# Chapter 7 : Induction Machines¶

## Example 7.1 Page No : 7.4¶

In [1]:
# Variables
P = 4.;				#no. of poles
f = 50;				#Hz
S = 4./100;				#slip
N = 600;				#rpm
p = P/2;				#pair of poles

# Calculations and Results
#(a)
Ns = 60*f/p;				#rpm(Synchronous speed)
print "(a) Synchronous speed(rpm) : %.2f"%Ns

#(b)
Nr = Ns-S*Ns;				#rpm(Rotor speed)
print "(b) Rotor speed(rpm) : %.2f"%Nr

#(c)
Sdash = (Ns-N)/Ns;				#per unot slip
fr = f*Sdash;				#Hz(Rotor frequency)
print "Rotor frequency(Hz) : %.2f"%fr

(a) Synchronous speed(rpm) : 1500.00
(b) Rotor speed(rpm) : 1440.00
Rotor frequency(Hz) : 30.00


## Example 7.2 Page No : 7.4¶

In [3]:
import math

# Variables
Zs = 240.;				#no. of conductors in stator winding
Zr = 48.;				#no. of conductors in rotor winding
Rr = 0.013;				#ohm/phase(ressmath.tance rotor windig)
XL = 0.048;				#ohm/phase(leakega reacmath.tance)
Vs = 400.;				#V

# Calculations and Results
#(a)
Eo = Vs*Zr/Zs;				#V(rotor emf)
print "(a) Rotor emf(V) : %.2f"%Eo

#(b)
S = 4./100;				#slip
Eo = Eo*S;				#V(rotor emf for 4% slip)
print "(b) Rotor emf at 4%% slip(V) :  %.2f"%Eo

Z = math.sqrt(Rr**2+(S*XL)**2);				#ohm/phase(rotor impedence at 4% slip)
Ir = Eo/Z;				#A(Rotor curren at 4% slip)
print "(b) Rotor curren at 4%% slip(A) : %.2f"%Ir

#(c)
fi_r = math.degrees(math.atan(S*XL/Rr));				#degree
print "(c) Phase difference at 4%% slip(degree) : %.2f"%fi_r

S = 100./100;				#100% slip
fi_r = math.degrees(math.atan(S*XL/Rr));				#degree
print "(c) Phase difference at 100%% slip(degree) : %.2f"%fi_r

# note : rounding off error.

(a) Rotor emf(V) : 80.00
(b) Rotor emf at 4% slip(V) :  3.20
(b) Rotor curren at 4% slip(A) : 243.51
(c) Phase difference at 4% slip(degree) : 8.40
(c) Phase difference at 100% slip(degree) : 74.85