +//Chapter 5:Dc Motor Drives +//Example 6 +clc; + +//Variable Initialization + +//The motor rating is same as that of Ex-5.5 +N=600 //value of the speed given from the magnetization curve in Ex-5.5 + +Ra=0.04 //armature resistance in ohms +Rf=10 //field resistance in ohms +T=400 //load torque in N-m +N1=1200 //given speed in rpm to hold the overhauling torque + +//Solution +Wm=2*%pi*N1/60 //angular speed at the given speed N1 + +//Magnetisation curve at N=600rpm +If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25] //field current in A +E =[25,50,73.5,90,102.5,110,116,121,125,129] //value of the back emf as given in Ex-5.5 for the speed N in V + +//Magnetisation curve at N=1200rpm +If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25] //field current in A +E1=N1/N*E //back emf at the speed N1 +mprintf("Hence the magnetization curve at 1200rpm is") +disp(If,"Field current If:in A") +disp(E1,"Back emf is E1 in V:") + +Pd=T*Wm //power developed +x=Pd*Ra +V=[] +for i=1:10 +V($+1)=E1(i)-x/E1(i) +end +disp(V,"Terminal voltage V:in V") + +//Results +//Plotting the values of V vs If +subplot(2,1,1) +plot(V,If) +xlabel('Terminal voltage V') +ylabel('Field current I_f') +title('V vs If') +xgrid(2) + +//Plotting the values of E vs If +If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25] //field current in A +E =[25,50,73.5,90,102.5,110,116,121,125,129] //value of the back emf as given in Ex-5.5 for the speed N in V +E1=N1/N*E //back emf at the speed N1 + +subplot(2,1,2) +plot(E1,If,'y') +xlabel('E') +ylabel('Field current I_f') +title('E vs If') +xgrid(2) + +mprintf("\nFrom the plot we can see that when the current If=25 A the terminal voltage is V=250 V with the back emf E=258V") + +E=258 //value of the back emf in V at from the plot +V=250 //value of terminal voltage in V from the plot at E=258 V +If=25 //value of If in A from the plot at E=258 V +Ia=(E-V)/Ra //armature current +If=V/Rf //field current +Ir=Ia-If +Rb=V/Ir //braking resistance + +mprintf("\nHence the rquired braking resistance is %.3f ohm",Rb) diff --git a/3731/CH5/EX5.7/Ex5_7.sce b/3731/CH5/EX5.7/Ex5_7.sce new file mode 100644 index 000000000..c4238f101 --- /dev/null +++ b/3731/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,53 @@ +//Chapter 5:Dc Motor Drives +//Example 7 +clc; + +//Variable Initialization + +//Ratings of the DC series motor which operated under dynamic braking +Ra=0.5 //total resistance of armature and field windings in ohms +Rf=10 //field resistance in ohms +T=500 //overhauling load torque in N-m +N=600 //speed at the overhauling torque T in rpm + +//Nagnetisation curve at a speed of 500 rpm +N1=500 //speed in rpm +Ia=[20, 30, 40, 50, 60, 70, 80] //armature current in A +E =[215,310,381,437,482,519,550] //back emf in V + +//Solution +Wm1=2*%pi*N1/60 +disp(Ia,"Armature current : in A") +Ke_flux=E / Wm1 //Ke*flux=constant +disp(Ke_flux,"Ke_flux :") +T=[] +for i=1:7 +T($+1)=(Ke_flux(i))*(Ia(i)) //torque +end +disp(T,"Torque :in N-m") + + +//Results +//Plotting the values of Ke*flux vs Ia and T vs Ia +subplot(2,1,1) +plot(Ia,Ke_flux,'y') +xlabel('Armature current I_a') +ylabel('Ke*flux') +title('Ke*flux vs Ia') +xgrid(2) + +subplot(2,1,2) +plot(T,Ia) +xlabel('Torque T') +ylabel('Armature current I_a') +title('T vs Ia') +xgrid(2) + +mprintf("\nFrom the plot we can see that at the given torque T=500 N-m the current Ia is 56 A, and Ke*flux is 8.9 at Ia=56 A") +Ke_flux=8.9 //value of Ke*flux at T=500 N-m from the plot +Ia=56 //value of Ia at at T=500 N-m from the plot +Wm=2*%pi*N/60 +E=Ke_flux*Wm //required emf +x=E/Ia //x=Ra+Rb +Rb=x-Ra //required braking resistance +mprintf("\nHence the rquired braking resistance is %.3f ohm",Rb) diff --git a/3731/CH5/EX5.8/Ex5_8.sce b/3731/CH5/EX5.8/Ex5_8.sce new file mode 100644 index 000000000..02f4e22e9 --- /dev/null +++ b/3731/CH5/EX5.8/Ex5_8.sce @@ -0,0 +1,37 @@ +//Chapter 5:Dc Motor Drives +//Example 8 +clc; + +//Variable Initialization + +//Ratings of the separately excited motor +V=220 // rated voltage in V +N=970 // rated speed in rpm +Ia=100 // rated current in A +Ra=0.05 // armature resistance in ohms +N1=1000 // initial speed of the motor in rpm + +//Solution +E=V-Ia*Ra +E1=N1/N*E //value of back emf at the speed N1 + +//(a)The resistance to be placed +Ia1=2*Ia //value of the braking current is twice the rated current +Rb=(E1+V)/Ia1-Ra //required resistance + +//(b)The braking torque +Wm=(2*%pi*N1)/60 +T=E1*Ia1/Wm + +//(c)When the speed has fallen to zero the back emf is zero +E2=0 +Ia2=V/(Ra+Rb) +T2=Ia2/Ia1*T //since the torque is directly proportional to the current + + +//Results +mprintf("(a)Hence required resistance is :%.2f ohm",Rb) +//Answer given for the resistance in the book is wrong + +mprintf("\n(b)Hence the required braking torque is :%.1f N-m",T) +mprintf("\n(c)Hence the required torque is :%.1f N-m",T2) diff --git a/3731/CH5/EX5.9/Ex5_9.sce b/3731/CH5/EX5.9/Ex5_9.sce new file mode 100644 index 000000000..d98a78d64 --- /dev/null +++ b/3731/CH5/EX5.9/Ex5_9.sce @@ -0,0 +1,79 @@ +//Chapter 5:Dc Motor Drives +//Example 9 +clc; + +//Variable Initialization + +//Ratings of the separately excited motor which operates under rheostatic braking +V=220 // rated voltage in V +N=1000 // rated speed in rpm +Ia=175 // rated current in A +Ra=0.08 // armature resistance in ohms +N1=1050 // initial speed of the motor in rpm +J=8 // moment of inertia of the motor load system kg-m2 +La=0.12 // armature curcuit inductance in H + +//Solution +E=V-Ia*Ra +Wm=N*2*%pi/60 //rated speed in rad/s + +//(a)When the braking current is twice the rated current +Ia1=2*Ia +E1=N1/N*E +x=E1/Ia1 //x=Rb+Ra +Rb=x-Ra //required braking resistance + +//(b)To obtain the expression for the transient value of speed and current including the effect of armature inductance +Ra=x //total armature current +K1=N1*2*%pi/60 //initial speed in rad/s +K=E/Wm +B=0 +ta=La/Ra //time constant in sec +Trated=E*Ia/Wm //rated torque +Tl=0.15*Trated //load torque is 15% of the rated torque +tm1= %inf //tm1=J/B and B=0 which is equal to infinity +tm2=J*Ra/(B*Ra+K**2) + +a = ta +b = -(1+ta/tm1) +c = 1/tm2 + +//Discriminant +d = (b**2) - (4*a*c) + +alpha1 = (-b-sqrt(d))/(2*a) +alpha2 = (-b+sqrt(d))/(2*a) + +K3=tm2*Tl/J +K4=tm2*K*Tl/J/Ra + +//Transient value for speed +x1=((J*alpha2-B)*K1-(Tl-J*alpha2*K3))/(J*(alpha2-alpha1)) +y1=((J*alpha1-B)*K1-(Tl-J*alpha1*K3))/(J*(alpha1-alpha2)) + +//Transient value for the current +x2=(K*K1+alpha2*La*K4)/(La*(alpha2-alpha1)) +y2=(K*K1+alpha1*La*K4)/(La*(alpha1-alpha2)) + + +//(c) To calculate the time taken by braking operation and the maximum value of the armature current +//now Wm=0 for the braking operation and hence 151.5 exp(-0.963*t1)- 8.247 = 0 from the previous answer in (b) +a=K3/x1 //a=exp(-0.963*t1) +t1=-alpha1*log(real(a)) //take log base e on both sides +//now d/dt(ia)=0 for themaximum current and hence d/dt(26.25-593.1exp(-0.963*t)+566.8exp(-4.19*t) = 0 from the previous answer in (b) +b=abs(alpha2*y2)/abs(alpha1*x2) //b=exp(-0.963*t)/exp(-4.19*t) +t2=log(b)/(-alpha1+alpha2) //take log base e on both sides +t2=abs(t2) +ia=K4-real(x2)*exp(real(-alpha1)*t2)-real(y2)*exp(real(-alpha2)*t2) + + +//Results +mprintf("(a)Hence the braking resistance is :%.3f ohm",Rb) +mprintf("\nb)The value of alpha1 :%.3f and alpha2 :%.3f ",real(alpha1),real(alpha2)) +mprintf("\nHence the expression for the transient value for the speed is") +mprintf("\nWm=%.1f exp( -%.3f *t)%.1f exp( -%.2f *t) - %.3f",real(x1),real(alpha1),real(y1),real(alpha2),K3) +mprintf("\nHence the expression for the transient value for the current is") +mprintf("\nia=%.2f -%.1f exp(-%.3f*t) +%.1f exp(%.2f*t)",K4,real(x2),real(alpha1),-real(y2),-real(alpha2)) +mprintf("\n(c)Hence the time taken is :%.2f sec",t2) +mprintf("\nHence the maximum current is:%.2f A",ia) +//There is a slight difference in the answers because of rounding |