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PROBLEM SET 5

IOE 491.023

Due: October 31, 2024

DELIVERABLES

1. Answers to below questions inserted into this document.

2. Your Python and any other files you used to solve the homework.

Please remember that homework questions should be posted to Piazza, not emailed to me. I encourage you to discuss questions and solution methods with your peers. Please note those peers here: ____________. If you use GenAI for this homework, please fully document your use of GenAI here: _______. Per the syllabus, you cannot use GenAI to complete this homework for you, but you can use it for basic coding help, checking or troubleshooting code, better understanding material, or similar assistance.

1. Price Taker Modeling for Storage (55 points)

You work for a grid-scale storage developer considering investing in a new storage asset. The primary application of the storage asset will be energy arbitrage in wholesale electricity prices. You, a Market Analyst at the company, have been tasked with estimating the net revenues of the storage asset under consideration. The development team has given you the parameterization of the storage asset under consideration (see StorageUnit.csv), and you have pulled historic hourly wholesale electricity prices where the storage asset would be cited (see Prices.csv).

a. Please code the price taker model in Python. Include below a screenshot of your model. (15 pts)

b. From your price taker model’s solution, display the storage asset’s charging, discharging, and state of charge decisions at each time step below using a bar plot. Provide a few sentences explaining the storage operations. What are your net revenues for the period? (20 pts)

c. The developer’s R&D team is considering projects that would increase the round-trip efficiency or maximum energy capacity of the storage asset by 10% each. Quantify the value of either outcome being realized. In other words, compare net revenues and storage operations (charging and discharging) from part (c) to net revenues and storage operations assuming a 10% increase in round-trip efficiency and to net revenues and storage operations assuming a 10% increase in maximum energy capacity. Use bar charts to compare storage operations over the day. Briefly explain the observed changes in storage operations under each of the 10% increase. What would you recommend the R&D team pursue? (20 pts)

BONUS. Transmission Modeling via Transport Method (35 points)

Gastopia has expanded into a second region, but the transmission network is weak between Gastopia’s two regions, resulting in a constrained transmission corridor. The region into which Gastopia expanded has excellent wind resources, so Gastopia is hoping to deploy wind power in that region to help it meets its decarbonization goals. Gastopia has hired you to analyze the effect of the constrained transmission corridor on its future wind development plans. PS5_ PS5_EconDispatchWithTransportMethod.py provides an economic dispatch with transmission between two regions modeled via transport method. Supporting CSV files provide data on the generator fleet, demand, and transmission capacity.

a. Run the provided economic dispatch model and confirm that supply and demand are balanced in each region. Show me proof of your confirmation – whether quantitative or visual – below with a brief explanation. (15 pts)

b. The file WindSites.csv contains a list of wind deployments Gastopia is considering, along with which zones they would be deployed in. WindSiteCFs.csv provides hourly capacity factors for those wind sites. Assuming all of these wind sites are built out, add them to your Gastopia system. Use a bar chart to visualize electricity flows between regions pre- and post-addition of these wind sites. Quantify curtailment of wind generation. What is the consequence of the inter-regional transmission constraint on Gastopia’s wind development plans? (10 pts)

c. Quantify the system value of doubling transmission capacity between Gastopia’s two regions. Quantify system value in three ways: (1) consumer costs, (2) producer costs, and (3) wind curtailment. Provide wind curtailment in absolute (MWh) and relative (%) terms. Comment on your results. (10 pts)

BONUS. Transmission Expansion Modeling with Transport Method (30 points)

(This is an optional bonus question. Points earned on this bonus will be added to the total score for this homework.)

Thanks to the analysis you conducted for Gastopia above, they have hired you again to help them understand whether they should invest in more transmission between their two regions.

a. Using TransmissionInvestmentOption.csv, create a transmission expansion model by modifying your model from question (2). Assume the wind sites from (2b) have been built. Your new model should include a binary investment decision in expanding inter-regional transmission capacity. Provide a screenshot of your modified code below. Remember to scale your operating costs to be comparable to the capital costs. (15 pts)

b. Solve your transmission expansion model. Does the expansion model invest in new transmission capacity or not? Quantify wind curtailment and total system costs with and without the new transmission investment. Provide a qualitative explanation for why Gastopia should invest in new transmission or not. (15 pts)