a) The bus impedance matrix for a three- bus power system isj0.12 j0.08 j0.04]

Z

j0.08 j0.12 j0.07
bus
j0.04 j0.07 j0.08
per unit
If a three-phase fault occurs at bus 2 through impedance Z f = j0.13 pu, determine the sub- transient fault current and the voltages at buses 1, 2, and 3 during the fault t bus 2.
(8 marks)
b) Modify the Z bus matrix in part a) if a branch having impedance j0.05 pu is added between bus 2 and 3.
(7 marks)

Answer

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Part a:

  1. Calculate the Thevenin impedance seen from bus 2:
    • Remove the row and column corresponding to bus 2 from the Zbus matrix:Zth = [j0.12 j0.04]

[j0.04 j0.08]

Calculate the equivalent impedance: Zth = j0.12 – (j0.04 * j0.04) / j0.08 = j0.1425 pu

Calculate the total fault impedance:

  • Zf_total = Zth + Zf = j0.1425 + j0.13 = j0.2725 pu

Calculate the sub-transient fault current:

  • If = Vprefault / Zf_total (assuming a pre-fault voltage of 1 pu for simplicity)
  • If = 1 / j0.2725 = -j3.668 pu

Calculate the voltages at buses 1, 2, and 3:

  • V1 = Vprefault – Z12 * If = 1 – j0.08 * (-j3.668) = 1.2934 pu
  • V2 = 0 (fault bus)
  • V3 = Vprefault – Z32 * If = 1 – j0.07 * (-j3.668) = 1.2567 pu

Part b:

  1. Modify the Zbus matrix:
    • Add the new branch impedance (j0.05 pu) between bus 2 and 3:Zbus_new = [j0.12 j0.08 j0.04] [j0.08 j0.17 j0.12] (Z23 + j0.05)

[j0.04 j0.12 j0.13]

Remember:

  • Use appropriate units (pu or ohms) throughout the calculations.
  • Consider the pre-fault voltage for accurate results.
  • Double-check calculations for clarity and accuracy.

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