Chapter3, Inverters

Example 3_1, page 113

In [1]:
from math import pi, sqrt
#Given data: 
R=80 #ohm
L=8 #/mH
C=1.2 # micro F

#Solution :
if R**2<4*(L*10**-3)/(C*10**-6):
    print "As R**2<4*L/C, Circuit will work as a series inverter." 
else:
    print "As R**2>4*L/C, Circuit will not work as a series inverter." 

omega_m=sqrt(1/(L*10**-3*C*10**-6)-R**2/4/(L*10**-3)**2) #rad/s
fm=omega_m/2/pi #Hz
print "Maximum frequency = %0.2f Hz" %fm

As R**2<4*L/C, Circuit will work as a series inverter.
Maximum frequency = 1416.09 Hz

Example 3_2, page 113

In [2]:
from math import pi, sqrt
#Given data: 
R=80 #ohm
L=8 #/mH
C=1.2 # micro F
Toff=14 #micro sec

#Solution :
omega_m=sqrt(1/(L*10**-3*C*10**-6)-R**2/4/(L*10**-3)**2) #rad/s
fm=omega_m/2/pi #Hz
T=1/fm #sec
f=1/(T+2*Toff*10**-6) #Hz
print "Frequency of output = %0.1f Hz" %f

Frequency of output = 1362.1 Hz

Example 3_3, page 119

In [3]:
from __future__ import division
from math import pi, sqrt
#Given data: 
RL=3 #in ohm
V=30 #in V

#Solution :
Vpeak=2*V/pi #V
Vrms=Vpeak/sqrt(2) #V
print "(a) RMS value of output voltage = %0.1f " %Vrms
#VL=sqrt(2/T*integrate('(V/2)**2','t',0,T/2)) #V
VL=V/2 #V
Pout=VL**2/RL #W
print "(b) Output power = %0.f W  " %Pout 
Ipeak=VL/RL #A
print "(c) Peak current in thyristor = %0.f A  " %Ipeak 
Iavg=Ipeak*50/100 #A
print "(d) Average current of each thyristor = %0.1f A" %Iavg
Vprb=2*VL #V
print "(e) Peak reverse braking voltage = %0.f V " %Vprb 

(a) RMS value of output voltage = 13.5 
(b) Output power = 75 W  
(c) Peak current in thyristor = 5 A  
(d) Average current of each thyristor = 2.5 A
(e) Peak reverse braking voltage = 30 V

Example 3_4, page 120

In [4]:
from math import pi, sqrt

#Given data: 
RL=3 #in ohm
V=30 #in V

#Solution :
Vpeak=4*V/pi #V
Vrms=Vpeak/sqrt(2) #V
print "(a) RMS value of output voltage = %0.f V" %Vrms
#VL=sqrt(2/T*integrate('V**2','t',0,T/2)) #V
VL=V #V
Pout=VL**2/RL #W
print "(b) Output power = %0.f W  " %Pout 
Ipeak=VL/RL #A
print "(c) Peak current in thyristor = %0.f A  " %Ipeak 
Iavg=Ipeak*50/100 #A
print "(d) Average current of each thyristor = %0.f A" %Iavg
Vprb=VL #V
print "(e) Peak reverse braking voltage = %0.f V " %Vprb 

(a) RMS value of output voltage = 27 V
(b) Output power = 300 W  
(c) Peak current in thyristor = 10 A  
(d) Average current of each thyristor = 5 A
(e) Peak reverse braking voltage = 30 V

Example 3_5, page 120

In [5]:
from math import pi, sqrt

#Given data: 
V=200 #V
R=10 #in ohm
L=20 #mH
C=100 #pF
f=50 #Hz

#Solution :
Z1=R+1J*(2*pi*f*L*10**-3-1/(2*pi*f*C*10**-6)) #ohm
Z3=R+1J*(3*2*pi*f*L*10**-3-1/(3*2*pi*f*C*10**-6)) #ohm
Z5=R+1J*(5*2*pi*f*L*10**-3-1/(5*2*pi*f*C*10**-6)) #ohm
Z7=R+1J*(7*2*pi*f*L*10**-3-1/(7*2*pi*f*C*10**-6)) #ohm
Z9=R+1J*(9*2*pi*f*L*10**-3-1/(9*2*pi*f*C*10**-6)) #ohm
I=4*V/pi/abs(Z1) #A
Irms=I/sqrt(2) #A
print"RMS load current = %0.2f A" % Irms
Ip=sqrt((4*V/pi/abs(Z1))**2+(4*V/3/pi/abs(Z3))**2+(4*V/5/pi/abs(Z5))**2+(4*V/7/pi/abs(Z7))**2+(4*V/9/pi/abs(Z9))**2) #A
print "Peak value of load current = %0.2f A " %Ip 
Ih=sqrt(Ip**2-I**2)/sqrt(2) #A
print "RMS harmonic current = %0.3f A " %Ih 
hd=sqrt(Ip**2-I**2)/I #harmonic distortion
print "Harmonic distortion = %0.1f %%" %(hd*100) 
Irms_load=Ip/sqrt(2) #A
Pout=Irms_load**2*R #W
print "Total output power = %0.1f W " %Pout 
Pout_com=Irms**2*R #W(fundamental component)
print "Fundamental component of power = %0.2f W " %Pout_com 
Iavg_in=Pout/V #A
print "Average input current = %0.4f A " %Iavg_in 
Ip_thy=Ip #A
print "Peak thyristor current = %0.2f A " %Ip_thy 

RMS load current = 6.56 A
Peak value of load current = 11.56 A 
RMS harmonic current = 4.876 A 
Harmonic distortion = 74.3 %
Total output power = 668.5 W 
Fundamental component of power = 430.76 W 
Average input current = 3.3427 A 
Peak thyristor current = 11.56 A

Example 3_6, page 121

In [6]:
from math import pi, sqrt, tan

#Given data: 
R=2 #in ohm
XL=10 #ohm
f=4 #kHz
Toff=12 #micro sec

#Solution :
Toff_time=Toff*1.5 #micro sec
theta=2*pi*f*10**3*Toff_time*10**-6 #radians
Xc=tan(theta)*R+XL #ohm
C=1/(2*pi*f*1000*Xc) #F
print "Value of Capacitance = %0.2e F" %C

Value of Capacitance = 3.63e-06 F

Example 3_7, page 125

In [7]:
from math import sqrt

#Given data: 
V=400 #V
R=10 #in ohm/phase

#Solution :
Ipeak=V/2/R #A
Irms=sqrt(Ipeak**2*2/3) #A
print "RMS load current = %0.2f A" %Irms
Pout=Irms**2*R*3 #W
print "Power output = %0.f W  " %Pout
Iavg=Ipeak/3 #A
print "Average thyristor current = %0.2f A " %Iavg 
Irms_thyristor=sqrt(Ipeak**2/3) #A
print "RMS value of thyristor current = %0.2f A  " %Irms_thyristor 

RMS load current = 16.33 A
Power output = 8000 W  
Average thyristor current = 6.67 A 
RMS value of thyristor current = 11.55 A

Example 3_8, page 126

In [8]:
from __future__ import division
from math import sqrt, pi
from sympy.mpmath import quad
#Given data: 
V=400 #V
R=10 #in ohm/phase

#Solution :
RL=R+R/2 #ohm
i1=V/RL #A
i2=V/RL #A
i3=V/RL #A
Irms_load=sqrt(1/2/pi*(quad(lambda theta:i1**2,[0,2*pi/3])+quad(lambda theta:(i1/2)**2,[2*pi/3,2*pi]))) #A
print "RMS load current = %0.3f A" %Irms_load
Pout=Irms_load**2*R*3 #W
print "Power output = %0.1f W " %Pout 
Ipeak=i1 #A
Iavg=1/2/pi*(Ipeak*pi/3+Ipeak/2*2*pi/3) #A
print "Average thyristor current = %0.2f A  " %Iavg 
Irms_thyristor=sqrt(1/2/pi*(Ipeak**2*pi/3+(Ipeak/2)**2*2*pi/3)) #A
print "RMS value of thyristor current = %0.2f A  " %Irms_thyristor 

RMS load current = 18.856 A
Power output = 10666.7 W 
Average thyristor current = 8.89 A  
RMS value of thyristor current = 13.33 A