Chapter5 Line Commutated converters¶

Example 5.1,Pg.no15¶

In [11]:
import math
from math import pi
Edc=440                                       #dc terminal voltage of the thyristor in volts
E2=415                                        #input voltage of the thyristor in volts
Id=100                                        #dc motor current in amps
C=Edc/(1.35*E2)
C=round(C,2)
print 'cosine of the firing angle=C=',C
A=math.acos(C)*180/pi
A=round(A,2)
print 'firing angle of the converter=A=',A,'degrees'
Pac=1.05*1.35*E2*Id/1000                     #Ac terminal power in Kilo watts
Pac=round(Pac,2)
print 'AC terminal power=Pac=',Pac,'KW'

cosine of the firing angle=C= 0.79
firing angle of the converter=A= 37.81 degrees
AC terminal power=Pac= 58.83 KW


Example 5.2,Pg.no15¶

In [12]:
import math
from math import sqrt
Id=200                                                     #rated dc current in amperes
I2=0.817*Id                                                #AC line current in amperes
print 'AC line current of the thyristor=I2=',I2,'amperes'
E2=415                                                     #AC line voltage in volts
Xt=0.06*E2/I2                                              #effective reactance of the thyristor in ohms
Xt=round(Xt,2)
print 'effective reactance of the thyristor=Xt=',Xt,'ohms'
C=1-((Id*Xt)/(E2*sqrt(3)))                                 #cosine value of the commutational angle
C=round(C,2)
print 'cosine value of the commutational angle=C=',C
CA=math.acos(C)*180/pi
print 'commutation angle=CA=',CA,'degrees'
IVR=(1-C)/2                                                #inductive voltage regulation
IVR=round(IVR,3)
print 'Inductive voltage regulation=IVR=',IVR

AC line current of the thyristor=I2= 163.4 amperes
effective reactance of the thyristor=Xt= 0.15 ohms
cosine value of the commutational angle=C= 0.96
commutation angle=CA= 16.2602047083 degrees
Inductive voltage regulation=IVR= 0.02


Example 5.3,Pg.no16¶

In [13]:
import math
from math import sqrt,pi
E2=415 #input voltage in volts
Edc=1.17*E2          #dc terminal voltage in volts
Emax2=sqrt(2)*E2     #maximum value of dc voltage
Z=2                  #total impedance in ohms
Emax2=round(Emax2,2)
print 'maximum value of dc voltage=Emax2=',Emax2,'volts'
Irms=Emax2*sqrt(pi/3+sqrt(3)/4)/(2*pi*Z)
Irms=round(Irms,2)
print 'rms current through the device=Irms=',Irms,'amps'

maximum value of dc voltage=Emax2= 586.9 volts
rms current through the device=Irms= 56.82 amps


Example 5.4,Pg.no 17¶

In [14]:
import math
from math import sqrt,pi
Edc=460    #dc terminal voltage of the thyristor in volts
E2=415     #input voltage of the thyristor in volts
Id=200     #dc motor current in amps
C=Edc/(1.35*E2)
C=round(C,2)
print 'cosine of the firing angle=C=',C
A=math.acos(C)*180/pi
A=round(A,2)
print 'firing angle of the converter=A=',A,'degrees'
Pdc=Edc*Id/1000       #dc power delivered by the converter in kilo Watts
print 'dc power delivered by the converter=Pdc=',Pdc,'KW'
Pac=1.05*Pdc           #Ac terminal power in KVA
print 'AC terminal power=Pac=',Pac,'KVA'
Iac=Pac*1000/(sqrt(3)*E2)
Iac=round(Iac,2)
print 'AC line current=Iac=',Iac,'amps'
Ib=0.58*Id              #Branch current through the device in amps
print 'Branch current through the device=Ib=',Ib,'amps'

cosine of the firing angle=C= 0.82
firing angle of the converter=A= 34.92 degrees
dc power delivered by the converter=Pdc= 92 KW
AC terminal power=Pac= 96.6 KVA
AC line current=Iac= 134.39 amps
Branch current through the device=Ib= 116.0 amps


Example 5.5,Pg.no 17¶

In [15]:
import math
from math import pi,sqrt
Id=150                  #rated dc current in amperes
E2=415                  #AC line voltage in volts
Emax=sqrt(2)*E2
C=math.cos(16*pi/180)       #cosine value of the commutational angle
C=round(C,2)
print 'cosine value of the commutational angle=C=',C
Xt=(1-C)*E2*sqrt(3)/Id  #effective reactance of the thyristor in ohms
Xt=round(Xt,2)
print 'effective reactance of the thyristor=Xt=',Xt,'ohms'

cosine value of the commutational angle=C= 0.96
effective reactance of the thyristor=Xt= 0.19 ohms


Example 5.6,Pg.no 18¶

In [16]:
import math
from math import sqrt,pi
E2=230                 #AC line voltage in volts
Emax=sqrt(2)*E2
C=math.cos(13*pi/180)       #cosine value of the commutational angle
Xt=0.16                #effective reactance of the thyristor in ohms
Id=(1-C)*E2*sqrt(3)/Xt    #AC load current in amperes
Id=round(Id,2)

AC load current=Id= 63.81 amps


Example 5.7,Pg.no 18¶

In [17]:
import math
from math import sqrt,pi
E2=230                                      #input voltage in volts
Emax=sqrt(2)*E2                             #maximum value of dc voltage
A=pi/6
Edc=Emax*(1+math.cos(A))/(2*pi)
Edc=round(Edc,2)
print 'Average value of dc voltage=Edc=',Edc,'volts'
Eeff=Emax*sqrt((pi-A)/(4*pi)+(math.sin(2*A)/(8*pi)))
Eeff=round(Eeff,2)
print 'Effective value of voltage=Eeff=',Eeff,'volts'
R=10                                        #total impedance in ohms
Id=Edc/R
Id=round(Id,2)

Average value of dc voltage=Edc= 96.6 volts
Effective value of voltage=Eeff= 160.27 volts


Example 5.8,Pg.no 19¶

In [18]:
import math
from math import sqrt,pi
E2=415                     #input voltage in volts
Emax=sqrt(2)*E2            #maximum value of dc voltage
A=pi/6                     #triggering angle in degrees
Edc=Emax*math.cos(A)/pi    #dc output voltage in volts
Edc=round(Edc,2)
print 'dc output voltage=Edc=',Edc,'volts'

dc output voltage=Edc= 161.79 volts