1. Chapter 12 Three-Phase Circuit Analysis

2. A three phase generator has three coils each represent a phaseVa N S N S N S N S N S N S N S N S Vb I b Vb I a Va Vc Vc I c

3. Three-phase system

4. Why do we use 3-phase systems?
Three-phase system produces rotating magnetic field.
Three-phase motors can start without the need for extra equipment.
For the same physical size, a three-phase generator produces more power than a single phase generator.
Three-phase lines transmit more power.
Three-phase lines are more reliable.
In distribution circuit, you can operate the system with one missing phase.

5. Y-Connection-Source

6. Phase voltage V V a n b V c V V V n c a b cn an bn cn bn an Reference
Transmission
Line
Generator V an
Reference a n a b V bn c b
Van
Vbn
Vcn V cn V bn V an n

10. Line-to-line voltage V ca bc ab n c b a
Van
Vbn
Vcn

11. Reference V ab ca n bn cn an bc -V
The other line to line voltages

12. Main Conclusions Line-to-line voltage is greater than phase voltage by
Line-to-line voltage leads phase voltage by

13. Example v v Let for a balanced three phase system
Reference 30
Calculate the line-to-line voltages v an
The other voltages can be computed by the
balanced system relationship

14. Y-Connected System I I I I I I I I I a a Z n n Z Z c c V V V
Line current
Transmission
Line
Source
Load I
Phase current a a a + + I Z V I a an a I n b n V V Z Z cn bn + I c + b c + b I + I I b c c b I c

15. Three Phase System

16. Y-Connection
For balanced system

17. V cn I c q n V an
Reference I b q V bn I a q

18. Neutral Current of Balanced LoadI c
For balanced system I a I b

19. Main Conclusions for Y-Connected Load
Line-to-line voltage is greater than phase voltage by
Line-to-line voltage leads phase voltage by
Line current equals phase current

20. Example: For the three phase system shown , find
The load currents of each phase
The neutral current
The magnitude of the line to line voltage Ia a b c b c Ib Ic

21. The load currents of each phase
The other currents can be computed by the balanced
system relationship
The neutral current
The magnitude of the line to line voltage

22. Delta () Connection: LoadIa a _
Ica +
Iab I bc ab n V ca
Reference q _ Ib + b _ c + Ic
Ibc

23. I ca V ab
Reference n q I ab I bc
300 I a
- Ica

24. Main Conclusions for Delta-Connected Load
Line-to-line voltage of the source is equal to phase voltage (across load).
The line current (coming from the source) is greater than phase current (of the load) by
Line current lags phase current by

25. Example Calculate the phase currents of the load a Iab Ia Ica c b b cIb
Ibc Ic

26. a b c Ia Ic
Van Ib Z

27. Power of 3-phase circuits
Iphase
Vphase
For Single phase
IMPORTANT
 is the angle between
phase voltage and
phase current.
Use voltage as a
reference
For 3-phase

28. Real Power in Y Circuit a b c Ia Ib Ic
Van
Vcn
Vbn

29. Reactive Power in Y Circuitb c Ia Ib Ic Va Vc Vb

30. Real Power in Delta Circuitb c Ia Ib Ic
Iab
Ica
Ibc + _

31. Reactive Power in Delta Circuitb c Ia Ib Ic
Iab
Ica
Ibc + _

32. Two-meter method for measuring three-phase power
Three Phase Power Measurement
Two-meter method for measuring three-phase power