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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
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Transformers
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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.
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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
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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
++
__
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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
)(
)(
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iP
iS
vP
vS
NP
NS
++
__
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Transformer Schematic Transformer schematic symbols:
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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
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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
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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.
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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
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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
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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
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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
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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 ?
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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 ?
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Zload
Zline
VG= 13.2 0o
kV
60 53.1o
500 36.87o