Transformer

EKT 103CHAPTER 3

1

By: Dr Rosemizi Abd Rahim

1.1 Introduction to Transformer.

Transformer is a device that changes ac electrical power at one voltage level to ac electric power at another voltage level through the action of magnetic field.

Figure 1.1: Block Diagrams of Transformer.

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1.2 Applications of Transformer.Why do we need transformer?

The Power Grid 3

1.2 Applications of Transformer.Why do we need transformer?

(a) Step Up.

In modern power system, electrical power is generated at

voltage of 12kV to 25kV.

Transformer will step up the voltage to between 110kV to

1000kV for transmission over long distance at very low lost.

The Power Grid

The Transmission Tower

4

1.2 Applications of Transformer.Why do we need transformer?

(b) Step Down.

The transformer will stepped down the voltage to the 12kV

to 34.5kV range for local Distribution.

In homes, offices and factories stepped down to 240V.

The Power Grid

The Substation

The Utility poles

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1.3 Types and Constructions of Transformer. Power transformers are constructed on two types of

cores;

(i) Core form.

(ii) Shell form.

Figure 1.2: Core Form and Shell Form.

A) Core type B) Shell type

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Core form. The core form construction consists of a simple

rectangular laminated piece of steel with the transform winding wrapped around the two sides of the rectangle.

Shell form. The shell form construction consists of a three-legged

laminated core with the winding wrapped around the center leg.

A) Core type B) Shell type

Cont’d…

7

Construction. Transformer consists of two or more coils of wire wrapped around a

common ferromagnetic core. The coils are usually not directly connected.

The common magnetic flux present within the coils connects the coils. There are two windings;

(i) Primary winding (input winding); the winding that is connected to the power source.

(ii) Secondary winding (output winding); the winding connected to the loads.

Cont’d…

Figure 1.3: A Simple Transformer.

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Operation. When AC voltage is applied to the primary winding of the

transformer, an AC current will result iL or i2 (current at load).

The AC primary current i2 set up time varying magnetic flux f in the

core. The flux links the secondary winding of the transformer.

Cont’d…

9

Operation. From the Faraday law, the emf will be induced in the secondary

winding. This is known as transformer action.

The current i2 will flow in the secondary winding and electric power

will be transfer to the load. The direction of the current in the secondary winding is determined

by Len’z law. The secondary current’s direction is such that the flux produced by this current opposes the change in the original flux with respect to time.

Cont’d…

10

FARADAY’S LAW

In 1831 two people, Michael Faraday in the UK and Joseph Henry in the US performed experiments that clearly

demonstrated that a changing magnetic field produces an induced EMF (voltage) that would produce a current if the circuit

was complete.

If current produces a magnetic field, why can't a magnetic field produce a

current ?

Michael Faraday

1.4 General Theory of Transformer Operation.

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• When the switch was closed, a momentary deflection was noticed in the galvanometer after which the current returned to zero.

• When the switch was opened, the galvanometer deflected again momentarily, in the other direction. Current was not detected in the secondary circuit when the switch was left closed. 

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• Faraday found that the induced e.m.f. increases if

(i) the speed of motion of the magnet or coil increases.

(ii) the number of turns on the coil is made larger.

(iii) the strength of the magnet is increased.

An e.m.f. is made to happen (or induced) in a conductor (like a piece of metal) whenever it 'cuts' magnetic field lines by moving across

them. This does not work when it is stationary. If the conductor is part of a complete circuit a

current is also produced.

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Faraday’s Law• E = Electromotive force (emf)• Φ = Flux• N = Number of turn• t = time

• Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated.

• The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc.

ΔtNE

14

• Inserting a magnet into a coil also produces an induced voltage or current.

• The faster speed of insertion/ retraction, the higher the induced voltage.

15

According to the Faraday’s law of electromagnetic induction, electromagnetic force (emf’s) are induced in N1 and N2 due to a

time rate of change of fM,

Where, (1.1)

e = instantaneous voltage induced by magnetic field (emf),

= number of flux linkages between the magnetic field and the electric circuit.

f = effective flux

dt

dN

dt

de

dt

dNe

22 ;11

dt

dNe

Figure 1.4: Basic Transformer Components.

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Lenz’s Law states that the direction of e1 is such to produce a current that opposes the flux changes.

If the winding resistance is neglected, then equation (1.1) become;

(1.2)

Taking the voltage ratio in equation (1.2) results in,

(1.3)

);(111dt

dNev )(222dt

dNev

2

1

2

1

e

e

N

N

Cont’d…

17

Neglecting losses means that the instantaneous power is the same on both sides of the transformer;

(1.4)

Combining all the above equation we get the equation (1.5) where a is the turn ratio of the transformer.

(1.5)

Cont’d…

2211 ieie

1

2

2

1

2

1

i

i

v

v

N

Na

a > 1 Step down transformer

a < 1 Step up transformer

a = 1 Isolation Transformer18

According to Lenz’a Law, the direction of e is oppose the flux changes, and the flux varies sinusoidally such that

(1.6)

Substitute eqn(1.6) into eqn(1.2)

(1.7)

The rms value of the induce voltage is;

(1.8)

)2sin( max ftdt

dN

dt

dNe

= max sin t

maxmaxmax

44.42

2

2

fNNfN

E

Cont’d…

max

19

Losses are composed of two parts;

(a) The Eddy-Current lost. Eddy current lost is basically loss due to the induced current in the

magnetic material. To reduce this lost, the magnetic circuit is usually made of a stack of thin laminations.

(b) The Hysteresis loss.Hysteresis lost is caused by the energy used in orienting the magnetic

domains of the material along the field. The lost depends on the material used.

Cont’d…

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1.5 The Ideal Transformer. An Ideal transformer is a lossless device with an input

winding and an output winding. Zero resistance result in zero voltage drops between

the terminal voltages and induced voltages Figure below shows the relationship of input voltage

and output voltage of the ideal transformer.

An Ideal Transformer and the Schematic Symbols.21

The relationship between voltage and the number of turns. Np , number of turns of wire on its primary side.

Ns , number of turns of wire on its secondary side.

Vp(t), voltage applied to the primary side.

Vs(t), voltage applied to the secondary side.

where a is defined to be the turns ratio of the transformer.

aN

N

tv

tv

s

p

s

p )(

)(

Cont’d…

22

The relationship between current into the primary side, Ip(t), of transformer versus the secondary side, Is(t), of the transformer;

In term of phasor quantities;

-Note that Vp and Vs are in the same phase angle. Ip and Is are in the same phase angle too.

- the turn ratio, a, of the ideal transformer affects the magnitude only but not the their angle.

)()( tINtIN sspp

Cont’d…

atI

tI

s

p 1

)(

)(

aV

V

s

p aI

I

s

p 1

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The dot convention appearing at one end of each winding tell the polarity of the voltage and current on the secondary side of the transformer.

If the primary voltage is positive at the dotted end of the winding with respect to the undotted end, then the secondary voltage will be positive at the dotted end also. Voltage polarities are the same with respect to the doted on each side of the core.

If the primary current of the transformer flow into the dotted end of the primary winding, the secondary current will flow out of the dotted end of the secondary winding.

Cont’d…

24

Example 1: Transformer.

How many turns must the primary and the secondary windings of a 220 V-110 V, 60 Hz ideal transformer have if the core flux is not allowed to exceed 5mWb?

Solution:

For an ideal transformer with no losses,

From the emf equation, we have

VVE

VVE

110

220

22

11

.83)105)(60)(11.4(

110

.166)105)(60)(11.4(

220

**11.4

32

3

max

11

turnsX

N

turnsX

f

EN

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1.5.1 Power in an Ideal Transformer. Power supplied to the transformer by the primary circuit is given

by ;

where, qp is the angle between the primary voltage and the primary

current. The power supplied by the transformer secondary circuit to its

loads is given by the equation;

where, qs is the angle between the secondary voltage and the

secondary current. Voltage and current angles are unaffected by an ideal transformer ,

qp – qs = . q The primary and secondary windings of an ideal

transformer have the same power factor.

sssout IVP cos

pppin IVP cos

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The power out of a transformer;

- apply Vs= Vp/a and Is= aIp into the above equation gives,

- The output power of an ideal transformer is equal to the input power.

cosssout IVP

Cont’d…

inppout

pp

out

PIVP

aIa

VP

cos

cos)(

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The reactive power, Q, and the apparent power, S;

In term of phasor quantities;

-Note that Vp and Vs are in the same phase angle. Ip and Is are in the same phase angle too.

- the turn ratio, a, of the ideal transformer affects the magnitude only but not the their angle.

Cont’d…

outssppin

outssppin

SIVIVS

QIVIVQ

sinsin

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Example 2: Ideal Transformer.

Consider an ideal, single-phase 2400V-240V transformer. The primary is

connected to a 2200V source and the secondary is connected to an

impedance of 2 < 36.9W o, find,

(a) The secondary output current and voltage.

(b) The primary input current.

(c) The load impedance as seen from the primary side.

(d) The input and output apparent power.

(e) The output power factor.

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Example 2: Ideal Transformer.

Consider an ideal, single-phase 2400V-240V transformer. The primary is

connected to a 2200V source and the secondary is connected to an

impedance of 2 < 36.9W o, find,

Solution:

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Cont’d…Example 2

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Real Transformer

Real Transformer Leakage flux in the real transformer

m

p_leakage

s_leakage

Winding resistance & magnetic leakage

R 1X 1 I1

E 1V 1

R 2X 2 I2

V 2E 2

R1 & R2 : resistances of primary & secondary windings respectively.

X1 & X2 : leakage reactances of primary & secondary windings respectively.

1.7 The Exact Equivalent Circuit of a Real Transformer.

Figure below is an exact model of a transformer.

To analyze the transformer it is necessary to convert the entire circuit to an equivalent circuit at a single voltage level

Model of a Real Transformer

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(a) The Transformer Model Referred to its Primary Windings.

(b) The Transformer Model Referred to its Secondary Windings.

Symbols used for the Exact Equivalent Circuit

35

1.7 The Exact Equivalent Circuit of a Real Transformer.

To analyze the transformer it is necessary to convert the entire circuit to an equivalent circuit at a single voltage level.

(a) The Transformer Model Referred to its Primary Windings.

36

2

2

I

V

I

VZ

L

LL L

P

PL Za

I

Va

aI

aV

I

VZ 2

2

22

2

2'

Impedance transformation through a Transformer

The Approximate Equivalent Circuit of a Transformer

Approximate Transformer Model Referred to the Primary Side.

37

The equivalent impedance for the circuit is;

1.7 The Exact Equivalent Circuit of a Real Transformer.

To analyze the transformer it is necessary to convert the entire circuit to an equivalent circuit at a single voltage level.

(b) The Transformer Model Referred to its Secondary Windings.

38

Approximate Circuit Model of a Transformer Referred to the Secondary.

The equivalent impedance for the circuit is;

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1.9 Transformer Voltage Regulation and Efficiency.

Voltage regulation is a measure of the change in the terminal voltage of the transformer with respect to loading. Therefore the voltage regulation is defined as:

At no load, Vs = Vp/a and the voltage regulation can also be express as;

%100,

,,

fls

flsnls

V

VVVR

%100,

,

fls

flsp

V

Va

V

VR

41

“the change in secondary voltage when rated load at a specified power is removed”.

1.9 Transformer Voltage Regulation and Efficiency.

In the per-unit system;

For ideal transformer VR=0. It is a good practice to have as small voltage regulator as possible.

%100,,

,,,

pufls

puflspup

V

VVVR

42

Example of Transformer Voltage Regulation.

Cont’d…

43

Transformer Efficiency, efficiency of a transformer is defined as follows;

For Non-Ideal transformer, the output power is less than the input power because of losses.

These losses are the winding or I2R loss (copper losses) and the core loss (hysteresis and eddy-current losses).

1

2

P

P

Powerinput

PowerOutput

Cont’d…

44

Thus, in terms of the total losses, Plosses, the above equation may be expressed as;

The winding or copper loss is load dependent, whereas the core loss is constant and almost independent of the load on the transformer.

Cont’d…

corecopperlosses

losses

PPP

P

PP

P

P

PP

2

2

2

2

1

1

45

Example 3: Transformer Voltage Regulation.

46

Cont’d…Example 3

47

1.10 Open Circuit and Short Circuit. - Determination of transformer parameter by measurement

Open Circuit Test. Provides magnetizing reactance and core loss resistance Obtain components are connected in parallel The open circuit test is conducted by applying rated voltage at rated

frequency to one of the windings, with the other windings open circuited. The input power and current are measured. For reasons of safety and convenience, the measurements are made on the

low-voltage (LV) side of the transformer.

V1 V2=E2V

AW

Low Voltage winding High Voltage winding

I0

The secondary / high voltage (HV) side is open, the input current is equal to the no load current or exciting current (I0),

and is quite small. The input power is almost equal to the core loss at rated voltage

and frequency.

Cont’d…

Equivalent Circuit of the Open-Circuit Test.

Cont’d…Open circuit test evaluation

Short Circuit Test. The short-circuit test is used to determine the equivalent series

resistance and reactance.

Provides combined leakage reactance and winding resistance

One winding is shorted at its terminals, and the other winding is connected

through proper meters to a variable, low-voltage, high-current source of

rated frequency.

The source voltage is increased until the current into the transformer

reaches rated value. To avoid unnecessary high currents, the short-circuit

measurements are made on the high-voltage side of the transformer.

LV supply V

AW

Low Voltage windingHigh Voltage winding

Equivalent Circuit of the Short-Circuit Test.

Cont’d…

2_

2__ HVeqHVeqHVeq RZX

sc

scHVeq I

VZ _HVeqscsc RIP _

2

2_sc

scHVeq I

PR

Example Open Circuit Test

53

54

Example Open Circuit Test

55

Example Open Circuit Test