Download 01 - Transformer

EKT 451
CHAPTER 1
SHAIFUL NIZAM MOHYAR
UNIVERSITI MALAYSIA PERLIS
SCHOOL OF MICROELECTRONIC ENGINEERING
1.0 Transformer
Introduction to Transformer.
Applications of Transformer.
Types and Constructions of Transformers.
General Theory of Transformer Operation.
The Ideal Transformer.
Real Single-Phase Transformer.
The Exact Equivalent Circuit of a Real
Transformer.
 The Approximate Equivalent Circuit of a
Transformer.
 Transformer Voltage Regulation and Efficiency.
 Open Circuit and Short Circuit.
 Three Phase Transformer.
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The Power Grid
Diagram courtesy howstuffworks.com
Power Grid
3-phase
industrial
Intertie
Power Plants
Generator
0.5 – 5kV
Step-up
Transformer
Generator
0.5 – 5kV
Step-up
Transformer
Step-down
Transformer
Substation
Step-down
Transformer
100-750 kV
Step-down
Transformer
35-70 kV
4-15 kV
Step-down
Transformer
120/240V
residential
Transmission Tower
Substation
Utility Pole Carrying Three Phase
1.1 Introduction to Transformer.
 Transformer is a device
that changes ac electrical
power at one voltage level
to ac electric power at
another voltage level
through the action of
magnetic field.
 Figure 1.1 is the block
diagrams of;
(a) transformer,
(b) electric motor
(c) generator.
Figure 1.1: Block Diagrams of
Transformer, an Electric Motor and
a Generator.
Figure 1.2(a) A 500 MVA Power Transformer. (left)
(b) A Pole-Mount 15 kVA Distribution Transformer. (right) (Courtesy of ABB)
1.2 Applications of Transformer.
Why do we need transformer ?
(a) Step Up.
 Step up transformer, it will decrease the current to keep
the power into the device equal to the power out of it.
 In modern power system, electrical power is generated
at voltage of 12kV to 25kV. Transformer will step up the
voltage to between 110kV to 1000kV for transmission
over long distance at very low lost.
(b) Step Down.
 The transformer will stepped down the voltage to the
12kV to 34.5kV range for local distribution in the
homes, offices and factories as low as 120V (America)
and 240V (Malaysia).
1.3 Types and Constructions of
Transformer.
 Power transformers are constructed on two types of cores;
(i) Core form.
(ii) Shell form.
A) Core type
B) Shell type
Figure 1.3: Core Form and Shell Form.
Core form.
 The core form construction consists of a simple
rectangular laminated piece of steel with the
transform winding wrapped around the two sides of the rectangle.
Shell form.
 The shell form construction consists of a three-legged laminated core
with the winding wrapped around the center leg.
 In both cases the core is constructed of thin
laminations electrically isolated from each other
in order to minimize eddy current.
 The coils are usually not directly connected.
 The common magnetic flux present within the
coils connects the coils.
Figure 1.4: A Simple Transformer.
Construction.
 Transformer consists of two or more coils of wire wrapped
around a common ferromagnetic core. The coils are usually
not directly connected.
 The common magnetic flux present within the coils connects
the coils.
 There are two windings;
(i) Primary winding (input winding); the winding that is
connected to the power source.
(ii) Secondary winding (output winding); the winding
connected to the loads.
Operation.
 When AC voltage is applied to the primary winding of the
transformer, an AC current will result iL or i2 (current at load).
 The AC primary current i2 set up time varying magnetic flux
f in the core. The flux links the secondary winding of the
transformer.
Cont’d…
Operation.
 From the Faraday law, the emf will be induced in the secondary
winding. This is known as transformer action.
 The current i2 will flow in the secondary winding and electric
power will be transfer to the load.
 The direction of the current in the secondary winding is
determined by Len’z law. The secondary current’s direction is such
that the flux produced by this current opposes the change in the
original flux with respect to time.
 1.4 General Theory of Transformer
Operation.
FARADAY’S LAW
If current produces a
magnetic field, why can't a
magnetic field produce a
current ?
Michael Faraday
In 1831 two people, Michael Faraday in
the UK and Joseph Henry in the US
performed experiments that clearly
demonstrated that a changing magnetic
field produces an induced EMF (voltage)
that would produce a current if the circuit
was complete.
 When the switch was closed, a momentary deflection was
noticed in the galvanometer after which the current returned
to zero.
 When the switch was opened, the galvanometer deflected
again momentarily, in the other direction. Current was not
detected in the secondary circuit when the switch was left
closed.
An e.m.f. is made to happen (or induced) in a
conductor (like a piece of metal) whenever it
'cuts' magnetic field lines by moving across
them. This does not work when it is stationary. If
the conductor is part of a complete circuit a
current is also produced.
 Faraday found that the induced e.m.f. increases if
(i) the speed of motion of the magnet or coil increases.
(ii) the number of turns on the coil is made larger.
(iii) the strength of the magnet is increased.
Faraday’s Law
f
EN
Δt
E = Electromagnetic force (emf)
Φ = Flux
N = Number of turn
t = time
 Any change in the magnetic environment of a coil of wire
will cause a voltage (emf) to be "induced" in the coil. No
matter how the change is produced, the voltage will be
generated.
 The change could be produced by changing the magnetic
field strength, moving a magnet toward or away from the
coil, moving the coil into or out of the magnetic field,
rotating the coil relative to the magnet, etc.
 Inserting a magnet into a coil also
produces an induced voltage or
current.
 The faster speed of insertion/
retraction, the higher the induced
voltage.
Figure 1.5: Basic
Transformer Components.
 According to the Faraday’s law of electromagnetic induction,
electromagnetic force (emf’s) are induced in N1 and N2 due to a
time rate of change of fM,
d
d
e
 N
dt
dt
where
e1 
df
df
N1
; e2  N 2
dt
dt
(1.1)
e = instantaneous voltage induced by magnetic field (emf),
 = number of flux linkages between the magnetic field and the
electric circuit.
f = effective flux
Cont’d…
 Lenz’s Law states that the direction of e1 is such to
produce a current that opposes the flux changes.
 If the winding resistance is neglected, then equation
(1.1) become;
df
v1  e1  N1 ( );
dt
df
v 2  e2  N 2 ( )
dt
(1.2)
 Taking the voltage ratio in equation (1.2) results in,
N 1 e1

N 2 e2
(1.3)
Cont’d…
 Neglecting losses means that the instantaneous power is
the same on both sides of the transformer;
e1i1  e2 i2
(1.4)
 Combining all the above equation we get the equation
(1.5) where a is the turn ratio of the transformer.
N 1 v1 i 2
a
 
N 2 v 2 i1
a > 1  Step down transformer
a < 1  Step up transformer
a = 1  Isolation Transformer
(1.5)
 The flux varies sinusoidally such that;
fmax
f = fmax sin t
 The rms value of the induce voltage is;
df
d
eN
 N (f max sin 2ft )
dt
dt
E
Nf max
2
 4.44 fNf max
 Losses are composed of two
parts;
(a) The Eddy-Current lost.
(b) The Hysteresis loss.
 Eddy current lost is basically
loss due to the induced current in
the magnetic material. To
reduce this lost, the magnetic
circuit is usually made of a stack
of thin laminations.
 Hysteresis lost is caused by the
energy used in orienting the
magnetic domains of the material Figure 1.5: A Magnetic Hysteresis
along the field. The lost depends or B-H Curve of Core Steel.
on the material used.
Example 1: Transformer.
How many turns must the primary and the
secondary windings of a 220 V-110 V, 60 Hz
ideal transformer have if the core flux is not
allowed to exceed 5mWb?
 1.5 The Ideal Transformer.
 An Ideal transformer is a lossless device with an input
winding and an output winding.
 Zero resistance result in zero voltage drops
between the terminal voltages and induced voltages
 Figure 1.6 shows the relationship of input voltage and
output voltage of the ideal transformer.
Figure 1.6: An Ideal Transformer and the Schematic Symbols.
 The relationship between voltage and the number of turns.
Np , number of turns of wire on its primary side.
Ns , number of turns of wire on its secondary side.
Vp(t), voltage applied to the primary side.
Vs(t), voltage applied to the secondary side.
v p (t )
v s (t )

Np
Ns
a
 where a is defined to be the turns ratio of the transformer.
 The relationship between current into the primary
side, Ip(t), of transformer versus the secondary side,
Is(t), of the transformer;
N p I p (t )  N s I s (t )
I p (t )
1

I s (t ) a
 In term of phasor quantities;
- Note that Vp and Vs are in the same phase angle. Ip
and Is are in the same phase angle too.
- the turn ratio, a, of the ideal transformer affects the
magnitude only but not the their angle.
Vp
Vs
 a
Ip
Is
1

a
 The dot convention appearing at one end of each winding tell the
polarity of the voltage and current on the secondary side of the
transformer.
 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 doted on each side of the core.
 If the primary current
of the transformer flow
into the dotted end of
the primary winding, the
secondary current will
flow out of the dotted
end of the secondary
winding.
 1.5.1 Power in an Ideal Transformer.
 Power supplied to the transformer by the primary circuit is
given by ;
Pin  V p I p cos  p
where, qp is the angle between the primary voltage and the
primary current.
 The power supplied by the transformer secondary circuit to
its loads is given by the equation;
Pout  Vs I s cos  s
where, qs is the angle between the secondary voltage and the
secondary current.
 Voltage and current angles are unaffected by an ideal
transformer , qs – qs = q. The primary and secondary
windings of an ideal transformer have the same power factor.
 The power out of a transformer;
 Apply Vs= Vp/a and Is= aIp
into the above equation gives,
Pout  Vs I s cos 
Pout 
Pout
Vp
( aI p ) cos 
a
 V p I p cos   Pin
 The output power of an ideal transformer is equal to the input
power.
 The reactive power, Q, and
the apparent power, S;
Qin  V p I p sin   Vs I s sin   Qout
S in  V p I p  Vs I s  S out
 In term of phasor quantities;
 Note that Vp and Vs are in the same phase angle. Ip and Is are
in the same phase angle too.
 The turn ratio, a, of the ideal transformer affects the magnitude
only but not the their angle.
Example 2: Ideal Transformer.
Consider an ideal, single-phase 2400V-240V transformer.
The primary is connected to a 2200V source and the secondary
is connected to an impedance of 2 W < 36.9o,
find,
(a) The secondary output current and voltage.
(b) The primary input current.
(c) The load impedance as seen from the primary side.
(d) The input and output apparent power.
(e) The output power factor.