1. 10. THREE PHASE POWER CIRCUITS by Ulaby & Maharbiz All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

2. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

3. Transformers in Power Grid All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

4. A 4800-V rms single-phase connected to residential user through a 20 : 1 step-down transformer  All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

5. Balanced Three Phase Common practice is to adopt a positive (123) phase sequence wherein the phase of V2 follows behind that of V1 by 120 ◦ and the phase of V3 follows behind that of V2 by 120 ◦. Hence, the phases of V1, V2, and V3 are 0, − 120 ◦, and − 240 All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

6. Y & Delta For a balanced source, V1 + V2 + V3 = 0. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

7. Source-Load Configurations Y-Y Y-Delta All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

8. Source-Load Configurations Delta-Y Delta-Delta All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

9. Why 3-Phase?  Transmission of three-phase power from the generator to loads is more efficient than three separate, single-phase transmissions. A three-phase -source configuration uses 3 transmission wires and a Y-source configuration uses 3 or 4 wires (the neutral wire is not always used), whereas 6 wires are required to support three separate single- phase transmissions. Y-Delta configuration is the most common. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

10. Balanced Circuits All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

11. Y-Source Connected to a Y-Load All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

12. For a balanced source, V1 + V2 + V3 = 0. Hence, V N = 0 (balanced network). All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

13. Example 10-2 (cont.) All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

14. Transformation Between Balanced Loads All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

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17. Example 10-3 (cont.) All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

18. Power in Balanced Networks Line-to-line voltage V L is related to the rms phase voltages by V L =√3 V YL. Also, I L =I YL. Hence All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

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20. Total Instantaneous Power All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

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22. Power Factor Compensation All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

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26. Wattmeters Single Phase: Three Phase : Uses 2 Wattmeters All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

27. Two-Wattmeter Method All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

28. Two-Wattmeter Method But, the total power absorbed by the load is: Hence: Also, for a balanced load: All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

29. Summary All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press