The document provides an overview of transformers, including: 1. Transformers transfer electrical energy from one circuit to another through mutual induction between windings, without changing frequency but changing voltage and current. 2. Transformers can be classified as step-up, step-down, or isolation based on their voltage and turn ratios. 3. An ideal transformer has no losses and perfect coupling between windings, while a practical transformer has iron losses, winding resistance, and leakage flux.

1. Unit-3
Transformers
• Topics:(syllabus)
• 1.Principle of Transformer
• 2.Types of Transformers
• 3.Ideal and practical Transformer
• 4.Emf equation of the Transformer
• 5.Equalent circuit of Transformer
• 6.O.C.and S.C Test of Transformer
• 7.Losses ,Efficiency and Regulation of
Transformer
• 8.Auto Transformer

2. Transformers
Introduction:

3. • Defination : Transformer is a static device ,Which Transfers
electrical energy from one circuit to another circuit without
change in frequency, but change in voltage and current.
• Step up Transformer : E2>E1,N2>N1
• Step down Transformer : E2<E1,N2<N1
• Isolation Transformer : E2=E1,N2=N1
• V1= Supply voltage, E1=Primary winding induced voltage,
I1=Primary winding current ,N1=Primary winding turns ,
E2=Secondary winding induced voltage, I2= secondary winding
current N2= secondary winding turns,V2= load across voltage.

4. Working Principle of Transformer:

5. • Mutual induction between two or more windings (also known as coils)
allows for electrical energy to be transferred between circuits. This
principle is explained in further detail below.
• When an alternating voltage V1 is applied to the primary, an alternating flux
Φ is set up in the core. This alternating flux links both the windings and
induces emfs E1 and E2 in them according to Faraday’s laws of
electromagnetic induction. The emf E1 is termed as primary emf and emf
E2 is termed as Secondary emf.

6. Types of Transformers
• Based on the construction transformers are classified 2 types.
• 1.Core type transformer
• 2.Shell type transformer
1.Core type transformer: In a core-type transformer, half of the primary
winding and half of the secondary winding are placed round each limb to
reduce the leakage flux.

7. 2.Shell type transformer: This method of construction involves the use
of a double magnetic circuit. Both the windings are placed round the central
limb to ensure a low-reluctance flux path.

9. Comparison of core and shell type Tranformer
Core type Transformer shell type Transformer

10. EMF Equation of a Transformer

11. EMF Equation of a Transformer
• Consider that an alternating voltage V1 of frequency f is applied to the primary as
shown in Fig. 3-2b. The sinusoidal flux Φ produced by the primary can be
represented as:

12. • Voltage Transformation Ratio (K):
• From the above equations of induced emf, we have,
• The constant K is called voltage transformation ratio.
•
N1
N2
Is called turns ratio.

16. Ideal transformer
• A transformer is said to be ideal if it satisfies following properties:
• It has no losses.
• Its windings have zero resistance.
• Leakage flux is zero i.e. 100 % flux produced by primary links with
the secondary.
• Permeability of core is so high that negligible current is required to
establish the flux in it.
• NOTE:
• For an ideal transformer, the primary applied voltage V1 is same as the primary
induced emf E1 as there are no voltage drops.
• Ideal Transformer on No Load:
• Consider an ideal transformer in Fig. 3-5. For no load I2 =0. I1 is just
necessary to produce flux in the core, which is called magnetizing current
denoted as Im. Im is very small and lags V1 by 900 as the winding is purely
inductive. According to Lenz's law, the induced e.m.f. opposes the cause
producing it which is supply voltage V1. Hence E1 and E2 are in antiphase with
V1 but equal in magnitude and E1 and E2 are in phase

17. This can be illustrated in the phase diagram as shown below:

18. Ideal Transformer on Load
• Let us connect a load ZL across the secondary of an ideal transformer as
shown in Figure below:
• The secondary emf E2 will cause a current I2 to flow through the load:

20. • The Phasor diagram for the ideal transformer on load is shown in Figure
(ii) above.
• The secondary current I2 lags behind V2 (or E2) by Φ2. It causes a primary
current I1 = KI2 = I2 (for K=1) which is in antiphase with it.

21. Practical Transformer
• A practical transformer differs from the ideal transformer in many respects.
The practical transformer has (i) iron losses (ii) winding resistances and
(iii) magnetic leakage, giving rise to leakage reactance.
• Iron losses. Since the iron core is subjected to alternating flux, there occurs
eddy current and hysteresis loss in it.
• 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 below:

22. • Leakage reactance. Both primary and secondary currents produce flux.
The flux Φ which links both the windings is the useful flux
• However, primary current would produce some flux Φ which would not
link the secondary winding and is called mutual flux.

23. Practical Transformer on No Load
• Consider the figure below
• The primary will draw a small current I0 to supply (i) the iron losses and
(ii) a very small amount of copper loss in the primary. Hence the primary
no load current I0 is not 90° behind the applied voltage V1 but lags it by an
angle Φ0 < 90° as shown in the phasor diagram.

25. Modelling and Equivalent Circuits of Single Phase
Transformers
• The term equivalent circuit of a transformer means the combination of
fixed and variable resistances and reactance's which exactly simulates
performance and working of the transformer.
• Impedance Ratio:
• Consider a transformer having impedance Z2 in the secondary as shown in
the figure below:

26. • Shifting Impedances in a Transformer
Consider the following figure:

27. • We can transfer the parameters from one winding to the other. Thus:
► A resistance R1 in the primary becomes K2 R1 when transferred to the
secondary.
► AresistanceR2 inthesecondarybecomesR2/K2whentransferredtothe
primary.
► A reactance X1 in the primary becomes K2 X1 when transferred to the
secondary.
► AreactanceX2 inthesecondarybecomesX2/K2 whentransferredtothe
primary.
► Whentransferringresistanceorreactancefromprimarytosecondary,
multiply it by K2
.
► Whentransferringresistanceorreactancefromsecondarytoprimary,
divide it by K2
.
Whentransferringvoltageorcurrentfromone windingtotheother,only K is used

28. Secondary parameters Referred to primary
• Secondary parameters Referred to primary
• Equivalent resistance of transformer referred to primary
• Equivalent reactance of transformer referred to primary

29. • Equivalent impedance of transformer referred to primary
• The value of primary current I1
Primary parameters Referred to secondary:

30. • Equivalent resistance of transformer referred to secondary
• Equivalent reactance of transformer referred to secondary
• Equivalent impedance of transformer referred to secondary
• The value of secondary voltage referred to primary
V2 = KV1

31. Simplified Equivalent Circuit of a Loaded Transformer
• If I0 of a transformer is small as compared to the rated primary current I1,
voltage drops in R1 and X1 due to I0 are negligible. Hence, the exact
equivalent circuit can be simplified by transferring the shunt circuit R0 - X0
to the input terminals as shown below:
• If all the secondary quantities are referred to the primary, we can get the
simplified equivalent circuit of the transformer referred to the primary as
shown below

34. • If all the primary quantities are referred to the secondary, we can get
the simplified equivalent circuit of the transformer referred to the
secondary as shown below

35. • From the above circuit:
• Where
The approximate equivalent circuit of transformer referred to secondary is
shown below

36. Transformer Tests
• The circuit constants, efficiency and voltage regulation of a transformer
can be determined by two simple tests:
• (i) open-circuit test and (ii) short-circuit test
• Open-Circuit Test:
• This test is conducted to determine:
• The iron losses (or core losses)
• Parameters R0 and X0 of the transformer
• In this test (see Figure below), the rated voltage is applied to the primary
(usually low-voltage winding) while the secondary is left open-circuited.
• As the normal rated voltage is applied to the primary, therefore, normal iron
losses will occur in the transformer core.
• Cu losses in the primary under no-load condition are negligible as
compared with iron losses

37. NOW ITS NOT POSSIBLE
• For the figure above:
• Iron losses, Pi = Wattmeter reading = W0
• No load current = Ammeter reading = I0
• Applied voltage = Voltmeter reading = V1
• Input power, W0 = V1 I0 cosϕ0
•

39. Short-Circuit or Impedance Test
• This test is conducted to determine:
• Full-load copper losses of the transformer and
• R01 (or R02), X01 (or X02)
• In this test (see Figure below), the secondary (usually low-voltage winding) is short-circuited
by a thick conductor and variable low voltage is applied to the primary.
• The low input voltage is gradually raised till at voltage VSC, full-load current I1 flows in the
primary. Then I2 in the secondary also has full-load value since I1/I2 = N2/N1. Under such
conditions, the copper loss in the windings is the same as that on full load.

40. • Full load Cu loss, PC = Wattmeter reading = WS
• Applied voltage = Voltmeter reading = VSC
• F.L. primary current = Ammeter reading = I1
• where R01 is the total resistance of transformer referred to primary Total impedance
referred to primary
• Total leakage reactance referred to primary,
• Short-circuit pf

41. • Efficiency from Transformer Tests:
• The efficiency for any load,
• where: Pi = Iron loss can be obtained from open-circuit test
• Pc = Copper loss can be obtained from short-circuit test
• x= Fraction of full-load

42. • Regulation of Transformer:
• The voltage regulation of a transformer is the arithmetic difference (not
phasor difference) between the no-load secondary voltage (0V2) and the
secondary voltage V2 on load expressed as percentage of no-load voltage
i.e.
Where V2 = No-load secondary voltage = K V1
• V2 = Secondary voltage on load
•

43. Transformer losses
• The power losses in a transformer are of two types, namely;
• 1. Core or Iron losses 2. Copper losses
• Iron losses (Pi): These are due to the transformer core
• These consist of hysteresis and eddy current losses and occur in the transformer core
due to the alternating flux. These can be determined by open-circuit test .
• copper Cu losses: These are the Losses are due to the winding of the transformer.
These can be determined by short-circuit test
• Total copper Cu losses:
• Hence, total losses in a transformer are:

44. Efficiency of a Transformer
• Like any other electrical machine, the efficiency of a transformer is defined as the ratio of
output power (in watts or kW) to input power (watts or kW) i.e.
• In practice, open-circuit and short-circuit tests are carried out to find the efficiency,
• Output power = V2I2 cosϕ2
• If R02 is the total resistance of the transformer referred to secondary, then,

45. • For a load of given pf, efficiency depends upon load current I2. Hence, the efficiency to be
maximum the denominator should be minimum i.e.
• dŋ/di2 = 0 ;
• i.e., Iron losses = Copper losses
• From above, the load current I2 corresponding to maximum efficiency is:

46. Regulation of Transformer:
• Regulation of Transformer:
• The voltage regulation of a transformer is the arithmetic difference (not
phasor difference) between the no-load secondary voltage (0V2) and the
secondary voltage V2 on load expressed as percentage of no-load voltage
i.e.
Where 0V2 = No-load secondary voltage = K V1
• V2 = Secondary voltage on load
•

47. Auto transformer

48. Single phase Auto transformer working
principle
• The auto transformer works on the same principle of two
winding transformer.
• Auto transformer has one winding (ACB) only in which a
part of the winding (CB)is common to both high voltage and
low voltage sides
• The winding CB is called the common winding and the AC is
called series winding
• AB is the primary winding with N1 turns and the voltage
applied across the primary of the transformer is V1.
• CB is the secondary winding where C is a suitable tapping
point and secondary turns areN2
• V2 is the terminal voltage of the secondary and I2 is the
secondary output current .

49. Explanation ..
• When an alternating voltage V1 is applied to the auto
transformer i.e., alternating current (I1) is produced . This
in turn produces alternating flux in the winding of
autotransformer.
• According to the Faraday’s laws of electromagnetic
induction e.m.f is induced the winding of auto transformer.
• If the tapping point C is connected to the load the
alternating current I2 flows through the load.
• The power is transferred in auto transformer both by
means of induction as well as conduction process
• kVA Inductive power = (V1-V2)I1
• Input kVA = V1I1
• kVA conductive = (Input kVA) –(kVA)inductive.

50. Advantages of auto transformer
• An auto transformer uses less winding material
than a two winding transformer
• It is smaller in size and cheaper than the two
winding transformer of the same output.
• As there is a reduction in conductor and core
materials , the auto transformer has higher
efficiency than the equivalent two winding
transformer
• An auto transformer has variable output voltage
when a sliding contact is used for the secondary.

51. Disadvantages of Auto-Transformer
• There is a direct connection between the
high-voltage and low-voltage sides. In case of
an open circuit in the common winding ,the
full primary voltage would be applied to the
load on the secondary. This high voltage may
damage the equipment connected to the
secondary side

52. Applications
• Interconnection of power systems of different voltages.
• Boosting of supply voltage by a small amount in
distribution systems to compensate the voltage drop.
• Auto transformer with a number of tappings are used
for starting induction motors and synchronous motors.
• Auto –transformer is used as a variac( variable a.c) in
laboratory and other situations that require
continuously variable voltage over broad ranges