Transcript Introduction to Transformer

EET 103
Chapter 5
Transformer
1
Introduction to Transformer
A transformer is a device that changes ac electric
energy at one voltage level to ac electric energy
at another voltage level through the action of a
magnetic field.
2
Introduction to Transformer
•
Transformers are constructed of two coils or
more
placed
around
the
common
freeomagnetic core so that the charging flux
developed by one will link to the other.
•
The coil to which the source is applied is called the
primary coil.
•
The coil to which the load is applied is called the
secondary coil.
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The most important tasks performed by
transformers are:
•Changing voltage and current levels in electric
power systems.
•Matching source and load impedances for
maximum power transfer in electronic and control
circuitry.
•Electrical isolation (isolating one circuit from
another or isolating DC while maintaining AC
continuity between two circuits).
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5
Mutual Inductance
• Mutual inductance exits between coils of the
same or different dimensions.
• Mutual inductance is a phenomenon basic to
the operation of the transformer.
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Mutual Inductance
• A transformer is constructed of 2 coils placed so that
the changing flux developed by one will link the other.
• The coil to which the source is applied is called
primary
• The coil which the load is applied is called secondary.
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Mutual Inductance (Cont…)
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Ideal Transformer
An ideal transformer is a lossless device with an
input winding and output winding.
vp
vs

Np
Ns
a
ip
1

is a
N pi p  Nsis
a = turns ratio of the transformer
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Power in ideal transformer
Pin  Pout  V p I p cos   Vs I s cos 
Qin  Qout  V p I p sin   Vs I s sin 
Sin  Sout  V p I p  Vs I s
Where  is the angle between voltage and current
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Impedance transformation
transformer
through
the
The impedance of a device – the ratio of the
phasor voltage across it in the phasor current
flowing through it
ZL 
VL
IL
Z L'  a2Z L
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Non-ideal or actual transformer
Mutual flux
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Losses in the transformer
• Copper (I2R) losses: Copper losses are the resistive
heating in the primary and secondary windings of
the transformer. They are proportional to the square
of the current in the windings.
• Eddy current losses: Eddy current losses are
resistive heating losses in the core of the
transformer. They are proportional to the square of
the voltage applied to the transformer.
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Losses in the transformer
• Hysteresis losses: Hysteresis losses are
associated with the arrangement of the magnetic
domain in the core during each half cycle. They
are complex, nonlinear function of the voltage
applied to the transformer.
• Leakage flux: The fluxes ΦLP and ΦLS which
escape the core and pass through only one of the
transformer windings are leakage fluxes. These
escaped fluxes produce a self inductance in the
primary and secondary coils, and the effects of
this inductance must be accounted for.
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Transformer equivalent circuit
Ie
Ic
Im
Ep = primary induced voltage
Vp = primary terminal voltage
Ip = primary current
Ie = excitation current
XM = magnetizing reactance
RC = core resistance
Rs = resistance of the secondary winding
Xs = secondary leakage reactance
Es = secondary induced voltage
Vs = secondary terminal voltage
Is = secondary current
IM = magnetizing current
IC = core current
Rp = resistance of primary winding
Xp = primary leakage reactance
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Dot convention
1. 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 dots on each side of the core.
2. If the primary current of the transformer flows into the
dotted end of the primary winding, the secondary
current will flow out of the dotted end of the secondary
winding.
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Exact equivalent circuit the actual transformer
a. The transformer model referred to primary side
b. The transformer model referred to secondary
side
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Approximate equivalent circuit the actual
transformer
a. The
transformer
model referred to
primary side
b. The
transformer
model referred to
secondary side
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Exact equivalent circuit of a transformer
refer to primary side
Ep = primary induced voltage
Vp = primary terminal voltage
Ip = primary current
Ie = excitation current
XM = magnetizing reactance
RC = core resistance
winding
Rs = resistance of the secondary winding
Xs = secondary leakage reactance
Es = secondary induced voltage
Vs = secondary terminal voltage
Is = secondary current
IM = magnetizing current
IC = core current
Rp = resistance of primary
Xp = primary leakage reactance
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The Equation:
Primary side
Secondary side
I p  Ie  Is / a
ES  I s ( Rs  jX s )  Vs
Ie  IC  I M
Vs  I s Z L
V p  I p ( R p  jX p )  E p
E p  I C RC
Vp
Ep
Is N p
a



Vs Es I p N s
E p  I M ( jX M )
E p  I e ( RC // jX M )
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Exact equivalent circuit of a transformer referred to
primary side
Rp
Ip
a2Xs
Xp
Is/a
a2Rs
Ie
Vp
Ep
aVs
Exact equivalent circuit of a transformer referred to
secondary side
Rp/a2
aIp
Xp/a2
Rs
Is
Xs
aIe
Vp/a
aIc
Rc/a2
aIm
Ep/a = Es
Vs
XM/a2
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Approximate equivalent circuit of a transformer referred
to primary side
Ip
Reqp
jXeqp
Is/a
+
+
Reqp=Rp+a2Rs
Vp
Rc
aVs
jXM
-
Xeqp=Xp+a2Xs
-
Approximate equivalent circuit of a transformer referred to
secondary side
aIp
Reqs
+
jXeqs
Is
+
Reqs=Rp / a2+Rs
Vp/a
Rc/a2
-
jXM/a2
Vs
Xeqs=Xp / a2+Xs
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Parameter determination of the transformer
Open circuit test
Provides magnetizing reactance and core loss
resistance
Obtain components are connected in parallel
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Experiment Setup
In the open circuit test, transformer rated voltage
is applied to the primary voltage side of the
transformer with the secondary side left open.
Measurements of power, current, and voltage are
made on the primary side.
Since the secondary side is open, the input
current IOC is equal to the excitation current
through the shunt excitation branch. Because this
current is very small, about 5% of rated value,
the voltage drop across the secondary winding
and the winding copper losses are neglected.
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Admittance
Yoc
I oc

Voc
Open circuit Power Factor
Poc
PF  cos  
Voc I oc
Open circuit Power Factor Angle
  cos
1
Poc
Voc I oc
Angle of current always lags angle of voltage by 
I oc
1
1
Yoc      GC  jBM   j
Voc
RC
XM
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Short circuit test
– Provides combined leakage reactance and
winding resistance
– Obtain components are connected in series
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Experiment Setup
In the short circuit test, the secondary side is
short circuited and the primary side is
connected to a variable, low voltage source.
Measurements of power, current, and voltage
are made on the primary side. The applied
voltage is adjusted until rated short circuit
currents flows in the windings.
This voltage is generally much smaller than the
rated voltage.
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Impedances referred to the primary side
Z sc
Vsc

I sc
Power Factor of the current
Psc
PF  cos  
Vsc I sc
Angle Power Factor
1 Psc
  cos
Vsc I sc
Therefore
Z sc
Vsc 0
0
Vsc
0



0
I sc
I sc    

 
Z sc  Req  jX eq  R p  a Rs  j X p  a X s
2
2

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The equivalent circuit impedances of a 20-kVA,
8000/240-V, 60-Hz transformer are to be
determined. The open circuit test and the short
circuit test were performed on the primary side of
the transformer and the following data were taken:
Open- circuit test (on Short- circuit test (on
primary)
primary)
Voc = 8000 V
Vsc = 489 V
Ioc = 0.214 A
Isc = 2.5 A
Poc = 400 W
Psc = 240 W
Find the impedances of the approximate
equivalent circuit referred to the primary side and
sketch that circuit
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Voltage Regulation (VR)
The voltage regulation of a transformer is defined
as the change in the magnitude of the secondary
voltage as the current changes from full load to
no load with the primary held fixed.
VR 
At no load,
V
VS  P
Vp
VR  a
VS , fl
Req
a
 VS , fl
VS , fl
VS ,nl  VS , fl
X 100%
Is
X 100%
Xeq
+
+
Vp/a
Vs
-
-
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Phasor Diagram
Vp/a
jIsXeq
Vs
IsReq
Is
Vp/a
Lagging power factor
jIsXeq
Is
Vs
IsReq
Unity power factor
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Vp/a
jIsXeq
Is
IsReq
Vs
Leading power factor
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Efficiency
The efficiency of a transformer is defined as the ratio of the
power output (Pout) to the power input (Pin).
Pout

X 100%
Pin

Pout
Pout   P losses
Pcore = Peddy current + Physteresis
Pcu= Pcopper losses
X 100%
Vs I s cos 

X 100%
Vs I s cos   Pcu  Pcore
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Pcu = Copper losses are resistive losses in the primary and
secondary winding of the transformer core. They are modeled by
placing a resistor Rp in the primary circuit of the transformer and
resistor Rs in the secondary circuit.
PCORE = Core loss is resistive loss in the primary winding of the
transformer core. It can be modeled by placing a resistor Rc in the
primary circuit of the transformer.
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Example
A 15 kVA, 2400/240-V transformer is to be tested
to determine its excitation branch components,
its series impedances and its voltage regulation.
The following test data have been taken from the
primary side of the transformer
Open- circuit test
Short- circuit test
Voc = 2400 V
Vsc = 48 V
Ioc = 0.25 A
Isc = 6.0 A
Poc = 50 W
Psc = 200 W
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The data have been taken by using the
connections of open circuit test and short circuit
test
a. Find the equivalent circuit of this transformer
referred to the high voltage side.
b. Find the equivalent circuit of this transformer
referred to the low voltage side.
c. Calculate the full load voltage regulation at
0.8 lagging power factor and 0.8 leading
power factor.
d. What is the efficiency of the transformer at full
load with a power factor of 0.8 lagging?
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