Transformers.pptx

Transformers

Introduction

• _{A transformer is a device which uses the phenomenon of mutual}

induction to change the values of alternating voltages and currents. In fact, one of the main advantages of a.c. transmission and distribution is the ease with which an alternating voltage can be increased or

decreased by transformers.

Transformers

•_{An AC transformer consists of} two coils of wire wound around a core of iron.

•_{The side connected to the input} AC voltage source is called the

primary and has N₁ turns. •_{The other side, called the} secondary, is connected to a resistor and has N₂ turns.

•_{The core is used to increase the} magnetic flux and to provide a medium for the flux to pass from one coil to the other.

Transformer

An A.C. device used to change high voltage low current A.C. into low voltage high current A.C. and vice-versa without changing the frequency

In brief, a transformer:

1. Transfers electric power from one circuit to another 2. It does so without a change of frequency

3. It accomplishes this by electromagnetic induction

• _{Transformers range in size from the miniature units used in electronic}

applications to the large power transformers used in power stations. The principle of operation is the same for each.

• _{A transformer is shown on the next slide as consisting of two}

electrical circuits linked by a common ferromagnetic core. One coil is termed the primary winding which is connected to the supply of

Principle of operation

It

is

based

on

principle of

MUTUAL

INDUCTION.

According to which

an e.m.f. is induced

in

a

coil

when

current

in

the

Constructional detail :

Shell type

• Windings are wrapped around the center leg of a

Core type

• _{Windings are wrapped around two sides of a laminated square}

Sectional view of transformers

Note:

Working of a transformer

changes being alternating in

nature, a changing magnetic field is produced

2. This changing magnetic field gets associated with the secondary

through the soft iron core

3. Hence magnetic flux linked with the secondary coil changes.

Ideal Transformers

• Zero leakage flux:

-Fluxes produced by the primary and secondary currents are confined within the core

• The windings have no resistance:

- Induced voltages equal applied voltages

• The core has infinite permeability

- Reluctance of the core is zero

- Negligible current is required to establish magnetic flux

• Loss-less magnetic core

Ideal transformer

V₁ – supply voltage ; I₁- noload input current ; V_2- output voltgae; I₂- output current

I_m- magnetising current;

Transformers, cont.

Eddy-current losses are minimized by using a laminated core.

•_{Assume an ideal transformer}

•_{One in which the energy losses in the windings and the core are zero.}

• Typical transformers have power efficiencies of 90% to 99%.

•_{In the primary,}

•_{The rate of change of the flux is the same for both coils.} •_{The voltage across the secondary is}

Section 33.8

1 1 B

d

v N

dt

   

2 2 B

d

v N

dt

Transformers – up and

Step-down

•The voltages are related by

•_{When N2 > N1, the transformer is referred to as a step-up transformer.} •_{When N2 < N1, the transformer is referred to as a step-down transformer.}

•_{The power input into the primary equals the power output at the secondary.}

• _{I1ΔV1 = I2ΔV2}

•The equivalent resistance of the load resistance when viewed from the primary is

Transformer principle of

operation

• _{When the secondary is an open-circuit and an alternating voltage V1}

is applied to the primary winding, a small current—called the no-load current I₀—flows, which sets up a magnetic flux in the core. This

alternating flux links with both primary and secondary coils and

induces in them e.m.f.’s of E₁ and E₂ respectively by mutual induction.

• _{The induced e.m.f. E in a coil of N turns is given by} • _{E = -Nvolts,}

• _{In an ideal transformer, the rate of change of flux is the same for both}

primary and secondary and thus E₁/N₁ = E₂/N₂, i.e. the induced e.m.f. per turn is constant.

• _{Assuming no losses, E₁ = V₁ and E₂ = V₂. Hence}

• _{V₁/V₂ is called the voltage ratio and N₁/N₂ the turns ratio, or the}

‘transformation ratio’ of the transformer. If N₂ is less than N₁ then V₂ is less than V₁ and the device is termed a step-down transformer. If N₂ is greater then N₁ then V₂ is greater than V₁ and the device is

termed a step-up transformer.

• _{When a load is connected across the secondary winding, a current I₂}

• _{Hence input power = output power, or V₁I₁ = V₂, i.e., in an ideal}

transformer, the primary and secondary volt-amperes are equal. =

Thus in general, =

• _{The rating of a transformer is stated in terms of the volt-amperes that}

Transformer Efficiency

Electrical Machines

Transformer efficiency is defined as (applies to motors and generators ):

Types of losses incurred in a transformer: Copper I2_{R losses winding losses}

Iron or Core losses Hysteresis losses Eddy current losses

Therefore, for a transformer, efficiency may be calculated using the following:

Losses in a transformer

Core or Iron loss:

Contd.,

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AUTO TRANSFORMER

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But it differs essentially in the manner of

conne-ction to the circuits in the primary and secondary

systems.

In the ordinary transformers the primary and

secondary windings are magnetically

interconne-cted but electrically separate.

Autotransformers

_{Autotransformers are transformers in which the primary} and secondary windings are coupled magnetically and electrically.

_{This results in lower cost, and smaller size and weight.} _{The key disadvantage is loss of electrical isolation}

between the voltage levels. This can be an important safety consideration when the turns ratio is large. For

example in stepping down 7160/240 V we do not ever

want 7160 on the low side!

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Some of the advantages of the auto-transformer

over the ordinary transformer having the same

output are:



_{Lower cost,}



_{Smaller size and weight,}



_{Greater efficiency since the losses are lower,}

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DISADVANTAGES

a) The secondary winding of the auto-transformer

will experience high voltage in step down

operation when an open circuit occurs on the

common winding. This occurrence is very rare.

b) The impedance of the auto-transformer due to

the common winding is less than the two

winding transformer resulting in a higher fault

current being available. This can be overcome

by

specifying

the

correct

transformer

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c) The auto-transformer provides less of a barrier

to electrical noise than does a comparable two

winding transformer.

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e) Auto-transformers have the limitation of not

suppressing harmonic currents and acting as

another source of ground fault currents. An

auxiliary Delta winding not connected to the

outside of the tank may be required to absorb

some of the harmonic currents.

example

• A transformer for home use of a portable radio reduces 120-V ac to 9.0-V ac. (Such a device also contains diodes to change the 9.0-9.0-V ac to dc.). The secondary contains 30 turns and the radio draws 400 mA. Calculate: • _{(i) the number of turns in the primary;}

• _{(ii) the current in the primary; and} • _{(iii) the power transformed.}

Why power is transmitted at very

high voltages

• _{Transformers play an important role in the transmission of electricity.}

• _{Transmission lines. An average of 120 kW of electric power is sent to}

a small town from a power plant 10 km away. The transmission lines have a total resistance of 0.40 Ω. Calculate the power loss if the

power is transmitted at a) 240 V and b) 24,000 V.

• _{SOLUTION We cannot use P = V²/R because if R is the resistance of the}

• (a) If 120 kW is sent at 240 V, the total current will be

I = P/V = 120,000/240 = 500 A

The power loss in the lines, P_L,is then P_L= I²R

= (500)²(0.40) = 100 kW.

• _{(b) If 120 kW is sent at 24,000 V, the total current will be}

I = P/V = 120,000/24000 = 5.0 A

The power loss in the lines is then

P_L= I²R = (5.0)²(0.40) = 10 W,

which is less than 1/100 of 1 %. We see that the greater the voltage, the less the current and thus the less power is wasted in the

More practice problems

• A transformer has 500 primary turns and 3000 secondary turns. If the primary voltage is 240 V, determine the secondary voltage, assuming an ideal

transformer.

• An ideal transformer, connected to a 240 V mains, supplies a 12 V, 150 W lamp. Calculate the transformer turns ratio and the current taken from the supply.

• A transformer for home use of a portable radio reduces 120-V ac to 9.0-V ac.

(Such a device also contains diodes to change the 9.0-V ac to dc.). The secondary contains 30 turns and the radio draws 400 mA. Calculate:

• (i) the number of turns in the primary;

• (ii) the current in the primary; and