#Variable declaration
N = 300.0 #Speed of water turbine(rpm)
f = 50.0 #Frequency of induced voltage(Hz)
#Calculation
P = 120*f/N #Number of poles
#Result
print('Number of poles of the generator , P = %.f poles' %P)
print('Alternatively , %.f pairs of north(N) and south(S) poles' %(P/2))
import math
#Variable declaration
P = 8.0 #Number of poles
m = 3.0 #Number of phase
S = 144.0 #Number of slots
#Calculation
T_p = S/P #Pole pitch(slots)
slots_1 = 180/T_p #Pole pitch per slot(degree)
gamma = 2*slots_1 #Short pitch angle(degree)
y = gamma*math.pi/180 #Short pitch angle(radian)
k_p = math.cos(y/2) #Pitch factor
#Result
print('Pitch factor , k_p = %.2f ' %k_p)
import math
#Variable declaration
P = 4.0 #Number of poles
m = 3.0 #Number of phase
S = 40.0 #Number of slots
s_1 = 1.0 #Coil span
s_2 = 9.0 #Coil span
#Calculation
T_p = S/P #Pole pitch(slots)
T_c = s_2-s_1 #Coil pitch for coil spans 1 to 9(slots)
slots = 180/T_p #Pole pitch per slot(degree)
y = T_p-T_c #Short pitch angle(slots)
gamma = y*slots #Short pitch angle(degree)
y = gamma*math.pi/180 #Short pitch angle(radian)
k_p = math.cos(y/2) #Pitch factor
#Result
print('Pitch factor , k_p = %.2f ' %k_p)
import math
#Variable declaration
P = 4.0 #Number of poles
S = 48.0 #Number of slots
m = 3.0 #Number of phase
#Calculation
T_p = S/P #Pole pitch(slots)
slot = 180/T_p #Pole pitch per slot(degree)
a = slot*math.pi/180 #Pole pitch per slot(radian)
n = S/(P*m) #Number of slots or coils per pole per phase
k_d = math.sin(n*a/2)/(n*math.sin(a/2)) #Distribution factor
#Result
print('Distribution factor , k_d = %.2f ' %k_d)
import math
#Variable declaration
P = 12.0 #Number of poles
S = 180.0 #Number of slots
phi_m = 0.05 #Flux per pole(Wb)
N = 600.0 #Speed of machine(rpm)
m = 3.0 #Number of phase
#Calculation
T_p = S/P #Pole pitch(slots)
slot = 180/T_p #Slots per pole(degree)
n = S/(P*m) #Number of slots or coils per pole per phase
a = slot*math.pi/180 #Pole pitch per slot(radian)
k_d = math.sin(n*a/2)/(n*math.sin(a/2)) #Distribution factor
k_p = 1.0 #Pitch factor
Z = (180/m)*slot #Number of conductors per phase
T = Z/2 #Number of turns per phase
f = P*N/120 #Frequency(Hz)
E = 4.44*k_p*k_d*f*phi_m*T #Induced voltage(V)
E_L = 3**0.5*E #Line voltage(V)
#Result
print('Line voltage , E_L = %.1f V' %E_L)
print('\nNOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places')
import math
#Variable declaration
P = 4.0 #Number of poles
m = 3.0 #Number of phase
f = 50.0 #Frequency(Hz)
phi_m = 0.05 #Flux per pole(Wb)
n = 6.0 #Number of slots per pole per phase
cond = 5.0 #Conductors per layer
no_layer = 2.0 #Number of layer winding
#Calculation
T_p = n*m #Slots per pole
slot = 180/T_p #Slots per pole(degree)
a = slot*math.pi/180 #Pole pitch per slot(radian)
T_c = (5.0/6)*T_p #Coil pitch is 5/6 of full pitch
gamma = T_p-T_c #Short pitch angle(slots)
y_angle = gamma*slot #Short pitch(angle)
y = y_angle*math.pi/180 #Short pitch(radians)
k_p = math.cos(y/2) #Pitch factor
k_d = math.sin(n*a/2)/(n*math.sin(a/2)) #Distribution factor
T = 1.0/2*n*P*cond*no_layer #Number of turns in any phase
E = 4.44*k_p*k_d*f*phi_m*T #Voltage per phase(V)
#Result
print('Voltage per phase , E = %.2f V' %E)
print('\nNOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places')
import math
#Variable declaration
P = 10.0 #Number of poles
m = 3.0 #Number of phase
f = 50.0 #Frequency(Hz)
n = 3.0 #Number of slots per pole per phase
phi_m1 = 0.05 #Fundamental component of flux(Wb)
phi_m3 = 0.006 #Third harmonic component of flux(Wb)
T_c = 150.0 #Coil span(degree)
cond = 5.0 #Conductors per layer
no_layer = 2.0 #Number of layer winding
#Calculation
T_p = n*m #Slots per pole
slot = 180/T_p #Slots per pole(degree)
a = slot*math.pi/180 #Pole pitch per slot(radian)
gamma = 180-T_c #Short pitch angle(degree)
y = gamma*math.pi/180 #Short pitch angle(radian)
T = 1.0/2*P*n*cond*no_layer #Number of turns
k_p1 = math.cos(y/2) #Fundamental pitch factor
k_d1 = math.sin(n*a/2)/(n*math.sin(a/2)) #Fundamental distribution factor
E_1 = 4.44*k_p1*k_d1*f*phi_m1*T #Fundamental emf per phase(V)
k_p3 = math.cos(3*y/2) #Third harmonic pitch factor
k_d3 = math.sin(3*n*a/2)/(n*math.sin(3*a/2)) #Third harmonic distribution factor
E_3 = 4.44*k_p3*k_d3*f*phi_m3*T #Voltage(V)
E = (E_1**2+E_3**2)**0.5 #Induced voltage per phase(V)
#Result
print('rms value of induced voltage per phase , E = %.1f V' %E)
print('\nNOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places')
import math
#Variable declaration
kVA = 50.0 #Ratings(kVA)
V_t = 220.0 #Voltage(V)
R_a = 0.011 #Effective resistance(ohm)
X_s = 0.09 #Synchronous reactance(ohm)
pf = 0.85 #Lagging power factor
#Calculation
phi = math.acos(pf) #Power factor angle(radians)
I_a = kVA*10**3/V_t #Armature current(A)
E_f = ((V_t*pf+I_a*R_a)**2+(V_t*math.sin(phi)+I_a*X_s)**2)**0.5 #Induced voltage per phase(V)
VR = ((E_f-V_t)/V_t)*100 #Voltage regulation(percent)
#Result
print('No-load induced voltage per phase , E_f = %.1f V' %E_f)
print('Voltage regulation , VR = %.1f percent' %VR)
print('\nNOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places')
import math
#Variable declaration
kVA = 200.0 #Rating(kVA)
V_t = 33.0*10**3 #Voltage(V)
R_a = 0.54 #Armature resistance(ohm)
V_L = 415.0 #Voltage between lines for SC test(V)
I_sh = 25.0 #Short circuit current(A)
pf = 0.9 #Lagging power factor
#Calculation
#For case(i)
V_P = V_L/3**0.5 #Phase voltage during short circuit test(V)
Z_s = V_P/I_sh #Synchronous impedance(ohm)
#For case(ii)
X_s = (Z_s**2-R_a**2)**0.5 #Synchronous reactance(ohm)
#For case(iii)
I_a = kVA*1000/(3**0.5*V_t) #Full load current(A)
V_ta = V_t/3**0.5 #Voltage per phase of alternator(V)
phi = math.acos(pf) #Power factor angle(radians)
E_f = ((V_ta*pf+I_a*R_a)**2+(V_ta*math.sin(phi)+I_a*X_s)**2)**0.5 #No-load voltage per phase(V)
VR = ((E_f-V_ta)/V_ta)*100 #Voltage regulation
#Result
print('(i) Synchronous impedance , Z_s = %.1f ohm' %Z_s)
print('(ii) Synchronous reactance , X_s = %.2f ohm' %X_s)
print('(iii) Voltage regulation , VR = %.2f percent' %VR)
print('\nNOTE : ERROR : In textbook calculation , R_a is taken instead of X_s in calculation of E_f')
import math
#Variable declaration
MVA = 30.0 #Rating(MVA)
V = 20.0 #Supply voltage(kV)
N = 1800.0 #Speed(rpm)
V_t = 15.0 #Voltage per phase(kV)
E_f = 10.0 #Per phase terminal voltage(kV)
delta = 40.0 #Power angle(degree)
X_s = 6.0 #Per phase synchronous reactance(ohm)
#Calculation
#For case(i)
d = delta*math.pi/180 #Power angle(radians)
P = 3*V_t*E_f*math.sin(d)/X_s #3-phase power delivered to the load(MW)
#For case(ii)
P_max = 3*V_t*E_f/X_s #Three phase maximum power(MW)
#Result
print('(i) Three-phase real power delivered to the load , P = %.2f MW' %P)
print('(ii) Three-phase maximum power , P_max = %.f MW' %P_max)
import math
#Variable declaration
kVA = 25.0 #Rating(kVA)
V = 440.0 #Suppy voltage(V)
f = 50.0 #Supply frequency(Hz)
pf = 0.8 #Lagging power factor
R_a = 0.3 #Resistance of machine per phase(ohm)
X_d = 5.0 #Reactance of machine per phase(ohm)
X_q = 3.0 #Reactance of machine per phase(ohm)
#Calculation
#For case(i)
phi = math.acos(pf) #Power factor angle(radians)
phi_deg = phi*180/math.pi #Power factor angle(degree)
V_t = V/3**0.5 #Terminal voltage per phase(V)
I_a = kVA*10**3/(3**0.5*V) #Armature current(A)
tan_d = (I_a*X_q*pf/(V_t+I_a*X_q*math.sin(phi)))
d = math.atan(tan_d) #Torque angle(radians)
d_angle = d*180/math.pi #Torque angle(degree)
#For case(ii)
I_d = I_a*math.sin(d+phi) #Direct axis component of the current(A)
E_f = V_t*math.cos(d)+I_d*X_d #Induced voltage per phase(V)
#For case(iii)
VR = ((E_f-V_t)/V_t)*100 #Voltage regulation(percent)
#Result
print('(i) Torque angle , δ = %.2f° ' %d_angle)
print('(ii) Induced voltage per phase , E_f = %.2f V' %E_f)
print('(iii) Voltage regulation , VR = %.2f percent' %VR)
print('\nNOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places')
import math
import cmath
#Variable declaration
E_1 = 220.0 #Induced voltage per phase by alternator 1(V)
E_2 = 220*cmath.exp(1j*5*math.pi/180) #Induced voltage per phase by alternator 2(V)
Z_1 = complex(0,3) #Impedance of alternator 1(ohm)
Z_2 = complex(0,4) #Impedance of alternator 2(ohm)
Z = 5.0 #Load(ohm)
#Calculation
#For case(i)
I = (E_1*Z_2+E_2*Z_1)/(Z_1*Z_2+Z*(Z_1+Z_2)) #Load current(A)
#For case(ii)
V_t = I*Z #Terminal voltage(V)
#For case(iii)
I_a1 = ((E_1-E_2)*Z+E_1*Z_2)/(Z_1*Z_2+Z*(Z_1+Z_2)) #Armature current(A)
P_1 = abs(V_t*I_a1)*math.cos(cmath.phase(V_t)-cmath.phase(I_a1))*10**-3 #Power per phase delivered by the first alternator(W)
#Result
print('(i) Load current , I = %.1f∠%.f° A' %(abs(I),cmath.phase(I)*180/math.pi))
print('(ii) Terminal voltage , V_t = %.f∠%.f° V' %(abs(V_t),cmath.phase(V_t)*180/math.pi))
print('(iii) Power per phase delivered by the first alternator , P_1 = %.1f kW' %P_1)
print('\nNOTE : ERROR : In textbook case(iii) power calculation current I is taken instead of I_a1')