In [1]:

```
#Question:
"""Finding the synchronous speed of an induction motor and the frequency of rotor currents at standstill."""
#Variable Declaration:
P=6.0 #Number of poles
f=50.0 #Operating frequency of the induction motor(in Hertz)
s_no_load=0.01 #Slip at no-load
s_full_load=0.03 #Slip at full-load
#Calculations:
Ns=(120.0*f)/P
N_no_load=Ns*(1-s_no_load)
N_full_load=Ns*(1-s_full_load)
s_standstill=1.0
fr_standstill=s_standstill*f
fr_full_load=s_full_load*f
#Result:
print "(a)The synchronous speed is %d rpm." %(Ns)
print "(b)The no-load speed is %d rpm." %(N_no_load)
print "(c)The full-load speed is %d rpm." %(N_full_load)
print "(d)The frequency of rotor-currents at standstill is %.2f Hz." %(fr_standstill)
print "(e)The frequency of rotor-currents at full-load is %.2f Hz." %(fr_full_load)
```

In [2]:

```
#Question:
"""Finding the frequency of rotor-current in an induction motor."""
#Variable Declaration:
P=12.0 #Number of poles
f=50.0 #Operating frequency of induction motor(in Hertz)
N=485.0 #Speed of the motor(in rpm)
#Calculations:
Ns=(120.0*f)/P
s=(Ns-N)/Ns
fr=s*f
#Result:
print "The frequency of the rotor-currents is %.2f Hz." %(fr)
```

In [3]:

```
#Question:
"""Finding the full-load slip and speed of an induction motor."""
#Variable Declaration:
fr=2.0 #Frequency of thr rotoremf at full-load(in Hertz)
f=50.0 #Frequency of the supply(in Hertz)
P=6.0 #Number of poles
#Calculations:
s=fr/f
Ns=(120*f)/P
N=Ns*(1-s)
#Result:
print "The slip at full-load is %.2f percent." %(s*100)
print "The full-load speed is %d rpm." %(N)
```

In [5]:

```
#Question:
"""Finding the synchronous speed and the rotor frequency of an induction motor."""
#Variable Declaration:
f=50.0 #Frequency of the supply(in Hertz)
P=4.0 #Number of poles
#Calculations:
Ns=(120*f)/P
s1=0.04
N1=Ns*(1-s1)
N2=600
s2=(Ns-N2)/Ns
fr=s2*f
#Result:
print "(a)The synchronous speed is %d rpm." %(Ns)
print "(b)The speed of the rotor when the slip is 0.04 is %d rpm." %(N1)
print "(c)The rotor frequency when the speed of the rotor is 600 rpm is %.2f Hz." %(fr)
```

In [17]:

```
#Question:
"""Finding the rotor current of a three-phase induction motor."""
from math import sqrt,pow,acos,radians,degrees
#Variable Declaration:
E_L=100.0 #Induced EMF(in Volts)
R2=0.05 #Resistance of rotor windings(in Ohms)
X_20=0.1 #Standstill reactance of rotor windings(in Ohms)
#Calculations:
E_20=E_L/sqrt(3.0)
s_a=0.04
E2_a=s_a*E_20
Z2_a=sqrt((R2*R2)+pow((s_a*X_20),2))
I2_a=E2_a/Z2_a
angle_a=acos(R2/Z2_a)
s_b=1.0
E2_b=s_b*E_20
Z2_b=sqrt((R2*R2)+pow((s_b*X_20),2))
I2_b=E2_b/Z2_b
angle_b=acos(R2/Z2_b)
#Result:
print "(a)At 4% slip : "
print " The rotor current is %.2f A." %(round(I2_a,2))
print " The phase difference between the rotor voltage and the rotor current is %.2f degrees." %(round(degrees(angle_a),2))
print "\n(b)At 100% slip :"
print " The rotor current is %.2f A." %(round(I2_b,2))
print " The phase difference between the rotor voltage and the rotor current is %.2f degrees." %(round(degrees(angle_b),2))
```

In [11]:

```
#Question:
"""Finding the developed power,air-gap power,rotor copper loss,and stator loss in an induction motor."""
#Variable Declaration:
HP=746.0 #Value of Horse-Power(in Watts)
f=50.0 #Operating frequency of the induction motor(in Hertz)
N=1470.0 #Speed of the motor(in rpm)
P=4.0 #Number of poles
phase=3.0 #Number of phases
effi=87.5e-02 #Efficiency of the motor at full-load
#Calculations:
Po=5.0*HP
Pin=Po/effi
total_loss=Pin-Po
mech_loss=0.05*total_loss
elec_loss=total_loss-mech_loss
dev_pow=Po+mech_loss
Ns=(120*f)/P
s=(Ns-N)/Ns
Pg=dev_pow/(1-s)
P_R=s*Pg
P_S=Pin-Pg
#Result:
print "The developed power is %.2f W." %(round(dev_pow,2))
print "The air-gap power is %.2f W." %(round(Pg,2))
print "The rotor copper loss is %.2f W." %(round(P_R,2))
print "The stator loss is %.2f W." %(round(P_S,2))
```

In [18]:

```
#Question:
"""Finding the rotor speed,the stator current,the power factor and the efficiency of an induction motor. """
from math import sqrt,cos,degrees
from cmath import rect,phase
#Variable Declaration:
V_L=400.0 #Operating voltage of the induction motor(in Volts)
P=4.0 #Number of poles
f=50.0 #Operating frequency of the motor(in Hertz)
s=0.02 #Slip at rated load
rot_loss=0.34e03 #Rotational losses(in Watts)
R1=0.641 #Impedance per phase on the stator side(in Ohms)
X1=1.106 #Impedance per phase on the stator side(in Ohms)
R2_eq=0.332 #Impedance per phase on the stator side(in Ohms)
X_20_eq=0.464 #Impedance per phase on the stator side(in Ohms)
Xg=26.3 #Impedance per phase on the stator side(in Ohms)
#Calculations:
V1_mod=V_L/sqrt(3)
V1=rect(V1_mod,0)
Ns=(120*f)/P
N=Ns*(1-s)
V_Th=V1*((Xg/(R1+(X1+Xg)*1j))*1j)
Z_Th=((Xg*(R1+X1*1j))/(R1+(X1+Xg)*1j))*1j
R_L_eq=((1-s)/s)*R2_eq
I1=V_Th/(Z_Th +(R2_eq+X_20_eq*1j)+R_L_eq)
angle=phase(I1)
pf=cos(angle)
Po=(3*abs(I1)*abs(I1)*R_L_eq)-rot_loss
Pi=3*abs(V1)*abs(I1)*cos(phase(I1))
effi=(Po/Pi)*100
#Result:
print "(a)The rotor speed is %d rpm." %(round(N,0))
print "(b)The stator current is %.2f A at a phase angle of %.2f degrees." %(abs(I1),degrees(phase(I1)))
print "(c)The power factor is %.3f lagging." %(pf)
print "(d)The output power is %.2f W." %(Po)
print " The input power is %.2f W." %(Pi)
print "(e)The efficiency of the motor is %.2f percent." %(effi)
```

In [6]:

```
#Question:
"""Finding the standstill rotor reactance of an induction motor."""
#Variable Declaration:
f=50.0 #Operating frequency of induction motor(in Hertz)
P=6.0 #Number of poles
N=940.0 #Speed of motor(in rpm)
R2=0.1 #Resistance per phase(in Ohms)
#Calculations:
Ns=(120*f)/P
s=(Ns-N)/Ns
X_20=R2/s
#Result:
print "The standstill rotor resistance is %.3f Ohms." %(X_20)
```

In [7]:

```
#Question:
"""Finding the full-load slip of an induction motor."""
#Variable Declaration:
P_motor=6.0 #Number of poles in the induction motor
N_motor=960.0 #Full-load speed of the induction motor(in rpm)
P_alt=4.0 #Number of poles in the alternator
N_alt=1500.0 #Speed of the alternator(in rpm)
#Calculations:
f=(N_alt*P_alt)/120.0
Ns=(120.0*f)/P_motor
s=(Ns-N_motor)/Ns
#Result:
print "The full-load slip of the motor is %.2f percent." %(s*100)
```

In [13]:

```
#Question:
"""Finding the rotor input,motor input and the efficiency of an induction motor."""
from math import pi
#Variable Declaration:
P=4.0 #Number of poles in the induction motor
useful_tor=160.0 #Useful torque(in Newton-metre)
s=0.05 #Slip
P_S=1000.0 #Stator losses(in Watts)
Pm=500.0 #Frictional and windage losses(in Watts)
f=50.0 #Frequency of induction motor(in Hertz)
#Calculations:
Ns=(120.0*f)/P
N=(1-s)*Ns
Po=(2*pi*useful_tor*N)/60.0
Pd=Po+Pm
Pg=Pd/(1-s)
Pin=Pg+P_S
effi=Po/Pin
#Result:
print "(a)The rotor input is %.4f kW." %(Pg/1000.0)
print "(b)The motor input is %.4f W." %(Pin)
print "(c)The efficiency is %.4f percent." %(effi*100)
```

In [8]:

```
#Question:
"""Finding the slip of an induction motor."""
#Variable Declaration:
effi=0.9 #Efficiency of the induction motor
Po=50e03 #Load driven by the motor(in Watts)
#Calculations:
Pin=Po/effi
P_tot=Pin-Po
"""The no-load losses comprise of the stator iron loss(Pi) and mechanical losses(Pm)
(since the stator and rotor copper losses are negligible).These two losses are independent of the load.
Given,the mechanical loss,Pm=(no-load loss)/3.0=((Pi+Pm)/3.0).
Therefore,Pm=(Pi/2.0).
Total loss=(Stator copper loss)+(Stator iron loss)+(Rotor copper loss)+(Mechanical loss)."""
Pi=(2.0/7.0)*P_tot
P_R=Pi
Pm=Pi/2.0
Pd=Po+Pm
Pg=Pd+P_R
s=P_R/Pg
#Result:
print "The slip of the induction motor is %.2f percent." %(s*100)
```

In [10]:

```
#Question:
"""Finding the rotor current in an induction motor."""
from math import sqrt
#Variable Declaration:
V2=100.0 #Induced emf between slip ring terminals(in Volts)
R2=0.4 #Resistance per phase of star-connected rotor windings(in Ohms)
s=0.04 #Slip of rotor
#Calculations:
E20=V2/sqrt(3.0)
"""The rotor reactance X2=(s*X20) is negligible for small values of sand hence cam be ignored."""
I2=(s*E20)/R2
#Result:
print "The rotor current is %.3f A." %(I2)
```

In [3]:

```
#Question:
"""Finding the number of poles and the slip of an induction motor."""
#Variable Declaration:
N=285.0 #Full-load speed of an induction motor(in rpm)
f=50.0 #Frequency of supply(in Hertz)
P_R=250.0 #Original rotor losses(in Watts)
#Calculations:
P=(120.0*f)/N
"There has to be even number of poles,such that Ns>N.Thus,the actual number of poles is 20."""
P=round((P-1),0)
Ns=(120.0*f)/P
s=(Ns-N)/Ns
"""For small values of s,the reactance of (s*X20) is much smaller than the resistance R2,hence
torque is directly proportional to (s/R2).
It means that the to keep the torque same,the (s/R2) ratio should remain the same.If R2 is doubled,then s also has to be
doubled."""
s_new=2*s
"""Since the full-load current remains the same,on doubling the rotor resistance,the copper loss(I*I*R) is also doubled."""
P_R_new=2*P_R
#Result:
print "(a)The number of poles is %d." %(P)
print "(b)The slip is %.2f percent." %(s*100)
print "(c)The slip for full-load torque if the rotor resistance is doubled is %.2f percent." %(s_new*100)
print "(d)The rotor copper losses with added rotor resistance is %.2f W." %(P_R_new)
```

In [7]:

```
#Question:
"""Finding the slip and the power output of an induction motor when external resistances are inserted in each rotor phase."""
#Variable Declaration:
s=0.02 #Full-load slip of the induction motor
Po=500 #Power rating of the motor(in HorsePower)
R2=0.25 #Resistance per phase of the rotor(in Ohms)
#Calculations:
R2_new=2.0+R2
s_new=(s/R2)*(R2_new)
"""If Ns is the synchronous speed of the motor,then the speed of the rotor before inserting external resistance,
N=(1-s)*Ns;
The speed of the rotor after inserting external resistance is N_new=(1-s_new)*Ns;"""
Po_new=((1-s_new)/(1-s))*Po
#Result:
print "The new slip is %.2f percent." %(s_new*100)
print "The new power output is %.2f HP." %(Po_new)
```

In [1]:

```
#Question:
"""Finding the full-load speed of an induction motor."""
from sympy import *;
#Variable Declaration:
P=4.0 #Number of poles in the induction motor
f=50.0 #Rated frequency of the induction motor(in Hertz)
#Calculations:
""" Starting torque(tor_st)=1.6*(tor_fl) where tor_fl=full-load torque;
Maximum torque(tor_max)=2.0*(tor_fl);
tor_st/tor_max=0.8;
(tor_st/tor_max)=(2*s_m)/((s_m*s_m)+1))
(s_m*s_m)-(2.5*s_m)+1=0 is a quadratic equation whose roots are 2 and 0.5
s_m has to be less than 1. Therefore, s_m=0.5;
Similarly,
(tor_fl)/(tor_max)=0.5;
(tor_fl)/(tor_max)=(2*s_fl*s_m)/((s_m*s_m)+(s_fl*s_fl))
Substituting s_m=0.5,we get a quadratic equation,
(s_fl*s_fl)-(s_fl)+0.125=0 whose roots are 0.8535,0.1465.
s_fl=0.1465 as s_fl should be less than s_m. """
"""Finding the roots:"""
s_m,s_fl= symbols('s_m s_fl')
a=solve(s_m**2-(2.5*s_m)+1.0,s_m)
b=solve(s_fl**2-s_fl+0.125, s_fl)
Ns=(120*f)/P
Nfl=Ns*(1-b[0])
Nm=Ns*(1-a[0])
#Result:
print "(a)The full-load speed is %.2f rpm." %(Nfl)
print "(b)The speed at maximum torque is %.2f rpm." %(Nm)
```

In [8]:

```
#Question:
"""Finding the rotor copper loss and the gross torque for an induction motor."""
from math import pi
#Variable Declaration:
s=0.04 #Full-load slip
P=4.0 #Number of poles
f=50.0 #Frequency of the induction motor(in Hertz)
Po=18.65e03 #Power output(in Watts)
#Calculations:
Pm=0.025*Po
Pd=Pm+Po
P_R=Pd*(s/(1-s))
Pg=P_R/s
Ns=(120*f)/P
N=Ns*(1-s)
sh_tor=Po/(2*pi*(N/60.0))
gross_tor=Pd/(2*pi*(N/60.0))
#Result:
print "(a)The rotor copper loss is %.2f W." %(P_R)
print "(b)The rotor input is %.2f W." %(Pg)
print "(c)The output(shaft) torque is %.2f Nm." %(sh_tor)
print "(d)The gross torque is %.2f Nm." %(gross_tor)
```

In [7]:

```
#Question:
"""Finding the rotor current and the rotor power factor for an induction motor."""
from math import sqrt,pow,cos,atan
#Variable Declaration:
P=4.0 #Number of poles in the induction motor
E1=1100.0 #Line voltage(in Volts)
f=50.0 #Operating frequency of the motor(in Hertz)
K=1.0/3.8 #Transformation ratio
R2=0.012 #Rotor resistance per phase(in Ohms)
X20=0.25 #Rotor stanstill reactance per phase(in Ohms)
N=1440.0 #Full-load speed of the motor(in rpm)
#Calculations:
Ns=(120.0*f)/P
s=(Ns-N)/Ns
E20=K*E1
Z20=sqrt((R2*R2)+(X20*X20))
Z2=sqrt((R2*R2)+(s*X20*s*X20))
I20=E20/Z20
pf_20=cos(atan(X20/R2))
I2=(s*E20)/Z2
pf=R2/Z2
I1=100.0/sqrt(3.0)
I_20=I1/K
Z2_rot=E20/I_20
r=sqrt((Z2_rot*Z2_rot)-(X20*X20))-R2
#Result:
print "(a)The rotor current at starting with slip-rings shorted is %.2f A." %(I20)
print "(b)The rotor power factor at starting with slip-rings shorted is %.5f,lagging." %(pf_20)
print "(c)The rotor current while running at full load with slip-rings shorted is %.3f A." %(I2)
print "(d)The rotor power factor while running at full-load with slip-rings shorted is %.5f,lagging." %(pf)
print "(e)The external rotor resistance is %.4f Ohms." %(r)
```