import math
# GIVEN DATA
# For Case (a)
S_a = 30; # Total number of Slots
m_a = 3; # Total number of Poles
p_a = 2; # Total number of Phases
# For Case (b)
S_b = 60; # Total number of Slots
m_b = 3; # Total number of Poles
p_b = 4; # Total number of Phases
# For Case (c)
S_c = 24; # Total number of Slots
m_c = 3; # Total number of Poles
p_c = 4; # Total number of Phases
# For Case (d)
S_d = 12; # Total number of Slots
m_d = 3; # Total number of Poles
p_d = 2; # Total number of Phases
# CALCULATIONS
# For Case (a)
spp_a = S_a/(p_a*m_a); # Slot per poles per phase
# For Case (b)
spp_b = S_b/(p_b*m_b); # Slot per poles per phase
# For Case (c)
spp_c = S_c/(p_c*m_c); # Slot per poles per phase
# For Case (d)
spp_d = S_d/(p_d*m_d); # Slot per poles per phase
# DISPLAY RESULTS
print ("EXAMPLE : 5.1 : SOLUTION :-") ;
print " For case a) Slot per poles per phase, spp = %.f "%(spp_a);
print " For case b) Slot per poles per phase, spp = %.f "%(spp_b);
print " For case c) Slot per poles per phase, spp = %.f "%(spp_c);
print " For case d) Slot per poles per phase, spp = %.f "%(spp_d);
import math
# GIVEN DATA
# For Case (a)
S_a = 54; # Total number of Slots
m_a = 3; # Total number of Poles
p_a = 8; # Total number of Phases
# For Case (b)
S_b = 32; # Total number of Slots
m_b = 3; # Total number of Poles
p_b = 4; # Total number of Phases
# For Case (c)
S_c = 30; # Total number of Slots
m_c = 3; # Total number of Poles
p_c = 4; # Total number of Phases
# CALCULATIONS
# For Case (a)
spp_a = S_a/(p_a*m_a); # Slot per poles per phase
l_a = 0 * spp_a; # Phase allociation Series
m_a = 1 * spp_a; # Phase allociation Series
n_a = 2 * spp_a; # Phase allociation Series
o_a = 3 * spp_a; # Phase allociation Series
p_a = 4 * spp_a; # Phase allociation Series
d_a = 0; # d_a = l_a (Rounding off)
e_a = 2; # e_a = m_a (Rounding off)
f_a = 4; # f_a = n_a (Rounding off)
g_a = 6; # g_a = o_a (Rounding off)
h_a = 9; # h_a = p_a (Rounding off)
R_a = e_a - d_a; # Phase allociation
Y_a = f_a - e_a; # Phase allociation
B_a = g_a - f_a; # Phase allociation
R1_a = h_a - g_a; # Phase allociation
# For Case (b)
spp_b = S_b/(p_b*m_b); # Slot per poles per phase
l_b = 0 * spp_b; # Phase allociation Series
m_b = 1 * spp_b; # Phase allociation Series
n_b = 2 * spp_b; # Phase allociation Series
o_b = 3 * spp_b; # Phase allociation Series
d_b = 0; # d_b = l_b (Rounding off)
e_b = 2; # e_b = m_b (Rounding off)
f_b = 5; # f_b = n_b (Rounding off)
g_b = 8; # g_b = o_b (Rounding off)
R_b = e_b - d_b; # Phase allociation
Y_b = f_b - e_b; # Phase allociation
B_b = g_b - f_b; # Phase allociation
# For Case (c)
spp_c = S_c/(p_c*m_c); # Slot per poles per phase
l_c = 0 * spp_c; # Phase allociation Series
m_c = 1 * spp_c; # Phase allociation Series
n_c = 2 * spp_c; # Phase allociation Series
d_c = 0; # d_b = l_b (Rounding off)
e_c = 2; # e_b = m_b (Rounding off)
f_c = 5; # f_b = n_b (Rounding off)
R_c = e_c - d_c; # Phase allociation
Y_c = f_c - e_c; # Phase allociation
# DISPLAY RESULTS
print ("EXAMPLE : 5.2 : SOLUTION :-") ;
print " For Case a) Slot per poles per phase , spp = %.3f "%(spp_a);
print " Phase allociation series is %.f, %.f, %.f, %.f, %.f, %.f, %.f, %.f, %.f, slots are allocated respectively\
to R, Y, B, R, Y, B, R, Y, B....... phase in Sequence "%(R_a,Y_a,B_a,R1_a,R_a,Y_a,B_a,R1_a,R_a);
print " By seeing Sequence its Slot per pole per phase is an Integer and such, balanced winding may be possible "
print " For Case b) Slot per poles per phase , spp = %.3f "%(spp_b);
print " Phase allociation series is %.f, %.f, %.f "%(R_b,Y_b,B_b);
print " By seeing Sequence its Slot per pole per phase are not Integer therefore R-phase will have 8 slots\
whereas Y-phase and B-phase will have 12 slots ";
print " For Case c) Slot per poles per phase , spp = %.1f "%(spp_c);
print " Phase allociation series is %.f, %.f, %.f, %.f, %.f, %.f, %.f, %.f, %.f, %.f, %.f, %.f slots\
are allocated respectively to R, Y, B, R, Y, B, R, Y, B, R, Y, B....... phase in Sequence "%(R_c,Y_c,R_c,Y_c,R_c,Y_c,R_c,Y_c,R_c,Y_c,R_c,Y_c);
print " By seeing Sequence its Slot per pole per phase is an Integer and such, balanced winding may be possible "
import math
# GIVEN DATA
s = 24.; # Total number of the pole
p = 4.; # Total number of the poles in the Alternator
# CALCULATIONS
# For Case (a) Short pitching by one Slots
spp = s/p; # Slot per pole
E_a = ((180*2)/24.)*(4/2); # Slot angle in Electrical
kp_a = math.cos(math.radians(E_a/2)); # Pitch Factor
kp5_a = math.cos(math.radians((5*E_a)/2)); # Pitch Factor
kp7_a = math.cos(math.radians((7*E_a)/2)); # Pitch Factor
# For Case(b) Short pitching by two Slots
E_b = 2*((180*2)/24)*(4/2); # Slot angle in Electrical
kp_b = math.cos(math.radians(E_b/2)); # Pitch Factor
kp5_b = math.cos(math.radians((5*E_b)/2)) # Pitch Factor
kp7_b = math.cos(math.radians((7*E_b)/2)); # Pitch Factor
# DISPLAY RESULTS
print ("EXAMPLE : 5.3 : SOLUTION :-") ;
print " For Case a) Short pitching by one Slots:- Pitch Facor , kp = %.4f "%(kp_a);
print " kp5 = %.4f "%(kp5_a);
print " kp7 = %.4f "%(kp7_a);
print " For Case a) Short pitching by Two Slots:- Pitch Facor , kp = %.4f "%(kp_b);
print " kp5 = %.4f "%(kp5_b);
print " kp7 = %.4f "%(kp7_b);
import math
# GIVEN DATA
s = 60.; # Total number of Slot
m = 3.; # Total number of Phase
p = 4.; # Total number of Pole
# CALCULATIONS
M = s/(m*p); # Slot per pole per Phase
sigma = 180/m; # Phase Spread in angle (deg)
Ka = math.sin(math.radians((M*sigma)/2))/(M*math.sin(math.radians(sigma/2))); # Distribution Factor
# DISPLAY RESULTS
print ("EXAMPLE : 5.4 : SOLUTION :-");
print " a) Distribution Factor, Ka = %.1f "%(Ka)
import math
# GIVEN DATA
f = 50.; # Frequency of the 2-pole Induction Motor
p = 2.; # Total Number of Poles
# CALCULATIONS
Ns = (120*f)/p; # Synchronous Speed in RPM
Ns5 = -(120*f)/(5*p); # Synchronous Speed of 5th order space harmonic in RPM
N5 = -(120*5*f)/p; # Synchronous Speed of 5th order time harmonic in RPM
Ns7 = (120*f)/(7*p); # Synchronous Speed of 7th order space harmonic in RPM
N7 = (120*7*f)/p; # Synchronous Speed of 7th order time harmonic in RPM
# DISPLAY RESULTS
print ("EXAMPLE : 5.7 : SOLUTION :-");
print " a.1) Synchronous Speed of 5th order space harmonic, Ns5 = %.f RPM "%(Ns5)
print " a.2) Synchronous Speed of 5th order time harmonic, N5 = %.f RPM "%(N5)
print " b.1) Synchronous Speed of 7th order space harmonic, Ns7 = %.2f RPM "%(Ns7)
print " b.2) Synchronous Speed of 7th order time harmonic, N7 = %.f RPM "%(N7)
import math
# GIVEN DATA
p_a = 6; # Total number of Poles in the Alternator
p_m = 4; # Total number of Poles of Induction Motor
N_a = 900; # Running Speed of the Alternator in RPM
N_m = 1250; # Running Speed of the Induction Motor in RPM
m = 3; # Total Number of phase in Induction Motor
# CALCULATIONS
f = (N_a*p_a)/120; # Frequency of the 6-pole Alternator running at 900 RPM in Hertz
Ns = (120*f)/p_m; # Synchronous Speed of 4-pole Induction Motor in RPM
s = (Ns-N_m)/Ns; # Slip
fr = s*f; # Frequency of the Rotor Current in Hertz
# DISPLAY RESULTS
print ("EXAMPLE : 5.8 : SOLUTION :-");
print " a) Frequency of the Rotor Current , fr = %.2f Hz "%(fr)
import math
# GIVEN DATA
p = 2; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
Nr = 2800; # Running Speed of the Induction Motor in RPM
m = 3; # Total Number of phase in Induction Motor
V = 400; # Operating Voltage of Induction Motor in Volts
# CALCULATIONS
Ns = (120.*f)/p; # Synchronous Speed in RPM
s = 100*((Ns-Nr)/Ns); # Slip in Percentage
fr = (s/100)*f; # Frequency of the Rotor Current in Hertz
# DISPLAY RESULTS
print ("EXAMPLE : 5.9 : SOLUTION :-");
print " a) Slip, s = %.2f percent "%(s);
print " b) Frequency of the Rotor Current, fr = %.2f Hz "%(fr)
# GIVEN DATA
m = 3; # Total Number of phase in Induction Motor
p = 4; # Total number of Poles in Induction Motor
f = 50; # Frequency in Hertz
s = 0.03; # Slip
# CALCULATIONS
Ns = (120*f)/p; # Synchronous Speed in RPM
Nr = (1-s)*Ns; # Rotor Speed in RPM
# DISPLAY RESULTS
print ("EXAMPLE : 5.10 : SOLUTION :-");
print " a) Rotor Speed , Nr = %.f RPM "%(Nr)
# GIVEN DATA
m = 3; # Total Number of phase in Induction Motor
p = 6; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
s = 0.03; # Slip
# CALCULATIONS
Ns = (120*f)/p; # Synchronous Speed in RPM
Nr = (1-s)*Ns; # Rotor Speed in RPM
Nf = Ns - Nr; # Speed of Forward Rotating magnetic fields with respect to stator and rotor in RPM
Nb = Ns + Nr; # Speed of Backward Rotating magnetic fields with respect to stator and rotor in RPM
# DISPLAY RESULTS
print ("EXAMPLE : 5.11 : SOLUTION :-");
print " a) Speed of Forward Rotating magnetic fields with respect to stator and rotor is equal to + %.f RPM "%(Nf)
print " b) Speed of Backward Rotating magnetic fields with respect to stator and rotor is equal to + %.f RPM "%(Nb)
# GIVEN DATA
m = 3; # Total Number of phase in Induction Motor
p = 2; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
s = 0.05; # Slip
# CALCULATIONS
Ns = (120*f)/p; # Synchronous Speed in RPM
Nr = (1-s)*Ns; # Rotor Speed in RPM
Nf = s*Ns; # Speed of Forward Rotating magnetic fields with respect to stator and rotor in RPM
Nb = (p-s)*Ns; # Speed of Backward Rotating magnetic fields with respect to stator and rotor in RPM
fr = (p-s)*f; # Backward rotating magnetic field induces a current of frequency in Hertz
# DISPLAY RESULTS
print ("EXAMPLE : 5.12 : SOLUTION :-");
print " a) Speed of Forward Rotating magnetic fields with respect to stator and rotor is equal to + %.f RPM "%(Nf)
print " b) Speed of Backward Rotating magnetic fields with respect to stator and rotor is equal to + %.f RPM "%(Nb)
# GIVEN DATA
m = 3; # Total Number of phase in Induction Motor
p = 4; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
s = 0.05; # Slip
# CALCULATIONS
Ns = (120*f)/p; # Synchronous Speed in RPM
fr = s*f; # Rotor-induced Frequency of forward field in Hertz
Nfr = s*Ns; # Speed of Forward Rotating magnetic fields with respect to rotor surface in RPM
f2r = s*f; # Rotor-induced Frequency of Backward field in Hertz
Nbr = -(s*Ns); # Speed of Backward Rotating magnetic fields with respect to rotor surface in RPM
Nr = (1-s)*Ns; # Rotor running in Forward direction in RPM
Nfs = Nr+(s*Ns); # Speed of Forward Rotating magnetic fields with respect to stator surface in RPM
Nbs = Nr-(s*Ns); # Speed of Backward Rotating magnetic fields with respect to stator surface in RPM
Nbs_new = -(0.5*Ns)+(1-0.5)*Nr; # Speed of Backward Rotating magnetic fields with respect to stator for 50% of slip in RPM
# DISPLAY RESULTS
print ("EXAMPLE : 5.13 : SOLUTION :-");
print " a.1) Speed of Forward Rotating magnetic fields with respect to rotor surface is equal to + %.f RPM "%(Nfr)
print " a.2) Speed of Backward Rotating magnetic fields with respect to rotor surface is equal to + %.f RPM "%(Nbr)
print " b.1) Speed of Forward Rotating magnetic fields with respect to stator surface is equal to + %.f RPM "%(Nfs)
print " b.2) Speed of Backward Rotating magnetic fields with respect to stator surface is equal to + %.f RPM "%(Nbs)
print " c) Speed of Backward Rotating magnetic fields with respect to stator for 50 percenatge slip is equal to %.1f RPM "%(Nbs_new)
print " [ TEXT BOOK SOLUTION IS PRINTED WRONGLY I verified by manual calculation ]" ;
print " WRONGLY PRINTED ANSWERS ARE :- a) Speed of Backward Rotating magnetic fields with respect to stator for 50 percenatge slip is equal to 0 RPM instead of %.1f RPM "%(Nbs_new);
# GIVEN DATA
f = 50; # Stator Frequency of Inductor Motor in Hertz
fr = 10; # Rotor Frequency of Inductor Motor in Hertz
p = 2; # Number of poles
# CALCULATIONS
Ns = (120*f)/p; # Synchronous Speed of Induction Motor in RPM
s = fr/f; # Slip of the Induction Motor
Nr = (1-s)*Ns; # Rotor Speed of the Induction Motor
# DISPLAY RESULTS
print ("EXAMPLE : 5.14 : SOLUTION :-");
print " a) Rotor Speed of Induction Motor, Nr = %.f RPM "%(Nr)
import math
# GIVEN DATA
print " EXAMPLE : 5.15 : Given Data No-load test : 440V, 30A, 4.5KW ";
print " Blocked rotor test : 90V%(50Hz, 120A, 16KW ";
m = 3; # Total Number of phase in Induction Motor
p = 6; # Total number of Poles of Induction Motor
V = 440; # Operating voltage of the Induction motor in Volts
out_hp = 100; # Output of the Induction motor in Horse-Power
R = 0.15; # Average dc resistance in Ohms
Wsc = 16000; # Power at Blocked Rotor test in Watts
Vsc = 90; # Voltage at Blocked Rotor test in Volts
Isc = 120; # Current at Blocked Rotor test in Amphere
W0 = 4500; # Power at No-load test in Watts
V0 = 440; # Voltage at No-load test in Volts
I0 = 30; # Current at No-load test in Amphere
s = 0.05; # Slip
f = 50; # Frequency in Hertz
# CALCULATIONS
R1 = R/2; # DC winding resistance per phase in Ohms
Rac = Wsc/(3*Isc**2); # AC resistance referred to stator from locked rotor test at supply frequency in Ohms
R_2 = Rac - R1; # Per phase Rotor resistance to Stator in Ohms
Zsc = Vsc/(math.sqrt(3)*Isc); # Per phase Impedance from locked rotor test in Ohms
Xs = math.sqrt((Zsc**2)-(Rac**2)); # Per phase leakage reactance referred to stator in Ohms
theta_0 = math.acos(math.radians(W0/(V0*I0*math.sqrt(3)))); # No-load power factor angle in degree
Im = I0*math.degrees(math.sin(math.radians(theta_0))); # Reactive component of no-load current in Amphere
Xm = V0/(Im*math.sqrt(3)); # Magnetizing reactance in Ohms
Pc = W0 - 3*I0**2*R1; # Total Core loss in Watts
Rc = (V0/math.sqrt(3))**2*(3/Pc); # Per phase core loss resistance in Watts
Vph = V0/math.sqrt(3); # Per phase Voltage in Volts
Ic = Vph/Rc; # Core loss current in Amphere
I_m = Vph/(1j * Xm); # Magnetizing Current in Amphere
I_o = Ic + I_m; # No-load current in Amphere
I_2 = Vph/(R1+(R_2/s)+(1j*Xs)); # Current in Amphere
I1 = I_o + I_2; # Input Current in Amphere
Pf = math.cos(math.radians(math.degrees(math.atan(I1.imag/I1.real)))); # Power factor
P1 = (3*(abs(I_2)**2*R_2)/s)/1000.; # 3-phase air gap power or Rotor intake Power in Kilo-Watts
Po = P1*(1-s); # Output Power in Kilo-Watts
Ws = 2*math.pi*((120*f/p)*(1./60.)); # Angular Roatation in Radians per Seconds
T = P1*1000/Ws; # Torque in Newton-Meter
# DISPLAY RESULTS
print ("EXAMPLE : 5.15 : SOLUTION :-") ;
print " a.1) DC winding resistance per phase, R1 = %.3f Ohms "%(R1)
print " a.2) AC resistance referred to stator from locked rotor test at supply frequency = %.4f Ohms "%(Rac)
print " a.3) Per phase Rotor resistance to Stator, R2 = %.4f Ohms "%(R_2)
print " a.4) Per phase Impedance from locked rotor test, Zsc = %.3f Ohms "%(Zsc)
print " a.5) Per phase leakage reactance referred to stator, Xs = %.4f Ohms "%(Xs)
print " a.6) No-load power factor angle, theta_O = %.2f Degree "%(theta_0)
print " a.7) Reactive component of no-load current, Im = %.1f A "%(Im)
print " a.8) Magnetizing reactance, Xm = %.2f Ohms "%(Xm)
print " a.9) Total Core loss, Pc = %.1f W "%(Pc)
print " a.10) Per phase core loss resistance, Pc = %.f Ohms "%(Rc)
print " a.11) Per phase Voltage, Vph = %.f V "%(Vph)
print " a.12) Core loss current, Ic = %.2f < %.f A "%(abs(Ic),math.degrees(math.atan2(Ic.imag,Ic.real)))
print " a.13) Magnetizing Current, Im = %.1f < %.f A "%(abs(I_m),math.degrees(math.atan2(I_m.imag,I_m.real)))
print " a.14) No-load current, I0 = %.2f < %.2f A "%(abs(I_o),math.degrees(math.atan2(I_o.imag,I_o.real)))
print " a.15) Current, I2 = %.2f < %.2f A "%(abs(I_2),math.degrees(math.atan2(I_2.imag,I_2.real)))
print " b) Input current, I1 = %.2f < %.2f A "%(abs(I1),math.degrees(math.atan2(I1.imag,I1.real)))
print " c) Power Factor, Pf = %.4f Lagging "%(Pf)
print " d) Output Power, P0 = %.1f kW "%(Po)
print " e) Torque, T = %.2f NM "%(T)
import math
# GIVEN DATA
print " EXAMPLE : 5.17 : Given Data No-load test : 440V%( 3.0A, 500KW, 50Hz ";
print " Blocked rotor test at rated frequency : 110V%( 18A, 2500W, 50Hz ";
print " DC test on Stator per phase : 10V, 15A ";
m = 3; # Total Number of phase in Induction Motor
p = 4; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
V = 440; # Operating Voltage of the Inductuon Motor
out_hp = 20; # Motor Power Rating in Horse-Power
Vdc = 10; # DC Voltage in Volts
Idc = 15; # DC Current in Amphere
Wsc = 2500; # Power at Blocked Rotor test rated frequency in Watts
Wsc_red = 2050; # Power at Blocked Rotor test reduced frequency in Watts
Vsc = 110; # Voltage at Blocked Rotor test rated frequency in Volts
Isc = 18; # Current at Blocked Rotor test rated frequency in Amphere
Wo = 500; # Power at No-load test in Watts
Vo = 440; # Voltage at No-load test in Volts
Io = 4.0; # Current at No-load test in Amphere
fsc = 50; # Rated Frequency at blocked rotor test in Hertz
fo = 50; # Rated Frequency at no-load test in Hertz
fsc1 = 15; # Reduced Frequency at blocked rotor in Hertz
Pfw = 200; # Friction and Windage loss in Watts
# CALCULATIONS
R1dc = Vdc/Idc; # DC winding resistance per phase in Ohms
Rac = Wsc/(3*Isc**2); # AC resistance from Locked rotor test at supply frequency
Rac_red = Wsc_red/(3*Isc**2); # AC resistance from Locked rotor test at reduced frequency
R1ac = (Rac/Rac_red)*R1dc; # Corrected Value of AC stator winding resistance in Ohms
R2dc = Rac_red - R1dc; # Second rotor parameter, rotor resistance referred to stator is at low frequency in Ohms
Zsc = Vsc/(math.sqrt(3)*Isc); # Per phase Impedance from locked rotor test at power frequency in Ohms
Xs = math.sqrt((Zsc**2)-(Rac**2)); # Per phase leakage reactance referred to stator in Ohms
theta_0 = math.acos(math.radians(Wo/(Vo*Io*math.sqrt(3)))); # No-load power factor angle in degree
Im = Io*math.degrees(math.sin(math.radians(theta_0))); # Reactive component of no-load current in Amphere
Xm = Vo/(Im*math.sqrt(3)); # Magnetizing reactance in Ohms
Pc = Wo - 3*Io**2*R1ac-Pfw; # Total Core loss in Watts
Rc = (Vo/math.sqrt(3))**2*(3/Pc); # Per phase core loss resistance in Watts
# DISPLAY RESULTS
print ("EXAMPLE : 5.17 : SOLUTION :-") ;
print " a) Magnetizing reactance of Equivalent circuit, Xm = %.1f Ohms "%(Xm)
print " b) Per phase core loss resistance, Pc = %.f Ohms "%(Rc)
import math
# GIVEN DATA
# From Previous problem data (Example 5.17)
R1ac = 0.8127; # Corrected Value of AC stator winding resistance in Ohms
R2dc = 1.4433; # Second rotor parameter, rotor resistance referred to stator is at low frequency in Ohms
Xs = 2.42; # Per phase leakage reactance referred to stator in Ohms
Xm = 64.4; # Magnetizing reactance in Ohms
Rc = 742; # Per phase core loss resistance in Watts
s = 0.035; # Slip
m = 3; # Total Number of phase in Induction Motor
p = 4; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
V = 440; # Operating Voltage of the Inductuon Motor
out_hp = 20; # Motor Power Rating in Horse-Power
# CALCULATIONS
Vph = V/math.sqrt(3); # Per phase Voltage in Volts
Ic = Vph/Rc; # Core loss current in Amphere
I_m = Vph/(1j * Xm); # Magnetizing Current in Amphere
I_o = Ic + I_m; # No-load current in Amphere
I_2 = Vph/(R1ac+(R2dc/s)+(1j*Xs)); # Current in Amphere
I1 = I_o + I_2; # Input Current in Amphere
Pf = math.cos(math.radians(math.degrees(math.atan(I1.imag/I1.real)))); # Power factor
P1 = 3*(abs(I_2)**2*R2dc)/s; # 3-phase air gap power or Rotor intake Power in Watts
Po = P1*(1-s); # Output Power in Watts
Ws = 2*math.pi*((120*f/p)*(1./60)); # Angular Roatation in Radians per Seconds
T = P1/Ws; # Torque in Newton-Meter
# DISPLAY RESULTS
print ("EXAMPLE : 5.18 : SOLUTION :-");
print " a) Input current, I1 = %.2f < %.2f A "%(abs(I1),math.degrees(math.atan2(I1.imag,I1.real)))
print " b) Power Factor, Pf = %.3f Lagging "%(Pf)
print " c) Output Power, P0 = %.2f W "%(Po)
print " d) Torque, T = %.2f NM "%(T)
print " [ TEXT BOOK SOLUTION IS PRINTED WRONGLY I verified by manual calculation ]" ;
print " WRONGLY PRINTED ANSWERS ARE :- a) T = 4340.82 Nm instead of %.2f Nm "%(T);
print " IN TEXT BOOK, CALCULATION OF TORQUE IS NOT DONE ";
import math
from numpy import imag,real
# GIVEN DATA
s = 0.05; # Slip
m = 3; # Total Number of phase in Induction Motor
p = 4; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
V = 440; # Operrating Voltage of the Inductuon Motor
R1 = 0.10; # Circuit Parameter in Ohms
R2 = 0.11; # Circuit Parameter in Ohms
X1 = 0.35; # Circuit Parameter in Ohms
X2 = 0.40; # Circuit Parameter in Ohms
pf = 0.2; # Power factor (Lagging)
Pr = 900; # Rotational Loss in Watts
Psc = 1000; # Stator core loss in Watts
I = 15; # Line current draws by the motor in Amphere
# CALCULATIONS
Vph = V/math.sqrt(3); # Per phase Voltage in Volts
I_2 = Vph/(R1+(R2/s)+(1j*(X1+X2))); # Current in Amphere
Io = I * (-(1j * math.degrees(math.acos(pf)) * math.pi/180.))**2; # No-load current in Amphere
I1 = Io + I_2; # Input line Current in Amphere
PF = math.cos(math.radians(math.degrees(math.atan(I1.imag/I1.real)))); # Power factor
Ws = 2*math.pi*((120*f/p)*(1./60.)); # Angular Roatation in Radians per Seconds
Pg = (3*(abs(I1)**2*R2))/s; # 3-phase air gap power or Rotor intake Power in Watts
T = Pg/Ws; # Torque in Newton-Meter
Po = Pg*(1-s)-Pr; # Output Power in Watts
Po_HP = Po/746; # Output Power in Horse-Power
eta = (Po/(Po+Psc+Pr))*100.; # Efficiency in Percentage
# DISPLAY RESULTS
print ("EXAMPLE : 5.19 : SOLUTION :-");
print " a) Input line current, I1 = %.1f < %.2f A "%(abs(I1),math.degrees(math.atan2(I1.imag,I1.real)))
print " b) Power Factor, Pf = %.4f Lagging "%(PF)
print " c) Output Power, P0 = %.1f HP "%(Po_HP)
print " d) Torque, T = %.2f Nm "%(T)
print " e) Efficiency, eta = %.1f Percenatge "%(eta)
print " [ TEXT BOOK SOLUTION IS PRINTED WRONGLY I verified by manual calculation ]" ;
print " WRONGLY PRINTED ANSWERS ARE :- a) I1 = 114.2<-24.68 A instead of %.1f<%.2f A "%(abs(I1),math.degrees(math.atan2(I1.imag,I1.real)));
print " b) T = 548.24 Nm instead of %.2f Nm "%(T);
print " c) Po = 108.4 HP instead of %.1f HP "%(Po_HP);
import math
from numpy import imag,real
# GIVEN DATA
m = 3; # Total Number of phase in Induction Motor
p = 6; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
V = 440; # Operating Voltage of the Inductuon Motor
R1 = 0.25; # Circuit Parameter in Ohms
R2 = 0.25; # Circuit Parameter in Ohms
X1 = 0.75; # Circuit Parameter in Ohms
X2 = 0.75; # Circuit Parameter in Ohms
Xm = 1000; # Circuit Parameters in Ohms
Rc = 100; # Circuit Parameters in Watts
s = 0.025; # Slip
Pr = 450; # Rotational Loss in Watts
Psc = 800; # Stator core loss in Watts
# CALCULATIONS
Vph = V/math.sqrt(3); # Per phase Voltage in Volts
I_2 = Vph/(R1+(R2/s)+(1j*(X1+X2))); # Current in Amphere
Ic = Vph/Rc; # Core loss current in Amphere
I_m = Vph/(1j * Xm); # Magnetizing Current in Amphere
I_o = Ic + I_m; # No-load current in Amphere
I1 = I_o + I_2; # Input Current in Amphere
Pf = math.cos(math.radians(math.degrees(math.atan(I1.imag/I1.real)))); # Power factor
Ns = (120*f)/p; # Synronous Speed in RPM
Pg = 3*(abs(I_2)**2*R2)/s; # 3-phase air gap power or Rotor intake Power in Watts
Pm = Pg*(1-s); # Output Power in Watts
Ws = 2*math.pi*Ns*(1./60.); # Angular Roatation in Radians per Seconds
T = Pg/Ws; # Torque in Newton-Meter
Po = Pm-Pr; # Output Power in Watts
Po_HP = Po/746; # Output Power in Horse-Power
eta = (Po/(Po+Psc+Pr))*100; # Efficiency in Percentage
# DISPLAY RESULTS
print ("EXAMPLE : 5.20 : SOLUTION :-");
print " a) Input line current, I1 = %.f < %.2f A "%(abs(I1),math.degrees(math.atan(I1.imag%(I1.real))))
print " b) Power Factor, Pf = %.4f Lagging "%(Pf)
print " c) Output Power, P0 = %.2f HP "%(Po_HP)
print " d) Torque, T = %.1f Nm "%(T)
print " e) Efficiency, eta = %.1f Percenatge "%(eta)
print " [ TEXT BOOK SOLUTION IS PRINTED WRONGLY I verified by manual calculation ]" ;
print " WRONGLY PRINTED ANSWERS ARE :- a) I1 = 26.8-j3.584 {27<-7.62} A in instead of %.1f)+j%.3f) {%.f<%.2f} A "%(I1.real,I1.imag,abs(I1),math.degrees(math.atan2(I1.imag,I1.real)));
print " b) pf = 0.9885 Lagging instead of %.4f Lagging "%(Pf);
import math
from numpy import roots
# GIVEN DATA
m = 3; # Total Number of phase in Induction Motor
p = 4; # Total number of Poles of Induction Motor
s = 0.05; # Slip
f = 50; # Frequency in Hertz
Tm = 500; # Maximum Torque in Newton-Meter
Tst = 200; # Starting Torque in Newton-Meter
sst = 1.0; # Starting Slip
# CALCULATONS
p1 = [1, -5, 1] # Slip at Maximum Torque (obtained from Equation Tst = (2*Tm)/((sst/sm)+(sm+sst))
a = roots(p1); # Value of slip at Maximum Torque (obtained from Equation Tst = (2*Tm)/((sst/sm)+(sm+sst))
sm = a[1]#(2,1); # Slip at Maximum Torque (obtained from Equation Tst = (2*Tm)/((sst/sm)+(sm+sst)) { 1st root is 4.8 so its out of range because slip value is lies between 0-1 so its neglected and second root will be slip }
T = (2*Tm)/((s/sm)+(sm/s)); # Torque at 0.05 slip
Ns = (120*f)/p; # Synchronous Speed in RPM
Wr = (2*math.pi)*(1-s)*(Ns/60); # Angular Velocity in Radians-per-Second
P = T * Wr; # Power Output in Watts
P_HP = P/746; # Power Output in Horse-Power
# DISPLAY RESULTS
print ("EXAMPLE : 5.21 : SOLUTION :-");
print " a) Torque at 0.05 slip, T = %.2f Nm "%(T)
print " b) Power Output at 0.05 slip, P = %.1f W = %.2f HP "%(P,P_HP)
import math
# GIVEN DATA
Wsc = 1000.; # Power at Blocked Rotor test in Watts
Vsc = 56.; # Voltage at Blocked Rotor test in Volts
Isc = 18.; # Current at Blocked Rotor test in Amphere
Woc = 52.; # Power at No-load test in Watts
Voc = 220.; # Voltage at No-load test in Volts
Ioc = 2.6; # Current at No-load test in Amphere
m = 3.; # Total Number of phase in Induction Motor
p = 4.; # Total number of Poles of Induction Motor
V = 220.; # Operating voltage of the Induction motor in Volts
f = 50.; # Frequency in Hertz
s = 0.05; # Slip
R = 0.65; # Per phase stator resistance in Ohms
# CALCULATIONS
Vph = Voc/math.sqrt(3); # Per phase Voltage in Volts
Wo = Woc/m; # Per phase No-load loss in Watts
theta_0 = math.acos(math.radians(Wo/(Voc*Ioc*math.sqrt(3)))); # No-load power factor angle in degree
VSC = Vsc/math.sqrt(3); # Per phase locked rotor Voltage in Volts
WSC = Wsc/m; # Per phase locked rotor loss in Watts
theta_sc = math.acos(math.radians(WSC/(VSC*Isc))); # No-load power factor angle in degree
ISC = Isc*(Voc/Vsc); # locked rotor current at full Voltage in Amphere
Re = WSC/Isc**2; # resistance in Ohms
R1 = R*1.1; # Per phase AC stator resistance in Ohms
R_2 = Re - R1; # Per phase rotor resistance in Ohms
Zsc = VSC/Isc; # Per phase impedance in Ohms
Xs = math.sqrt((Zsc**2)-(Re**2)); # Leakage reactance in Ohms
I_2 = (Voc/math.sqrt(3))/math.sqrt((R1+(R_2/s))**2+(Xs**2)); # Current in Amphere
pf = math.cos(math.radians(math.degrees(math.atan(Xs/(R1+(R_2/s)))))); # Power Factor
Ws = 2*math.pi*((120*f/p)*(1./60.)); # Rotational Speed in Radians per Seconds
Pg = (3*(abs(I_2)**2*R_2))/s; # 3-phase air gap power or Rotor intake Power in Watts
T = Pg/Ws; # Torque in Newton-Meter
# CALCULATIONS OR DATA OBTAINED FROM CIRCLE DIAGRAM FIGURE 5.35 and PAGE NO:-303
OA = 2.60; # Correspounding Current in Amphere at 87' from Y-axis (from Circle diagram)
OE = 70.70; # Correspounding Current in Amphere at 55' from Y-axis (from Circle diagram)
OP = 17.77; # Current in Amphere (from Circle diagram)
OV = Voc/math.sqrt(3); # Phase Voltage in No-load test or value obatined from circle diagram in Volts
PK = 11.6; # Correspounding Value from Circle diagram
JK = 0.8; # Correspounding Value from Circle diagram
PJ = 10.8; # Correspounding Value from Circle diagram
PM = 11.6; # Correspounding Value from Circle diagram
Pir = 3*OV*PK; # Total Rotor intake in Watts
Plr = 3*OV*JK; # Total Rotor loss in Watts
Po = 3*OV*PJ; # Total Mechanical power output in Watts
T_c = (3*OV*PK)/Ws; # Total Torque in Newton-Meter
s_c = JK/PK; # Slip obtained from Circle diagram
s_pc = 100*s_c; # Slip in percentage
eta = 100*(PJ/PM); # Eifficiency in Percentage
# DISPLAY RESULTS
print ("EXAMPLE : 5.22 : SOLUTION :-");
print " a) Input line current, I2 = %.2f A "%(I_2)
print " b) Power Factor, Pf = %.3f "%(pf)
print " c) Torque, T = %.2f Nm "%(T)
print " Verification Results from Circle Diagram :-";
print " a) Efficency, eta = %.2f Percent "%(eta)
print " b) slip, s = %.3f = %.f percent "%(s_c,s_pc)
print " c) Torque, T = %.2f Nm "%(T_c)
import math
from numpy import real,imag
# GIVEN DATA
R1 = 0.2; # Circuit Parameter in Ohms
R2 = 0.4; # Circuit Parameter in Ohms
X1 = 1.0; # Circuit Parameter in Ohms
X2 = 1.5; # Circuit Parameter in Ohms
m = 3; # Total Number of phase in Induction Motor
p = 2; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
V = 440; # Operating Voltage of the Inductuon Motor
# CALCULATIONS
Ws = 2*math.pi*f; # Synchronous angular speed in Radians per second
Z = (R1+R2)+((1j)*(X1+X2)); # At slip s=1, the impedance seen from the terminals in Ohms
s = 1; # Slip
# For Case(a) Winding is connected in star
Isy_a = V/(abs(Z)*math.sqrt(3)); # Current in Amphere
Tsy_a = (3*Isy_a**2*R2)/(s*Ws); # Torque in Newton-Meter
# Winding is connected in delta
Isd_a = (V*math.sqrt(3))/abs(Z); # Current in Amphere
Tsd_a = (3*(Isd_a/math.sqrt(3))**2*R2)/(s*Ws); # Torque in Newton-Meter
I_R = Isd_a/Isy_a; # Ratio of the line current
T_R = Tsd_a/Tsy_a; # Ratio of the Torque
# For Case(b) Machine is started umath.sing auto-transfromer and voltage is 50% reduced
Isy_b = (0.5*V)/(abs(Z)*math.sqrt(3)); # Current in Amphere when Winding is connected star
Tsy_b = (3*Isy_b**2*R2)/(s*Ws); # Torque in Newton-Meter when Winding is connected star
Isd_b = (0.5*V*math.sqrt(3))/abs(Z); # Current in Amphere when Winding is connected delta
Tsd_b = (3*(Isd_b/math.sqrt(3))**2*R2)/(s*Ws); # Torque in Newton-Meter when Winding is connected delta
# For Case(c) Both Voltage and Frequency are reduced to 50%
f_new = (10./100)*f; # New Frequency
Ws_c = 2*math.pi*f_new; # Synchronous angular speed in Radians per second
Z_c = ((R1+R2)+((1j)*(X1+X2))*(f_new/f)); # At slip s=1, the impedance seen from the terminals in Ohms
Isy_c = (0.1*V)/(abs(Z_c)*math.sqrt(3)); # Current in Amphere when Winding is connected star
Tsy_c = (3*Isy_c**2*R2)/(s*Ws_c); # Torque in Newton-Meter when Winding is connected star
Isd_c = (0.1*V*math.sqrt(3))/abs(Z_c); # Current in Amphere when Winding is connected delta
Tsd_c = (3*(Isd_c/math.sqrt(3))**2*R2)/(s*Ws_c); # Torque in Newton-Meter when Winding is connected delta
# DISPLAY RESULTS
print ("EXAMPLE : 5.23 : SOLUTION :-");
print " For Case a.1 Winding is connected in star ";
print " a.1.1) Per phase impedance seen from the terminals in Ohms, Z = %.3f < %.1f Ohms "%(abs(Z),math.degrees(math.atan2(Z.imag,Z.real)));
print " a.1.2) Initial Starting Current , Isy = %.2f A "%(Isy_a)
print " a.1.3) Starting Torque , Tsy = %.1f Nm "%(Tsy_a)
print " For Case a.2 Winding is connected in delta " ;
print " a.2.1) Initial Starting Current , Isd = %.2f A "%(Isd_a)
print " a.2.2) Starting Torque , Tsd = %.2f Nm "%(Tsd_a)
print " For Case b Machine is started umath.sing auto-transfromer and voltage is 50 percentage reduced :- b.1 Winding is connected in star "
print " b.1.1) Per phase impedance seen from the terminals in Ohms, Z = %.3f<%.1f Ohms "%(abs(Z),math.degrees(math.atan2(Z.imag,Z.real)));
print " b.1.2) Initial Starting Current , Isy = %.1f A "%(Isy_b)
print " b.1.3) Starting Torque , Tsy = %.2f Nm "%(Tsy_b)
print " For Case b.2 Winding is connected in delta " ;
print " b.2.1) Initial Starting Current , Isd = %.2f A "%(Isd_b)
print " b.2.2) Starting Torque , Tsd = %.f Nm "%(Tsd_b)
print " For Case c Both Voltage and Frequency are reduced to 50 percentage :- c.1 Winding is connected in star ";
print " c.1.1) Per phase impedance seen from the terminals in Ohms, Z = %.2f<%.2f Ohms "%(abs(Z_c),math.degrees(math.atan2(Z_c.imag,Z_c.real)));
print " c.1.2) Initial Starting Current , Isy = %.2f A "%(Isy_c)
print " c.1.3) Starting Torque , Tsy = %.2f Nm "%(Tsy_c)
print " For Case c.2 Winding is connected in delta " ;
print " c.2.1) Initial Starting Current , Isd = %.2f A "%(Isd_c)
print " c.2.2) Starting Torque , Tsd = %.2f Nm "%(Tsd_c)
print 'Comparing the Calculated values of starting current and torque eid rated frequency and rated voltage'
print " star delta"
print " 440V%(50Hz 44V%(5Hz 440V,50Hz 44V,5Hz "
print " starting current %.2f A %.f A %.f A %.2f A "%(Isy_a,Isy_c,Isd_a,Isd_c)
print " starting Torque %.1f Nm %.2f Nm %.f Nm %.2f Nm "%(Tsy_a,Tsy_c,Tsd_a,Tsd_c)
print " [ TEXT BOOK SOLUTION IS PRINTED WRONGLY I verified by manual calculation ]" ;
print " WRONGLY PRINTED ANSWERS ARE :- For Case a.2) Winding is connected in delta :- a) Initial Starting Current Isy = 254.01 A instead of %.2f A "%(Isd_a);
import math
from numpy import imag,real
# GIVEN DATA
m = 3; # Total Number of phase in Induction Motor
f = 50; # Frequency in Hertz
V = 440; # Operating voltage of the Induction Motor in Volts
R1 = 0.2; # Circuit Parameter in Ohms
R2 = 0.4; # Circuit Parameter in Ohms
X1 = 1.0; # Circuit Parameter in Ohms
X2 = 1.5; # Circuit Parameter in Ohms
Rc = 150; # Circuit Parameter in Ohms
Xm = 30; # Circuit Parameter in Ohms
# CALCULATIONS
V1 = V/math.sqrt(3); # Rated Voltage in Volts
Zdol = (R1+1j*X1)+(Rc*1j*Xm*(R2+1j*X2))/(Rc*1j*Xm+Rc*(R2+1j*X2)+(1j*Xm)*(R2+1j*X2)); # Equivalent impedance per phase in DOL starter in Ohms
I = V1/Zdol; # Starting Current in DOL starter in Amphere
# For Case(a) A per Phase resistance of 0.5 Ohms is added in Series with the stator circuit
Zsr = (0.5+R1+1j*X1)+((Rc*1j*Xm*(R2+1j*X2))/((Rc*1j*Xm+Rc*(R2+1j*X2)+(1j*Xm)*(R2+1j*X2)))); # Total impedance seen from the terminals in Ohms
Isr = V1/Zsr; # Starting Current in DOL starter in Amphere
# For Case(b) A per Phase resistance of 0.5 Ohms is added in Series with the rotor circuit here assumed that stator to rotor turn ratio is 1.0
Zrr = (R1+1j*X1)+((Rc*1j*Xm*(0.5+R2+1j*X2))/(Rc*1j*Xm+Rc*(0.5+R2+1j*X2)+(1j*Xm)*(0.5+R2+1j*X2))); # Total impedance seen from the terminals in Ohms
Irr = V1/Zrr; # Starting Current in DOL starter in Amphere
# For Case(c) When applied Voltage reduced to 50%
I_c = (0.5*V1)/Zdol; # Starting Current in DOL starter in Amphere
# For Case(d) When Motor is supplied by reduced Voltage of 44V ( Voltage is reduced by 10%) and the reduced frequency is 5Hz
f_n = 5; # Reduced Frequency in Hertz
X1_n = (f_n/f)*X1; # Changed Circuit Parameter in Ohms
X2_n = (f_n/f)*X2; # Changed Circuit Parameter in Ohms
Xm_n = (f_n/f)*Xm; # Changed Circuit Parameter in Ohms
Zdol_n = (R1+1j*X1_n)+((Rc*1j*Xm_n*(R2+1j*X2_n))/(Rc*1j*Xm_n+Rc*(R2+1j*X2_n)+(1j*Xm_n)*(R2+1j*X2_n))); # Equivalent impedance per phase in DOL starter in Ohms
I_n = (V1*0.1)/Zdol_n; # Starting Current in DOL starter in Amphere
Ratio = abs(I_n)/abs(I); # Ratio of the Starting Current witha the rated Voltage and frequency to the reduced Voltage and frequency
# DISPLAY RESULTS
print ("EXAMPLE : 5.24 : SOLUTION :-");
print " Normal Initial Starting Current in DOL starter, I = %.1f <%.1f A "%(abs(I),math.degrees(math.atan2(I.imag,I.real)))
print " For Casea A per Phase resistance of 0.5 Ohms is added in Series with the stator circuit "
print " Initial Starting Current in DOL starter, I = %.1f <%.2f A "%(abs(Isr),math.degrees(math.atan2(Isr.imag,Isr.real)))
print " For Caseb A per Phase resistance of 0.5 Ohms is added in Series with the rotor circuit "
print " Initial Starting Current in DOL starter, I = %.2f <%.1f A "%(abs(Irr),math.degrees(math.atan2(Irr.imag,Irr.real)))
print " For Casec When applied Voltage reduced to 50 percentage "
print " Initial Starting Current in DOL starter, I = %.2f <%.1f A "%(abs(I_c),math.degrees(math.atan2(I_c.imag,I_c.real)))
print " For Cased When Motor is supplied by reduced Voltage of 44V Voltage is reduced by 10 percenatge and the reduced frequency is 5Hz "
print " Initial Starting Current in DOL starter, I = %.1f <%.1f A "%(abs(I_n),math.degrees(math.atan2(I_n.imag,I_n.real)))
print " By reducing volatge as well as the frequency, the peak starting current at the insmath.tant os starting is reduced by a fector of %.4f of the starting current with the reted volatge and frequency "%(Ratio)
print " [ TEXT BOOK SOLUTION IS PRINTED WRONGLY I verified by manual calculation ]" ;
print " WRONGLY PRINTED ANSWERS ARE :- For Cased) When Motor is supplied by reduced Voltage of 44V Voltage is reduced by 10 percenatge ) and the reduced frequency is 5Hz, I = 24.1 < 25.6 A instead of %.1f < %.2f) A "%(abs(I_n),math.degrees(math.atan2(I_n.imag,I_n.imag)));
print " Ratio of the Starting Current with the rated Voltage and frequency to the reduced Voltage and frequency, Ratio = 0.2518 instead of %.4f "%(Ratio);
import math
# GIVEN DATA
m1 = 3; # Total Number of phase in 1st Induction Motor
p1 = 6; # Total number of Poles of 1st Induction Motor
f = 50; # Frequency in Hertz
m2 = 3; # Total Number of phase in 2nd Induction Motor
p2 = 10; # Total number of Poles of 2nd Induction Motor
# CALCULATIONS
Ns1 = (120*f)/p1; # Synchronous speed of 1st Induction Motor in RPM
Ns2 = (120*f)/p2; # Synchronous speed of 2nd Induction Motor in RPM
Nscu = (120*f)/(p1+p2); # Speed during cumalative casade in RPM
Ndiff = (120*f)/(p2-p1); # Speed during cumalative casade in RPM
# DISPLAY RESULTS
print ("EXAMPLE : 5.25 : SOLUTION :-");
print " a) Range of speed is %.f - %.f - %.f - %.f RPM "%(Nscu,Ns2,Ns1,Ndiff)
import math
from numpy import real,imag
# GIVEN DATA
m = 3; # Total Number of phase in Induction Motor
p = 4; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
V = 440; # Operating Voltage of the Inductuon Motor
R1 = 0.25; # Circuit Parameter in Ohms
R2 = 0.5; # Circuit Parameter in Ohms
X1 = 1.5; # Circuit Parameter in Ohms
X2 = 1.5; # Circuit Parameter in Ohms
# CALCULATIONS
Vph = V/math.sqrt(3); # Per phase Voltage in Volts
Ns = (120.*f)/p; # Synchoronous Speed in RPM
Ws = (2.*math.pi*Ns)/60.; # Roatation Speed in Radians per Seconds
# For Case (a) Machine running at, N = 1400 RPM
N_a = 1400.; # Machine running in RPM
s_a = (Ns-N_a)/Ns; # Slip
I_2_a = Vph/(R1+(R2/s_a)+(1j*(X1+X2))); # Rotor per phase Current referred to the stator side in Amphere
Pg_a = 3*(abs(I_2_a)**2*R2)/s_a; # 3-phase air gap power or Rotor intake Power in Watts
T_a = Pg_a/Ws; # Torque in Newton-Meter
# For Case (b) Machine running at, N = 1600 RPM
N_b = 1600; # Machine running in RPM
s_b = (Ns-N_b)/Ns; # Slip
I_2_b = Vph/(R1+(R2/s_b)+(1j*(X1+X2))); # Rotor per phase Current referred to the stator side in Amphere
Pg_b = 3*(abs(I_2_b)**2*R2)/s_b; # 3-phase air gap power or Rotor intake Power in Watts
T_b = Pg_b/Ws; # Torque in Newton-Meter
# For Case (b) Machine running at, N = -100 RPM
N_c = -100; # Machine running in RPM
s_c = (Ns-N_c)/Ns; # Slip
I_2_c = Vph/(R1+(R2/s_c)+(1j*(X1+X2))); # Rotor per phase Current referred to the stator side in Amphere
Pg_c = 3*(abs(I_2_c)**2*R2)/s_c; # 3-phase air gap power or Rotor intake Power in Watts
T_c = -Pg_c/Ws; # Torque in Newton-Meter (minus sign because its counter oppomath.sing torque)
# DISPLAY RESULTS
print ("EXAMPLE : 5.26 : SOLUTION :-");
print " For Case a) Machine running at, N = 1400 RPM "
print " a.1) Rotor per phase Current referred to the stator side, I2 = %.2f < %.2f A "%(abs(I_2_a),math.degrees(math.atan2(I_2_a.imag,real(I_2_a))))
print " a.2) Developed Torque, T = %.2f Nm "%(T_a)
print " For Case b) Machine running at, N = 1600 RPM "
print " a.1) Rotor per phase Current referred to the stator side, I2 = %.2f < %.2f A "%(abs(I_2_b),math.degrees(math.atan2(I_2_b.imag,real(I_2_b))))
print " ( angle -157.52 + 180 = 22.48 ) "
print " a.2) Developed Torque, T = %.2f Nm "%(T_b)
print " For Case c) Machine running at, N = -100 RPM "
print " c.1) Rotor per phase Current referred to the stator side, I2 = %.2f < %.2f A "%(abs(I_2_c),math.degrees(math.atan2(I_2_c.imag,real(I_2_c))))
print " c.2) Developed Torque, T = %.2f Nm "%(T_c)
import math
# GIVEN DATA
m = 3.; # Total Number of phase in Induction Motor
p = 2.; # Total number of Poles of Induction Motor
f = 50.; # Frequency in Hertz
V = 440.; # Operating Voltage of the Inductuon Motor
R1 = 0.25; # Circuit Parameter in Ohms
R2 = 0.25; # Circuit Parameter in Ohms
X1 = 0.75; # Circuit Parameter in Ohms
X2 = 0.75; # Circuit Parameter in Ohms
out_hp = 50.; # Output of the induction motor in HP
# CALCULATIONS
V1 = V/math.sqrt(3); # Phase Voltage in Volts
I = (out_hp*746.)/(V*math.sqrt(3)); # Rated Current in Amphere
sm = R2/(math.sqrt(R1**2+(X1+X2)**2)); # Slip at Maximum torque both its in Positive and negative sign
Ws = 2*math.pi*((120.*f/p)*(1./60.)); # Angular Roatation in Radians per Seconds
Tm = (3*V1**2)/((2*Ws)*(R1+math.sqrt((R1**2)+(X1+X2)**2))); # Maximum torque during motoring in Newton-Meter
Tg = -(3*V1**2)/((2*Ws)*(-R1+math.sqrt((R1**2)+(X1+X2)**2))); # Maximum torque during generating in Newton-Meter
# For Case (a) slip = 0.05
s_a = 0.05; # Slip
T_a = (2*Tm)/((s_a/sm)+(sm/s_a)); # Torque in Newton-Meter
# For Case (b) slip = -0.05
s_b = -0.05; # Slip
T_b = (2*Tg)/((s_b/sm)+(sm/s_b)); # Torque in Newton-Meter
# DISPLAY RESULTS
print ("EXAMPLE : 5.27 : SOLUTION :-");
print " Maximim Torque during Motoring Tm = %.f N-m "%(Tm)
print " Maximim Torque during Generating Tm = %.2f N-m "%(Tg)
print " For Case a slip = 0.05 "
print " a.1) Torque, T = %.2f Nm "%(T_a)
print " For Case b slip = -0.05 "
print " b.1) Torque, T = %.2f Nm "%(T_b)
import math
# GIVEN DATA
m = 3; # Total Number of phase in Induction Motor
p = 2; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
V = 440; # Operating Voltage of the Inductuon Motor in Volts
R0 = 0.5; # Circuit Parameter in Ohms
Ri = 0.05; # Circuit Parameter in Ohms
X0 = 0.2; # Circuit Parameter in Ohms
Xi = 0.9; # Circuit Parameter in Ohms
s = 0.07; # Slip
# CALCULATIONS
Ws = 2*math.pi*f; # Synchronous speed in Radins per second
v = V/math.sqrt(3); # Phase Voltage in Volts
Io = v/(R0+1j*X0); # Starting Current in the outer cage in Amphere
Ii = v/(Ri+1j*Xi); # Starting Current in the inner cage in Amphere
Tst = ((3*abs(Io)**2*R0)/Ws)+((3*abs(Ii)**2*Ri)/Ws); # Starting torque i.e at smath.degrees(math.atanstill, s=1
Ios = v/((R0/s)+(1j*X0)); # Current in the outer cage at slip = 0.07
Iis = v/((Ri/s)+(1j*Xi)); # Current in the outer cage at slip = 0.07
T = ((3*abs(Ios)**2*R0)/(s*Ws))+((3*abs(Iis)**2*Ri)/(s*Ws)); # Starting torque at s=0.07 in Newton-Meter
# DISPLAY RESULTS
print ("EXAMPLE : 5.28 : SOLUTION :-");
print " a) Starting torque Tst = %.2f Nm "%(Tst)
print " b) Running torque at slip = 0.07 T = %.2f Nm "%(T)
import math
# GIVEN DATA
p = 4; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
V = 440; # Operating Voltage of the Inductuon Motor in Volts
out = 25*1000; # Power rating of the Induction motor in Watts
R0 = 2.5; # Circuit Parameter in Ohms
Ri = 0.5; # Circuit Parameter in Ohms
X0 = 1.0; # Circuit Parameter in Ohms
Xi = 5.0; # Circuit Parameter in Ohms
Rc = 500; # Circuit Parameter in Ohms
R1 = 0.2; # Circuit Parameter in Ohms
Xm = 50; # Circuit Parameter in Ohms
X123 = 2.0; # Circuit Parameter in Ohms
s = 0.05; # Slip
# CALCULATIONS
Ws = (2*math.pi*120*f)/(p*60); # Synchronous speed in Radins per second
Zo = (R0/s)+(1j*X0); # Outer cage impedance at slip = 0.05 in Ohms
Zi = (Ri/s)+(1j*Xi); # Inner cage impedance at slip = 0.05 in Ohms
Z = (R1+1j*X123)+((Zo*Zi)/(Zo+Zi)); # Total impdance in Ohms
I = V/Z; # Current in the Cage winding in Amphere
Io = (I*((Zo*Zi)/(Zo+Zi)))/Zo; # Current in the outer cage in Amphere
Ii = (I*((Zo*Zi)/(Zo+Zi)))/Zi; # Current in the inner cage in Amphere
T = ((3*abs(Io)**2*R0)/(s*Ws))+((3*abs(Ii)**2*Ri)/(s*Ws)); # Starting torque in Newton-Meter
# DISPLAY RESULTS
print ("EXAMPLE : 5.29 : SOLUTION :-");
print " a) Torque at slip %.2f T = %.2f Nm "%(s,T)
import math
from numpy import real,imag
# GIVEN DATA
m = 1; # Total Number of phase in Induction Motor
p = 2; # Total number of Poles of Induction Motor
f = 50; # Frequency in Hertz
V = 220; # Operating Voltage of the Inductuon Motor in Volts
R1 = 10; # Circuit Parameter in Ohms
R2 = 11; # Circuit Parameter in Ohms
X1 = 12; # Circuit Parameter in Ohms
X2 = 12; # Circuit Parameter in Ohms
Xm = 125; # Circuit Parameter in Ohms
s = 0.03; # Slip
# CALCULATIONS
Zf = ((1j*Xm/2)*((R2/(2*s))+(1j*X2/2)))/((1j*Xm/2)+(R2/(2*s))+(1j*X2/2)); # Impedance offered by the forward field in Ohms
Zb = ((1j*Xm/2)*((R2/(2*(2-s)))+(1j*X2/2)))/((1j*Xm/2)+(R2/(2*(2-s)))+(1j*X2/2)); # Impedance offered by the backward field in Ohms
Z = (R1+1j*X1)+Zf+Zb; # Total Impedance in Ohms
I = V/Z; # Total input current in Amphere
pf = math.cos(math.radians(math.degrees(math.atan2(I.imag,I.real)))); # Power Factor (lagging)
Vf = I*Zf; # Forward Volatge at slip 0.03 in Volts
Vb = I*Zb; # Backward Volatge at slip 0.03 in Volts
If = Vf/(0.5*R2/s); # Forward Current in Amphere
Ib = Vb/(0.5*R2/(2-s)); # Forward Current in Amphere
Ws = 2*math.pi*f; # Synchronous Speed in radians per second
T = ((0.5*(If**2)*R2)/(s*Ws))-((0.5*(Ib**2)*R2)/((2-s)*Ws)); # Starting torque
# DISPLAY RESULTS
print ("EXAMPLE : 5.30 : SOLUTION :-");
print " a) Input Current, I = %.2f < %.f A "%(abs(I),math.degrees(math.atan2(I.imag,I.real)))
print " b) Power factor, pf = %.2f Lagging "%(pf)
print " c) Developed Torque, T = %.3f Nm "%(T.real)
import math
from numpy import real,imag
# GIVEN DATA
Wsc = 900; # Power at Blocked Rotor test in Watts
Vsc = 200; # Voltage at Blocked Rotor test in Volts
Isc = 5.0; # Current at Blocked Rotor test in Amphere
Wo = 60; # Power at No-load test in Watts
Vo = 220; # Voltage at No-load test in Volts
Io = 1.5; # Current at No-load test in Amphere
m = 1; # Total Number of phase in Induction Motor
p = 4; # Total number of Poles of Induction Motor
V = 220; # Operating voltage of the Induction motor in Volts
f = 50; # Frequency in Hertz
s = 0.07; # Slip
R1 = 12; # resistance of the main primary winding in Ohms
# CALCULATIONS
Zsc = Vsc/Isc; # Impedance in Blocked Rotor test in Ohms
Rsc = Wsc/(Isc**2); # resistance in Blocked Rotor test in Ohms
Xsc = math.sqrt((Zsc**2)-(Rsc**2)); # reactance in Blocked Rotor test in Ohms
Xl1 = Xsc/2; # Leakage reactance of stator and rotor to be equal in Ohms
Xl2 = Xsc/2; # Leakage reactance of stator and rotor to be equal in Ohms
R2 = Rsc-R1; # Equivalent resistance of rotor referred to stator in Ohms
Z0 = Vo/Io; # Impedance in Blocked Rotor test in Ohms
R0 = Wo/(Io**2); # resistance in Blocked Rotor test in Ohms
X0 = math.sqrt((Z0**2)-(R0**2)); # reactance in Blocked Rotor test in Ohms
Wloss = Wo - ((Io**2)*(R1+R2)); # Loss in Watts
Xm_half = X0-Xl1-Xl2/2;
R2f = (R2/s)+((1j*Xl2)/2); # Forward resiamath.tance in Ohms
Zf = ((1j*Xm_half)*R2f)/(1j*Xm_half+R2f); # Total Forward impedance in Ohms
R2b = (R2/(2-s))+((1j*Xl2)/2); # Backward resiamath.tance in Ohms
Zb = ((1j*Xm_half)*R2b)/(1j*Xm_half+R2b); # Total Backward impedance in Ohms
Z = Zf+Zb+(R1+1j*Xl1); # Total impedance in Ohms
I = V/Z; # Motor Current in Amphere
pf = math.cos(math.radians(math.degrees(math.atan2(I.imag,I.real)))); # Power Factor (lagging)
# DISPLAY RESULTS
print ("EXAMPLE : 5.31 : SOLUTION :-");
print " Circuit Parameters are a) Leakage reactance of stator and rotor to be equal, Xl1 = Xl2 = %.2f Ohms "%(Xl1)
print " b) Equivalent resistance of rotor referred to stator, R2 = %.f Ohms "%(R2)
print " c) Total Forward impedance, Zf = %.1f < %.2f Ohms "%(abs(Zf),math.degrees(math.atan2(Zf.imag,Zf.real)))
print " c) Total Backward impedance, Zb = %.2f < %.2f Ohms "%(abs(Zb),math.degrees(math.atan2(Zb.imag,Zb.real)))
print " d) Total impedance, Z = %.2f < %.2f Ohms "%(abs(Z),math.degrees(math.atan2(Z.imag,Z.real)))
print " e) Input Current, I = %.2f < %.2f A "%(abs(I),math.degrees(math.atan2(I.imag,I.real)))
print " f) Power factor, pf = %.2f Lagging "%(pf)
import math
from numpy import imag,real
# GIVEN DATA
Wsc = 600; # Power at Blocked Rotor test in Watts
Vsc = 125; # Voltage at Blocked Rotor test in Volts
Isc = 15.0; # Current at Blocked Rotor test in Amphere
Wo = 360; # Power at No-load test in Watts
Vo = 220; # Voltage at No-load test in Volts
Io = 6.5; # Current at No-load test in Amphere
m = 1; # Total Number of phase in Induction Motor
p = 4; # Total number of Poles of Induction Motor
V = 220; # Operating voltage of the Induction motor in Volts
f = 50; # Frequency in Hertz
s = 0.05; # Slip
R1 = 1.2; # resistance of the main primary winding in Ohms
# CALCULATIONS
Zlr = Vsc/Isc; # Impedance in Blocked Rotor test in Ohms
Rlr = Wsc/(Isc**2); # resistance in Blocked Rotor test in Ohms
Xlr = math.sqrt((Zlr**2)-(Rlr**2)); # reactance in Blocked Rotor test in Ohms
Xl1 = Xlr/2; # Leakage reactance of stator and rotor to be equal in Ohms
Xl2 = Xlr/2; # Leakage reactance of stator and rotor to be equal in Ohms
R2 = (Rlr-R1); # Equivalent resistance of rotor referred to stator in Ohms
R2_half = R2/2; # Equivalent resistance of rotor referred to stator in Ohms
Z0 = Vo/Io; # Impedance in Blocked Rotor test in Ohms
R0 = Wo/(Io**2); # resistance in Blocked Rotor test in Ohms
X0 = math.sqrt((Z0**2)-(R0**2)); # reactance in Blocked Rotor test in Ohms
Wloss = Wo - ((Io**2)*(R1+R2)); # Loss in Watts
Xm_half = X0-Xl1-Xl2/2;
R2f = (R2/(2*s))+((1j*Xl2)/2); # Forward resiamath.tance in Ohms
Zf = ((1j*Xm_half)*R2f)/(1j*Xm_half+R2f); # Total Forward impedance in Ohms
R2b = (R2/(2*(2-s)))+((1j*Xl2)/2); # Backward resiamath.tance in Ohms
Zb = ((1j*Xm_half)*R2b)/(1j*Xm_half+R2b); # Total Backward impedance in Ohms
Z = Zf+Zb+(R1+1j*Xl1); # Total impedance in Ohms
I = V/Z; # Motor Current in Amphere
pf = math.cos(math.radians(math.degrees(math.atan2(I.imag,I.real)))); # Power Factor (lagging)
Vf = I*Zf; # Voltage across forward impedance in Volts
If = Vf/R2f; # Forward current producing torque in Amphere
Tf = ((abs(If)**2)*R2)/(2*s); # Forward torque in synchronous Watts
Vb = I*Zb; # Voltage across Backward impedance in Volts
Ib = Vb/R2b; # Backward current producing torque in Amphere
Tb = ((abs(Ib)**2)*R2)/(2*(2-s)); # Backward torque in synchronous Watts
T = Tf-Tb; # Net torque in Synchronous Watts
# DISPLAY RESULTS
print ("EXAMPLE : 5.32 : SOLUTION :-");
print " Circuit Parameters are a) Leakage reactance of stator and rotor to be equal, Xl1 = Xl2 = %.2f Ohms "%(Xl1)
print " b) Equivalent resistance of rotor referred to stator,R2 = %.2f Ohms "%(R2)
print " c) Total Forward impedance, Zf = %.1f < %.2f Ohms "%(abs(Zf),math.degrees(math.atan2(Zf.imag,Zf.real)))
print " c) Total Backward impedance, Zb = %.2f < %.2f Ohms "%(abs(Zb),math.degrees(math.atan2(Zb.imag,Zb.real)))
print " d) Total impedance, Z = %.2f < %.2f Ohms "%(abs(Z),math.degrees(math.atan2(Z.imag,Z.real)))
print " e) Input Current, I = %.2f < %.f A "%(abs(I),math.degrees(math.atan2(I.imag,I.real)))
print " f) Power factor, pf = %.4f Lagging "%(pf)
print " g) Forward torque, Tf = %.2f Synchronous Watts "%(Tf)
print " h) Backward torque, Tb = %.2f Synchronous Watts "%(Tb)
print " i) Net torque, T = %.2f Synchronous Watts "%(T)