Zth (Positive) = j0.1512pu Zth (Negative) = j0.1596pu Zth (Zero) = j0.208pu Calc

Question

Zth (Positive) = j0.1512pu

Zth (Negative) = j0.1596pu

Zth (Zero) = j0.208pu

Calculate the Bus-3 phase voltages at 1.02 pu , line-to-line-to-ground at Bus-2. Specify your answers in per-unit.

Description: The single-line diagram of the power system for fault study is shown in Figure 1. The power and voltage rating for generators G1 and G2 (note that Gl and G2 are two identical generators). motor M, transmission line, transformer T1 and transformer T2 are given in Table 1. The neutrals of the generator are solidly grounded. The motor neutral is grounded through a reactance 0.03 pu on the motor base Bus-1 Bus-3 Bus-4 Bus-2 G1 T1 T2 Transmission Line 0.03 pu G2 Figure 1: Single-line diagram Table:1 Ratings of the system components Rated power of generators (G1 & G2 Rated power of motor MM Rated voltage of (G 1 & G2 Rated voltage of M Transformer T1 primary voltage rating Transformer T1 secondary voltage rating Transformer T2 primary voltage rating Transformer T2 secondary voltage rating 100 MVA 100 MVA 13.8 kV 13.8 kV 13.8 kV 138 kV 13.8 kV 138 kV

Explanation / Answer

from the question per unit impedance of generator at positive sequence, negative sequance, zero sequence are given and per unit impedance of transformer are given and base MVA of motor also given then

calculate the base impedance of Zbus for a transmission line.

letus neglect the phase shift associated with star delta transformers and draw the separate positive , negative, zero sequnce figures

from the line diagrams of positive , negative sequance we can calculate the Ybus positive = Ybus nagative by inverting this we get Zbus matrics

same as above find the Ybus matrix of zero sequance and inverting that we get Zbus matrix

then calculate the double line ground fault at bus 2 for that first we have to calculate the equivalent impedance

from that we can compute the postive sequance current and negative sequance current and zero sequance current

then we can write these currents into matrix formate drom that we can calculate the voltages ata that bus.

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