1. EKT103 ELECTRICAL ENGINEERING Chapter 1 Three-Phase System Dr. Rosemizi Abdul Rahim Dr. Amir Razif Arief Jamil Abdullah (019 4659277) Dr. Junita Mohd Nordin School of Computer and Communication Engineering (SCCE), University Malaysia Perlis (UniMAP), Perlis, MALAYSIA. amirrazif@unimap.edu.my 1

2. COURSE OUTCOME (CO) CO1: Ability to define and explain the concept of single-phase and three-phase system. 2

3. 3 sinusoid A sinusoid is a signal that has the form of the sine or cosine function. A general expression for the sinusoid, where V m = the amplitude of the sinusoid ω = the angular frequency in radians/s Ф = the phase Revision

4. 4 periodic function A periodic function is one that satisfies v(t) = v(t + nT), for all t and for all integers n. same frequency Only two sinusoidal values with the same frequency can be compared by their amplitude and phase difference. phase difference is zeroin phase not zeroout of phase If phase difference is zero, they are in phase; if phase difference is not zero, they are out of phase. Revision

5. 5 Revision Example 1 Given a sinusoid,, calculate its amplitude, phase, angular frequency, period, and frequency. Solution: Amplitude = 5, phase = –60 o, angular frequency = 4  rad/s, Period = 0.5 s, frequency = 2 Hz.

6. 6 Revision Example 2 Find the phase angle between and, does i 1 lead or lag i 2 ?Solution: Since sin( ω t+90 o ) = cos ω t therefore, i 1 leads i 2 155 o.

7. 7 Revision Impedance transformation

8. Single-Phase Circuit Three wired system, same magnitude, same phase. single phase A single phase circuit consists of a generator connected through a pair of wires to a load. Two wire system

9. A a Two-Phase Circuit Three wired system Second source with 90° out of phase Three wired system: same magnitude different phase

10. three sources out of phase 120° 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°. 10 What is a Three-Phase Circuit? Three sources with 120° out of phase Four wired system

11. stationary winding (stator). A three-phase generator consists of a rotating magnet (rotor) surrounded by a stationary winding (stator). 11 Balance Three-Phase Voltages A three-phase generatorThe generated voltages

12. Two Two possible configurations: 12 Balance Three-Phase Voltages Three-phase voltage sources: Y-connected (a) Y-connected Δ -connected (b) Δ -connected

13. 13 Phase sequences positive sequence negative sequence a) abc or positive sequence b) acb or negative sequence Balance Three-Phase Voltages

14. 14 same amplitude and frequency out of phase 120 o If the voltage source have the same amplitude and frequency ω and are out of phase with each other by 120 o, the voltage are said to be balanced. Balanced phase voltages Balanced phase voltages are equal in magnitude and out of phase with each other by 120 o Balance Three-Phase Voltages

15. 15 positive sequence abc sequence or positive sequence: negative sequence acb sequence or negative sequence: is the effective or rms value Balance Three-Phase Voltages

16. Example 1 Determine the phase sequence of the set of voltages. 16 Balance Three-Phase Voltages

17. Solution: The voltages can be expressed in phasor form as We notice that V an leads V cn by 120° and V cn in turn leads V bn by 120°. Hence, we have an acb sequence. 17 Balance Three-Phase Voltages Example 1 Determine the phase sequence of the set of voltages.

18. 18 Two possible three-phase load configurations: a) a wye-connected load b) a delta-connected load Balance Three-Phase Voltages

19. 19 balanced load 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: Balance Three-Phase Voltages

20. Four possible connections Y-Y connection 1. Y-Y connection (Y-connected source with a Y-connected load) Y- Δ connection 2. Y- Δ connection (Y-connected source with a Δ -connected load) Δ - Δ connection 3. Δ - Δ connection 4. Δ -Y connection 20 Balance Three-Phase Connection

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

22. 22 Source impedance Line impedance Load impedance Total impedance per phase Since all impedance are in series, Thus Balance Y-Y Connection

24. 24 Applying KVL to each phase: Balance Y-Y Connection

25. line voltages Line to line voltages or line voltages: Magnitude Magnitude of line voltages: Balance Y-Y Connection

26. Example 2 Calculate the line currents in the three-wire Y-Y system shown below: 26 Balance Y-Y Connection

27. Example 2 Calculate the line currents in the three-wire Y-Y system shown below: 27 Balance Y-Y Connection

28. 28 P1: Y-Y Solution:

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

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

31. A single phase equivalent circuit Line voltages: Balance Y- Δ Connection

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

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

34. P2: Y-  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 34 Balance Y- Δ Connection

35. 35 Cont.. Solution:

36. 36 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.

37. 37 Line voltages: Line currents: Magnitude line currents: Total impedance: Phase currents: Balance Δ - Δ Connection

38. P3:  –  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.Solution: The phase currents The line currents 38 Balance Δ - Δ Connection

39. 39 Cont.. Solution:

40. 40 Balance Δ -Y Connection balanced Δ -Y A balanced Δ -Y system is a three-phase system with a balanced y-connected source and a balanced y-connected load.

41. 41 aANBba Applying KVL to loop aANBba: From: Line currents: Balance Δ -Y Connection

42. 42 Replace Δ connected source to equivalent Y connected source. Phase voltages: Balance Δ -Y Connection

43. 43 A single phase equivalent circuit Balance Δ -Y Connection

44. P4:  –Y 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 V ab as reference.Solution: The phase currents 44 Balance Δ -Y Connection

45. 45 Cont.. Solution:

46. 46 Summary of phase and line voltages/currents for balanced three-phase systems.

47. 47 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 Power in a Balanced System

48. 48 For Y connected load, the phase voltage: Power in a Balanced System

49. 49 Phase current lag phase voltage by θ. If The phase current: Power in a Balanced System

50. 50 Total instantaneous power: Average power per phase: Apparent power per phase: Reactive power per phase: Complex power per phase: Power in a Balanced System

51. 51 Total average power: Total reactive power: Total complex power: Power in a Balanced System

52. 52 Power loss in two wires: Power loss in three wires: P L : power absorbed by the load I L : magnitude of line current V L : line voltage R : line resistance Power in a Balanced System

53. 53 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. apparent power The apparent power is real power The real power is power factor The power factor is

54. 54 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. Answer :

55. 55 Exercise 7 For the Y-Y circuit in Exercise 2, calculate the complex power at the source and at the load.