Chapter 11: Induction Motors

Example 1: pg 363

In [1]:
#pg 363
#calculate the synchronous speed, speed and rotor current
#  Given data
P = 4.;
f = 50.;#  in Hz
s = 4.;
#calculations
Ns = (120*f)/P;#  in rpm
# s = ((Ns-N)/Ns)*100;
N = Ns - ( (s*Ns)/100. );#  in rpm
print "The speed of the motor in rpm is",N
N = 1000.;#  in rpm
s = ((Ns-N)/Ns);
f_desh= s*f;#  in Hz
#results
print "The synchronous speed in rpm is",Ns
print "The rotor current frequency in Hz is",round(f_desh,1)

The speed of the motor in rpm is 1440.0
The synchronous speed in rpm is 1500.0
The rotor current frequency in Hz is 16.7

Example 2: pg 363

In [2]:
#pg 363
#calculate the slip and speed
#  Given data
f = 50.;#  in Hz
P = 4.;
f_DASH = 2;#  in Hz
#calculations
#  f_DASH = s*f;
s = (f_DASH/f)*100;#  in %
N_S = (120*f)/P;#  in rpm
#  s = (N_S-N)/N_S;
N = N_S - (s/100*N_S);#  in rpm
#results
print "The slip in percentage is",s
print "The speed of the motor in rpm is",N
print 'The answer is a bit different due to rounding off error in textbook'

The slip in percentage is 4.0
The speed of the motor in rpm is 1440.0
The answer is a bit different due to rounding off error in textbook

Example 3: pg 364

In [3]:
#pg 364
#calculate the speed, frequency
#  Given data
P = 6.;
f = 50.;#  in Hz
Snl = 1./100;
Sfl = 3./100;
#calculations
N_S = (120.*f)/P;#  in rpm
print "The synchronous speed in rpm is",N_S
Nnl = N_S*(1-Snl);#  in rpm
print "No load speed in rpm is",Nnl
Nfl = N_S*(1-Sfl);#  in rpm.. correction 
print "The full load speed in rpm is",Nfl
#  frequency of rotor current 
s = 1;
Sf = s*f;#  in Hz
print "The frequency of rotor current in Hz is",Sf
#  frequency of rotor current at full load 
f_r = Sfl * f;#  in Hz
print "The frequency of rotor current at full load in Hz is",f_r

print 'Note : The calculated value of Nnl is wrong and value of Nfl is correct but at last they printed wrong.'

The synchronous speed in rpm is 1000.0
No load speed in rpm is 990.0
The full load speed in rpm is 970.0
The frequency of rotor current in Hz is 50.0
The frequency of rotor current at full load in Hz is 1.5
Note : The calculated value of Nnl is wrong and value of Nfl is correct but at last they printed wrong.

Example 4: pg 364

In [4]:
#pg 364
#calculate the numbers and percentage slip
#  Given data
Pa= 12.;
N= 1440.;#  in rpm
Na= 500.;#  in rpm
Nm= 1450.;#  in rpm
#calculations
fa= Pa*Na/120;#  in Hz
Pm= round(120*fa/Nm);
#  Synchronous speed of motor
Ns= 120*fa/Pm;#  in rpm
s= (Ns-N)/Ns*100;#  in percentage
#results
print "The numbers of pole is : ",Pm
print "The percentage slip is : ",s

The numbers of pole is :  4.0
The percentage slip is :  4.0

Example 5: pg 365

In [5]:
#pg 365
#calculate the frequency, induced emf
#  Given data
from math import sqrt
K = 1./2;
P = 4.;
f = 50.;#  in Hz
N = 1445.;#  in rpm
E1line = 415.;#  in V
N = 1455.;#  in rpm
#calculations
Ns = (120*f)/P;#  in rpm
s = (Ns-N)/Ns*100;#  in %
f_r = s/100*f;#  in Hz
print "The frequency of rotor in Hz is",f_r
E1ph = E1line/sqrt(3);#  in V
# E2ph/E1ph = K;
E2ph = E1ph*K;#  in V
print "The magnitude of induced emf in V is",round(E2ph,1)
E2r = s/100*E2ph;#  in V
print "The magnitude of induced emf in the running condition in V is",round(E2r,3)

The frequency of rotor in Hz is 1.5
The magnitude of induced emf in V is 119.8
The magnitude of induced emf in the running condition in V is 3.594

Example 6: pg 366

In [6]:
#pg 366
#calculate the rotor speed, frequency and Ns
#  Given data
P = 4.;
S =4./100;
f = 50.;#  in Hz
#calculations
Ns = (120*f/P);#  in rpm
print "The value of Ns in rpm is",Ns
#  The rotor speed when slip is 4 %
N = Ns*(1-S);#  in rpm
print "The rotor speed when slip is 4 percent in rpm is",N
#  The rotor speed when rotor runs at 600 rpm
N1 = 600;#  in rpm
s1 = ((Ns-N1)/Ns)*100;#  in %
f_r = (s1/100)*f;#  in Hz
print "The rotor frequency when rotor runs at 600 rpm in Hz is",f_r

The value of Ns in rpm is 1500.0
The rotor speed when slip is 4 percent in rpm is 1440.0
The rotor frequency when rotor runs at 600 rpm in Hz is 30.0

Example 7: pg 366

In [7]:
#pg 366
#calculate the poles, full load slip, induced voltage and frequency
#  Given data
V_L = 230.;#  in V
f = 50.;#  in Hz
N = 950.;#  in rpm
E2 = 100.;#  in V
Ns =1000.;#  in rpm
#calculations
#  Ns = 120*f/P;
P = (120*f)/Ns;
print "The Number of poles is",P
s = ((Ns-N)/Ns)*100;#  %s in %
print "The percentage of full load slip in percent is",s
#  The rotor induced voltage at full load
E2r = (s/100)*E2;#  in V
print "The rotor induced voltage in V is",E2r
#  The rotor frequency at full load
f_r = (s/100)*f;#  in Hz
print "The frequency at full load in Hz is",f_r

The Number of poles is 6.0
The percentage of full load slip in percent is 5.0
The rotor induced voltage in V is 5.0
The frequency at full load in Hz is 2.5

Example 8: pg 367

In [8]:
#pg 367
#calculate the poles, speed, emf and frequency
#  Given data
V = 440.;#  in V
f = 50.;#  in Hz
N = 1450.;#  in rpm
Ns = 1450.;#  in rpm
Nr = 1450.;#  in rpm
#calculations
P = round((120*f)/Ns);
print "The number of poles in the machine is",P
P = 4;
Ns = (120*f)/P;#  in rpm
print "Speed of rotation air gap field in rpm is",Ns
k = 0.8/1;
# Pemf = k*E1 = k*V;
Pemf = k*V;#  produced emf in rotor in V
print "Produced emf in rotor in V is",Pemf
s = ((Ns-Nr)/Ns)*100;#  in %
Ivoltage = k*(s/100)*V;#  rotor induces voltage in V
f_r = (s/100)*f;#  in Hz
print "The frequency of rotor current in Hz is ",round(f_r,2)

The number of poles in the machine is 4.0
Speed of rotation air gap field in rpm is 1500.0
Produced emf in rotor in V is 352.0
The frequency of rotor current in Hz is  1.67

Example 9: pg 367

In [9]:
#pg 367
#calculate the full load slip, speed
#  Given data
P = 8.;
f = 50.;#  in Hz
f_r = 2.;#  in Hz
#calculations
#  f_r = s*f;
s = (f_r/f)*100;#  in %
#  s = Ns-N/Ns;
Ns = (120*f)/P;#  in rpm
N = Ns*(1-(s/100));#  in rpm
#results
print "The full load slip in percent is",s
print "The corresponding speed in rpm is",N

The full load slip in percent is 4.0
The corresponding speed in rpm is 720.0

Example 10: pg 368

In [10]:
#pg 368
#calculate the speed
#  Given data
R2 = 0.024;#  in per phase
X2 = 0.6;#  in ohm per phase
#calculations
s = R2/X2;
f = 50;#  in Hz
P = 4;
Ns = (120*f)/P;#  in rpm
#  Speed corresponding to maximum torque
N = Ns*(1-s);#  in rpm
#results
print "The speed at which maximum torque is developed in rpm is",N

The speed at which maximum torque is developed in rpm is 1440.0

Example 11: pg 368

In [11]:
#pg 368
#calculate the speed, frequency
#  Given data
P = 4.;
f =60.;#  in Hz
s = 0.03;
#calculations
Ns = (120*f)/P;#  in rpm
N = Ns*(1-s);#  in rpm
print "The synchronous speed in rpm is : ",Ns
print "The rotor speed in rpm is",N
f_r = s*f;#  in Hz
print "The rotor current frequency in Hz is",f_r
#  Rotor magnetic field rorats at speed 
Rm = (120*f_r)/P;#  in rpm
print "The rotor magnetic field rotates at speed in rpm is",Rm

The synchronous speed in rpm is :  1800.0
The rotor speed in rpm is 1746.0
The rotor current frequency in Hz is 1.8
The rotor magnetic field rotates at speed in rpm is 54.0

Example 12: pg 369

In [12]:
#pg 369
#calculate the frequency, poles and speed
#  Given data
N = 960.;#  in rpm
f = 50.;#  in Hz
Ns = 1000.;#  in rpm
#calculations
s = ((Ns-N)/Ns)*100;#  %s in %
print "The slip in percent is",s
f_r = (s/100)*f;#  in Hz
print "The frequency of rotor induced emf in Hz is",f_r
#  Ns = (120*f)/P;
P = (120*f)/Ns;
print "The number of poles is",P
#  Speed of rotor field with respect to rotor structure 
s1 = (120*f_r)/P;# in rpm
print "Speed of rotor field with respect to rotor structure in rpm is",s1

The slip in percent is 4.0
The frequency of rotor induced emf in Hz is 2.0
The number of poles is 6.0
Speed of rotor field with respect to rotor structure in rpm is 40.0

Example 13: pg 369

In [13]:
#pg 369
#calculate the full load speed 
#  Given data
P = 4.;
f = 50.;#  in Hz
Sfl = 4./100;
#calculations
Ns = (120*f)/P;#  in rpm
# The full load speed, Sfl = (Ns-Nfl)/Ns;
Nfl = Ns - (Sfl*Ns);#  in rpm
#results
print "The full load speed in rpm is",Nfl

The full load speed in rpm is 1440.0