Chapter 4 - AC to AC Converters

Ex 4.1 page 158

In [1]:
from __future__ import division
from math import sqrt,pi,sin
R=5    #  ohm
Vs=230    #  V
f=50    #  Hz
alpha = 120    #  degree

Vor=Vs*sqrt(1/pi*(pi-alpha*pi/180+sin(2*alpha*pi/180)/2))    #  V
print '\n rms load voltage = %.2f V'%( Vor)
Ior=Vor/R    #  A
print '\n rms load current = %.2f A'%( Ior)
Irms=Ior/sqrt(2)    # A
print '\n rms thyristor current = %.2f A'%( Irms)
pf=sqrt(1/pi*((pi-alpha*pi/180)+sin(2*alpha*pi/180)/2))    #  power factor
print '\n input power factor = %.3f '%(pf)

 rms load voltage = 101.70 V

 rms load current = 20.34 A

 rms thyristor current = 14.38 A

 input power factor = 0.442

Ex 4.2 page 158

In [2]:
from __future__ import division
from math import sqrt,pi,sin
R=10    #  ohm
Vs=230    #  V
f=50    #  Hz
nc=18    #  conducting cycles
noff=32    #  off cycles

k=nc/(nc+noff)    #  duty ratio
Vor=Vs*sqrt(k)    #  V
Po=Vor**2/R    #  W
Pi=Po    #  W (losses are negligble)
Ior=Vor/R    # A
pf=Po/Vs/Ior    # W
Im=Vs*sqrt(2)/R    # A
Irms=Im*sqrt(k)/2    # A
Iav=k*Im/pi    # A
print '\n (a) rms output voltage = %.0f V'%( Vor)
print '\n (b) Power output to load = %.1f W'%( Po)
print '\n (c) Power input to regulator = %.1f W'%( Pi)
print '\n (d) input power factor = %.1f '%(pf)
print '\n (e) average scr current = %.3f A'%( Iav)
print '\n     rms scr current = %.3f A'%( Irms)

 (a) rms output voltage = 138 V

 (b) Power output to load = 1904.4 W

 (c) Power input to regulator = 1904.4 W

 (d) input power factor = 0.6 

 (e) average scr current = 3.727 A

     rms scr current = 9.758 A

Ex 4.3 page 159

In [3]:
from __future__ import division
from math import sqrt,pi,sin
R=10    #  ohm
Vs=230    #  V
f=50    #  Hz
alpha = 90    #  degree

Vor=Vs*sqrt(1/pi*(pi-alpha*pi/180+sin(2*alpha*pi/180)/2))    #  V
Ior=Vor/R    #  A
P=Ior**2*R    #  W
pf=Vor/Vs    #  power factor
print '\n rms load voltage = %.2f V'%( Vor)
print '\n rms load current = %.2f A'%( Ior)
print '\n power input = %.2f W'%( P)
print '\n load power factor = %.1f '%(pf)

 rms load voltage = 162.63 V

 rms load current = 16.26 A

 power input = 2645.00 W

 load power factor = 0.7

Ex 4.4 page 160

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

R=30    #  ohm
Vs=230    #  V
f=50    #  Hz
alpha = 45    #  degree

Vor=Vs*sqrt(1/pi*(pi-alpha*pi/180+sin(2*alpha*pi/180)/2))    #  V
Ior=Vor/R    #  A
print '\n rms load voltage = %.2f V'%( Vor)
print '\n rms load current = %.2f A'%( Ior)

 rms load voltage = 219.30 V

 rms load current = 7.31 A

Ex 4.5 page 160

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

R=10    #  ohm
Vs=230    #  V
f=50    #  Hz
fi = 45    #  degree

Vmax=Vs    #  V(max supply voltage)
XL=R*tan(fi*pi/180)    #  ohm
Z=XL*sqrt(2)    #  ohm
Imax=Vs/Z    # A

print '\n max load voltage = %.2f V'%( Vmax)
print '\n max load current = %.3f A'%( Imax)
print '\n range of delay angle = %d to %d'%(0,fi)

 max load voltage = 230.00 V

 max load current = 16.263 A

 range of delay angle = 0 to 45

Ex 4.7 page 161

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

R=3    #  ohm
wL=4    # ohm
Vs=230    #  V
f=50    #  Hz

fi=atan(wL/R)*180/pi    # degree
print '\n (i) control range of firing angle = %.2f to pi'%(fi)
Imax=Vs/sqrt(R**2+wL**2)    #  A
print '\n (ii) max rms load current = %.f A'%( Imax)
Pmax=Imax**2*R    # W
print '\n (iii) max power input to load = %.f W'%( Pmax)
pf_max=Pmax/Vs/Imax    #  power factor
print '\n (iv) max power factor = %.1f '%( pf_max)
Ithrms=Imax/sqrt(2)    #  A
Ithav=Ithrms/1.57    #  A
print '\n (v) max rms thyristor current = %.3f A'%( Ithrms)
print '\n     max average thyristor current = %.3f A'%( Ithav)

 (i) control range of firing angle = 53.13 to pi

 (ii) max rms load current = 46 A

 (iii) max power input to load = 6348 W

 (iv) max power factor = 0.6 

 (v) max rms thyristor current = 32.527 A

     max average thyristor current = 20.718 A