05_HW_EEE598

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Electrical Engineering

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Apr 3, 2024

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Homework 05 EEE 598 – Electric Energy Markets Professor Kory W. Hedman Homework 5: Due by 5pm AZ time, Friday, March 22. You are always required to show your work. 1) 40 Points You are required to read the article by the NYISO titled: “Uniform-Pricing versus Pay-as-Bid in Wholesale Electricity Markets: Does it Make a Difference?” This article has been posted on Canvas (go to Canvas: Files/Papers/Uniform_PayAsBid.zip and find NYISO_Uniform_PAB.pdf). I encourage you to utilize the other sources that I have provided on Canvas (in the same zip file and you are welcome to find other papers online, through IEEE Xplore). You are required to write a summary on the debate over Uniform Pricing and Pay-as-Bid. You are required to type this summary: Times New Roman, 12 font, 1 inch margins, single spaced. At least ½ of a page on the summary itself. You are required to give your own personal view on this debate and critique both sides. You are encouraged to discuss this debate with your fellow students; however, ultimately what you write/type MUST be your own group work. Note that I did not cover everything discussed in these papers so I expect to see a discussion on more than just what I presented in class (for instance, there are a number of pages on the discussion of market power from the NYISO paper). If you plagiarize, you will be reported to the university for cheating and you will be penalized accordingly. If you simply rewrite what is in the article (take a sentence and change a couple words or reorder the ordering of the sentence) – you will receive a zero as this does not demonstrate that you understand the material. And, based on to what extent you do this, you may be guilty of cheating. If you do not understand what Plagiarism is or is not, you should speak with me, your professor. Page 1 of 4

A B z1 Ga Gb Lb P1 Homework 05 2. (45 points) For this problem you should consider the LMP to be a dual variable. Solve the following two-node examples (DC OPF-lossless) by hand and calculate the LMP at bus A and bus B (by hand as well – you are not allowed to use any software ). Report the dispatch value from the generators, the line flow value, and the LMP values. If there are non-unique solutions for the LMP, then you must provide the range of LMP values. Show your work and EXPLAIN your LMP answers. a) (5 points) Cost of Ga: $60/MWh (no minimum or maximum capacity for Ga) Lb: 80MW P1: Line Limit is: 80MW LMP_A LMP_B b) (5 points) Cost of Ga: $60/MWh (Minimum Output: 0MW. No maximum capacity for Ga) Cost of Gb: $40/MWh (Minimum Output: 0MW. Maximum Output: 80MW) Lb: 80MW P1: Line Limit is: 80MW LMP_A LMP_B c) (10 points) Prove that the answers that you provide above for the LMPs are the optimal solutions for the corresponding dual variables (for both parts a and b). Page 2 of 4 A B z1 Ga Lb P 1

Homework 05 d) (25 points) Solve the 3-bus DCOPF below and solve for the LMPs at each bus. G A : G C : LMP A : LMP B : LMP C : P 1 : P 2 : P 3 : Page 3 of 4

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Homework 05 3. (15 points) Many ISOs have bid caps, that is, a generator is not allowed to bid above a certain value. This was initially implemented because many people thought that, by limiting the generator’s bid, this would limit the LMP so that the LMP never exceeds the bid cap. Is this statement true? Explain. Prove or disprove that it is possible that the LMP can be higher than the highest bid of any of the generators. Explain. You must type your answer below. Page 4 of 4