A Brief History of Matlabeeeforum.weebly.com/uploads/1/0/2/5/10254481/15eee111_lec12.pdf · secondary winding according to the Faraday’s law of electromagnetic induction Thus due

Department of Electrical & Electronics Engineering, Amrita Vishwa Vidyapeetham, Coimbatore.

Transformers

Types

Operation

EMF equation

Three phase transformers



Why transformers?

The electrical energy is generated and transmitted at

extremely high voltages.

The voltage is to be then reduced to a lower value for its

domestic and industrial use.

This is done by using a transformer.

Thus it is possible to reduce/increase the voltage level

using a transformer


Transformers

static device which is used to transfer electrical energy

from one ac circuit to another ac circuit by

electromagnetic induction.

Increase or decrease in voltage/current but without

any change in frequency.


Types

Based on application

Step-up transformer

Step-down transformer


Types

Based on construction

Core type transformer

Shell type transformer



Types

Based on number of phases

Single phase transformer

Three phase transformer


Principle of operation

The winding connected to ac supply is called as primary

winding whereas the other one is called as the

secondary winding

The ac primary current produces an alternating flux ø in

the core.

Most of this changing flux gets linked with the secondary

winding through the core and will induce voltage into the

secondary winding according to the Faraday’s law of

electromagnetic induction

Thus due to primary current, voltage is induced in the

secondary winding due to mutual induction.

Hence the induced emf in secondary is called as the

mutually induced emf.


Can the transformer operate on DC?

NO.

With a DC primary current, the flux produced in the

core will not alternate, it is of constant value.



Transformer turns ratio

Ratio between the number of turns of the primary coil

divided by the number of turns of the secondary coil

Turns ratio value dictates the operation of the transformer

and the corresponding voltage available on the secondary

winding

For ideal transformer,


Example #1

A voltage transformer has 1500 turns of wire on its

primary coil and 500 turns of wire for its secondary

coil. What will be the turns ratio of the transformer?

If 240 volts is applied to the primary winding of the

transformer, what will be the resulting secondary no

load voltage.

3:1

80 V


EMF equation

Let, N1 and N2 be the number of turns of primary and

secondary,

ɸm be the maximum value of flux and f be the frequency

emf / number of turns is same for both primary and secondary

winding


Example #2


Three Phase Transformers

Generated and distribution of the electric power is three

phase.

The voltage generation takes place at very high level

typically at 13.2kV or 22 kV or even higher. The

transmission of electricity takes place at voltage level such

as 110kV, 132kV.

So it is necessary to use the step up transformer to raise

the voltage levels from 13.2kV to 132 kV etc. The three

phase transformer are used for the same.

Such high voltages can not be used by the domestic or

industrial users. So the voltage should be stepped down.

Three phase step down transformer are used as

distribution transformer.


Three phase transformer


Transformer connections


Transformer connections


Induction Motors

3 ɸ Induction motor

Types




Introduction

Three-phase induction motors are the most common and

frequently encountered machines in industry

simple design, rugged, low-price, easy maintenance

wide range of power ratings: fractional horsepower to 10 MW

run essentially as constant speed from no-load to full load

No starting device required.


Construction


squirrel-cage rotor

conducting bars laid into slots

wound-rotor

complete set of three-phase windings


Rotating Magnetic Field

Balanced three phase windings, i.e.

mechanically displaced 120 degrees

form each other, fed by balanced three

phase source

A rotating magnetic field with

constant magnitude is produced,

rotating with a speed

Where f is the supply frequency and

P is the no. of poles and nsync is called

the synchronous speed in rpm

(revolutions per minute)









This rotating magnetic field cuts the rotor windings and

produces an induced voltage in the rotor windings

The rotor current produces another magnetic field

A torque is produced as a result of the interaction of those two

magnetic fields

Where ind is the induced torque and BR and BS are the magnetic

flux densities of the rotor and the stator respectively

ind R skB B


Induction motor speed

At what speed will the IM run?

Can the IM run at the synchronous speed, why?

If rotor runs at the synchronous speed, which is the same

speed of the rotating magnetic field, then the rotor will

appear stationary to the rotating magnetic field and the

rotating magnetic field will not cut the rotor.

So, no induced current will flow in the rotor and no rotor

magnetic flux will be produced so no torque is generated

and the rotor speed will fall below the synchronous speed

When the speed falls, the rotating magnetic field will cut

the rotor windings and a torque is produced


Induction motor speed

So, the IM will always run at a speed lower than the

synchronous speed

The difference between the motor speed and the synchronous

speed is called the Slip

Where nslip= slip speed

nsync= speed of the magnetic field

nm = mechanical shaft speed of the motor

nsync- nm = Slip Speed

slip sync mn n n


The Slip

sync m

sync

n ns

n

Where s is the slip

Notice that : if the rotor runs at synchronous speed

s = 0

if the rotor is stationary

s = 1

Slip may be expressed as a percentage by multiplying the above

eq. by 100, notice that the slip is a ratio and doesn’t have units


Frequency

The frequency of the voltage induced in the rotor is given by

Where fr = the rotor frequency (Hz)

P = number of stator poles

n = slip speed (rpm)

120r

P nf


Frequency

What would be the frequency of the rotor’s induced voltage at

any speed nm?

When the rotor is blocked (s=1) , the frequency of the

induced voltage is equal to the supply frequency

On the other hand, if the rotor runs at synchronous speed

(s = 0), the frequency will be zero


Torque

While the input to the induction motor is electrical power, its

output is mechanical power

Any mechanical load applied to the motor shaft will introduce a

Torque on the motor shaft. This torque is related to the motor

output power and the rotor speed as

.outload

m

PN m

2/

60

mm

nrad s


Torque-speed characteristics

Typical torque-speed characteristics of induction motor

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A Brief History of Matlabeeeforum.weebly.com/uploads/1/0/2/5/10254481/15eee111_lec12.pdf · secondary winding according to the Faraday’s law of electromagnetic induction Thus due