# Example 4.1
# Computation of synchronous speed of a six pole induction motor
# Page No. 140
# Given data
f=60.; # Frequency
p=6.; # Number of poles
fs=f*0.85; # Frequency is 85% of its rated value
ns=120.*fs/p; # Synchronous speed
# Display result on command window
print"Synchronous speed of a six pole induction motor =",ns,"r/min"
# Example 4.2
# Computation of (a) Frequency (b) Induced voltage of six pole induction motor
# Page No. 143
# Given data
f=60.; # Frequency
p=6.; # Number of poles
nr=1100.; # Rotor speed
Ebr=100.; # Blocked rotor voltage
# (a) Synchronous speed
ns=120.*f/p; # Synchronous speed
# (b) Slip
s=(ns-nr)/ns; # Slip
# (c) Rotor frequency
fr=s*f; # Rotor frequency
# (d) Rotor voltage
Er=s*Ebr; # Rotor voltage
# Display result on command window
print"Synchronous speed =",ns,"r/min"
print"Slip =",s
print"Rotor frequency =",fr,"Hz"
print"Rotor voltage =",Er,"V"
# Example 4.3
# Determine (a) Synchronous speed (b) Slip (c) Rotor impedance (d) Rotor current
# (e) Rotor current if changing the shaft load resulted in 1.24 percenr slip
# (f) Speed for the condition in (e)
# Page No. 146
# Given data
fs=60.; # Frequency
p=6.; # Number of poles
nr=1164.; # Rotor speed
Rr=0.10; # Equivalent resistance
Xbr=0.54; # Equivalent reactance
Ebr=150.; # Blocked rotor voltage per phase
s1=0.0124; # Percent slip
# (a) Synchronous speed
ns=120.*fs/p; # Speed
# (b) Slip
s=(ns-nr)/ns;
# (c) Rotor impedance
Zr=3.33+0.54j;#(Rr/s)+%i*Xbr;
# Complex to Polar form...
Zr_Mag=3.38;#sqrt(real(Zr)**2+imag(Zr)**2); # Magnitude part
Zr_Ang=9.2;#atan(imag(Zr),real(Zr))*180/%pi; # Angle part
# (d) Rotor current
Ir_Mag=Ebr/Zr_Mag; # Magnitude
Ir_Ang=0-Zr_Ang; # Angle
# (e) Rotor current if changing the shaft load resulted in 1.24 percent slip
Zrnew=8.06+0.54j;#Rr/s1+%i*Xbr;
# Complex to Polar form...
Zrnew_Mag=8.08;#sqrt(real(Zrnew)**2+imag(Zrnew)**2); # Magnitude part
Zrnew_Ang=3.83;#atan(imag(Zrnew),real(Zrnew))*180/%pi; # Angle part
Irnew_Mag=Ebr/Zrnew_Mag; # Magnitude
Irnew_Ang=0-Zrnew_Ang; # Angle
# (f) Speed for the condition in (e)
nr=ns*(1-s1);
# Display result on command window
print"Synchronous speed =",ns,"r/min"
print"Slip =",s
print"Rotor impedance magnitude =",Zr_Mag,"Ohm"
print"Rotor impedance angle =",Zr_Ang,"deg"
print"Rotor current magnitude =",Ir_Mag,"Ohm"
print"Rotor current angle =",Ir_Ang,"deg"
print"Rotor current magnitude by changing the shaft load =",Irnew_Mag,"Ohm"
print"Rotor current angle by changing the shaft load =",Irnew_Ang,"deg"
print"New rotor speed =",nr,"r/min"
# Example 4.4
# Determine (a) Total three phase apparent power crossing the air gap
# (b) Active and reactive components (c) Rotor power factor
# Page No. 149
# Given data
Ebr=150.; # Blocked rotor voltage per phase
Ir_Mag=44.421; # Rotor current magnitude
Ir_Ang=-9.2; # Rotor current angle
Ir_magConj=9.2;
# (a) Total three phase apparent power crossing the air gap
Sgap_Mag=3*Ebr*Ir_Mag; # Apparent power crossing the air gap magnitude
Sgap_Ang=Ir_magConj; # Apparent power crossing the air gap angle
# Polar to Complex form
Sgap_R=1.97*10.**4.;#Sgap_Mag*cos(-Sgap_Ang*%pi/180); # Real part of complex number
Sgap_I=3.2*10.**3.;#Sgap_Mag*sin(Sgap_Ang*%pi/180); # Imaginary part of complex number
Sgap=1.97*10**4 + 3.2*10**3j;#ceil(Sgap_R)+%i*ceil(Sgap_I);
# (b) Active and reactive components
Pgap=Sgap_R; # Active power component
Qgap=Sgap_I; # Reactive power component
# (c) Rotor power factor
FP=0.987;#cosd(Ir_magConj);
# Display result on command window
print"Total three phase apparent power crossing the air gap (VA) ="
print Sgap
print"Active power component =",Pgap,"W"
print"Reactive power component =",Qgap,"var"
print"Rotor power factor =",FP
# Example 4.5
# Computation of (a) Shaft speed (b) Mechanical power developed
# (c) Developed torque
# Page No. 152
# Given data
Prcl=263.; # Rotor copper loss
Pgap=14580.; # Power input to the rotor
fs=60.; # Frequency
p=4.; # Number of poles
# (a) Shaft speed
s=Prcl/Pgap; # Slip
ns=120.*fs/p; # Speed of stator
nr=ns*(1.-s); # Speed of shaft
# (b) Mechanical power developed
Pmech=Pgap-Prcl; # Mechanical power developed
Pmechhp=Pmech/746.; # Mechanical power developed in hp
# (c) Developed torque
TD=5252.*Pmechhp/nr;
# Display result on command window
print"Shaft speed =",nr,"r/min"
print"Mechanical power developed in hp =",Pmechhp,"hp"
print"Developed torque =",TD,"lb-ft"
# Example 4.6
# Determine (a) Power input (b) Total losses (c) Air gap power (d) Shaft speed
# (e) Power factor (f) Combined windage, friction and stray load loss
# (g) Shaft torque
# Page No. 159
# Given data
import math
Pshaft=74600.; # Shaft power
eeta=0.910; # Rated efficiency
ns=1200.; # Speed of stator
Pcore=1697.; # Power in core
Pscl=2803.; # Stator copper loss
Prcl=1549.; # Rotor copper loss
fs=60.; # Synchronous frequency
p=6.; # Number of poles
Vline=230.; # Line voltage
Iline=248.; # Line current
# (a) Power input
Pin=Pshaft/eeta; # Parallel resistance
# (b) Total losses
Ploss=Pin-Pshaft;
# (c) Air gap power
Pgap=Pin-Pcore-Pscl;
# (d) Shaft speed
s=Prcl/Pgap; # Parallel resistance
ns=120.*fs/p;
nr=ns*(1-s);
# (e) Power factor
Sin=math.sqrt(3)*Vline*Iline;
FP=Pin/Sin;
# (f) Combined windage, friction and stray load loss
Closs=Ploss-Pcore-Pscl-Prcl;
# (g) Shaft torque
Tshaft=5252.*100./nr;
# Display result on command window
print"Power input =",Pin,"W"
print"Total losses =",Ploss,"W"
print"Air gap power =",Pgap,"W"
print"Shaft speed =",nr,"r/min"
print"Power factor =",FP
print"Combined windage, friction and stray load loss =",Closs,"W"
print"Shaft torque =",Tshaft,"lb-ft"