Chapter 10 - Three Phase Induction Motors

Example 1 - pg 10_14

In [1]:
#Chapter-10,Example10_1,pg10_14
#calculate the full load slip
#given
P=4.
f=50.
N=1410.
#calculations
Ns=120*f/P
s=(Ns-N)/Ns
s=s*100#%s
#results
print"full load slip (percent) = ",s

full load slip (percent) =  6.0

Example 2 - pg 10_14

In [2]:
#Chapter-10,Example10_2,pg10_14
#calculate the full load speed of motor
#given
P=4.
f=50.
sfl=4/100.
#calculations
Ns=120*f/P
Nfl=Ns-sfl*Ns
#results
print"full load speed of motor (rpm) = ",Nfl

full load speed of motor (rpm) =  1440.0

Example 3 - pg 10_16

In [3]:
#Chapter-10,Example10_3,pg10_16
#calculate the frequency of induced emf
#given
P=4.
f=50.
N=1470.
#calculations
Ns=120*f/P
s=(Ns-N)/Ns
fr=s*f
#results
print"frequency of induced e.m.f (Hz) = ",fr

frequency of induced e.m.f (Hz) =  1.0

Example 4 - pg 10_20

In [4]:
#Chapter-10,Example10_4,pg10_20
#calculate the full load slip and speed of motor
#given
P=8.
f=50.
fr=2.
#calculations
s=fr/f
s=s*100.
#results
print"full load slip (percent)= ",s
s=s/100
Ns=120*f/P
N=Ns*(1-s)
print"speed of motor (rpm) = ",N

full load slip (percent)=  4.0
speed of motor (rpm) =  720.0

Example 5 - pg 10_20

In [5]:
#Chapter-10,Example10_5,pg10_20
import math
#calculate the frequency of rotor, magnitude of induced emf
#given
P=4.
f=50.
N=1455.
E1line=415.
#calculations
Ns=120*f/P
s=(Ns-N)/Ns
fr=s*f
E1ph=E1line/math.sqrt(3)
E2ph=0.5*E1ph#K=2
E2r=s*E2ph
#results
print"frequency of rotor e.m.f (Hz) = ",fr
print"magnitude of induced e.m.f standstill (V) = ",round(E2ph,1)
print"magnitude of induced e.m.f running (V) = ",round(E2r,3)

frequency of rotor e.m.f (Hz) =  1.5
magnitude of induced e.m.f standstill (V) =  119.8
magnitude of induced e.m.f running (V) =  3.594

Example 6 - pg 10_21

In [6]:
#Chapter-10,Example10_6,pg10_21
#calculate the rotor current and power factor
import math
from math import sqrt
#given
P=4
f=50
R2=0.2
X2=1
E2line=120
#calculations and results
E2ph=E2line/sqrt(3)
Ns=120*f/P
#at start
pf=R2/sqrt((R2**2)+(X2**2))#power factor
I2=E2ph/sqrt((R2**2)+(X2**2))
print" at start"
print"pf (lagging) = ",round(pf,3)
print"I2 (A) = ",round(I2,2)
#on full load
N=1440.
s=(Ns-N)/Ns
pf=R2/sqrt((R2**2)+((s*X2)**2))
I2=E2ph*s/sqrt((R2**2)+((s*X2)**2))
print" on full load"
print"pf (lagging) = ",round(pf,4)
print"I2 (A) = ",round(I2,3)

 at start
pf (lagging) =  0.196
I2 (A) =  67.94
 on full load
pf (lagging) =  0.9806
I2 (A) =  13.587

Example 7 - pg 10_24

In [7]:
#Chapter-10,Example10_7,pg10_24
#calculate the torque on full load
import math
#given
P=4.
f=50.
R2=0.1
X2=1.
N=1440.
K=0.5
#calculations
Ns=120*f/P
E1line=400.
E1ph=E1line/math.sqrt(3)
E2ph=0.5*E1ph
s=(Ns-N)/Ns
ns=Ns/60#synchronous speed (r.p.s)
T=(3/(2*math.pi*ns))*(s*(E2ph**2)*R2/((R2**2)+((s*X2)**2)))
#results
print "torque on full load (Nm) = ",round(T,2)

torque on full load (Nm) =  87.81

Example 8 - pg 10_27

In [8]:
#Chapter-10,Example10_8,pg10_27
#calculate the starting torque, max torque, speed
import math
from math import sqrt
P=4.
f=50.
K=1/4.
R2=0.01
X2=0.1
E1line=400.
E1ph=E1line/sqrt(3)
E2=E1ph/4
Ns=120*f/P
#at start
s=1
ns=Ns/60
k=3/(2*math.pi*ns)
Tst=k*(E2**2)*R2/((R2**2)+(X2**2))
print"starting torque (Nm) = ",round(Tst,3)

#slip at max torque
sm=R2/X2
sm=sm*100
print"slip at which max torque occurs (percent) = ",round(sm,0)
#speed at max torque
sm=sm/100
N=Ns*(1-sm)
print"speed at which max torque occurs (rpm) ",N

#max. torque
Tm=k*(E2**2)/(2*X2)
sf=0.04
Tfl=k*sf*(E2**2)*R2/((R2**2)+((sf*X2)**2))
print"max torque (Nm) = ",round(Tm,2)
print"full load torque (Nm) = ",round(Tfl,2)	

starting torque (Nm) =  63.032
slip at which max torque occurs (percent) =  10.0
speed at which max torque occurs (rpm)  1350.0
max torque (Nm) =  318.31
full load torque (Nm) =  219.52

Example 9 - pg 10_33

In [9]:
#Chapter-10,Example10_9,pg10_33
#calculate the full load torque and starting torque
#given
P=24.
f=50.
R2=0.016
X2=0.265
N=247.
#calculations
Ns=120*f/P
sf=(Ns-N)/Ns
sm=R2/X2
Tfm=2*sm*sf/((sm**2)+(sf**2))
Tsm=2*sm/(1+(sm**2))
#results
print"full load torque to max torque = ",round(Tfm,4)
print"starting torque to max torque = ",round(Tsm,4)

full load torque to max torque =  0.3824
starting torque to max torque =  0.1203

Example 10 - pg 10_36

In [10]:
#Chapter-10,Example10_10,pg10_36
#calculate the external resistance
#given
import math
R2=0.04
X2=0.2
#for Tm=Tst, sm=1
#calculations
R21=X2
Rex=R2-R21
#for Tst=Tm/2........(1)
#Tst=k*(E2**2)*R21/((R21**2)+(X2**2))......(2)with added resistance
#from (1) and (2)
#(R21**2)-0.8*R21+0.04=0
a=1
b=-0.8
c=0.04
R21=(-b-math.sqrt((b**2)-4*a*c))/(2*a)#neglecting higher value
Rex=R21-R2
#results
print"external resistance (ohm/phase) = ",round(Rex,4)

external resistance (ohm/phase) =  0.0136

Example 11 - pg 10_42

In [11]:
#Chapter-10,Example10_11,pg10_42
#calculate the rotor copper loss
#given
import math
Tsh=190.
P=8.
f=50.
fr=1.5
ML=700.
#calculations
s=fr/f
Ns=120*f/P
N=Ns*(1-s)
Po=Tsh*(2*math.pi*N/60.)
Pm=Po+ML
Pc=Pm*s/(1-s)
#results
print"rotor copper loss (W) = ",round(Pc,3)

rotor copper loss (W) =  469.326

Example 12 - pg 10_43

In [12]:
#Chapter-10,Example10_12,pg10_43
#calculate the full load efficiency
#given
P=4.
f=50.
Pi=50.*10**3
N=1440.
Sl=1000.
Fl=650.
#calculations
Ns=120*f/P
s=(Ns-N)/Ns
P2=Pi-Sl
Pc=s*P2
Pm=P2-Pc
Po=Pm-Fl
n=Po*100/Pi
#results
print"full load efficiency (percent) = ",n

full load efficiency (percent) =  92.78

Example 13 - pg 10_44

In [14]:
#Chapter-10,Example10_13,pg10_44
#calculate the net output power, rotor copper loss,efficiency and resistance per phase
#given
import math
P=4.
f=50.
Tsh=300.
Tlost=50.
fr=120/60.#Hz
#calculations
s=fr/f
s=s*100.
print"slip (percent) = ",s
Ns=120.*f/P
s=s/100.
N=Ns*(1-s)
Po=Tsh*2*math.pi*N/60
Fl=Tlost*2*math.pi*N/60
Pm=Po+Fl
Pc=Pm*s/(1-s)
Rcl=Pc/3#rotor copper loss per phase
P2=Pc/s
n=Pm*100./P2
I2r=60
R2=Rcl/(I2r**2)
#results
print"net output power (kW) = ",round(Po/1000.,4)
print"rotor copper loss per phase (W) = ",round(Rcl,4)
print"rotor efficiency (percent) = ",n
print"rotor resistance per phase (ohm/phase) = ",round(R2,4)

slip (percent) =  4.0
net output power (kW) =  45.2389
rotor copper loss per phase (W) =  733.0383
rotor efficiency (percent) =  96.0
rotor resistance per phase (ohm/phase) =  0.2036

Example 14 - pg 10_45

In [16]:
#Chapter-10,Example10_14,pg10_45
#calculate the gross mechanical power, rotor copper losses, resistance and full load efficiency
#given
Po=25.*10**3
f=50.
P=4.
#calculations
Ns=120*f/P
N=1410
s=(Ns-N)/Ns
Ml=850
Pm=Po+Ml
Pc=Pm*s/(1-s)
I2r=65
R2=Pc/(3*(I2r**2))
Sl=1.7*Pc
P2=Pc/s
Pin=P2+Sl
n=Po*100/Pin
#results
print"gross mechanical power (W) = ",Pm
print"rotor copper losses (W) = ",Pc
print"rotor resistance per phase (ohm/phase) = ",round(R2,2)
print"full load efficiency (percent) = ",round(n,2)

gross mechanical power (W) =  25850.0
rotor copper losses (W) =  1650.0
rotor resistance per phase (ohm/phase) =  0.13
full load efficiency (percent) =  82.49

Example 15 - pg 10_47

In [17]:
#Chapter-10,Example10_15,pg10_47
#calculate the shaft torque, gross, rotor copper losses, stator copper and iron losses and overall efficiency 
#given
import math
Po=24.*10**3
Il=57.
Is=Il
P=8.
N=720.
f=50.
Vl=415.
pf=0.707
#calculations
Ns=120*f/P
s=(Ns-N)/Ns
Ml=1000.
Pm=Po+Ml
Pc=Pm*s/(1-s)
Tsh=Po*60/(2*math.pi*N)
T=Pm*60/(2*math.pi*N)
Rcl=1041.66#rotor copper loss
P2=Pc/s
Pi=math.sqrt(3)*Vl*Il*pf
Rs=0.1
Scl=3*(Is**2)*Rs#stator copper loss
Sl=Pi-P2
Sil=Sl-Scl#stator iron loss
n=Po*100/Pi
#results
print"shaft torque (N-m) = ",round(Tsh,3)
print"gross torque (N-m) = ",round(T,3)
print"rotor copper losses (W) = ",round(Pc,2)
print"stator copper losses (W) = ",Scl
print"stator iron losses (W) = ",round(Sil,2)
print"overall efficiency (percent) = ",round(n,2)

shaft torque (N-m) =  318.31
gross torque (N-m) =  331.573
rotor copper losses (W) =  1041.67
stator copper losses (W) =  974.7
stator iron losses (W) =  1950.6
overall efficiency (percent) =  82.85

Example 16 - pg 10_52

In [18]:
#Chapter-10,Example10_16,pg10_52
#calculate the supply current
#given
import math
sf=0.05
#Tst=Tfl
Ifs=1/6.#Isc/Ifl=6
#calculations
x=math.sqrt((Ifs**2)/sf)#tapping on transformer
t=x*100
Ist=(x**2)*6
#results
print "supply current (times Ifl) = ",round(Ist,2)

supply current (times Ifl) =  3.33

Example 17 - pg 10_54

In [19]:
#Chapter-10,Example10_17,pg10_54
#calculate the ratio of starting torque to full load torque
#given
R2=0.4
X2=4.
#Tm=k*(E2**2)/(2*X2)
#Tfl=Tm/2.5
#Tfl=k*(E2**2)/20
#Tst=k*(E2**2)*R2/((R2**2)+(X2**2))
#E2=E2/sqrt(3)
T=20*R2/(3*(((R2**2)+(X2**2))))
#results
print "ratio of starting torque to full load torque = ",round(T,3)

ratio of starting torque to full load torque =  0.165

Example 18 - pg 10_57

In [20]:
#Chapter-10,Example10_18,pg10_57
#calculate the rotor power factor, external resistance and current
#given
import math
from math import sqrt
Vl=1000.
f=50.
K=3.6
R2=0.01
X2=0.2
E1line=1000.
#calculations and results
E1=E1line/sqrt(3)
E2=E1/K
#at start,s=1
I2=160.37/sqrt((R2**2)+(X2**2))
pf=R2/sqrt((R2**2)+(X2**2))
print"rotor current at start (A) = ",round(I2,2)
print"rotor power factor lagging (answer in book is wrong)= ",round(pf,4)
#at s=0.03
s=0.03
I2r=s*160.37/sqrt((R2**2)+((s*X2)**2))
print"rotor current at slip 0.03 (A) = ",round(I2r,2)
I2=200.
R21=sqrt(((E2/I2)**2)-(X2**2))
Rex=R21-R2
print"external resistance (ohm/ph) (answer in book is wrong) = ",round(Rex,4)

rotor current at start (A) =  800.85
rotor power factor lagging (answer in book is wrong)=  0.0499
rotor current at slip 0.03 (A) =  412.55
external resistance (ohm/ph) (answer in book is wrong) =  0.7665

Example 19 - pg 10_58

In [21]:
#Chapter-10,Example10_19,pg10_58
#calculate the starting torque, full load torque, maximum torque and speed at max torque
import math
#given
P=12.
f=50.
R2=0.15
X2=0.25
E2=32.
#calculations
Ns=120*f/P
ns=Ns/60
Tst=3*(E2**2)*R2/((2*math.pi*ns)*((R2**2)+(X2**2)))
N=480.
s=(Ns-N)/Ns
Tfl=3*s*(E2**2)*R2/((2*math.pi*ns)*((R2**2)+((s*X2)**2)))
Tm=3*(E2**2)/(2*math.pi*ns*2*X2)
sm=R2/X2
N=Ns*(1-sm)
#results
print"starting torque (Nm) = ",round(Tst,2)
print"full load torque (Nm) = ",round(Tfl,3)
print"maximum torque (Nm) = ",round(Tm,3)
print"speed at max torque (rpm) = ",N

starting torque (Nm) =  103.54
full load torque (Nm) =  15.576
maximum torque (Nm) =  117.342
speed at max torque (rpm) =  200.0

Example 20 - pg 10_59

In [22]:
#Chapter-10,Example10_20,pg10_59
#calculate the efficiency in full load
#given
Po=50.*735.5#(in W)
s=0.04
#calculations
#Rcl=X...............rotor copper loss
#Sil=1.25X...........stator iron loss
#Ml=Y, Y=(Y+1.25X)/3, Y=0.625X
#TL=Sil+Rcl+Scl+Ml, TL=3.875X.........(a)
#Pm=Po+Y, 36775+625X..........(1)
#Pc=Pm*s/(1-s).............(2)
#Pc=X, from (1) and (2)
X=(s*Po)/(1-s-s*0.625)
TL=3.875*X#from (a)
n=Po*100./(Po+TL)
#results
print"efficiency on full load (percent) = ",round(n,2)

efficiency on full load (percent) =  85.78

Example 21 - pg 10_61

In [23]:
#Chapter-10,Example10_21,pg10_61
#calculate the new speed of motor
#given
import math
P=4.
f=50.
R2=0.25
X2=0.55
N1=1440
#calculations
Ns=120*f/P
s1=(Ns-N1)/Ns
Rex=0.2
R21=R2+Rex
#T1 at s1=T2 at s2
#0.3025*s2^2-2.8342*s2+0.2025=0, s1=0.04
a=0.3025
b=-2.8342
c=0.2025
s2=(-b-math.sqrt((b**2)-4*a*c))/(2*a)#neglecting higher value
N2=Ns*(1-s2)
#results
print"new speed of motor (rpm) = ",round(N2,0)

new speed of motor (rpm) =  1392.0

Example 22 - pg 10_62

In [24]:
#Chapter-10,Example10_22,pg10_62
#calculate the rotor current, full load current , power factor and rotor emf
#given
import math
from math import sqrt
E2line=50.
R2=0.5
X2=3.
E2=E2line/sqrt(3)
#calculations and results
#at start
s=1
I2r=s*E2/(sqrt((R2**2)+((s*X2)**2)))
print"rotor current at start (A) = ",round(I2r,4)
Rx=6.
I2r=s*E2/(sqrt(((R2+Rx)**2)+((s*X2)**2)))
print"rotor current for rheostat of 6 ohm (A) = ",round(I2r,4)
#at full load
s=0.04
I2r=s*E2/(sqrt((R2**2)+((s*X2)**2)))
pf=R2/(sqrt((R2**2)+((s*X2)**2)))
print"full load rotor current (A) = ",round(I2r,4)
print"full load power factor (lagging) = ",round(pf,4)
E2r=s*E2
print"rotor e.m.f on full load (V) = ",round(E2r,4)

rotor current at start (A) =  9.4916
rotor current for rheostat of 6 ohm (A) =  4.0324
full load rotor current (A) =  2.2456
full load power factor (lagging) =  0.9724
rotor e.m.f on full load (V) =  1.1547

Example 23 - pg 10_63

In [25]:
#Chapter-10,Example10_23,pg10_63
#calculate the starting,full load, maximum torque and speed
#given
import math
P=12.
f=50.
R2=0.15
X2=0.25
E2=32.
#calculations
Ns=120*f/P
ns=Ns/60.
k=3.
Tst=k*(E2**2)*R2/((2*math.pi*ns)*((R2**2)+(X2**2)))
N=480.
s=(Ns-N)/Ns
Tfl=k*s*(E2**2)*R2/((2*math.pi*ns)*((R2**2)+((s*X2)**2)))
Tm=k*(E2**2)/(2*math.pi*ns*2*X2)
sm=R2/X2
N=Ns*(1-sm)
#results
print"starting torque (Nm) = ",round(Tst,2)
print"full load torque (Nm) = ",round(Tfl,3)
print"maximum torque (Nm) = ",round(Tm,3)
print"speed at max torque (rpm) = ",N

starting torque (Nm) =  103.54
full load torque (Nm) =  15.576
maximum torque (Nm) =  117.342
speed at max torque (rpm) =  200.0

Example 24 - pg 10_64

In [27]:
#Chapter-10,Example10_24,pg10_64
#calculate the full load torque and external resistance required
#given
import math
P=4.
f=50.
R2=0.4
X2=2.
E2b=520.#between slip rings
#calculations
E2ph=E2b/math.sqrt(3)
Ns=120*f/P
N=1425.
sf=(Ns-N)/Ns
ns=Ns/60.
Tfl=3*sf*(E2ph**2)*R2/((2*math.pi*ns)*((R2**2)+((sf*X2)**2)))
Tst=3*(E2ph**2)*R2/((2*math.pi*ns)*((R2**2)+((X2)**2)))
T=Tst/Tfl
Tm=3*(E2ph**2)/((2*math.pi*ns)*((R2**2)+((X2)*2)))
T1=Tm/Tfl
#at start
sm=1
R21=X2
Rex=R21-R2
#results
print"full load torque (Nm) = ",round(Tfl,2)
print"ratio of Tst to Tfl = ",round(T,3)
print"ratio of Tm to Tfl = ",round(T1,3)
print"external resistance required (ohm/ph) = ",Rex

full load torque (Nm) =  202.52
ratio of Tst to Tfl =  0.817
ratio of Tm to Tfl =  2.043
external resistance required (ohm/ph) =  1.6

Example 25 - pg 10_65

In [28]:
#Chapter-10,Example10_25,pg10_65
#calculate the slip, rotor frequency, copper loss and efficiency
#given
import math
Po=33.73*10**3
P=4.
Vl=400.
f=50.
Nfl=1440.
pf=0.8
Ml=1.3*10**3
#calculations
Ns=120*f/P
s=(Ns-Nfl)/Ns
fr=s*f
Pm=Po+Ml
Pc=Pm*s/(1-s)
Pcp=Pc/3#copper loss per phase
P2=Pc/s
Sl=1.4*10**3
Pi=P2+Sl
n=Po*100/Pi
Il=Pi/(math.sqrt(3)*Vl*pf)
#results
print"slip at full load = ",s
print"rotor frequency (Hz) = ",round(fr,1)
print"rotor copper loss per phase (kW) = ",round(Pcp,2)
print"total copper loss (kW) = ",round(Pc/1000.,4)
print"efficiency at full load (percent) = ",round(n,2)
print"line current drawn (A) = ",round(Il,3)

slip at full load =  0.04
rotor frequency (Hz) =  2.0
rotor copper loss per phase (kW) =  486.53
total copper loss (kW) =  1.4596
efficiency at full load (percent) =  89.02
line current drawn (A) =  68.361

Example 26 - pg 10_66

In [29]:
#Chapter-10,Example10_26,pg10_66
#calculate the power factor of rotor
#given
import math
R2=0.04
X2=0.2
sfl=0.03
#at Tst, s=1
#Tfl=Tst
#(R21**2)-1.3633*R21+0.04=0
a=1
b=-1.3633
c=0.04
#calculations
R21=(-b+math.sqrt((b**2)-4*a*c))/(2*a)
Rex=R21-R2
pf=R21/math.sqrt((R21**2)+(X2**2))
#results
print"power factor of rotor (lagging) = ",round(pf,3)

power factor of rotor (lagging) =  0.989

Example 27 - pg 10_67

In [30]:
#Chapter-10,Example10_27,pg10_67
#calculate the full load speed, speed at max torque
#given
import math
P=4.
f=50.
Po=8.*10**3
#Tst=1.5*Tfl and Tm=2*Tfl
#(R2**2)+((sfl*X2)**2)=1.5*sfl*((R2**2)+(X2**2)).................(1)
#(R2**2)+((sfl*X2)**2)=2*(sfl/sm)*((R2**2)+((sm*X2)**2))..........(2)
#dividing (1) and (2) by (X2**2) on both sides and R2/X2=sm
#(sm**2)+(sfl**2)=5*(1+(sm**2))*sfl.............(3)
#(sm**2)+(sfl**2)=2*(2*(sm**2))*(sfl/sm)=4*sm*sfl...........(4)
#dividing (3) by (4)
#(sm**2)-2.667*sm+1=0
a=1
b=-2.667
c=1
#calculations
sm=(-b-math.sqrt((b**2)-4*a*c))/(2*a)
Ns=120*f/P
#substituting sm in (4)
#(sfl**2)-1.8052*sfl+0.2036=0
a=1
b=-1.8052
c=0.2036
sfl=(-b-math.sqrt((b**2)-4*a*c))/(2*a)
N=Ns*(1-sfl)
Nm=Ns*(1-sm)
#results
print"full load speed (rpm) = ",round(N,1)
print"speed at max. torque (rpm) = ",round(Nm,2)

full load speed (rpm) =  1318.7
speed at max. torque (rpm) =  823.0

Example 28 - pg 10_68

In [32]:
#Chapter-10,Example10_28,pg10_68
#calculate the starting torque
import math
#given
Po=10*735.5#(in W)
Nfl=1410.
P=4.
f=50.
#calculations
Ns=120.*f/P
sfl=(Ns-Nfl)/Ns
Nm=1200.
sm=(Ns-Nm)/Ns
T=2*sfl*sm/((sm**2)+(sfl**2))#Tfl/Tm
T1=(1+(sm**2))/(2*sm)#Tm/Tst
T2=T1*T#Tfl/Tst
Tfl=Po*60./(2*math.pi*Nfl)
Tst=Tfl/T2
#results
print"starting torque (Nm) = ",round(Tst,1)

starting torque (Nm) =  34.8

Example 29 - pg 10_70

In [33]:
#Chapter-10,Example10_29,pg10_70
#calculate the maximum torque, speed and external resistance
#given
P=4.
f=50.
R2=0.025
X2=0.15
sfl=0.04
Tfl=150.
#calculations
sm=R2/X2
Tm=Tfl*((R2**2)+((sfl*X2)**2))*sm/(sfl*((R2**2)+((sm*X2)**2)))
Ns=120*f/P
N=Ns*(1-sm)
#at start
R21=X2
Rex=R21-R2
#results
print"maximum torque (Nm) = ",Tm
print"speed (r.p.m) = ",N
print"external resistance (ohm/ph) = ",Rex

maximum torque (Nm) =  330.5
speed (r.p.m) =  1250.0
external resistance (ohm/ph) =  0.125

Example 30 - pg 10_70

In [35]:
#Chapter-10,Example10_30,pg10_70
#calculate the motor output, copper loss and efficiency
#given
import math
Tsh=162.84
P=6.
f=50.
Tlost=20.36
fr=1.5
#calculations
s=fr/f
Ns=120*f/P
N=Ns*(1-s)
Po=Tsh*(2*math.pi*N)/60
Fl=Tlost*(2*math.pi*N)/60
Pm=Po+Fl
Pc=Pm*s/(1-s)
P2=Pc/s
Sl=830
Pi=P2+Sl
n=Po*100/Pi
#results
print"motor output (kW) = ",round(Po/1000.,5)
print"copper loss in rotor (W) = ",round(Pc,3)
print"motor input (kW) = ",round(Pi/1000.,4)
print"efficiency of motor (percent) = ",round(n,3)

motor output (kW) =  16.54099
copper loss in rotor (W) =  575.54
motor input (kW) =  20.0147
efficiency of motor (percent) =  82.644

Example 31 - pg 10_71

In [36]:
#Chapter-10,Example10_31,pg10_71
#calculate the ratio of max to full load torque and speed at max torque
#given
f=50.
P=8.
R2=0.01
X2=0.1
sfl=0.04
#calculations
#for Tmax
sm=R2/X2
#for Tfl
s=sfl
T=sm*R2*((R2**2)+((sfl*X2)**2))/((sfl*R2)*((R2**2)+((sm*X2)**2)))#Tmax/Tfl
Ns=120*f/P
sm=0.1
N=Ns*(1-sm)
#results
print"ratio of max to full load torque = ",T
print"speed at max torque (rpm) = ",N

ratio of max to full load torque =  1.45
speed at max torque (rpm) =  675.0