PS3_MAE206_GPPA463_2024

Problem Set #3 MAE 206/GPPA 463 W24 Professors Tynan & Victor February 20, 2024 Due: 29 ?ℎ February, 2024 at 11:59 PM PST Submission Instructions: • Turn in your assignment as a PDF through Canvas. Use your PID instead of your name in your homework file as the filename (e.g., A12345678.pdf ) • Avoid written handwriting as much as possible and keep solutions concise • Highlight or box your final answers and reference any external values used in your calculations, as well as reference sources • Discussion with peers is encouraged, however, the final solution should be your own • In case of any questions/clarifications please email Shiny and Zhenhua at schoudhury@ucsd.edu and zhz121@ucsd.edu 1

1 All Class: Electricity Markets (30 pts) Recall from the Electricity Markets lecture that in deregulated electricity markets, the market operator has to clear the market by matching electricity supply and demand in real-time and determining the equilibrium prices at each of the pricing nodes/zones. The equilibrium price is when the supply is equal to the electricity demand, and then used to calculate the payment that goes to each generator. The table below shows the available power generation capacity and marginal costs of generation in a given hour ( ? ) in a hypothetical market. In this problem, assume that the generators bid all their available capacity with marginal costs into the electricity markets. Also, assume that we have a single pricing zone where the price is universal across locations and ignore the transmission network. Generator Available Capacity (MW) Marginal Cost of Generation ($/MWh) Coal 2,400 50 Natural Gas 1,500 35 Solar 700 0 Wind 600 0 Nuclear 400 5 1. Calculate the equilibrium prices under each of the following demand scenarios. (a) The electricity demand always stays at a level of 800 MW. (b) The electricity demand always stays at a level of 4,000 MW. (c) The electricity demand is highly inelastic and can be characterized by a function ? ( ? ) = − 10 ? + 4500, where ? ( ? ) is the demand and ? is the electricity price. (d) The electricity demand is highly elastic and can be characterized by a function ? ( ? ) = − 60 ? + 4500, where ? ( ? ) is the demand and ? is the electricity price. 2. Calculate the total revenues and profits that can be obtained by each generator type in hour ? , assuming that the electricity demand is highly inelastic and always stays at a level of 4,000 MW. 3. Suppose the available wind and solar capacities increase by 80% in the next hour ( ? + 1). What would be the resulting equilibrium prices and generator profits in hour ? + 1? Assume that the electricity demand is the same as Part (1c). 2 All Class: Pro Forma (50 pts) Imagine you are the project developer of a 400 MW wind power plant and are using a pro forma template to model your key financial considerations. Alter the template (provided as an MS Excel file) to create a simple pro forma for your 400 MW wind project. Use the “20-year annual w/ taxes” tab to help answer the following questions. 1. Basic understanding: Before diving into the detailed calculations, let’s build a basic understanding of the pro forma template. For each of the questions below, limit your answers to 1-2 sentences for clarity and brevity. (a) How would you characterize the costs relevant to the wind project? 2