Q1) A Three phase line, which has an impedance of (2+j4) Ω per phase, feeds two balanced three-phase loads that are connected in parallel. One of the loads is Y-connected with an impedance of (30 + j40)Ω per phase, and the other is Δ-connected with an impedance of (60-j45) Ω per phase. The line is energized at the sending end from a 60-Hz, three phase, balanced voltage source of 120√3 V (rms, line-to-line). Determine:-
a. The current, real power and reactive power delivered by the sending end source.
b. The line-to-line Voltage at the load.
c. The current per-phase on each load.
d. The total three-phase real and reactive powers absorbed by each load.
Q2) The equivalent circuit impedances of a 20-kVA, 8000/240 V, 60-Hz transformer are to be determined. The open-circuit test and the short-circuit test were Performed on the primary side of the transformer, and the following data were taken:
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Open-circuit test
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Short-circuit test
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(on primary)
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(on primary)
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IOC = 0.214A
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Vsc = 489V
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POC = 400W
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Psc = 240W
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Find the impedances of the approximate equivalent circuit referred to the primary side, and referred to the secondary side and sketch that circuit.
Also find the power factor of the Open-circuit test and the power factor of the Short-circuit test.
Q3) A simple power system is shown in the Figure below. This system contains a 480-V generator connected to an ideal 1:10 step-up transformer, a transmission line, an ideal 20:1 step-down transformer and a load. The impedance of the transmission line is (20 + j60)Ω, and the impedance of the load is 10 L 30 Ω. The base values for this system are chosen to be 480V and 10kVA at the generator side.
1. Find the base voltage, current, impedance, and apparent power at every point in the power system.
2. Convert this system to its per-unit equivalent circuit.
3. Find the power supplied to the load in this system.
4. Find the power lost in the transmission line.