1. Introduction to Three-Phase Power
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2. Typical Transformer Yard
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3. Basic Three-Phase Circuit
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4. What is Three-Phase Power?
Three sinusoidal voltages of equal amplitude and frequency out of phase with each other by 120°. Known as “balanced”.
Phases are labeled A, B, and C.
Phases are sequenced as A, B, C (positive) or A, C, B (negative).
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5. Three-Phase Power
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6. Definitions 4 wires Color Code 3 “active” phases, A, B, C
1 “ground”, or “neutral”
Color Code
Phase A Red
Phase B Black
Phase C Blue
Neutral White or Gray
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7. Phasor (Vector) Form for abc
Vc=Vm/+120°
Va=Vm/0°
Vb=Vm/-120°
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8. Phasor (Vector) Form for abc
Vc=Vm/+120°
Va=Vm/0°
Vb=Vm/-120°
Note that KVL applies Va+Vb+Vc=0
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9. Three-Phase Generator
2-pole (North-South) rotor turned by a “prime mover”
Sinusoidal voltages are induced in each stator winding
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11. How are the sources connected?
(a) shows the sources (phases) connected in a wye (Y).
Notice the fourth terminal, known as Neutral.
(b) shows the sources (phases) connected in a delta (∆).
Three terminals
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12. Look at a Y-Y System
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13. Definitions Zg represents the internal generator impedance per phase
Zl represents the impedance of the line connecting the generator to the load
ZA,B,C represents the load impedance per phase
Zo represents the impedance of the neutral conductor
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14. Look at the Line and Load Voltages
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15. Phase Voltages
Line Voltages
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16. Vector addition to find VAB=VAN-VBN
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17. Using the Tip-to-Tail Method
-VBN
VΦ = Line-to-Neutral, or Phase Voltage
VAB = VAN – VBN = √3VΦ
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18. Conclusions for the Y connection
The amplitude of the line-to-line voltage is equal to √3 times the amplitude of the phase voltage.
The line-to-line voltages form a balanced set of 3-phase voltages.
The set of line-to-line voltages leads the set of line-to-neutral (phase) voltages by 30°.
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19. Summary
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20. Look at the Delta-Connected Load
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22. Phase Currents
Line Currents
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23. Vector Addition to find IaA=IAB-ICA
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24. Using the Tip-to-Tail Method
-ICA
IaA = √3IΦ/-30°
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25. Conclusions for the Delta Connection
The amplitude of the line current is equal to √3 times the phase current.
The set of line currents lags the phase currents by 30°.
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