1. Chapter 4.
Transformer

2. Transformer- Introduction
Two winding transformers
Construction and principles
Equivalent circuit
Determination of equivalent circuit parameters
Voltage regulation
Efficiency
Auto transformer
3 phase transformer

3. Transformer- Introduction
Varieties of transformers

4. Transformer- Introduction

5. Transformer- Introduction
Transformer is a device that makes use of the magnetically coupled coils to transfer energy
It is typically consists of one primary winding coil and one or more secondary windings
The primary winding and its circuit is called the Primary Side of the transformer
The secondary winding and its circuit is called the Secondary Side of the transformer

6. Transformer- Introduction
If one of those winding, the primary, is connected to an alternating voltage source, an alternating flux will be produced. The mutual flux will link the other winding, the secondary, and will induced a voltage in it.

7. Transformer- Introduction
Transformers are adapted to numerous engineering applications and may be classified in many ways:
Power level (from fraction of a volt-ampere (VA) to over a thousand MVA),
Application (power supply, impedance matching, circuit isolation),
Frequency range (power, audio, radio frequency (RF))
Voltage class (a few volts to about 750 kilovolts)
Cooling type (air cooled, oil filled, fan cooled, water cooled, etc.)
Purpose (distribution, rectifier, arc furnace, amplifier output, etc.).

8. Transformer- Introduction
Power transmission

9. Transformer- Introduction
Power transmission

10. Transformer
4.1 Construction

11. Transformer- construction
Basic components of single phase transformer

12. Transformer- construction
Single phase transformer construction

13. Transformer- construction

14. Transformer- construction

15. Transformer
4.2 Ideal Transformer

16. Transformer i e1 Φ v1 v2 e2
The emf which induced in transformer primary winding is known as self induction emf as the emf is induced due to to flux which produced by the winding itself.
While the emf which induced in transformer secondary winding is known as mutual induction emf as the emf is induced due to to flux which produced by the other winding.

17. Transformer Φ i e1 v1 v2 e1 = e2 e1 =
Acording to Faraday’s Law, the emf which induced in the primary winding is,
e1 =
Since the flux is an alternating flux,
e1 =

18. Transformer i e1 Φ v1 v2 e2 e1
where, =

19. Transformer Φ e2 = i e1 v1 v2 e2 E2 rms
Similarly it can be shown that,
E2 rms
k is transformation ratio

20. Transformer
The voltage ratio of induced voltages on the secondary to primary windings is equal to the turn ratio of the winding turn number of the secondary winding to the winding turn number of the primary winding. Therefore the transformers can be used to step up or step down voltage levels by choosing appropriate number their winding turns. In power system it’s necessary to step up the output voltage of a generator which less than 30kV to up 500kV for long distance transmission. High voltage for long distance power transmission can reduce current flow in the transmission lines, thus line losses and voltage drop can be reduced.

21. Transformer- Ideal Transformer
Winding resistances are zero, no leakage inductance and iron loss
Magnetization current generates a flux that induces voltage in both windings
Current, voltages and flux in an unloaded ideal transformer

22. Transformer i e1 Φ v1 v2 e2
Transformer on no load. 22

23. Transformer- Ideal Transformer
Loaded transformer i Φ V1 E2 E1
V2 ZL I2 Φ2 N1 N2 Φ1
When a load is connected to the secondary output terminals of a transformer as shown in Figure 4.5, a current I2 flows into the load and into transformer secondary winding N2. The current I2 which flowing in N2 produces flux Φ2 which opposite –by Lenz’s law- to the main magnetic flux Φ in the transformer core. This will weaken or slightly reduce the main flux Φ to Φ’.

24. Transformer- Ideal Transformer
Loaded transformer i Φ V1 E2 E1
V2 ZL I2 Φ2 N1 N2 Φ1
The reduction of main flux Φ –by Faraday’s law- could also reduce the induced voltage in primary winding E1. Consequently E1 is now smaller than the supply voltage V1, then the primary current would be increased due to that potential differences. Therefore on loaded transformer, the primary current has an additional current of I1’.

25. Transformer- Ideal Transformer
Loaded transformer i Φ V1 E2 E1
V2 ZL I2 Φ2 N1 N2 Φ1
The extra current I1’ which flowing in the primary winding N1 produces flux Φ1 which naturally react according to Lenz’s law, demagnetize the flux Φ2. Therefore the net magnetic flux in the core is always maintained at original value, it is the main flux Φ (the flux which produced by the magnetizing current).

26. Transformer- Ideal Transformer
Loaded transformer i Φ V1 E2 E1
V2 ZL I2 Φ2 N1 N2 Φ1
The magneto motive force (mmf) source N2I2 at the secondary winding produces flux Φ2, while the mmf N1I1‘ produces flux Φ1. Since the magnitude of Φ1 equal to magnitude of Φ2 and the reluctance seen by these two mmf sources are equal, thus
N1I1‘ = N2I2

27. Transformer- Ideal Transformer
Loaded transformer
Currents and fluxes in a loaded ideal transformer

28. Transformer- Ideal Transformer
Turn ratio
If the primary winding has N1 turns and secondary winding has N2 turns, then:
The input and output complex powers are equal

29. Transformer- Ideal Transformer
Functional description of a transformer:
When a = Isolation Transformer
When | a | < Step-Up Transformer Voltage is increased from Primary side to secondary side
When | a | > Step-Down Transformer Voltage is decreased from Primary side to secondary side

30. Transformer- Ideal Transformer
Transformer Rating
Practical transformers are usually rated based on:
Voltage Ratio (V1/V2) which gives us the turns-ratio
Power Rating, small transformers are given in Watts (real power) and Larger ones (Power Transformers) are given in kVA (apparent power)

31. Transformer- Ideal Transformer
Example 4.1
Determine the turns-ratio of a 5 kVA 2400V/120V Power Transformer
Turns-Ratio = a = V1/V2 = 2400/120 = 20/1 = 20
This means it is a Step-Down transformer

32. Transformer- Ideal Transformer
Example 4.2
A 480/2400 V (r.m.s) step-up ideal transformer delivers 50 kW to a resistive load. Calculate:
(a) the turns ratio, (0.2)
(b) the primary current, (104.17A)
(c) the secondary current. (20.83A)

33. Transformer- Ideal Transformer
Nameplate of transformer

34. Transformer- Ideal Transformer
Equivalent circuit
Equivalent circuit of an ideal transformer

35. Transformer- Ideal Transformer
Transferring impedances through a transformer
Equivalent circuit of an ideal transformer

36. Transformer- Ideal Transformer
a) Equivalent circuit when secondary impedance is transferred to primary side and ideal transformer eliminated
b) Equivalent circuit when primary source is transferred to secondary side and ideal transformer eliminated
Thévenin equivalents of transformer circuit

37. Transformer- practical transformer

38. Transformer
4.3 Equivalent Circuits

39. Transformer- equivalent circuit

40. Transformer- equivalent circuit
Development of the transformer equivalent circuits
The effects of winding resistance and leakage flux are respectively accounted for by resistance R and leakage reactance X (2πfL).

41. Transformer- practical equivalent circuit
In a practical magnetic core having finite permeability, a magnetizing current Im is required to establish a flux in the core.
This effect can be represented by a magnetizing inductance Lm. The core loss can be represented by a resistance Rc.

42. Transformer- practical equivalent circuit
Rc :core loss component,
Xm : magnetization component,
R1 and X1 are resistance and reactance of the primary winding
R2 and X2 are resistance and reactance of the secondary winding

43. Transformer- practical equivalent circuit
The impedances of secondary side such as R2, X2 and Z2 can be moved to primary side and also the impedances of primary side can be moved to the secondary side, base on the principle of:
The power before transferred = The power after transferred.

44. Transformer- practical equivalent circuit
The power before transferred = The power after transferred.
I22R2 = I1’ 2R2’
Therefore R2’= (I2/ I1’ ) 2 R2
= a2R2

45. Transformer- practical equivalent circuit
The turns can be moved to the right or left by referring all quantities to the primary or secondary side.
The equivalent circuit with secondary side moved to the primary.

46. Transformer- Approximate equivalent circuit
For convenience, the turns is usually not shown and the equivalent circuit is drawn with all quantities (voltages, currents, and impedances) referred to one side.

47. Transformer- equivalent circuit
Example 4.3
A 100kVA transformer has 400 turns on the primary and 80 turns on the secondary. The primary and secondary resistance are 0.3 ohm and 0.01 ohm respectively and the corresponding leakage reactances are 1.1 ohm and ohm respectively. The supply voltage is 2200V. Calculate:
(a) the equivalent impedance referred to the primary circuit (2.05 ohm)
(b) the equivalent impedance referred to the secondary circuit

48. 4.4 Determination of Equivalent Circuit Parameter
Transformer
4.4 Determination of Equivalent Circuit Parameter

49. Transformer- o/c-s/c tests
The equivalent circuit model for the actual transformer can be used to predict the behavior of the transformer.
The parameters R1, X1, Rc, Xm, R2, X2 and N1/N2 must be known so that the equivalent circuit model can be used.
These parameters can be directly and more easily determined by performing tests:
1. No-load test (or open-circuit test).
2. Short-circuit test.

50. Transformer- o/c-s/c tests
No load/Open circuit test
Provides magnetizing reactance (Xm) and core loss resistance (RC)
Obtain components are connected in parallel
Short circuit test
Provides combined leakage reactance and winding resistance
Obtain components are connected in series

51. Transformer- open circuit test
No load/Open circuit test
Equivalent circuit for open circuit test, measurement at the primary side.
Simplified equivalent circuit

52. Transformer- open circuit test
Open circuit test evaluation

53. Transformer- short circuit test
Secondary (normally the LV winding) is shorted, that means there is no voltage across secondary terminals; but a large current flows in the secondary.
Test is done at reduced voltage (about 5% of rated voltage) with full-load current in the secondary. So, the ammeter reads the full-load current; the wattmeter reads the winding losses, and the voltmeter reads the applied primary voltage.

54. Transformer- short circuit test
Equivalent circuit for short circuit test, measurement at the primary side
Simplified equivalent circuit for short circuit test

55. Transformer- short circuit test
Simplified circuit for calculation of series impedance
Primary and secondary impedances are combined

56. Transformer- short circuit test
Short circuit test evaluation

57. Transformer- o/c-s/c tests
Equivalent circuit obtained by measurement
Equivalent circuit for a real transformer resulting from the open and short circuit tests.

58. Transformer- o/c-s/c tests
Example 4.4
Obtain the equivalent circuit of a 200/400V, 50Hz
1-phase transformer from the following test data:-
O/C test : 200V, 0.7A, 70W - on L.V. side
S/C test : 15V, 10A, 85W on H.V. side
(Rc =571.4 ohm, Xm=330 ohm, Re=0.21ohm, Xe=0.31 ohm)

59. Transformer – voltage regulation
Most loads connected to the secondary of a transformer are designed to operate at essentially constant voltage. However, as the current is drawn through the transformer, the load terminal voltage changes because of voltage drop in the internal impedance.
To reduce the magnitude of the voltage change, the transformer should be designed for a low value of the internal impedance Zeq
The voltage regulation is defined as the change in magnitude of the secondary voltage as the load current changes from the no-load to the loaded condition.

60. Transformer – voltage regulationZ V2
I2’ I2
V12’=V20
R1’ R2
Ze2
X1’
Rc’
Xm’ X2
Ze2 = R1’ + R2 + jX1’ + jX2
  = Re2 + jXe2

61. Transformer – voltage regulationZ V2
I2’ I2
V12’=V20
R1’ R2
Ze2
X1’
Rc’
Xm’ X2
Applying KVL, V20 = I2 (Ze2 ) + V2 = I2 (Re2 + jXe2 ) + V2  
Or V2 = V20 - I2 (Ze2 )

62. Transformer – voltage regulation
I2Xe2 A O V2 θ2
I2Re2 I2

63. Transformer – voltage regulation
I2Xe2
V20
I2Xe2 A O V2 θ2
I2Re2
I2Re2 B I2
V20 = I2 (Ze2 ) + V2 = I2 (Re2 + jXe2 ) + V2  

64. Transformer – voltage regulation
I2Xe2 C
V20 θ2
I2Xe2 A D O N M V2 θ2
I2Re2
I2Re2 B L θ2 I2
Voltage drop = AM = OM – OA
= AD + DN + NM

65. Transformer – voltage regulation
I2Xe2 C
V20 θ2
I2Xe2 A D O N M V2 θ2
I2Re2
I2Re2 B L θ2 I2
AD = I2 Re2 cosθ2
DN=BL= I2 Xe2 sinθ2

66. Transformer – voltage regulation
I2Xe2 C
V20 θ2
I2Xe2 A D O N M V2 θ2
I2Re2
I2Re2 B L θ2 I2
Applying Phytogrus theorem to OCN triangle.
(NC)2 = (OC)2 – (ON)2
= (OC + ON)(OC - ON) ≈ 2(OC)(NM)

67. Transformer – voltage regulation
I2Xe2 C
V20 θ2
I2Xe2 A D O N M V2 θ2
I2Re2
I2Re2 B L θ2 I2
Therefore NM = (NC)2/2(OC)
NC = LC – LN = LC – BD
= I2 Xe2 cosθ2 - I2 Re2 sinθ2

68. Transformer – voltage regulation
I2Xe2 C
V20 θ2
I2Xe2 A D O N M V2 θ2
I2Re2
I2Re2 B L θ2 I2
NM =
AM = AD + DN + NM
= I2 Recosθ2 + I2 Xe2 sin θ2 +

69. Transformer – voltage regulation
I2Xe2 C
V20 θ2
I2Xe2 A D O N M V2 θ2
I2Re2
I2Re2 B L θ2
thus,
votage regulation = (AM)/V20 per unit I2
In actual practice the term NM is negligible since its value is very small compared with V2. Thus the votage regulation formula can be reduced to:

70. Transformer – voltage regulation
I2Xe2 C
V20 θ2
I2Xe2 A D O N M V2 θ2
I2Re2
I2Re2 B L θ2 I2
Voltage regulation =

71. Transformer- voltage regulation
The voltage regulation is expressed as follows:
V2NL= secondary voltage (no-load condition)
V2L = secondary voltage (full-load condition)

72. Transformer- voltage regulation
For the equivalent circuit referred to the primary:
V1 = no-load voltage
V2’ = secondary voltage referred to the primary (full-load condition)

73. Transformer- voltage regulation
Consider the equivalent circuit referred to the secondary,
Re2
Xe2
(-) : power factor leading
(+) : power factor lagging

74. Transformer- voltage regulation
Consider the equivalent circuit referred to the primary,
Re1
Xe1
(-) : power factor leading
(+) : power factor lagging

75. Transformer- voltage regulation
Example 4.5
Based on Example 4.3 calculate the voltage regulation and the secondary terminal voltage for full load having a power factor of
(i) 0.8 lagging (0.0336pu,14.8V)
(ii) 0.8 leading ( pu,447V)

76. Transformer- Efficiency
Losses in a transformer
Copper losses in primary and secondary windings
Core losses due to hysteresis and eddy current. It depends on maximum value of flux density, supply frequency and core dimension. It is assumed to be constant for all loads

77. Transformer- Efficiency
As always, efficiency is defined as power output to power input ratio
The losses in the transformer are the core loss (Pc) and copper loss (Pcu).

78. Transformer- Efficiency
Efficiency on full load
where S is the apparent power (in volt amperes)

79. Transformer- Efficiency
Efficiency for any load equal to n x full load
where corresponding total loss =

80. Transformer- Efficiency
Example 4.6
The following results were obtained on a 50 kVA transformer: open circuit test – primary voltage, 3300 V; secondary voltage, 400 V; primary power, 430W.Short circuit test – primary voltage, 124V;primary current, 15.3 A; primary power, 525W; secondary current, full load value. Calculate the efficiency at full load and half load for 0.7 power factor.
(97.3%, 96.9%)

81. Transformer- Efficiency
For constant values of the terminal voltage V2 and load power factor angle θ2 , the maximum efficiency occurs when
If this condition is applied, the condition for maximum efficiency is
that is, core loss = copper loss.

82. Transformer- Efficiency

83. Transformer- Auto transformer
It is a transformer whose primary and secondary coils are in a single winding
Autotransformer

84. Transformer- Auto transformer
Same operation as two windings transformer
Physical connection from primary to secondary
Sliding connection allows for variable voltage
Higher kVA delivery than two windings connection

85. Transformer- Auto transformer
Advantages:
A tap between primary and secondary sides which
may be adjustable to provide step-up/down capability
Able to transfer larger S apparent power than the two winding transformer
Smaller and lighter than an equivalent two-winding transformer
Disadvantage:
Lacks electrical isolation

86. Transformer- Auto transformer
A Step Down Autotransformer:
and

87. Transformer- Auto transformer
A Step Up Autotransformer:
and

88. Transformer- Auto transformer
Example 4.7
An autotransformer with a 40% tap is supplied by a 400-V, 60-Hz source and is used for step-down operation. A 5-kVA load operating at unity power factor is connected to the secondary terminals.
Find:
(a) the secondary voltage,
(b) the secondary current,
(c) the primary current.

89. Transformer- Auto transformer
Solution

90. Transformer -3 phase transformer
Three phase transformers
The three-phase transformer can be built by:
the interconnection of three single-phase transformers
using an iron core with three limbs
The usual connections for three-phase transformers are:
wye / wye seldom used, unbalance and 3th harmonics problem
wye / delta frequently used step down.(345 kV/69 kV)
delta / delta used medium voltage (15 kV), one of the transformer can be removed (open delta)
delta / wye step up transformer in a generation station
For most cases the neutral point is grounded

91. Transformer -3 phase transformer
Analyses of the grounded wye / delta transformer A B C
Each leg has a primary and a secondary winding.
The voltages and currents are in phase in the windings located on the same leg.
The primary phase-to- line voltage generates the secondary line-to- line voltage. These voltages are in phase
VAN
VB N
VC N N
Vab
Vbc
Vca a b c

92. Transformer -3 phase transformer
Analyses of the grounded wye / delta transformer IA IB IC N
IAN
ICN
IBN
Iab
Ibc
Ica Ib Ia Ic

93. Transformer -3 phase transformer
Analyses of the grounded wye / delta transformer A
VA N
Vbc a
VBN
VC N
VAB
Vab
Vab N B c
Vbc
VCA
VB C
Vca
Vbc C b

94. Transformer -3 phase transformer
Three phase transformer

95. Transformer
Three phase transformer

96. Transformer
Three phase transformer

97. Transformer
Three phase transformer

98. Transformer
Three phase transformer

99. Transformer Three phase transformer Transformer Construction Iron Core
The iron core is made of thin laminated silicon steel (2-3 % silicon)
Pre-cut insulated sheets are cut or pressed in form and placed on the top of each other .
The sheets are overlap each others to avoid (reduce) air gaps.
The core is pressed together by insulated yokes.

100. Transformer Three phase transformer Transformer Construction Winding
Small transformer winding
Transformer Construction Winding
The winding is made of copper or aluminum conductor, insulated with paper or synthetic insulating material (kevlar, maylard).
The windings are manufactured in several layers, and insulation is placed between windings.
The primary and secondary windings are placed on top of each others but insulated by several layers of insulating sheets.
The windings are dried in vacuum and impregnated to eliminate moisture.

101. Transformer Three phase transformer Transformer Construction
Iron Cores
The three phase transformer iron
core has three legs.
A phase winding is placed in each leg.
The high voltage and low voltage windings are placed on top of each other and insulated by layers or tubes.
Larger transformer use layered construction shown in the previous slides.
Three phase transformer iron core A B C

102. Transformer Three phase transformer Transformer Construction
The dried and treated transformer is placed in a steel tank.
The tank is filled, under vacuum, with heated transformer oil.
The end of the windings are connected to bushings.
The oil is circulated by pumps and forced through the radiators.
Three phase oil transformer

103. Transformer Three phase transformer Transformer Construction
Three phase oil transformer
Transformer Construction
The transformer is equipped with cooling radiators which are cooled by forced ventilation.
Cooling fans are installed under the radiators.
Large bushings connect the windings to the electrical system.
The oil is circulated by pumps and forced through the radiators.
The oil temperature, pressure are monitored to predict transformer performance.

104. Transformer Three phase transformer Transformer Construction
Dry type transformer
Transformer Construction
Dry type transformers are used at medium and low voltage.
The winding is vacuumed and dried before the molding.
The winding is insulated by epoxy resin
The slide shows a three phase, dry type transformer.