1. Transformer Professor Mohamed A. El-Sharkawi

2. Why do we need transformers?
Increase voltage of generator’s output
Transmit high power at low current
Reduce cost of transmission system
Adjust voltage to a usable level
Create electrical isolation
Match load impedance
Filters
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3. El-Sharkawi@University of Washington
220kV-750kV
Distribution
Transformer
Transmission
Transformer
15 kV- 25kV
Service
Transformer
208V- 416V
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4. Transmission Transformer
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5. Distribution Transformer
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6. Distribution Transformer
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7. El-Sharkawi@University of Washington
Service Transformer
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8. Service Transformer bank
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9. Service Transformer bank
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10. El-Sharkawi@University of Washington
Service Transformer
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11. El-Sharkawi@University of Washington
Service Transformer
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12. El-Sharkawi@University of Washington
Service Transformer
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13. El-Sharkawi@University of Washington
Service Transformer
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14. El-Sharkawi@University of Washington
Service Transformer
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15. El-Sharkawi@University of Washington
Low power Transformer
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16. El-Sharkawi@University of Washington
Basic Components
Iron Core
Insulated Copper Wire
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17. El-Sharkawi@University of Washington
Basic Components
Laminated iron core
Insulated copper wire
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18. El-Sharkawi@University of Washington

19. El-Sharkawi@University of Washington

20. El-Sharkawi@University of Washington

21. El-Sharkawi@University of Washington
Secondary
Primary
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22. Basic Analysis: Voltage+ _ N2 e2
Volts/turn is constant
Voltages are in phase (no phase shift)
Voltage magnitudes vary with turns ratio.
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23. Basic Analysis: Power and current i2+ _ N2 e2
Ampere turn is constant
Currents are in phase.
Current ratio is opposite to the voltage ratio
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24. Basic Analysis: Reflected impedance
Primary
Secondary
Source
Load
Flux
Zload
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25. Basic Analysis: Reflected impedance+ _ N2 E2
Source E1
Primary
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26. El-Sharkawi@University of Washington
Key relationships
Constant voltage per turn I1 I2 N1 E1 + _ N2 E2
Constant Ampere turn
Reflected impedance
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27. Single-Phase, Ideal Transformer Ratings+ - V 1 I 2
Apparent Power (S)
2 KVA, 120/240 V
Primary Voltage (V1)
Secondary Voltage (V2)
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28. El-Sharkawi@University of Washington
Rated Values
Rated voltage: The device can continuously operate at the rated voltage without being damaged due to insulation failure
Rated current: The device can continuously operate at the rated current without being damaged due to thermal destruction
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29. El-Sharkawi@University of Washington
Example N2 N1 + - V 1 I 2
Transformer rating:
2 KVA, 240/120 V
Compute the currents
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30. Multi-Secondary Transformer
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31. Multi-secondary windings
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32. El-Sharkawi@University of Washington
Voltage/Turn I3 I1 N3 E3 E1 I2 N1 E2 N2
Primary
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33. El-Sharkawi@University of Washington
Primary I3 N3 E3
Ampere’s law
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34. El-Sharkawi@University of Washington
Primary I3 N3 E3
Power
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35. El-Sharkawi@University of Washington
Example
The transformer consists of one primary winding and two secondary windings. The number of turns is each winding is
A voltage source of 120V is applied to the primary winding, and purely resistive loads are connected across the secondary windings. A wattmeter placed in the primary circuit measures 300W. Another wattmeter placed in the secondary winding N2 measures 90W. Compute the following:
The voltages of the secondary windings
The currents in N3
The power consumed by the load connected across N3
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36. El-Sharkawi@University of Washington
Solution
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37. El-Sharkawi@University of Washington
Solution
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38. El-Sharkawi@University of Washington
Solution
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39. El-Sharkawi@University of Washington
Autotransformer
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40. El-Sharkawi@University of WashingtonB1 V1 E1 E2 N1 N2 V2 A2 B2
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41. Autotransformer: Voltage and currentI2 N2 V1 N1 I1 Is
Iload V2 A1 A2 B1 B2 E1 E2
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42. El-Sharkawi@University of Washington
Autotransformer N2 N1 + - E 1 I 2 I2 N2 V1 N1 I1 Is
Iload V2 A1 A2 B1 B2 E1 E2
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43. Autotransformer: Power
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44. El-Sharkawi@University of Washington
Example
Ratings of regular transformer: 10 kVA, 400/200 V
New voltage ratio: 600/200 V
Compute the new ratings
Solution I2 N2 V1 N1 I1 Is
Iload V2 A1 A2 B1 B2 E1 E2
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45. El-Sharkawi@University of Washington
VARIAC: Variable Auto-Transformer I2 N2 V1 N1 I1 Is
Iload V2 N3 Z Y
Sliding terminal
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46. El-Sharkawi@University of Washington
Output Voltage I2 N2 Vs N1 I1 Is
Iload
Vload N3 Z Y
Sliding terminal
At Y
At Z
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47. Three-Phase Transformer
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48. El-Sharkawi@University of Washington
3-phase transformer
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49. El-Sharkawi@University of Washington
3-phase transformer
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50. El-Sharkawi@University of Washington
3-phase transformer
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51. El-Sharkawi@University of Washington
single-phase transformer
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52. El-Sharkawi@University of Washington
3-phase transformer bank
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53. El-Sharkawi@University of Washington
3-phase transformer
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54. El-Sharkawi@University of Washington
3-Phase Transformer
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55. 3-phase transformer Y-Y connection. Also known as star-star connection
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56. 3-phase transformer Y-Y connection. Also known as star-star connectionb A B C N1 N2
Voltage per turn
Ratio of Line Voltage n N
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57. 3-phase transformer ( -)
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58. 3-phase transformer ( -)B C a b c N 2 N1
Voltage per turn
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59. 3-phase transformer (Y-) Also known as star-delta connection
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60. 3-phase transformer (Y-) Also known as star-delta connection
Ratio of Line Voltage N 1
Voltage per turn N 2 B n c b C
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61. 3-phase transformer bank (Y-)2 1 V an V ab V AB B b N 2 1 C c N 2 1
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62. Ratings of Ideal 3-phase Transformer
Apparent Power (3-phase)
100 MVA, 13.8/138 KV
Primary Voltage
line-to-line
Secondary Voltage
line-to-line
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63. El-Sharkawi@University of Washington
Example
Three single-phase transformers are used to form a three-phase transformer bank. Each single-phase transformer is rated at 10 kVA, 13.8 KV/240 V. One side of the transformer bank is connected to a three-phase, 13.8 kV transmission line. The other side of the transformer is connected to a three-phase residential load of 415.7V, 9kVA at 0.8 power factor lagging. Determine the connection of the transformer bank, the voltage ratio of the transformer bank, and the line current of the bank at the 13.8 kV side
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64. El-Sharkawi@University of Washington
Solution
Secondary voltage (Low voltage side) should be in Y to provide the needed residential voltage
The high voltage side must be Delta-connection
The line-to-line voltage of the supply is 13.8 kV. Same as the transformer rating of the primary.
If the primary is connected in Y, the voltage of the load would be lower than 240 V.
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65. El-Sharkawi@University of Washington
Solution
Van= 240 V A a N2 N1
Van
VAB= 13.8 kV
Vab B b N2 N1 C c
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66. El-Sharkawi@University of Washington
Solution N2 N1
Van a c A B C
VAB= 13.8 kV
Vab b
Van= 240 V
Phase current of the load
Phase current of the Transformer primary
Line Current in primary
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67. El-Sharkawi@University of Washington
Actual Transformer
Windings:
Resistance
Inductance
Core:
Eddy Current
Hysteresis I1 I2 N1 E1 + _ N2 E2
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68. El-Sharkawi@University of Washington
Windings Impedance R1 X1 R2 X2 N1 N2
Ideal Transformer
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69. El-Sharkawi@University of Washington
Core Hysteresis i B H N e + _
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70. El-Sharkawi@University of Washington

71. El-Sharkawi@University of Washington
Core Model e i R
Let i
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72. El-Sharkawi@University of Washington
Core Model i e Xl
Let i
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73. El-Sharkawi@University of WashingtonXl i i
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74. El-Sharkawi@University of Washington
Equivalent Circuit X1 R1 R2 X2 N1 N2 Io
load I1 I2 V1 E1 E2 V2 Ro Xo
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75. El-Sharkawi@University of Washington
Key Relations Ro Xo R1 X1 R2 X2 V1 I1 Io I2 V2 E1 E2 N1 N2
load
Voltage per turn
Ampere turn
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76. Referred (reflected) impedanceX1 R1 R2 X2 N1 N2 Io I1 I2 V1 E1 E2 V2 Ro Xo
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77. Referred (reflected) impedanceX1 R1 R2 X2 N1 N2 Io I1 I2 V1 E1 E2 V2 Ro Xo
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78. El-Sharkawi@University of Washington
Define:
Then:
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79. El-Sharkawi@University of Washington
Equivalent Circuit Referred to
Source Side Ro Xo R1 X1 R2 X2 V1 I1 Io I2 E1 E2 N1 N2 V2 X1 R1 Io I1 V1 E1 Ro Xo
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80. Practical ConsiderationsX1 R1 Ro Xo V1 I1 Io E1
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81. El-Sharkawi@University of WashingtonRo Xo Io R1 X1 OK V1 I1 Ro Xo Io R1 X1 OK
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82. El-Sharkawi@University of WashingtonX1 OK
Define:
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83. Analysis of TransformerV1 Z’
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84. El-Sharkawi@University of Washington
Terminologies
Load Voltage
Load Voltage referred to Source side
Impedance referred to Source side
Load Current
Load current referred to Source side
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85. El-Sharkawi@University of WashingtonZ’
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86. El-Sharkawi@University of WashingtonZ
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87. Ratings of Actual 3-phase Transformer
Apparent Power (3-phase)
100 MVA, 13.8/138 KV
line-to-line
line-to-line
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88. El-Sharkawi@University of Washington
Example
A transformer has the following parameters:
The rated voltage of the primary winding (V1) is 1000V.
Compute the load voltage.
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89. El-Sharkawi@University of Washington
Solution V1 Z’
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90. El-Sharkawi@University of Washington
Voltage Regulation VR V1
Load
Measured at the load side
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91. El-Sharkawi@University of Washington
Example
Calculate the voltage regulation of the transformer in the
previous problem.
Solution:
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92. El-Sharkawi@University of Washington
Efficiency  V1 I1 Ro Xo Io
Req
Xeq
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93. El-Sharkawi@University of Washington
Example
A 10 kVA, 2300/230 V, single phase distribution transformer
has the following parameters:
At full load and 0.8 power factor lagging, compute the efficiency
of the transformer.
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94. El-Sharkawi@University of Washington
Solution
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