Chapter 3 - AC to DC Converters

Ex 3.1 page 117

In [1]:
from __future__ import division
from math import sqrt,pi,cos,sin
R=100    #  ohm
Vs=230    #  V
f=50    #  Hz
alpha=45    #  degree

Vo=Vs*sqrt(2)/2/pi*(1+cos(pi/180*alpha))    #  V
Io=Vo/R    #  A
Vor=Vs/sqrt(2)*sqrt(1/180*((180-alpha)+sin(pi/180*2*alpha)/2))    #  V
Ior=Vor/R    #  A
P=Ior**2*R    #  W
print 'Power delivered = %.2f W'%(P)

#Ans in the textbook is not accurate.
Power delivered = 199.11 W

Ex 3.2 page 118

In [2]:
from __future__ import division
from math import sqrt,pi,asin,cos,sin

R=10    #  ohm
E=165    #  V
#vt=330*sin(314*t)
Vm=330    #  V
f=314/2/pi    #  Hz
alpha1=asin(E/Vm)    #  radian
alpha2=pi-alpha1    #  radian
Io=1/2/pi/R*(2*Vm*cos(alpha1)-E*(alpha2-alpha1))    #  A
P=E*Io    #  W

print 'Power supplied to battery = %d W'%(P)
Power supplied to battery = 593 W

Ex 3.3 page 119

In [3]:
from __future__ import division
from math import sqrt,pi,cos,sin

#v2t = 325*sin(w*t)
R=20    #  ohm
alfa=45    #  degree
vm=325    #  V
V=230    #  V
print 'part (a)\n'
Vo=vm/2/pi*(1+cos(pi/180*alfa))     #  V
Io=Vo/R    #  A
print ' dc voltage Vo = %.1f V'%(Vo)
print '\n & Current Io = %.3f A'%(Io)
print '\n\n part (b)\n'
Vor=vm/2/sqrt(pi)*sqrt((pi-pi/180*alfa)+1/2*sin(pi/180*2*alfa))    #  V
Ior=Vor/R    #  A
print ' rms voltage Vor = %.3f V'%(Vor)
print '\n & Current Ior = %.3f A'%(Ior)
print '\n\n part (c)'
Pdc=Vo*Io    #  W
Pac=Vor*Ior    #  W
eta=Pdc/Pac    #  rectification efficiency
print "\n dc Power = %.2f W"%(Pdc)
print "\n ac Power = %.2f W"%(Pac)
print "\n Rectification efficiency = %.4f"% (eta)
print '\n\n part (d)'
FF=Vor/Vo    #  form factor
RF=sqrt(FF**2-1)
print '\n Form factor = %.3f '%(FF)
print '\n Ripple factor = %.3f '%(RF)
print '\n\n part (e)'
VA=V*Ior    #  VA
TUF=Pdc/V/Ior    #  Transformer Utilization factor
print "\n VA rating = %.1f VA"%(VA)
print "\n Transformer Utilization factor = %.4f"%TUF
print '\n\n part (f)'
Vp=vm    #  V
print "\n Peak inverse voltage = %d V"%Vp
part (a)

 dc voltage Vo = 88.3 V

 & Current Io = 4.415 A


 part (b)

 rms voltage Vor = 154.943 V

 & Current Ior = 7.747 A


 part (c)

 dc Power = 389.85 W

 ac Power = 1200.37 W

 Rectification efficiency = 0.3248


 part (d)

 Form factor = 1.755 

 Ripple factor = 1.442 


 part (e)

 VA rating = 1781.8 VA

 Transformer Utilization factor = 0.2188


 part (f)

 Peak inverse voltage = 325 V

Ex 3.4 page 120

In [4]:
from __future__ import division
from math import sqrt,pi,cos,sin,asin

R=10    #  ohm
E=165    #  V
#vt=330*sin(314*t)
Vm=330    #  V
Vs=233    #  V
f=314/2/pi    #  Hz
theta1=asin(E/Vm)    #  radian
#alpha2=pi-alpha1    #  radian
Io=1/2/pi/R*(2*Vm*cos(theta1)-E*(pi-2*theta1))    #  A
print '(a) Average value of current = %.2f A'%(Io)
P=E*Io    #  W
print '\n (b) Power supplied to battery = %d W'%(P)
Ior=sqrt(1/2/pi/R**2*((pi-2*theta1)*(Vs**2+E**2)+Vm**2*sin(2*theta1)-4*Vm*E*cos(theta1)))    #  A
Pr=Ior**2*R    #  W
print '\n (c) Power dissipated in the resistor = %.2f W'%(Pr)
pf=(Pr+P)/Vs/Ior    #  power factor
print '\n (d) Power factor = %.4f'%(pf)
(a) Average value of current = 3.60 A

 (b) Power supplied to battery = 593 W

 (c) Power dissipated in the resistor = 1216.14 W

 (d) Power factor = 0.7043

Ex 3.5 page 122

In [5]:
from __future__ import division
from math import sqrt,pi,cos,sin

R=20    #  ohm
V=230    #  V
f=50    #  Hz
alpha=30    #  degree
Vm=V*sqrt(2)    # V
Vo=Vm/pi*(1+cos(alpha*pi/180))    #  V
print 'Average load voltage = %.1f V'%(Vo)
Io=Vo/R    #  A
print '\n Average load current = %.2f A'%( Io)
Vor=V/sqrt(pi)*sqrt((pi-alpha*pi/180)+sin(2*alpha*pi/180)/2)    #  V
Ior=Vor/R    #  A
print '\n rms load current = %.2f A'%( Ior)
Iav=Io/2    # A
print '\n Average thyristor current = %.2f A'%( Iav)
Irms=Ior/sqrt(2)    #  A
print '\n rms thyristor current = %.3f A'%( Irms)
Average load voltage = 193.2 V

 Average load current = 9.66 A

 rms load current = 11.33 A

 Average thyristor current = 4.83 A

 rms thyristor current = 8.014 A

Ex 3.6 page 122

In [6]:
from __future__ import division
from math import sqrt,pi,cos,sin

R=10    #  ohm
L=100/1000    #  H
E=100    #  V
Vs=230    #  V
f=50    #  Hz
alpha = 45    #  degree
Vm=Vs*sqrt(2)    #  V
Vo=2*Vm/pi*cos(alpha*pi/180)    #  V
Io=(Vo-E)/R    #  A
print 'Average load current = %.3f A'%(Io)
Average load current = 4.642 A

Ex 3.7 page 123

In [7]:
from __future__ import division
from math import sqrt,pi,cos,sin

R=2    #  ohm
L=0.3    #  H
E=100    #  V
Vs=230    #  V
f=50    #  Hz
alpha = 30    #  degree
Vm=Vs*sqrt(2)    #  V
Vo=2*Vm/pi*cos(alpha*pi/180)    #  V
print ' Average load voltage = %.2f V'%( Vo)
Io=(Vo)/R    #  A
print '\n Average load current = %.2f A'%( Io)
Is=Io    #  A
Is1=4*Io/pi/sqrt(2)    #  A
PF=Vo*Io/Vs/Is    #  power factor
print '\n Power factor = %.4f'%(PF)
 Average load voltage = 179.33 V

 Average load current = 89.67 A

 Power factor = 0.7797

Ex 3.8 page 123

In [8]:
from __future__ import division
from math import sqrt,pi,cos,sin

R=5    #  ohm
L=1    #  H
E=10    #  V
Vs=230    #  V
f=50    #  Hz
alpha = 45    #  degree
Vm=Vs*sqrt(2)    #  V
Vo=Vm/pi*(1+cos(alpha*pi/180))    #  V
print ' Average load voltage = %.2f V'%( Vo)
Io=(Vo-E)/R    #  A
print '\n Average load current = %.2f A'%( Io)
PF=(Io**2*R+E*Io)/Vs/Io    #  power factor
print '\n Power factor = %.4f'%(PF)
 Average load voltage = 176.75 V

 Average load current = 33.35 A

 Power factor = 0.7685

Ex 3.9 page 124

In [9]:
from __future__ import division
from math import sqrt,pi,cos,sin

R=50    #  ohm
Vs=230    #  V
f=50    #  Hz
alpha = 30    #  degree
Vm=Vs*sqrt(2)    #  V
Vo=2*Vm/pi*cos(alpha*pi/180)    #  V
print ' (i) Average voltage across 50 ohm resistor = %.2f V'%( Vo)
Io=(Vo)/R    #  A
Ior=Io/sqrt(2)    #  A
print '\n (ii) rms current = %.4f A'%( Ior)
 (i) Average voltage across 50 ohm resistor = 179.33 V

 (ii) rms current = 2.5361 A

Ex 3.10 page 124

In [10]:
from __future__ import division
from math import sqrt,pi,cos,sin

R=2    #  ohm
Vs=230    #  V
f=50    #  Hz
alpha = 120    #  degree
Ia=10    #  A

Vo=2*sqrt(2)*Vs*cos(alpha*pi/180)/pi
V=Ia*R-Vo    #  V
print 'emf on load side = %.2f V'%( V)
emf on load side = 123.54 V

Ex 3.11 page 125

In [11]:
from __future__ import division
from math import sqrt,pi,cos,sin

Vs=230    #  V
Io=5    #  A
alpha = 45    #  degree
print 'part(i)'
Vo=2*sqrt(2)*Vs/pi*cos(alpha*pi/180)    #  V
print '\n dc output voltage = %.1f V'%(Vo)
Pi=Vo*Io    #  W
print '\n Active power = %.1f W'%(Pi)
Qi=2*sqrt(2)*Vs/pi*sin(alpha*pi/180)*Io    #  VAR
print '\n Reactive power = %.1f VAR'%(Qi)
print '\n\n part(ii)'
R=Vo/Io    #  ohm
Vo=sqrt(2)*Vs/pi*(1+cos(alpha*pi/180))    #  V
print '\n dc output voltage = %.1f V'%(Vo)
Io=Vo/R    #  A
Pi=Vo*Io    #  W
print '\n Active power = %.1f W'%(Pi)
Qi=sqrt(2)*Vs/pi*sin(alpha*pi/4)*Io    #  VAR
print '\n Reactive power = %.1f VAR'%(Qi)
print '\n\n part(iii)'
Vo=sqrt(2)*Vs/pi/2*(1+cos(alpha*pi/180))    #  
print '\n Average load voltage = %.0f V'%(Vo)
Io=Vo/R    #  A
print '\n Average load current = %.2f A'%(Io)
part(i)

 dc output voltage = 146.4 V

 Active power = 732.1 W

 Reactive power = 732.1 VAR


 part(ii)

 dc output voltage = 176.7 V

 Active power = 1066.8 W

 Reactive power = -441.9 VAR


 part(iii)

 Average load voltage = 88 V

 Average load current = 3.02 A

Ex 3.12 page 126

In [12]:
from __future__ import division
from math import sqrt,pi,cos,sin

R=20    #  ohm
Vs=400    #  V
f=50    #  Hz
alpha = 30    #  degree

Vm=Vs*sqrt(2)    #  V
Vo=3*Vm/pi*cos(alpha*pi/180)    #  V
Io=Vo/R    #  A
print '\n Average load voltage = %.3f V'%(Vo)
print '\n Average load current = %.3f A'%(Io)
 Average load voltage = 467.818 V

 Average load current = 23.391 A

Ex 3.13 page 126

In [13]:
from __future__ import division
from math import sqrt,pi,cos,sin

n=3    #  no. of phase
Vs=400    #  V
f=50    #  Hz
Io=100    #  A
alpha = 60    #  degree

Vm=Vs*sqrt(2)    #  V
Vo=n*Vm/pi*cos(alpha*pi/180)    #  V
Po=Vo*Io    #  W
print ' (i)'
print '\n Output voltage = %.0f V'%(Vo)
print '\n Output power = %.0f W'%(Po)
print '\n\n (ii)'
Iav=Io*2*pi/3/2/pi    #  A
print '\n average current through thyristor = %.2f A'%( Iav)
Ior=sqrt(Io**2*2*pi/3/2/pi)    #  A
print '\n rms current through thyristor = %.2f A'%( Ior)
Ip=Io    # A
print '\n peak current through thyristor = %.2f A'%( Ip)
print '\n\n (iii)'
PIV=sqrt(2)*Vs    # V
print '\n PIV of thyristor = %.1f V'%(PIV)
# Ans in the book is not accurate.
 (i)

 Output voltage = 270 V

 Output power = 27009 W


 (ii)

 average current through thyristor = 33.33 A

 rms current through thyristor = 57.74 A

 peak current through thyristor = 100.00 A


 (iii)

 PIV of thyristor = 565.7 V

Ex 3.14 page 127

In [14]:
from __future__ import division
from math import sqrt,pi,cos,sin

n=3    #  no. of phase
R=60    #  ohm
Vs=400    #  V
alpha = 30    #  degree

Vm=Vs*sqrt(2)    #  V
Vo=3*Vm/pi*cos(alpha*pi/180)    #  V
Io=Vo/R    #  A
P=Io**2*R    #  W
pf=P/sqrt(3)/Vs/Io    #  power factor

print '\n Average load voltage = %.3f V'%(Vo)
print '\n Average load current = %.1f A'%(Io)
print '\n input power factor = %.4f'%(pf)
 Average load voltage = 467.818 V

 Average load current = 7.8 A

 input power factor = 0.6752

Ex 3.15 page 127

In [15]:
from __future__ import division
from math import sqrt,pi,cos,sin

n=3    #  no. of phase
R=50    #  ohm
Vs=400    #  V
f=50    #  Hz
alpha = 45    #  degree

Vm=Vs*sqrt(2)    #  V
Vo=3*Vm/2/pi*(1+cos(alpha*pi/180))    #  V
Io=Vo/R    #  A
print '\n Average load voltage = %.2f V'%(Vo)
print '\n Average load current = %.2f A'%(Io)
 Average load voltage = 461.08 V

 Average load current = 9.22 A

Ex 3.16 page 128

In [16]:
from __future__ import division
from math import sqrt,pi,cos,sin,acos

n=3    #  no. of phase
Vs=400    #  V
f=50    #  Hz
Ls=5/1000    #  H
Io=20    #  A
Ri=1    #  ohm
Vdc=400    #  V

Vo=Vdc+Io*Ri    #  V
# Vo=3*Vm/pi*cos(alpha*pi/180)-3*2*pi*f*Ls/pi*Io
Vm=sqrt(2)*Vs    #  V
alpha=acos((Vo+3*2*pi*f*Ls/pi*Io)/(3*Vm/pi))*180/pi    #  degree

# Vo=3*Vm/pi*cos((alpha+mu)*pi/180)-3*2*pi*f*Ls/pi*Io
mu=acos((Vo-3*2*pi*f*Ls/pi*Io)/(3*Vm/pi))*180/pi-alpha    #  degree
print '\n Firing angle = %.2f degree'%(alpha)
print '\n Overlap angle = %.2f degree'%(mu)
# ans in the textbook is not accurate.
 Firing angle = 33.59 degree

 Overlap angle = 10.20 degree

Ex 3.17 page 128

In [17]:
from __future__ import division
from math import sqrt,pi,cos,sin,acos

n=3    #  no. of phase
Vs=400    #  V
f=50    #  Hz
alpha = pi/4    #  radian
Io=10    #  A
Vo=360    #  V

# Vo=n*Vs*sqrt(2)/pi/sqrt(2)-3*2*pi*f*Ls*Io/pi
Ls=(n*Vs*sqrt(2)/pi/sqrt(2)-Vo)/(3*2*pi*f)/(Io/pi)*1000    #  mH
R=Vo/Io    #  ohm
print ' Load resistance = %.f ohm'%(R)
print '\n Source inductance = %.1f mH'%(Ls)
# Vo = n*Vs*sqrt(2)/pi*cos(alpha+mu)+3*2*pi*f*Ls*Io/pi
mu=acos((Vo-3*2*pi*f*Ls/1000*Io/pi)/(n*Vs*sqrt(2)/pi))-alpha    #  radian
mu=mu*180/pi    #  degree
print '\n Overlap angle = %.d degree'%(mu)
 Load resistance = 36 ohm

 Source inductance = 7.3 mH

 Overlap angle = 6 degree