Question 1 -

In the four-bus system, the positive sequence line impedances are given on the figure, and the rated line voltage is 345 KV Consider B12, with 3000:1 VT and 1500:5 CT ratios.

a) Find the mho settings for Z_r1 for 80% coverage of line 1- 2, Z_r2 for 100% of line 1 - 2, and Z_r3 for 120% of line 2 - 4.

b) Assuming the maximum loading of line 1-2 under emergency loading to be 1600 A at 0.9 power factor lagging, determine if B12 will trip or stay on during such emergency loading.

Questions 2 -

For the figure on assume S_base = 100 MPA. Convert given quantities that are not given in pu, into their pu equivalents.

a) Form the Υ_bus matrix with entries in cartesian format.

b) Rewrite the Υ_bus matrix with entries in their polar format.

c) Write the equations for calculation of P₂, P₃, and Q₂ using formulas given in 6.6.2 and 6.6.3 of text.

d) Using initial values of previous values of V₂, δ₂, and δ₃ calculate P₂, P₃ and Q₂ using formulas in part (c) Note: use V₂ = 1 pu, δ₂ = 0 and δ₃ = 0 on the first run.

e) Form ΔP₂, ΔP₃, and ΔQ₂: differences between the previous values for P₂, P₃, and Q₂ and those found in part (d). Note: Use values given on the figure for P₂, P₃, and Q₂ as the previous values on the first run.

f) Form the 3x3 Jacobian matrix by taking partial derivatives of each of P₂, P₃, and Q₂ with respect to each of δ₂, δ₃ and V₂ one at a time.

g) Using and solving equation 6.6.6 of the text calculate Δδ₂ , Δδ₃, and ΔV₂.

h) Calculate δ₂, δ₃, and V₂ given the previous values for these parameter and the deltas found in step (g).

i) Repeat steps (e) through (h) above two more times.

j) Use the values of δ₂, δ₃, and V₂ found after the third iteration to calculate P₁, Q₁, and Q₃, using 6.6.2 and 6.6.3 of text.

Note: As usual you may use matlab to work out this problem, but please show all intermediate results including the Jacobian matrix for each iteration.

Textbook: Glover, D. J., Sarma, M.S., & Overbye, T. (2012). Power system analysis and design (5th ed.). Boston, MA: Cengage Learning.