Chapter 12 : Electic Drives

Example 12.1, Page No 658

In [1]:
import math
#initialisation of variables
T_e=15.0 #Nm
K_m=0.5 #V-s/rad
I_a=T_e/K_m
n_m=1000.0

#Calculations
w_m=2*math.pi*n_m/60
E_a=K_m*w_m
r_a=0.7
V_t=E_a+I_a*r_a
V_s=230.0
V_m=math.sqrt(2)*V_s
a=math.degrees(math.acos(2*math.pi*V_t/V_m-1))
print("firing angle delay=%.3f deg" %a)
I_Tr=I_a*math.sqrt((180-a)/360)    
print("rms value of thyristor current=%.3f A" %I_Tr)
I_fdr=I_a*math.sqrt((180+a)/360)    
print("rms value of freewheeling diode current=%.3f A" %I_fdr)
pf=V_t*I_a/(V_s*I_Tr)  

#Results  
print("input power factor=%.4f" %pf)

firing angle delay=65.349 deg
rms value of thyristor current=16.930 A
rms value of freewheeling diode current=24.766 A
input power factor=0.5652

Example 12.2, Page No 660

In [2]:
import math
#initialisation of variables
V=230.0
E=150.0
R=8.0

#Calculations
th1=math.sin(math.radians(E/(math.sqrt(2)*V)))
I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180))    
P=E*I_o    
I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))
P_r=I_or**2*R    
pf=(P+P_r)/(V*I_or)

#Results
print("avg charging curent=%.4f A" %I_o)
print("power supplied to the battery=%.2f W" %P)
print("power dissipated by the resistor=%.3f W" %P_r)    
print("supply pf=%.3f" %pf)

avg charging curent=3.5679 A
power supplied to the battery=535.18 W
power dissipated by the resistor=829.760 W
supply pf=0.583

Example 12.3 Page No 661

In [3]:
import math
#initialisation of variablesV_s=250
V_m=math.sqrt(2)*V_s
a=30.0
k=0.03 #Nm/A**2
n_m=1000.0

#Calculations
w_m=2*math.pi*n_m/60
r=.2 #r_a+r_s
V_t=V_m/math.pi*(1+math.cos(math.radians(a)))
I_a=V_t/(k*w_m+r)   
print("motor armature current=%.2f A" %I_a)
T_e=k*I_a**2    
print("motor torque=%.3f Nm" %T_e)
I_sr=I_a*math.sqrt((180-a)/180)
pf=(V_t*I_a)/(V_s*I_sr)    

#Results
print("input power factor=%.2f" %pf)

motor armature current=57.82 A
motor torque=100.285 Nm
input power factor=0.92

Example 12.4, Page No 663

In [4]:
import math
#initialisation of variables
V_s=400.0
V_m=math.sqrt(2)*V_s
V_f=2*V_m/math.pi
r_f=200.0
I_f=V_f/r_f
T_e=85.0
K_a=0.8

#Calculations
I_a=T_e/(I_f*K_a)    
print("rated armature current=%.2f A" %I_a)
n_m=1200.0
w_m=2*math.pi*n_m/60
r_a=0.2
V_t=K_a*I_f*w_m+I_a*r_a
a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))
print("firing angle delay=%.2f deg" %a)
E_a=V_t
w_mo=E_a/(K_a*I_f)
N=60*w_mo/(2*math.pi)
reg=((N-n_m)/n_m)*100    
print("speed regulation at full load=%.2f" %reg)
I_ar=I_a
pf=(V_t*I_a)/(V_s*I_ar)    
print("input power factor of armature convertor=%.4f" %pf)
I_fr=I_f
I_sr=math.sqrt(I_fr**2+I_ar**2)
VA=I_sr*V_s
P=V_t*I_a+V_f*I_f

#Results
print("input power factor of drive=%.4f" %(P/VA))
 #Answers have small variations from that in the book due to difference in the rounding off of digits.

rated armature current=59.01 A
firing angle delay=57.63 deg
speed regulation at full load=6.52
input power factor of armature convertor=0.4821
input power factor of drive=0.5093

Example 12.5 Page No 664

In [5]:
import math
#initialisation of variables
V_s=400.0
V_m=math.sqrt(2)*V_s
V_f=2*V_m/math.pi

#Calculations
a1=math.degrees(math.acos(V_t*math.pi/(2*V_m))) 
print("delay angle of field converter=%.0f deg" %a1)
r_f=200.0
I_f=V_f/r_f
T_e=85.0
K_a=0.8
I_a=T_e/(I_f*K_a)
n_m=1200.0
w_m=2*math.pi*n_m/60
r_a=0.1
I_a=50.0
V_t=-K_a*I_f*w_m+I_a*r_a
a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))

#Results
print("firing angle delay of armature converter=%.3f deg" %a)
print("power fed back to ac supply=%.0f W" %(-V_t*I_a))

delay angle of field converter=58 deg
firing angle delay of armature converter=119.260 deg
power fed back to ac supply=8801 W

Example 12.6 Page No 665

In [6]:
import math
#initialisation of variables
V_t=220.0
n_m=1500.0
w_m=2*math.pi*n_m/60
I_a=10.0
r_a=1.0

#Calculations
K_m=(V_t-I_a*r_a)/(w_m)
T=5.0
I_a=T/K_m
V_s=230.0
V_m=math.sqrt(2)*V_s
a=30.0
V_t=2*V_m*math.cos(math.radians(a))/math.pi
w_m=(V_t-I_a*r_a)/K_m
N=w_m*60/(2*math.pi)    

print("motor speed=%.2f rpm" %N)
a=45
n_m=1000
w_m=2*math.pi*n_m/60
V_t=2*V_m*math.cos(math.radians(a))/math.pi
I_a=(V_t-K_m*w_m)/r_a
T_e=K_m*I_a    

#Results
print("torque developed=%.3f Nm" %T_e)
 #Answers have small variations from that in the book due to difference in the rounding off of digits.

motor speed=1254.22 rpm
torque developed=8.586 Nm

Example 12.7, Page No 666

In [7]:
import math
#initialisation of variables
V_t=220.0
n_m=1000.0
w_m=2*math.pi*n_m/60
I_a=60.0
r_a=.1

#Calculations
K_m=(V_t-I_a*r_a)/(w_m)
V_s=230
V_m=math.sqrt(2)*V_s
print("for 600rpm speed")
n_m=600.0
w_m=2*math.pi*n_m/60
a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m))) 
print("firing angle=%.3f deg" %a)
print("for -500rpm speed")
n_m=-500.0
w_m=2*math.pi*n_m/60
a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m)))
print("firing angle=%.2f deg" %a)
I_a=I_a/2
a=150
V_t=2*V_m*math.cos(math.radians(a))/math.pi
w_m=(V_t-I_a*r_a)/K_m
N=w_m*60/(2*math.pi)    

#Results
print("motor speed=%.3f rpm" %N)

for 600rpm speed
firing angle=49.530 deg
for -500rpm speed
firing angle=119.19 deg
motor speed=-852.011 rpm

Example 12.8 Page No 672

In [8]:
import math
#initialisation of variables
K_m=1.5
T_e=50.0
I_a=T_e/K_m
r_a=0.9
a=45.0
V_s=415.0

#Calculations
V_ml=math.sqrt(2)*V_s
w_m=((3*V_ml*(1+math.cos(math.radians(a)))/(2*math.pi))-I_a*r_a)/K_m
N=w_m*60/(2*math.pi)    

#Results
print("motor speed=%.2f rpm" %N)

motor speed=2854.42 rpm

Example 12.9 Page No 672

In [9]:
import math
#initialisation of variablesV_t=600
n_m=1500.0
w_m=2*math.pi*n_m/60
I_a=80.0
r_a=1.0

#Calculations
K_m=(V_t-I_a*r_a)/(w_m)
V_s=400.0
V_m=math.sqrt(2)*V_s
print("for firing angle=45deg and speed=1200rpm")
a=45.0
n_m=1200.0
w_m=2*math.pi*n_m/60
I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a
I_sr=I_a*math.sqrt(2/3)    
print("rms value of source current=%.3f A" %I_sr)
print("rms value of thyristor current=%.3f A" %(I_a*math.sqrt(1/3)))
print("avg value of thyristor current=%.2f A" %I_a*(1/3))
pf=(3/(2*math.pi)*(1+math.cos(math.radians(a))))    
print("input power factor=%.3f" %pf)

print("for firing angle=90deg and speed=700rpm")
a=90
n_m=700
w_m=2*math.pi*n_m/60
I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a
I_sr=I_a*math.sqrt(90/180)    


#Results
print("rms value of source current=%.3f A" %I_sr)
print("rms value of thyristor current=%.3f A" %(I_a*math.sqrt(90.0/360)))
print("avg value of thyristor current=%.3f A" %I_a*(1/3))
pf=(math.sqrt(6)/(2*math.pi)*(1+math.cos(math.radians(a))))*math.sqrt(180/(180-a))    
print("input power factor=%.4f" %pf)

for firing angle=45deg and speed=1200rpm
rms value of source current=0.000 A
rms value of thyristor current=0.000 A

input power factor=0.815
for firing angle=90deg and speed=700rpm
rms value of source current=0.000 A
rms value of thyristor current=195.558 A

input power factor=0.5513

Example 12.10 Page No 676

In [10]:
import math
#initialisation of variables
V_s=400.0
V_m=math.sqrt(2)*V_s
a=30
V_t=3*V_m*math.cos(math.radians(a))/math.pi
I_a=21.0
r_a=.1
V_d=2.0
K_m=1.6

#Calculations
w_m=(V_t-I_a*r_a-V_d)/K_m
N=w_m*60/(2*math.pi)    
print("speed of motor=%.1f rpm" %N)

N=2000
w_m=2*math.pi*N/60
I_a=210
V_t=K_m*w_m+I_a*r_a+V_d
a=math.degrees(math.acos(V_t*math.pi/(3*V_m)))
print("firing angle=%.2f deg" %a)
I_sr=I_a*math.sqrt(2.0/3.0)
pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr)    
print("supply power factor=%.3f" %pf)

I_a=21
w_m=(V_t-I_a*r_a-V_d)/K_m
n=w_m*60/(2*math.pi)
reg=(n-N)/N*100    

#Results
print("speed regulation(percent)=%.2f" %reg)

speed of motor=2767.6 rpm
firing angle=48.48 deg
supply power factor=0.633
speed regulation(percent)=5.64

Example 12.11, Page No 677

In [11]:
import math
#initialisation of variables
V_t=230.0
V_l=V_t*math.pi/(3*math.sqrt(2))
V_ph=V_l/math.sqrt(3)
V_in=400     #per phase voltage input

#Calculations
N1=1500.0
I_a1=20.0
r_a1=.6
E_a1=V_t-I_a1*r_a1
n1=1000.0
E_a2=E_a1/1500.0*1000.0
V_t1=E_a1+I_a1*r_a1
a1=math.degrees(math.acos(V_t1*math.pi/(3*math.sqrt(2.0)*V_l)))
I_a2=.5*I_a1
n2=-900.0
V_t2=n2*E_a2/N1+I_a2*r_a1
a2=math.degrees(math.acos(V_t2*math.pi/(3*math.sqrt(2)*V_l))) 

#Results
print("transformer phase turns ratio=%.3f" %(V_in/V_ph))
print("for motor running at 1000rpm at rated torque")
print("firing angle delay=%.2f deg" %a1)
print("for motor running at -900rpm at half of rated torque")
print("firing angle delay=%.3f deg" %a2)

transformer phase turns ratio=4.068
for motor running at 1000rpm at rated torque
firing angle delay=0.00 deg
for motor running at -900rpm at half of rated torque
firing angle delay=110.674 deg

Example 12.12, Page No 678

In [12]:
import math
#initialisation of variablesV_s=400
V_ml=math.sqrt(2)*V_s
V_f=3*V_ml/math.pi
R_f=300.0
I_f=V_f/R_f
T_e=60.0
k=1.1

#Calculations
I_a=T_e/(k*I_f)
N1=1000.0
w_m1=2*math.pi*N1/60
r_a1=.3
V_t1=k*I_f*w_m1+I_a*r_a1
a1=math.degrees(math.acos(V_f*math.pi/(3*V_ml)))
N2=3000
w_m2=2*math.pi*N/60
a2=0
V_t2=3*V_ml*math.cos(math.radians(a))/math.pi
I_f2=(V_t2-I_a*r_a)/(w_m2*k)
V_f2=I_f2*R_f
a2=math.degrees(math.acos(V_f2*math.pi/(3*V_ml)))

#Results
print("firing angle=%.3f deg" %a)
print("firing angle=%.3f deg" %a)

firing angle=48.477 deg
firing angle=48.477 deg

Example 12.13, Page No 679

In [13]:
import math
#initialisation of variables
 #after calculating
 #t=w_m/6000-math.pi/360

N=1000.0

#Calculations
w_m=2*math.pi*N/60
t=w_m/6000-math.pi/360    

#Results
print("time reqd=%.2f s" %t)
 #printing mistake in the answer in book

time reqd=0.01 s

Example 12.14, Page No 679

In [14]:
import math
#initialisation of variables
I_a=1.0 #supposition
a=60.0

#Calculations
I_s1=2*math.sqrt(2)/math.pi*I_a*math.sin(math.radians(a))
I_s3=2*math.sqrt(2)/(3*math.pi)*I_a*math.sin(math.radians(3*a))
I_s5=2*math.sqrt(2)/(5*math.pi)*I_a*math.sin(math.radians(5*a))
per3=I_s3/I_s1*100    
print("percent of 3rd harmonic current in fundamental=%.2f" %per3)
per5=I_s5/I_s1*100    

#Results
print("percent of 5th harmonic current in fundamental=%.2f" %per5)

percent of 3rd harmonic current in fundamental=0.00
percent of 5th harmonic current in fundamental=-20.00

Example 12.15, Page No 680

In [15]:
import math
#initialisation of variables
I_a=60.0
I_TA=I_a/3    

#Calculations
print("avg thyristor current=%.0f A" %I_TA)
I_Tr=I_a/math.sqrt(3)    
print("rms thyristor current=%.3f A" %I_Tr)
V_s=400
V_m=math.sqrt(2)*V_s
I_sr=I_a*math.sqrt(2.0/3)
a=150
V_t=3*V_m*math.cos(math.radians(a))/math.pi
pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr)    
print("power factor of ac source=%.3f" %pf)

r_a=0.5
K_m=2.4
w_m=(V_t-I_a*r_a)/K_m
N=w_m*60/(2*math.pi)    

#Results
print("Speed of motor=%.2f rpm" %N)
 #Answers have small variations from that in the book due to difference in the rounding off of digits.

avg thyristor current=20 A
rms thyristor current=34.641 A
power factor of ac source=-0.827
Speed of motor=-1980.76 rpm

Example 12.16, Page No 685

In [16]:
import math
#initialisation of variables
I_a=300.0
V_s=600.0
a=0.6
V_t=a*V_s
P=V_t*I_a    

#Calculations
print("input power from source=%.0f kW" %(P/1000))
R_eq=V_s/(a*I_a)    
print("equivalent input resistance=%.3f ohm" %R_eq)
k=.004
R=.04+.06
w_m=(a*V_s-I_a*R)/(k*I_a)
N=w_m*60/(2*math.pi)    
print("motor speed=%.1f rpm" %N)
T_e=k*I_a**2    

#Results
print("motor torque=%.0f Nm" %T_e)

input power from source=108 kW
equivalent input resistance=3.333 ohm
motor speed=2626.1 rpm
motor torque=360 Nm

Example 12.17, Page No 686

In [17]:
import math
#initialisation of variables
T_on=10.0
T_off=15.0

#Calculations
a=T_on/(T_on+T_off)
V_s=230.0
V_t=a*V_s
r_a=3
K_m=.5
N=1500
w_m=2*math.pi*N/60
I_a=(V_t-K_m*w_m)/r_a    

#Results
print("motor load current=%.3f A" %I_a)

motor load current=4.487 A

Example 12.18, Page No 686

In [18]:
import math
#initialisation of variables
w_m=0    
print("lower limit of speed control=%.0f rpm" %w_m)
I_a=25.0
r_a=.2
V_s=220
K_m=0.08

#Calculations
a=(K_m*w_m+I_a*r_a)/V_s    
print("lower limit of duty cycle=%.3f" %a)
a=1    
print("upper limit of duty cycle=%.0f" %a)
w_m=(a*V_s-I_a*r_a)/K_m    

#Results
print("upper limit of speed control=%.1f rpm" %w_m)

lower limit of speed control=0 rpm
lower limit of duty cycle=0.023
upper limit of duty cycle=1
upper limit of speed control=2687.5 rpm

Example 12.21, Page No 691

In [19]:
import math
#initialisation of variables
a=0.6
V_s=400.0
V_t=(1-a)*V_s
I_a=300.0
P=V_t*I_a  

#Calculations  
print("power returned=%.0f kW" %(P/1000))
r_a=.2
K_m=1.2
R_eq=(1-a)*V_s/I_a+r_a    
print("equivalent load resistance=%.4f ohm" %R_eq)
w_mn=I_a*r_a/K_m
N=w_mn*60/(2*math.pi)    
print("min braking speed=%.2f rpm" %N)
w_mx=(V_s+I_a*r_a)/K_m
N=w_mx*60/(2*math.pi)    
print("max braking speed=%.1f rpm" %N)
w_m=(V_t+I_a*r_a)/K_m
N=w_m*60/(2*math.pi)    

#Results
print("max braking speed=%.1f rpm" %N)

power returned=48 kW
equivalent load resistance=0.7333 ohm
min braking speed=477.46 rpm
max braking speed=3660.6 rpm
max braking speed=1750.7 rpm

Example 12.22, Page No 699

In [20]:
import math
#initialisation of variables
N=1500.0

#Calculations
print("when speed=1455rpm")
n=1455.0
s1=(N-n)/N
r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1))    
print("I_2mx/I_2r=%.3f" %r)
print("when speed=1350rpm")
n=1350
s1=(N-n)/N
r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1))    

#Results
print("I_2mx/I_2r=%.3f" %r)

when speed=1455rpm
I_2mx/I_2r=0.000
when speed=1350rpm
I_2mx/I_2r=0.000

Example 12.24, Page No 705

In [21]:
import math
#initialisation of variables
V1=400.0
r1=0.6
r2=0.4
s=1.0
x1=1.6
x2=1.6

#Calculations
print("at starting in normal conditions")
I_n=V1/math.sqrt((r1+r2/s)**2+(x1+x2)**2)    
print("current=%.2f A" %I_n)
pf=(r1+r2)/math.sqrt((r1+r2/s)**2+(x1+x2)**2)    
print("pf=%.4f" %pf)
f1=50
w_s=4*math.pi*f1/4
T_en=(3/w_s)*I_n**2*(r2/s)    
print("\nTorque developed=%.2f Nm" %T_en)
print("motor is operated with DOL starting")
I_d=V1/2/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2)    
print("current=%.0f A" %I_d)
pf=(r1+r2)/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2)    
print("pf=%.2f" %pf)
f1=25
w_s=4*math.pi*f1/4
T_ed=(3/w_s)*I_d**2*(r2/s)    
print("Torque developed=%.3f Nm" %T_ed)
print("at max torque conditions")
s_mn=r2/math.sqrt((r1)**2+((x1+x2))**2)
I_n=V1/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2)    
print("current=%.3f A" %I_n)
pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2)    
print("pf=%.4f" %pf)
f1=50
w_s=4*math.pi*f1/4
T_en=(3/w_s)*I_n**2*(r2/s_mn)    
print("Torque developed=%.2f Nm" %T_en)
print("motor is operated with DOL starting")
s_mn=r2/math.sqrt((r1)**2+((x1+x2)/2)**2)
I_d=V1/2/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2)    
print("current=%.3f A" %I_d)
pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2)    
print("\npf=%.3f" %pf)
f1=25
w_s=4*math.pi*f1/4
T_en=(3/w_s)*I_d**2*(r2/s_mn)  


#Results  
print("Torque developed=%.3f Nm" %T_en)

at starting in normal conditions
current=119.31 A
pf=0.2983

Torque developed=108.75 Nm
motor is operated with DOL starting
current=106 A
pf=0.53
Torque developed=171.673 Nm
at max torque conditions
current=79.829 A
pf=0.7695
Torque developed=396.26 Nm
motor is operated with DOL starting
current=71.199 A

pf=0.822
Torque developed=330.883 Nm

Example 12.25, Page No 709

In [22]:
import math
#initialisation of variables
x1=1.0
X_m=50.0
X_e=x1*X_m/(x1+X_m)
V=231.0
V_e=V*X_m/(x1+X_m)
x2=1.0
r2=.4
r1=0

#Calculations
s_m=r2/(x2+X_e)    
print("slip at max torque=%.2f" %s_m)
s_mT=r2/(x2+X_m)    
print("slip at max torque=%.5f" %s_mT)
f1=50.0
w_s=4*math.pi*f1/4
print("for constant voltage input")
T_est=(3/w_s)*(V_e/math.sqrt(r2**2+(x2+X_e)**2))**2*(r2)    
print("starting torque=%.3f Nm" %T_est)
T_em=(3/w_s)*V_e**2/(2*(x2+X_e))    
print("maximum torque developed=%.2f Nm" %T_em)
print("for constant current input")
I1=28
T_est=(3/w_s)*(I1*X_m)**2/(r2**2+(x2+X_m)**2)*r2    
print("starting torque=%.3f Nm" %T_est)
T_em=(3/w_s)*(I1*X_m)**2/(2*(x2+X_m))   
print("maximum torque developed=%.3f Nm" %T_em)
s=s_mT
i=1
I_m=I1*(r2/s+i*x2)/(r2/s+i*(x2+X_m))
I_m=math.fabs(I_m)
V1=math.sqrt(3)*I_m*X_m    

#Results
print("supply voltage reqd=%.1f V" %V1)

slip at max torque=0.20
slip at max torque=0.00784
for constant voltage input
starting torque=95.988 Nm
maximum torque developed=247.31 Nm
for constant current input
starting torque=5.756 Nm
maximum torque developed=366.993 Nm
supply voltage reqd=1236.2 V

Example 12.27, Page No 718

In [23]:
import math
#initialisation of variables
V=420.0
V1=V/math.sqrt(3)
T_e=450.0
N=1440.0
n=1000.0
T_L=T_e*(n/N)**2
n1=1500.0

#Calculations
w_s=2*math.pi*n1/60
w_m=2*math.pi*n/60
a=.8
I_d=T_L*w_s/(2.339*a*V1)
k=0
R=(1-w_m/w_s)*(2.339*a*V1)/(I_d*(1-k))    
print("value of chopper resistance=%.4f ohm" %R)
n=1320.0
T_L=T_e*(n/N)**2
I_d=T_L*w_s/(2.339*a*V1)    
print("Inductor current=%.3f A" %I_d)
w_m=2*math.pi*n/60
k=1-((1-w_m/w_s)*(2.339*a*V1)/(I_d*R))    
print("value of duty cycle=%.4f" %k)
s=(n1-n)/n1
V_d=2.339*s*a*V1    
print("Rectifed o/p voltage=%.3f V" %V_d)
P=V_d*I_d
I2=math.sqrt(2/3)*I_d
r2=0.02
Pr=3*I2**2*r2
I1=a*I2
r1=0.015
Ps=3*I1**2*r1
Po=T_L*w_m
Pi=Po+Ps+Pr+P
eff=Po/Pi*100   

#Results
print("Efficiency(in percent)=%.2f" %eff)

value of chopper resistance=2.0132 ohm
Inductor current=130.902 A
value of duty cycle=0.7934
Rectifed o/p voltage=54.449 V
Efficiency(in percent)=88.00

Example 12.28, Page No 720

In [24]:
import math
#initialisation of variables
V=400.0
V_ph=V/math.sqrt(3)
N_s=1000.0
N=800.0
a=.7
I_d=110
R=2.0

#Calculations
k=1-((1-N/N_s)*(2.339*a*V_ph)/(I_d*R))    
print("value of duty cycle=%.3f" %k)
P=I_d**2*R*(1-k)
I1=a*I_d*math.sqrt(2/3)
r1=0.1
r2=0.08
Pr=3*I1**2*(r1+r2)
P_o=20000
P_i=P_o+Pr+P
eff=P_o/P_i*100    
print("Efficiency=%.2f" %eff)
I11=math.sqrt(6)/math.pi*a*I_d
th=43
P_ip=math.sqrt(3)*V*I11*math.cos(math.radians(th))
pf=P_ip/(math.sqrt(3)*V*I11)    

#Results
print("Input power factor=%.4f" %pf)

value of duty cycle=0.656
Efficiency=70.62
Input power factor=0.7314

Example 12.29, Page No 724

In [25]:
import math
#initialisation of variables
V=420.0
V1=V/math.sqrt(3)
N=1000.0
w_m=2*math.pi*N/60
N_s=1500.0

#Calculations
s=(N_s-N)/N_s
a=0.8
V_d=2.339*a*s*V1    
print("rectified voltage=%.2f V" %V_d)
T=450.0
N1=1200.0
T_L=T*(N/N1)**2
f1=50
w_s=4*math.pi*f1/4
I_d=w_s*T_L/(2.339*a*V1)    
print("inductor current=%.2f A" %I_d)
a_T=-.4
a1=math.degrees(math.acos(s*a/a_T))
print("delay angle of inverter=%.2f deg" %a1)

P_s=V_d*I_d
P_o=T_L*w_m
R_d=0.01
P_i=I_d**2*R_d
I2=math.sqrt(2/3)*I_d
r2=0.02
r1=0.015
P_rol=3*I2**2*r2
I1=a*I2
P_sol=3*I1**2*r1
P_i=P_o+P_rol+P_sol+P_i
eff=P_o/P_i*100    
print("\nefficiency=%.2f" %eff)
w_m=w_s*(1+(-a_T/a)*math.cos(math.radians(a1))-w_s*R_d*T_L/(2.339*a*V1)**2)
N=w_m*60/(2*math.pi) 

#Results   
print("motor speed=%.1f rpm" %N)
 #Answers have small variations from that in the book due to difference in the rounding off of digits.

rectified voltage=151.25 V
inductor current=108.18 A
delay angle of inverter=131.81 deg

efficiency=99.64
motor speed=996.4 rpm

Example 12.30, Page No 726

In [26]:
import math
#initialisation of variables
V=700.0
E2=V/math.sqrt(3)
N_s=1500.0
N=1200.0

#Calculations
s=(N_s-N)/N_s
V_dd=0.7
V_dt=1.5
V_d=3*math.sqrt(6)*s*E2/math.pi-2*V_dd
V1=415.0
a=math.degrees(math.acos((3*math.sqrt(2)*E2/math.pi)**-1*(-V_d+2*V_dt)))

#Results
print("firing angle advance=%.2f deg" %(180-a))

firing angle advance=70.22 deg

Example 12.31, Page No 726

In [27]:
import math
#initialisation of variables
V=700.0
E2=V/math.sqrt(3)
N_s=1500.0
N=1200.0

#Calculations
s=(N_s-N)/N_s
V_dd=.7
V_dt=1.5
a=0
u=18 #overlap angle in case of rectifier
V_d=3*math.sqrt(6)*s*E2*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dd
V1=415
V_ml=math.sqrt(2)*V1
u=4 #overlap anglein the inverter
 #V_dc=-(3*V_ml*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dt)
 #V_dc=V_d
 #after solving %  (1+math.cos(math.radians(u)))*math.cos(math.radians(a))-math.sin(math.radians(u))*math.sin(math.radians(a))=-.6425
a=math.degrees(math.acos(-.6425/(math.sqrt((1+math.cos(math.radians(u)))**2+math.sin(math.radians(u))**2))))-math.degrees(math.asin(math.sin(math.radians(a))/(1+math.cos(math.radians(u)))))

#Results
print("firing angle advance=%.2f deg" %(180-a))

firing angle advance=71.25 deg

Example 12.32, Page No 727

In [28]:
import math
#initialisation of variables
V=700.0
E2=V
N_s=1500.0
N=1200.0

#Calculations
s=(N_s-N)/N_s
V1=415.0
a_T=s*E2/V1    

#Results
print("voltage ratio of the transformer=%.2f" %a_T)

voltage ratio of the transformer=0.34

Example 12.33, Page No 733

In [29]:
import math
#initialisation of variables
P=6.0
N_s=600.0
f1=P*N_s/120.0
V=400.0
f=50.0

#Calculations
V_t=f1*V/f    
print("supply freq=%.0f Hz" %V_t)
T=340.0
N=1000.0
T_L=T*(N_s/N)**2
w_s=2*math.pi*N_s/60
P=T_L*w_s
I_a=P/(math.sqrt(3)*V_t)    
print("armature current=%.2f A" %I_a)
Z_s=2
X_s=f1/f*math.fabs(Z_s)
V_t=V_t/math.sqrt(3)
Ef=math.sqrt(V_t**2+(I_a*X_s)**2)
print("excitation voltage=%.2f V" %(math.sqrt(3)*Ef))
dl=math.degrees(math.atan(I_a*X_s/V_t))
print("load angle=%.2f deg" %dl)
T_em=(3/w_s)*(Ef*V_t/X_s)    

#Results
print("pull out torque=%.2f Nm" %T_em)

supply freq=240 Hz
armature current=18.50 A
excitation voltage=243.06 V
load angle=9.10 deg
pull out torque=773.69 Nm

Example 12.34, Page No 736

In [30]:
import math
#initialisation of variables
P=4.0
f=50.0
w_s=4*math.pi*f/P
X_d=8.0
X_q=2.0
T_e=80.0
V=400.0

#Calculations
V_t=V/math.sqrt(3)
dl=(1/2)*math.degrees(math.asin(T_e*w_s/((3/2)*(V_t)**2*(1/X_q-1/X_d))))    
print("load angle=%.3f deg" %dl)
I_d=V_t*math.cos(math.radians(dl))/X_d
I_q=V_t*math.sin(math.radians(dl))/X_q
I_a=math.sqrt(I_d**2+I_q**2)    
print("armature current=%.2f A" %I_a)
pf=T_e*w_s/(math.sqrt(3)*V*I_a)    

#Results
print("input power factor=%.4f" %pf)

load angle=0.000 deg
armature current=28.87 A
input power factor=0.6283

Example 12.35, Page No 737

In [31]:
import math
#initialisation of variables
T_e=3.0
K_m=1.2
I_a=T_e/K_m
r_a=2.0
V=230.0

#Calculations
E_a=(0.263*math.sqrt(2)*V-I_a*r_a)/(1-55/180)
w_m=E_a/K_m
N=w_m*60/(2*math.pi)    

#Results
print("motor speed=%.2f rpm" %N)

motor speed=640.96 rpm

Example 12.36, Page No 738

In [32]:
import math
#initialisation of variables
K_m=1.0
N=1360.0

#Calculations
w_m=2*math.pi*N/60
E_a=K_m*w_m
 #after calculations V_t % calculated
V_t=163.45
r_a=4
I_a=(V_t-E_a)/r_a
T_e=K_m*I_a    

#Results
print("motor torque=%.4f Nm" %T_e)

motor torque=5.2578 Nm

Example 12.37, Page No 740

In [33]:
import math
#initialisation of variables
K_m=1.0
N=2100.0

#Calculations
w_m=2*math.pi*N/60
E_a=K_m*w_m
 #after calculations V_t % calculated
V_t=227.66
r_a=4
I_a=(V_t-E_a)/r_a
T_e=K_m*I_a    

#Results
print("motor torque=%.2f Nm" %T_e)

motor torque=1.94 Nm

Example 12.38, Page No 742

In [34]:
import math
#initialisation of variables
K_m=1.0
N=840.0

#Calculations
w_m=2*math.pi*N/60
E_a=K_m*w_m
V=230.0
a=75.0
V_t=math.sqrt(2)*V/math.pi*(1+math.cos(math.radians(a)))
r_a=4
I_a=(V_t-E_a)/r_a
T_e=K_m*I_a    

#Results
print("motor torque=%.4f Nm" %T_e)
 #Answers have small variations from that in the book due to difference in the rounding off of digits.

motor torque=10.5922 Nm

Example 12.39, Page No 743

In [35]:
import math
#initialisation of variables
K_m=1.0
N=1400.0

#Calculations
w_m=2*math.pi*N/60
E_a=K_m*w_m
V=230.0
a=60.0
a1=212
V_t=math.sqrt(2)*V/math.pi*(math.cos(math.radians(a))-math.cos(math.radians(a1)))+E_a*(180+a-a1)/180
r_a=3
I_a=(V_t-E_a)/r_a
T_e=K_m*I_a   

#Results
print("motor torque=%.3f Nm" %T_e)

motor torque=5.257 Nm

Example 12.40, Page No 745

In [36]:
import math
#initialisation of variables
K_m=1.0
N=600.0
w_m=2*math.pi*N/60
E_a=K_m*w_m
V=230.0
a=60.0

#Calculations
V_t=2*math.sqrt(2)*V/math.pi*(math.cos(math.radians(a)))
r_a=3
I_a=(V_t-E_a)/r_a
T_e=K_m*I_a    


#Results
print("motor torque=%.3f Nm" %T_e)

motor torque=13.568 Nm

Example 12.41, Page No 745

In [37]:
import math
#initialisation of variables
r1=.6
r2=.4
s=0.04
x1=1.6
x2=1.6
Z=(r1+r2/s)+(x1+x2)
V=400.0
I1=V/Z    
print("source current=%.3f A " %math.degrees(math.atan(I1.imag/I1.real)))
print("and with %.1f deg phase" %math.fabs(I1))
I2=V/Z
N=1500
w_s=2*math.pi*N/60
T_e=(3/w_s)*abs(I2)**2*r2/s    
print("motor torque=%.2f Nm" %T_e)
N_r=N*(1-s)

f=45
N_s1=120*f/4
w_s=2*math.pi*N_s1/60
s1=(N_s1-N_r)/N_s1
Z=(r1+r2/s1)+(x1+x2)*f/50.0
V=360
I1=V/Z    
print("source current=%.3f A " %math.degrees(math.atan(I1.imag/I1.real)))
print("and with %.1f deg phase" %math.fabs(I1))
I2=V/Z
T_e=(3/w_s)*abs(I2)**2*r2/s1    
print("motor torque=%.2f Nm" %T_e)

source current=0.000 A 
and with 29.0 deg phase
motor torque=160.46 Nm
source current=-0.000 A 
and with 142.9 deg phase
motor torque=-2598.45 Nm