1. ECE 4411 Introduction to Three-Phase Power

2. ECE 4412 Typical Transformer Yard

3. ECE 4413 Basic Three-Phase Circuit

4. ECE 4414 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).

5. ECE 4415 Three-Phase Power

6. ECE 4416 Definitions 4 wires –3 “active” phases, A, B, C –1 “ground”, or “neutral” Color Code –Phase ARed –Phase BBlack –Phase CBlue –NeutralWhite or Gray

7. ECE 4417 Phasor (Vector) Form for abc V a =V m /0° V b =V m /-120° V c =V m /+120°

8. ECE 4418 Phasor (Vector) Form for abc V a =V m /0° V b =V m /-120° V c =V m /+120° Note that KVL applies.... V a +V b +V c =0

9. ECE 4419 Three-Phase Generator 2-pole (North-South) rotor turned by a “prime mover” Sinusoidal voltages are induced in each stator winding

10. ECE 44110

11. ECE 44111 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

12. ECE 44112 Look at a Y-Y System

13. ECE 44113 Definitions Z g represents the internal generator impedance per phase Z l represents the impedance of the line connecting the generator to the load Z A,B,C represents the load impedance per phase Z o represents the impedance of the neutral conductor

14. ECE 44114 Look at the Line and Load Voltages

15. ECE 44115 Line Voltages Phase Voltages

16. ECE 44116 - V BN Vector addition to find V AB =V AN -V BN

17. ECE 44117 -V BN Using the Tip-to-Tail Method V AB = V AN – V BN = √3V Φ V Φ = Line-to-Neutral, or Phase Voltage

18. ECE 44118 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°.

19. ECE 44119 Summary

20. ECE 44120 Look at the Delta-Connected Load

21. ECE 44121

22. ECE 44122 Line Currents Phase Currents

23. ECE 44123 -I CA Vector Addition to find I aA =I AB -I CA

24. ECE 44124 -I CA Using the Tip-to-Tail Method I aA = √3I Φ /-30°

25. ECE 44125 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°.