= equivalent reactance due to the power develop by the rotor
S= slip
Rs-1= rotor resistance referred to the stator
X2-1= stator reactance referred to the stator
Induction motor = rotating inductor transformer
IT= stator current/ph
¬IR = rotor current/ph
I2= component of I1 that will supply ¬IR
IN=no load current
I= magnetizing current
r2= rotor resistance/ph
r1= stator resistance/ph
X1= stator leakage reactance/ ph
X2= stator leakage reactance/ ph
Xn= magnetizing reactance

AC MOTORS

Induction motors (1 & 3)
 Is one in which the motor field is induced by currents flowing through the stator. The rotor circuit has no connection whatsoever to supply the circuit. The power factor of this motor is lagging and operate with a lagging pf.

General types of 3 and 1 INDUCED MOTOR

a) Squirrel cage rotor type = its rotor is self contained and resembles a bird cage. The rotor conductors are permanently short circuited by end rings.

Speed characteristic: nearly constant or adjustable speed
Torque characteristic: in general it has medium starting torque
Uses: blower, compressor, pump, prime mover of generators

b) Wound rotor = its rotor has insulated coil of wire and resembles a DC armature. The rotor conductors are connected to slip rings and shorted through branches.

Speed characteristic: variable speed
Torque characteristic: high starting torque
Uses: hoist, crane, escalator, conveyor, elevator, etc.





CIRCUIT DIAGRAM

EΦ= generated voltage per phase volts
NΦ = No. of turns per phase
f = frequency, hertz, cps
Φe = effective flux per pole, wb

Kd = distribution factor (decimal)

KpKd = winding factor

Where:

n = number of slot/pole/phase

d⁰ = no. of electrical degrees per slot

p⁰ = span of coil (electrical degrees) = to coil pitch

Where:
Kp = pitch factor (decimal)

Where:
f = frequency in hertz
P = number of poles
Ns = speed in rpm

Equation of induced emf (3Φ)

Advantages of Rotating Field with Stationary Armature

1. Rotating field is comparatively light and can run with high speed.
2. High voltage can be generate due to high speed and there is very little difficulty in providing high voltage on a stationary part than a moving part.
3. It is easier to insulate armature coils for high pressure usually generated (6.6 to 11 kV). Since the stator is outside the rotor, so more space is available for greater insulation required for armature winding.
4. Very little difficulty is experience in supplying the field magnet current as it is very low in comparison with the armature current.

Relationship among f. P. and N

Two Types of Rotor

1. Salient Pole or Projecting Pole Rotor
- it has large number of poles. It is made of cast iron or steel of good magnetic quality. These type of rotors are use in low speed and medium speed machines. These machines have short axial length and large diameter. Hydropower alternators and diesel engine alternators are of this type.

CONTROL & TESTING OF DC MACHINE

Brake Test:
• It is a method of testing which consists of applying a brakes of a water-cooled fully mounted in the machine itself.

PROBLEM:

Given:
Z = no. of coils = 15 coils
P = no. of poles = 2 poles

# of conductors = 15 x 2 = 30 elements

Progressive lap winding
YB = (Z/P)+1=(30/2)+1=16approx.17

Use: YB = 17 since should always odd #
YB & YF = odd #’s
YB & YF = should differ each other by 2
Since YB = 17 then YF =15
Note*: YF should less than YB for progressive commutator pitch YC=1
No. of commutator segments = no. of coils
YC = +1
Winding Table
1 – 18 – 3 – 20 – 5 – 22 – 7 – 9 – 26
11 – 28 – 13 – 15 – 2 – 17 – 4 – 19
6 – 21 – 8 – 23 – 10 – 25 – 12 – 29 -27
17 – 29 – 16 – 1

SIMPLEX WAVE WINDING DESIGN
1. Both pitcher YB & YF are odd numbers.
2. Back and Front Pitcher are nearly equal to the pole pitch and maybe equal or differ by 2.
3. Resultant Pitch (YR = YB + YF )
4. Commutator Pitch YC = YA
5. The average pitch which must be an integer is given by YA =
Given:
No. of poles = 4
No. of coils = 15

Design a simplex wave winding progressive.

YB = (30+2)/4
YB = 8 approx. 9
YA = YB

for progressive type :
YB > YF
for retrogressive type :
YB < YF

YC = YA = YF

YC = 1 – 8 – 15 – 7 – 14 – 6 – 13 – 5 – 12 – 4 – 11 – 3 – 10 – 2 – 9

Winding Table
1 – 10 – 17 – 26 – 3 – 2 – 19 – 28 – 5 – 14 – 21 – 30
7 – 16 – 23 – 2 – 9 – 18 – 25 – 4 – 11 – 20 – 27 – 6 – 13
29 – 8 – 15 – 24 – 1

When:
YB = YF

1 – 8 – 15 – 22 – 29 – 6 – 13 – 20 – 27 – 4 – 11 – 18 – 25
2 – 9 – 16 – 23 – 30 – 7 – 14 – 21 – 28 – 5 – 12 – 19 – 26
3 – 10 – 17 – 24 - 1

FOR PROGRESSIVE WINDING FOR RETROGRESSING WINDING

YB = (Z/P)+1 YB = (Z/P)-1

YF = (Z/P)+1 YF = (Z/P)+1


Z = no. of conductors or 2 x # of coils
P = no. of poles

Note* : no. of coils = no. of slots

SIMPLEX LAP WINDING DESIGN

1. The back pitch and front pitch core always odd nos. they differ by two and cannot be equal.

2. Both back pitch (YB) and front pitch (YF) should be nearly equal to the pole pitch.


3. Average pitch = (Yb+Yf)/2

4. Commutator pitch YC = +1