ECE 332:494:01/599:02 – Smart Grid – Homework Assignment – Set 4 Solved

  
332:494:01/599:02 – Smart Grid –
Homework Assignment – Set 4 

 

General guidelines for homework assignments: Homework should be submitted online (via Canvas)  

 

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:

 

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  

 

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 
 

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

c)       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

(a)       Find the admittance matrix Y

(b)       Write the equations for the Gauss-Seidel iteration: 𝑉 𝑎𝑛𝑑                      𝑉1(%&!) and given an initial estimate that  𝑉#(0)                             𝑝𝑢       find 

𝑉#(!), 𝑉((!), 𝑎𝑛𝑑  𝑉1(!) 

332:494/599– HW Set 4                                                                                                           2 

                         

 

 

 

 

 

 

Figure 3

 

 

332:494/599– HW Set 4                                                                                                           3