1. DKT213 ELECTRICAL TECHNOLOGY
Chapter 3
Three-Phase System

2. Single-Phase Circuit

3. Second source with 90° out
Two-Phase Circuit A a
Three wired system
Second source with 90° out
of phase

4. What is a Three-Phase Circuit?
It is a system produced by a generator consisting of three sources having the same amplitude and frequency but out of phase with each other by 120°.
Three sources with 120° out
of phase
Four wired system

5. What is a Three-Phase Circuit?
Advantages:
Most of the electric power is generated and distributed in three-phase.
The instantaneous power in a three-phase system can be constant.
The amount of power, the three-phase system is more economical that the single-phase.
In fact, the amount of wire required for a three-phase system is less than that required for an equivalent single-phase system.

6. Balance Three-Phase Voltages
A three-phase generator consists of a rotating magnet (rotor) surrounded by a stationary winding (stator).
A three-phase generator
The generated voltages

7. Balance Three-Phase Voltages
Two possible configurations:
Three-phase voltage sources: (a) Y-connected ; (b) Δ-connected

8. Balance Three-Phase Voltages
Phase sequences
a) abc or positive sequence b) acb or negative sequence

9. Balance Three-Phase Voltages
If the voltage source have the same amplitude and frequency ω and are out of phase with each other by 120o, the voltage are said to be balanced.
Balanced phase voltages are equal in magnitude and out of phase with each other by 120o

10. Balance Three-Phase Voltages
abc sequence or positive sequence:
is the effective or rms value
acb sequence or negative sequence:

11. Balance Three-Phase Voltages
Example 1
Determine the phase sequence of the set of voltages.

12. Balance Three-Phase Voltages
Solution:
The voltages can be expressed in phasor form as
We notice that Van leads Vcn by 120° and Vcn in turn leads Vbn by 120°.
Hence, we have an acb sequence.

13. Balance Three-Phase Voltages
Two possible three-phase load configurations:
a) a wye-connected load b) a delta-connected load

14. Balance Three-Phase Voltages
A balanced load is one in which the phase impedances are equal in magnitude and in phase.
For a balanced wye connected load:
For a balanced delta connected load:

15. Balance Three-Phase Connection
Four possible connections
Y-Y connection (Y-connected source with a Y-connected load)
Y-Δ connection (Y-connected source with a Δ-connected load)
Δ-Δ connection
Δ-Y connection

16. Balance Y-Y Connection
A balanced Y-Y system is a three-phase system with a balanced y-connected source and a balanced y-connected load.

17. Balance Y-Y Connection
Source impedance
Line impedance
Load impedance
Total impedance per phase

18. Balance Y-Y Connection
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19. Balance Y-Y Connection
Applying KVL to each phase:

20. Balance Y-Y Connection
Line to line voltages or line voltages:
Magnitude of line voltages:
ale29559_12011.jpg

21. Balance Y-Y Connection
Example 2
Calculate the line currents in the three-wire Y-Y system shown below:

22. Balance Y-Y Connection
Example 2
Calculate the line currents in the three-wire Y-Y system shown below:

23. Balance Y-Δ Connection
A balanced Y-Δ system is a three-phase system with a balanced y-connected source and a balanced Δ-connected load.

24. Balance Y-Δ Connection
A single phase equivalent circuit
ale29559_12016.jpg

25. Balance Y-Δ Connection
A single phase equivalent circuit
Line voltages:
ale29559_12016.jpg

26. Balance Y-Δ Connection
A single-phase equivalent circuit of a balanced Y- circuit
Line currents:
Phase currents:
ale29559_12015.jpg

27. Balance Y-Δ Connection
A single-phase equivalent circuit of a balanced Y- circuit
Magnitude line currents:
ale29559_12015.jpg

28. Balance Y-Δ Connection
Example 3
A balanced abc-sequence Y-connected source with ( ) is connected to a Δ-connected load (8+j4) per phase. Calculate the phase and line currents.
Solution
Using single-phase analysis,
Other line currents are obtained using the abc phase sequence

29. Balance Δ-Δ Connection
A balanced Δ-Δ system is a three-phase system with a balanced Δ -connected source and a balanced Δ -connected load.

30. Balance Δ-Δ Connection
Phase currents:
Line voltages:
Line currents:
Magnitude line currents:
Total impedance:

31. Balance Δ-Δ Connection
Example 4
A balanced Δ-connected load having an impedance 20-j15  is connected to a Δ-connected positive-sequence generator having ( ). Calculate the phase currents of the load and the line currents.
Ans:
The phase currents
The line currents

32. Balance Δ-Y Connection
A balanced Δ-Y system is a three-phase system with a balanced y-connected source and a balanced y-connected load.

33. Balance Δ-Y Connection
Applying KVL to loop aANBba:
From:
Line currents:

34. Balance Δ-Y Connection
Replace Δ connected source to equivalent Y connected source.
Phase voltages:

35. Balance Δ-Y Connection
A single phase equivalent circuit

36. Balance Δ-Y Connection
Example 5
A balanced Y-connected load with a phase impedance 40+j25  is supplied by a balanced, positive-sequence Δ-connected source with a line voltage of 210V. Calculate the phase currents. Use Vab as reference.
Answer
The phase currents

37. Power in a Balanced System
Comparing the power loss in (a) a single-phase system, and (b) a three-phase system
If same power loss is tolerated in both system, three-phase system use only 75% of materials of a single-phase system

38. Power in a Balanced System
For Y connected load, the phase voltage:

39. Power in a Balanced System
Phase current lag phase voltage by θ. If
The phase current:

40. Power in a Balanced System
Total instantaneous power:
Average power per phase:
Reactive power per phase:
Apparent power per phase:
Complex power per phase:

41. Power in a Balanced System
Total average power:
Total reactive power:
Total complex power:

42. Power in a Balanced System
Power loss in two wires:
Power loss in three wires:
PL : power absorbed by the load
IL : magnitude of line current
VL : line voltage
R : line resistance

43. Example 6 A three-phase motor can be regarded as a balanced
Y-load. A three-phase motor draws 5.6 kW when the
line voltage is 220 V and the line current is 18.2 A.
Determine the power factor of the motor.

44. Exercise 6 Calculate the line current required for a 30-kW
three-phase motor having a power factor of 0.85
lagging if it is connected to a balanced source
with a line voltage of 440 V.

45. Exercise 7 For the Y-Y circuit in Exercise 2, calculate the
complex power at the source and at the load.

46. Unbalanced Three-Phase Systems
An unbalanced system is due to unbalanced voltage sources or an unbalanced load.
To calculate power in an unbalanced three-phase system requires that we find the power in each phase.
The total power is not simply three times the power in one phase but the sum of the powers in the three phases.

47. Unbalanced Three-Phase Systems
Example 6
Determine the total average power, reactive power, and complex power at the source and at the load
Ans
At the source:
Ss = -( j834.6) VA
Pa = -2087W
Pr = VAR
At the load:
SL = ( j1113) VA
Pa = 1392W
Pr = 1113VAR