A) For the Y-Y circuit shown in Fig. 1, find the line currents, the line voltages, and the load voltages.

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1 Salman Bin Abdul Aziz University Faculty of Engineering Electrical Engineering department Electric Circuit Analysis (EE 2020) Sheet (2) Three-Phase Circuits < < <ˆèˆÃÖ]< fâ<àe<á^û ˆèˆÃÖ]< fâ<àe<á^û <íãú^q <íãú^q < < <t ^e t ^e<í ß]<íé Ò íéñ^e ãóö]<í ß]<ÜŠÎ < < <DNLNL NLNL< ãò ãòe<íée ãóö]< ñ]æ Ö]<Øé äqæù]<íémøm< ñ]æ Ö]<D <DNE<ké <ké Problem #1 A) If V ab = 400 V in a balanced Y-connected three-phase generator, find the phase voltages, assuming the phase sequence is: (a) abc (b) acb B) What is the phase sequence of a balanced three-phase circuit for which V an = V and V cn = V? Find V bn. C) Determine the phase sequence of a balanced three-phase circuit in which V bn = V and V cn = V. Obtain V an. D) Assuming abc sequence, if V ca = V in a balanced three-phase circuit, find V ab, V bc, V an, and V bn. E) Given that the line voltages of a three-phase Y-connected circuit are: V ab = 420 0, V bc = V ac = V Find the phase voltages V an, V bn, and V cn. Problem #2 A) For the Y-Y circuit shown in Fig. 1, find the line currents, the line voltages, and the load voltages. Fig. 1 Problem 2-A B) Obtain the line currents in the three-phase circuit shown in Fig. 2. Fig. 2 Y-Y Problem 2-B

2 C) A balanced Y-Y, four-wire system has phase voltages V an = 120 0, V bn = V cn = V. The load impedance per phase is 19 + j13 Ω, and the line impedance per phase is 1 + j2 Ω. Solve for the line currents and neutral current. D) For the circuit shown in Fig. 3, determine the current in the neutral line. Fig. 3 Y-Y Problem 2-D Problem #3 A) For the positive-sequence, three-phase circuit shown in Fig. 4, I bb = A and V BC = V. Find V an, V AB, I AC, and Z. Fig. 4. Problem 3-A B) Find the line and phase currents at the load side in the Y- circuit shown in Fig. 5. Take Z = Fig. 5. Problem 3-B C) In a Y-, 3-ph circuit, the source is a balanced, positive sequence with V an = V. It feeds a balanced load with Z = 9 + j 12 Ω per phase through a balanced line with Z l = 1 + j 0.5 Ω per phase. Calculate the phase voltages and currents at the load side.

3 Problem #4 A) Find the currents I a, I b, and I c in the 3-ph network shown in Fig. 6. Take Z = 12 j15 Ω, Z Y = 4 + j6 Ω, and Z l = 2 Ω. Fig. 6. Problem 4-A B) For the - circuit shown in Fig. 7. Find the line and phase currents. Assume that the load impedance Z l = 12 + j9 Ω per phase. Fig. 7. Problem 4-B C) A balanced delta-connected source has phase voltage V ab = V and a positive phase sequence. If this is connected to a balanced delta-connected load, find the line and phase currents. Take the load impedance per phase as Ω and line impedance per phase as 1 + j1 Ω. Problem #5 A) In the circuit of Fig. 8, if V ab = , V bc = , V ca = V, find the line currents and the load voltages. Fig. 8. Problem 5-A

4 B) A delta-connected generator supplies a balanced Y-connected load with an impedance of Ω. If the line voltages of the generator have a magnitude of 400 V and are in the positive phase sequence, find the line currents and the phase voltages at the load. Problem #6 A) A balanced Y-connected load absorbs a 3-ph power of 5 kw at a leading power factor of 0.6 when connected to a line voltage of 240 V. Find the impedance of each phase and the total complex power of the load. B) A balanced Y-load is connected to a 60-Hz three-phase source with V ab = V. The load has pf = 0.5 lagging and each phase draws 5 kw. (a) Determine the load impedance Z Y. (b) Find I a, I b, and I c. C) A three-phase source delivers 4800 VA to a Y-connected load with a phase voltage of 208 V and a power factor of 0.9 lagging. Calculate the source line current and the source line voltage. D) Given the circuit in Fig. 9 below, find the total complex power absorbed by the load. Fig. 9. Problem 6-D E) The following three parallel-connected three-phase loads are fed by a balanced threephase source. Load #1: 250 kva, 0.8 pf lagging Load #2: 300 kva, 0.95 pf leading Load #3: 450 kva, unity pf If the line voltage is 13.8 kv, calculate the line current and the power factor of the source. Assume that the line impedance is zero. F) Assume that the two balanced loads shown in Fig. 10 are supplied by an 840-V rms 60- Hz line. Load #1: Y-connected with 30+j40 Ω per phase, Load #2: balanced three-phase motor drawing 48 kw at a power factor of 0.8 lagging.

5 Assuming abc sequence, calculate: a) The complex power absorbed by the combined load, b) The kvar rating of each of the three capacitors -connected in parallel with the load to raise the power factor to unity, c) The current drawn from the supply at unity power factor condition. Fig. 10 Problem 6-F Problem #7 A) Find the real power absorbed by unbalanced 3-phase load given in Fig. 11. Fig. 11 Problem 7-A B) A balanced, positive-sequence Y-connected source has V an = V rms and supplies an unbalanced delta-connected load via a transmission line with impedance 2 + j3 Ω per phase. (a) Calculate the line currents if Z AB = 40 + j15 Ω, Z BC = 60 Ω, Z CA = 18 j12ω. (b) Find the complex power supplied by the source. C) Consider the Δ - Δ system shown in Fig. 12. Take Z 1 = 8 + j6 Ω, Z 2 = 4.2 j2.2 Ω, Z 3 = 10 + j0ω. (a) Find the phase current I AB, I BC, I CA. (b) Calculate line currents I aa, I bb, and I cc. Fig. 12, Problem 7-C

6 D) In the Y-Y system shown in Fig. 13, loads connected to the source are unbalanced. (a) Calculate I a, I b, and I c. (b) Find the total power delivered to the load. Take V p = 240 V rms. Fig. 13, Problem 7-D E) A balanced three-phase Y-source with V P = 210 V rms drives a Y-connected threephase load with phase impedance Z A = 80Ω, Z B = 60 + j90ω, and Z C = j80ω. Calculate the line currents and total complex power delivered to the load. Assume that the neutrals are connected.