# Chapter 2: Induction Motors¶

## Example 2.1, Page 130¶

In [124]:
#Given data :
P=2;#no. of poles
f=60;#in Hz
N=3460.;#in rpm

#Calculations
Ns=120*f/P;#in rpm
Slip=Ns-N;#in rpm
PercentageSlip=((Ns-N)/Ns)*100;#in %

#Results
print "Synchronous speed in rpm : ",Ns;
print "Percentage Slip : ",round(PercentageSlip,2);

Synchronous speed in rpm :  3600
Percentage Slip :  3.89


## Example 2.2, Page 131¶

In [125]:
#Given data :
P=8.;#no. of poles
f=50.;#in Hz
N=700.;#in rpm

#Calculations&Results
#Part (a) :
Ns=120*f/P;#in rpm
print "Synchronous speed in rpm : ",Ns;
#Part (b) :
S=(Ns-N)*100/Ns;#in %
print "Slip(in %) : ",round(S,2);
#Part (c) :
#At the time of stsrt S=1;
fdash=f;#in Hz
print "Rotor frequeny at the time of starting(in Hz) : ",fdash;
#Part (d) :
fdash=(S/100)*f;#in Hz
print "Rotor frequeny at the given speed(in Hz) : ",round(fdash,1);

Synchronous speed in rpm :  750.0
Slip(in %) :  6.67
Rotor frequeny at the time of starting(in Hz) :  50.0
Rotor frequeny at the given speed(in Hz) :  3.3


## Example 2.3, Page 131¶

In [126]:
#Given data :
P=10;#no. of poles
f=50;#in Hz
N=600;#in rpm
Nr=1440;#in rpm

#Calculations&Results
f=P*N/120;#in Hz
#When P=2
P=2;#no. of poles
Ns=120*f/P;#in rpm
#When P=4
P=4;#no. of poles
Ns=120*f/P;#in rpm
S=(Ns-Nr)*100/Ns;#Slip in %
print "Percentage Slip(in %) : ",(S);
print "No. of poles : ",(S);

Percentage Slip(in %) :  4
No. of poles :  4


## Example 2.4, Page 132¶

In [8]:
#Given data :
P=8;#no. of poles
f=50;#in Hz
fr=1.5;#in Hz

#Calculations
#Formula : fr=S*f
S=fr/f;#slip(unitless)
Ns=120*f/P;#in rpm
#Formula : S=(Ns-Nr)/Ns
Nr=Ns-S*Ns;#in rpm

#Results
print "Motor running speed in rpm : ",round(Nr);
print "Slip(in %):",(S*100);

Motor running speed in rpm :  728.0
Slip(in %): 3.0


## Example 2.5, Page 133¶

In [10]:
#Given data :
P=2;#no. of poles
f=50;#in Hz
S=4.;#in %

#Calculations&Results
#Part (i) :
Ns=f/P;#in rps
Ns=Ns*60;#in rpm
print "Synchronous speed in rpm : ",Ns;
#Part (ii) :
print "Slip = ",(S),"% or ",(S/100);
#Part (iii) :
N=Ns*(1-S/100);#in rpm
print "Actual speed in rpm :",N;

Synchronous speed in rpm :  1500
Slip =  4.0 % or  0.04
Actual speed in rpm : 1440.0


## Example 2.6, Page 133¶

In [11]:
#Given data :
P=4;#no. of poles
f1=50;#in Hz
fdash=1.5;#in Hz

#Calculations
S=fdash/f1;#unitless
print "Slip : ",S;
Ns=120*f1/P;#in rpm
N=Ns*(1-S);#in rpm

#Result
print "Speed of motor in rpm :",N;

Slip :  0.03
Speed of motor in rpm : 1455.0


## Example 2.7, Page 138¶

In [12]:
#Given data :
N=1440;#in rpm

#Calculations&Results
f=50;#in Hz
print "For this speed of 1440 rpm the synchronous speed may be either 1500 rpm or 3000 rpm.";
Ns=1500;#in rpm
P=4;#no. of poles
print "No. of poles : ",P;
Slip=(Ns-N)*100/Ns;#in %
print Slip,"Slip(in %) : ",Slip;
speed1=Ns-N;#Speed of rotor flux with respect to rotor
print "Speed of rotor flux with respect to rotor in rpm : ",speed1;
speed2=(speed1)+N;#Speed of rotor flux with respect to stator
print "Speed of rotor flux with respect to stator in rpm :",speed2;

For this speed of 1440 rpm the synchronous speed may be either 1500 rpm or 3000 rpm.
No. of poles :  4
4 Slip(in %) :  4
Speed of rotor flux with respect to rotor in rpm :  60
Speed of rotor flux with respect to stator in rpm : 1500


## Example 2.8, Page 140¶

In [2]:
from math import pi, sqrt, sin, cos, acos, tan, atan, degrees

#Given data :
E2=100;#in volt
R2=0.05;#in ohm
X2=0.1;#im ohm

#Calculations&Results
E2perphase=E2/sqrt(3);#in volt
#part (a) :
S=0.04;#slip
I2=S*E2perphase/sqrt(R2**2+(S*X2)**2);#in Ampere
print "At 4% slip, Rotor current in Ampere : ",round(I2,2);
fi2=degrees(acos(R2/sqrt(R2**2+(S*X2)**2)));#in degree
print "At 4% slip, Phase angle between rotor voltage and rotor current in degree :",round(fi2,2);
#part (b) :
S=1;#slip
I2=S*E2perphase/sqrt(R2**2+(S*X2)**2);#in Ampere
print "At 100% slip, Rotor current in Ampere : ",round(I2,2);
fi2=degrees(acos(R2/sqrt(R2**2+(S*X2)**2)));#in degree
print "At 100% slip, Phase angle between rotor voltage and rotor current in degree :",round(fi2,2);

At 4% slip, Rotor current in Ampere :  46.04
At 4% slip, Phase angle between rotor voltage and rotor current in degree : 4.57
At 100% slip, Rotor current in Ampere :  516.4
At 100% slip, Phase angle between rotor voltage and rotor current in degree : 63.43


## Example 2.9, Page 141¶

In [3]:
from math import sqrt

#Given data :
E2=100.;#in volt
R2=0.4;#in ohm
X2=2.25;#im ohm

#Calculations
E2perphase=E2/sqrt(3);#in volt
S=4.;#in %
E=(S/100)*E2perphase;#rotor induced emf at a slip=4% in volt
Z2=sqrt(R2**2+((S/100)*X2)**2);
I2=E/Z2;#in Ampere

#Result
print "Rotor current in Ampere : ",round(I2,2);

Rotor current in Ampere :  5.63


## Example 2.10, Page 141¶

In [1]:
from math import pi, sqrt, sin, cos

#Given data :
f=50;#in Hz
R2=0.2;#in ohm
X2=2;#im ohm
E2=60;#in volt

#Calculations&Results
E2perphase=E2/sqrt(3);#in volt
#case (i) : S=1
S=1;#unitless
Z2=sqrt(R2**2+(S*X2)**2);
I2=E2perphase*S/Z2;#in Ampere
print "At standstill : Rotor current in Ampere : ",round(I2,2);
#case (ii) : S=0.1
S=0.1;#unitless
Z2=sqrt(R2**2+(S*X2)**2);
I2=E2perphase*S/Z2;#in Ampere
print "for 10% slip : Rotor current in Ampere : ",round(I2,2);
#case (iii) : S=0.05
S=0.05;#unitless
Z2=sqrt(R2**2+(S*X2)**2);
I2=E2perphase*S/Z2;#in Ampere
print "for 5% slip : Rotor current in Ampere : ",round(I2,2);
#case (iv) : S=0.01
S=0.01;#unitless
Z2=sqrt(R2**2+(S*X2)**2);
I2=E2perphase*S/Z2;#in Ampere
print "for 1% slip : Rotor current in Ampere : ",round(I2,2);
#Note : Answer in the book is wrong for S=0.05 and S=0.01

At standstill : Rotor current in Ampere :  17.23
for 10% slip : Rotor current in Ampere :  12.25
for 5% slip : Rotor current in Ampere :  7.75
for 1% slip : Rotor current in Ampere :  1.72


## Example 2.11, Page 142¶

In [5]:
from math import pi, sqrt, sin, cos

#Given data :
R2=0.5;#in ohm
X=4.5;#im ohm
E=50;#line voltage in volt

#Calculations&Results
Eperphase=E/sqrt(3);#in volt
#part (a) : Sliprings are short circuited
Z2=sqrt(R2**2+X**2);#in ohm
I2=Eperphase/Z2;#in Ampere
print "Sliprings are short circuited, Rotor current in Ampere : ",round(I2,2);
cosfi2=R2/Z2;#unitless
print "Power factor : ",round(cosfi2,2);
#part (b) : Sliprings are connected
R2=0.4;#in ohm
Z2=sqrt(R2**2+X**2);#in ohm
I2=Eperphase/Z2;#in Ampere
print "Sliprings are short circuited, Rotor current in Ampere : ",round(I2,2);
cosfi2=R2/Z2;#unitless
print "Power factor : ",round(cosfi2,2);
#Note : answer of part (a) I2 is not curate in the book.

Sliprings are short circuited, Rotor current in Ampere :  6.38
Power factor :  0.11
Sliprings are short circuited, Rotor current in Ampere :  6.39
Power factor :  0.09


## Example 2.12, Page 146¶

In [22]:
#Given data :
R2=0.02;#in ohm
X2=0.1;#im ohm

#Calculations&Results
#let external resistance per phase = r then R2=R2+r ohm
S=1;#slip at starting
print "Since at start speed is zero and slip is, therefore, unity or R2=X2";
r=X2-R2;#in ohm
print "External resistance per phase added to the rotor circuit in ohms : ",r;

Since at start speed is zero and slip is, therefore, unity or R2=X2
External resistance per phase added to the rotor circuit in ohms :  0.08


## Example 2.13, Page 147¶

In [6]:
from math import pi, sqrt, sin, cos

#Given data :
P=4;#no. of poles
f=50;#in Hz
R2=0.03;#in ohm
X2=0.12;#im ohm

#Calculations&Results
Smax=R2/X2;#unitless
Ns=120*f/P;#in rpm
N=Ns*(1-Smax);#in rpm
print "Speed corresponding to maximum torque(in rpm) :",N;
#alfa=(R2+r)/X2
#Ratio of starting torque to max torque=75/100=2*alfa/(alfa^2+1)
#It gives : 3*alfa^2-8*alfa+3=0
#coefficients :
a=3;b=-8;c=3;
alfa1=(-b+sqrt(b**2-4*a*c))/(2*a);alfa2=(-b-sqrt(b**2-4*a*c))/(2*a);
print "rejecting higher values, alfa = ",round(alfa2,4);
fdash=1.5;#in Hz
r=alfa2*X2-R2;#in ohm;
print "External rotor resistance per phase(in ohm) : ",round(r,4);

Speed corresponding to maximum torque(in rpm) : 1125.0
rejecting higher values, alfa =  0.4514
External rotor resistance per phase(in ohm) :  0.0242


## Example 2.14, Page 147¶

In [26]:
#Given data :
P=4;#no. of poles
f=50;#in Hz
R2=0.024;#in ohm
X2=0.6;#in ohm

#Calculations&Results
Sm=R2/X2;#slip corresponding to max torque
Ns=120*f/P;#in rpm
N=Ns*(1-Sm);#in rpm
print "Speed corresponding to maximum torque in rpm : ",N;

Speed corresponding to maximum torque in rpm :  1440.0


## Example 2.15, Page 148¶

In [28]:
#Given data :
P=6;#no. of poles
f=50;#in Hz
Sf=4.;#in %
R2=0.01;#in ohm
X2=0.05;#im

#Calculations&Results
Ratio=((R2/X2)**2+(Sf/100)**2)/(2*R2*(Sf/100)/X2);#ratio of max torque to full load torque
print "Maximum torque, Tmax=",(Ratio),"Tf";
Sm=R2/X2;#slip corresponding to max torque
Ns=120*f/P;#in rpm
N=Ns*(1-Sm);#in rpm
print "Speed corresponding to maximum torque in rpm : ",N;

Maximum torque, Tmax= 2.6 Tf
Speed corresponding to maximum torque in rpm :  800.0


## Example 2.16, Page 149¶

In [142]:
#Given data :
P=12;#no. of poles
f=50.;#in Hz
R2=0.03;#in ohm
X2=0.5;#im

#Calculations&Results
S=R2/X2;#unitless
Ns=120*f/P;#in rpm
N=Ns*(1-S);#in rpm
print "Speed at maximum torque in rpm : ",N;
S=(Ns-495)/Ns;#slip at 495 rpm speed
Ratio=(2*R2*S/X2)/((R2/X2)**2+S**2);#ratio of max torque to full load torque
print "Ratio of full load torque to max torque(in %) :",round((Ratio*100),1);

Speed at maximum torque in rpm :  470.0
Ratio of full load torque to max torque(in %) : 32.4


## Example 2.17, Page 149¶

In [7]:
from math import pi, sqrt, sin, cos

#Given data :
P=12;#no. of poles
f=50;#in Hz
R2=0.5;#in ohm
N=475.;#in rpm

#Calculations&Results
Ns=120*f/P;#in rpm
S=(Ns-N)/Ns;#unitless
X2=R2/S;#in ohm
#"At maximum torque, Tmax is proportional to 1/2*X2 or 1/20";
# "Ts is proportional to (R2+R)/((R2+R)^2+X2^2)";
# "Also, Ts is proportional to 1(20*3)";
# "Equating the two eqn we have : (0.5*R)/(R2+R)^2+X2^2";
#R^2-59R+70.25=0 :
#coefficients :
a=1;b=-59;c=70.25;
R=(-b-sqrt(b**2-4*a*c))/(2*a);
print "Resistance R to be inserted in series (in ohm) :",round(R,1);
#Note : answer in the book is wrong.

Resistance R to be inserted in series (in ohm) : 1.2


## Example 2.18, Page 150¶

In [144]:
#Given data :
P=4;#no. of poles
f=50;#in Hz
R2=0.04;#in ohm
N=1200.;#in rpm(speed at max torque)

#Calculations
Ns=120*f/P;#in rpm(synchronous speed)
S=(Ns-N)/Ns;#unitless
X2=R2/S;#in ohm
#Starting torque is the torque devloped when S=1: Tst=K*R2/(R2^2+X2^2)
#Let say, m=R2/(R2^2+X2^2) then Tst=K*m
m=R2/(R2**2+X2**2);#assumed

#Results
print "Starting torque, Tst=",round(m,2),"k";
print "Maximum torque, Tm=K/",(2*X2);
print "Thus, Tst in terms of Tm can be expressed as : ";
print "Tst/Tm=",(0.96*0.4)," or Tst=",(0.96*0.4),"Tm";
print "Therefore, staring torque is ",(0.96*0.4*100),"% of maximum torque.";

Starting torque, Tst= 0.96 k
Maximum torque, Tm=K/ 0.4
Thus, Tst in terms of Tm can be expressed as :
Tst/Tm= 0.384  or Tst= 0.384 Tm
Therefore, staring torque is  38.4 % of maximum torque.


## Example 2.19, Page 155¶

In [146]:
#Given data :
P=6;#no. of poles
f=50;#in Hz
fr=3.;#in Hz
R2=0.5;#in ohm
N=475;#in rpm
RotorInput=111.9;#in KW

#Calculations&Results
Ns=120*f/P;#in rpm
S=fr*100/f;#unitless
print "% Slip : ",S;
N=Ns*(1-S/100);#in rpm
print "Speed of motor in rpm : ",N;
RotorCopperLoss=RotorInput*S/100;#in KW
RotorCopperLoss=RotorCopperLoss/3;#in KW/Phase
print "Rotor Copper Loss per phase(in KW) : ",RotorCopperLoss;

% Slip :  6.0
Speed of motor in rpm :  940.0
Rotor Copper Loss per phase(in KW) :  2.238


## Example 2.20, Page 156¶

In [40]:
#Given data :
phase=3.;#no. of phase
Pin_stator=60.;#Power input of stator in KW
TotalStatorLosses=1.;#in KW

#Calculations&Results
Pin_rotor=Pin_stator-TotalStatorLosses;#Power input of rotor in KW
S=3.;#slip in %
RotorCopperLosses=(S/100)*Pin_rotor;#in KW
RotorCopperLosses=RotorCopperLosses/phase;#in KW per phase
print "Rotor Copper Losses per phase(in watts) : ",(RotorCopperLosses*10**3);
TotalMechPowerDev=Pin_rotor*(1-S/100);#in KW
print "Total mechanial power developed(in KW) : ",TotalMechPowerDev;

Rotor Copper Losses per phase(in watts) :  590.0
Total mechanial power developed(in KW) :  57.23


## Example 2.21, Page 156¶

In [147]:
#Given data :
P=6;#no. of poles
S=4.;#slip in %
Output=20;#in KW

#Calculations&Results
FrictionalLoss=250;#in watts
f=50;#in Hz
Ns=120*f/P;#in rpm
N=Ns-Ns*(S/100);#in rpm
print "Speed of motor(in rpm) : ",N;
MechPowerDeveloped=Output*10**3+FrictionalLoss;#in Watts
S=S/100;#unitless
RotorCopperLoss=(S/(1-S))*MechPowerDeveloped;#in watts
print "Rotor Copper Loss(in watts) : ",RotorCopperLoss;

Speed of motor(in rpm) :  960.0
Rotor Copper Loss(in watts) :  843.75


## Example 2.22, Page 157¶

In [148]:
#Given data :
phase=3;#no. of phase
P=6;#no. of poles
Pin_rotor=80;#Power input of rotor in KW
f=50;#in Hz
fdash=100;#alternations per minute

#Calculations&Results
fdash=100./60;#in Hz
S=fdash/f;#unitless
print "Slip : ",round(S,4);
Ns=120*f/P;#synchronous speed in rpm
N=Ns-Ns*S;#in rpm
print "Rotor Speed(in rpm) : ",round(N);
MechPowerDev=Pin_rotor*(1-S)*10**3/735.5;#in H.P.
print "Total mechanial power developed(in KW) : ",round(MechPowerDev,2);
RotorCopperLoss=S*Pin_rotor*10**3;#in watts
print "Rotor Copper Loss(in watts) : ",RotorCopperLoss;
CopperLoss=RotorCopperLoss/phase;#in watts/phase
print "Copper Loss per phase(in watts) : ",round(CopperLoss);
I2=60;#in Ampere
R2=CopperLoss/I2**2;#in ohm
print "Rotor resistance per phase(in ohm) : ",round(R2,3);
#Note : Some answers are not accurate in the book.

Slip :  0.0333
Rotor Speed(in rpm) :  967.0
Total mechanial power developed(in KW) :  105.14
Rotor Copper Loss(in watts) :  2666.66666667
Copper Loss per phase(in watts) :  889.0
Rotor resistance per phase(in ohm) :  0.247


## Example 2.23, Page 158¶

In [149]:
#Given data :
UsefulOutput=55;#in H.P.
MechLosses=2;#in H.P.
Stator_Losses=13.5;#in KW

#Calculations&Results
MechPowerDev=UsefulOutput+MechLosses;#in H.P.
MechPowerDev=MechPowerDev*735.5/1000;#in KW
S=50.;#in %
Pin_Rotor=MechPowerDev/(1-S/100);#in KW
RotorCopperLoss=(S/100)*Pin_Rotor;#in KW
print "Rotor Copper Loss(in KW) : ",round(RotorCopperLoss,2);
Pin_Motor=Pin_Rotor+Stator_Losses;#in KW
Efficiency=UsefulOutput*0.7355/Pin_Motor;#/unitless
print "Effiiency(in %) :",round((Efficiency*100),1);

Rotor Copper Loss(in KW) :  41.92
Effiiency(in %) : 41.6


## Example 2.24, Page 159¶

In [150]:
#Given data :
phase=3;#no. of phase
P=6;#no. of poles
Pin_rotor=80;#Power input of rotor in KW
f=50;#in Hz
fdash=100;#alternations per minute

#Calculations&Results
fdash=100./60;#in Hz
S=fdash/f;#unitless
print "Slip : ",round(S,3);
Ns=120*f/P;#synchronous speed in rpm
N=Ns-Ns*S;#in rpm
print "Rotor Speed(in rpm) : ",round(N);
RotorCopperLoss=S*Pin_rotor*10**3;#in watts
#print "Rotor Copper Loss(in watts) : ",RotorCopperLoss;
CopperLoss=RotorCopperLoss/phase;#in watts/phase
print "Copper Loss per phase(in watts) : ",round(CopperLoss);
I2=60;#in Ampere
R2=CopperLoss/I2**2;#in ohm
print "Rotorresistance per phase(in ohm) : ",round(R2,3);
MechPowerDev=Pin_rotor*(1-S)*10**3/735.5;#in H.P.
print "Total mechanial power developed(in H.P.) : ",round(MechPowerDev,1);
#Note : Some answers are not accurate in the book.

Slip :  0.033
Rotor Speed(in rpm) :  967.0
Copper Loss per phase(in watts) :  889.0
Rotorresistance per phase(in ohm) :  0.247
Total mechanial power developed(in H.P.) :  105.1


## Example 2.25, Page 160¶

In [154]:
#Given data :
Efficiency=0.9;#unitless
Output=50;#in H.P.

#Calculations
#formula : Efficiency=Output/(Output+Losses)
Losses=((1-Efficiency)/Efficiency)*Output*735.5;#in watts
Losses=round(Losses);#round
#Let, Ststor Cu loss = Rotor Cu los = Iron loss=K
#Mechanical Loss = Iron Loss/3 = K/3
#TotalLosses=k+K+K+K/3
K=Losses*3/10;#in watts
Pin_rotor=Output*735.5+Losses;#in watts
Slip=K/Pin_rotor;#unitless

#Results
print "Slip :",round(Slip,3);
print "or ",round((Slip*100)),"%";  #answer differes due to rouding

Slip : 0.03
or  3.0 %


## Example 2.26, Page 160¶

In [155]:
#Given data :
Pin_rotor=20;#Power input of rotor in KW
phase=3;#no. of phase
P=6;#no. of poles
f=50.;#in Hz
N=960;#in rpm(Actual speed of motor)

#Calculations
Ns=120*f/P;#synchronous speed in rpm
S=(Ns-N)/Ns;#unitless
RotorCuLoss=S*Pin_rotor*10**3;#in watts
RotorCuLoss=RotorCuLoss/phase;#in watts/phase
R2=1./3;#in ohm(Rotor resistance per phase)
I2=sqrt(RotorCuLoss/R2);#in Ampere

#Result
print "Motor current per phase(in Ampere) :",round(I2,1);

Motor current per phase(in Ampere) : 28.3


## Example 2.27, Page 161¶

In [156]:
#Given data :
V=500;#in volt
Pout_rotor=20;#Power output of rotor in H.P.
phase=3;#no. of phase
P=6;#no. of poles
f=50;#in Hz
N=995.;#in rpm(Actual speed of motor)
cosfi=0.87;#powerfactor(unitless)

#Calculations&Results
Ns=120*f/P;#synchronous speed in rpm
S=(Ns-N)/Ns;#unitless
print "Slip : ",S;
RotorCuLoss=(S/(1-S))*Pout_rotor*735.5;#in watts
print "Rotor Cu Loss(in watts) : ",round(RotorCuLoss,2);
Pin_rotor=RotorCuLoss/S;#in watts
print "Power input to rotor(in KW) :",round((Pin_rotor/10**3),2);
LineCurrent=Pin_rotor/(sqrt(3)*V*cosfi);#in Ampere
print "Line Current(in A) :",round(LineCurrent,2);
RotorFreq=S*f;#in Hz
print "Rotor Frequency(in Hz) :",RotorFreq;

Slip :  0.005
Rotor Cu Loss(in watts) :  73.92
Power input to rotor(in KW) : 14.78
Line Current(in A) : 19.62
Rotor Frequency(in Hz) : 0.25


## Example 2.28, Page 162¶

In [157]:
#Given data :
phase=3;#no. of phase
Efficiency=90;#in %
Speed=480;#in rpm
VL=400;#in volt
IL=75;#in Ampere
cosfi=0.77;#powerfactor(unitless)
d=0.75;#diameter of pulley in meter

#Calculations
Pin_motor=sqrt(3)*VL*IL*cosfi;#Power input of motor in watts
OutputPower=Pin_motor*Efficiency/100;#in watts
Torque=OutputPower/Omega;#in N-meter
Torque=Torque/9.81;#in Kg-meter
PullOnBelt=Torque/(d/2);#in Kg

#Result
print "Pull On Belt(in Kg.) : ",round(PullOnBelt,2);

Pull On Belt(in Kg.) :  194.74


## Example 2.29, Page 162¶

In [158]:
#Given data :
#At 3% slip
OutputPower=24;#in KW(At 3% slip)
S=3.;#in %

#Calculations
Efficiency=(1-S/100);#unitless
InputPower=OutputPower/Efficiency;#in KW
#At 5% slip
S=5;#in %
Efficiency=(1-S/100);#unitless
OutputPower=InputPower*Efficiency;#in KW

#Result
print "Mechanical power output at a slip of 5%(in KW) : ",round(OutputPower,1);

Mechanical power output at a slip of 5%(in KW) :  24.7


## Example 2.30, Page 162¶

In [159]:
#Given data :
#At 50% speed of synchronous speed
S=50.;#in %
UsefulOutput=55;#in H.P.
MechLoss=2;#in H.P.
StatorLoss=13.5;#in KW

#Calculations&Results
Pout_rotor=UsefulOutput+MechLoss;#in H.P.
Pout_rotor=Pout_rotor*0.7355;#in KW
Efficiency=(1-S/100);#unitless
RotorInputPower=Pout_rotor/Efficiency;#in KW
RotorCuLoss=RotorInputPower-Pout_rotor;#in KW
print "Cu Loss in the rotor circuit(in KW) :",round(RotorCuLoss,2);
TotalLosses=StatorLoss+RotorCuLoss+MechLoss*0.7355;#in KW
MotorEfficiency=UsefulOutput*0.7355/(UsefulOutput*0.7355+TotalLosses);
print "Motor Efficiency(in %) : ",round((MotorEfficiency*100),1);

Cu Loss in the rotor circuit(in KW) : 41.92
Motor Efficiency(in %) :  41.6


## Example 2.31, Page 163¶

In [8]:
from math import pi, sqrt, sin, cos

#Given data :
P=4;#no. of poles
phase=3;#no. of phase
N=1440.;#in rpm(Actual speed of motor)
Power_dev=10;#Power developed in H.P.
VL=400;#in volt
cosfi=0.8;#powerfactor(unitless)
f=50;#in Hz

#Calculations&Results
Ns=120*f/P;#in rpm
S=(Ns-N)/Ns;#fractional slip(unitless)
print "Slip :",S;
Torque=Power_dev*735.5/Omega;#in N-meter
Torque=Torque/9.81;#in Kg-meter
print "Torque(in Kg-meter) :",round(Torque,2);
RotorCuLoss=(S/(1-S))*Power_dev*735.5;#in watts
print "Rotor Cu Loss per phase(in watts) : ",round((RotorCuLoss/3),1);
Pin_rotor=RotorCuLoss/S;#in watts
print "Power input to rotor(in KW) :",round((Pin_rotor/10**3),2);
LineCurrent=Pin_rotor/(sqrt(3)*VL*cosfi);#in Ampere
print "Line Current(in A) :",round(LineCurrent,2);

Slip : 0.04
Torque(in Kg-meter) : 4.97
Rotor Cu Loss per phase(in watts) :  102.2
Power input to rotor(in KW) : 7.66
Line Current(in A) : 13.82


## Example 2.32, Page 164¶

In [161]:
#Given data :
VL=440;#in volt
f=50;#in Hz
P=6;#no. of poles
phase=3;#no. of phase
Pin_rotor=80;#in KW
fr=100;#revolutions/min

#Calculations&Results
fr=100./60;#in Hz
S=fr/f;#slip(unitless)
print "Slip : ",round(S,3);
Ns=120*f/P;#in rpm
N=Ns*(1-S);#in rpm(Speed of Rotor)
print "Rotor speed(in rpm) : ",round(N);
RotorCuLoss=S*Pin_rotor*10**3;#in watts
print "Rotor Cu Loss per phase(in watts) : ",round(RotorCuLoss/phase);
I2=65;#in Ampere
R2=(RotorCuLoss/phase)/I2**2;#in ohm
print "Rotor resistance per phase(in ohm) : ",round(R2,2);
Pout_rotor=Pin_rotor-RotorCuLoss/10**3;#in KW
print "Output power of rotor(in H.P.) : ",round((Pout_rotor/0.735),1);
#Note : answers of few part are not accurate in the book.

Slip :  0.033
Rotor speed(in rpm) :  967.0
Rotor Cu Loss per phase(in watts) :  889.0
Rotor resistance per phase(in ohm) :  0.21
Output power of rotor(in H.P.) :  105.2


## Example 2.33, Page 165¶

In [162]:
#Given data :
VL=440;#in volt
f=50.;#in Hz
P=6;#no. of poles
phase=3;#no. of phase
Pin_rotor=20;#in KW
N=960.;#in rpm(Speed of Motor)

#Calculations
Ns=120*f/P;#in rpm
S=(Ns-N)/Ns;#slip(unitless)
RotorCuLoss=S*Pin_rotor*10**3;#in watts
RotorCuLoss=RotorCuLoss/phase;#in watts/phase
R2=1./3;#Rotor Resistance in ohm per phase
I2=sqrt(RotorCuLoss/R2)

#Result
print "Motor current per phase(in Ampere) :",round(I2,2);

Motor current per phase(in Ampere) : 28.28


## Example 2.34, Page 166¶

In [9]:
from math import pi, sqrt, sin, cos

#Given data :
VL=500;#in volt
f=50;#in Hz
P=6;#no. of poles
phase=3;#no. of phase
Pout_rotor=20;#in H.P.
cosfi=0.87;#power factor
N=995.;#in rpm(Speed of Motor)

#Calculations&Results
Ns=120*f/P;#in rpm
S=(Ns-N)/Ns;#slip(unitless)
print "Slip : ",S;
RotorCuLoss=(S/(1-S))*Pout_rotor*735.5;#in watts
print "Rotor Cu Loss(in watts) :",round(RotorCuLoss,2);
Pin_rotor=RotorCuLoss/S;#in watts
print "Power input to rotor(in KW) :",round((Pin_rotor/10**3),3);
IL=Pin_rotor/(sqrt(3)*VL*cosfi);#in Ampere
print "Line current (in Ampere) :",round(IL,2);
Rotorfreq=S*f;#in Hz
print "Rotor frequency(in Hz) :",round(Rotorfreq,2);

Slip :  0.005
Rotor Cu Loss(in watts) : 73.92
Power input to rotor(in KW) : 14.784
Line current (in Ampere) : 19.62
Rotor frequency(in Hz) : 0.25


## Example 2.35, Page 166¶

In [164]:
#Given data :
f=50;#in Hz
P=4;#no. of poles
phase=3;#no. of phase
Efficiency=85.;#in %
OutputPower=17.;#in KW
OutputPower=17*10**3;#in watts
StatorLosses=900.;#in watt
MechLosses=1100;#in watt

#Calculations&Results
Pin=OutputPower/(Efficiency/100);#in watts
#Stator input or rotor input :
Pin_rotor=Pin-StatorLosses;#in watts
P_MechDev=OutputPower+MechLosses;#in watts
RotorCuLosses=Pin_rotor-P_MechDev;#in watts
S=RotorCuLosses/Pin_rotor;#slip(unitless)
print "Slip :",round(S,3);
Ns=120*f/P
N=Ns*(1-S);#in rpm(Speed of Motor)
Torque=P_MechDev/Omega;#in Nm
print "Torque developed(in Nm) :",round(Torque,1);
Tm=OutputPower/Omega;#in Nm
Tm=Tm/9.81;#in Kg-meter
print "Torque at the shaft(in Kg-meter) :",round(Tm,2);

Slip : 0.052
Torque developed(in Nm) : 121.6
Torque at the shaft(in Kg-meter) : 11.64


## Example 2.36, Page 168¶

In [165]:
#Given data :
VL=500;#in volt
f=50;#in Hz
P=6;#no. of poles
phase=3;#no. of phase
Pin_stator=50;#in KW
Statorlosses=2;#in KW
MechLosses=1;#in KW

#Calculations&Results
Pin_rotor=Pin_stator-Statorlosses;#in KW
S=3.;#in %
RotorI2RLoss=(S/100)*Pin_rotor;#in KW
print "Rotor I2R Loss(in KW) :",RotorI2RLoss;
print "Rotor core loss at 3% slip is very less and can be neglected.";
Power_dev=Pin_rotor-RotorI2RLoss;#in KW
print "Power developed by the rotor(in H.P.) : ",round((Power_dev/0.7355),1);
Outputpower=Power_dev-MechLosses;#in KW
Efficiency=Outputpower/Pin_stator;#unitless
print "Efficiency of the motor(in %) :",(Efficiency*100);

Rotor I2R Loss(in KW) : 1.44
Rotor core loss at 3% slip is very less and can be neglected.
Power developed by the rotor(in H.P.) :  63.3
Efficiency of the motor(in %) : 91.12


## Example 2.37, Page 168¶

In [80]:
#Given data :
f=50;#in Hz
P=4;#no. of poles
phase=3;#no. of phase
MotorOutput=20;#in H.P.
MotorOutput=20*735.5;#in watts
MechLosses=500;#in watts

#Calculations&Results
Pdev_rotor=MotorOutput+MechLosses;#in watts
S=S/100;#fractional slip
RotorI2RLoss=(S/(1-S))*Pdev_rotor;#in watts
print "Rotor I2R Loss(in watts) :",RotorI2RLoss;
Ns=120*f/P;#in rpm
Nr=Ns-Ns*S;#in rpm
print "Rotor speed(in rpm) :",Nr;

Rotor I2R Loss(in watts) : 633.75
Rotor speed(in rpm) : 1440.0


## Example 2.38, Page 169¶

In [166]:
from math import pi, sqrt, sin, cos

#Given data :
f=50;#in Hz
P=6;#no. of poles
phase=3;#no. of phase
R2=0.02;#in ohm
X2=0.1;#in ohm

#Calculations
S=R2/X2;#slip(unitless)
Ns=120*f/P;#in rpm
Nr=Ns-Ns*S;#in rpm
#At starting S=1
S=1;#slip
#Formula : T=K*S*R2/(R2^2+X2^2)
#Starting torque, Tst=K*R2/(R2^2+S^2*X2^2)
#Maximum torque, Tm=K/(2*X2)
#Tst=(2/3)*Tm : gives a equation
#100*R2^2-30*R2+1=0
a=100;b=-30;c=1;
R21=(-b+sqrt(b**2-4*a*c))/(2*a);#in ohm
R22=(-b-sqrt(b**2-4*a*c))/(2*a);#in ohm
#This R2 is the value of rotor circuit resistance.
RotWinResistance=0.02;#in ohm per phase
Extra_R1=R21-RotWinResistance;#in ohm
Extra_R2=R22-RotWinResistance;#in ohm

#Result
print "Extra Resistance(in ohm) : ",round(Extra_R1,3)," ohm or ",round((Extra_R2),3)," ohm.";

Extra Resistance(in ohm) :  0.242  ohm or  0.018  ohm.


## Example 2.39, Page 170¶

In [167]:
#Given data :
f=50;#in Hz
P=4;#no. of poles
phase=3;#no. of phase
MotorShaftOutput=20;#in H.P.

#Calculations&Results
MotorShaftOutput=20*735.5;#in watts
MechLosses=MotorShaftOutput*2/100;#in watts(2% of the output)
Pdev_rotor=MotorShaftOutput+MechLosses;#in watts
S=3.;#slip in %
S=S/100;#fractional slip
RotorI2RLoss=(S/(1-S))*Pdev_rotor;#in watts
print "Rotor I2R Loss(in watts) :",round(RotorI2RLoss);
print "Rotor iron loss at 3% slip is very small and can be neglected.";
RotorInput=Pdev_rotor+RotorI2RLoss;#in watts
print "Rotor Input(in Watts) :",round(RotorInput,1);
Ns=120*f/P;#in rpm
Nr=Ns-Ns*S;#in rpm
Nr=Nr/60;#in rps
T=MotorShaftOutput/(2*pi*Nr);#in Nm
print "Output torque(in Nm) : ",round(T,2);

Rotor I2R Loss(in watts) : 464.0
Rotor iron loss at 3% slip is very small and can be neglected.
Rotor Input(in Watts) : 15468.2
Output torque(in Nm) :  96.54


## Example 2.40, Page 171¶

In [168]:
#Given data :
VL=500;#in volt
f=50;#in Hz
P=6;#no. of poles
phase=3;#no. of phase
Nr=975.;#in rpm

#Calculations&Results
Ns=120*f/P;#in rpm
S=(Ns-Nr)/Ns;#slip
print "Slip :",S;
Pin_stator=40;#in KW
StatorLosses=1;#in KW
Pin_rotor=Pin_stator-StatorLosses;#in KW
RotorCuLosses=S*Pin_rotor;#in KW
print "Rotor Cu Losses(in KW) :",RotorCuLosses;
RotorOutput=Pin_rotor-RotorCuLosses;#in KW
OutputHP=RotorOutput/0.735;#in H.P.
print "Output Horse Power : ",round(OutputHP,2);
Efficiency=RotorOutput/Pin_stator;#unitless
print "Efficiency(in %) :",round(Efficiency*100);

Slip : 0.025
Rotor Cu Losses(in KW) : 0.975
Output Horse Power :  51.73
Efficiency(in %) : 95.0


## Example 2.41, Page 172¶

In [169]:
#Given data :
VL=440;#in volt
f=50.;#in Hz
P=6;#no. of poles
phase=3.;#no. of phase

#Calculations&Results
Ns=120*f/P;#in rpm
fr=120;#alternations per minute
fr=fr/60;#in Hz
S=fr/f;#slip
print "Slip : ",S;
Nr=Ns-S*Ns;#in rpm
print "Rotor speed(in rpm) :",Nr;
Rotor_input=80;#in KW
RotorCuLoss=S*Rotor_input;#in KW
print "Rotor Cu Loss per phase(in watts) :",round((RotorCuLoss*10**3)/phase);
P_Mechdev=Rotor_input*10**3-RotorCuLoss*10**3;#in watts
P_Mechdev=P_Mechdev/735.5;#in H.P.
print "Mechanical power devloped(in H.P.) :",round(P_Mechdev,1);
Ir=60;#in Ampere
R2=(RotorCuLoss*10**3/phase)/Ir**2;#in ohm
print "Rotor resistance per phase(in ohm) :",round(R2,3);

Slip :  0.04
Rotor speed(in rpm) : 960.0
Rotor Cu Loss per phase(in watts) : 1067.0
Mechanical power devloped(in H.P.) : 104.4
Rotor resistance per phase(in ohm) : 0.296


## Example 2.43, Page 175¶

In [91]:
#Given data :
f=50.;#in Hz
P=6;#no. of poles
R2=0.2;#rotor resistance per phase in ohm
Nr=960;#in rpm
Nr_dash=600;#in rpm

#Calculations
Ns=120*f/P;#in rpm
S=(Ns-Nr)/Ns;#slip(unitless)
Sdash=(Ns-Nr_dash)/Ns;#slip(unitless)
#Let the new value of resistance is R2dash=(R+0.2)
R=R2*(Sdash/S)-R2;#Resistance to be added in ohm

#Result
print "Resistance to be added(in ohm) : ",R;

Resistance to be added(in ohm) :  1.8


## Example 2.44, Page 176¶

In [92]:
#Given data :
f=50;#in Hz
P=6;#no. of poles
phase=3;#no. of phase
RotorIntResistance=0.1;#in ohm per phase
X2=1;#in ohm/phase

#Calculation
Rext=X2-RotorIntResistance;#in ohm

#Result
print "External resistance to be included(in ohm/phase) : ",Rext;

External resistance to be included(in ohm/phase) :  0.9


## Example 2.45, Page 176¶

In [97]:
#Given data :
f=50.;#in Hz
P=6.;#no. of poles
phase=3.;#no. of phase
R2=0.2;#rotor resistance per phase in ohm

#Calculations
Ns=120*f/P;#in rpm
N2=N1*(1-10./100);#New speed in rpm(reduced 10%)
S2=(Ns-N2)/Ns;#New slip(unitless)
#Formula : S=RotorCuLoss/Pin_rotor=3*I2^2*R2/Pin_rotor
#Let the additional resistance is R
R=R2*S2/S1-R2;#Resistance to be added in ohm

#Result
print "Additional Rotor Resistance(in ohm) : ",R;

Additional Rotor Resistance(in ohm) :  0.48


## Example 2.46, Page 180¶

In [171]:
#Given data :
R2inner=0.4;#in ohm
X2inner=2;#in ohm
R2outer=2;#in ohm
X2outer=0.4;#in ohm
#At standstill :
S=1;#unitless

#Calculations&Results
Ratio=(R2outer*S/(R2outer**2+S**2*X2outer**2))/(R2inner*S/(R2inner**2+S**2*X2inner**2));#unitless
print "Ratio of torque produced by two cages at standstill : ",Ratio;
S=5;#in %
S=5./100;#fractional
Ratio=(R2outer*S/(R2outer**2+S**2*X2outer**2))/(R2inner*S/(R2inner**2+S**2*X2inner**2));#unitless
print "Ratio of torque produced by two cages at full load(slip=5%) : ",round(Ratio,2);

Ratio of torque produced by two cages at standstill :  5.0
Ratio of torque produced by two cages at full load(slip=5%) :  0.21


## Example 2.47, Page 187¶

In [10]:
from math import sqrt

#Given data :
Output=10;#in H.P.
Output=Output*735.5;#in watts
cosfi=0.8;#unitless
ETA=0.83;#unitless
ISCbyIFL=3.5;#ratio of SC current to full load current
VL=500;#in volt

#Calculations
Input=Output/ETA;#in watts
IFL=Input/(sqrt(3)*VL*cosfi);#in Ampere
ISC=IFL*ISCbyIFL;#in Ampere
Is=ISC/3;#in Ampere

#Result
print "Strting current(in Ampere) :",round(Is,2);

Strting current(in Ampere) : 14.92


## Example 2.48, Page 187¶

In [173]:
#Given data :
ISCbyIFL=5;#ratio of SC current to full load current

#Calculations&Results
#(i) for star delta starter :
print "for star delta starter : ";
Ratio=(1./3)*(ISCbyIFL)**2*S;#Ratio of starting torque to full load torque
print "Starting torque is ",round((Ratio*100),2),"% of full load torque.";
#(i) for auto transformer starter :
print "for auto transformer starter : ";
K=50./100;#tappings
Ratio=K**2*(ISCbyIFL)**2*S;#Ratio of starting torque to full load torque
print "Starting torque is ",(Ratio*100),"% of full load torque.";

for star delta starter :
Starting torque is  33.33 % of full load torque.
for auto transformer starter :
Starting torque is  25.0 % of full load torque.


## Example 2.49, Page 188¶

In [174]:
#Given data :
ISCbyIFL=4;#ratio of SC current to full load current
TsBYTf=1./4;#ratio of atarting torque to full load torque
Slip=3;#in %
Slip=3./100;#in fraction

#Calculations
#Formula : TsBYTf=Percent_Tapping^2*ISCbyIFL^2*Slip
tapping=sqrt(TsBYTf/(Slip*ISCbyIFL**2));#in %

#Result
print "Tapping(in %) :",round((tapping*100),1);

Tapping(in %) : 72.2


## Example 2.50, Page 189¶

In [175]:
#Given data :
ISCbyIFL=5.;#ratio of SC current to full load current
Slip=5;#in %
Slip=5./100;#in fraction

#Calculations
#Formula : 3*IFL=K^2*ISC
K=sqrt(1./(ISCbyIFL/3));#unitless
TsBYTfl=K**2*(ISCbyIFL)**2*Slip;#ratio of starting torque to full load torque

#Result
print "Starting torque is ",(TsBYTfl*100),"% of full load torque.";

Starting torque is  75.0 % of full load torque.


## Example 2.51, Page 189¶

In [176]:
#Given data :
print "Star delta starter :";
ISCbyIFL=6;#ratio of SC current to full load current
Slip=4;#in %
Slip=4./100;#in fraction

#Calculations&Results
TsBYTfl=(1./3)*(ISCbyIFL)**2*Slip;#ratio of starting torque to full load torque
print "Starting torque is ",(TsBYTfl*100),"% of full load value.";
print "For an auto transformer :";
K=70.70;#in %
K=70.70/100;#in fraction
TsBYTfl=K**2*(ISCbyIFL)**2*Slip;#ratio of starting torque to full load torque
print "Starting torque is ",round(TsBYTfl*100),"% of full load torque.";

Star delta starter :
Starting torque is  48.0 % of full load value.
For an auto transformer :
Starting torque is  72.0 % of full load torque.


## Example 2.52, Page 190¶

In [179]:
#Given data :
V=400.;#in volt
S=3.5;#in %
S=3.5/100;#in fraction
VL=92;#in volts

#Calculations&Results
#ISC=(V/VL)*IFL;#in Ampere
ISCbyIFL=V/VL;#ratio of SC current to full load current
#2*IFL=K^2*ISC imples that 2*IFL=K^2*(V/VL)*IFL
K=sqrt(2./(V/VL));#in fraction
print "Necessary tapping(in %) :",round((K*100),1);
TsBYTfl=K**2*(ISCbyIFL)**2*S;#ratio of starting torque to full load torque
print "Starting torque is ",round((TsBYTfl*100),1),"% of full load value.";

Necessary tapping(in %) : 67.8
Starting torque is  30.4 % of full load value.


## Example 2.53, Page 190¶

In [180]:
#Given data :
ISCbyIFL=4;#ratio of SC current to full load current
ISbyIFL=2;#ratio of Supply current to full load current
S=2.5;#in %
S=2.5/100;#in fraction

#Calculations
#Formula : ISbyIFL=(1/K^2)*ISCbyIFL
K=sqrt(ISCbyIFL/ISbyIFL);#in fraction
print "Auto Transormation ratio :",round(K,2);
TsBYTfl=(1./K**2)*(ISCbyIFL)**2*S;#ratio of starting torque to full load torque

#Results
print "Ratio of starting torque to full load torque :",TsBYTfl;
print "or Starting torque is ",(TsBYTfl*100),"% of full load value.";

Auto Transormation ratio : 1.41
Ratio of starting torque to full load torque : 0.2
or Starting torque is  20.0 % of full load value.


## Example 2.54, Page 191¶

In [181]:
#Given data :
ISCbyIFL=4;#ratio of SC current to full load current
S=3;#in %
S=3./100;#in fraction
TsBYTfl=1./4;#ratio of starting torque to full load torque

#Calculations
#Formula : TsBYTfl=ISCbyIFL^2*K^2*S
K=sqrt(TsBYTfl/(ISCbyIFL**2*S));#in fraction

#Result
print "Auto Transormation ratio(in %) :",round((K*100),2);

Auto Transormation ratio(in %) : 72.17


## Example 2.55, Page 191¶

In [11]:
from math import sqrt

#Given data :
Output=3;#in H.P.
Output=3*735.5;#in watts
Efficiency=0.83;#unitless
cosfi=0.8;#power factor

#Calculations
Vl=500;#in volt
Input=Output/Efficiency;#in watts
#Formula : Input=sqrt(3)*Vl*Il*cosfi
Il=Input/(sqrt(3)*Vl*cosfi);#in Ampere
ISCbyIFL=3.5;#ratio of SC current to full load current
ISC=ISCbyIFL*Il;#in Ampere
LineCurrent=ISC/3;#in Ampere(for star delta starter)

#Result
print "Line Current(in Ampere) :",round(LineCurrent,2);
#Note : Ans in the book is not accurate.

Line Current(in Ampere) : 4.48


## Example 2.56, Page 192¶

In [12]:
from math import sqrt

#Given data :
Output=15;#in H.P.
Output=15*735.5;#in watts
Vl=400;#in volt
ISCat200=40;#in Ampere(at 200 volt)
Efficiency=0.88;#unitless
cosfi=0.85;#power factor

#Calculations
ISCat400=ISCat200*(400./200);#in Ampere(at 400 volt)
Input=Output/Efficiency;#in watts
Ifl=Input/(sqrt(3)*Vl*cosfi);#in Ampere
#starting line current with star delta starter
Is=ISCat400/3;#in Ampere
Ratio=Is/Ifl;#ratio of starting current to full load current

#Result
print "Ratio of line current at starting to full load current :",round(Ratio,2);

Ratio of line current at starting to full load current : 1.25


## Example 2.57, Page 192¶

In [13]:
from math import sqrt

#Given data :
#With star delta starter :
TstBYTfl=0.35;#ratio of starting torque to full load torque
IstBYIfl=1.75;#ratio of starting current to full load current

#Calculations&Results
ISCBYIs=sqrt(3);#ratio of SC current to starting current
ISCBYIfl=sqrt(3)*IstBYIfl;#ratio of SC current to full load current
#Formula : TstBYTfl=(ISCBYIfl)^2*S
S=TstBYTfl/(ISCBYIfl)**2;#in fraction
print "Full load Slip : ",round(S,3);
#With auto transformer with winding in delta :
Ip=sqrt(3)*1.750*0.8;#full voltage phase current in Ampere
IlBYIf=4.2;#ratio of Line current to full load current
Ratio=IlBYIf**2*S;#ratio of starting current to full load current
print "Ratio of line current at starting to full load current :",round(Ratio,2);

Full load Slip :  0.038
Ratio of line current at starting to full load current : 0.67


## Example 2.58, Page 196¶

In [114]:
#Given data :
f=50;#in Hz
P=4;#no. of poles
phase=3;#no. of phase
R2=0.25;#in ohm per phase
S=2;#in %
S=2./100;#in fraction

#Calculations
Ns=120*f/P;#in rpm
Nr=Ns-Ns*S;#in rpm
#When speed reduced to 10%
NewSpeed=Nr*90/100;#in rpm
Sdash=(Ns-NewSpeed)/Ns;#in fraction
R2dash=(Sdash/S)*R2;#in ohm per phase
R=R2dash-R2;#in ohm

#Result
print "Value of resistance to be added(in ohm) :",R;

Value of resistance to be added(in ohm) : 1.225


## Example 2.59, Page 197¶

In [194]:
#Given data :
f=50;#in Hz
P=4;#no. of poles
R2=0.25;#in ohm per phase
NewSpeed=1200;#in rpm

#Calculations&Results
Ns=120*f/P;#in rpm
S=(Ns-N)/Ns;#in %
NewS=(Ns-NewSpeed)/Ns;#in fraction
S1=S;S2=NewS;#slip new and old
#Torque remaining same : S1/R2=S2/(R2+R)
R=S2*R2/S1-R2;#in ohm
print "External resistance per phase(in ohm) :",R;  #incorrect answer in textbook
Nr=Ns-Ns*S;#in rpm
#If S1 is taken as 0.03 and S2 as 0.127
S1=0.03;#slip in fraction
S2=0.127;#slip in fraction
R=S2*R2/S1-R2;#in ohm
print "External resistance per phase(in ohm) :",round(R,3);

External resistance per phase(in ohm) : -0.25
External resistance per phase(in ohm) : 0.808


## Example 2.60, Page 198¶

In [118]:
#Given data :
f=50;#in Hz
P=4;#no. of poles
phase=3;#no. of phase
S=4;#in %
S=4./100;#in fraction

#Calculations&Results
Ns=120*f/P;#in rpm
N1=Ns-Ns*S;#in rpm
#When speed reduced to 10%
N2=N1*85/100;#in rpm(NewSpeed)
print "New speed(in rpm) :",N2;
#New speed is reduced by 15 %
Sdash=(Ns-N2)/Ns;#in fraction
print "New Slip : ",Sdash;

New speed(in rpm) : 1224.0
New Slip :  0.184


## Example 2.61, Page 202¶

In [195]:
#Given data :
f=50;#in Hz
P=4;#no. of poles
phase=3;#no. of phase
Pin=60;#in KW
StatorLoss=1.2;#in KW
WindingLoss=1.8;#in KW
S=4;#in %
S=4./100;#in fraction

#Calculations&Results
Ns=120*f/P;#in rpm
Nr=Ns-Ns*S;#in rpm
print "Rotor speed(in rpm) :",Nr;
Pin_rotor=Pin-StatorLoss;#in KW
RotorCuLoss=S*Pin_rotor;#in KW
print "Rotor Cu Loss(in KW) : ",RotorCuLoss;
Pout_rotor=Pin_rotor-WindingLoss-RotorCuLoss;#in KW
Efficiency=(Pout_rotor/Pin)*100;#in %
print "Efficiency(in %) :",round(Efficiency);
HP=Pout_rotor*10**3/735.5;#in H.P.
print "Horse Power(inH.P.) :",round(HP,2);

Rotor speed(in rpm) : 1440.0
Rotor Cu Loss(in KW) :  2.352
Efficiency(in %) : 91.0
Horse Power(inH.P.) : 74.3