import math
import numpy as np
# Variables
V_l = 400.
R_a = 0.2
X_s = 2. #armature resistance and synchronous reactance
I_L = 25.
I_aph = I_L
V_ph = V_l/math.sqrt(3)
Z_s = complex(R_a,X_s) #synchronous impedance
angle = math.atan(Z_s.imag/Z_s.real)
angle = math.degrees(angle)
E_Rph=I_aph*abs(Z_s)
theta = (math.pi/180.)*angle
# Calculations and Results
#case 1
phi = math.acos(0.8) #lagging
E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta-phi) )
print 'i)Back EMF induced with 0.8 lagging pf is %.3f V'%(E_bph)
#case 2
phi = math.acos(0.9) #leading
E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta+phi) )
print 'ii)Back EMF induced with 0.8 lagging pf is %.3f V'%(E_bph)
#case 3
phi = math.acos(1)
E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta) )
print 'iii)Back EMF induced with 0.8 lagging pf is %.3f V'%(E_bph)
import math
from numpy import cos
# Variables
V_l = 500.
R_a = 0.4
X_s = 4. #armature resistance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = (math.pi/180)*angle #phasemag returns angle in degrees,not radians
V_ph = V_l/math.sqrt(3)
I_l = 50.
I_aph = I_l
E_Rph = I_aph*abs(Z_s)
# Calculations and Results
#case 1
E_bline = 600
E_bph = E_bline/math.sqrt(3)
phi = math.acos( (-E_bph**2 + E_Rph**2 + V_ph**2 )/(2*E_Rph*V_ph) ) -theta #leading
#because E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta+phi) )
print 'i)power factor is %.4f leading'%(cos(phi))
#case 2
E_bline = 380
E_bph = E_bline/math.sqrt(3)
phi = theta-math.acos( (-E_bph**2 + E_Rph**2 + V_ph**2 )/(2*E_Rph*V_ph) ) #leading
#because E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta-phi)
print 'ii)power factor is %.4f lagging'%(cos(phi))
import math
# Variables
V_L = 6600.
P_out = 500.*10**3
eta = 83./100 #efficiency
R_a = 0.3
X_s = 3.2 #armature resistance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = (math.pi/180)* angle #phasemag returns the angle in degrees not radians
phi = math.acos(0.8) #leading
V_ph = V_L/math.sqrt(3)
P_in = P_out/eta
# Calculations and Results
I_L = P_in/ (math.sqrt(3) * V_L * math.cos(phi) )
# because P_in = math.sqrt(3) * V_L * I_L * math.cos(phi)
I_aph = I_L
E_Rph = I_aph*abs(Z_s)
E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta+phi) )
print 'i) Generated EmF on full loaad is %.2f V'%(E_bph)
delta = math.degrees(math.asin( (E_Rph/E_bph))*math.sin(theta+phi) )
#This is obtained after applying sune rule to triangle OAB from thre phasor diagram
print 'ii) load angle is %.2f degrees'%(delta)
import math
from numpy import roots
# Variables
V_L = 500.
V_ph = V_L/math.sqrt(3)
phi = math.acos(0.9) #lagging
output_power = 17.*10**3
R_a = 0.8 #armaature reactance
mechanical_losses = 1300. #mechanical losses is W
P_m = output_power+mechanical_losses #gross mechanical power developed
# P_m = input_power - stator losses
# input_power = 3* V_ph * I_aph * math.cos(phi)
# Stator losses = 3*I_aph**2*R_a
# solving above equations we get 2.4 I_a**2 - 779/.4225*I_a + 18300 = 0
I_a_eqn = [2.4, -779.4225, 18300]
I_a_roots = roots(I_a_eqn)
I_a = I_a_roots[1] #neglecting higher value
I_aph = I_a
print 'Current drawn by the motor is %.3f A'%(I_a)
input_power = 3* V_ph * I_aph * math.cos(phi)
eta = 100*output_power/input_power
print 'Full load efficiency is %.2f percent'%(eta)
import math
# Variables
#subscript 1 is for industrial load and 2 for synchronous motor
P_1 = 800. # Active power in KW
phi_1 = math.acos(0.6) #lagging
Q_1 = P_1*math.tan(phi_1) #reactive power by load 1
# Calculations and Results
output_power = 200.
eta = 91./100 #efficiency of synchronous motor
input_power = output_power/eta
P_2 = input_power # active power drawn by synchronous motor
P_T = P_1 + P_2 #combined total load of industry and synchronous motor
phi_T = math.acos(0.92 ) #lagging
Q_T = P_T* math.tan(phi_T) #from power triangle
Q_2 = Q_T - Q_1 #it turns out to be negative indicating its leading nature
S_2 = math.sqrt( P_2**2 + Q_2**2 )
print 'Desired kVA rating of Synchronous motor is %.3f kVA'%(S_2)
phi_2 = math.atan (Q_2/P_2)
print 'Power factor of synchronous motor is %.4f LEADING'%(math.cos(phi_2))
import math
# Variables
V_L = 400.
output_power = 37.3*1000 #Watts on full load
Z_s = complex(0.2,1.6) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = (math.pi/180)*angle #phase mag returns the angle in degrees and not raidians
phi = math.acos(0.9) #leading
V_ph = V_L/math.sqrt(3)
eta = 88. #efficiency in percentage
# Calculations
input_power = 100*output_power/eta
I_L = input_power/(math.sqrt(3)*V_L*math.cos(phi))
I_aph = I_L
E_Rph = I_aph*abs(Z_s)
E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta+phi) )
E_line = math.sqrt(3)*E_bph
# Results
print 'Induced EMF is %.2f V and its line value is %.2f V'%(E_bph,E_line)
import math
# Variables
V_L = 400.
input_power = 20.*1000
R_a = 0.
X_s = 4. #armature reactance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag))
theta = (math.pi/180)*angle #phase mag returns the angle in degrees and not raidians
V_ph = V_L/math.sqrt(3)
E_bline = 550. #star connection
E_bph = E_bline/math.sqrt(3)
# Calculations
I_a_cos_phi = input_power/(math.sqrt(3)*V_L) #product of I_a and math.cos(phi)
I_a_sin_phi = ( math.sqrt(E_bph**2- (abs(Z_s)*I_a_cos_phi)**2 ) -V_ph )/abs(Z_s) #from triangle DAB
phi = math.atan(I_a_sin_phi/I_a_cos_phi)
I_a = I_a_cos_phi/math.cos(phi)
# Results
print 'Motor power fctor is %.3f Leading'%(cos(phi))
print 'Current drawn by the motor is %.2f A'%(I_a)
import math
# Variables
V_L = 3300.
V_ph = V_L/math.sqrt(3)
R_a = 2.
X_s = 18. #armature reactance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = (math.pi/180)*angle #phasemag returns angle in degrees not radians
E_bline = 3800.
E_bph = E_bline/math.sqrt(3)
#part(i)
P_m_max = (E_bph*V_ph/abs(Z_s))- (E_bph**2/abs(Z_s))*math.cos(theta)
print 'i)Max total mechanical power developed that motor can develop is %.2f W per phase'%(P_m_max)
#part(ii)
#from phasor diagram applying math.comath.sine rule to triangle OAB
E_Rph = math.sqrt( E_bph**2 + V_ph**2 -2*E_bph*V_ph*math.cos(theta) )
I_aph = E_Rph/abs(Z_s)
print 'ii)Current at max power developed is %.1f A'%(I_aph)
copper_loss = 3* I_aph**2 * R_a
P_in_max_total = 3 * P_m_max #input power at max power developed
total_P_in = P_in_max_total + copper_loss #total input power
pf = total_P_in/(math.sqrt(3)*I_aph*V_L)
print 'Power factor at max power developed is %.3f leading'%(pf)
# 'Answer in part1 mismatched because of improper approximation in book'
import math
# Variables
V_L = 500.
R_a = 0.03
X_s = 0.3 #armature reactance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = (math.pi/180)*angle #phasemag returns angle in degrees not radians
phi = math.acos(0.8)
eta = 93/100.
output_power = 100.*746
input_power = output_power/eta
I_L = input_power/(math.sqrt(3)*V_L*math.cos(phi))
I_aph = I_L
E_Rph = I_aph*abs(Z_s)
#from the phasor diagram
E_bph = math.sqrt( E_Rph**2 + (V_L/math.sqrt(3))**2 - 2*E_Rph*(V_L/math.sqrt(3))*math.cos(phi+theta) )
cu_losses = 3*(I_aph)**2*R_a #total copper losses
P_m = input_power - cu_losses #total mechanical power developed
print 'EMF developed per phase is %.4f V \nTotal mechanical power developed is %.1f watts'%(E_bph,P_m)
import math
# Variables
V_L = 415.
V_ph = V_L #due to delta connection
E_bline = 520.
R_a = 0.5
X_s = 4. #armature reactance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = (math.pi/180.)*angle #phasemag returns angle in degrees not radians
delta = theta #for maximum power
P_m_max = (E_bline*V_ph/abs(Z_s))- (E_bline**2/abs(Z_s))*math.cos(theta)
P_m_max_total = 3* P_m_max
fi_loss = 1000. #frictional and iron losses
P_out_total = P_m_max_total-fi_loss
HP_output = P_out_total/746 #converting watts to horse power
print 'HP output for maximum power output is %.2f HP'%(HP_output)
#from the phasor diagram
E_Rph = math.sqrt( E_bline**2 + V_ph**2 -2*E_bline*V_ph*math.cos(delta) )
I_aph = E_Rph/abs(Z_s)
I_L = I_aph*math.sqrt(3)
print 'Line current is %f A'%(I_L)
cu_loss_total = 3*(I_aph)**2*R_a #total copper losses
input_power = P_m_max_total+ cu_loss_total
pf = input_power/(math.sqrt(3)*I_L*V_L) #leading
print 'Power factor for maximum power output is %.2f leading '%(pf)
eta = 100*P_out_total /input_power
print 'Efficiency for maximum power output is %.2f percent'%(eta)
# 'Answer might mismatch because of improper approximation done in book'
import math
# Variables
P = 8.
f = 50. #Pole and frequency
N_s = 120.*f/P #synchronous speed
V_L = 6.6*10**3
V_ph = V_L/math.sqrt(3)
Z_s = complex(0.66,6.6) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = (math.pi/180)*angle #phasemag returns angle in degree not radians
E_bph = 4500.
input_power = 2500.*10**3
I_a_cosphi = input_power/(math.sqrt(3)*V_L) #Its product of I_a and math.cos(phi);I_a = I_l for star conneted load
# Calculations
#applying math.comath.sine rule to triangle ABC from phasor diagram and solve
#math.tan(phi)**2 + 5.2252 math.tan(phi)-2.2432 = 0
p = [1, 5.2252, -2.2432]
tan_phi = roots(p)
phi = math.atan(tan_phi[1])
pf = math.cos(phi)
I_a = I_a_cosphi/ math.cos(phi)
#apply math.sine rule to triangle ABC
delta = math.asin(I_a*abs(Z_s)*math.sin(theta+phi)/E_bph)
P_m = 3*E_bph*I_a*math.cos(delta+phi)
T_g = P_m/(2*math.pi*N_s/60)
# Results
print 'i)Torque developed is %f N-m'%(T_g)
print 'ii)Input current is %.4f A'%(I_a)
print 'iii)Power factor is %.4f leading'%(pf)
print 'iv)Power angle is %.2f degrees '%((180/math.pi)*delta)
# note : rounding off error.
import math
from numpy import roots
# Variables
input_power = 15.*10**3
V_L = 400.
V_ph = V_L/math.sqrt(3)
E_b = 480.
E_bph = E_b/math.sqrt(3)
Z_s = complex(1,5) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = (math.pi/180)*angle #phasemag returns angle in degree not radians
# Calculations
I_a_cosphi = input_power/(math.sqrt(3)*V_L) #product of I_a & math.cos(phi)
#Applying math.comath.sine rule to triangle OAB and solving
#math.tan(phi)**2+ 4.101*math.tan(phi)-1.7499 = 0
p = [1,4.101,-1.7449]
tan_phi = roots(p)
phi = math.atan(tan_phi[1]) #ignoring negative vaule
I_a = I_a_cosphi/ math.cos(phi)
#applying math.sine rule to Triangle OAB
delta = math.asin( I_a*abs(Z_s)* math.sin(theta+phi)/E_bph )
# Results
print 'Load angle is %.1f degrees'%(delta*180/math.pi)
print 'Armature current is %.4f A'%(I_a)
print 'Power factor is %.3f leading'%(cos(phi))
import math
from numpy import roots
# Variables
V_L = 400.
V_ph = V_L/math.sqrt(3)
E_b = 460.
E_bph = E_b/math.sqrt(3)
input_power = 3.75*10**3
Z_s = complex(1,8) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = math.degrees(angle) #phasemag returns angle in degree ,not radians
I_L_cos_phi = input_power/(math.sqrt(3)*V_L)
# Calculations and Results
#Applying math.comath.sine rule to triangle OAB and solving further
#math.tan(phi)**2 + 458.366*math.tan(phi) -450.65 = 0
p = [1,458.366-450.65]
tan_phi = roots(p)
phi = math.atan(tan_phi[0]) #ignoring negative value
print 'Required power factor is %.4f leading'%(cos(phi))
I_L = I_L_cos_phi /math.cos(phi)
print 'Required current is %.4f A'%(I_L)
# roots() python gives some different answer. Kindly check.
import math
# Variables
#subscript 1 indicates induction motor 1
P_1 = 350.
phi_1 = math.acos(0.7071) #lagging
Q_1 = P_1*math.tan(phi_1) #from power triangle
#subscript 2 indicates induction motor 2
P_2 = 190.
# Calculations
#subscript T indicates total
P_T = P_1+P_2
phi_T = math.acos(0.9) #lagging
Q_T = P_T*math.tan(phi_T)
Q_2 = Q_T-Q_1
kva_rating = math.sqrt(P_2**2+ Q_2**2)
# Results
print 'kVA rating of synchronous motor is %.2f kVA'%(kva_rating)
import math
# Variables
V_L = 400.
V_ph = V_L/math.sqrt(3)
Pole = 6.
f = 50.
R_a = 0.2
X_s = 3. #armature reactance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
theta = math.atan(Z_s.imag/Z_s.real) # calculates angle in radians
N_s = 120*f/Pole #synchronous speed
# Calculations
#subscript 1` refers to load 1
I_a1 = 20.
phi_1 = math.acos(1)
E_R1 = I_a1* abs(Z_s)
E_bph = math.sqrt( E_R1**2 + V_ph**2 - 2*E_R1*V_ph*math.cos(phi_1+theta) )
#subscript 2` refers to load 2
I_a2 = 60.
E_R2 = I_a2* abs(Z_s)
phi_2 = math.acos ((E_R2**2 + V_ph**2 -E_bph**2 )/(2*E_R2*V_ph)) -theta #new power factor
input_power = math.sqrt(3)*V_L*I_a2*math.cos(phi_2)
cu_loss = 3*I_a2**2*R_a
P_m = input_power-cu_loss
T_g = P_m /(2*math.pi*N_s/60) #gross mechanical power developed
# Results
print 'Gross torque developed is %.4f N-m and new power factor is %.4f lagging'%(T_g,cos(phi_2))
import math
# Variables
V_L = 3300.
V_ph = V_L/math.sqrt(3)
E_bph = V_ph
Z_s = complex(0.5,5) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = (math.pi/180)*angle #phasemag returns angle in degrees, not radians
P = 8.
f = 50. #pole and frequency
delta_mech = 3. #mechanical angle in degrees by which rotor is behind
delta_elec = (P/2)*delta_mech #delta mech converted to electrical degrees
E_Rph = math.sqrt( E_bph**2 + V_ph**2 -2*E_bph*V_ph*math.cos(math.radians(delta_elec) ))
I_aph = E_Rph/abs(Z_s)
#from the phasor diagram
phi = theta- math.asin( math.sin(math.radians(delta_elec))*E_bph/E_Rph )
pf = math.cos(phi)
print 'power factor of the motor is %.5f lagging'%(pf)
import math
# Variables
V_L = 400.
V_ph = V_L/math.sqrt(3)
E_bph = V_ph
P = 4.
f = 50. #Pole and frequency
delta_mech = 4*(math.pi/180) #mechanical angle in degrees by which rotor is behind
delta_elec = delta_mech *(P/2) #delta_mech convertd to electrical degrees
Z_s = complex(0,2) #synchronous impedance
# Calculations
#referring to phasor diagram
BC = E_bph*math.sin(delta_elec)
AB = E_bph
OA = V_ph
AC = math.sqrt(AB**2-BC**2)
OC = OA-AC
phi = math.atan(OC/BC)
OB = math.sqrt(OC**2 + BC**2)
I_a = OB/abs(Z_s)
# Results
print 'Armature current drawn by the motor is %.4f A'%(I_a)
import math
# Variables
V_L = 400.
V_ph = V_L/math.sqrt(3)
input_power = 5472.
Z_s = complex(0,10) #synchronous impedance
I_L_cosphi = input_power/(math.sqrt(3)*V_L) #product of I_L & math.cos(phi)
BC = 10*I_L_cosphi
AB = V_ph
OA = V_ph
# Calculations
#from Triangle ABC in phasor diagram
AC = math.sqrt(AB**2- BC**2)
OC = OA - AC
#from Triangle OCB
OB = math.sqrt( OC**2+ BC**2 )
E_Rph = OB
I_L = E_Rph/abs(Z_s)
phi = math.atan(OC/BC)
pf = math.cos(phi)
delta = math.atan(BC/AC) #load angle
# Results
print 'Power factor is %.4f lagging'%(pf)
print 'Load angle is %.0f degrees'%(delta*180/math.pi)
print 'Armature current is %.3f A'%(I_L)
import math
# Variables
V_L = 6600.
V_ph = V_L/math.sqrt(3)
Z_s = complex(2,20) #synchronous impedance
angle = math.degrees(math.atan(Z_s.imag/Z_s.real))
theta = (math.pi/180) * angle #phasemag returns angle in degrees not radians
P_1 = 1000*10**3
P_2 = 1500*10**3
phi_1 = math.acos(0.8) #leading
# Calculations
I_L1 = P_1/(math.sqrt(3)*V_L*math.cos(phi_1))
I_a1ph = I_L1
E_R1ph = I_a1ph*abs(Z_s)
E_bph = math.sqrt( V_ph**2 + E_R1ph** -2*V_ph*E_R1ph*math.cos(theta+phi_1) )
I_a2_cosphi_2 = P_2/(math.sqrt(3)*V_L)
#Refer to the phasor diagram and solving for I_y
#404I_y**2 -152399.968 I_y -4543000 = 0
p = [404, -152399.968, -4543000]
ans = roots(p)
I_y = abs(ans[1]) #becuase root 1 is too high and root is -ve
I_a2 = complex(I_a2_cosphi_2,I_y)
phi_2 = math.degrees(math.atan(I_a2.imag/I_a2.real))
print 'Required power factor is %.3f leading'%(math.cos(math.radians(phi_2)))
import math
V_L = 2300.
V_ph = V_L/math.sqrt(3)
I_L = 200.
I_a = I_L
Z_s = complex(0.2,2.2) #synchronous impedance
theta = math.atan(Z_s.imag/Z_s.real)
phi = math.acos(0.5)
# Calculations
E_Rph = I_a*abs(Z_s)
E_bph = math.sqrt( E_Rph**2 + V_ph**2 - 2*E_Rph*V_ph*math.cos(phi+theta) )
# Results
print 'Generated EMF per phase is %.3f V'%(E_bph)
import math
# Variables
V_L = 3300.
V_ph = V_L/math.sqrt(3)
E_bline = 3800.
E_bph = E_bline/math.sqrt(3)
R_a = 2.
X_s = 18. #armature resistance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
theta = math.atan(Z_s.imag/Z_s.real)
#part(i)
P_m_max = (E_bph*V_ph/abs(Z_s))- (E_bph**2/abs(Z_s))*math.cos(theta) #maximum total mechanical power
print 'i)Maximum total mechanical power that the motor can develop is %.2f W per phase'%(P_m_max )
#part(ii)
delta = theta #for max P_m
E_Rph = math.sqrt( E_bph**2 + V_ph**2 -2*E_bph*V_ph*math.cos(delta) )
I_aph = E_Rph/abs(Z_s)
print 'ii)Current at maximum power developed is %.1f A'%(I_aph)
cu_loss_total = 3*I_aph**2*R_a #total copper loss
P_m_max_total = 3*P_m_max #total maximum total mechanical power
P_in_total = P_m_max_total+ cu_loss_total #total input power
pf = P_in_total/(math.sqrt(3)*V_L*I_aph)
print ' Power factor at maximum power developed is %.3f leading'%(pf)
# note : rounding off error.
import math
#subscript 1 refers to load 1
I_1 = 18.
phi_1 = math.acos(0.8)
V_L = 440.
S_1 = math.sqrt(3)*I_1*V_L /1000 #kVA for load 1
P_1 = S_1*math.cos(phi_1)
Q_1 = S_1*math.sin(phi_1)
# Calculations
P_out = 6.
eta_motor = 88./100
P_2 = P_out/eta_motor
P_T = P_1+P_2
phi_T = math.acos(1) #total power factor angle
Q_T = P_T*math.tan(phi_T)
Q_2 = Q_T - Q_1 #kVAR supplied by motor
#this will have a negative sign just indicating its leading nature
phi_2 = math.atan(abs(Q_2)/P_2)
pf = math.cos(phi_2) #leading
S_2 = P_2/math.cos(phi_2) #kVA input to the motor
# Results
print 'kVA input to the motor is %.3f kVA '%(S_2)
print 'Power factor when driving a 6kW mechanical load is %.4f leading'%(pf)
import math
# Variables
output_power = 8.*10**3
V_L = 400.
V_ph = V_L/math.sqrt(3)
R_a = 0.
X_s = 8. #armature resistance and syncronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
theta = math.atan(Z_s.imag) # returns angle in radians
eta = 88./100
input_power = output_power/eta
# Calculations and Results
#minimum current occurs at max power factors
phi = math.acos(1)
I_a_min = input_power/(math.sqrt(3)*V_L*math.cos(phi)) #required minimum current
print 'Minimum current is %.3f A'%(I_a_min)
E_R = I_a_min * abs(Z_s)
E_bph = math.sqrt( E_R**2 + V_ph**2 - 2*E_R*V_ph*math.cos(phi+theta) )
print 'Induced EMF at full-load is %.3f V'%(E_bph)
# note : rounding off error.
import math
# Variables
R_a = 0.8
X_s = 5.
Z_s = complex(R_a,X_s) #armature resistance and syncronous reactance
theta = math.atan(Z_s.imag/Z_s.real) # returns angle in radians
alpha = (math.pi/2) - theta
V_t = 3300/math.sqrt(3)
P_e_in = 800./(3) #per phase
phi = math.acos(0.8) #leading
Q_e_in = -P_e_in*math.tan(phi)
# Calculations
# using the following equation
# P_e_in = V_t**2*R_a/(abs(Z_s))**2 + V_t*E_b*math.sin(delta-alpha)/abs(Z_S)
# Q_e_in = V_t**2*X_s/(abs(Z_s))**2 - V_t*E_b*math.cos(delta-alpha)/abs(Z_S)
E_b_sin_delta_minus_9 = 407.2
E_b_cos_delta_minus_9 = 2413.6
#solving further
delta = math.atan(E_b_sin_delta_minus_9/E_b_cos_delta_minus_9 ) + 9
E_b = E_b_sin_delta_minus_9/math.sin(math.radians(delta-9))
P_e_in_new = 1200*10**3/3
# using the following equation again
# P_e_in = V_t**2*R_a/(abs(Z_s))**2 + V_t*E_b*math.sin(delta-alpha)/abs(Z_S)
# Q_e_in = V_t**2*X_s/(abs(Z_s))**2 - V_t*E_b*math.cos(delta-alpha)/abs(Z_S)
alpha = delta - math.asin(math.radians(P_e_in_new - V_t**2*R_a/(abs(Z_s))**2 ) / (V_t*E_b/abs(Z_s)))
Q_e_in_new = V_t**2*X_s/(abs(Z_s))**2 - V_t*E_b*math.cos(math.radians(delta - alpha))/abs(Z_s)
pf = math.cos ( math.atan(abs(Q_e_in_new/P_e_in_new)))
# Results
print 'New power factor is %.2f leading '%(pf)
import math
# Variables
V_L = 6.6*10**3
V_ph = V_L/math.sqrt(3)
P_in = 900.*10**3
R_a = 0.
X_s = 20. #armature resistance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
theta = math.atan(Z_s.imag) # returns angle in radians
E_b_L = 8.6*10**3
E_bph = E_b_L/math.sqrt(3)
# Calculations
#refer to phasor diagram
OA = V_ph
AB = E_bph #OB = E_Rph
I_a_cosphi = P_in/(math.sqrt(3)*V_L) #I_a*math.cos(phi)
BC = I_a_cosphi*abs(Z_s) #BC is a vector in phasor diagram
OC = math.sqrt(AB**2 -BC**2 )- OA #from phasor diagram
I_a_sinphi = OC/abs(Z_s) #product of I_a and math.sin(phi)
phi = math.atan (I_a_sinphi/I_a_cosphi)
I_a = I_a_cosphi/math.cos(phi) #product of I_a and math.cos(phi)
# Results
print 'Motor current is %.3f A'%(I_a)
print 'Power factor of motor is %f leading'%(cos(phi))
print 'Note:There is slight mismatch in answer due to the approximation made during I_a* sinphi calculation'
import math
# Variables
#subscipt 1 refers to factory load
P_1 = 1800.
phi_1 = math.acos(0.6) #lagging
Q_1 = P_1*math.tan(phi_1)
#Subscript 2 refers to synchronous condenser
P_2 = 0.
# Calculations
#Subscript T refers to combination of condenser and factory load
P_T = P_1+P_2
phi_T = math.acos(0.95) #lagging
Q_T = P_T*math.tan(phi_T)
kva_rating = math.sqrt(P_T**2+ Q_T**2)
Q_2 = Q_T - Q_1
# Results
print 'i)kVA rating of synchronous condender is %.3f kVA Minus sign indicates leading nature'%(Q_2)
print 'ii)kVA rating of total factory is %.4f kVA'%(kva_rating)
import math
# Variables
I_1 = 35.
phi_1 = math.acos(0.8)
V_L = 440.
S_1 = math.sqrt(3)*I_1*V_L /1000 #in kVA
# Calculations
P_1 = S_1*math.cos(phi_1)
Q_1 = S_1*math.sin(phi_1)
P_out = 12. #motor load
eta_motor = 85./100
P_2 = P_out/eta_motor
P_T = P_1 + P_2
phi_T = math.acos(1)
Q_T = P_T * math.tan(phi_T)
Q_2 = Q_T - Q_1 #kVA supplied by motor
#negative sign of Q_2 indicates its leading nature
phi_2 = math.atan(abs(Q_2)/P_2)
S_2 = P_2/math.cos(phi_2)
# Results
print 'Power factor when motor supplies 12kW load is %.4f leading'%(math.cos(phi_2))
print 'kVA input to the motor is %.3f kVA'%(S_2)
import math
# Variables
V_L = 400
V_ph = V_L/math.sqrt(3)
Z_s = complex(0.5,4) #synchronous impedance
theta = math.atan(Z_s.imag/Z_s.real) # returns angle in radians
I_aph = 60.
phi = math.acos(0.866) #leading
power_losses = 2*10**3
# Calculations
E_bph = math.sqrt( (I_aph*abs(Z_s))**2 + (V_ph)**2 - 2*(I_aph*abs(Z_s))*(V_ph)*math.cos(phi+theta) )
delta = theta #for P_m_max
P_m_max = (E_bph*V_ph/abs(Z_s))- (E_bph**2/abs(Z_s))*math.cos(delta)
P_m_max_total = 3 * P_m_max
P_out_max = P_m_max_total- power_losses
# Results
print 'Maximum power output is %.4f kW'%(P_out_max*10**-3)
import math
# Variables
V_L = 6.6*10**3
V_ph = V_L/math.sqrt(3)
I_L = 50.
I_aph = I_L
Z_s = complex(1.5,8) #synchronous impedance
theta = math.atan(Z_s.imag/Z_s.real) # returns angle in radians
E_Rph = I_aph*abs(Z_s)
# Calculations and Results
#part(i)
phi = math.acos(0.8)
P_in = math.sqrt(3)*V_L*I_L*math.cos(phi) #for both lag and lead supplied power will be the same
print 'i)Power supplied to the motor is %.3f kW'%(P_in*10**-3)
#part(ii)
E_bph_lag = math.sqrt( E_Rph**2 + V_ph**2 - 2*E_Rph*V_ph*math.cos(theta-phi) ) #for lagging power factor
#Note that E_bph_lag > V_ph
print 'ii)Induced EMF for 0.8 power factor lag is %.3f V'%(E_bph_lag)
E_bph_lead = math.sqrt( E_Rph**2 + V_ph**2 - 2*E_Rph*V_ph*math.cos(theta+phi) ) #for leading power factor
#Note that E_bph_lead < V_ph
print ' Induced EMF for 0.8 power factor lead is %.3f V'%(E_bph_lead)
import math
# Variables
V_L = 400.
V_ph = V_L/math.sqrt(3)
P_out = 7.5*735.5
eta = 85./100 #efficiency
R_a = 0.
X_s = 10. #armature resistance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
theta = math.atan(Z_s.imag) # returns angle in radians
# Calculations and Results
P_in = P_out/eta
phi = math.acos(1) #for mimimum current power factor is maximum
I_L = P_in/(math.sqrt(3)*V_L*math.cos(phi))
I_aph = I_L
print 'Minimum current is %.3f A at full load condition '%(I_L)
E_Rph = I_aph*abs(Z_s)
E_bph = math.sqrt( E_Rph**2 + V_ph**2 - 2*E_Rph*V_ph*math.cos(phi+theta) )
print 'and corresponding EMF is %.4f V'%(E_bph)
# note : rounding off error.
import math
# Variables
V_L = 3.3*10**3
V_ph = V_L/math.sqrt(3)
V_t = V_ph
Pole = 24.
f = 50. #Pole and frequency
P = 1000.*10**3
R_a = 0
X_s = 3.24 #armature resistance and synchronous reactance
Z_s = complex(R_a,X_s) #synchronous impedance
theta = math.atan(Z_s.imag) # returns angle in radians
phi = math.acos(1)
I_aph = P/(math.sqrt(3)*V_L*math.cos(phi))
# Calculations
E_Rph = I_aph*abs(Z_s)
E_bph = math.sqrt( E_Rph**2 + V_ph**2 - 2*E_Rph*V_ph*math.cos(phi+theta) )
P_m_max = 3*(E_bph*V_ph/abs(Z_s)) #maximum power that can be delivered
N_s = 120*f/Pole #synchronous speed
T_max = P_m_max /(2*math.pi*N_s/60) #maximum torque that can be developed
# Results
print 'Maximum power and torque the motor can deliver is %.3f kW and %.2f *10**3 Nm respectively'%(P_m_max*10**-3,T_max/1000)
# rounding off error.