Chapter 5 Induction (Asychronous) Machines

Example 5.1,Pg no.219

In [1]:
from math import sqrt
#given
F=60                                                                  #frequency in Hz
P=4                                                                   #power
S=0.05                                                                #slip 
Ns=1800                                                               #in rpm
V=460                                                                 #voltage
Tr=0.5
Ns=(120*F)/(P)                                                        #synchronous speed
N=(1-S)*Ns                                                            #motor speed
F2=S*F                                                                #frequency of the rotor circuit
Sliprpm=S*Ns                                                          #slip in rpm   
A=S*Tr*V/sqrt(3)                                                      #rotor induced voltage
A=round(A,2)
print 'Synchronous speed=',Ns,'rpm'
print 'motor speed=',N,'rpm'
print 'Speed of the rotatind air-gap field=',Ns,'rpm'
print 'frequency of the rotor circuit=',F2,'Hz'
print 'Slip rpm=',Sliprpm,'rpm'
print 'Rotor induced voltage=',A,'V/phase'

Synchronous speed= 1800 rpm
motor speed= 1710.0 rpm
Speed of the rotatind air-gap field= 1800 rpm
frequency of the rotor circuit= 3.0 Hz
Slip rpm= 90.0 rpm
Rotor induced voltage= 6.64 V/phase

Example 5.2,Pg.no 226

In [10]:
from math import sqrt,pi
#given
Hp=15
Loss=750                                                    #windage and friction loss of the motor
Fp=11190                                                    #full-load shaft power
F=60
P=4
N=1728
#calculations
Mecp=Fp+Loss                                                #mechanical power
Ns=120*F/P                                                  #synchronous speed
S=0.04                                                      #slip=(Ns-N)/Ns
Pag=Mecp/(1-S)
P2=S*Pag
print 'Mechanical power developed is',Mecp,'W'
print 'Air-gap power=',Pag,'W'
print 'Rotor power loss is',P2,'W'

Mechanical power developed is 11940 W
Air-gap power= 12437.5 W
Rotor power loss is 497.5 W

Example 5.3,Pg.no 229

In [11]:
from math import sqrt,pi
#given
#for no-load test
Nof=60                                                       #supply frequency
NoV=2200                                                     #line voltage
NoI=4.5                                                      #line current
NoP=1600                                                     #input power
#for blocked-rotor test
BF=15                                                        #frequency
BV=270                                                       #line-voltage
BI=25                                                        #line-current
BP=9000                                                      #input power
R1=2.8                                                       #avg.dc resistance
V=2200
F=60
Rbl=4.8
Pnl=1600
#calculations
Prot=Pnl -(3*NoI**2*R1)
Vt=V/sqrt(3)
Znl=(Vt/NoI)                                                #no-load impedance
Rnl=(Pnl)/(3*NoI**2)                                        #no-load reactance
Xnl=(Znl**2-Rnl**2)**(1/2)
Rbl=BP/(3*(BI**2))                                          #blocked rotor resistance
Zbl=(BV)/(sqrt(3)*BI)                                       #blocked rotor reactance
Xbl=(Zbl**2-Rbl**2)**(1/2)
Xbl=Xbl*(F/BF)
X1=Xbl/2
Xm=(Xnl-X1)                                                 #magnetizing reactance
Xm=273.04
R=Rbl-R1
R2=((X1+Xm)/(Xm))**2*2
Vth=(Xm)/(X1+Xm)                                            #thevenin's voltage
Rth=(Vth**2)*R1                                             #thevenin's resistance
Znl=round(Znl,2)
Rnl=round(Rnl,2)
Rbl=round(Rbl,2)
Zbl=round(Zbl,2)
Vth=round(Vth,2)
Rth=round(Rth,2)
print 'No-load rotational loss=',Prot,'W'
print 'parameters: no-load impedance=',Znl,'ohms','\nNo-load reactance=',Rnl,'ohms'
print 'Blocked rotor resistance=',Rbl,'ohms','\nBlocked rotor reactance=',Zbl,'ohms'
print 'Thevenin voltage=',Vth,'V1'
print 'Thevenin resistance=',Rth,'ohms'

No-load rotational loss= 1429.9 W
parameters: no-load impedance= 282.26 ohms 
No-load reactance= 26.34 ohms
Blocked rotor resistance= 4.0 ohms 
Blocked rotor reactance= 6.24 ohms
Thevenin voltage= 0.99 V1
Thevenin resistance= 2.76 ohms

Example 5.5,Pg.no 244

In [12]:
import math
#given
F=60                         #frequency in Hz
P=6
RPM=1140
RPM1=1000
R=0.2                         #rotor-winding resistance
Ns=(120*F/P)                  #synchronous speed
S1=0.05                        #formula for slip =(Ns-RPM)/(Ns)
S2=0.167
Rext=((R/S1)*S2)-(R)
print 'Resistance=',Rext,'ohms/phase'

Resistance= 0.468 ohms/phase

Example 5.6,Pg.no 244

In [13]:
import math
#given
F=60                         #frequency in hz
P=4
N=1710
RI=6
Ns=(120*F)/P                 #synchronous speed
Sfl=0.05                    #full-load slip=(Ns-N)/Ns
Tst=RI**2*Sfl
Stmax=0.31
NMaxT=(1-Stmax)*Ns
Tmax=(1+Stmax**2)/(2*Stmax)*Tst*100
Tmax=round(Tmax,0)
print 'Speed at maximum torque=',NMaxT,'rpm'
print 'Maximum torque developed',Tmax,'%'

Speed at maximum torque= 1242.0 rpm
Maximum torque developed 318.0 %

Example 5.7,Pg.no 246

In [14]:
import math
#given
F1=60.0                      #frequency
F2=15.0
F3=120.0
F=60.0
P=6.0
V=240.0                   #open-circuit rotor voltage
A=2.0
#calculations
S=F2/F1                   #slip
Ns=(120*F)/P              #synchronous speed
N=(1+S)*Ns                #speed of the system for 15Hz
N1=(1-S)*Ns
S1=F3/F1
n=(1+S1)*Ns               #speed of the system for 120Hz
n1=(1-S1)*Ns
Pac=1/S
Pac1=-1/S
Pdcl1=-(1-(S))/S
Pdcl=-(1+(S))/-S
Pac1=1/S1
Pdc=-(1-S1)/S1
Pdc1=-(1+S1)/-S1
print 'speed in rpm to give 15Hz is',N,'and',N1,'rpm'
print 'speed in rpm to give 120Hz is',n,'and',n1,'rpm'
print 'rotor voltage with 120 Hz=',Pac1,'P2,',Pdc1,'P2'
print 'rotor voltage with 15 Hz=',Pdcl1,'P1,',Pdcl,'P1'

speed in rpm to give 15Hz is 1500.0 and 900.0 rpm
speed in rpm to give 120Hz is 3600.0 and -1200.0 rpm
rotor voltage with 120 Hz= 0.5 P2, 1.5 P2
rotor voltage with 15 Hz= -3.0 P1, 5.0 P1

Example 5.11,Pg.no 273

In [15]:
from math import sqrt,pi
#given
F=60.0                 #frequency
P=4.0                  #no.of poles
N=1740.0               #in rpm
R1=R2=0.5              #resistance
X1=X2=1.0              #impedance
Xm=35.0
I=1.1                  #current
Peak=10.0
H=5.0
H1=7.0
Phase=3.0               #phase
Ns=120*(F/P)            #synchronous speed
S1=0.03333333333        #slip
A=R2/S1
Z1=complex(12.08,6.0)               #1st harmonic impedance
Rth=12.08
Pg1=Phase*((I*Peak)/sqrt(2))**2*Rth
Wsyn=(Ns/60)*2*pi
T1=Pg1/Wsyn
Ns1=-(120*H*F)/P
S2=(Ns1-N)/Ns1
B=R2/S2
Xm1=H*Xm
hX2=H*X2
Z2=complex(0.4,4.86)               #2nd harmonic impedance
Rth2=0.39
Pg2=Phase*((0.22*Peak)/sqrt(2))**2*Rth2
Wsyn2=(Ns1/60)*2*pi
T2=Pg2/Wsyn2
Ns3=(120*H1*F)/P
S3=(Ns3-N)/Ns3
C=R2/S3
Xm3=H1*Xm
hX3=H1*X2
Z3=complex(0.549,6.807)
Rth3=0.54
Pg3=Phase*((0.16*Peak)/sqrt(2))**2*Rth3
Wsyn3=(Ns3/60)*2*pi
T3=Pg3/Wsyn3
T2=round(T2,3)
T3=round(T3,4)
print 'Parasitic torque for the fifth harmonic=',T2,'N-m'
print 'parasitic torque for the seventh harmonic=',T3,'N-m'

Parasitic torque for the fifth harmonic= -0.003 N-m
parasitic torque for the seventh harmonic= 0.0016 N-m

Example 5.12,Pg no.281

In [16]:
from math import sqrt,pi
#given
S=2                
Pole=50
F=50
Slip=0.25
Pole=Pole*10**-2
#calculations
Vs=S*Pole*F          #synchronous speed 
Vs=Vs*3600/1000
V=(1-Slip)*(Vs)
print 'synchronous speed=',Vs,'km/hr'
print 'vehicle speed=',V,'km/hr'

synchronous speed= 180.0 km/hr
vehicle speed= 135.0 km/hr