Auto-Transformer:

A transformer in which a part of the winding is common to both primary and secondary
circits is called an auto-transtormer.
Types of Auto-Transformers:

Step-Down Auto-Transformer: In this case, the complete winding acts as primary

winding while the tapped section of this winding works as secondary winding as shown
in figure (a). The current in section CB is vector difference of I2 and I1. But as the two
currents are practically in phase opposition, the resultant current is (I2 – I1) where I2, is
greater than I1.
Step-Up Auto-Transformer: In this case, the whole winding works as a secondary
winding and its portion performs the function of primary winding as shown in figure (b).
The current in section CB is vector difference of I1 and I2.But as the two currents are
practically in phase opposition, the resultant current is (I1 – I2) where I2.is less than I1.
Transformation Ratio of an Auto-Transformer:
Power Transter in an Auto-Transformer:
Since the primary and secondary windings of an autotransformer are connected
magnetically as well as electrically, the power from primary is transferred to the
secondary inductively (transformer action) as well as conductively (i.e., directly as
windings are electrically connected).
THREE-PHASE TRANSFORMER:

shows the schemaric diagram of a threephase core type and shell type transformer
respectively. The primary and secondary winding of a three-phase transformer can be
connected in star or delta Hence four main connections are possiblo star-star connection
both the primary and secondary windings are connected in star. The neutral point is
denoted by N for high voltage Winding and n for low voltage winding and the connection
is shown in Fig.(3). The phase current is equal to the line current but the line voltage is
(√3) times the phase voltage in both the primary and secondary winding.For delta-delta
connection both the primary and secondary windings are connected in delta as shown in
Fig.(4) Three-phase shell type Fig.(4). Here the line voltage is equal to phase voltage on
each side.
The phase current is line current divided by (√3).
As compared to a star-star connection for the same terminal voltage and current, a delta-
delta connection has more number of turns in each phase winding but less cross sectional
area of conductors. Hence a delta-delta connection is more transformer economical for
large transformers of relatively lower voltage rating. The star-star connection is not used
in a three-phase three-wire system due to undesirable effects of a third harmonic current.
 INDUCTION MOTOR
Construction:
Stator:
The construction of the stator, i.e. the stationary part of the induction motor is sketched in
Fig. below. To minimize the eddy current loss, the stator in made thin (<0.5 mm)
laminated. A number of slots with teeth are there on the inner periphery of the cylindrical
Structure. The teeth make the slots semi-closed. It makes the insertion of coil winding
Costlier, but the advantages are –
(i) better magnetic condition with uniform reluctance.
(ii) reduction of exciting current.
(iii) increase of power factor.
Three phase stator winding, either star or delta connected, are accommodated in the stator
slots. Ventilating ducts are provided along the length for cooling purpose.

Rotor:
This is the moving part of the induction motor. This is also laminated and provided with
ventilating ducts. The laminations are slotted on the outer periphery to house the rotor
winding. The following two types of rotor are generally used:

Squirrel cage rotor:

The slots for rotor windings are not parallel to the shaft but a bit 'skewed' or tilted
as shown in Fig.(a).
It has the following advantages
(i) magnetic noise is reduced,
(ii) the hazard of magnetic locking of the rotor with the stator is avoided and
(iii) uniform torque is produced.
The rotor bars are short circuited at each end by metallic rings. The structure, as apparent
from Fig.(a), looks like a cage for small pets, such as squirrels. Electrically it is
equivalent to a three-phase winding which is shorted permanently. No external resistance
can be included in it. The view of complete squirrel cage rotor is presented in Fig (b).
Wound rotor:
This is also called slip ring rotor. It consists of three-phase windings on the rotor slots
similar to stator winding. The rotor windings are star-connected and the ends are
connected to slip rings placed on the shaft. Because of the three-phase rotor winding, it is
called 'wound rotor. Additional external resistances can be connected in series with each
rotor phase, as indicated in Fig. (a). This helps in increasing the starting torque and
reducing the starting current. The view of a complete wound rotor is presented in Fig. (b).
Comparision of squirrel cage and wound rotors:

Principle of Operation:
Athree-phase alternating voltage is applied to the stator winding. The three-phase current
flowing through the stator winding produces a magnetic field that rotates in space and
causes the rotor to rotate. The rotor winding is short circuited and acts as a closed
conductor path. The stator field flux cuts it and because of electromagnetic induction, a
voltage is induced in the rotor winding. Since it is a closed circuit, a current flows
through it. According to Lenz's law, this current produces a force on the rotor making it
to move in the same direction as that of the rotating magnetic field of the stator. (Thus is
opposes the cause, i.e. the relative motion between the rotating stator field and the rotor
movement). The rotor rotates in the same direction as that of the stator magnetic field but
not with the same speed as explained below.
When the rotor is just about to move, the frequency of the induced emf in the rotor is
equal to the frequency of supply voltage in the stator. In that case, the rotor speed
becomes equal to the speed of rotation of the stator field flux, known as synchronous
speed.
If P be the number of poles and f be the frequency of the alternating voltage applied to
the stator, then synchronous speed is expressed as - Ns = 120f / P.
But this is not possible to be maintained all the way. When the rotor moves at
synchronous speed, there is no relative motion between this one and the rotating magnetic
field of the stator. No relative motion means no induced voltage and hence no current in
rotor coil. The magnitude of the induced voltage, that causes the rotor movement,
depends on this relative motion. Therefore, when the rotor picks up speed, the speed
becomes less (5%) than the synchronous speed even at no load condition. When the
motor is loaded, the speed falls further causing increase in the relative motion and
thereby increasing the induced voltage, hence torque.
Production of Rotating Field :
Rotor Speed and Slip:
Effect of Slip on Rotor Parameters:
(i)Effect on Frequency of Rotor Voltage and Current:

(ii) Effect on Magnitude of Rotor Induced emf:

(iii) Effect on Rotor Resistance and Reactance:

(iv) Effect on Rotor Current and Rotor Power Factor:

Under Running Condition:

Torque Equation of a 3-Phase Induction Motor:

(i) Starting Torque: