The document provides information about transformers, including: 1. It describes the basic working principle of a transformer, which operates on mutual induction between two inductively coupled coils. 2. It classifies transformers based on their duty, construction, voltage output, application, cooling method, and input supply. 3. It discusses the constructional details of transformers including their cores, windings, and magnetic circuits. 4. It covers transformer testing methods like open circuit, short circuit, and load tests used to determine losses, efficiency, and other parameters.

1. EE8301 – ELECTRICAL MACHINES - I
Unit – II – TRANSFORMERS
By
Mr. D. Karthik Prabhu,
Assistant Professor,
Department of Electrical and Electronics Engineering.
Email: karthikprabhu@ritrjpm.ac.in 1

2. transformers

3. Transformer
• The transformer is a static piece of apparatus
by means of which an electrical power is
transformed from one alternating current
circuit to another with the desired change in
voltage and current, without any change in
the frequency.

4. Working principle
A transformer operates on the principle of mutual induction between
two inductively coupled coils.
The two windings are magnetically coupled, there is no electrical
connection between two winding.
Primary winding is energised by sinusoidal voltage. The secondary
winding feeds the load. The alternating current in the primary winding sets up
an alternating flux (Ф) in the core. The secondary winding is linked by most of
this flux and EMF is induced in the secondary winding.

5. TRANSFORMERS

6. Classification of Transformers
• (i) Duty they perform:
1. Power transformer – for transmission and
distribution purposes
2. Current transformer – instrument transformers
3. Potential transformers – instrument
transformers
• (ii) construction:
1. Core type transformer
2. Shell type transformer
3. Berry type transformer

7. Classification of Transformers
• (iii) Voltage output:
1. Step down transformer (Higher to lower)
2. Step up transformer (Lower to Higher)
3. Auto transformer (Variable from ‘0’ to rated
value)
• (iv) Application:
1. Welding transformer
2. Furnace transformer

8. Classification of Transformers
• (v) Cooling:
1. Duct type transformer (Air natural (or) Air blast)
2. Oil immersed
(a) Self cooled
(b) forced air cooled
(c) water cooled
(d) forced oil cooled

9. Classification of Transformers
• (vi) Input Supply:
1. Single phase transformer
2. Three phase transformer
(a) star – star
(b) star – Delta
(c) Delta – Delta
(d) Delta – Star
(e) Open – Delta
(f) Scott connection

11. Constructional Details

12. Constructional details of Transformer
1. Core
It is made up of high grade silicon steel.
Its function is to carry the flux providing low reluctance path. E
shaped , I shaped, L shaped cores are used

13. Windings:
The coils used are wound on the limbs and are insulated from each
other. The function of the windings is to carry current and produce the flux
necessary for the functioning of the transformer.
The different types of transformer windings are:
1. Concentric windings:
Cross-over, Helical, Disc
2. Sandwich windings:

14. Magnetic Core

15. Types of Transformer Core
• Core type
• Shell type
• Berry type

16. Core type

17. Core Type Transformer

18. Shell type

19. Shell type Transformer

20. Berry Type Transformer

21. Constructional Details of Transformer

24. 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

27. Core Type Shell Type
The winding encircles the core The core encircles most part of
the windings
The cylindrical type of coils are
used
Generally, multilayer disc type
or sandwich coils are used
As windings are distributed,
the natural cooling is more
effective
As windings are surrounded by
the core, the natural cooling
does not exist.
The coils can be easily
removed from maintenance
point of view
For removing any winding for
the maintenance, large
number of laminations are
required to be removed. This is
difficult.

28. Core Type Shell Type
The construction is preferred
for low voltage transformers.
The construction is used for
very high voltage
transformers
It has a single magnetic
circuit
It has a double magnetic
circuit
In a single phase type, the
core has two limbs
In single phase type, the core
has three limbs

29. Can D.C supply be used for Transformers
• The transformer works on principle of mutual
induction, for which current in one coil must
change uniformly. If dc supply is given, the
current will not change due to constant supply
and transformer will not work.
• Practically winding resistance is very small. For dc
the inductive reactance XL is zero as dc has no
frequency. So total impedance of winding is very
low for dc. Thus winding will draw very high
current if dc supply is given to it. This may cause
the burning of windings due to extra heat
generated and may cause permanent damage to
the transformer.

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

33. 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

34. 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

35. 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

36. 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.

37. 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.

38. Ideal transformer

39. Ideal transformer
• Vector diagram

40. Practical Transformer on No-Load

41. 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.

42. Transformer on load

43. Transformer on load

44. 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 I0 and I’ 2

45. Transformer winding resistance

46. Transformer winding leakage reactance

47. Transformer winding resistances and
leakage reactance's

48. Vector diagram of transformer on load

49. 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.

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

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

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

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

54. Transformer with resistances and reactances

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

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

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

58. Shifting Impedances in a transformer

59. Equivalent Circuit of a Transformer

60. Equivalent Circuit of a Transformer

61. Equivalent Circuit of a Transformer
referred to Primary

62. Approximate Equivalent Circuit of a
Transformer referred to Primary

63. Approximate Equivalent Circuit of a
Transformer referred to Primary

64. Approximate Equivalent Circuit of a
Transformer referred to Secondary

65. Voltage Regulation of a Transformer
• Definition:
The regulation of a transformer is the arithmetic
difference between the no-load secondary
voltage and the secondary voltage on load
expressed as percentage of no-load voltage.
• For an ideal transformer, regulation is 0% since
voltage drops, due to R1,X1,R2,X2 are negligible.

66. 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.

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

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

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

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

71. 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.

72. Applications of Transformer
Transformers are used
• In 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.
• In Radio and TV circuits, telephone circuits
and instrumentation circuits.
• In Furnaces and welding transformer.

73. Losses in a Transformer
• Iron (or) Core loss (Hysteresis & eddy current)
• Copper loss (I1
2R1 & I2
2R2)

74. 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

75. 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

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

77. 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.

78. 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

79. 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

80. 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

81. 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

82. 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

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

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

85. 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.

86. 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

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

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

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

90. Sumpner Test or Back to Back Test

91. Advantages of Sumpner Test
• The power required to carry out the test is
small
• The transformers are tested under full-load
conditions
• The iron losses and full load copper losses are
measured simultaneously
• The temperature rise of the transformer can
be noted

92. Disadvantages of Sumpner Test
• Two identical transformers are required
• In practice exact identical transformers cannot
be obtained
• As two transformers are required, the test is
not economical

93. All Day Efficiency (or) Energy Efficiency

94. 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.

95. 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)

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

97. 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

98. 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

99. 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 occurrence.
• The short circuit current in an autotransformer is
higher than that in a two winding transformer

100. 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

101. Three Phase Transformers

102. Advantages Three Phase Transformers
• It occupies less space for same rating, compared
to a bank of three single phase transformers
• It has less weight
• The cost is also low
• Easy to handle
• It can be transported very easily
• The core is of a smaller size and hence less
material is required.

103. Three Phase Transformer connections
• Star-star connection
• Delta-delta connection
• Star-delta connection
• Delta-star connection

104. Star-star connection

105. Advantages of Star-star connection
• Less number of turns and less quality of
insulation is required because Vph = VL/√3
• Since Iph = IL, the current through the winding is
high. The windings must have a large cross
section and must be mechanically strong so that
they can bear heavy load and short circuit.
• There is no phase shift between the primary and
secondary voltages.
• It is suitable for three phase and four wire system
because of the presence of neutral point.

106. Disadvantages of Star-star connection
• The neutral point shifts due to unbalanced load
and performance is not satisfactory.
• Inspite of connecting neutral point to earth, the
third harmonic present in the alternator voltage
may appear and cause distortion of secondary
voltage.

107. Delta-delta connection

108. Advantages of Delta-delta connection
• This connection permits unbalanced loading also.
• If one transformer is inoperative, V-V operation is
still possible with reduced rating.
• No distortion in secondary voltage occurs
• For delta connection Ip=IL/√3 and cross section of
the winding is low which makes the connection
economical for low voltage transformers.

109. Disadvantages of Delta-delta connection
• It is not suitable for three phase four wire
system because neutral point is absent.
• This connection is generally used for low
voltage transformers.

110. Star-delta connection

111. Advantages of Star-delta connection
• Since primary is star connected, fewer number of
turns are required in primary which makes it
economical for high voltage, step-down power
transformer.
• The available neutral point on primary side can
be earthed to avoid distortion.
• It is possible to handle large, unbalanced load.

112. Disadvantages of Star-delta connection
• Since the secondary voltage is not inphase
with the primary, it is not possible to make it
parallel with star-star and delta-delta
transformers.

113. Delta-star connection

114. Advantages of Delta-star connection
• Since primary is delta connected, the winding
cross section is small.
• Since neutral is available on the secondary side,
three phase four wire supply can be carried out.
• No distortion occurs due to third harmonic
component.
• Saving in cost of insulation is possible due to
availability of star connection on secondary side.

115. Disadvantages of Delta-star connection
• Since the secondary voltage is not inphase
with primary, it is not possible to make it
parallel with star-star and delta-delta
transformers.
• Since secondary is connected in star, this type
of transformer is affected by unbalanced load.

118. Open-delta or V-V connection

119. Applications of Open-delta or V-V connection
• If one of the transformers in delta-delta bank is
inoperative, it is possible to continue service with
reduced capacity.
• If the three phase load is small, it is preferable to
use a V-V connection.
• If the load increases, in future, the open delta can
be closed to increase the rating.

120. Scott or T-T connection

121. Scott or T-T connection

122. Scott or T-T connection

123. Parallel operation of a transformer

124. Parallel operation of a transformer
• There are three principle reasons for connecting
transformers in parallel.
1. If one transformer fails, the continuity of supply
can be maintained through other transformer.
2. When the load on the sub station becomes more
than the capacity of the existing transformer,
another transformer can be added in parallel
3. Any transformer can be taken out of the circuit
for repair/routine maintenance without
interrupting supply to the consumers.

125. Conditions for satisfactory parallel operation
1. Transformers should be properly connected with
regard to their polarities.
2. The voltage ratings and voltage ratios of the
transformers should be the same
3. The per unit or percentage impedances of the
transformers should be equal.
4. The reactance/resistance ratios of the
transformers should be the same

126. Parallel operation of a transformer
• Condition (i)

127. Parallel operation of a transformer
• Condition (ii)
Circulating current, I c = (EA-EB)/(ZA+ZB)
assuming EA>EB

128. Parallel operation of a transformer
• Condition (iii)
• By inserting proper amount of resistance or reactance or
both in series with either primary or secondary.
• Condition (iv)
• If the reactance/resistance ratios of the two
transformers are not equal, the power factor of the load
supplied by the transformers will not be equal.
• In other wards, one transformer will be operating with a
higher and the other with a lower power factor than that
of the load.
• This may be improved by inserting external impedance
of proper value.

129. Single phase equal voltage ratio transformers in parallel

130. Single phase equal voltage ratio transformers in parallel

131. Single phase equal voltage ratio transformers in parallel

132. Single phase unequal voltage ratio transformers in parallel

133. Single phase unequal voltage ratio transformers in parallel

134. Single phase unequal voltage ratio transformers in parallel

135. Tap changing Transformer
Regulating the voltage of a transformer is a requirement that often
arises in a power application or power system.
In an application it may be needed
1. To supply a desired voltage to the load.
2. To counter the voltage drops due to loads.
3. To counter the input supply voltage changes on load.
Two Methods of tap changing
1. ON load Tap changer
2. OFF load Tap changer

136. Tappings are on HV side because of the
following reason:
1. It carries large number of turns , adjusting
number of turns is possible
2. Low voltage winding carries high current,
interruption of high current is impractical
3. LV winding is placed near the core, HV
winding is placed outside the core. Hence
practically It is easier to provide tappings
in HV winding.

137. Off load Tap changer

138. On load Tap changer

139. On load Tap changer

140. Tertiary Winding
In some high rating transformer, one winding in addition to its
primary and secondary winding is used. This additional winding, apart
from primary and secondary windings, is known as Tertiary winding of
transformer. Because of this third winding, the transformer
Advantages of teritary windings:
1.It reduces the unbalancing in the primary due to unbalancing in
three phase load.
2. It redistributes the flow of fault current.
3. As the tertiary winding is connected in delta formation in 3 winding
transformer, it assists in limitation of fault current in the event of a
short circuit from line to neutral.