1. CIRCUITS by Ulaby & Maharbiz
10. Three Phase Power
CIRCUITS by Ulaby & Maharbiz
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3. Transformers in Power Grid
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Transformers in Power Grid

4. A 4800-V rms single-phase connected to residential user through a 20 : 1 step-down transformer
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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

6. Y & Delta For a balanced source, V1 + V2 + V3 = 0.
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Y & Delta
For a balanced source,
V1 + V2 + V3 = 0.

7. Source-Load Configurations
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Source-Load Configurations
Y-Y
Y-Delta

8. Source-Load Configurations
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Source-Load Configurations
Delta-Y
Delta-Delta

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.
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10. Balanced Circuits
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11. Y-Source Connected to a Y-Load
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12. VN = 0 (balanced network).
For a balanced source,
V1 + V2 + V3 = 0.
Hence,
VN = 0 (balanced network).
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13. Example 10-2 (cont.) All rights reserved. Do not copy or distribute.
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14. Transformation Between Balanced Loads
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17. Example 10-3 (cont.)
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18. Power in Balanced Networks
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Line-to-line voltage VL is related to the rms phase voltages by VL =√3 VYL. Also, IL=IYL. Hence

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20. Total Instantaneous Power
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Total Instantaneous Power

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22. Power Factor Compensation
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26. Wattmeters Single Phase: Three Phase : Uses 2 Wattmeters
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27. Two-Wattmeter Method All rights reserved. Do not copy or distribute.
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28. Two-Wattmeter Method But, the total power absorbed by the load is:
Also, for a balanced load:
Hence:
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29. Summary
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