Transformer Professor Mohamed A. El-Sharkawi
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 El-Sharkawi@University of Washington
El-Sharkawi@University of Washington 220kV-750kV Distribution Transformer Transmission Transformer 15 kV- 25kV Service Transformer 208V- 416V El-Sharkawi@University of Washington
Transmission Transformer El-Sharkawi@University of Washington
Distribution Transformer El-Sharkawi@University of Washington
Distribution Transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Service Transformer El-Sharkawi@University of Washington
Service Transformer bank El-Sharkawi@University of Washington
Service Transformer bank El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Service Transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Service Transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Service Transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Service Transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Service Transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Low power Transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Basic Components Iron Core Insulated Copper Wire El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Basic Components Laminated iron core Insulated copper wire El-Sharkawi@University of Washington
El-Sharkawi@University of Washington
El-Sharkawi@University of Washington
El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Secondary Primary El-Sharkawi@University of Washington
Basic Analysis: Voltage + _ N2 e2 Volts/turn is constant Voltages are in phase (no phase shift) Voltage magnitudes vary with turns ratio. El-Sharkawi@University of Washington
Basic Analysis: Power and current i2 + _ N2 e2 Ampere turn is constant Currents are in phase. Current ratio is opposite to the voltage ratio El-Sharkawi@University of Washington
Basic Analysis: Reflected impedance Primary Secondary Source Load Flux Zload El-Sharkawi@University of Washington
Basic Analysis: Reflected impedance + _ N2 E2 Source E1 Primary El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Key relationships Constant voltage per turn I1 I2 N1 E1 + _ N2 E2 Constant Ampere turn Reflected impedance El-Sharkawi@University of Washington
Single-Phase, Ideal Transformer Ratings + - V 1 I 2 Apparent Power (S) 2 KVA, 120/240 V Primary Voltage (V1) Secondary Voltage (V2) El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Example N2 N1 + - V 1 I 2 Transformer rating: 2 KVA, 240/120 V Compute the currents El-Sharkawi@University of Washington
Multi-Secondary Transformer El-Sharkawi@University of Washington
Multi-secondary windings El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Voltage/Turn I3 I1 N3 E3 E1 I2 N1 E2 N2 Primary El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Primary I3 N3 E3 Ampere’s law El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Primary I3 N3 E3 Power El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Solution El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Solution El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Solution El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Autotransformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington B1 V1 E1 E2 N1 N2 V2 A2 B2 El-Sharkawi@University of Washington
Autotransformer: Voltage and current I2 N2 V1 N1 I1 Is Iload V2 A1 A2 B1 B2 E1 E2 El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
Autotransformer: Power El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
El-Sharkawi@University of Washington VARIAC: Variable Auto-Transformer I2 N2 V1 N1 I1 Is Iload V2 N3 Z Y Sliding terminal El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Output Voltage I2 N2 Vs N1 I1 Is Iload Vload N3 Z Y Sliding terminal At Y At Z El-Sharkawi@University of Washington
Three-Phase Transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington 3-phase transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington 3-phase transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington 3-phase transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington single-phase transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington 3-phase transformer bank El-Sharkawi@University of Washington
El-Sharkawi@University of Washington 3-phase transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington 3-Phase Transformer El-Sharkawi@University of Washington
3-phase transformer Y-Y connection. Also known as star-star connection El-Sharkawi@University of Washington
3-phase transformer Y-Y connection. Also known as star-star connection b A B C N1 N2 Voltage per turn Ratio of Line Voltage n N El-Sharkawi@University of Washington
3-phase transformer ( -) El-Sharkawi@University of Washington
3-phase transformer ( -) B C a b c N 2 N1 Voltage per turn El-Sharkawi@University of Washington
3-phase transformer (Y-) Also known as star-delta connection El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
3-phase transformer bank (Y-) 2 1 V an V ab V AB B b N 2 1 C c N 2 1 El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
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. El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Actual Transformer Windings: Resistance Inductance Core: Eddy Current Hysteresis I1 I2 N1 E1 + _ N2 E2 El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Windings Impedance R1 X1 R2 X2 N1 N2 Ideal Transformer El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Core Hysteresis i B H N e + _ El-Sharkawi@University of Washington
El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Core Model e i R Let i El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Core Model i e Xl Let i El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Xl i i El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Equivalent Circuit X1 R1 R2 X2 N1 N2 Io load I1 I2 V1 E1 E2 V2 Ro Xo El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
Referred (reflected) impedance X1 R1 R2 X2 N1 N2 Io I1 I2 V1 E1 E2 V2 Ro Xo El-Sharkawi@University of Washington
Referred (reflected) impedance X1 R1 R2 X2 N1 N2 Io I1 I2 V1 E1 E2 V2 Ro Xo El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Define: Then: El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
Practical Considerations X1 R1 Ro Xo V1 I1 Io E1 El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Ro Xo Io R1 X1 OK V1 I1 Ro Xo Io R1 X1 OK El-Sharkawi@University of Washington
El-Sharkawi@University of Washington X1 OK Define: El-Sharkawi@University of Washington
Analysis of Transformer V1 Z’ El-Sharkawi@University of Washington
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 El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Z’ El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Z El-Sharkawi@University of Washington
Ratings of Actual 3-phase Transformer Apparent Power (3-phase) 100 MVA, 13.8/138 KV line-to-line line-to-line El-Sharkawi@University of Washington
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. El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Solution V1 Z’ El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Voltage Regulation VR V1 Load Measured at the load side El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Example Calculate the voltage regulation of the transformer in the previous problem. Solution: El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Efficiency V1 I1 Ro Xo Io Req Xeq El-Sharkawi@University of Washington
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. El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Solution El-Sharkawi@University of Washington