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 of Washington

3 El-Sharkawi@University of Washington220kV-750kV Distribution Transformer Transmission Transformer 15 kV- 25kV Service Transformer 208V- 416V of Washington

4 Transmission Transformerof Washington

5 Distribution Transformerof Washington

6 Distribution Transformerof Washington

7 El-Sharkawi@University of WashingtonService Transformer of Washington

8 Service Transformer bankof Washington

9 Service Transformer bankof Washington

10 El-Sharkawi@University of WashingtonService Transformer of Washington

11 El-Sharkawi@University of WashingtonService Transformer of Washington

12 El-Sharkawi@University of WashingtonService Transformer of Washington

13 El-Sharkawi@University of WashingtonService Transformer of Washington

14 El-Sharkawi@University of WashingtonService Transformer of Washington

15 El-Sharkawi@University of WashingtonLow power Transformer of Washington

16 El-Sharkawi@University of WashingtonBasic Components Iron Core Insulated Copper Wire of Washington

17 El-Sharkawi@University of WashingtonBasic Components Laminated iron core Insulated copper wire of Washington

18 El-Sharkawi@University of Washington

19 El-Sharkawi@University of Washington

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21 El-Sharkawi@University of WashingtonSecondary Primary of Washington

22 Basic Analysis: Voltage+ _ N2 e2 Volts/turn is constant Voltages are in phase (no phase shift) Voltage magnitudes vary with turns ratio. of Washington

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 of Washington

24 Basic Analysis: Reflected impedancePrimary Secondary Source Load Flux Zload of Washington

25 Basic Analysis: Reflected impedance+ _ N2 E2 Source E1 Primary of Washington

26 El-Sharkawi@University of WashingtonKey relationships Constant voltage per turn I1 I2 N1 E1 + _ N2 E2 Constant Ampere turn Reflected impedance of Washington

27 Single-Phase, Ideal Transformer Ratings+ - V 1 I 2 Apparent Power (S) 2 KVA, 120/240 V Primary Voltage (V1) Secondary Voltage (V2) of Washington

28 El-Sharkawi@University of WashingtonRated 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 of Washington

29 El-Sharkawi@University of WashingtonExample N2 N1 + - V 1 I 2 Transformer rating: 2 KVA, 240/120 V Compute the currents of Washington

30 Multi-Secondary Transformerof Washington

31 Multi-secondary windingsof Washington

32 El-Sharkawi@University of WashingtonVoltage/Turn I3 I1 N3 E3 E1 I2 N1 E2 N2 Primary of Washington

33 El-Sharkawi@University of WashingtonPrimary I3 N3 E3 Ampere’s law of Washington

34 El-Sharkawi@University of WashingtonPrimary I3 N3 E3 Power of Washington

35 El-Sharkawi@University of WashingtonExample 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 of Washington

36 El-Sharkawi@University of WashingtonSolution of Washington

37 El-Sharkawi@University of WashingtonSolution of Washington

38 El-Sharkawi@University of WashingtonSolution of Washington

39 El-Sharkawi@University of WashingtonAutotransformer of Washington

40 El-Sharkawi@University of WashingtonB1 V1 E1 E2 N1 N2 V2 A2 B2 of Washington

41 Autotransformer: Voltage and currentI2 N2 V1 N1 I1 Is Iload V2 A1 A2 B1 B2 E1 E2 of Washington

42 El-Sharkawi@University of WashingtonAutotransformer N2 N1 + - E 1 I 2 I2 N2 V1 N1 I1 Is Iload V2 A1 A2 B1 B2 E1 E2 of Washington

43 Autotransformer: Powerof Washington

44 El-Sharkawi@University of WashingtonExample 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 of Washington

45 El-Sharkawi@University of WashingtonVARIAC: Variable Auto-Transformer I2 N2 V1 N1 I1 Is Iload V2 N3 Z Y Sliding terminal of Washington

46 El-Sharkawi@University of WashingtonOutput Voltage I2 N2 Vs N1 I1 Is Iload Vload N3 Z Y Sliding terminal At Y At Z of Washington

47 Three-Phase Transformerof Washington

48 El-Sharkawi@University of Washington3-phase transformer of Washington

49 El-Sharkawi@University of Washington3-phase transformer of Washington

50 El-Sharkawi@University of Washington3-phase transformer of Washington

51 El-Sharkawi@University of Washingtonsingle-phase transformer of Washington

52 El-Sharkawi@University of Washington3-phase transformer bank of Washington

53 El-Sharkawi@University of Washington3-phase transformer of Washington

54 El-Sharkawi@University of Washington3-Phase Transformer of Washington

55 3-phase transformer Y-Y connection. Also known as star-star connectionof Washington

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 of Washington

57 3-phase transformer ( -)of Washington

58 3-phase transformer ( -)B C a b c N 2 N1 Voltage per turn of Washington

59 3-phase transformer (Y-) Also known as star-delta connectionof Washington

60 3-phase transformer (Y-) Also known as star-delta connectionRatio of Line Voltage N 1 Voltage per turn N 2 B n c b C of Washington

61 3-phase transformer bank (Y-)2 1 V an V ab V AB B b N 2 1 C c N 2 1 of Washington

62 Ratings of Ideal 3-phase TransformerApparent Power (3-phase) 100 MVA, 13.8/138 KV Primary Voltage line-to-line Secondary Voltage line-to-line of Washington

63 El-Sharkawi@University of WashingtonExample 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 of Washington

64 El-Sharkawi@University of WashingtonSolution 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. of Washington

65 El-Sharkawi@University of WashingtonSolution Van= 240 V A a N2 N1 Van VAB= 13.8 kV Vab B b N2 N1 C c of Washington

66 El-Sharkawi@University of WashingtonSolution 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 of Washington

67 El-Sharkawi@University of WashingtonActual Transformer Windings: Resistance Inductance Core: Eddy Current Hysteresis I1 I2 N1 E1 + _ N2 E2 of Washington

68 El-Sharkawi@University of WashingtonWindings Impedance R1 X1 R2 X2 N1 N2 Ideal Transformer of Washington

69 El-Sharkawi@University of WashingtonCore Hysteresis i B H N e + _ of Washington

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71 El-Sharkawi@University of WashingtonCore Model e i R Let i of Washington

72 El-Sharkawi@University of WashingtonCore Model i e Xl Let i of Washington

73 El-Sharkawi@University of WashingtonXl i i of Washington

74 El-Sharkawi@University of WashingtonEquivalent Circuit X1 R1 R2 X2 N1 N2 Io load I1 I2 V1 E1 E2 V2 Ro Xo of Washington

75 El-Sharkawi@University of WashingtonKey Relations Ro Xo R1 X1 R2 X2 V1 I1 Io I2 V2 E1 E2 N1 N2 load Voltage per turn Ampere turn of Washington

76 Referred (reflected) impedanceX1 R1 R2 X2 N1 N2 Io I1 I2 V1 E1 E2 V2 Ro Xo of Washington

77 Referred (reflected) impedanceX1 R1 R2 X2 N1 N2 Io I1 I2 V1 E1 E2 V2 Ro Xo of Washington

78 El-Sharkawi@University of WashingtonDefine: Then: of Washington

79 El-Sharkawi@University of WashingtonEquivalent 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 of Washington

80 Practical ConsiderationsX1 R1 Ro Xo V1 I1 Io E1 of Washington

81 El-Sharkawi@University of WashingtonRo Xo Io R1 X1 OK V1 I1 Ro Xo Io R1 X1 OK of Washington

82 El-Sharkawi@University of WashingtonX1 OK Define: of Washington

83 Analysis of TransformerV1 Z’ of Washington

84 El-Sharkawi@University of WashingtonTerminologies Load Voltage Load Voltage referred to Source side Impedance referred to Source side Load Current Load current referred to Source side of Washington

85 El-Sharkawi@University of WashingtonZ’ of Washington

86 El-Sharkawi@University of WashingtonZ of Washington

87 Ratings of Actual 3-phase TransformerApparent Power (3-phase) 100 MVA, 13.8/138 KV line-to-line line-to-line of Washington

88 El-Sharkawi@University of WashingtonExample A transformer has the following parameters: The rated voltage of the primary winding (V1) is 1000V. Compute the load voltage. of Washington

89 El-Sharkawi@University of WashingtonSolution V1 Z’ of Washington

90 El-Sharkawi@University of WashingtonVoltage Regulation VR V1 Load Measured at the load side of Washington

91 El-Sharkawi@University of WashingtonExample Calculate the voltage regulation of the transformer in the previous problem. Solution: of Washington

92 El-Sharkawi@University of WashingtonEfficiency  V1 I1 Ro Xo Io Req Xeq of Washington

93 El-Sharkawi@University of WashingtonExample 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. of Washington

94 El-Sharkawi@University of WashingtonSolution of Washington