7-0-dasar-trafo.ppt

8/9/2019 7-0-dasar-trafo.ppt

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Transformer

Laboratorium Penelitian Konversi Energi ElektrikInstitut Teknologi Bandung


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Transformer

AA transformer transformer is a device thatis a device that

convert ac electric energy atconvert ac electric energy at

one voltage level at anotherone voltage level at another

voltage level.voltage level.


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Transformer are important tomodern life

• Thomas A. Edison (1882)

Power Distribution System : New or!"#SA $ 12% &d'

Probems : osses * &ota+e Dro, - inei'ient

12% !&A /% !&A 0% !&A

%58=η

Example :

12% & 0% !&A

s-%%/ ohm31%!m1%%% A

/% &

0%&

1.


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High Voltage

0% !& 0% !&A

s-%%/ ohm31%!m1 A

%%/ &

0%!&~

0% !&A %%/ &A 0% !&A


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Transormer

are im,ortant to modern ,ower system

Low voltage High Voltage


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Real Appliation on Po!er "#stem

380 V/20 kV 20 kV/380 V


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Transformer

1. Power 4re5uen'y /%36% 7

2. adio re5uen'y 9 % !7

1. Power Transormer

2. ;nstrument Transormer


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2. Ty,e and


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$% The Ideal Transformer

V P (t)

I P (t) I

S (t)

V S (t)N P N S

>

"

>

"

S

P

N

N a =a

N

N

t v

t v

S

P

S

P ==

)(

)(Turn ratio a


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The Ideal Transformer

V P (t)

I P (t) I

S (t)

V S (t)N

P N

S

>

"

>

"

at it i

S

P 1)()( =Turn ratio a )(.)(. t I N t i N

S S P P =


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The Ideal Transformer

V P (t)

I P (t) I

S (t)

V S (t)N

P N

S

>

"

>

"

aV

V

S

P =

a I

I

S

P 1=

In term of phasor &uantities


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Po!er in ideal Transformer

P P P IN I V P θ cos= S S S OUT I V P θ cos=

θ θ θ == S P θ cosS S OUT I V P =

P S P S aI I and aV V == /

IN P P

OUT P aI a

V P == θ cos

Po!erinput

Po!erinput

ideal

Turn ratio

e&uation


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Po!er in ideal Transformer

IN P P OUT P I V P == θ cos

IN P P S S OUT Q I V I V Q === θ θ sinsin

IN P P S S OUT S I V I V S ===

Ativepo!er

reativepo!er

Apparentpo!er


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Evaluasi

' (ntuk memahami konsep trafo ideal berikan kemahasis!a) ontoh sederhana misaln#a *

+ ,ara mendapatkan tegangan sekunder # volt -ika tegangan primern#a . volt%

+ Arus sekunder b ampere pada tegangan # volt) ari arus primer a ampere padategangan / volt%

+ Ambil nilai . dan # #ang bedan#a sangatbesar

+ "oal pada sistem 0 fasa dulu sa-a%


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Impedane Transformer

L

L

L

I

V Z =

Impedane 1

ratio of the phasor voltage aross it ti the phasor urrent

Z L

V L

I L


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Impedane Transformer

S

S

S

S

P

P

L I

V

aa I

aV

I

V

Z

2

/' ===

S P aV V =

S

S

L

I

V Z =

P

P

L

I

V Z ='

a I I S P

/=

L L Z a Z

2' =

Z L

I P

I S

V P V

S

+

-

+

-

if


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Theor# of operation of real single2phase transformers

The basis transformer operation an be derivedfrom 3arada#4s la! dt

d eind

λ =

∑=

= N

i

i

1

φ λ λ Flux

linkage N

λ φ =

dt

d N e

ind

φ =

V P (t)

I P (t) I

S (t)

V S (t)N

P N

S

>

"

>

"

φ


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E53 e&uation of a transformer

dt d N e φ −=Faraday law of

electromagneticinduction

t ω φ φ cosmax=

t N e ω ωφ sinmax=

RMS Value

mm fN N E φ φ ω 44,4

2==


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Transformer Losses

' ,opper 6I7R8 losses

' Edd# urrent losses

' H#steresis losses

' Leakage flu.


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The e&uivalent iruit of a transformer

the model of a real transformer


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The equivalent circuit of a

transformer


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Phasor diagram orresponding + referred toprimar#

a&2

a;2 1

2

;1 1

1

j ;1 ?

1

φ

;m

;% ; 1

;2 3a

;<

2θ


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The equivalent circuit of a

transformer


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Test on transformers

• Open-Circuit Test

• Result : V OC IOC P

OC


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9pen2,iruit Test Result

,ondutane of the ore2lossresistor C

C R

G 1=

M

M

X

B 1=

M C E jBGY −=

C C

E X

j R

Y 11−=

OC

OC E

V I Y =

"useptane of the magneti:ing indutor

Admittane

5agnitude admittane


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9pen2,iruit Test Result

OC OC

OC

I V

P PF

.cos == θ

OC OC

OC

I V

P

.cos 1−=θ

θ −∠=OC

OC

E V

I Y

PF V

I Y

OC

OC E

1cos−−∠=

Po!er 3ator

Po!er 3ator angle

Admittane


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Test on transformers

Short-Circuit Test

Result * V ", )I ", )P 9,


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Short-Circuit Test Result

Series impedance

SC

SC SE

I

V Z =

SC SC

SC

I V

P PF

.cos == θ

SC SC

SC

I V

P

.cos 1−=θ

Power Facor o! "e curren

#a$$in$ % &urren an$le '%()*mpedance an$le '+(

θ θ

∠=−∠

∠=

SC

SC

SC

SC

SE

I

V

I

V Z

00,"ere!ore)


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"hort2,iruit Test Result

Admittane

eqeqSE jX R Z +=

)()( 22

S P S P SE X a X j Ra R Z +++=

"eries impedane


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2-2

,"e e.uialen circui impedances o! a 20 kV) 8000 / 210 V) 0 4

rans!ormer are o 5e deermined- ,"e open circui es were per!ormed

on "e primar6 side o! "e rans!ormer) and "e !ollowin$ daa were

aken :Open-circuit

test onprimary!

"hots-circuittest onprimary!

V OC 7 8000 V

I OC

7 0)21

P OC

7 100 9

V OC

7 18 V

I OC

7 2);

P OC

7 210 9


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I a

I !

V !V a" R m X j

e# I

+

m I

eq R eq X j

Ω192 jΩ4.38

Ω$ j 4.38Ω$ 159

> >

" "


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The per2unit s#stem of measurement

q%antit&'f va(%e)a!e

q%antit&a"t%a( %nit e* Q%antit& =

*n sin$le%p"ase s6sem : )a!e)a!e)a!e)a!e)a!e I V S '* Q P =,

)a!e

)a!e)a!e

I

V Z =

)a!e

)a!e

)a!e V

I

Y =

)a!e

)a!e

)a!e

S

V Z

2)(=


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Voltage Regulation ; Effiien#

%100,

,, +

V

V V VR

('ad f%(( S

('ad f%(( S ('ad n'S −=

Effiien#

%100 + P

P

in

'%t =η %100 + P P

P

('!!'%t

'%t

+=η

Voltage Regulation


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Autotransformer

I SE

I LV

H

V L

N SE

N C

I C

I H "tep2do!n autotransformer

SE

C

SE

C

N

N

V

V = SE SE C C I N I N =

C L V V = SE C , V V V +=

SE , I I = C SE L I I I +=

C SE

C

,

L

N N

N

V

V

+=

C

C SE

,

L

N

N N

I

I +=


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Po!er rating 2autotransformer

SE

C SE

-

IO

N

N N

S

S +=

S IO

#$nput and Output apparent powers

SW

# apparent power in the

transformer windings

For example) a ;000 kV auorans!ormer connecin$ a 0 kV

s6sem o a 38 kV s6sem would "ae an


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Three2phase transformer

N P1

N S1

N P2

N S2

N P3

N S3

"ree%p"ase rans!ormer 5ank composed o! independen rans!ormer

N P1

N P2

N P3

N S1

N S2

N S3

"ree%p"ase rans!ormer wound on a sin$le "ree%le$$ed core


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Three2phase transformer onnetions

' elta2!#e 6>#8' >elta2delta 6>d8


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>elta2!#e 6>#8 ,onnetion

S

P

LS

LP

V

V

V

V

φ

φ

3=

3

a

V

V

LS

LP =


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>elta2delta 6>d8 ,onnetion

aV

V

V

V

S

P

LS

LP ==φ

φ


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A /% !&A 1.8%% 3 2%8 & Dy distribution transormerhas a resistan'e o 1 ,er'ent and rea'tan'e o 0,er'ent ,er unit.

(a) @hat is the transormers ,hase im,edan'ereerred to the hi+h"Bota+e sideC(b)


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Instrument transformers

' Potential transformer 6PT8

' ,urrent transformers 6,T8

& @

S

A

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