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DKT213 ELECTRICAL TECHNOLOGY

DKT213 ELECTRICAL TECHNOLOGY. Chapter 3 Three-Phase System. Single-Phase Circuit. Two-Phase Circuit. a. A. Three wired system. Second source with 90° out of phase. What is a Three-Phase Circuit?.

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DKT213 ELECTRICAL TECHNOLOGY

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  1. DKT213 ELECTRICAL TECHNOLOGY Chapter 3 Three-Phase System

  2. Single-Phase Circuit

  3. 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

  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:

  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

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

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

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

  28. Balance Y-ΔConnection 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-ΔConnection • 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-ΔConnection Phase currents: Line voltages: Line currents: Magnitude line currents: Total impedance:

  31. Balance Δ-ΔConnection 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: Complex power per phase: Apparent 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 = -(2087 + j834.6) VA Pa = -2087W Pr = -834.6VAR At the load: SL = (1392 + j1113) VA Pa = 1392W Pr = 1113VAR

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