Chapter 12 : AC Steadystate Circuit Analysis

Example 12.1, Page No 148

In [1]:
import math
#initialisation of variables
#calculate power fed to load
 
V=100.0 

#Calculations
Va=(V/(math.sqrt(2)*math.pi))*(2+1/math.sqrt(2)) 
Rd=10.0 
Pa=Va**2/Rd 

#Results
print(Pa,'load power(W)') 

(371.26245525794906, 'load power(W)')

Example 12.2, Page No 149

In [2]:
import math
#initialisation of variables
#calculate firing angle value

Po=15000.0 
Ro=1.5 
Va=math.sqrt(Po*Ro) 

#Calculations
a=math.degrees(math.acos((Va*2*math.pi/(3*math.sqrt(6)*V))-1))
print(a,'firing angle(deg)') 
Ia=Va/Ro 
Ith=Ia/3.0 

#Results
print(Ith,'avg current through diodes(A)') 

(73.58755434217028, 'firing angle(deg)')
(33.333333333333336, 'avg current through diodes(A)')

Example 12.3, Page No 149

In [3]:
import math
#initialisation of variables
#calculate value of commutating capacitor
Iamax=100.0 
V=100.0 
f_max=400.0 

#Calculations
c=Iamax/(2*V*f_max) 

#Results
print(c,'value of commutating capacitor(F)') 

(0.00125, 'value of commutating capacitor(F)')

Example 10.4 Page No 150

In [4]:
import math
#initialisation of variables
#to determine value of capacitor

  
f=50.0 
w=2*math.pi*f 
Z_lm=complex(3,2.7) 
Z_la=complex(7,3) 

#Calculations
I_m=(-1)*math.degrees(math.atan((Z_lm.imag)/(Z_la.imag))) 
a=90.0 
I_a=a+I_m 
c=1/(w*((Z_lm.real)-(Z_la.real)*math.cos(math.radians((-1)*I_a)))) 

#Results
print(c,'value of capacitor(F)') 

(-0.0018916018169502632, 'value of capacitor(F)')

Example 10.6, Page No 151

In [5]:
import math
#initialisation of variables
#to calculate starting torque and atarting current,motor performance

  
V_a=110*complex(math.cos(math.radians(90)),math.sin(math.radians(90))) 
V_m=220*complex(math.cos(math.radians(0)),math.sin(math.radians(0))) 
R_1=3 
R_2=2.6 
X_1=2.7 
X_2=2.7 
X=110 
V_f=(1.0/2)*(V_m-1j*V_a)
V_b=(1.0/2)*(V_m+1j*V_a) 
Z_f=(complex(0,X)*complex(R_2,X_2))/(complex(0,X)+complex(R_2,X_2)) 
Z_b=Z_f 
Z_ftot=complex(R_1,X_1)+Z_f 
Z_btot=complex(R_1,X_1)+Z_b 
I_f=V_f/Z_ftot 
I_b=V_b/Z_btot 
T_s=(2/157)*(Z_f.real)*(abs(I_f)**2-abs(I_b)**2) 
print(T_s,'starting torque(Nm)') 
I_m=I_f+I_b 
I_a=1j*(I_f-I_b) 
print(abs(I_a),'starting current(A)') 
s=0.04 

Z_f=(complex(0,X)*complex(R_2/s,X_2))/(complex(0,X)+complex(R_2/s,X_2)) 
Z_b=(complex(0,X)*complex(R_2/(2-s),X_2))/(complex(0,X)+complex(R_2/(2-s),X_2)) 
Z_ftot=complex(R_1,X_1)+Z_f 
Z_btot=complex(R_1,X_1)+Z_b 
I_f=V_f/Z_ftot 
I_b=V_b/Z_btot 
w_s=157.1 
T_s=(2/157.1)*(abs(I_f)**2*(Z_f.real)-abs(I_b)**2*(Z_b.real)) 
print(T_s,'starting torque(Nm)') 
I_m=I_f+I_b 

#Calculations
m=math.degrees(math.atan((I_m.imag)/(I_m.real)))
I_a=1j*(I_f-I_b) 
a=math.degrees(math.atan((I_a.imag)/(I_a.real)))
P_m=w_s*(1.0-s)*T_s 
P_L=200.0 
P_out=P_m-P_L 
P_min=V*abs(I_m)*math.cos(math.radians(m)) 
P_ain=V*abs(I_a)*math.cos(math.radians(a))
P_in=P_min+P_ain 
n=P_out/P_in 
print(n,'efficiency') 

r=Z_ftot/Z_btot     #r=V_mf/V_bf
#V_mf+V_bf=220
V_mf=220/(1+r) 
V_mb=220-V_mf 
V_a=1j*(V_mf-V_mb) 

#Results
print(abs(V_a),'V_a(V)') 

(0.0, 'starting torque(Nm)')
(14.313452498677325, 'starting current(A)')
(3.5887587638431966, 'starting torque(Nm)')
(0.2815652638045585, 'efficiency')
(176.4417668704772, 'V_a(V)')