Description
Question 1:
For the power system given in figure 1 bus 1 is a slack bus with 𝑉! , bus 2 is a load bus (PQ) with 𝑆2 = 300𝑀𝑊 + 𝑗1270𝑀𝑉𝐴𝑟 and 𝑆3 = 400𝑀𝑊 + 𝑗220𝑀𝑉𝐴𝑟. The line impedances are 𝑍12 = 0.01 + 𝑗0.03 𝑝𝑢 and are . The base power is 100𝑀𝑉𝐴.
(a) Use the Gauss-Seidel method to write the expression to calculate 𝑉#(%&!) 𝑎𝑛𝑑 𝑉((%&!)as a function of 𝑉#(%) , 𝑉((%)
B1 B3
S2
`
Figure 1
(b) If after several iterations the voltages at buses B2 and B3 converge to 𝑉# =
0.9046 − 𝑗0.073 and 𝑉( = 0.7618 − 𝑗0.116 determine the following:
- Power flowing from bus 1 out to bus 2: 𝑆!# =
- Power flowing from bus 1 to bus 3: 𝑆!( =
- Power generated by the source: 𝑆! = 𝑆)*+ =
- Line losses for the line connecting bus 1 to bus 2: 𝑆,-…!# =
- Line losses for the line connecting bus 1 to bus 3: 𝑆,-…!( =
Question 2:
For the power system given in figure 2 bus 1 is a slack bus with 𝑉! = 1∠0∘ 𝑝𝑢 and bus 2 is a load bus (PQ) with 𝑆2 = 280𝑀𝑊 + 𝑗60𝑀𝑣𝑎𝑟. The line impedance is
0.02 + 𝑗0.04 𝑝𝑢 and the base power is 100𝑀𝑉𝐴
- a) Use the Gauss-Seidel method to write the expression to calculate
𝑉#(%&!) as a function of 𝑉#(%) and solve for 𝑉#(!) 𝑖𝑓 𝑉#(0) = 1∠0∘ 𝑝𝑢
B1
Figure 2
- If after several iterations the voltage at bus 2 converges to 𝑉# = 0.9 − 𝑗0.1 determine the poser S1
- For part (b) determine the line losses for the line connecting bus 1 and bus 2
Question 3:
For the power system in figure 3, assume a base power of 100MVA
- Find the admittance matrix Y
- Write the equations for the Gauss-Seidel iteration: 𝑉𝑎𝑛𝑑 𝑉1(%&!) and given an initial estimate that 𝑉#(0) 𝑝𝑢 find
𝑉#(!), 𝑉((!), 𝑎𝑛𝑑 𝑉1(!)
332:494/599– HW Set 4 2
Figure 3
