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 Zr1 for 80% coverage of line 1- 2, Zr2 for 100% of line 1 - 2, and Zr3 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 Sbase = 100 MPA. Convert given quantities that are not given in pu, into their pu equivalents.
a) Form the Υbus matrix with entries in cartesian format.
b) Rewrite the Υbus 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.