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Electrical Engineering
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Apr 3, 2024
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Homework 04
EEE 598 – Electric Energy Markets
Professor Kory W. Hedman
Homework 4: Due by 5pm AZ time, Friday, February 23. You are always required to show your work. If you use AMPL, turn in your code with your assignment. You can download the free class version of AMPL from Canvas. There is AMPL starter code provided for you on canvas. You are allowed to use the code, which I have provided, as a starter for this assignment. Much of the work is already done. 1. 100 Points
a) (10 points)
Assume bus C is the reference bus.
PTDF
k,i
r
: Power Transfer Distribution Factor for line k for the net injection from bus i
to the reference bus r
.
Determine the following PTDFs. If the flow from bus i
’s injection (to bus r
) is in the opposite direction as the direction I have listed for each flow variable, make sure you assign a negative to the PTDF value. (There is not enough room in the table below to write your answer so just write them on a separate sheet of paper – this is just to let you know what is required)
Line k:
PTDF
k,A
C
PTDF
k,B
C
PTDF
k,C
C
PTDF
k,D
C
k =
1
k = 2
k =
3
k =
4
Page 1 of 4
A
B
D
C
z1
z2
z4
z3
Ga
Gd
Gb
Gc
Ld
Lb
Lc
La
P
4
P
1
P
3
P
2
Homework 04
b) (40 points)
Take the example from part A above. Solve the DCOPF problem from part A above with the information in the following tables. You are allowed to use AMPL. If you use a program you must provide your code; otherwise, you will receive no credit. Copying someone’s code is a violation of AIP (you are allowed to work with your HW partner)
.
Assume that z1 = 2, z2 = 2, z3 = 2, z4 = 1.
Generator Information:
Pmin:
Pmax:
Startup Cost:
No Load Cost:
Operating Cost:
Initial Status:
Gen A
25
110
$1700
$800
25 $/MWh
Off
Gen B
40
160
$3500
$400
65 $/MWh
Off
Gen C
15
200
$2200
$40
55 $/MWh
Off
Gen D
35
250
$600
$700
90 $/MWh
Off
Note that you are not solving a unit commitment problem for part B. All units will be committed for each period. And you will need to properly account for startup and no-load cost for the committed units.
Line Information:
Pmin:
Pmax:
P1
-35
35
P2
-35
35
P3
-45
45
P4
-35
35
Load Information: Period 1:
Period 2:
Period 3:
La
25
30
80
Lb
45
40
240
Lc
35
100
190
Ld
50
70
160
Note that there are three periods. You must solve this problem for each period. You are required to report the output from each generator for each period, the flow on the lines for each period, and the optimal objective value, as shown below.
Period 1:
Period 2:
Period 3:
Gen A
Gen B
Gen C
Gen D
P1
P2
P3
P4
The total cost (objective) is: ____________________________________
Page 2 of 4
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