Circuit analysis using phasor/impedance, complex power calculation: A three-phase RLC circuit is shown below. The reactance of the capacitor is 40 Ohm. The reactance of the inductor is 80 Ohm, and the resistor is 8 Ohm. The sending end voltage is v₁(t) = √2³45 cos(wt +) kV, where w = 2π - 60 rad/s. The receiving end voltage is v₂(t) = √2345 cos(wt) kV. The power base is 1000 MVA and the voltage base (L-L) is 345 kV. Please compute total transferred complex power S₁ and S₂ in the physical unit. Please draw a per-phase phasor/impedance diagram using per unit values. Please compute the per unit complex power S₁ and 5₂. Find out the real power loss by the resistor, reactive power consumption by the inductor and the reactive power generated by the series capacitor in per unit. f Si 777 Figure R L с mm F S₂ + Vr

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This is a part of a review I'm studying, NOT a graded assignment, please do not reject. Thank you!

I only want the solution for the 4th question that the black arrow is pointing to!

The answers for the first and third question are given below; I dont think the solution to the second question is necesarry to solve the 4th:

S1 = 1510.6 at 3.69 degrees MVA

S2 = 1510.6 at -26.3 degrees MVA

S1 p.u. = 1.51 at 3.69 degrees p.u.

S2 p.u. = 1.51 at -26.3 degrees p.u.

Circuit analysis using phasor/impedance, complex power calculation: A three-phase RLC circuit
is shown below. The reactance of the capacitor is 40 Ohm. The reactance of the inductor is 80 Ohm, and the
resistor is 8 Ohm. The sending end voltage is v₁ (t) = √2³45 cos(wt + 7) kV, where w = 27 · 60 rad/s. The
receiving end voltage is v2(t) = √√2³45 cos(wt) kV. The power base is 1000 MVA and the voltage base (L-L) is
345 kV.
Please compute total transferred complex power S₁ and S₂ in the physical unit.
Please draw a per-phase phasor/impedance diagram using per unit values.
Please compute the per unit complex power S₁ and S₂.
Find out the real power loss by the resistor, reactive power consumption by the inductor and the reactive
power generated by the series capacitor in per unit.
S₁
→>>>>
R
L
с
qoldingu
Figure
Vr
Transcribed Image Text:Circuit analysis using phasor/impedance, complex power calculation: A three-phase RLC circuit is shown below. The reactance of the capacitor is 40 Ohm. The reactance of the inductor is 80 Ohm, and the resistor is 8 Ohm. The sending end voltage is v₁ (t) = √2³45 cos(wt + 7) kV, where w = 27 · 60 rad/s. The receiving end voltage is v2(t) = √√2³45 cos(wt) kV. The power base is 1000 MVA and the voltage base (L-L) is 345 kV. Please compute total transferred complex power S₁ and S₂ in the physical unit. Please draw a per-phase phasor/impedance diagram using per unit values. Please compute the per unit complex power S₁ and S₂. Find out the real power loss by the resistor, reactive power consumption by the inductor and the reactive power generated by the series capacitor in per unit. S₁ →>>>> R L с qoldingu Figure Vr
Expert Solution
Step 1: Summarize the given information.

For a three-phase RLC circuit, the following information is given:

  • base parameters: Sb=100 MVA, Vb=345 kV
  • circuit parameter: R=8 Ω, XL=80 Ω,  XC=40 Ω
  • source voltage: v1(t)=23453cos(ωt+π6) kV, v2(t)=23453cos(ωt) kV.
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