# Chapter 1 : D.C. Generators¶

## Example 1.1 page no : 17¶

In :
import math

# Variables
p = 4.
Z = 440.
theta = 0.07    # Wb
N = 900.        # rpm

# calculations and results
E = theta*N*Z/60.
print "For lap wound : E = %.f V"%E

E = theta*N*Z*4/120.
print "For wave wound : E = %.f V"%E

# note : rounding off error.

For lap wound : E = 462 V
For wave wound : E = 924 V


## Example 1.2 page no : 18¶

In :
import math

# Variables
Pole = 4.
phi = 21.*10**-3  			#flux produced by each pole in webers
N = 1120.        			#Speed of armature in r.p.m
Coils = 42.
turns_per_coil = 8.
Turns = Coils * turns_per_coil
Z = 2*Turns  			#Number of armature conductors

# Calculations and Results
#Part(i)
A1 = Pole  			#no of parallel paths for lap winding
E1 = phi*N*Z*Pole/(60*A1)
print 'i)  e.m.f generated is %.3f V'%(E1)

#Part(ii)
A2 = 2  			#wave winding
E2 = E1 			#as mentioned in the question
N2 = E2/(phi*Z*Pole/(60*A2)) 			#E = phi*N*Z*Pole/(60*A)
print 'ii)  For wave-wound armature,above calculated e.m.f is generated at %.0f r.p.m'%(N2)

i)  e.m.f generated is 263.424 V
ii)  For wave-wound armature,above calculated e.m.f is generated at 560 r.p.m


## Example 1.3 page no: 27¶

In :
import math

# Variables
Pole = 4.
coils = 12.
commutator_segments = coils
coil_sides = coils*2
Z = coil_sides  			#No of conductors
pole_pitch = Z/Pole

# Calculations and Results
#for Simplex lap winding
y_f = pole_pitch-1
y_b = pole_pitch+1

y_c = 1  			#Note that it's positive and it's progressive type of Simplex lap winding

print 'WINDING TABLE:   1<-    8->    3<-   10->    5<-   12-> 7<-   14->    9<-   16->   11<-   18->13<-   20->   15<-   22->   17<-   24->19<-    2->   21<-    4->   23<-    6-> 1                                                  '
print 'Note that <- indicates back connection with  y_back = %.0f and -> indicates front connection with y_front = %.0f'%(y_b,y_f)
print 'Another form of winding table:'
print '      BACK CONNECTIONS                                FRONT CONNECTIONS'

print '       1 to 1+7  =  8                        ->        8 to 8-5  =  3'
print '       3 to 3+7  = 10                        ->       10 to 10-5 =  5'
print '       5 to 5+7  = 12                        ->       12 to 12-5 =  7'
print '       7 to 7+7  = 14                        ->       14 to 14-5 =  9'
print '       9 to 9+7  = 16                        ->       16 to 16-5 = 11'
print '      11 to 11+7 = 18                        ->       18 to 18-5 = 13'
print '      13 to 13+7 = 20                        ->       20 to 20-5 = 15'
print '      15 to 15+7 = 22                        ->       22 to 22-5 = 17'
print '      17 to 17+7 = 24                        ->       24 to 24-5 = 19'
print '      19 to 19+7 = 26 = 26-24 = 2              ->        2 to 26-5 = 21'
print '      21 to 21+7 = 28 = 28-24 = 4              ->        4 to 28-5 = 23'
print '      23 to 23+7 = 30 = 30-24 = 6              ->        6 to 30-5 = 25   =  25-24 = 1'

WINDING TABLE:   1<-    8->    3<-   10->    5<-   12-> 7<-   14->    9<-   16->   11<-   18->13<-   20->   15<-   22->   17<-   24->19<-    2->   21<-    4->   23<-    6-> 1
Note that <- indicates back connection with  y_back = 7 and -> indicates front connection with y_front = 5
Another form of winding table:
BACK CONNECTIONS                                FRONT CONNECTIONS
1 to 1+7  =  8                        ->        8 to 8-5  =  3
3 to 3+7  = 10                        ->       10 to 10-5 =  5
5 to 5+7  = 12                        ->       12 to 12-5 =  7
7 to 7+7  = 14                        ->       14 to 14-5 =  9
9 to 9+7  = 16                        ->       16 to 16-5 = 11
11 to 11+7 = 18                        ->       18 to 18-5 = 13
13 to 13+7 = 20                        ->       20 to 20-5 = 15
15 to 15+7 = 22                        ->       22 to 22-5 = 17
17 to 17+7 = 24                        ->       24 to 24-5 = 19
19 to 19+7 = 26 = 26-24 = 2              ->        2 to 26-5 = 21
21 to 21+7 = 28 = 28-24 = 4              ->        4 to 28-5 = 23
23 to 23+7 = 30 = 30-24 = 6              ->        6 to 30-5 = 25   =  25-24 = 1


## Example 1.4 page no : 32¶

In :
import math

# Variables
Pole = 4.
Z = 18.               			#no of armature conductors
Y_A = (Z+2)/Pole     			#For progressive type wave winding,positive sign is used
Y_C = Y_A            			#For wave winding

# Calculations
#Since Y_A = (y_b+y_f)/2, we let y_b = Y_f
y_b = Y_A/2   			#say
y_f = y_b

coils = Z/2
slots = coils
commutator_segments = coils

print commutator_segments
print 'WINDING TABLE:   1<-    6->  11<-  16->   3<-   8->13<-   18->   5<-  10->  15<-   2-> 7<-   12->  17<-   4->   9<-  14->1                                                  '

print 'Another form of winding table:'

print '      BACK CONNECTIONS                                FRONT CONNECTIONS'

print '       1 to 1+5   =  6                       ->        6 to 6+5  =  11'
print '      11 to 11+5  = 16                       ->       16 to 16+5 =  21 -18 = 3'
print '       3 to 3+5   =  8                       ->        8 to  8+5 =  13'
print '      13 to 13+5  = 18                       ->       18 to 18+5 =  23 -18 = 5'
print '       5 to 5+5   = 10                       ->       10 to 10+5 =  15'
print '      15 to 15+5  = 20 -18 = 2                 ->        2 to  2+5 =   7'
print '       7 to 7+5   = 12                       ->       12 to 12+5 =  17'
print '      17 to 17+5  = 22 -18 = 4                 ->        4 to  4+5 =   9'
print '       9 to 9+5   = 14                       ->       14 to 14+5 =  19 -18 = 1'

9.0
WINDING TABLE:   1<-    6->  11<-  16->   3<-   8->13<-   18->   5<-  10->  15<-   2-> 7<-   12->  17<-   4->   9<-  14->1
Another form of winding table:
BACK CONNECTIONS                                FRONT CONNECTIONS
1 to 1+5   =  6                       ->        6 to 6+5  =  11
11 to 11+5  = 16                       ->       16 to 16+5 =  21 -18 = 3
3 to 3+5   =  8                       ->        8 to  8+5 =  13
13 to 13+5  = 18                       ->       18 to 18+5 =  23 -18 = 5
5 to 5+5   = 10                       ->       10 to 10+5 =  15
15 to 15+5  = 20 -18 = 2                 ->        2 to  2+5 =   7
7 to 7+5   = 12                       ->       12 to 12+5 =  17
17 to 17+5  = 22 -18 = 4                 ->        4 to  4+5 =   9
9 to 9+5   = 14                       ->       14 to 14+5 =  19 -18 = 1


## Example 1.5 page no : 42¶

In :
import math

# Variables
Pole = 4.
Z = 480.             			#No of armature conductors
I_a = 144.
I = I_a/2           			#For wave wound
theta_m = 10.        			#lead angle in DEGREES

# Calculations
amp_turns_PP_d = Z*I*theta_m/360  			#demagnetising Ampere-turns per pole
amp_turns_PP_c = Z*I*(1/(2*Pole)-theta_m/360) 			#cross-magnetising Ampere-turns per pole

# Results
print 'De-magnetising ampere-turns per pole is %.0f'%(amp_turns_PP_d)
print 'Cross-magnetising ampere-turns per pole is %.0f'%(amp_turns_PP_c)

De-magnetising ampere-turns per pole is 960
Cross-magnetising ampere-turns per pole is 3360


## Example 1.6 page no : 46¶

In :
import math

# Variables
Pole = 10.
Z = 800.            			#No of armature conductors
A = Pole            			#For lap wound
ratio = 0.7           			#ratio of pole arc to pole pitch

# Calculations
#amp_turns_PP = ratio*(I_a*Z)/(2*A*P)
turns_PP = ratio*(Z)/(2*A*Pole)   			#turns per pole
conductors_PP = turns_PP*2 			#multiplied with 2 because 2 conductors form 1 turn

# Results
print 'Compensating conductors per pole =  %.f'%(conductors_PP)

Compensating conductors per pole =  6


## Example 1.7 page no : 52¶

In :
# Variables
I_L = 150.
A = 4.
N = 1800.   			#in rpm
W_b = 1.2   			#Brush width
W_m = 0     			#width of mica insulation
L = 0.06*10**-3 			#Inducmath.tance
segments = 64.
n_s = 1800./60   			#in rps and not rpm
v = n_s*segments  			#peripheral speed in segments per second

# Calculations and Results
T_c = (W_b-W_m)/v  			#Time of commutation
I = I_L/A  			#Current through a conductor

#Part(i)
E_l = L*2*I/T_c
print 'i)   Reactive voltage using Linear commutation is %.1f V'%(E_l)

#Part(ii)
E_s = 1.11*L*2*I/T_c
print 'ii)  Reactive voltage using Sinusoidal commutation is %.3f V'%(E_s)

i)   Reactive voltage using Linear commutation is 7.2 V
ii)  Reactive voltage using Sinusoidal commutation is 7.992 V


## Example 1.8 page no : 63¶

In :
# Variables
V_t = 250.  			#Terminal voltage
R_sh = 100.  			#resistance of shunt field winding
I_sh = V_t/R_sh 			#shunt current
R_a = 0.22  			#Armature resistance

# Calculations
I_a = I_L+I_sh 			#armature current

E = V_t + I_a*R_a  			#Induced emf

# Results
print 'Induced e.m.f to supply the 5kW load is %.2f V'%(E)

Induced e.m.f to supply the 5kW load is 254.95 V


## Example 1.9 page no : 63¶

In :
# Variables
V_t = 250.  			#terminal voltage
P = 10.*10**3  			#10kW power of generator
I_a = I_L  	    		#As seperately excited
V_brush = 2.*2 			# 2 * no of brushes

E = 255.      			#on full load

# Calculations
R_a = (E-V_t-V_brush)/I_a 			#Because E = V_t+ I_a*R_a  + V_brush

# Results
print 'Armature resistance of generator is %.3f ohm'%(R_a)

Armature resistance of generator is 0.025 ohm


## Example 1.10 page no : 64¶

In :
import math

# Variables
R_a = 0.5
R_se = 0.03  			#resimath.tance due to armature and series field winding
V_brush = 2. 			#brush drop
N = 1500. 			#generator speed in r.p.m
coils = 540.
turns_per_coil = 6.

# Calculations
total_turns =  coils*turns_per_coil
Z = 2*total_turns 			#Total conductors
I_a = 50         			#armature current

phi = 2*10**-3  			#flux per pole in webers
E = phi*N*Z/(60)  			#A = P for lap-wound and they cancel out
V_t  = E- (I_a*(R_a+R_se)  + V_brush)   			#Because E = V_t+ I_a*R_a  + V_brush

# Results
print 'Terminal voltage is %.1f V'%(V_t)

Terminal voltage is 295.5 V


## Example 1.11 page no : 65¶

In :
# Variables
V_t = 225. 			#voltage across winding
R_a = 0.04 			#armature resistance
R_sh = 90 			#shunt resistance
R_se = 0.02			#resistance of series field winding

# Calculations
#E -I_a*R_a = V_t+I_L*R_se
I_sh = (V_t+I_L*R_se)/R_sh  			#current through shunt field winding

I_a = I_L + I_sh  			        #armature current
E = V_t+ I_a*R_a+I_L*R_se  			#induced emf

# Results
print 'Generated voltage is %.1f V'%(E)

Generated voltage is 229.6 V


## Example 1.12 page no : 76¶

In :
# Variables
R_sh = 53.  			#resistance of field winding
V_t = 100.   			#terminal voltage
I_sh  = V_t/R_sh 			#shunt current
I_f = I_sh
R_a = 0.1 			#armature resistance
E_o = 143. 			# for I_sh =  I_f  =  1.8867 as obtained from graph

# Calculations
I_a = (E_o-V_t)/R_a  			#Because E_o = V_t + I_a*R_a
I_L = I_a-I_sh  			#no load current

# Results
print 'Note: Open circuit voltage was obtained as followsE_o = R_sh*I_f   			# y = mx+c form with c = 0 and R_sh = 53Hence%( a line with slope 53 through origin is made to intersect OCC at 150 V'
print 'Therefore, Open circuit voltage is 150 V'
print 'No load current is %.4f A    '%(I_L)

Note: Open circuit voltage was obtained as followsE_o = R_sh*I_f   			# y = mx+c form with c = 0 and R_sh = 53Hence%( a line with slope 53 through origin is made to intersect OCC at 150 V
Therefore, Open circuit voltage is 150 V
No load current is 428.1132 A


## Example 1.13 page no : 79¶

In :
# Variables
#part(1)

# Calculations and Results
#Draw horizontal line from 240 V, to intersect OCC at A. corresponding I_f is 2.25 A
#The slope pf OA is corresponding R_sh
I_f = 2.25  			#Corresponds to 240 V when intersected OCC
R_sh = E_o/I_f  			#shunt resistance
print 'i)Field resistance that gives 240 V on no-load is %.2f ohms '%(R_sh)

#Part(ii)
N1 = 1000. 			#speed of shunt generator in rpm
I_f = 1.

#Draw line OP math.tangential to OCC at N1 = 1000 r.p.m.
#Select I_f = 1A i.e. point R
#Draw vertical from R to intersect OP at S and OA at T....this gives RT = 105 and RS = 159
#At critcal speed generator just fails to build up

RT = 105.
RS = 159.
N_C = N1*RT/RS 			#Critical speed
print 'ii)Critical speed is %.2f r.p.m '%(N_C)

i)Field resistance that gives 240 V on no-load is 106.67 ohms
ii)Critical speed is 660.38 r.p.m


## Example 1.14 page no : 80¶

In :
# Variables
P = 4.  			#number of poles
A = 2. 			#because wave wound
Z = 792 			#No of conductors
phi = 0.012  			#flux per pole in weber

# Calculations
#running speed
N = E_g*60*A/(phi*P*Z) 			#becuase E_g =  phi*P*N*Z/(60*A)

# Results
print 'Required running speed is %.3f r.p.m'%(N)

Required running speed is 757.576 r.p.m


## Example 1.15 page no : 80¶

In :
import math

# Variables
#open circuit condition
I_L = 0.  			#because of open circuit
V_t = 127. 			#terminal voltage
E_g = V_t 			#because I_L = 0

# Calculations
V_t = 120
R_sh = 15.
R_a = 0.02  			#shunt and armature resistance
I_sh1 = V_t/R_sh 			#current through shunt winding in loaded condition

I_L  = (E_g-V_t)/R_a  -  I_sh1 			#because I_a1 = I_L+I_sh1    and    E_g = V_t + I_a1*R_a

# Results
print 'Load current is %.0f A'%(I_L)

Load current is 342 A


## Example 1.16 page no : 81¶

In :
# Variables
V_t = 550.  			#Terminal voltage
R_lamp = 500. 			#Each lamp
I_lamp = V_t/R_lamp  			#each lamp ; V_t because all lamps are in parallel

# Calculations
I_L = 20*I_lamp  			#there exist 20 lamps
R_sh = 25.
R_a = 0.06
R_se = 0.04  			#resistance of shunt winding,armature,series field
I_sh = V_t/R_sh 			#current throough shunt winding
I_a = I_L+I_sh			#armature current
E = V_t + I_a*(R_a+R_se)  			#generated emf

# Results
print 'Armature current and generated e.m.f is %.0f A and %.1f V respectively '%(I_a,E )

Armature current and generated e.m.f is 44 A and 554.4 V respectively


## Example 1.17 page no : 82¶

In :
# Variables
P = 4. 			#number of poles
A = P 			# because of lap wound
N = 750. 			#speed in rpm
Z = 720. 			#number of armature conductors
phi = 30.*10**-3  			#flux per pole in weber
R_sh = 200.
R_a = 0.4
R_L = 15. 			#resistance of shunt winding,armature,series field
E = phi*P*N*Z/(60*A) 			#generated emf

# Calculations
#solving the following equations for V_t
#E =  V_t + I_a*R_a
#E =  V_t + (I_L + I_sh)*R_a
#E =  V_t + ((V_t/R_L) + (V_t/R_sh))*R_a
V_t = E/(1+(R_a/R_L)+(R_a/R_sh))

# Results
print 'Terminal voltage  =  %.4f V'%(V_t)

Terminal voltage  =  262.4757 V


## Example 1.18 page no : 83¶

In :
# Variables
P = 6. 			#number of poles
A = 2. 			# because of wave wound
N_1 = 300. 			#speed of generator
Z = 600. 			#number of armature conductors
phi_1 = 0.06  			#flux per pole in webers

# Calculations and Results
E_g1 = phi_1*P*N_1*Z/(60*A) 			#generated emf
print 'Emf generated is %.0f V'%(E_g1)

phi_2 = 0.055 			#new flux per pole
E_g2 = 550.			# new generated emf
N_2 = E_g2/(phi_2*P*Z/(60*A)) 			#new speed of generator
print 'Required speed is %.2f r.p.m'%(N_2)

Emf generated is 540 V
Required speed is 333.33 r.p.m


## Example 1.19 page no : 84¶

In :
import math

print 'Refer to code for explanation'

# Variables
N_1 = 300.
N_2 = 375. 			#generator speeds

#E_g2 = E_g1*(N_2/N_1)
#using this new table OCC at N_2 = 375 is made
#Draw a line with slope R_sh = 40 through origin which cuts this OCC at 248
#I_f_table = [0,2,3,4,5,6,7]
#Arm_vol_table = [9.375,115,165,202.5,228.75,237.5,265]

#part(i)
#at V = 200 volts, I_f = 3.9 from the graph
V = 200.
I_f = 3.9

# Calculations and Results
R_sh2 = V/I_f
R_sh = 40.
print 'Additional resistance required is %.3f ohms  '%(R_sh2-R_sh)

#part(ii)
V_t = 200.
I_f = V_t/R_sh
E_g = 228.75   			#For this I_f from the table
R_a = 0.4
I_a = (E_g-V_t)/R_a   			#Because E_g = V_t + I_a*R_a
I_L = I_a-I_f
print 'Load current supplied by the generator is %.3f A'%(I_L)

Refer to code for explanation
Additional resistance required is 11.282 ohms
Load current supplied by the generator is 66.875 A


## Example 1.20 page no : 86¶

In :
# Variables
I_a = 750. 			#full load current
Pole = 6.
A = Pole 			#lap winding
I = I_a/A  			#Full-load current per path
Z = 900. 			#no of conductors
lambda1 = 1.4  			#leakage coefficient
theta_e = 21. 			#lead angle in degrees electrical

# Calculations
theta_m = theta_e/(Pole/2)  			#lead angle in degrees mechanical
amp_turns_PP_d = Z*I*theta_m/360  			#demagnetising ampere turns per pole
amp_turns_PP_c = Z*I*(1./(2*Pole)-theta_m/360)  			#cross-magnetising ampere turns per pole
balance_turns = amp_turns_PP_d*lambda1/I_a 			#series turns required to balance demagnetising component

# Results
print 'i)  De-magnetising ampere-turns per pole is %.1f'%(amp_turns_PP_d)
print 'ii) Cross-magnetising ampere-turns per pole is %.1f'%(amp_turns_PP_c)
print 'iii)Turns required to balance demagnetising component is %.0f'%(balance_turns)

i)  De-magnetising ampere-turns per pole is 2187.5
ii) Cross-magnetising ampere-turns per pole is 7187.5
iii)Turns required to balance demagnetising component is 4


## Example 1.21 page no : 87¶

In :
# Variables
Pole = 4.
Z = 32.  			#no of conductors
coil_sides = Z
segments = 16.
pole_pitch = Z/Pole
slots = 16.
slots_per_pole = slots/Pole

# Calculations
#for Simplex lap winding
y_b = pole_pitch+1  			#back pitch
y_f = pole_pitch-1  			#front pitch

y_c = 1  			#Commutator pitch; Note that it is positive and it is progressive type of Simplex lap winding

# Results
print 'WINDING TABLE:   1<-   10->    3<-   12->    5<-   14-> 7<-   16->    9<-   18->   11<-   20->13<-   22->   15<-   24->   17<-   26->19<-   28->   21<-   30->   23<-   32->25<-    2->   27<-    4->   29<-    6->31<-   8->1                                                  '
print 'Note that <- indicates back connection with  y_back = %.0f and -> indicates front connection with y_front = %.0f'%(y_b,y_f)

print 'Another form of winding table:'

print '      BACK CONNECTIONS                                FRONT CONNECTIONS'

print '       1 to 1+9  = 10                        ->       10 to 10-7  = 3'
print '       3 to 3+9  = 12                        ->       12 to 12-7 =  5'
print '       5 to 5+9  = 14                        ->       14 to 14-7 =  7'
print '       7 to 7+9  = 16                        ->       16 to 16-7 =  9'
print '       9 to 9+9  = 18                        ->       18 to 18-7 = 11'
print '      11 to 11+9 = 20                        ->       20 to 20-7 = 13'
print '      13 to 13+9 = 22                        ->       22 to 22-7 = 15'
print '      15 to 15+9 = 24                        ->       24 to 24-7 = 17'
print '      17 to 17+9 = 26                        ->       26 to 26-7 = 19'
print '      19 to 19+9 = 28                        ->       28 to 28-7 = 21'
print '      21 to 21+9 = 30                        ->       30 to 30-7 = 23'
print '      23 to 23+9 = 32                        ->       32 to 32-7 = 25'
print '      25 to 25+9 = 34 = 34-32 = 2              ->        2 to 34-7 = 27'
print '      27 to 27+9 = 36 = 36-32 = 4              ->        4 to 36-7 = 29'
print '      29 to 29+9 = 38 = 38-32 = 6              ->        6 to 38-7 = 31'
print '      31 to 31+9 = 40 = 40-32 = 4              ->        8 to 40-7 = 33 -32 =  1'

WINDING TABLE:   1<-   10->    3<-   12->    5<-   14-> 7<-   16->    9<-   18->   11<-   20->13<-   22->   15<-   24->   17<-   26->19<-   28->   21<-   30->   23<-   32->25<-    2->   27<-    4->   29<-    6->31<-   8->1
Note that <- indicates back connection with  y_back = 9 and -> indicates front connection with y_front = 7
Another form of winding table:
BACK CONNECTIONS                                FRONT CONNECTIONS
1 to 1+9  = 10                        ->       10 to 10-7  = 3
3 to 3+9  = 12                        ->       12 to 12-7 =  5
5 to 5+9  = 14                        ->       14 to 14-7 =  7
7 to 7+9  = 16                        ->       16 to 16-7 =  9
9 to 9+9  = 18                        ->       18 to 18-7 = 11
11 to 11+9 = 20                        ->       20 to 20-7 = 13
13 to 13+9 = 22                        ->       22 to 22-7 = 15
15 to 15+9 = 24                        ->       24 to 24-7 = 17
17 to 17+9 = 26                        ->       26 to 26-7 = 19
19 to 19+9 = 28                        ->       28 to 28-7 = 21
21 to 21+9 = 30                        ->       30 to 30-7 = 23
23 to 23+9 = 32                        ->       32 to 32-7 = 25
25 to 25+9 = 34 = 34-32 = 2              ->        2 to 34-7 = 27
27 to 27+9 = 36 = 36-32 = 4              ->        4 to 36-7 = 29
29 to 29+9 = 38 = 38-32 = 6              ->        6 to 38-7 = 31
31 to 31+9 = 40 = 40-32 = 4              ->        8 to 40-7 = 33 -32 =  1


## Example 1.22 page no : 89¶

In :
from numpy import array

# Variables
Z = 496. 			#no of conductors
P = 4. 			#poles
slots = 31.
coilsides_per_slot = 4.
coilsides = slots*coilsides_per_slot
coils = coilsides/2
turns = Z/2
turns_per_coil = turns/coils

# Calculations
y_c = array([(Z-2)/P, (Z+2)/P]) 			#commutator pitch
coils_active = (Z/(2*P))-1 			# because y_c didnt turn out to be integer, 1 coil was made inactive/dummy
segments = coils_active  			#no of commutative segments
Y_A = [ (segments+1)/(P/2), (segments-1)/(P/2)   ]
Y_A = Y_A   			#Y_A(2) is discarded because of progressive wave winding
y_f = 29.
y_b = 33.  			#front and back pitch ; note that Y_A = (y_b+y_f)/2
resultant_pitch = 2*Y_A  			#because Y_A = (y_b+y_f)/2 and resultant pitch  =  y_b+ y_f

# Results
print 'i)   Total number of coils  =  %.0f'%(coils)
print 'ii)  Turns per coils  =  %.0f'%(turns_per_coil)
print 'iii) Commutator pitch  =  %.0f'%((y_c+y_c)/2)
print 'iv)  Back pitch =  %.0f    front pitch =  %.0f   total pitch =  %.0f'%(y_b,y_f,resultant_pitch)
print 'v)   No of commutator segments  =  %.0f'%(segments)

i)   Total number of coils  =  62
ii)  Turns per coils  =  4
iii) Commutator pitch  =  124
iv)  Back pitch =  33    front pitch =  29   total pitch =  62
v)   No of commutator segments  =  61


## Example 1.23 page no : 90¶

In :
import math

# Variables
slots = 13.
Pole = 4.
conductors_per_slot = 2.
Z = conductors_per_slot*slots
Y_A = (Z+2)/Pole  			#For progressive type wave winding

# Calculations
#Since Y_A = (y_b+y_f)/2, we let y_b = y_f
y_b = Y_A
y_f = y_b 		    	#because y_b = Y_A/2

segments = 13. 			#commutator segments

# Results
print 'WINDING TABLE:   1<-    8->  15<-  22->   3<-   10->17<-   24->   5<-  12->  19<-   26-> 7<-   14->  21<-   2->   9<-   16->23<-    4->  11<-  18->  25<-    6->13<-   20->   1                                                  '
print 'Note that <- indicates back connection with y_back = %.0f and -> indicates front connection with y_front = %.0f'%(y_b,y_f)

print 'Another form of winding table:'

print '      BACK CONNECTIONS                                FRONT CONNECTIONS'

print '       1 to 1+7   =  8                   ->        8 to 8+7  =  15'
print '      15 to 15+7  = 22                   ->       22 to 22+7 =  29 -26 = 3'
print '       3 to 3+7   = 10                   ->       10 to 10+7 =  17'
print '      17 to 17+7  = 24                   ->       24 to 24+7 =  31 -26 = 5'
print '       5 to 5+7   = 14                   ->       12 to 12+7 =  19'
print '      19 to 19+7  = 26                   ->       26 to 26+7 =  33 -26 = 7'
print '       7 to 7+7   = 14                   ->       14 to 14+7 =  21'
print '      21 to 21+7  = 28 -26 = 2             ->        2 to  2+7 =   9'
print '       9 to 9+7   = 16                   ->       16 to 16+7 =  23 '
print '      23 to 23+7  = 30 -26 = 4             ->        4 to  4+7 =  11'
print '       11to 11+7  = 18                   ->       18 to 18+7 =  25'
print '      25 to 25+7  = 32 -26 = 6             ->        6 to  6+7 =  13'
print '      13 to13+7  = 20                   ->       20 to 20+7 =  27 -26 = 1'

WINDING TABLE:   1<-    8->  15<-  22->   3<-   10->17<-   24->   5<-  12->  19<-   26-> 7<-   14->  21<-   2->   9<-   16->23<-    4->  11<-  18->  25<-    6->13<-   20->   1
Note that <- indicates back connection with y_back = 7 and -> indicates front connection with y_front = 7
Another form of winding table:
BACK CONNECTIONS                                FRONT CONNECTIONS
1 to 1+7   =  8                   ->        8 to 8+7  =  15
15 to 15+7  = 22                   ->       22 to 22+7 =  29 -26 = 3
3 to 3+7   = 10                   ->       10 to 10+7 =  17
17 to 17+7  = 24                   ->       24 to 24+7 =  31 -26 = 5
5 to 5+7   = 14                   ->       12 to 12+7 =  19
19 to 19+7  = 26                   ->       26 to 26+7 =  33 -26 = 7
7 to 7+7   = 14                   ->       14 to 14+7 =  21
21 to 21+7  = 28 -26 = 2             ->        2 to  2+7 =   9
9 to 9+7   = 16                   ->       16 to 16+7 =  23
23 to 23+7  = 30 -26 = 4             ->        4 to  4+7 =  11
11to 11+7  = 18                   ->       18 to 18+7 =  25
25 to 25+7  = 32 -26 = 6             ->        6 to  6+7 =  13
13 to13+7  = 20                   ->       20 to 20+7 =  27 -26 = 1


## Example 1.24 page no : 93¶

In :
import math

# Variables
P = 4.
I_L = 150.
N = 1500. 			#commutator speed in rpm
n_s = N/60.  			#commutator speed in r.p.s
W_b = 1.2 			#Brush pitch
W_m = 0			#Pitch of mica insulation
L = 0.05*10**-3  			#inducmath.tance of armature coils in henry
A = P 			#A = P for lap wound
segments = 64.

# Calculations
v = n_s*segments 			#peripheral speed in segments per second
T_c = (W_b-W_m)/v  			#Time of commutation
I = I_L/A  			#current through each conductor
E = L*2*I/T_c  			#Linear commutation
E2 = 1.11*L*2*I/T_c  			#Sinusoidal commutation

# Results
print 'Reactive voltage linear commutation) is %.0f V'%(E)
print 'Reactive voltage math.sinusoidal commutation) is %.2f V'%(E2)

Reactive voltage linear commutation) is 5 V
Reactive voltage math.sinusoidal commutation) is 5.55 V


## Example 1.25 page no : 94¶

In :
# Variables
P = 4.  			#Pole
Z = 386. 			#no of wave connected conductors
A = 2.  			#Wave winding
R_a = 1.
R_sh = 100.
R_L = 40  			#Armature ,shunt field and load resistance
phi = 25.*10**-3  			#flux per pole in weber
N = 1000.  			#speed in rpm

# Calculations
E_g = (phi*P*N*Z)/(60*A)  			#generated emf

#Solving following equations for V_t
#E_g = V_t+I_a*R_a
#I_a = (I_L+I_sh)   I_L = V_t/R_L  I_sh = V_t/R_sj
#E_g = V_t(1 + (R_a/R_L) + (R_a/R_sh)
V_t = E_g/(1 + (R_a/R_L) + (R_a/R_sh))

I_L = V_t/R_L 			# load current
I_sh = V_t/R_sh 			# current through shunt field resistance

# Results
I_a = I_L+I_sh 			#armature current
print 'armature current is  is %.4f A'%(I_a)

output_power = V_t*I_L
print 'output power is %.3f W'%(output_power)

# Note :answer obtained will not match with textbook answer because I_L = V_t/R_L = 310.79/40 = 7.77
#Awhile its taken as 8.045 A in textbook'

armature current is  is 10.8776 A
output power is 2414.746 W


## Example 1.26 page no : 94¶

In :
# Variables
I = 40.  		    	#current PER conductor
W_b = 3.
W_m = 0.			    #brush width and width of mica insulation
N = 600. 			    #commutator speed in rpm
n_s = N/60 			    #commutator speed in rps
L = 0.15*10**-3 			#self inducmath.tance in Henry
segments = 50.
v = n_s*segments 			#peripheral speed in segments per second
T_c = (W_b-W_m)/v 			#time of commutation

# Calculations
E = L*2*I/T_c  			#Linear commutation
E2 = 1.11*L*2*I/T_c  			#Sinusoidal commutation

# Results
print 'Reactive voltage linear commutation) is %.0f volts'%(E)
print 'Reactive voltage math.sinusoidal commutation) is %.2f volts'%(E2)

Reactive voltage linear commutation) is 2 volts
Reactive voltage math.sinusoidal commutation) is 2.22 volts


## Example 1.27 page no : 96¶

In :
import math

# Variables
V = 400.
P = 6. 			    #Poles
A = P  		    	#For lap wound
output_power = 250.*10**3
R_sh = 200. 			#shunt field circuit resistance
Z = 720.     			#number of lap wound conductors

theta_m = 2.5 			#brush lead angle in degree mechanical
I_L = output_power/V
V_sh = V

# Calculations
I_sh = V_sh/R_sh 			#Current through shunt field circuit resistance
I_a = I_L+I_sh 			#armature currrent
I = I_a/P

#Part(i)
amp_turns_PP_d = Z*I*theta_m/360			#demagnetising ampere turns per pole
#Part(ii)
amp_turns_PP_c = Z*I*(1/(2*P)-theta_m/360) 			#cross-magnetising ampere turns per pole

# Results
print 'i)  De-magnetising ampere-turns per pole is %.1f'%(amp_turns_PP_d)
print 'ii) Cross-magnetising ampere-turns per pole is %.1f'%(amp_turns_PP_c)

i)  De-magnetising ampere-turns per pole is 522.5
ii) Cross-magnetising ampere-turns per pole is 5747.5


## Example 1.28 page no : 96¶

In :
# Variables
I_L = 100.
P = 4. 			    #Poles
A = P 			    #for lap wound armature
W_b = 1.4
W_m = 0. 			#Brush width and width of mica insulation
N = 1400.			#armature speed in r.p.m
segments = 64. 			#no of commutator segments
L = 0.05*10**-3 			#inducmath.tance of armature coil in henry

# Calculations
n_s = N/60  			#speed in r.p.s
v = n_s*segments 			#Segments per second
T_c = (W_b-W_m)/v 			#time of commutation
I = I_L/A   			#Current through conductor
E = L*2*I/T_c  			#Linear commutation

# Results
print 'Reactive voltage considering linear commutation is %.2f volts'%(E)

Reactive voltage considering linear commutation is 2.67 volts


## Example 1.29 page no : 97¶

In :
import math

# Variables
P = 8. 		    	#Poles
A = 2. 		    	#Wave wound armature
Z = 480. 			#number of armature conductors
I_a = 200.
I = I_a/A

# Calculations and Results
#Part(i)
theta_m = 0. 			#Geometric nuetral axis
amp_turns_PP_d = Z*I*theta_m/360    			#De-magnetising ampere-turns per pole
amp_turns_PP_c = Z*I*(1/(2*P)-theta_m/360) 			#Cross-magnetising ampere-turns per pole
print 'Parti)De-magnetising ampere-turns per pole is %.0f'%(amp_turns_PP_d)
print 'Cross-magnetising ampere-turns per pole is %.0f'%(amp_turns_PP_c)

#Part(ii)
theta_e2 = 6.             			#angle shift of brushes in degrees electrical
theta_m2 = theta_e2/(P/2) 			#angle shift of brushes in degrees mechanical
amp_turns_PP_d2 = Z*I*theta_m2/360   			#De-magnetising ampere-turns per pole
amp_turns_PP_c2 = Z*I*(1/(2*P)-theta_m2/360) 			#Cross-magnetising ampere-turns per pole
print 'Partii)De-magnetising ampere-turns per pole is %.0f'%(amp_turns_PP_d2)
print 'Cross-magnetising ampere-turns per pole is %.0f'%(amp_turns_PP_c2)

Parti)De-magnetising ampere-turns per pole is 0
Cross-magnetising ampere-turns per pole is 3000
Partii)De-magnetising ampere-turns per pole is 200
Cross-magnetising ampere-turns per pole is 2800


## Example 1.30 page no : 98¶

In :
# Variables
P_input = 7.46*10**3
V = 230.
Pole = 8.
Z = 188. 			#number of armature consuctors
I_L = P_input/V
theta_m = 7.5  			#brush lead angle in degree mechanical

A = 2. 			# assumed wave wound because of low-current and high voltage
I = I_L/A

#Part(i)
amp_turns_PP_d = Z*I*theta_m/360  			#De-magnetising ampere-turns per pole
#Part(ii)
amp_turns_PP_c = Z*I*(1/(2*Pole)-theta_m/360) 			#Cross-magnetising ampere-turns per pole

print 'De-magnetising ampere-turns per pole is %.2f'%(amp_turns_PP_d)
print 'Cross-magnetising ampere-turns per pole is %.2f'%(amp_turns_PP_c)

# note : The difference in answer occured because I is approximated to 16 in last 2 steps in book

De-magnetising ampere-turns per pole is 63.52
Cross-magnetising ampere-turns per pole is 127.04


## Example 1.31 page no : 99¶

In :
# Variables
N_1 = 1200.   			#initial speed
I_L1 = 200.   			#initial load current
V_t1 = 125.
N_2 = 1000.  			#altered speed
R_a = 0.04  			#armature resistance
V_brush = 2.  			#brush drop

# Calculations
I_a1 = I_L1
E_g1 = V_t1+I_a1*R_a+V_brush  			#induced emf

E_g2 = E_g1*(N_2/N_1)  			#Because E_g proportional to N during constant flux

Load current at new speed is 166.1654 A