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Pharos University EE-385

Pharos University EE-385. Electrical Power & Machines “Electrical Engineering Dept” Prepared By: Dr. Sahar Abd El Moneim Moussa. Three-Phase System . Balanced Three-Phase System.

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Pharos University EE-385

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  1. Pharos UniversityEE-385 Electrical Power & Machines “Electrical Engineering Dept” Prepared By: Dr. SaharAbd El MoneimMoussa Dr. Sahar Abd El Moneim Moussa

  2. Three-Phase System Dr. Sahar Abd El Moneim Moussa

  3. Balanced Three-Phase System Balanced three-phase voltage consists of three sinusoidal voltage having the same amplitude & frequency but are out of phase with each other exactly by 120o Dr. Sahar Abd El Moneim Moussa

  4. 3 Phase Voltages in Time Domain • Va = Vm Sin ωt • Vb = Vm Sin (ωt-120) • Vc = Vm Sin (ωt-240) Phase (a) Phase (c) Phase b Dr. Sahar Abd El Moneim Moussa

  5. 3-Phase Voltages in Terms of Phasors • Va = Vm∠0 • Vb = Vm∠-120 • Vc = Vm∠-240 = Vm∠120 Dr. Sahar Abd El Moneim Moussa

  6. Dr. Sahar Abd El Moneim Moussa

  7. Wye Connection “Y” • Wye Connection: “Y” For Y circuit: Iline = Iphase Dr. Sahar Abd El Moneim Moussa

  8. Delta Connection “∆” • For Delta Circuit: Eline = Ephase Dr. Sahar Abd El Moneim Moussa

  9. Relationship between three-phase delta-connected and wye connected impedance Wye connected load Delta connected load Dr. Sahar Abd El Moneim Moussa

  10. Four Different Configurations for the three-phase source and loads Connections Dr. Sahar Abd El Moneim Moussa

  11. Power in 3-φ System • P(total) = • Q(total) = • S(total) = Dr. Sahar Abd El Moneim Moussa

  12. Example 1: A balanced three-phase Y-connected generator with positive sequence has an impedance of 0.2 +j0.5 / and internal voltage 120V/ feeds a -connected load through a distribution line having an impedance of 0.3 +j0.9 /. The load impedance is 118.5+ j85.8 /. Use the a phase internal voltage of the generator as a reference. • Construct the single-phase equivalent circuit of the 3- system. • Calculate the line currents IaA, IbB and IcC. • Calculate the phase voltages at the load terminals. • Calculate the phase currents of the load. • Calculate the line voltages at the source terminals. • Calculate the complex power delivered to the -connected load. Dr. Sahar Abd El Moneim Moussa

  13. Solution: A. The load impedance of the Y equivalent is Dr. Sahar Abd El Moneim Moussa

  14. B. The a-phase line current is A. Therefore, IbB=2.4-156.87 A. IcC= 2.483.13 A. C. because the load is - connected, the phase voltages are the same as the line voltages. To calculate the line voltages, VA=(39.5 + j28.6)(2.4-36.87) = 117.04-0.96 Dr. Sahar Abd El Moneim Moussa

  15. The line voltage VABis = 202.72 29.04V Therefore, VBC=202.72 -90.96 V VCA= 202.72 149.04 V D. The phase currents of the load will be, = 1.39 -6.87 A. Dr. Sahar Abd El Moneim Moussa

  16. Therefore, IBC=1.39-126.87 A ICA=1.39113.13 A E. The line voltage at the source terminals will be, Va=(39.8 + j29.5) (2.4-36.87) =118.9 -0.32 V. The line voltage will be = 205.9429.68 V. Therefore , Vbc=205.94 -90.32 V. Vca= 205.94149.68 V. Dr. Sahar Abd El Moneim Moussa

  17. F. The total complex power delivered to the load will be, V=VAB= 202.72 29.04 V. I=iAB=1.39-6.87 A. Therefore, ST= 3 (202.72 29.04) (1.396.87) = 682.56 +j 494.21 VA Dr. Sahar Abd El Moneim Moussa

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