# Variables
Pole = 4.
Slots = 24.
Phase = 3. #number of phases
# Calculations
n = Slots/Pole #slots per pole
m = Slots/Pole/Phase #slots per pole per phase
beeta = 180/n #Slot angle
# results
print "Slot angle : %.f degrees"%beeta
import math
# Variables
Slots = 120.
Pole = 8.
Phase = 3. #number of phases
# Calculations
n = Slots/Pole #Slots per Pole
m = Slots/Pole/Phase #Slots per Pole per Phase
beeta = 180/n #Slot angle in degree
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) #Distribution Factor
# Results
print 'Distribution Factor:K_d = %.3f'%(K_d)
import math
# Variables
Slots = 36.
Pole = 4.
Phase = 3. #number of phases
n = Slots/Pole #Slots per pole
beeta = 180/n #Slot angle in degrees
# Calculations
#coil is shorted by 1 slot i.e. by beeta degrees to full pitch dismath.tance
alpha = beeta #angle of short pitch
K_c = math.cos(math.radians(alpha/2)) #Coil span Factor
# Results
print 'Coil Span Factor:K_c = %.4f'%(K_c)
import math
# Variables
N_s = 250. #Synchronous speed in r.p.m
f = 50. #Frequency of generated e.m.f in hertz
Slots = 216.
phi = 30.*10**-3 #flux per pole in weber
Pole = 120*f/N_s
n = Slots/Pole #Slots per Pole
m = n/3 #Slots per Pole per Phase
beeta = 180/n #Slot angle in degree
# Calculations
K_d = math.sin(math.radians(m*beeta/2))/(m*math.sin(math.radians(beeta/2))) #distribution factor
K_c = 1 #Coil Span Factor for full pitch coils = 1
Z = Slots*5 #Z is total no of conductors
Z_ph = Z/3 #Conductors Per Phase
T_ph = Z_ph/2 #Turns per phase
E_ph = 4.44*K_c*K_d*f*phi*T_ph #induced emf
E_line = E_ph*math.sqrt(3)
# Results
print 'Induced e.m.f across the Terminals is %.2f V'%(E_line)
import math
# Variables
Pole = 16.
N_s = 375. #synchronous speed in rpm
Slots = 144.
E_line = 2.657*10**3 #line value of emf across terminals
f = Pole*N_s/120 #frequency
# Calculations
K_c = 1 #assuming full pitch winding Coil span Factor = 1
n = Slots/Pole #slots per pole
m = n/3 #slots per pole per phase
beeta = 180/n
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) #Distribution Fcator
conductors_per_slot = 10
Z = Slots*conductors_per_slot #total conductors
Z_ph = Z/3 #number of conductors per phase
T_ph = Z_ph/2 #no of turns per phase
E_ph = E_line/math.sqrt(3) #phase value of emf across terminals
phi = E_ph/(4.44*K_c*K_d*f*T_ph) #E_ph = 4.44*K_c*K_d*f*phi*T_ph
# Results
print 'Frequency of Induced e.m.f is %.0fHz \nFlux per Pole is %.0f mWb'%(f,phi*1000)
import math
# Variables
d = 0.25 #Diameter in metre
l = 0.3 #Length in metre
Pole = 4.
A1 = math.pi*d*l/Pole #Area of each fundamental pole
f = 50. #frequency in hertz
B_m1 = 0.15
B_m3 = 0.03
B_m5 = 0.02 #Amplitude of 1st 3rd and 5th harmonics
phi_1 = (2/math.pi)*B_m1*A1 #average value of fundamental flux per pole in weber
# Calculations and Results
#PART A
E_c1 = 1.11*2*f*phi_1 #R.M.S value of fundamental frequency e.m.f generated in math.single conductor
Coil_span = (13./15)*180 #math.since winding coil span is 13/15 of pole pitch
alpha = 180-Coil_span
#Pitch factor for 1st 3rd and 5th harmonic
K_c1 = math.cos(math.radians(alpha/2))
K_c3 = math.cos(math.radians(3*alpha/2))
K_c5 = math.cos(math.radians(5*alpha/2))
#using E_cx = E_c1 * (B_mx/B_m1)
E_c3 = E_c1 * (B_m3/B_m1)
E_c5 = E_c1 * (B_m5/B_m1)
E_t1 = K_c1 * (2*E_c1) #R.M.S Vaue of fundamental frequency EMF generated in 1 turn (in volts)
E_t3 = K_c3 * 2*E_c3
E_t5 = K_c5 * 2*E_c5
E_t = math.sqrt(E_t1**2 +E_t3**2 +E_t5**2)
V = 10*E_t #(number of turns per coil )* (Total e.m.f per turn)
print 'Voltage generated per coil is %.1f V'%(V)
# PART B
#E_1ph = 4.44*K_c1*K_d1*phi_1*f*T_ph
T_ph = 200. #T_ph = (60 coils * 10 turns per coil)/3
Total_Conductors = 1200. # 60 coils * 10 turns per coil * 2
Conductors_per_Slot = 20. #2 conductors per turn * 10 turns per slot
Slots = Total_Conductors/Conductors_per_Slot
n = Slots/Pole
m = n/3
beeta = 180/n #Slot angle in degree
K_d1 = math.sin(math.radians(m*1*beeta/2)) /(m*math.sin(math.radians(1*beeta/2)))
K_d3 = math.sin(math.radians(m*3*beeta/2)) /(m*math.sin(math.radians(3*beeta/2)))
K_d5 = math.sin(math.radians(m*5*beeta/2)) /(m*math.sin(math.radians(5*beeta/2)))
E_1ph = 4.44 * K_c1 * K_d1*phi_1 * f * T_ph
# using E_xph = E_1ph* (B_mx*K_cx*K_dx)/(B_m1*K_c1*K_d1)
E_3ph = E_1ph* (B_m3*K_c3*K_d3)/(B_m1*K_c1*K_d1)
E_5ph = E_1ph* (B_m5*K_c5*K_d5)/(B_m1*K_c1*K_d1)
E_ph = math.sqrt( E_1ph**2 + E_3ph**2 + E_5ph**2 ) #voltage generated per phase
print 'Voltage generated per phase is %.f V'%(E_ph)
#PART c
E_line = math.sqrt(3) * math.sqrt( E_1ph**2 + E_5ph**2 ) #terminal voltage
print 'Terminal Voltage is %.1f V '%(E_line)
import math
# Variables
Ns = 250. #Synchronous speed in rpm
f = 50.
Slots = 288.
E_line = 6600.
Pole = 120*f/Ns
n = Slots/Pole #slots per pole
m = n/3 #slots per pole per phase
beeta = 180/n #slot angle
conductors_per_slot = 32 #16 conductors per coil-side *2 coil-sides per slot
# Calculations
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) #distribution factor
alpha = 2*beeta # angle of short pitch
K_c = math.cos(math.radians(alpha/2)) #coil span factor
Z = Slots*conductors_per_slot #total conductors
Z_ph = Z/3 #Conductors per phase
T_ph = Z_ph/2 #turns per phase
E_ph = E_line/math.sqrt(3)
phi = E_ph/(4.44*K_c*K_d*f*T_ph) #Because E_ph = 4.44 *K_c *K_d *phi *f *T_ph
# Results
print 'Flux per pole is %.0f mWb '%(phi*1000)
import math
# Variables
Ns = 1500. #synchronous speed in rpm
Pole = 4.
Slots = 24.
conductor_per_slot = 8.
phi = 0.05 #flux per pole in weber
f = Pole*Ns/120 #frequenccy
n = Slots/Pole #slots per pole
m = n # as number of phases is 1
beeta = 180/n #slot angle
# Calculations
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) #distribution factor
#Full pitch = n = 6 slots
#(1/6)th of full pitch = 1slot
#angle of short pitch = 1 slot angle
alpha = beeta
K_c = math.cos(math.radians(alpha/2)) #coil span factor
Z = conductor_per_slot*Slots #total conductors
Z_ph = Z # as number of phases is 1
T_ph = Z_ph/2 #turns per phase
E_ph = 4.44*K_c*K_d* phi *f *T_ph #induced emf
# Results
print 'Induced e.m.f is %.1f V '%(E_ph)
import math
# Variables
Pole = 48.
n = 9. #slots per pole
phi = 51.75*10**-3 #flux per pole in weber
Ns = 125.
f = Ns*Pole/120 #frequency
K_c = 1. #due to full pitch winding
m = n/3 #slots per pole per phase
beeta = 180/n #slot angle
# Calculations
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) #distribution factor
conductor_per_slot = 4*2 #Each slot has 2 coil sides and each coil side has 4 conductors
Slots = n*Pole
Z = conductor_per_slot*Slots #total number of conductors
Z_ph = Z/3 #conductors per phase
T_ph = Z_ph/2 #turns per phase
E_ph = 4.44 *K_c *K_d *phi *f *T_ph #induced emf
E_line = (math.sqrt(3))*E_ph #due to star connection
# Results
print 'Induced e.m.f is %.0f kV '%(E_line/1000)
import math
# Variables
Slots = 180.
Pole = 12.
Ns = 600. #Synchronous speen in rpm
f = Pole*Ns/120 #frequency
phi = 0.05 #flux per pole in weber
# Calculations and Results
#Part(i)
#Average EMF in a conductor = 2*f*phi
rms_value_1 = 1.11*2*f*phi #rms value of emf in a conductor
print 'i)r.m.s value of e.m.f in a conductor is %.2f V '%(rms_value_1)
#part(ii)
#Average EMF in a turn = 4*f*phi
rms_value_2 = 1.11*4*f*phi #r.m.s value of e.m.f in a turn
print 'ii)r.m.s value of e.m.f in a turn is %.2f V '%(rms_value_2)
#part(iii)
conductors_per_coilside = 10/2
rms_value_3 = rms_value_2*conductors_per_coilside #r.m.s value of e.m.f in a coil
print 'iii)r.m.s value of e.m.f in a coil is %.1f V '%(rms_value_3)
#part(iv)
conductors_per_slot = 10
Z = conductors_per_slot * Slots #total number of conductors
Z_ph = Z/3 #conductors per phase
T_ph = Z_ph/2 #turns per phase
n = Slots/Pole #slots per pole
m = n/3 #slots per pole per phase
beeta = 180/n #slot angle
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2)))
K_c = 1 #distribution & coil-span factor
E_ph = rms_value_2*T_ph*K_d*K_c #induced emf
print 'iv)per phase induced e.m.f is %.1f V '%(E_ph)
import math
# Variables
Pole = 8.
f = 50. #frequency
phi = 60.*10**-3 #flux per pole in weber
Slots = 96.
n = Slots/Pole #slots per pole
beeta = 180/n #slot angle
m = n/3 #slots per pole per phase
# Calculations and Results
coil_pitch = 10*beeta #10 slots
alpha = 180-coil_pitch
K_c = math.cos(math.radians(alpha/2)) #coi;-span factor
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) #distribution factor
conductors_per_slot = 4
Z = Slots*conductors_per_slot #total conductors
Total_turns = Z/2
T_ph = Total_turns/3 #turns per phase
#part (i)
E_ph = 4.44 *K_c *K_d *phi *f *T_ph
print '\The phase voltage is %.2f V '%(E_ph)
#part(ii)
E_line = E_ph*math.sqrt(3)
print 'The Line Voltage is %.2f V '%(E_line)
#part(iii)
I_ph = 650
I_l = I_ph # Star Connection
kVA_rating = math.sqrt(3)*E_line*I_l
print 'kVA rating is %.1f kVA '%(kVA_rating/1000)
import math
# Variables
Ns = 600. #synchronous speed in rpm
Pole = 10.
l = 30./100 #divided by 100 for centimetre-metre conversion
Pole_pitch = 35./100 #numerically equal to pi*d/Pole
Phase = 3.
conductors_per_slot = 8.
A1 = Pole_pitch*l #Area of each fundamental pole
m = 3. #Slot per Pole per Phase
n = Phase*m #slots per pole
beeta = 180/n #slot angle
B_m1 = 1.
B_m3 = 0.3
B_m5 = 0.2 #amplitude of 1st 3rd and 5th harmonic
phi_1 = (2/math.pi)*A1*B_m1 #average value of fundamental flux per pole
f = Ns*Pole/120 #frequency
# Calculations
Coil_span = (8./9)*180
alpha = 180-Coil_span
#pitch factor for 1st 3rd and 5th harmonic
K_c1 = math.cos(math.radians(alpha/2))
K_c3 = math.cos(math.radians(3*alpha/2))
K_c5 = math.cos(math.radians(5*alpha/2))
# using K_dx = math.sin(m*x*beeta*(math.pi/180)/2) /(m*math.sin(x*beeta*(math.pi/180)/2))
#distribution factor for 1st 3rd and 5th harmonic
K_d1 = math.sin(math.radians(m*1*beeta/2)) /(m*math.sin(math.radians(1*beeta/2)))
K_d3 = math.sin(math.radians(m*3*beeta/2)) /(m*math.sin(math.radians(3*beeta/2)))
K_d5 = math.sin(math.radians(m*5*beeta/2)) /(m*math.sin(math.radians(5*beeta/2)))
Slots = n*Pole
Total_conductors = conductors_per_slot * Slots
Total_turns = Total_conductors/2
T_ph = Total_turns/3 #turns per phase
#EMF of 1st 3rd and 5th harmonic
E_1ph = 4.44 * K_c1 * K_d1*phi_1 * f * T_ph
E_3ph = E_1ph* (B_m3*K_c3*K_d3)/(B_m1*K_c1*K_d1)
E_5ph = E_1ph* (B_m5*K_c5*K_d5)/(B_m1*K_c1*K_d1)
# Results
# using E_xph = E_1ph* (B_mx*K_cx*K_dx)/(B_m1*K_c1*K_d1)
E_ph = math.sqrt( E_1ph**2 + E_3ph**2 + E_5ph**2 )
print 'Phase value of induced e.m.f is %.2f V '%(E_ph)
E_line = math.sqrt(3) * math.sqrt( E_1ph**2 + E_5ph**2 ) #no 3rd harmonic appears in line value
print 'line value of induced e.m.f is %.2f V '%(E_line)
print 'Answer mismatches due to approximation'
import math
# Variables
Pole = 16.
phi = 0.03 #flux per pole
Ns = 375. #synchronous speed in rpm
# Calculations and Results
f = Ns*Pole/120 #frequency
print 'frequency is %.0f Hz '%(f)
Slots = 144
n = Slots/Pole #slots per pole
m = n/3 #slots per pole per phase
beeta = 180/n #slot angle
K_c = 1 #assuming Full-Pitch coil
Conductors_per_slot = 10
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) #distribution factor
Total_conductors = Slots*Conductors_per_slot
Total_turns = Total_conductors/2
T_ph = Total_turns/3 #turns per phase
E_ph = 4.44* K_c* K_d*phi* f* T_ph
E_line = E_ph*math.sqrt(3)
print 'line voltage is %.2f V '%(E_line)
# note : rounding off error.
import math
# Variables
Ns = 250. #Speed in rpm
f = 50. #frequency
I_l = 100.
Slots = 216.
Conductors_per_slot = 5
Pole = 120.*f/Ns
phi = 30.*10**-3 #flux per pole in weber
Z = Slots*Conductors_per_slot #Total Conductors
Z_ph = Z/3 #conductors per phase
T_ph = Z_ph/2 #turns per phase
n = Slots/Pole #slots per pole
m = n/3 #slots per pole per phase
beeta = 180./n #Slot angle
# Calculations
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) #distribution factor
e_av = 2*f*phi #Average Value of EMF in each conductor
E_c = 1.11*(2*f*phi) #RMS value of EMF in each conductor
E = 2*E_c*K_d #RMS value of EMF in each turn
E_ph = T_ph*E #RMS value of EMF in each phase
E_line = E_ph*math.sqrt(3) #As Star Connected Alternator
# Results
print 'RMS value of EMF in each phase = %.3f V'%(E_ph)
print 'RMS value of EMF line value = %.3f V'%(E_line)
kVA_rating = math.sqrt(3)*E_line*I_l
print 'kVA rating is %.3f kVA '%(kVA_rating/1000)
import math
# Variables
Pole = 10.
Slots = 90.
E_l = 11000.
f = 50.
phi = 0.15 #flux per pole in weber
n = Slots/Pole #slots per pole
m = n/3 #slots per pole per phase
beeta = 180/n #slot angle
# Calculations
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) #distribution factor
K_c = 1 #coil span factor
E_ph = E_l/math.sqrt(3)
T_ph = ( E_ph/(4.44*K_c*K_d*phi*f) )
#T_ph should necessarily be an integer
Z_ph = (T_ph)*2
# Results
print 'Required number of armature conductors is %d'%(Z_ph)
# note : rounding off error.
import math
# Variables
Pole = 10.
Ns = 600. #speen in rpm
conductor_per_slot = 8.
n = 12. #slots per pole
Slots = Pole*n
m = n/3 #slots per pole per phase
beeta = 180/n #slot angle
alpha = 2*beeta #short by 2 slots
#flux per pole corresponding to 1st 3rd and 5th harmonic
phi_1 = 100*10**-3
phi_3 = (33./100)*phi_1
phi_5 = (20./100)*phi_1
#coil span factor corresponding to 1st 3rd and 5th harmonic
K_c1 = math.cos(math.radians( alpha/2))
K_c3 = math.cos(math.radians( 3*alpha/2))
K_c5 = math.cos(math.radians( 5*alpha/2))
# using K_dx = math.sin(m*x*beeta /2) /(m*math.sin(x*beeta /2))
#distribution factor corresponding to 1st 3rd and 5th harmonic
K_d1 = math.sin(math.radians(m*1*beeta/2)) /(m*math.sin(math.radians(1*beeta /2)))
K_d3 = math.sin(math.radians(m*3*beeta/2)) /(m*math.sin(math.radians(3*beeta /2)))
K_d5 = math.sin(math.radians(m*5*beeta/2)) /(m*math.sin(math.radians(5*beeta /2)))
Z = conductor_per_slot*n*Pole #Total Conductors
Zph = Z/3 #conductors per phase
T_ph = Zph/2 #turns per phase
f = Ns*Pole/120
E_1ph = 4.44*K_c1*K_d1*phi_1*f*T_ph
E_3ph = 4.44*K_c3*K_d3*phi_3*f*T_ph
E_5ph = 4.44*K_c5*K_d5*phi_5*f*T_ph
E_ph = math.sqrt( E_1ph**2 + E_3ph**2 + E_5ph**2 )
# Results
print 'Phase value of induced e.m.f is %.0f V '%(E_ph)
E_line = math.sqrt(3)*math.sqrt( E_1ph**2 + E_5ph**2 ) #In a line value 3rd harmonic doesnt appear
print 'line value of induced e.m.f is %d V '%(E_line)
# note : rounding off error.
import math
# Variables
Pole = 6.
Ns = 1000. #speed in rpm
d = 28./100 #Divided by 100 to convert from centimeters to metres
l = 23./100 #Divided by 100 to convert from centimeters to metres
m = 4. #slots per pole per phase
B_m1 = 0.87 #amplitude of 1st harmonic component of flux density
B_m3 = 0.24 #amplitude of 3rd harmonic component of flux density
Conductors_per_slot = 8
f = Ns*Pole/120 #frequency
A1 = math.pi*d*l/Pole #area of each fundamental pole
phi_1 = (2/math.pi)*A1*B_m1 #flux per pole in weber
n = m*3 #slots per pole
beeta = 180/n #slot angle
alpha = beeta #because of 1 slot short
# Calculations
K_c1 = math.cos(math.radians(alpha/2)) #coil span factor corresponding to 1st harmonic
K_c3 = math.cos(math.radians(3*alpha/2)) #coil span factor corresponding to 3rd harmonic
# using K_dx = math.sin(m*x*beeta*(math.pi/180)/2) /(m*math.sin(x*beeta*(math.pi/180)/2))
K_d1 = math.sin(math.radians(m*1*beeta/2)) /(m*math.sin(math.radians(1*beeta/2))) #distribution factor corresponding to 1st harmonic
K_d3 = math.sin(math.radians(m*3*beeta/2)) /(m*math.sin(math.radians(3*beeta/2))) #distribution factor corresponding to 3rd harmonic
Slots = n*Pole
Z = Slots*Conductors_per_slot #total number of conductors
Z_ph = Z/3 #conductors per phase
T_ph = Z_ph/2 #turns per phase
E_1ph = 4.44*K_c1*K_d1*phi_1*f*T_ph
E_3ph = E_1ph* (B_m3*K_c3*K_d3)/(B_m1*K_c1*K_d1) #using E_xph = E_1ph* (B_mx*K_cx*K_dx)/(B_m1*K_c1*K_d1)
E_ph = math.sqrt( E_1ph**2 + E_3ph**2 )
print 'r.m.s value of resultant voltage is %.1f V'%(E_ph)
E_line = math.sqrt(3)*E_1ph #For line Value 3rd harmonic does not appear
print 'line voltage is %.3f V'%(E_line)
import math
# Variables
V_L = 125.
V_ph = V_L
VA = 600.*10**3
I_L = VA/(math.sqrt(3)*V_L) # Because VA = math.sqrt(3)* V_L * I_L
I_ph = I_L/(math.sqrt(3))
# Calculations and Results
#After Reconnection
V_ph = 125
V_L = V_ph*math.sqrt(3)
print 'New rating in volts is %.3f V'%(V_L)
#Winding Impedances remain the same
I_ph = 1600
I_L = I_ph
print 'New rating in amperes is %.0f A'%(I_L)
kVA = math.sqrt(3)*V_L*I_L*(10**-3)
print 'New rating in kVA is %.0f kVA'%(kVA)
import math
# Variables
Pole = 4.
f = 50. #frequency
phi = 0.12 #flux per pole in weber
m = 4. # slot per pole per phase
conductor_per_slot = 4.
coilspan = 150.
Ns = 120*f/Pole #synchronous speed in rpm
n = m*3 #Slots per pole
beeta = 180/n #slot angle
# Calculations
K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) # distribution factor
alpha = 180-coilspan #angle of short pitch
K_c = math.cos((math.pi/180)*alpha/2) #coil span factor
Z = m*(n*Pole) # Also equal to (conductors/slots)*slots
Z_ph = Z/3 #conductors per phase
T_ph = Z_ph/2 #turns per phase
E_ph = 4.44*K_c*K_d*phi*f*T_ph
E_line = math.sqrt(3)*E_ph
# Results
print 'e.m.f generated is %.2f Vphase, %.2f Vline)'%(E_ph,E_line)