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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