chap_2_transformer_1.pdf

7/25/2019 chap_2_Transformer_1.pdf

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EBB2133 Electrical Machine 1

Chapter 2: Transformer

Ideal Transformer

Lecturer:Dr Zuhairi Baharudin

Room: 22-03-09 Ext: 7810

email: [email protected]
mailto:[email protected]:[email protected]


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Outcomes

Students should be able to :a) describe the operation and the different types oftransformers

b) describe the characteristic of an ideal transformerc) analyze circuits containing ideal transformers

2


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Transformers

3

What is a TRANSFORMER ?

It is a device that converts ac electric energy

at one level into ac electric energy at another

level (can be either voltage or current).

What do we use a transformer for ?


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Transformers

In electric power generation and distributionsystems, transformers are used to :

make electricity generation possible at the most economic

generator voltage level make electric power transmission take place at the most

economic transmission voltage

supply electric power to users at a safe and suitable voltage.

4


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5

Power Plant

Load-Residential

Transmission line


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Transformers

In electronic and communication systems,transformers are used to :

match the impedance for maximum power transfer

isolate two electrical systems

transfer signals.

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Construction of a Transformer

7

iP

iS

vP

vS

NP

NS

++

__

Primary

Connected to

voltage source /

generator

Secondary

Connected to loadWindings,NPandNS

Core

Laminated electrical steel

core


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How does a Transformer Work ?

iP

iS

vP

vS

NP

NS

++

__

8

Primary coilNPexcited by

an AC source, vP

Resulting current

produces total flux, ,

flowing through the core

Secondary coilNSsurrounds total flux,

An AC voltage, vS, is

induced in the second coil


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Ideal Transformer

For ideal transformer, we assume that :

The permeability of the core, rnormally large 10 000 to50 000

Core losses are assumed zero

No resistance in the windings

No leakage flux

Therefore,

P

S

S

P

N

N

ti

ti

)(

)(

9

iP

iS

vP

vS

NP

NS

++

__


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Transformer Schematic Transformer schematic symbols:

10

vP(t)

iS(t)iP(t)

vS(t)

NP NS

++

__

vP

(t)

iS(t)i

P(t)

vS(t)

NP

NS

++

__

How do we determine the

polarity of the secondary

voltage ?

We use the dot convent ion:

If vPis positive at the dotted endof the winding with respect to the

undotted end, then vSwill bepositive at the dotted end.

If iPflows into the dotted end ofthe primary winding, iS will flowout of the dotted end of the

secondary winding.


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Types of TransformersPower transformers are built in one of 2 ways :

a) Shell-type transformerb) Core-type transformer

11

iP

iS

vP

vS

NP

NS

++

__


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Types of Transformers

a) Shell-type transformer Lower leakage flux

Lower voltage regulation

b) Core-type transformer Large gap between primary

and secondary windings

Regular use in high voltage

applications Simple to construct

Smaller in size

12


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Ideal Transformer Since the power losses are ignored, the input power must be

equal to output power :

vP iP= vS iS or

where ais called the turns ratio.

Voltage and current angles are unaffectedby the ideal

transformer.

Pin= VPIP cos P Pout= VSIS cos S

since P = S = Pin= Pout

Therefore,NPandNSof an ideal transformer have the same

power factor.

13

aN

N

i

i

tv

tv

S

P

P

S

S

P

)(

)(


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Ideal Transformer

Reactive power going into the primary winding is also equalto reactive power going into the secondary winding.

Qin= VPIP sin= VSIS sin= Qout

The same relationship also applies to apparent power S.

Sin= VPIP = VSIS = Sout

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Ideal Transformer

Impedance Transformation through A Transformer

A transformer changes voltage or current levels. This also

changes the ratio between voltage and current.

The transformer has the ability to transform the apparentimpedance of an element.

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How ?

L

L

L

IVZ


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Impedance Transformation

We know that VP= aVSand IP= IS/a, therefore

16

VP

ISIP

VS

+

+

_ _

ZL

P

P

LZ

I

V'

The impedance of the load

is

However, the source sees

an impedance between the

primary terminals as

S

S

LZ

I

V

P

P

LZ

I

V'

L

S

S

S

S

L Zaa

aaZ 2

2

/'

IV

IV

the impedance seen by the source is a2times the real

impedance.


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Impedance Transformation

Example: A 1000resistor placed across the secondary of an ideal

transformer with turns ratio of 1:5 will appear across the primary as

having a resistance of 1000 x (1/ 5)2= 40.

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An ideal transformer can

modify the value of any

component.

VP

IS

IP

VS

++

_ _

ZL

P

P

LZ

I

V'


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Ideal Transformer

Important relationshipsdescribing the ideal

transformer :

Voltage level

Current

18

Apparent impedance seenby the primary

We will use theserelationships to analyze

circuit with ideal

transformer.

Introduction

vP

(t)

iS(t)iP(t)

vS(t)

NP

NS

++

__

aN

N

ti

ti

P

S

S

P1

)(

)(

aN

N

tv

tv

S

P

S

P

)(

)(

LL ZaZ

2'


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Example

19

A speaker of 9resistive impedance is connected to a supply of10V with internal resistive impedance of 1.

a) Determine the power absorbed by the speakerb) To maximize the power transfer to the speaker, a transformer

of 1:3 turns ratio is used between source and speaker.Determine the power absorbed by the speaker.


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Exercise

20

A 1-phase two-winding transformer has 1000 turns on theprimary and 500 turns on the secondary. The primary winding isconnected to a 220V supply and the secondary winding isconnected to a 5 kVA load. The transformer can be consideredideal.

a) Determine the load voltageb) Determine the load impedancec) Determine the load impedance referred to primary

l f d l f


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Analysis of Ideal Transformer

The easiest way to analyze a circuit containing an ideal

transformer is to replace one side of the transformer by anequivalent circuit with the other sides voltage level.

This process is known as referringor shiftingthe first side ofthe transformer to the second side.

Using this method, values of voltages on the side being

replaced are scaled using VP/ VS= a and values of

impedances are also scaled usingZL = a2ZL.

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Lets look at an example !


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Examplea) What is the load voltage for the system shown below?

b) What are the transmission losses of the system ?

22

T1

Zload

Zline

T2

1:10 10:1V

G= 13.2 0o

kV

60 53.1o

500 36.87o


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Example (continued)c) If the generator is directly connected to the load, what is the

load voltage?d)What are the transmission losses of this new system ?

23

Zload

Zline

VG= 13.2 0o

kV

60 53.1o

500 36.87o

chap_2_transformer_1.pdf

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