CHAPTER 4: DIRECT CURRENT GENERATORS¶

Example 4.1, Page number 143¶

In [1]:
from sympy import *

#Variable declaration
N = 100.0         #Number of turns

#Calculation
t = Symbol('t')
e = N*diff(0.05*sin(314*t), t, 1)

#Result
print('Induced voltage at the coil terminals , e = ' + repr(e) + ' V')

Induced voltage at the coil terminals , e = 1570.0*cos(314*t) V


Example 4.2, Page number 145¶

In [1]:
#Variable declaration
l = 0.65       #Length of conductor(m)
v = 35.0       #Speed of conductor(m/s)
B = 0.8        #Magnetic flux density(Tesla)

#Calculation
e = B*l*v      #Induced voltage at the conductor(V)

#Result
print('Induced voltage at the conductor , e = %.1f V' %e)

Induced voltage at the conductor , e = 18.2 V


Example 4.3, Page number 145¶

In [1]:
import math

#Variable declaration
l = 1.5                    #Length of conductor(m)
v = 20.0                   #Velocity of conductor(m/s)
B = 0.9                    #Magnetic flux density(Wb/m^2)

#Calculation
e = B*l*v*math.sin(theta)  #Induced voltage at the conductor(V)

#Result
print('Induced voltage at the conductor , e = %.1f V' %e)

Induced voltage at the conductor , e = 15.5 V


Example 4.4, Page number 152-153¶

In [1]:
#Variable declaration
P = 4.0          #Number of poles
S = 40.0         #Number of slots
C = 10.0         #Number of conductors per slot
phi = 0.02       #Flux per pole(Wb)
N = 1200.0       #Speed(rpm)

#Calculation
Z = S*C                   #Total number of conductors
A = 2.0                   #Number of parallel paths for Wave winding
E_g = P*phi*Z*N/(60*A)    #Generated emf(V)

#Result
print('Generated emf , E_g = %.f V' %E_g)

Generated emf , E_g = 320 V


Example 4.5, Page number 153¶

In [1]:
import math

#Variable declaration
P = 6.0       #Number of poles
Z = 600.0     #Number of conductors
phi = 0.05    #Flux per pole(Wb)
N = 1000.0    #Speed of generator(rpm)
I_a = 120.0   #Current supplied by generator(A)

#Calculation
A = P                                 #Number of parallel paths for lap winding
E_g = P*phi*Z*N/(60*A)                #Generated voltage(V)
T_em = (P*Z*phi)/(2*math.pi*A)*I_a    #Electromagnetic torque(N-m)

#Result
print('Generated voltage , E_g = %.f V' %E_g)
print('Electromagnetic torque , T_em = %.2f N-m' %T_em)

Generated voltage , E_g = 500 V
Electromagnetic torque , T_em = 572.96 N-m


Example 4.6, Page number 156¶

In [1]:
#Variable declaration
V_t = 220.0     #Shunt generator voltage(V)
R_sh = 50.0     #Shunt field resistance(ohm)
R_a = 0.02      #Armature resistance(ohm)

#Calculation
I_sh = V_t/R_sh     #Shunt field current(A)
I_a = I_L+I_sh      #Armature current(A)
E_g = V_t+I_a*R_a   #Generated voltage(V)

#Result
print('Generated voltage , E_g = %.2f V' %E_g)

Generated voltage , E_g = 225.09 V


Example 4.7, Page number 158-160¶

In [1]:
#Variable declaration
E = 25.0          #Power of compound generator(kW)
V_t = 220.0       #Terminal voltage(V)
R_a = 0.07        #Armature resistance(ohm)
R_se = 0.05       #Series resistance(ohm)
R_sh = 55.0       #Shunt field resistance(ohm)
V_brush = 1.0     #Voltage drop per brush(V)

#Calculation
I_L = E*10**3/V_t                       #Load current in A
I_sh = V_t/R_sh                         #Shunt field current(A)
I_a = I_sh+I_L                          #Armature current(A)
#For case(i)
E_g1 = V_t+I_a*(R_a+R_se)+2*V_brush     #Generated emf(V)
#For case(ii)
V_ab = V_t+I_L*R_se                     #Voltage across the shunt field(V)
I_sh2 = V_ab/R_sh                       #Current in the shunt field(A)
I_a2 = I_sh2+I_L                        #Armature current(A)
E_g2 = V_ab+I_a2*R_a+2*V_brush          #Generated emf(V)

#Result
print('(i)  Generated emf when generator is connected in long shunt , E_g = %.f V' %E_g1)
print('(ii) Generated emf when generator is connected in short shunt , E_g = %.1f V' %E_g2)

(i)  Generated emf when generator is connected in long shunt , E_g = 236 V
(ii) Generated emf when generator is connected in short shunt , E_g = 235.9 V


Example 4.8, Page number 160-161¶

In [1]:
#Variable declaration
V_t = 220.0     #Shunt generator voltage(V)
I_L = 146.0     #Current delivered by generator(A)
R_sh = 55.0     #Shunt field resistance(ohm)
R_a = 0.012     #Armature resistance(ohm)
R_se = 0.02     #Series field resistance(ohm)
R_di = 0.03     #Diverter field resistance(ohm)

#Calculation
I_sh = V_t/R_sh               #Shunt field current(A)
I_a = I_L+I_sh                #Armature current(A)
R_com = R_se*R_di/(R_se+R_di) #Combined resistance(ohm)
E_g = V_t+I_a*(R_a+R_com)     #Generated voltage(V)
P_lsd = I_a**2*R_com          #Power loss in series field and diverter(W)
P_la = I_a**2*R_a             #Power loss in the armature circuit resistance(W)
P_lsh =  V_t*I_sh             #Power loss in shunt field resistance(W)
P_dl = I_L*V_t                #Power delivered(W)

#Result
print('Generated voltage , E_g = %.1f V' %E_g)
print('Power loss in the series field and diverter , P_lsd = %.1f W' %P_lsd)
print('Power loss in the armature circuit resistance , P_la = %.1f W' %P_la)
print('Power loss in the shunt field resistance , P_lsh = %.f W' %P_lsh)
print('Power delivered to the load , P_dl = %.f W' %P_dl)
print('\nNOTE : ERROR : Shunt field resistance is taken as 50 ohm while solving I_sh in textbook but it is 55 ohm as per textbook question')

Generated voltage , E_g = 223.6 V
Power loss in the series field and diverter , P_lsd = 270.0 W
Power loss in the armature circuit resistance , P_la = 270.0 W
Power loss in the shunt field resistance , P_lsh = 880 W
Power delivered to the load , P_dl = 32120 W

NOTE : ERROR : Shunt field resistance is taken as 50 ohm while solving I_sh in textbook but it is 55 ohm as per textbook question


Example 4.9, Page number 169¶

In [1]:
#Variable declaration
P = 4.0       #Number of poles
Z = 500.0     #Number of conductors
I_a = 30.0    #Current delivered by generator(A)
alpha = 6.0   #Angle at which brushes are displaced angle(degree)

#Calculation
A = 2.0                               #Number of parallel paths for Wave winding
I_c = I_a/A                           #Current per conductor(A)
#For case(i)
AT_d = Z*I_c*alpha/360                #Demagnetizing ampere-turns per pole(At)
#For case(ii)
AT_c = Z*I_c*((1/(2*P))-(alpha/360))  #Cross magnetizing ampere-turns per pole(At)

#Result
print('(i)  Demagnetizing ampere-turns , AT_d = %.f At' %AT_d)
print('(ii) Cross-magnetizing ampere-turns , AT_c = %.1f At' %AT_c)

(i)  Demagnetizing ampere-turns , AT_d = 125 At
(ii) Cross-magnetizing ampere-turns , AT_c = 812.5 At


Example 4.10, Page number 176¶

In [1]:
#Variable declaration
Power = 12.0     #Power(kW)
P = 4.0          #Number of poles
Z = 500.0        #Number of conductors
V_t = 250.0      #Generator voltage(V)
N = 1000.0       #Speed(rpm)
P_cu = 600       #Full load copper loss(W)
brush_drop = 2.0 #Total brush drop(V)

#Calculation
A = P                                 #Number of parallel paths for lap winding
I_a = Power*10**3/V_t                 #Armature current(A)
R_a = P_cu/I_a**2                     #Armature resistance(ohm)
E_g = V_t+I_a*R_a+brush_drop          #Generated voltage(V)
phi = E_g*60*A/(P*Z*N)                #Flux per pole(Wb)

#Result
print('Flux per pole , Φ = %.3f Wb' %phi)

Flux per pole , Φ = 0.032 Wb


Example 4.11, Page number 176-177¶

In [1]:
#Variable declaration
P = 4.0             #Number of poles
I_L = 25.0          #Current delivered by generator(A)
V_t = 230.0         #Generator terminal voltage(V)
R_a = 0.2           #Armature resistance(ohm)
R_sh = 55.0         #Shunt field resistance(ohm)
V_brush = 1.0       #Voltage drop per brush(V)

#Calculation
I_sh = V_t/R_sh                #Shunt field current(A)
I_a = I_L+I_sh                 #Armature current(A)
E_g = V_t+I_a*R_a+2*V_brush    #Induced voltage(V)
P_arm = E_g*I_a                #Power generated in armature(W)
P_L = V_t*I_L                  #Power absorbed by load(W)
n = (P_L/P_arm)*100            #Efficiency(percent)

#Result
print('Induced voltage , E_g = %.1f V' %E_g)
print('Efficiency of generator , η = %.1f percent' %n)

Induced voltage , E_g = 237.8 V
Efficiency of generator , η = 82.8 percent