Chapter 34:Induction Motors

Example Number 34.1, Page Number:1255

In [3]:
#variable declaration
n=290.0#rpm
f=50.0#Hz
Ns=300.0#rpm(considered)
#calculation
P=120*f/Ns
s=(Ns-n)/Ns

#result
print "no. of poles=",P
print "slip=",s*100,"%"

no. of poles= 20.0
slip= 3.33333333333 %

Example Number 34.2, Page Number:1255

In [5]:
#variable declaration
n=3
slot=3
f=50#Hz

#calculation
P=2*n
slots_total=slot*P*n
Ns=120*f/P

#result
print "No. of stator poles=",P
print "Total number of slots=",slots_total
print "Speed=",Ns,"rpm"

 No. of stator poles= 6
Total number of slots= 54
Speed= 1000 rpm

Example Number 34.3, Page Number:1255

In [7]:
#variable declaration
p=4
n=3
f=50#Hz
slip1=0.04
slip2=0.03

#calculation
Ns=120*f/p
N=Ns*(1-slip1)
f1=slip2*f*60
#at standstill s=1
f2=1*f

#calculation
print "speed at which magnetic field of the stator is rotating=",Ns,"rpm"
print "speed of the rotor when the slip is 0.04=",N
print "frequency of rotor current=",f1,"rpm"
print "frequency of the rotor current at standstill=",f2,"Hz"

speed at which magnetic field of the stator is rotating= 1500 rpm
speed of the rotor when the slip is 0.04= 1440.0
frequency of rotor current= 90.0 rpm
frequency of the rotor current at standstill= 50 Hz

Example Number 34.4, Page Number:1255

In [12]:
#variable declaration
n=3.0
p=4.0
f=50.0#Hz
slip=0.04
n=600.0#rpm

#calculations
Ns=120*f/p
N=Ns*(1-slip)
s=(Ns-n)/Ns
f1=s*f

#result
print "the synchronous speed=",Ns,"rpm"
print "the rotor speed=",N,"rpm"
print "the rotor frequency when n=600 rpm=",f1,"Hz"

the synchronous speed= 1500.0 rpm
the rotor speed= 1440.0 rpm
the rotor frequency when n=600 rpm= 30.0 Hz

Example Number 34.5, Page Number:1256

In [20]:
#variable declaration
p=12
n=3
N=500#rpm
p2=8
slip=0.03

#calculation
f=p*N/120
Ns=120*f/p2
N=Ns-slip*Ns

#result
print "full load speed of the motor=",N,"rpm"

full load speed of the motor= 727.5 rpm

Example Number 34.6, Page Number:1258

In [25]:
#variable declaration
e=80#V
r=1#ohm
x=4#ohm
rheo=3#ohm

#calculation
E=e/(3)**0.5
z=(r**2+x**2)**0.5
i=E/z
pf=r/z
R=rheo+r
z2=(R**2+x**2)**0.5
i2=E/z2

pf2=R/z2

#result
print "slip rings are short circuited:"
print "current/phase",i,"A"
print "pf=",pf
print "slip rings are onnected to a star-connected rheostat of 3  ohm",
print "current/phase",i2,"A"
print "pf=",pf2

slip rings are short circuited:
current/phase 11.2022406722 A
pf= 0.242535625036
slip rings are onnected to a star-connected rheostat of 3  ohm current/phase 8.16496580928 A
pf= 0.707106781187

Example Number 34.7, Page Number:1258

In [26]:
#variable declaration
n=3
v=400#V
ratio=6.5
r=0.05#ohm
x=0.25#ohm

#calculations
k=1/ratio
e2=v*k/(3**0.5)
R=x-r
r2=x
z=(x**2+r2**2)**0.5
i2=e2/z

#result
print "external resistance=",R,"ohm"
print "starting current=",i2,"A"

external resistance= 0.2 ohm
starting current= 100.491886883 A

Example Number 34.8, Page Number:1259

In [41]:
#variable declaration
v=1100#V
f=50#Hz
ratio=3.8
r=0.012#ohm
x=0.25#ohm
s=0.04
#calculation
e=v/ratio
z=(r**2+x**2)**0.5
i=e/z
pf=r/z
xr=s*x
zr=(r**2+xr**2)**0.5
er=s*e
i2=er/zr
pf2=r/zr
i2=100*ratio
z2=e/i2
r2=(z2**2-x**2)**0.5
R=r2-r

#result
print "current with slip rings shorted=",i,"A"
print "pf with slip rings shorted=",pf
print "current with slip=4% and slip rings shorted=",i2
print "pf withslip=4% and slip rings shorted=",pf2
print "external resistance=",R,"ohm"

current with slip rings shorted= 1156.56314266 A
pf with slip rings shorted= 0.0479447993684
current with slip=4% and slip rings shorted= 380.0
pf withslip=4% and slip rings shorted= 0.768221279597
external resistance= 0.70758173952 ohm

Example Number 34.9, Page Number:1259

In [49]:
#variable declaration
load=15#kW
v=3000#V
f=50#Hz
p=6
ratio=3.6
r=0.13#ohm
l=3.61*0.001#H

#calculation
v=v/3**0.5
x2=2*3.14*l*f
k=1/ratio
r2_=0.1/k**2
x2_=ratio**2*x2
is1=v/((r**2+x2_**2)**0.5)
ns=120*f/p
ts=(3*3/(2*3.14*f))*((v**2)*r2_)/(r2_**2+x2_**2)

#result
print "starting current=",is1,"A"
print "ts=",ts,"N-m"

starting current= 117.896733436 A
ts= 512.375725888 N-m

Example Number 34.10, Page Number:1261

In [51]:
#variable declaration
zs=complex(0.4,4)
zr=complex(6,2)
v=80#V
s=0.03

#calculation
e2=v/3**0.5
i=e2/abs(zr+zs)
er=s*e2
xr=s*zs.imag
ir=er/abs(complex(zs.real,xr))

#result
print "rotor current at standstill=",i,"A"
print "rotor current when slip-rings are short-circuited=",ir,"A"

rotor current at standstill= 5.26498126493 A
rotor current when slip-rings are short-circuited= 3.31800758166 A

Example Number 34.11, Page Number:1261

In [54]:
#variable declaration
n=3
e=120#V
r2=0.3#ohm
x2=1.5#ohm
s=0.04

#calculations
e2=e/3**0.5
er=s*e2
xr=s*x2
zr=(r2**2+xr**2)**0.5
i=er/zr
s=r2/x2
xr=s*x2
zr=(xr**2+r2**2)**0.5
er=s*e2
i2=er/zr

#result
print "rotor when running short-circuited=",i,"A"
print "slip=",s
print "current when torque is maximum=",i2,"A"

rotor when running short-circuited= 9.05821627316 A
slip= 0.2
current when torque is maximum= 32.6598632371 A

Example Number 34.12, Page Number:1264

In [3]:
#variable declaration
p=8
f=50.0#Hz
s=0.04
tb=150.0#kg-m
n=660.0#rpm
r=0.5#ohm

#calculation
ns=120*f/p
sb=(ns-n)/ns
x2=r/sb
t=tb*(2/((sb/s)+s/sb))

#result
print "torque=",t,"kg-m"

torque= 90.0 kg-m

Example Number 34.13(a), Page Number:1266

In [4]:
#variablde declaration
n=3
vd=0.90

#calculation
ratio_s=(1/vd)**2
ratio_i=ratio_s*vd
cu_loss_increase=ratio_i**2

#result
print "increase in motor copper losses=",cu_loss_increase

increase in motor copper losses= 1.23456790123

Example Number 34.13(b), Page Number:1264

In [10]:
#variable declaration
v=230.0#V
p=6
f=50.0#Hz
p1=15.0#kW
n=980.0#rpm
efficiency=0.93
vd=0.10
fd=0.05

#calculation
v2=(1-vd)*v
f2=(1-fd)*f
n1=120*f/p
n2=120*f2/p
s1=(n1-n)/n1
ratio_f=s1*(v*(1-vd)/v)**2*f2/f
n2=n2*(1-ratio_f)
p2=p1*n2/n1
#result
print "the new operating speed=",n2,"rpm"
print "the new output power=",p2,"kW"

the new operating speed= 935.3795 rpm
the new output power= 14.0306925 kW

Example Number 34.14(a), Page Number:1267

In [11]:
#variable declaration
p=3
v1=400#V
v2=200#V
r=0.06#ohm
x=0.3#ohm
a=1
#calculations
r=x-r

#result
print "additional resistance=",r,"ohm"

additional resistance= 0.24 ohm

Example Number 34.14(b), Page Number:1267

In [13]:
#variable declaration
n=3
f=50#Hz
p=8
s=0.02
r=0.001#ohm
x=0.005#ohm

#calculation
ns=120*f/p
a=r/x
n2=(1-s)*ns
ratio=2*s**2*a/(a**2+s**2)

#result
print "ratio of the maximum to full-load torque=",ratio*1000,"10^-3"

ratio of the maximum to full-load torque= 3.9603960396 10^-3

Example Number 34.14(c), Page Number:1267

In [15]:
#variable declaration
p=12
v=600#V
f=50#Hz
r=0.03#ohm
x=0.5#ohm
n=495#rpm
s=0.01
#calculation
Ns=120*f/p
a=r/x
n=Ns*(1-a)
ratio=2*a*s/(a**2+s**2)

#result
print "speed of max torque=",n,"rpm"
print "ratio of torques=",ratio

speed of max torque= 470.0 rpm
ratio of torques= 0.324324324324

Example Number 34.15, Page Number:1267

In [19]:
#variable declaration
load=746.0#kW
f=50.0#Hz
p=16
zr=complex(0.02,0.15)
n=360.0#rpm

#calculation
ns=120*f/p
s=(ns-n)/ns
a=zr.real/zr.imag
ratio=2*a*s/(a**2+s**2)
N=ns*(1-a)
R=zr.imag-zr.real

#result
print "ratio of torques=",ratio
print "speed at maximum torque=",N,"rpm"
print "rotor resistance=",R,"ohm"

ratio of torques= 0.550458715596
speed at maximum torque= 325.0 rpm
rotor resistance= 0.13 ohm

Example Number 34.16, Page Number:1268

In [24]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
a=Symbol('a')
p=4
f=50.0#Hz
r=0.025#ohm
x=0.12#ohm
ratio=3.0/4.0

#calculations
s=r/x
ns=120*f/p
n=ns*(1-s)
a=solve(ratio-(2*a/(1+a**2)),a)
r=a[0]*x-r

#result
print "speed at maximum torque=",n,"rpm"
print "additional resistance=",r,"ohm"

speed at maximum torque= 1187.5 rpm
additional resistance= 0.0291699475574164 ohm

Example Number 34.17, Page Number:1268

In [26]:
#variable declaration
f=50#Hz
s=0.04
r=0.01#ohm
x=0.1#ohm
p=8
#calculation
a=r/x
t_ratio=2*a*s/(a**2+s**2)
ns=120*f/p
n=(1-a)*ns

#result
print "ratio of torques=",1/t_ratio
print "speed=",n,"rpm"

ratio of torques= 1.45
speed= 675.0 rpm

Example Number 34.18, Page Number:1268

In [46]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
a=Symbol('a')
a2=Symbol('a2')
p=3
t_ratio=2.5
t_ratio2=1.5
s=0.03

#calculation
t_ratio3=t_ratio2/t_ratio
a=solve(t_ratio3-(2*a/(1+a**2)),a)
a2=solve(a2**2-0.15*a2+0.0009,a2)
r_red=(a[0]-a2[1])/a[0]
#result
print "percentage reduction in rotor circuit resistance=",r_red*100,"%"

percentage reduction in rotor circuit resistance= 56.8784093726987 %

Example Number 34.19, Page Number:1269

In [51]:
#variable declaration
p=8
f=50#Hz
r=0.08#ohm
n=650.0#rpm

#calculation
ns=120*f/p
sb=(ns-n)/ns
x2=r/sb
a=1
r=a*x2-r
#result
print "extra resistance=",r,"ohm"

extra resistance= 0.52 ohm

Example Number 34.20, Page Number:1269

In [56]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
R=Symbol('R')
p=4
f=50.0#Hz
t=162.8#N-m
n=1365.0#rpm
r=0.2#ohm

#calculations
ns=120*f/p
sb=(ns-n)/ns
x2=r/sb
R=solve(1.0/(4*x2)-((r+R)/((r+R)**2+x2**2)),R)

#result
print "resistance to be added=",round(R[0],1),"ohm"

resistance to be added= 0.4 ohm

Example Number 34.21, Page Number:1270

In [15]:
#variable declaration
p=4.0
f=50.0#Hz
load=7.46#kW
t_ratios=1.60
t_ratiom=2.0

#calcualtion
t_ratio=t_ratios/t_ratiom
#0.8a2-2*a+0.8 a=0.04
#0.5=2*a*sf/a2+sf2 sf=0.01
a=0.04
sf=0.01
ns=120*f/p
n=ns-sf*ns
N=ns-a*ns

#result
print "full-load speed=",n,"rpm"
print "speed at maximum torque=",N,"rpm"

full-load speed= 1485.0 rpm
speed at maximum torque= 1440.0 rpm

Example Number 34.22, Page Number:1270

In [16]:
#variable declaration
p=6
v=240#V
f=50#Hz
r=0.12#ohm
x=0.85#ohm
ratio=1.8
s=0.04

#calculations
k=1/ratio
e2=k*(v/3**0.5)
ns=120*f/p
tf=(3/(2*3.14*f/3))*(s*e2*e2*r/(r**2+(s*x)**2))
s=r/x
tmax=(3/(2*3.14*f/3))*(s*e2*e2*r/(r**2+(s*x)**2))
n=ns*(1-s)

#result
print "developed torque=",tf,"N-m"
print "maximum torque=",tmax,"N-m"
print "speed at maximum torque=",n,"rpm"

developed torque= 52.4097855621 N-m
maximum torque= 99.9125764956 N-m
speed at maximum torque= 858.823529412 rpm

Example Number 34.23, Page Number:1270

In [17]:
import math
#variable declaration
r=0.015#ohm
x=0.09#ohm
s=0.03

#calculation
ns=100#rpm considered
n=(1-s)*ns
n2=n/2
s2=(ns-n2)/ns
ratio=((s2/s)*(r**2+(s*x)**2)/(r**2+(s2*x)**2))**0.5
per=1-1/ratio
phi=math.atan(s2*x/r)
pf=math.cos(phi)

#result
print "percentage reduction=",per*100,"%"
print "pf=",pf

percentage reduction= 22.8528060715 %
pf= 0.307902262948

Example Number 34.26, Page Number:1272

In [18]:
#variable declaration
v=440#V
f=50#Hz
p=4
t=100#N-m
n=1200#rpm

#calculation
e2=v/2
ns=120*f/p
n=ns-n
n2=n+ns/2

#result
print "stator supply voltage=",e2,"V"
print "new speed=",n2,"rpm"

stator supply voltage= 220 V
new speed= 1050 rpm

Example Number 34.24, Page Number:1274

In [21]:
#variable delclaration
v=400.0#V
f=60.0#Hz
p=8.0
n=1140.0#rpm
e=440.0#V
e2=550.0#V

#calculations
ns=120*f/p
s1=(ns-n)/ns
s2=s1*(e/e2)**2
n2=ns*(1-s2)

#result
print "speed=",n2,"rpm"

speed= 1053.6 rpm

Example Number 34.25, Page Number:1274

In [24]:
#variable declaration
v=450.0#V
f=60.0#Hz
p=8.0
n=873.0#rpm
t=23.0#degrees
n2=864.0#rpm
alpha=1.0/234.0#per degrees centrigrade

#calculation
s1=(900-n)/900
s2=(900-n2)/900
ratio=s2/s1-1
t2=(s2/s1-1)/alpha+23  

#result
print "increase in rotor resistance=",ratio*100,"%"
print "approx temperature=",t2,"degrees centigrade"

increase in rotor resistance= 33.3333333333 %
approx temperature= 101.0 degrees centigrade

Example Number 34.27, Page Number:1283

In [36]:
#variable declaration
v=440.0#V
f=500.0#Hz
p=6.0
load=80.0#kW
alt=100.0
ns=120.0*f/60.0
#calculation
s=alt/(60.0*f)
n=(1-s)*ns
cu_loss=(1.0/3.0)*load*1000/3.0

#result
print "slip=",s*1000,"%"
print "rotor speed=",n,"rpm"
print "rotor copper loss=",cu_loss/10000,"kW"

slip= 3.33333333333 %
rotor speed= 996.666666667 rpm
rotor copper loss= 0.888888888889 kW

Example Number 34.28, Page Number:1283

In [47]:
#variable declaration
v=440.0#V
f=50.0#Hz
p=4.0
n=1425.0#rpm
z=complex(0.4,4)
ratio=0.8
loss=500.0#W

#calculation
ns=120*f/p
s=75/ns
e1=v/3**0.5
tf=(3*2/(2*3.14*f))*(((e1*ratio)**2)*z.real*s)/(z.real**2+(s*z.imag)**2)
ir=s*ratio*e1/(z.real**2+(s*z.imag)**2)**0.5
cu_loss=3*ir**2*z.real
pm=2*3.4*(n/60)*tf
pout=pm-loss
s=z.real/z.imag
tmax=(3*2/(2*3.14*f))*(((e1*ratio)**2)*z.real*s)/(z.real**2+(s*z.imag)**2)
nmax=ns-s*ns
i=ratio*e1/abs(z)
tst=(3*2/(2*3.14*f))*(((e1*ratio)**2)*z.real)/(z.real**2+(z.imag)**2)

#result
print " full load torque=",tf,"N-m"
print "rotor current=",ir,"A"
print "cu_loss=",cu_loss,"W"
print "power output=",pout,"W"
print "max torque=",tmax,"N-m"
print "speed at max torque=",nmax,"rpm"
print "starting current=",i,"A"
print "starting torque=",tst,"N-m"

 full load torque= 78.9197452229 N-m
rotor current= 22.7215022978 A
cu_loss= 619.52 W
power output= 12245.5388535 W
max torque= 98.6496815287 N-m
speed at max torque= 1350.0 rpm
starting current= 50.5546790867 A
starting torque= 19.5345904017 N-m

Example Number 34.29, Page Number:1285

In [3]:
#variable declaration
P=23#kW
p=4
e=0.92
n=1440#r.p.m
loss=0.25

#calculations
motor_input=P/e
total_loss=motor_input-P
friction_loss=total_loss/p
Pm=P+friction_loss
Psw=Pm*1500/n
ws=2*3.14*1500/60
Tsw=Psw*1000/ws

#result
print "Synchronous torque=",round(Tsw),"N-m"

Synchronous torque= 156.0 N-m

Example Number 34.30, Page Number:1286

In [52]:
#variable declaration
load=60#kW
loss=1#kW
s=0.03

#calculations
p2=load-loss
pm=(1-s)*p2
cu_loss=s*p2
rotor_loss=cu_loss*1000/3

#result
print "mechanical power developed=",pm,"kW"
print "rotor copper loss=",rotor_loss,"W"

mechanical power developed= 57.23 kW
rotor copper loss= 590.0 W

Example Number 34.31, Page Number:1287

In [54]:
#variable declaration
v=400#V
f=50#Hz
p=6
load=20#KW
s=0.03
i=60#A

#calculation
fr=s*f
ns=120*f/p
n=ns*(1-s)
cu_loss=s*load*1000
r2=cu_loss/(3*i**2)

#result
print "frequency of rotor current=",fr,"Hz"
print "rotor copper loss=",cu_loss,"W"
print "rotor resistance=",r2,"ohm"

frequency of rotor current= 1.5 Hz
rotor copper loss= 600.0 W
rotor resistance= 0.0555555555556 ohm

Example Number 34.32, Page Number:1287

In [55]:
#variable declaration
p=6
f=50#Hz
load=3.73#KW
n=960#rpm
loss=280#W

#calculation
ns=120*f/p
input_r=load*1000*ns/n
input_s=input_r+loss

#result
print "stator input=",input_s,"W"

stator input= 4165.41666667 W

Example Number 34.33, Page Number:1287

In [57]:
#variable declaration
v=400.0#V
f=50.0#Hz
p=6.0
p2=75.0#KW
alt=100.0

#calculations
f1=alt/60
s=f1/f
ns=120*f/p
n=ns*(1-s)
cu_loss_r_per_phase=s*p2/3
pm=(1-s)*p2

#result
print "slip=",s*100,"%"
print "rotor speed=",n,"rpm"
print "rotor copper loss per phase=",cu_loss_r_per_phase,"kW"
print "mechancal power=",pm,"kW"

slip= 3.33333333333 %
rotor speed= 966.666666667 rpm
rotor copper loss per phase= 0.833333333333 kW
mechancal power= 72.5 kW

Example Number 34.34, Page Number:1287

In [59]:
#variable declaration
v=500.0#V
f=50.0#Hz
p=6.0
n=975.0#rpm
p1=40.0#KW
loss_s=1.0#kW
loss=2.0#KW

#calculation
ns=120*f/p
s=(ns-n)/ns
p2=p1-loss_s
cu_loss=s*p2
pm=p2-cu_loss
pout=pm-loss
efficiency=pout/p1

#result
print "slip=",s*100,"%"
print "rotor copper loss=",cu_loss,"kW"
print "shaft power=",pout,"kW"
print "efficiency=",efficiency*100,"%"

slip= 2.5 %
rotor copper loss= 0.975 kW
shaft power= 36.025 kW
efficiency= 90.0625 %

Example Number 34.35, Page Number:1287

In [62]:
#variable declaration
output=100#KW
v=3300#V
f=50#Hz
n=500#rpm
s=0.018
pf=0.85
cu_loss=2440#W
iron_loss=3500#W
rotational_loss=1200#W

#calculations
pm=output+rotational_loss/1000
cu_loss_r=(s/(1-s))*pm
p2=pm+cu_loss_r
input_s=p2+cu_loss/1000+iron_loss/1000
il=input_s*1000/(3**0.5*v*pf)
efficiency=output/input_s

#result
print "rotor copper loss=",cu_loss_r,"kW"
print "line current=",il,"A"
print "efficiency=",efficiency*100,"%"

rotor copper loss= 1.85132382892 kW
line current= 22.1989272175 A
efficiency= 92.7202341611 %

Example Number 34.36, Page Number:1288

In [69]:
#variable declaration
v=440.0#V
f=50.0#Hz
p=6.0
p2=100.0#W
c=120.0

#calculations
s=c/(f*60)
ns=120*f/p
n=ns*(1-s)
pm=(1-s)*p2
cu_loss=s*p2/3
n2=ns-n

#result
print "slip=",s*100,"%"
print "rotor speed=",n,"rpm"
print "mechanical power=",pm,"kW"
print "copper loss=",cu_loss,"kW"
print "speed of stator field with respect to rotor=",n2,"rpm"

slip= 4.0 %
rotor speed= 960.0 rpm
mechanical power= 96.0 kW
copper loss= 1.33333333333 kW
speed of stator field with respect to rotor= 40.0 rpm

Example Number 34.37, Page Number:1288

In [74]:
#variable declaration
efficiency=0.9
output=37#kW
ratio=1.0/3.0

#calculation
input_m=output*1000/efficiency
total_loss=input_m-output*1000
x=total_loss/(3+0.5)
input_r=output*1000+x/2+x
s=x/input_r

#result
print "slip=",s*100,"%"

slip= 3.0303030303 %

Example Number 34.38, Page Number:1289

In [78]:
#variable declaration
v=400#V
f=50#Hz
p=6
load=45#KW
i=75#A
s=0.03
iron_loss=1200#kW
loss=900#kW
r=0.12#ohm

#calculations
pf=load*1000/(3**0.5*v*i)
r=r*3/2
cu_loss=3*(i/3**0.5)**2*r
cu_loss_r=s*42788
pm=42788-cu_loss_r
output_s=pm-loss
efficiency=output_s/(load*1000)
t=(output_s*60)/(2*3.14*970)

#result
print "pf=",pf
print "rotor cu loss=",cu_loss_r,"W"
print "p out=",output_s,"W"
print "efficiency=",efficiency*100,"%"
print "torque=",t,"N-m"

pf= 0.866025403784
rotor cu loss= 1283.64 W
p out= 40604.36 W
efficiency= 90.2319111111 %
torque= 399.937881673 N-m

Example Number 34.39(a), Page Number:1287

In [88]:
#variable declaration
p=4.0
v=220.0#V
f=50.0#Hz
r=0.1#ohm
x=0.9#ohm
ratio=1.75
s=0.05

#calculations
k=1/ratio
e1=v/3**0.5
e2=k*e1
z=(r**2+(s*x)**2)**0.5
i2=s*e2/z
pcr=3*i2**2*r
pm=pcr*(1-s)/s
ns=120*f/p
n=ns*(1-s)
tg=9.55*pm/n
sm=r/x
n=ns*(1-sm)
e3=sm*e2

#result
print "load torque=",tg/9.81,"kg-m"
print "speed at maximum torque=",n,"rpm"
print "rotor emf at max torque=",e3,"V"

load torque= 4.26478644041 kg-m
speed at maximum torque= 1333.33333333 rpm
rotor emf at max torque= 8.06457518868 V

Example Number 34.39(b), Page Number:1290

In [91]:
#variable declaration
v=400#V
f=50#Hz
p=4
i=10#A
pf=0.86
loss=0.05
cu_r=0.04
m_loss=0.03

#calculation
input_m=3**0.5*v*i*pf
loss_s=loss*input_m
input_r=input_m-loss_s
cu_lossr=cu_r*input_r
mec_loss=m_loss*input_r
output_shaft=input_r-cu_lossr-mec_loss
s=cu_lossr/input_r
ns=120*f/p
n=ns*(1-s)
wr=2*3.14*n/60
output_r=input_r-cu_lossr
tr=output_r/wr
tin=output_shaft/wr

#result
print "slip=",s*100,"%"
print "rotor speed=",n,"rpm"
print "torque developed in the rotor=",tr,"Nw-m"
print "shaft torque=",tin,"Nw-m"

slip= 4.0 %
rotor speed= 1440.0 rpm
torque developed in the rotor= 36.0531340072 Nw-m
shaft torque= 34.9264735695 Nw-m

Example Number 34.40, Page Number:1291

In [107]:
#variable declaration
v=440.0#V
p=40.0
f=50.0#Hz
r=0.1#ohm
x=0.9#ohm
ratio=3.5
s=0.05

#calculation
e1=v/3**0.5
k=1/ratio
e2=k*e1
er=s*e2
z=(r**2+(s*x)**2)**0.5
i2=er/z
cu_loss=3*i2**2*r
output=cu_loss*(1-s)/s
sm=r/x
er=sm*e2
zr=(r**2+(x*sm)**2)**0.5
i2=er/zr
cu_loss=3*i2**2*r
input_r=cu_loss/sm

#result
print "gross output at 5% slip=",output,"W"
print "maximum torque=",input_r,"W"

gross output at 5% slip= 6242.77652849 W
maximum torque= 8780.04535147 W

Example Number 34.41, Page Number:1291

In [109]:
#variable declaration
pout=18.65#kW
p=4.0
f=50.0#Hz
loss=0.025
s=0.04

#calculations
pw=loss*pout*1000
pm=pout*1000+pw
cu_loss=s*pm/(1-s)
p2=cu_loss/s
ns=120*f/p
n=ns*(1-s)
tsh=9.55*pout*1000/n
tg=9.55*pm/n

#result
print "rotor cu loss=",cu_loss,"W"
print "rotor input=",p2,"W"
print "shaft torque=",tsh,"N-m"
print "gross electromagnetic torque=",tg,"N-m"

rotor cu loss= 796.510416667 W
rotor input= 19912.7604167 W
shaft torque= 123.685763889 N-m
gross electromagnetic torque= 126.777907986 N-m

Example Number 34.42, Page Number:1291

In [113]:
#variable declaration
p=8
f=50.0#Hz
n=710#rpm
load=35#kW
loss=1200#W
loss_r=600#W

#calculation
p2=load*1000-loss
ns=120*f/p
s=(ns-n)/ns
cu_loss=s*p2
pm=p2-cu_loss
tg=9.55*pm/n
pout=pm-loss_r
tsh=9.55*pout/n

#result
print "rotor copper loss=",cu_loss/1000,"kW"
print "gross torque=",tg,"N-m"
print "mechanical power=",pm,"W"
print "net torque=",tsh,"N-m"
print "mechanical power output=",pout,"W"

rotor copper loss= 1.80266666667 kW
gross torque= 430.386666667 N-m
mechanical power= 31997.3333333 W
net torque= 422.316244131 N-m
mechanical power output= 31397.3333333 W

Example Number 34.43, Page Number:1292

In [116]:
#variable declaration
p=6
f=50.0#Hz
s=0.04
tsh=149.3#N-m
loss=200#W
cu_loss=1620#W

#calculations
ns=120*f/p
n=ns*(1-s)
pout=tsh*2*3.14*(n/60)
output=pout+loss
p2=output*ns/n
cu_lossr=p2-output
p1=p2+cu_loss
efficiency=pout*100/p1

#result
print "output power=",pout/1000,"kW"
print "rotor cu loss=",cu_lossr,"W"
print "the efficiency=",efficiency,"%"

output power= 15.001664 kW
rotor cu loss= 633.402666667 W
the efficiency= 85.9444669361 %

Example Number 34.44, Page Number:1291

In [120]:
#variable declaration
pout=18.65#kW
p=6
f=50.0#Hz
n=960#rpm
i2=35#A
loss=1#kW

#calculation
pm=pout+loss
ns=120*f/p
s=(ns-n)/ns
cu_lossr=pm*s*1000/(1-s)
r2=cu_lossr/(3*i2**2)

#result
print "resistane per phase=",r2,"ohm/phase"

resistane per phase= 0.222789115646 ohm/phase

Example Number 34.45, Page Number:1291

In [129]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
sf=Symbol('sf')
v=400#V
p=4
f=50#Hz
r=0.01#ohm
x=0.1#ohm
ratio=4

#calculation
e1=v/3**0.5
e2=e1/ratio
sm=r/x
ns=120*f/p
tmax=(3/(2*3.14*25))*(e2**2/(2*x))
a=r/x
sf=solve(0.5*(a**2+sf**2)-2*a*sf,sf)
n=ns*(1-sf[0])
tf=tmax/2
output=2*3.14*n*tf/60

#result
print "maximum torque=",tmax,"N-m"
print "full load slip=",sf[0]
print "power output=",output,"W"

maximum torque= 318.47133758 N-m
full load slip= 0.0267949192431123
power output= 24330.1270189222 W

Example Number 34.46, Page Number:1291

In [143]:
#variable declaration
p=4
f=50.0#Hz
v=200.0#V
r=0.1#ohm
x=0.9#ohm
k=0.67
s=0.04
#calculations
e1=v/3**0.5
e2=e1*k
z=(r**2+(s*x)**2)**0.5
i2=s*e2/z
cu_loss=3*i2**2*r
pm=cu_loss*(1-s)/s
ns=120*f/p
n=ns*(1-s)
tg=9.55*pm/n
sm=r/x
er=sm*e2
zr=(r**2+(sm*x)**2)**0.5
i2=er/zr
cu_lossr=3*i2**2*r
output=cu_lossr*(1-sm)/sm
n=(1-sm)*ns
tmax=9.55*output/n

#result
print "torque=",tg,"N-m"
print "maximum torque=",tmax,"N-m"
print "speed at max torque=",n,"rpm"

torque= 40.4815391879 N-m
maximum torque= 63.511037037 N-m
speed at max torque= 1333.33333333 rpm

Example Number 34.47, Page Number:1293

In [144]:
#variable declaration
r=0.015#ohm
x=0.09#ohm
f=50#Hz
s=0.04
p=4
e2=110#V

#calculations
z=(r**2+x**2)**0.5
pf=r/z
xr=s*x
zr=(r**2+xr**2)**0.5
pf2=r/zr
ns=120*f/p
n=ns*(1-s)
er=s*e2
i2=er/zr
cu_loss=3*i2**2*r
pm=cu_loss*(1-s)/s
tg=9.55*pm/n

#result
print "pf of motor at start=",pf
print "pf of motor at s=4%",pf2
print "full load torque=",tg,"N-m"

pf of motor at start= 0.164398987305
pf of motor at s=4% 0.972387301981
full load torque= 582.728189612 N-m

Example Number 34.48, Page Number:1294

In [146]:
#variable declaration
p=6.0
f=50.0#Hz
tsh=162.84#N-m
c=90.0
t=20.36#N-m
loss=830.0#W

#calculation
ns=120*f/p
fr=c/60
s=fr/f
n=ns*(1-s)
output=2*3.14*n*tsh/60
tg=tsh+t
p2=tg*ns/9.55
cu_lossr=s*p2
p1=p2+cu_lossr
efficiency=output*100/p1

#result
print "motor output=",output,"W"
print "cu loss=",cu_lossr,"W"
print "motor input",p1,"W"
print "efficiency=",efficiency,"%"

motor output= 16532.6024 W
cu loss= 575.497382199 W
motor input 19758.7434555 W
efficiency= 83.6723369441 %

Example Number 34.49, Page Number:1294

In [157]:
#variable declaration
load=18.65#kW
v=420.0#V
p=6
f=50.0#Hz
r=1.0#ohm
z=complex(0.25,0.75)
zr=complex(0.173,0.52)
v1=420.0#V
v2=350.0#V

#calculations
k=v2/v1
r02=zr.real+k**2*z.real
x02=zr.imag+k**2*z.imag
z02=((r+r02)**2+x02**2)**0.5
i2=v2/(3**0.5*z02)
cu_loss=i2**2*(r+zr.real)
p2=cu_loss*3
ns=120*f/p
tst=9.55*p2/(ns*9.81)
#result
print "torque=",tst,"kg-m"

torque= 48.2909354778 kg-m

Example Number 34.50, Page Number:1295

In [158]:
#variable declaration
p=8
load=37.3#ohm
v=280#V
f=50.0#Hz
i=200#A
pf=0.25
r=0.15#ohm
k=1.0/3
#calculation
wsc=2*v*i*pf
power_phase=v*i*pf
R=power_phase/i**2
r2_=R-r
r2=k**2*r2_
p2=3*i**2*r2_
ns=120*f/p
t=9.55*p2/ns

#result
print "resistance perphaseof therotor winding=",r2,"ohm"
print "startingtorque=",t,"N-m"

resistance perphaseof therotor winding= 0.0222222222222 ohm
startingtorque= 305.6 N-m

Example Number 34.51, Page Number:1295

In [159]:
#variable declaration
ratios=1.6
ratiom=2.0
sf=0.01
sb=0.04
#calculation
i=(ratios/sf)**0.5

#result
print "slip at full load=",sf
print "slip at maximum torque=",sb
print "rotor current=",i

slip at full load= 0.01
slip at maximum torque= 0.04
rotor current= 12.6491106407

Example Number 34.52, Page Number:1297

In [162]:
#variable declaration
v=200#km/h
f=100#Hz

#calculation
w=v*5.0/18/(2*f)

#result
print "pole pitch=",w*1000,"mm"

pole pitch= 277.777777778 mm

Example Number 34.53, Page Number:1297

In [163]:
#variable declaration
p=4
w=6#mm
f=25#Hz
p=6#kW
loss=1.2#kW
v=2.4#m/s

#calculation
vs=2*f*w/100
s=(vs-v)/vs
p2=p-loss
pcr=s*p2
pm=p2-pcr
f=p2*1000/vs

#result
print "synchronous speed=",vs,"m/s"
print "slip=",s
print "cu loss=",pcr,"kW"
print "mechanical power=",pm,"kW"
print "thrust=",f/1000,"kN"

synchronous speed= 3 m/s
slip= 0.2
cu loss= 0.96 kW
mechanical power= 3.84 kW
thrust= 1.6 kN

Example Number 34.54, Page Number:1304

In [166]:
#variable declaration
s=0.12
r=0.08#ohm/phase
pg=9000.0#W

#calculations
rl=r*(1/s-1)
v=(pg*rl/3)**0.5
il=v/rl

#result
print "load resistance=",rl,"ohm"
print "load voltage=",v,"V"
print "load current=",il,"A"

load resistance= 0.586666666667 ohm
load voltage= 41.9523539268 V
load current= 71.5096941934 A

Example Number 34.55, Page Number:1305

In [177]:
#variable declaration
v=400.0#V
f=50.0#Hz
p=4
r1=0.15#ohm
x1=0.45#ohm
r2_=0.12#ohm
x2_=0.45#ohm
xm=complex(0,28.5)#ohm
s=0.04
#calculations
rl_=r2_*(1/s-1)
i2_=(v/3**0.5)/complex(r1+rl_,x1)
i0=(v/3**0.5)/xm
i1=i0+i2_
pf=math.cos(math.atan(i1.imag/i1.real))

#result
print "stator current=",i1,"A"
print "power factor=",pf

stator current= (74.5730253701-19.1783634605j) A
power factor= 0.968485280755

Example Number 34.56, Page Number:1305

In [184]:
import math
#variable declaration
v=220#V
p=4
f=50#Hz
power=3.73#kW
r1=0.45#ohm
x1=0.8#ohm
r2_=0.4#ohm
x2_=0.8#ohm
b0=-1.0/30
loss=50#W
lossr=150#W
s=0.04

#calculations
zab=complex(30*complex(r2_/s,x2_))/complex(r2_/s,x2_-1/b0)
z01=complex(r1,x1)+zab
vph=v/3**0.5
i1=v1/z01
pf=math.cos(math.atan(i1.imag/i1.real))
p2=3*i1.real**2*zab.real
pm=(1-s)*p2
ns=120*f/p
n=ns*(1-s)
tg=9.55*pm/n
power_o=pm-lossr
cu_loss=3*i1.real**2*r1
cu_lossr=s*p2
total_loss=loss+cu_loss+cu_lossr+lossr
efficiency=power_o/(power_o+total_loss)

#result
print "input current=",i1,"A"
print "pf=",pf
print "air gap power=",p2,"W"
print "mechanical power=",pm,"W"
print "electro magnetic torque=",tg,"N-m"
print "output power=",power_o,"W"
print "efficiency=",efficiency*100,"%"

input current= (21.9914486234+42.6194245913j) A
pf= 0.45854949826
air gap power= 5173.46132109 W
mechanical power= 4966.52286825 W
electro magnetic torque= 32.9377037443 N-m
output power= 4816.52286825 W
efficiency= 81.9644851937 %

Example Number 34.57, Page Number:1306

In [186]:
#variable declaration
v=440#V
f=50#Hz
load=37.3#kW
r1=0.1#ohm
x1=0.4#ohm
r2_=0.15#ohm
x2_=0.44#ohm
loss=1250#W
lossr=1000#W
i=20#A
pf=0.09
s=0.03

#calculation
v1=v/3**0.5
i2_=v1/complex(r1+r2_/s,x1+x2_)
i1=i2_+complex(1.78,19.9)
pf=math.cos(math.atan(i1.imag/i1.real))
p2=3*i2_.real**2*r2_/s
ns=120*f/p
tg=9.55*p2/ns
pm=p2*(1-s)
pout=pm-1000
cu_losss=3*i1.real**2*r1
cu_lossr=s*p2
total_loss=loss+cu_losss+cu_lossr+lossr
efficiency=pout/(pout+total_loss)

#result
print "line current=",i1,"A"
print "pf=",pf
print "electromagnetic torque=",tg,"N-m"
print "output=",pout,"W"
print "efficiency=",efficiency*100,"%"

line current= (50.2750367599+11.9125821807j) A
pf= 0.973057118792
electromagnetic torque= 224.593900377 N-m
output= 33218.2329894 W
efficiency= 89.0932246577 %

Example Number 34.58, Page Number:1306

In [188]:
#variable declaration
v=400#V
z=complex(0.06,0.2)
zr=complex(0.06,0.22)

#calculation
r01=z.real+zr.real
x01=z.imag+zr.imag
z01=(r01**2+x01**2)**0.5
s=z.real/(z.real+z01)
v1=v/3**0.5
pmax=3*v1**2/(2*(r01+z01))

#result
print "maximum gross power=",pmax,"W"
print "slip=",s

maximum gross power= 143676.459572 W
slip= 0.120771344025

Example Number 34.59, Page Number:1307

In [3]:
import math
#variable declaration
v1=115#V
f=60.0#Hz
p=6
z=complex(0.07,0.3)
zr=complex(0.08,0.3)
gd=0.022#mho
bo=0.158#mho
s=0.02

#calculation
rl_=1/bo*(1/s-1)
z=complex(z.real+zr.real+rl_,0.6)
v=v1/3**0.5
i2=complex(16,-2.36)
io=v*complex(gd,-bo)
i1=io+i2
pf=math.cos(math.atan(i1.imag/i1.real))
pg=3*abs(i2)**2*rl_/100
ns=120*f/p
n=(1-s)*ns
tg=9.55*pg/n
p2=3**0.5*v1*abs(i1)*pf
efficiency=pg*100/p2

#result
print "secondary current=",i2,"A"
print "primary current=",i1,"A"
print "pf=",pf
print "power output=",pg,"W"
print "torque=",tg,"N-m"
print "input=",p2,"W"
print "efficiency=",efficiency,"%"

secondary current= (16-2.36j) A
primary current= (17.460696181-12.8504543912j) A
pf= 0.805393212665
power output= 2433.59058228 W
torque= 19.7625765823 N-m
input= 3477.92348593 W
efficiency= 69.9725164204 %

Example Number 34.60, Page Number:1308

In [1]:
#variable declaration
v=400.0#V
z=complex(0.4,1)
zr=complex(0.6,1)
zm=complex(10.0,50.0)
s=0.05

#calculation
sm=zr.real/(z.real**2+(z.imag+zr.imag)**2)**0.5
v1=v/3**0.5
i2=v1/((z.real+zr.real)**2+(zr.imag+z.imag)**2)**0.5
tgmax=3*i2**2*z.real*60.0/(sm*2*3.14*1500)
#result
print "maximum torque=",tgmax,"N-m"

maximum torque= 277.144160399 N-m
In [ ]: