[SOLVED] ECE599 Homework4

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:

1. Power flowing from bus 1 out to bus 2: 𝑆_!# =
2. Power flowing from bus 1 to bus 3: 𝑆_!( =
3. Power generated by the source: 𝑆_! = 𝑆_)*+ =
4. Line losses for the line connecting bus 1 to bus 2: 𝑆_,-…!# =
5. 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

1. 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

1. If after several iterations the voltage at bus 2 converges to 𝑉_# = 0.9 − 𝑗0.1 determine the poser S₁
2. 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