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Chapter 4.Transformer
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Transformer- Introduction Two winding transformers Construction and principles
Equivalent circuit Determination of equivalent circuit
parameters Voltage regulation
Efficiency Auto transformer 3 phase transformer
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Transformer- Introduction
Varieties of transformers
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Transformer- Introduction
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Transformer- Introduction
Transformer is a device that makes use of themagnetically coupled coils to transfer energy
It is typically consists of one primary windingcoil and one or more secondary windings
The primary winding and its circuit is called
the Primary Side of the transformer The secondary winding and its circuit is called
the Secondary Side of the transformer
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Transformer- Introduction
If one of those winding, the primary, isconnected to an alternating voltagesource, an alternating flux will beproduced. The mutual flux will link theother winding, the secondary, and will
induced a voltage in it.
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Transformer- Introduction Transformers are adapted to numerous engineering
applications and may be classified in many ways:
Power level (from fraction of a volt-ampere (VA) to over athousand MVA),
Application (power supply, impedance matching, circuitisolation),
Frequency range (power, audio, radio frequency (RF)) Voltage class (a few volts to about750 kilovolts) Cooling type (air cooled, oil filled, fan cooled, water
cooled, etc.) Purpose (distribution, rectifier, arc furnace, amplifier
output, etc.).
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Transformer- Introduction
Power transmission
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Transformer- Introduction
Power transmission
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Transformer
4.1 Construction
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Transformer- construction
Basic components of single phase transformer
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Transformer- construction
Single phase transformer construction
A) re ty e B ) S ell ty e
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Transformer- construction
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Transformer- constructionPrimar
Winding
econdarWinding
Multi-la er
Laminated
Iron Core
X1
X2H
1 H2
WindingTerminals
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4.2 Ideal Transformer
Transformer
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Transformer
i
e1
v1 v2
e2
The emf which induced in
transformer primary winding is
known as self induction emf asthe emf is induced due to to flux
which produced by the winding
itself.
While the emf which induced in
transformer secondary winding
is known as mutual induction
emf as the emf is induced due
to to flux which produced by the
other winding.
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Transformer
i
e1
v1 v2
e2
Acording to Faradays Law,theemf which induced in
the primary winding is,
e1 =dt
dN
J1
Since theflux is analternating flux,
tmak [sin!e1 = dt
tdN ak
)sin(1
[J
tmak [[ cos1!
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Transformer
i
e1
v1 v2
e2
e1
where,
tfmak [T cos21!
tE [cosmax1
!
max1E fN TJ 2max1=
2
max1
1
EErms ! fmax144.4 J!
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Transformer
i
e1
v1 v2
e2
e2 =
Similarly it can be shownthat,
dt
dN
J2
E2 rms fN max244.4 J
kf
f
E
E
1
2
max1
max2
1
2
44.4
44.4
J
Jk is transformation ratio
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Transformer
The voltage ratio ofinduced voltages on the secondary toprimary windings is equal to the turn ratio of the winding turn
number of the secondary winding to the winding turn numberof the primary winding. Therefore the transformers can beused to step up or step down voltage levels by choosingappropriate number their winding turns. In power system itsnecessary to step up the outputvoltage of a generator which
less than 30kV to up 500kV for long distance transmission.High voltage for long distance power transmission can reducecurrentflow in the transmission lines, thus line losses andvoltage drop can be reduced.
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2
NE m11
[*!
2
m22
[*!
Current, voltages and flux in an unloaded ideal transformer
Transformer- Ideal Transformer Winding resistances are zero, no leakage
inductance and iron loss
Magnetization current generates a flux thatinduces voltage in both windings
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Transformer
i
e1
v1 v2
e2
Transformer on no load.
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Transformer- Ideal Transformer Loaded transformer
i
V1
E2E1
V2Z
L
I2
2
N1 N
2
1
W
he
n aload is conn
ect
ed to th
es
econdary output t
er
mina
ls o
fa transformer as shown in Figure 4.5, a current I2flows into the
load and into transformer secondary winding N2. The current I2which flowing in N2produces flux 2which opposite by Lenzslaw- to themain magnetic flux in the transformer core. Thiswill weaken or slightly reduce themain flux to .
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Transformer- Ideal Transformer Loaded transformer
i
V1
E2E1
V2Z
L
I2
2
N1 N
2
1
The reduction ofmain flux by Faradays law- could alsoreduce the induced voltage in primary winding E1.Consequently E1is now smaller than the supply voltage V1,then the primary current would be increased due to thatpotential differences. Therefore on loaded transformer, theprimary current has an additional current of I1.
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Transformer- Ideal Transformer Loaded transformer
i
V1
E2E1
V2Z
L
I2
2
N1 N
2
1
Theextra current I1which flowing in the primary winding N1produces flux 1which naturally react according to Lenzslaw, demagnetize theflux 2. Therefore the net magneticflux in the core is always maintained at original value, it isthemain flux (theflux which produced by themagnetizingcurrent).
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Transformer- Ideal Transformer Loaded transformer
i
V1
E2E1
V2Z
L
I2
2
N1 N
2
1
Themagneto motiveforce (mmf) source N2I
2at the
secondary winding produces flux 2, while themmf N1I1produces flux 1. Since themagnitude of 1equal tomagnitude of2and the reluctance seen by these two mmfsources areequal, thus
N1I1 = N2I2
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Currents and fluxes in a loaded ideal transformer
Transformer- Ideal Transformer Loaded transformer
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Transformer- Ideal Transformer Turn ratio
Ifthe primary winding has N1 turns and
secondary winding has N2 turns, then:
The inputand outputcomplex powers are equal
1
2
2
1
2
1
I
I
E
E
N
Na !!!
**IESSIE 222111 !!!
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Transformer- Ideal Transformer Functional description of a transformer:
When a = 1 Isolation Transformer
When | a | < 1 Step-Up Transformer Voltageis increased from Primary
side to secondary side
When | a | > 1 Step-Down TransformerVoltage is decreased fromPrimary side to secondary
side
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Transformer- Ideal Transformer Transformer Rating
Practical transformers are usually rated
based on:Voltage Ratio (V1/V2) which gives us the
turns-ratio
Power Rating, small transformers are
given in Watts (real power) and Largerones (Power Transformers) are given inkVA (apparentpower)
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Transformer- Ideal Transformer
Example 4.1
Determine the turns-ratio of a 5 kVA2400V/120V Power Transformer
Turns-Ratio = a = V1/V2 = 2400/120 =20/1 = 20
This means itis a Step-Down transformer
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Transformer- Ideal Transformer
Example 4.2
A 480/2400 V (r.m.s) step-up idealtransformer delivers 50 kW to a resistiveload. Calculate:
(a) the turns ratio, (0.2)
(b) the primary current, (104.17A)(c) the secondary current. (20.83A)
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Transformer- IdealTransformer Nameplate oftransformer
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Transformer- IdealTransformer Equivalentcircuit
Equivalent circuit of an ideal transformer
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Transformer- IdealTransformer Transferring impedances through a transformer
2
22
2
2
1
11
I
V
I
V
I
VZ a
a
a!
!!
Equivalent circuit of an ideal transformer
load
a2
1
!
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a) Equivalent circuit when
secondary impedance istransferred to primary side and
ideal transformer eliminated
b) Equivalent circuit when
primary source is transferred tosecondary side and ideal
transformer eliminated
Thvenin equivalents of transformer circuit
Transformer- IdealTransformer
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Transformer- practical transformer PracticalTransformer
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4.3 Equivalent Circuits
Transformer
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Transformer- equivalent circuit
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Transformer- equivalent circuitDevelopment of the transformer equivalent circuits
The effects of winding resistance and leakage flux are
respectively accounted for by resistance R and leakagereactance X (2fL).
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In a practical magneticcore having finitepermeability, a magnetizing currentIm is
requiredto establish a flux in the core. This effectcan be represented by a
magnetizing inductance Lm. The core loss canbe represented by a resistance Rc.
Transformer- practical equivalentcircuit
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Rc :core loss component,
Xm : magnetization component,
R1 and X1 are resistance and reactance of the primary winding
R2 and X2 are resistance and reactance of the secondary winding
Transformer- practical equivalent circuit
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Transformer- practical equivalent circuit The impedances of secondary side such
as R2, X2 and Z2 can be moved to
primary side and also the impedancesof primary side can be moved to thesecondary side, base on the principle
of:The power before transferred = The
power after transferred.
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Transformer- practical equivalent circuitThe power before transferred = The power
after transferred.
I22R2 = I1
2R2
Therefore R2= (I2/ I1) 2 R2
= a2R2
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Transformer- practical equivalent circuitThe turns can be moved to the right or left by referring
all quantities to the primary or secondary side.
The equivalent circuit with secondary side moved to the primary.
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Transformer- Approximate equivalentcircuit
For convenience, the turns is usually notshown and the equivalent circuit is drawn
with allquantities (voltages, currents, andimpedances) referred to one side.
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Transformer- equivalent circuit Example 4.3
A 100
kVA transformer has400
turns on the primaryand80 turns on the secondary. The primary andsecondary resistance are 0.3 ohm and0.01 ohmrespectively and the corresponding leakagereactances are 1.1 ohm and0.035 ohm respectively.The supply voltage is 2200V. Calculate:
(a) the equivalent impedance referred to the primarycircuit(2.05 ohm)(b) the equivalent impedance referred to thesecondary circuit
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4.4D
etermination ofEquivalent Circuit
Parameter
Transformer
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1. No-load test (or open-circuit test).
2. Short-circuit test.
Transformer- o/c-s/c tests The equivalentcircuit model for the actual
transformer can be usedto predictthe behavior ofthe transformer.
The parameters R1, X1, Rc, Xm, R2, X2 and N1/N2mustbe known so thatthe equivalentcircuit modelcan be used.
These parameters can be directly and more easily
determined by performing tests:
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No load/Open circuit test
Provides magnetizing reactance (Xm) and core
loss resistance (RC) Obtain components are connected in parallel
Short circuit test
Provides combined leakage reactance and
winding resistance
Obtain components are connected in series
Transformer- o/c-s/c tests
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Transformer- open circuit test No load/Open circuit test
Equivalent circuit for open circuit test, measurement at the primary side.
Simplified equivalent
circuit
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Transformer- open circuit test Open circuit test evaluation
Q
V
XP
V
R
IVQIV
P
oc
m
oc
oc
c
ococ
ococ
oc
22
0
1
0 sincos
!!
!
! UU
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Transformer- short circuit test Short circuit test
Secondary (normally the LV winding) is shorted,that means there is no voltage across secondary
terminals; but a large current flows in thesecondary.
Test is done at reduced voltage (about5% ofrated voltage) with full-load current in the
secondary. So, the ammeter reads the full-loadcurrent; the wattmeter reads the winding losses,and the voltmeter reads the applied primaryvoltage.
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Transformer- short circuit test Short circuit test
Equivalent circuit for short circuit test, measurement at the primary side
Simplified equivalent circuit for short circuit test
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Transformer- short circuit test Short circuit test evaluation
21211
121
eee
sc
sce
sc
sce
RZX
I
VZ
I
PR
!
!!
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Transformer- o/c-s/c tests Equivalentcircuit obtained by measurement
Equivalent circuit for a real transformer resulting from the
open and short circuit tests.
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Transformer- o/c-s/c tests Example 4.4
Obtain the equivalentcircuit of a 200/400V, 50Hz
1-phase transformer from the following test data:-
O/C test : 200V, 0.7A, 70W - on L.V. side
S/C test : 15V, 10A, 85W - on H.V. side
(Rc =571.4 ohm, Xm=330 ohm, Re=0.21ohm,Xe=0.31 ohm)
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Transformer voltage regulation Voltage Regulation
Mostloads connected to the secondary of a transformer are
designed to operate at essentially constant voltage. However,as the current is drawn through the transformer, the loadterminalvoltage changes because of voltage drop in theinternal impedance.
To reduce the magnitude of the voltage change, thetransformer should be designed for a low value of theinternal impedance Zeq
The voltage regulation is defined as the change inmagnitude of the secondary voltage as the loadcurrentchanges from the no-load to the loadedcondition.
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ZV2
I2 I2
V12=V20
R1 R2
Ze2
X1
Rc Xm
X2
Ze2 = R1 + R2 + jX1 + jX2
= Re2 + jXe2
Transformer voltage regulation
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ZV2
I2 I2
V12=V20
R1 R2
Ze2
X1
Rc Xm
X2
Applying KVL, V20= I2 (Ze2 ) + V2 = I2 (Re2 + jXe2 ) + V2
Transformer voltage regulation
Or V2= V20 - I2(Ze2)
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I2Xe2
I2Re2
I2
V2
OA
2
Transformer voltage regulation
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I2Xe2
I2Re2
I2
V2
O
V20
I2Re2
I2Xe2
A
B
2
Transformer voltage regulation
V20= I2 (Ze2 ) + V2 = I2 (Re2 + jXe2 ) + V2
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I2Xe2
I2Re2
I2
V2
O
V20
I2Re2
I2Xe2
C
MNDA
B
2
L
2
2
Transformer voltage regulation
Voltage drop = AM = OM OA
= AD + DN + NM
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I2Xe2
I2Re2
I2
V2
O
V20
I2Re2
I2Xe2
C
MNDA
B
2
L
2
2
Transformer voltage regulation
AD = I2 Re2 cos2
DN=BL= I2 Xe2 sin2
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I2Xe2
I2Re2
I2
V2
O
V20
I2Re2
I2Xe2
C
MNDA
B
2
L
2
2
Transformer voltage regulation
Applying Phytogrus theorem to OCN triangle.
(NC)2 = (OC)2 (ON)2
= (OC + ON)(OC - ON) 2(OC)(NM)
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I2Xe2
I2Re2
I2
V2
O
V20
I2Re2
I2Xe2
C
MNDA
B
2
L
2
2
Transformer voltage regulation
Therefore NM = (NC)2/2(OC)
NC = LC LN = LC BD
= I2
Xe2
cos2
- I2
Re2
sin2
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I2Xe2
I2Re2
I2
V2
O
V20
I2Re2
I2Xe2
C
MNDA
B
2
L
2
2
20
2
222222
2
sincos
V
RIXIee
UU
20
2
222222
2
sincos
V
RIXIee
UU
NM =
AM = AD + DN + NM
= I2Recos
2 + I2Xe2sin
2 +
Transformer voltage regulation
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I2Xe2
I2Re2
I2
V2
O
V20
I2Re2
I2Xe2
C
MNDA
B
2
L
2
2
Transformer voltage regulation
thus,votage regulation = (AM)/V20 per unit
In actual practice the term NM is negligible since its value isvery small compared with V 2. Thus the votage regulation
formula can be reduced to:
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I2Xe2
I2Re2
I2
V2
O
V20
I2Re2
I2Xe2
C
MNDA
B
2
L
2
2
Transformer voltage regulation
Voltage regulation =
20
222222 sincos
V
XIRIee
UU s
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Transformer- voltage regulation The voltage regulation is expressed as
follows:
NL
LNL
V
VVregulationVoltage
2
22 !
V2 L= secondar voltage (no-load condition)
V2L = secondar voltage (full-load condition)
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Transformer- voltage regulation For the equivalentcircuit referred to the
primary:
1
21
V
VVregulationVoltage
'!
V1 = no-load voltage
V2 = secondar voltage referred to the primar (full-load condition)
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Transformer- voltage regulation Consider the equivalentcircuit referred to the
secondary,
Re2
Xe2
NL
ee
V
sinXIcosIregulationVoltage
2
222222 UsU!
(-) : power factor leading
(+) : power factor lagging
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Transformer- voltage regulation Consider the equivalentcircuit referred to the primary,
1
211211
V
sinXIcosIregulationVoltage ee
UsU!
Re1
Xe1
(-) : power factor leading
(+) : power factor lagging
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Transformer- voltage regulation Example 4.5
Based on Example 4.3 calculate thevoltage regulation and the secondaryterminalvoltage for fullload having apower factor of
(i) 0.8lagging (0.0336pu,14.8V)(ii) 0.8leading (-0.0154pu,447V)
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Transformer- Efficiency Losses in a transformer
Copper losses in primary and secondary
windings Core losses due to hysteresis and eddy
current. Itdepends on maximum value offlux density, supply frequencyand core
dimension. It is assumedto be constantforall loads
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Transformer- Efficiency As always, efficiency is defined as power outputto
power input ratio
The losses in the transformer are the core loss(Pc) and copper loss (Pcu).
lossesP
P
)P(powerinput)P(powe
routput
out
out
in
out
!
!L
222222
222
ec IPcosIV
cosIV
U
U!L
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Transformer- Efficiency Efficiencyon full load
where S is the apparentpower (in voltamperes)
scocFLFL
FLFL
PPSS
! U UL cos
cos
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Transformer- Efficiency Efficiency for any load equal to n x f ull load
where corresponding total loss =
scocFLFL
FLFL
PnPSn
Sn
vv
v!2cos
cosU
UL
scoc PnP v2
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Transformer- Efficiency Example 4.6
The following results were obtained on a 50 kVA
transformer: open circuittest primaryvoltage,3300 V; secondaryvoltage, 400 V; primarypower,430W.Shortcircuittest primaryvoltage,124V;primarycurrent, 15.3 A; primarypower,525W; secondarycurrent, full load value. Calculatethe efficiency at full load and half load for 0.7power factor.
(97.3%, 96.9%)
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Transformer- Efficiency For constantvalues ofthe terminal voltage V2 and
load power factor angle 2 , the maximum efficiencyoccurs when
Ifthis condition is applied, the condition for
maximum efficiency is
thatis, core loss = copper loss.
0
2
!LdI
d
222 ec IP !
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Transformer- Efficiency
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Transformer- Auto transformer Same operation as two windings
transformer
Physical connection from primary tosecondary
Sliding connection allows for variablevoltage
Higher kVA delivery than two windingsconnection
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Transformer- Auto transformer Advantages:
A tap between primary and secondary sides which
may be adjustable to provide step-up/downcapability
Able to transfer larger S apparent power than thetwo winding transformer
Smaller and lighter than an equivalent two-
winding transformer Disadvantage:
Lacks electrical isolation
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Transformer- Auto transformerA Step Down Autotransformer:
and
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Transformer- Auto transformerA Step Up Autotransformer:
and
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Transformer- Auto transformer Example 4.7
An autotransformer with a 40% tap is supplied by a
400-V, 60-Hz source andis used for step-downoperation. A5-kVA load operating at unity powerfactor is connected to the secondary terminals.
Find:
(a) the secondary voltage,(b) the secondary current,(c) the primary current.
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Transformer- Auto transformer Solution
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Transformer -3 phase transformer Analyses of the grounded wye / delta transformer
Each leg has a
primary and a
secondary winding.
The voltages and
currents are in phase
in the windings
located on the same
leg.
The primary phase-to-
line voltage generates
the secondary line-to-
line voltage. These
voltages are in phase
A B C
VAN VBN VCN
Vab Vbc Vca
N
a b c
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Transformer -3 phase transformer Analyses of the grounded wye / delta transformer
IA
IB
IC
N
IAN
ICNIBN
Iab
Ibc
Ica
Ib
Ia
Ic
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Transformer -3 phase transformer Analyses of the grounded wye / delta transformer
VCA
VAB
N
VAN
VCN
VBN
Vbc
Vbc
Vab
Vca
Vab
A
C
B
a
c
b
VB C Vbc
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Three phase transformerTransformer -3 phase transformer
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Three phase transformerTransformer
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Three phase transformerTransformer
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Three phase transformerTransformer
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Three phase transformerTransformer
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Transformer Three phase transformer
TransformerConstruction
Iron Core
The iron core is made of thin
laminated silicon steel (2-3 %
silicon)
Pre-cut insulated sheets are
cut or pressed in form and
placed on the top of eachother .
The sheets are overlap each
others to avoid (reduce) air
gaps.
The core is pressed together
by insulated yokes.
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Transformer Three phase transformer
TransformerConstruction Winding
The winding is made of copper or
aluminum conductor, insulated withpaper or synthetic insulating material
(kevlar, maylard).
The windings are manufactured in
several layers, and insulation is
placed between windings.
The primary and secondary windingsare placed on top of each others but
insulated by several layers of
insulating sheets.
The windings are dried in vacuum
and impregnated to eliminate
moisture.
Small transformer winding
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Transformer Three phase transformer
TransformerConstruction
Iron Cores
The three phase transformer iron
core has three legs.
A phase winding is placed in
each leg.
The high voltage and low voltage
windings are placed on top ofeach other and insulated by
layers or tubes.
Larger transformer use layered
construction shown in the
previous slides.
A B C
Three phase transformer iron core
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Transformer Three phase transformer
TransformerConstruction
The dried and treated
transformer is placed in a steeltank.
The tank is filled, under vacuum,
with heated transformer oil.
The end of the windings are
connected to bushings.
The oil is circulated by pumps
and forced through the radiators.
Three phase oil transformer
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Transformer Three phase transformer
TransformerConstruction
The transformer is equipped with
cooling radiators which arecooled by forced ventilation.
Cooling fans are installed under
the radiators.
Large bushings connect the
windings to the electrical system.
The oil is circulated by pumps
and forced through the radiators.
The oil temperature, pressure
are monitored to predict
transformer performance.
Three phase oil transformer
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Transformer Three phase transformer
TransformerConstruction
Dry type transformers are used
at medium and low voltage.
The winding is vacuumed and
dried before the molding.
The winding is insulated by
epoxy resin
The slide shows a three phase,
dry type transformer.
Dry type transformer