for be first year

1. transformers

2. TRANSFORMERS

3. Classification of Transformers

4. Classification of Transformers

5. Classification of Transformers

6. Constructional Details

7. Magnetic Core

8. Types of Transformer Core
• Core type
• Shell type

9. Core type

10. Shell type

11. Constructional Details of Transformer

12. Cooling arrangement in Transformers
• The various methods of cooling employed in a
transformer are
1. Oil immersed natural cooled transformers
2. Oil immersed forced air cooled transformers
3. Oil immersed water cooled transformers
4. Oil immersed forced oil cooled transformers
5. Air blast transformers

14. EMF Equation of a Transformer
• N1 – Number of primary turns
• N2 – Number of secondary turns

17. We know that T= 1/f, where f is the frequency in Hz
Average rate of change of flux = φm/(1/4f) wb/seconds
If we assume single turn coil, then according to Faradays
law of electromagnetic induction, the average value of
emf induced/turn = 4 f φm volt
Form factor = RMS Value/ Average Value
= 1.11 (since φm is sinusoidal)
RMS value = Form Factor × Average Value
RMS Value of emf induced/turn = (1.11)×(4 f φm )
= 4.44 f φm volts

18. RMS value of emf induced in the entire
primary winding E1 = 4.44 f φm × N1
E1 = 4.44 f Bm A × N1 Volts
Similarly RMS value of emf induced in the
secondary E2 = 4.44 f Bm A × N2 Volts

19. Transformation Ratio (K)
For an ideal transformer
V1 = E1 ; V2= E2;
V1I1 = V2I2
V2/V1 = I1/I2; E2/E1 = I1/I2
From transformer emf induced equation
E2/E1 = N2/N1
We have E2/E1 = N2/N1 = I1/I2= K
Where K is the transformation ratio.
If N2>N1 i.e. K>1, then transformer is a step up transformer.
If N2<N1 i.e. K<1, then transformer is a step down transformer
Voltage ratio = E2/E1 = K
Current ratio = I2/I1= 1/K

20. Ideal Transformer
The ideal transformer has the following
properties
• No winding resistance. i.e., purely inductive.
• No magnetic leakage flux.
• No I2 R loss i.e., no copper loss.
• No core loss.

21. Ideal Transformer
An ideal transformer consists of purely inductive
coil(winding) and loss free core. Windings are
wound on a core. It is shown in figure.

22. Ideal transformer

23. Ideal transformer
• Vector diagram

24. Practical Transformer on No-Load

25. Practical Transformer on No-Load
• Active or working or iron loss or wattfull component
I w= Io cosφo
• Reactive or magnetizing or wattless component
Iµ = Io sinφo
• From above relations
From the above discussion, the following points are noted
1. The no-load primary current Io is very small as compared
to the full load primary current
2. As Io is very small, the no load primary copper loss is
negligible. This no-load input power is practically equal
to the iron or core loss of the transformer.

26. Transformer on load

27. Transformer on load

28. Transformer on load
Thus when the transformer is loaded
• The flux passing through core is same that at no load i.e., flux
is constant at no-load as well as loaded condition. That is why
transformer is also called a constant flux apparatus
• The total primary current (I1) will be vector sum of Io and I2'

29. Transformer winding resistance

30. Transformer winding leakage reactance

31. Transformer winding resistances and
leakage reactance's

32. Vector diagram of transformer on load

33. Vector diagram of transformer on load
• When such a transformer is assumed to have
no windings resistance and leakage reactances
• When the transformer has winding resistance
and leakage reactances.

34. Vector diagram of transformer on load
• Case (i):
no windings resistance and leakage reactances

35. Vector diagram of transformer on load
• no windings resistance and leakage reactances
• A) unity power factor:

36. Vector diagram of transformer on load
• no windings resistance and leakage reactances
• B) Lagging power factor:

37. Vector diagram of transformer on load
• no windings resistance and leakage reactances
• C) Leading power factor

38. Transformer with resistances and reactances

39. Vector diagram of transformer on load
• With winding resistance and reactances
• A) unity power factor:

40. Vector diagram of transformer on load
• With winding resistance and reactances
• B) Lagging power factor:

41. Vector diagram of transformer on load
• With winding resistance and reactances
• C) Leading power factor:

42. Equivalent Circuit of a Transformer

43. Equivalent Circuit of a Transformer

44. Equivalent Circuit of a Transformer
referred to Primary

45. Approximate Equivalent Circuit of a
Transformer referred to Primary

46. Approximate Equivalent Circuit of a
Transformer referred to Primary

47. Approximate Equivalent Circuit of a
Transformer referred to Secondary

48. Voltage Regulation of a Transformer
• Definition:
The regulation of a transformer is defined as
reduction in magnitude of the terminal
voltage due to load, with respect to the no
load terminal voltage.
• For an ideal transformer, regulation is 0%
since voltage drops, due to R1,X1,R2,X2 are
negligible.

49. Voltage Regulation of a Transformer
• Figure shows the approximate equivalent
circuit of a transformer. From the figure we
can draw vector diagram for different power
factors.

50. Voltage Regulation of a Transformer
• Lagging power factor:

51. Voltage Regulation of a Transformer
• Leading power factor:

52. Voltage Regulation of a Transformer
• Unity power factor:

53. Rating of a Transformer
• Voltage rating
• Current rating
• Power rating

54. Why transformer rating given in kVA?
• We have seen that copper loss depends on
current and iron loss on voltage. Hence the
total loss in a transformer depends upon volt-
ampere (VA) only and not on the phase angle
between voltage and current i.e., it is
independent of load power factor. That is why
the rating of a transformer is given in kVA and
not in kW.

55. Applications of Transformer
• Electrical power engineering for transmission
and distribution.
• As an instrument transformer for measuring
current (C.T) and measuring voltage (P.T).
• As a step down and step up transformer to get
reduced or increased output voltage.
• Radio an TV circuits, telephone circuits and
instrumentation circuits.
• Furnaces and welding transformer.

56. Losses in a Transformer
• Iron (or) Core loss
• Copper loss

57. Efficiency of a Transformer
Transformer efficiency Ƞ:
Where, V2= secondary terminal voltage on load
I2= secondary current at load
cosφ = power factor of the load

58. Efficiency of a Transformer
Iron loss Pi = W0 determined from O.C. test
Cu loss Pcu = Ws determined from S.C. test at full load
Copper loss at a load n times the full load = n2 Pcu
Note: at full load n=1
at half load n= 1/2

59. Condition for Maximum Efficiency of a Transformer
If R02 is the total resistance of the transformer referred to
secondary, then

60. Condition for Maximum Efficiency of a Transformer
• Dividing both numerator and denominator by I2
• For maximum value of efficiency for given cosφ2 (pf)
the denominator must have the least value. The
condition for maximum efficiency is obtained by
differentiating the denominator and equating it to
zero.

61. Condition for Maximum Efficiency of a Transformer
• Iron loss = copper loss
constant loss = variable loss
Hence efficiency of a transformer will be maximum
when copper losses are equal to iron losses.
From last equation the load current corresponding to
maximum efficiency

62. Condition for Maximum Efficiency of a
Transformer
If we are given iron loss and full load copper
loss, then the load corresponding to the
maximum efficiency is given by

63. Testing of Transformer
• Open circuit test (or) No load test
• Short circuit test (or) Impedance test
by using these two tests we can find
1. Circuit constants (R0,X0,R01,X01,R02 and X02)
2. Core loss and full load copper loss
3. Predetermine the efficiency and voltage
regulation
• Load test
• Sumpner’s test

64. Open Circuit test
It is useful to find
• No-load loss (or) core loss
• No load current I0 which is helpful in finding
out R0 and X0

65. Open Circuit test
Iron losses Pi = wattmeter reading = W0
No-load current = ammeter reading = I0
Applied voltage = voltmeter reading = V1
Input power W0= V1I0cosφ0
No-load power factor
No-load wattful component
No-load magnetising component

66. Open Circuit test
No-load resistance
No-load reactance
Thus open circuit test gives no load loss Pi, IW,
Iµ,R0 and X0

67. Short circuit test
It is useful to find
• Full-load copper loss
• Equivalent resistance and reactance referred
to metering side.

68. Short circuit test
Full-load cu loss Pcu=watt meter reading = Ws
Applied voltage = voltmeter reading = Vsc
Full load primary current = ammeter reading = I1
Where R01 is the total resistance of transformer
referred to primary.

69. Short circuit test
Total impedance referred to primary
Total leakage reactance referred to primary
Short circuit power factor
Thus short circuit test gives full load cu loss, R01,
X01 and cosφ0

70. Efficiency from OC and SC test
For any load (n)

71. Load Test on Transformer
Load test is helpful to determine the following
• Efficiency of the transformer
• Regulation of the transformer

72. Load test on Transformer
Ws=output power, Wp=input power
Efficiency

73. All Day Efficiency (or) Energy Efficiency

74. Auto Transformer (or) Variac
A transformer in which part of the winding is
common to both the primary and secondary is
known as an auto transformer. The primary is
electrically connected to the secondary, as
well as magnetically coupled to it.

75. Auto Transformer (or) Variac
Saving of copper:
The cross section of the conductor is proportional to
the current carried and the length of the conductor
in winding is proportional to number of turns. Hence
the weight of copper in a winding is proportional to
the product of number of turns and current to be
carried.
Weight of copper in section AC α (N1 – N2) I1
Weight of copper in section BC α (N2(I2-I1))
Total weight of copper in auto transformer α (N1 – N2) I1 + (N2(I2-I1))
Weight of the copper in ordinary transformer α (N1 I1 + N2I2)

76. Auto Transformer (or) Variac
Saving of copper:

77. Auto Transformer (or) Variac
Saving of copper:
Weight of cu in auto transformer = (1-K) ×
weight of cu in ordinary transformer (W0)
Saving in cu = W0 – Wa
= W0 – (1-K) W0
= KW0
Saving in cu = K × weight of copper in ordinary
transformer

78. Advantages of auto transformer
• Higher efficiency
• Small size
• Smaller exciting current
• Lower cost
• Better voltage regulation compared to
conventional two winding transformer
• Continuously varying voltage can be obtained
• Required less copper

79. Disadvantages of auto transformer
• If the ratio of transformation K differs for from unity,
the economic advantages of auto transformer over
two-winding transformer decrease.
• The main disadvantage of an auto transformer is due to
the direct electrical connection between low tension
and high tension sides. If primary is supplied at high
voltage, then an open circuit in the common winding
BC, would result in the appearance of dangerously high
voltage on the low voltage side. This high voltage may
be determined to the load and the persons working
there. Thus a suitable protection must be provided
against such an occurance.
• The short circuit current in an autotransformer is
higher than that in a two winding transformer

80. Applications of auto transformer
• Autotransformers are used for starting of
induction motors and synchronous motors
• Continuously variable autotransformer finds
application in electrical testing laboratories
• Autotransformer are used as boosters to
increase the voltage in AC feeder
• As furnace transformers for getting a
convenient supply to suit the furnace winding
from 230V AC supply