Chapter 05 : Thyristor Commutation Techniques

Example 5.1, Page No 252

In [12]:
import math
#initialisation of variables
L=5.0*10**-3            #mH
C=20.0*10**-6           #µF
V_s=200                 #V

#Calculations
w_o=math.sqrt(1/(L*C))    #rad/s
t_o=math.pi/w_o           #ms

#Results
print('conduction time of thyristor = %.2f ms' %(t_o*1000))
print('voltage across thyristor=%.0f V' %V_s)

conduction time of thyristor = 0.99 ms
voltage across thyristor=200 V

Example 5.2, Page No 255

In [13]:
import math

#initialisation of variables
C=20.0*10**-6         #µF
L=5.0*10**-6          #µH
V_s=230.0             #V

#Calculations
I_p=V_s*math.sqrt(C/L)      #A
w_o=math.sqrt(1/(L*C))      #rad/sec
t_o=math.pi/w_o             #µS
I_o=300               
a = math.degrees(math.asin(I_o/(2*V_s)))   
V_ab = V_s*math.cos(math.radians(a))      #V 
t_c=C*V_ab/I_o     #µs

#Calculations
print("conduction time of auxillery thyristor=%.2f us" %(t_o*10**6))
print("voltage across main thyristor=%.2f V" %V_ab)
print("ckt turn off time=%.2f us" %(t_c*10**6))

conduction time of auxillery thyristor=31.42 us
voltage across main thyristor=174.36 V
ckt turn off time=11.62 us

Example 5.3 Page No 258

In [14]:
import math

#initialisation of variables
V_s=200.0           #V
R1=10.0             #Ω
R2=100.0            #Ω
C=0                 #  value of capacitor

#Calculations
I1=V_s*(1/R1+2/R2)    #A
I2=V_s*(2/R1+1/R2)    #A
t_c1=40*10**-6
fos=2    #factor of safety
C1=t_c1*fos/(R1*math.log(2))
C2=t_c1*fos/(R2*math.log(2))
if C1 > C2 :
    C = C1*10**6
else :
    C = C2*10**6


#Results
print("peak value of current through SCR1=%.2f A" %I1); 
print("Peak value of current through SCR2=%.2f A" %I2);
print("Value of capacitor=%.2f uF" %C);

peak value of current through SCR1=24.00 A
Peak value of current through SCR2=42.00 A
Value of capacitor=11.54 uF

Example 5.4, Page No 260

In [15]:
import math
#initialisation of variables
V_s=230.0             #V
L=20*10**-6           #µH
C=40*10**-6           #µF
I_o=120.0             #A

#Calculations
I_p=V_s*math.sqrt(C/L)   #A
t_c=C*V_s/I_o            #µs
w_o=math.sqrt(1/(L*C))  
t_c1=math.pi/(2*w_o)     #µs

#Results
print("current through main thyristor=%.2f A"  %(I_o+I_p))
print("Current through auxillery thyristor=%.2f A" %I_o)
print("Circuit turn off time for main thyristor=%.2f us" %(t_c*10**6))
print("Circuit turn off time for auxillery thyristor=%.2f us" %(t_c1*10**6))

current through main thyristor=445.27 A
Current through auxillery thyristor=120.00 A
Circuit turn off time for main thyristor=76.67 us
Circuit turn off time for auxillery thyristor=44.43 us

Example 5.5 Page No 263

In [16]:
import math
#initialisation of variables
C_j=25*10**-12      #pF
I_c=5*10**-3        #charging current
V_s=200.0           #V
R=50.0              #Ω

#Calculations
C=(C_j*V_s)/(I_c*R)


#RESULTS
print("Value of C=%.2f  µF" %(C*10**6))

Value of C=0.02  µF

Example 5.6 Page No 263

In [17]:
import math

#initialisation of variables
V_s=200.0         #V
R=5.0             #Ω

#Calculations
C=10.0*10**-6
#for turn off V_s*(1-2*exp(-t/(R*C)))=0,    so after solving
t_c=R*C*math.log(2.0)

#Results
print("circuit turn off time=%.2f us" %(t_c*10**6))

circuit turn off time=34.66 us

Example 5.7, Page No 264

In [18]:
import math
#initialisation of variables
R=1.0                   #Ω
L=20*10**-6             #µH
C=40*10**-6             #µF

#Calculations
w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)
t_1=math.pi/w_r

#Results
print("conduction time of thyristor=%.3f us" %(t_1*10**6))

conduction time of thyristor=125.664 us

Example 5.8 Page No 265

In [19]:
import math 

#initialisation of variables
dv=400*10.0**-6       #dv=dv_T/dt(V/s)
V_s=200.0             #v
R=20.0                #Ω

#Calculations
C=V_s/(R*dv)         
C_j=.025*10**-12
C_s=C-C_j
I_T=40;
R_s=1/((I_T/V_s)-(1/R)) 
#value of R_s in book is wrongly calculated

#Results
print("R_s=%.2f ohm" %R_s)
print("C_s=%.3f uF" %(C_s/10**6))

R_s=6.67 ohm
C_s=0.025 uF

Example 5.9 Page No 265

In [20]:
import math
#initialisation of variables
V_s=200.0          #V
C=20.0*10**-6      #µH   
L=0.2*10**-3       #µF
i_c=10.0

#Calculations
i=V_s*math.sqrt(C/L)
w_o=1.0/math.sqrt(L*C)
t_1 = (1/w_o)*math.degrees(math.asin(i_c/i))
t_o=math.pi/w_o
t_c=t_o-2*t_1    

#Results
print("reqd time=%.2f us" %(t_1*10**6))
print("ckt turn off time=%.2f us" %(t_c*10**6))
print("ckt turn off time=%.5f us" %t_1)
#solution in book wrong, as wrong values are selected while filling the formuleas

reqd time=575.37 us
ckt turn off time=-952.05 us
ckt turn off time=0.00058 us

Example 5.11 Page No 268

In [21]:
import math

#initialisation of variables
L=1.0              #µH
R=50.0             #Ω
V_s=200.0          #V
t=0.01             #sec
Vd=0.7

#Calculations
tau=L/R
i=(V_s/R)*(1-math.exp(-t/tau))
t=8*10**-3
i1=i-t*Vd  


#Results
print("current through L = %.2f A" %i1)
i_R=0                  #current in R at t=.008s
print("Current through R = %.2f A" %i_R)

current through L = 1.57 A
Current through R = 0.00 A

Example 5.12, Page No 269

In [22]:
import math

#initialisation of variables

#initialisation of variables
L=1.0                      #H
R=50.0                   #ohm
V_s=200.0                #V

#Calculations
tau=L/R
t=0.01                 #s
i=(V_s/R)*(1-math.exp(-t/tau))
C=1*10**-6            #F
V_c=math.sqrt(L/C)*i

#Results
print("current in R,L=%.2f A" %i)
print("voltage across C=%.2f kV" %(V_c/1000))

current in R,L=1.57 A
voltage across C=1.57 kV