Chapter 7 - Power Controllers - Their Applications

Ex 7.1 page 260

In [1]:
from __future__ import division
from math import sqrt,cos,pi
N1=1000    #  rpm
Va1=200    #  V
alfa=60    #  degree
Va2=230    #  V

N2=2*Va2*sqrt(2)*cos(alfa*pi/180)*N1/Va1/pi
print '\n Speed of motor = %d rpm'%(N2)
# ans in the textbook is not accurate.

 Speed of motor = 517 rpm

Ex 7.2 page 260

In [2]:
from __future__ import division

N1=1100    #  rpm
Va1=220    #  V
N2=900    #  rpm

Va2=Va1*N2/N1    #  V
delta=Va2/Va1    #  duty ratio
print '\n duty ratio = %.2f'%(delta)

 duty ratio = 0.82

Ex 7.3 page 261

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

N1=900    #  rpm
Va1=198    #  V
N2=500    #  rpm
Vs=230    #  V

Va2=Va1*N2/N1    #  V
# 2*sqrt(2)*Vs*cos(alfa)/pi=Va2
alfa=acos(Va2/(2*sqrt(2)*Vs)*pi)*180/pi    #  degree

print '\n triggering angle = %.1f degree'%(alfa)

 triggering angle = 57.9 degree

Ex 7.4 page 261

In [4]:
from __future__ import division
from math import pi
Vs=230    #  V
Ton=10    #  ms
Toff=25    #  ms
Ra=2    # ohm
N=1400    #  rpm
k=0.5    #  V/rad/s (back emf constant)
kt=0.5    #  NM-A**-1 (torque constant)

Eb=N*2*pi*k/60    #  V
Va=Vs*Ton/(Toff)    #  V
Ia=(Va-Eb)/Ra    #  A
T=kt*Ia    #  Nm
print '\n average armature current = %.2f A'%( Ia)
print '\n torque = %.3f Nm'%( T)

 average armature current = 9.35 A

 torque = 4.674 Nm