Chapter13 Choppers and Transportation system Application

Example 13.1,Pg.no.43

In [8]:
import math
from math import exp
E=220.0           #dc supply voltage in volts
El=22.0           #Load voltage in volts
Ton=1000.0        #conducting period in microseconds
T=2500.0          #Total timeperiod in microseconds
L=1.0             #inductance in milliHenry
R=0.25          #resistance in ohms
t=L/R           #time constant in milliseconds
print 'time constant=t=',t,'milliseconds'
A=0.133
Td=A*T          #Discontinuous condition starts at
print 'Discontinuous condition starts from Td=',Td,'microseconds'
Eo=0.4*E        #output voltage in volts
print 'Output voltage=Eo=',Eo,'volts'
Iav=(Eo-El)/R   #Average current in amps
print 'Average current=Iav=',Iav,'amp'
Imax=((E*(1-exp(-Ton/(t*1000))))/(R*(1-exp(-T/(t*1000)))))-(El/R)
Imax=round(Imax,2)
print 'Maximum current=Imax=',Imax,'amp'
Imin=((E*(exp(Ton/(t*1000))-1))/(R*(exp(T/(t*1000))-1)))-(El/R)
Imin=round(Imin,2)
print 'Minimum current=Imin=',Imin,'amp'

time constant=t= 4.0 milliseconds
Discontinuous condition starts from Td= 332.5 microseconds
Output voltage=Eo= 88.0 volts
Average current=Iav= 264.0 amp
Maximum current=Imax= 330.85 amp
Minimum current=Imin= 199.87 amp

Example 13.2,Pg.no.44

In [9]:
import math
f=1.0          #operating frequency in KHZ
E=220.0        #dc supply voltage in volts
El=165.0       #Load voltage in volts
Ton=El/(E*f)   #conduction period in ms
print 'Conduction period=Ton=',Ton,'ms'
T=1/f          #total time period in ms
print 'Total time period=T=',T,'ms'
Toff=T-Ton     #blocking period in ms
print 'Blocking period=Toff=',Toff,'ms'

Conduction period=Ton= 0.75 ms
Total time period=T= 1.0 ms
Blocking period=Toff= 0.25 ms

Example 13.3,Pg.no.44

In [10]:
import math
from math import pi
E=220.0       #dc supply voltage in volts
Toff=200.0    #blocking period in microseconds
Il=50.0         #load current in amps
C=pi*Toff*Il/(2*E)      #capacitance for optimum frequency in microfarad
C=75.0
print 'Load capacitance required for optimum frequency=C=',C,'microfarad'
L1=Toff**2*10**-3/C     #inductance required in milliHenry
L2=L1
L1=round(L1,2)
print 'Inductance parameters=L1=L2=',L1,'milliHenry'

Load capacitance required for optimum frequency=C= 75.0 microfarad
Inductance parameters=L1=L2= 0.53 milliHenry

Example 13.4,Pg.no.45

In [11]:
import math
E=220.0         #dc supply voltage in volts
El=660.0        #Load voltage in volts
Toff=100.0      #blocking period in microseconds
Ton=(El/E-1)*Toff      #Conduction period in microseconds
print 'Conduction period=Ton=',Ton,'microseconds'

Conduction period=Ton= 200.0 microseconds

Example 13.5,Pg.no.45

In [12]:
import math
f=200.0       #chopper frequency in HZ
E=220.0       #dc supply voltage in volts
Iav=100.0     #Average current in the circuit in amps
Ra=0.02     #Armature resistance in ohms
Rf=0.01     #Field resistance in ohms
Ebav=50     #Average value of the Back emf in volts
Eav=Iav*(Ra+Rf)+Ebav       #Average voltage in the circuit in volts
print 'Average voltage in the circuit=Eav=',Eav,'volts'
Ton=Eav*1000/(E*f)         #conduction period in ms
Ton=round(Ton,2)
print 'Conduction period=Ton=',Ton,'ms'

Average voltage in the circuit=Eav= 53.0 volts
Conduction period=Ton= 1.2 ms

Example 13.6,Pg.no.46

In [13]:
import math
f=200.0         #chopper frequency in HZ
T=1000/f      #total time period in ms
Toff=4.0        #Blocking period in ms
Ton=T-Toff    #conduction period in ms
R1=2.0          #R1 in ohms
R2=4.0          #R2 in ohms
R=((R1*Ton)+(R1+R2)*Toff)/T        #rotor resistance referred to stator in ohms
print 'Rotor resistance referred to stator=R=',R,'ohms'
V=415.0       #stator voltage in volts
s=0.02        #slip of the motor
MT=V**2*s/R    #motor torque in Syn . Watts
MT=round(MT,2)
print 'Motor torque=MT=',MT,'Snc . Watts'

Rotor resistance referred to stator=R= 5.2 ohms
Motor torque=MT= 662.4 Snc . Watts

Example 13.7,Pg.no.46

In [14]:
import math
#R1=rotor resistance before introduction of control
#R2=rotor resistance after introduction of control 
print 'R2=1.5*R1'
R2=((R1*Ton)+(R1+R1)*Toff)/T     #rotor resistance referred to stator in ohms
print 'the above condition satisfies when Ton= Toff'
T=4          #total time period in ms
f=1000/T     #chopper frequency in hz
f=round(f,1)
print 'Chopper frequency=f=',f,'hz'

R2=1.5*R1
the above condition satisfies when Ton= Toff
Chopper frequency=f= 250.0 hz