MODULE 4: TRANSFORMERS MAGNETIC MATERIALS, BH CHARACTERISTICS, IDEAL AND PRACTICAL TRANSFORMER

MAGNETIC MATERIALS, BH CHARACTERISTICS, IDEAL AND PRACTICAL TRANSFORMER,
EMF EQUATION, EQUIVALENT CIRCUIT, LOSSES IN TRANSFORMERS, REGULATION AND
EFFICIENCY. AUTO-TRANSFORMER AND THREE-PHASE TRANSFORMER CONNECTIONS.

1. BEE
Unit – 4
Transformers
4.1 Magnetic Materials


A magnetic material is a material that experiences a force when placed in a
magnetic field


Although all magnetic materials are metallic, not all metals are magnetic


Common magnetic materials include:
Iron
Steel (an alloy of iron)
Nickel
Cobalt


Note: Copper and Aluminium are non-magnetic


Magnetically soft materials (e.g. Iron):
Are easy to magnetise
Easily lose their magnetism


Magnetically hard materials (e.g. Steel):
Are hard to magnetise
Do not easily lose their magnetism


Permanent magnets are made from magnetically hard materials, as we don’t want
them to lose their magnetism

2. 
Electromagnets are made from magnetically soft materials, as we want them to be
able to easily gain and lose their magnetism.
Bh Characteristics
B-H Curve
 The curve plotted between flux density B and magnetizing force H of a material is
called magnetizing or B-H curve.
  The shape of curve is non-linear. This indicates that relative permeability (µr = B /
µ0H) of a material is not constant, but it varies.
 B-H curves are extremely useful to analyse the magnetic circuit. If value of flux
density and dimension of magnetic circuit is known than from B-H curve total
ampere turn can be easily known.
Ideal And Practical Transformer
Ideal Transformer
An ideal transformer is one that has
no winding resistance

no leakage flux i.e. the same flux links both the windings

no iron losses (i.e., eddy current and hysteresis losses) in the core.

Although an ideal transformer cannot be physically realized, yet its study provides
a very powerful tool in the analysis of a practical transformer. In fact, practical

3. transformers have properties that approach remarkably close to an ideal
transformer.
Ideal Transformer and Phasor Diagram
Consider an ideal transformer on no load i.e., the secondary is open circuited as
shown in the figure. Under such conditions, the primary is simply a coil of pure
inductance.
When an alternating voltage V₁ is applied to the primary, it draws a small
magnetizing current Iₘ which lags the applied voltage by 90°. This alternating
current Iₘ produces an alternating flux ϕ which is proportional to and in phase with
it.
The alternating flux ϕ links both the windings and induces e.m.f. E₁ in the primary
and e.m.f. E₂ in the secondary. The primary e.m.f. E₁ is, at every instant, equal to and
in opposition to V₁  (Lenz’s law). Both e.m.f.s E₁, and E₂ lag flux ϕ by 90°. However,
their magnitudes depend upon the number of primary and secondary turns.
Phasor Diagram of Ideal Transformer
The phasor diagram of an ideal transformer on no load is also shown above. Since
flux ϕ is common to both the windings, it has been taken as the reference phasor.
The primary e.m.f. E₁ and secondary e.m.f. E₂ lag behind the flux ϕ by 90°.
Note that E₁ and E₂ are in phase. But E₁ is equal to V₁ and 180° out of phase with it.
Practical Transformer

4. A practical transformer differs from the ideal transformer in many respects. The
practical transformer has,
iron losses,

winding resistances and,

magnetic leakage, giving rise to leakage reactance.

1. Iron Losses
Since the iron core is subjected to alternating flux, there occurs eddy current and
hysteresis loss in it. These two losses together are known as iron losses or core
losses. The iron losses depend upon the supply frequency, the maximum flux
density in the core, volume of the core, etc.
2. Winding resistances
Since the windings consist of copper conductors, it immediately follows that both
primary and secondary will have winding resistance. The primary resistance R₁ and
secondary resistance R₂ act in series with the respective windings as shown in the
figure.
When current flows through the windings, there will be power loss as well as a loss
in voltage due to IR drop. This will affect the power factor and E₁ will be less than
V₁ while V₂ will be less than E₂.
TYPES OF MAGNETIC MATERIAL
1.Paramagnetic Materials.
The materials, which are not strongly attracted by a magnet, such as aluminium, tin,
platinum, magnesium, manganese etc., are known as paramagnetic materials. Their
relative permeability is small but positive.
Such materials are slightly magnetized when placed in a strong magnetic field and
act in the direction of the magnetic field. In paramagnetic materials the individual
atomic dipoles are oriented in a random fashion, as shown in Figure.

5. The resultant magnetic field is, therefore, negligible. When an external magnetic
field is applied, the permanent magnetic dipoles orient themselves parallel to the
applied magnetic field and give rise to a positive magnetization. Since the
orientation of the dipoles parallel to the applied magnetic field is not complete,
the magnetization is small. These materials have little application in the field of
electrical engineering.
2. Diamagnetic Materials. The materials which are repelled by a magnet such as
zinc, mercury, lead, sulphur, copper, silver, bismuth, wood etc., are known as
diamagnetic materials.
Their permeability is slightly less than unity.
For example, the relative permeabilities of bismuth, copper and wood are 0.99983,
0.999995 and 0.9999995 respectively.
They are slightly magnetized when placed in a strong magnetic field and act in the
direction opposite to that of applied magnetic field. In diamagnetic materials, the
two relatively weak magnetic fields (one caused due to orbital revolution and other
due to axial rotation) are in opposite directions and cancel each other. Permanent
magnetic dipoles are absent in them.
3. Ferromagnetic Materials. Ferromagnetism may be thought of as a special case
of para magnetism in which the individual spin magnetic moments are interacting or
coupled. As with paramagnets, ferromagnets have strong and positive magnetic
susceptibility. Ferromagnetism is possible only when atoms are arranged in a lattice
and the atomic magnetic moments interact to align parallel with each other. This
field is sufficient to magnetize the material to saturation. Unlike paramagnets, when
the applied field is removed, they retain a component of magnetization in the
direction of the applied field – they are “permanently” magnetized Ferromagnetic
materials are of two types: (a) soft magnetic material and (b) hard magnetic
materials.

6. 4.2 Emf Equation
As primary winding excited by the a sinusoidal alternating voltage an alternating
current flows in the winding producing an alternating varying flux Ø
Ø = Øm sin wt
As per Faradays Law of Electromagnetic Induction emf E1 is induced
E1 = N1  
E1 = N1    (Ø Sin wt)
= -  N1  Øm w  Cos wt
Sin (90-wt)
= - Sin (wt-90)
 E1 = N1 Øm   w Sin (wt-90)
 w = 
 E1 =  N1 Ø m Sin (wt-90)
Max value of E1 = E max
Is when Sin (wt-90) =  1
E1 max =  N1 Ø m

7. Hence rms value of induced EMF in primary winding
E1 rms =   =   
 E1 = 4.44 F Ø m N1
 Similarly RMS value of induced EMF in secondary wdg Is
E2 = 4.44 F Ø m N2
4.3 Losses in Transformers


Losses in a Transformer [6m]
There are 2 types of losses occurring in a transformer
A)    1. Core loss or Iron loss
B)    2. Copper loss


Core losses:
This loss is due to the reversal of flux

The flux set up in the core is dependent on the i/p supply

as the i/p supply is constant in magnitude
the flux set up will be constant and
core losses are also constant.
Core losses are voltage dependent loss they can be subdivided in 2

1 Hysteresis loss
2 Reedy current loss
Hysteresis loss: The iron loss occurring in the core of T/F due to the Hysteresis
curve of the magnetic material used for core is called as Hysteresis loss.
Hysteresis curve is the curve as loop which shows the properly of magnetic material
to lag the flux density B behind the field Intensely H

8. Above is the 3 different loops (Hysteresis of 3 diff. Materials)
 the selection of magnetic material for the construction of core depends upon
Hysteresis loop of that material having tall and narrow Hysteresis loop is selected for
the T/F core
  silicon Steel
Hysteresis loss depends on fold factor
PH = KH. Bm
1.67
 F  V – watts
Where KH = constant (Hyst)
Bm = max Flux density
F = Frequency
 = Volume of core.
A] Reedy current loss :
This loss is due to the flow of reedy (circular) current in the core caused by induced
emf in core
PE = Ke Bm
2 
f
2 
t
2 
v – watts
Where

9. Ke = reedy current const.
t = thickness of core
It can be reduced by using stacks of laminations instead of solid core
B] Copper loss : PCU
The Copper loss is due to resistance of the primary and secondary winding.
It is load dependent / current dependent loss
As load on a transformer is variable (changing)  current changes  copper loss is
a variable loss           
Total C is loss = I12 R12
  
+  I22 R22
Copper loss depends upon load on T/F and is proportional to square of load current
or KVA rating of transformer
  PCU  
2
  (KVA)
2
F.L = full load
 PCU (at half load) = 
2 
PCu F.L
= (0.5)
2 
 PCU F.L.
Or PCu ( load)  = ()
2 
 PCu F.L
4.5 Regulation and Efficiency
Find no load vtg E2
Remove the load and measure the reading of V2 meter Ew will get no load vtg E2
 E2  = V2 when load is absent
Now connect load and measure V2 this is now the load voltage

10. For each reading E2 will be same but V2 will change acc. To load


Form Results Plot graph for efficiency and regulation against I2 and O/P power W2
Efficiency:
Efficiency it is the ratio output power to input power of transformer
 = 
Output power = input power – total loss
 Input power = O/P + losses
O/P power = KVA  Cos Ø2  1000
Or = V2  I2 Cos Ø2
Losses = Pi + PCU (F.L)
= iron + copper loss

11.  Full load = 
 Half load(H.L) or 50% or 0.5 = 
 = 
Maximum efficiency – for numerical :
The efficiency of T/F is maximum when copper loss equates iron loss this is the
condition for max efficiency
ie  Pi = PCU
 = 
 PCU = Pi at max n
where KVA at max n given = Full load KVA  
4.6 Autotransformer and Three-Phase Transformer Connections
Auto Transformer
An auto Transformer is a special types of transformer such that a part of the
winding is common to both primary as well as secondary
It has only One winding wended on a laminated magnetic core
With the help of auto Transformer the voltage can be stepped up and stepped
down at any desired value

12. Fig A shows auto T/F as step down T/F variable terminal B C is connected to load
and it acts as secondary wdg.
The position of point C is called as topping point can be selected as per requirement
Fig. B show auto T/F as step up T/F variable terminal B C is connected to supply side
ie ac side and it acts as secondary winding
The operating principle of auto Transformer is same as that of 2 winding Transformer
Advantages
Weight of copper required in an auto Transformer is always loss than that of the

conventional  2 winding Transformer and hence it is chaper
Com[act in size and loss costly.

Losses taking place in Transformer is reduced hence efficiency is higher than conventional

Transformer.
Due to reduced resistance, voltage, regulation is better than conventional T/F.

Disadvantage:
As low voltage and high voltage sides are not separate then there is always risk of
electric shocks when use for high vtg. Applications
Applications
Starting squirrel cage induction motor and synchronous motor.

Auto transformer as dimmer stat

Used as variable ac to variable

 ac Voltage

13. Three-Phase Transformer Connections:
      
ConnectionPhase
Voltage
Line
Voltage
Phase
current
Line  current
Star Vp = VL /3VL = √ 3
x VP
Ip = ILIp = IL
There are four different ways in which three single-phase transformers may be
connected together between their primary and secondary three-phase circuits.
These four standard configurations are given as: Delta-Delta (Dd), Star-Star (Yy),
Star-Delta (Yd), and Delta-Star (Dy).

14. The delta-delta connection nevertheless has one big advantage over the star-delta
configuration, in that if one transformer of a group of three should become faulty or
disabled, the two remaining ones will continue to deliver three-phase power with a
capacity equal to approximately two thirds of the original output from the
transformer unit.