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Chapter 12 Three-Phase Circuits

電路學 ( 二 ). Chapter 12 Three-Phase Circuits. 12.1 Introduction (1). Three-Phase Four Wire Systems. Single-Phase Systems. two-wire type. three-wire type. 12.1 Introduction (2). Nearly all electric power is generated and distributed in 3-phase.

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Chapter 12 Three-Phase Circuits

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  1. 電路學(二) Chapter 12 Three-Phase Circuits

  2. 12.1 Introduction (1) Three-Phase Four Wire Systems Single-Phase Systems two-wire type three-wire type

  3. 12.1 Introduction (2) • Nearly all electric power is generated and distributed in 3-phase. • Instantaneous power in a 3- system can be constant. • The 3- system is more economical than single-phase system.

  4. 12.2 Balanced Three-Phase Voltages (1) Van Vbn Vcn A three-phase generate

  5. 12.2 Balanced Three-Phase Voltages (2) Y-connected source -connected source

  6. 12.2 Balanced Three-Phase Voltages (2) negative sequence負向序 positive sequence正相序 Balanced phase voltages are equal in magnitude and are out of phase with each other by 120

  7. 12.2 Balanced Three-Phase Voltages (3) a Y-connected load. a -connected load. A Balanced Load is one in which the phase impedance are equal in magnitude and in phase. For a balanced Y-connected load Z1 = Z2 = Z3 = ZY For a balanced -connected load Za= Zb = Zc= Z

  8. 12.2 Balanced Three-Phase Voltages (4) Y- transformation • There are four possible connections in three-phase systems: • Y-Y connection • Y- connection • - connection • -Y connection

  9. 12.2 Balanced Three-Phase Voltages (5) Example 1 Determine the phase sequence of the set of voltages

  10. 12.3 Balanced Y-Y Connection (1) ZY = Zs + Zl+ ZL

  11. 12.3 Balanced Y-Y Connection (2) Assuming the positive sequence, The line-to-line voltages (line voltage) Similarly,

  12. 12.3 Balanced Y-Y Connection (3)

  13. 12.3 Balanced Y-Y Connection (4) Example 2 Calculate the line currents in the three-wire Y-Y system.

  14. 12.4 Balanced Y- Connection (1) Assuming the positive sequence,

  15. 12.4 Balanced Y- Connection (2) Example 3 A balanced abc-sequence Y-connected source with Van = 10010 V is connected to a -connected balanced load (8 + j4)  per phase. Calculate the phase and line currents.

  16. 12.5 Balanced - Connection (1) Assuming the positive sequence,

  17. 12.5 Balanced - Connection (2) Example 4 A balanced -connected load having an impedance 20 – j15  is connected to a -connected, positive-sequence generator having Vab = 3300 V. Calculate the phase currents of the load and the line currents.

  18. 12.6 Balanced -Y Connection (1) • Using KVL. • Replacing the -connected source with its equivalent Y-connected source. • Transforming the Y-connected load to an equivalent Y-connected load.

  19. 12.6 Balanced -Y Connection (2)

  20. 12.6 Balanced -Y Connection (3) Example 5 A balanced Y-connected load with a phase impedance 40 + j25  is supplied by a balanced, positive-sequence -connected source with a line voltage of 210 V. Calculate the phase currents. Use Vab as reference.

  21. 12.7 Power in a Balanced System (1) • The advantage of 3-phase systems for power distribution • The total instantaneous power in a balanced 3-phas system is constant. • The 3-phase system uses a lesser amount of wire than the single-phase system for the same line voltage VL and the same absorbed power PL. For a Y-connected load, the phase voltages are

  22. 12.7 Power in a Balanced System (2) If ZY = Z, the phase currents Appling

  23. 12.7 Power in a Balanced System (3) The complex per phase The total complex power where Vp, Ip, VL, and IL are all in rms values and  is the angle of the load impedance. for Y-connected loads, for -connected loads,

  24. 12.7 Power in a Balanced System (4)

  25. 12.7 Power in a Balanced System (5) Example 6 Determine the total average power, reactive power, and complex power at the source and at the load.

  26. 12.7 Power in a Balanced System (6) Example 7 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.

  27. 12.7 Power in a Balanced System (7) Example 8 Two balanced loads are connected to a 240-kV rms 60-Hz line, as shown in the figure (a). Load 1 draws 30 kW at a power factor of 0.6 lagging, while load 2 draws 45 kVAR at a power factor 0.8 lagging. Assuming the abc sequence, determine: (a) the complex, real and reactive powers absorbed by the combined load, (b) the line currents, and(c) the kVAR rating of the three capacitors -connected in parallel with the load that will raise the power factor to 0.9 lagging and the capacitance of each capacitor.

  28. 12.10 Applications (1) • Three-Phase Power Measurement.

  29. 12.10 Applications (2) Consider the balanced Y-connected load

  30. 12.10 Applications (3) • If P2 = P1, the load is resistive. • If P2 > P1, the load is inductive. • If P2 < P1, the load is capacitive.

  31. 12.10 Applications (4) Example 9 The two-wattmeter method produces wattmeter readings P1 = 1560 W and P2 = 2100 W when connected to a -connected load. If the line voltage is 220 V, calculate: (a) the per-phase average power, (b) the per-phase reactive power, (c) the power factor, and (d) the phase impedance.

  32. 12.10 Applications (5) Example 10 The three-phase balanced load in the figure has impedance per phase of ZY = 8 + j6 . If the load is connected to 208-V lines, predict the readings of W1 and W2. Find PT and QT.

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