CHAPTER 3: DC DYNAMO VOLTAGE RELATIONS-DC GENERATORS

Example 3.1, Page number 69

In [1]:
#Variable declaration
kW = 150.0        #Power rating of Shunt generator(kW)
V_1 = 250.0       #Voltage rating of Shunt generator(V)
V_a = V_1         #Voltage rating of Shunt generator(V)
R_f = 50.0        #Field resistance(ohm)
R_a = 0.05        #Armature resistance(ohm)

#Calculation
I_1 = kW*1000/V_1    #Full-load line current flowing to the load(A)
I_f = V_1/R_f        #Field current(A)
I_a = I_f+I_1        #Armature current(A)
E_g = V_a+(I_a*R_a)  #Full load generated voltage(V)

#Result
print('Case(a): Full-load line current flowing to the load , I_1 = %.f A' %I_1)
print('Case(b): Field current , I_f = %.f A' %I_f)
print('Case(c): Armature current , I_a = %.f A' %I_a)
print('Case(d): Full-load generated voltage , E_g = %.2f A' %E_g)

Case(a): Full-load line current flowing to the load , I_1 = 600 A
Case(b): Field current , I_f = 5 A
Case(c): Armature current , I_a = 605 A
Case(d): Full-load generated voltage , E_g = 280.25 A

Example 3.2, Page number 72

In [1]:
#Variable declaration
kW =100.0      #Power rating of the generator(kW)
V_1 = 500.0    #Voltage rating of hte generator(V)
R_a = 0.03     #Armature resistance(ohm)
R_f = 125.0    #Shunt field resistance(ohm)
R_s = 0.01     #Series field resistance(ohm)
I_d = 54.0     #Diverter current(A)

#Calculation
#Case(a)
I_1 = kW*1000/V_1          #Full-load line current flowing to the load(A)
I_f = V_1/R_f              #Shunt Field current(A)
I_a = I_f+I_1              #Armature current(A)
I_s = I_a-I_d              #Series Field current(A)
R_d = I_s*R_s/I_d          #Diverter resistance(ohm)
#Case(b)
E_g = V_1+I_a*R_a+I_s*R_s  #Generated voltage at full load(V)

#Result
print('Case(a): Diverter resistance at full load , R_d = %.4f Ω' %R_d)
print('Case(b): Generated voltage at full load , E_g = %.2f V' %E_g)

Case(a): Diverter resistance at full load , R_d = 0.0278 Ω
Case(b): Generated voltage at full load , E_g = 507.62 V

Example 3.3, Page number 75

In [1]:
#Variable declaration
E_orig = 150.0      #Armature voltage of the generator(V)
S_orig = 1800.0     #Speed of the generator(rpm)
S_final_a =2000.0   #Increased Speed of the generator(rpm)
S_final_b =1600.0   #Increased Speed of the generator(rpm)

#Calculation
E_final_a = E_orig*(S_final_a/S_orig)   #No-load voltage of the generator(V)
E_final_b = E_orig*(S_final_b/S_orig)   #No-load voltage of the generator(V)

#Result
print('Case(a): No-load voltage of the separately excited generator , E_final = %.2f V' %E_final_a)
print('Case(b): No-load voltage of the separately excited generator , E_final = %.2f V' %E_final_b)

Case(a): No-load voltage of the separately excited generator , E_final = 166.67 V
Case(b): No-load voltage of the separately excited generator , E_final = 133.33 V

Example 3.4, Page number 75

In [1]:
#Variable declaration
S_final = 1200.0      #Speed of the generator(rpm)
E_orig_a = 64.3       #Armature voltage of the generator(V) for case a
S_orig_a = 1205.0     #Varied Speed of the generator(rpm)
E_orig_b = 82.9       #Armature voltage of the generator(V) for case b
S_orig_b = 1194.0     #Varied Speed of the generator(rpm)
E_orig_c = 162.3      #Armature voltage of the generator(V) for case c
S_orig_c = 1202.0     #Varied Speed of the generator(rpm)

#Calculation
E_1 = E_orig_a*(S_final/S_orig_a)   #No-load voltage of the generator(V)
E_2 = E_orig_b*(S_final/S_orig_b)   #No-load voltage of the generator(V)
E_3 = E_orig_c*(S_final/S_orig_c)   #No-load voltage of the generator(V)

#Result
print('Case(a): No-load voltage of the generator , E_1 = %.1f V at %.f rpm' %(E_1,S_final))
print('Case(b): No-load voltage of the generator , E_2 = %.1f V at %.f rpm' %(E_2,S_final))
print('Case(c): No-load voltage of the generator , E_3 = %.1f V at %.f rpm' %(E_3,S_final))

Case(a): No-load voltage of the generator , E_1 = 64.0 V at 1200 rpm
Case(b): No-load voltage of the generator , E_2 = 83.3 V at 1200 rpm
Case(c): No-load voltage of the generator , E_3 = 162.0 V at 1200 rpm

Example 3.5, Page number 82

In [1]:
#Variable declaration
V = 125.0      #Rated voltage of the shunt generator(V)
R_a = 0.15     #Armature resistance(ohm)
V_a = 0        #Terminal voltage across the load(V)
I_l = 96.0     #Load current(A)
I_f = 4.0      #Field current in A

#Calculation
I_a = I_f+I_l      #Armature current(A)
E_g = V_a+I_a*R_a  #Voltage generated in the armature(V)

#Result
print('Voltage generated in the armature , E_g = %.f V' %E_g)

Voltage generated in the armature , E_g = 15 V

Example 3.6, Page number 84

In [1]:
#Variable declaration
V_nl = 135.0   #No-load voltage of the shunt generator(V)
V_fl = 125.0   #Full-load voltage of the shunt generator(V)

#Calculation
VR = (V_nl-V_fl)/V_fl*100  #Voltage regulation(%)

#Result
print('Voltage regulation , VR = %.f percent' %VR)

Voltage regulation , VR = 8 percent

Example 3.7, Page number 84

In [1]:
#Variable declaration
VR = 0.105     #Voltage regulation
V_fl = 250.0   #Full-load voltage of the shunt generator(V)

#Calculation
V_nl = V_fl+(V_fl*VR)   #No-load voltage of the generator(V)

#Result
print('No-load voltage of the generator , V_nl = %.1f V' %V_nl)

No-load voltage of the generator , V_nl = 276.2 V

Example 3.8, Page number 88

In [1]:
#Variable declaration
N_f = 1000.0    #Shunt field winding(turns/pole)
N_s = 4.0       #Series field winding(turns/pole)
I_f = 0.2       #Field current(A)
I_a = 80.0      #Full-load armature current(A)
R_s =0.05       #Series field resistance(ohm)

#Calculation
I_s_N_s = I_f*N_f     #Series field ampere-turns
I_s =(I_s_N_s)/N_s    #Desired current in the series field required to produce voltage rise(A)
I_d = I_a-I_s         #Diverter current(A)
R_d = (I_s*R_s)/I_d   #Diverter resistance(ohm)

#Result
print('Case(a): Number of series field ampere-turns required for flat-compound operation , I_sN_s = %.f At' %I_s_N_s)
print('Case(b): Diverter resistance required for flat-compound operation , R_d = %.4f Ω' %R_d)

Case(a): Number of series field ampere-turns required for flat-compound operation , I_sN_s = 200 At
Case(b): Diverter resistance required for flat-compound operation , R_d = 0.0833 Ω

Example 3.9, Page number 89

In [1]:
#Variable declaration
kW = 60.0    #Power rating of the generator(kW)
V = 240.0    #Voltage rating of the generator(V)
I_f = 3.0    #Increase in the field current(A)
OC_V = 275.0 #Over-compounded Voltage(V)
I_l = 250.0  #Rated load current(A)
N_f = 200.0  #Number of turns per pole in the shunt field winding 
N_s = 5.0    #Number of turns per pole in the series field winding 
R_f = 240.0  #Shunt field resistance(ohm)
R_s = 0.005  #Series field resistance(ohm)

#Calculation
#Case(a)
I_s_N_s = I_f * N_f        #Series field ampere-turns
I_s = (I_s_N_s)/N_s        #Desired current in the series field required to produce voltage rise(A)
I_d = I_l-I_s              #Diverter current(A)
R_d = (I_s*R_s)/I_d        #Diverter resistance(ohm)
#Case(b)
NL_MMF = (V/R_f)*N_f       #No-load MMF(At/pole)
I_f_N_f = NL_MMF
FL_MMF = I_f_N_f+I_s_N_s   #Full-load MMF(At/pole)

#Result
print('Case(a): Required diverter resistance , R_d = %.5f Ω' %R_d)
print('Case(b): Total air-gap MMF per pole at no load , No-load MMF = %.f At/pole' %NL_MMF)
print('         Total air-gap MMF per pole at full load , Full-load MMF = %.f At/pole' %FL_MMF)

Case(a): Required diverter resistance , R_d = 0.00462 Ω
Case(b): Total air-gap MMF per pole at no load , No-load MMF = 200 At/pole
         Total air-gap MMF per pole at full load , Full-load MMF = 800 At/pole

Example 3.10, Page number 93

In [1]:
#Variable declaration
kW= 50.0              #Power rating of the dynamo(kW)
V = 125.0             #Rated voltage(V)
S = 1800.0            #Speed of the dynamo(rpm)
I_f = 20.0            #Exciting field current(A)
Max_temp_rise = 25.0  #Maximum Temperature rise(degree celsius)
I_l = 400.0           #Load Current(A)

#Result
print('Case(a): Since the speed is reduced in half,we must reduce the kW rating in half.Consequently,the 25kW, 900rpm dynamo has the SAME size');
print('Case(b): Since we have cut the speed in half but maintained the same kW rating, the dynamo has TWICE the size as the original')
print('Case(c): HALF the size')
print('Case(d): SAME size')

Case(a): Since the speed is reduced in half,we must reduce the kW rating in half.Consequently,the 25kW, 900rpm dynamo has the SAME size
Case(b): Since we have cut the speed in half but maintained the same kW rating, the dynamo has TWICE the size as the original
Case(c): HALF the size
Case(d): SAME size