04_HW_EEE598

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Arizona State University *

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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

Homework 04 The DCOPF formulation with PTDFs is in Lecture 10. c) (40 points) Solve the problems defined in part b above now with unit commitment. You are not required to model minimum up and down times or the ramp rate constraints. You are required to incorporate a unit commitment variable reflecting the status of each generator and you must account for the startup cost and the no load cost listed in the table below. You are allowed to use AMPL/Gurobi/CPLEX but you must turn in your code. You are to assume that each generator is off the period before period 1; this means that if the unit is turned on in period 1 then there is a startup cost. 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 You are required to provide the following information: Period 1: Period 2: Period 3: Gen A Gen B Gen C Gen D U1 U2 U3 U4 P1 P2 P3 P4 The total cost (objective) is: ____________________________________ U1: Unit Commitment variable for generator 1. Likewise for U2, U3, U4. Page 3 of 4

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Homework 04 d) (10 points) You will find the following code in the starter code provided to you: display {i in 1..Bus} NodeBalance.dual[i,1]; display {i in 1..Bus} NodeBalance.dual[i,2]; display {i in 1..Bus} NodeBalance.dual[i,3]; Describe what these outputs represent. After you describe what these outputs represent, do you find anything peculiar with their values? Explain. Page 4 of 4