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Pharos University EE-385

This document, prepared by Dr. Sahar Abd El Moneim Moussa, explores the principles of balanced three-phase systems prevalent in electrical engineering. It covers the characteristics of balanced three-phase voltages—sinusoidal waves with equal amplitude and frequency, phase differences of 120 degrees, and the relationships in Wye and Delta connections. The paper includes practical examples, detailing the calculation of line and phase currents, voltages at load terminals, and complex power delivered to loads. A comprehensive understanding of these concepts is vital for electrical engineers.

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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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