代写IOE 491.023 PROBLEM SET 3调试Python程序

PROBLEM SET 3

IOE 491.023

Due: October 10, 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.

Economic Dispatch with Storage (75 points)

You are the grid system operator for the region Gastopia. Gastopia’s generator fleet is provided below and in a CSV file. Hourly electricity demand and solar capacity factors for a representative day are provided in Demand.csv and SolarCFs.csv, respectively. I have started you off with an economic dispatch file, PS3_EconDispatch.py. Below, I will ask you to compare your results to the economic dispatch of this initial generator fleet, so I would suggest you dispatch the initial fleet and save your results.

Table 1: Generator fleet for Gastopia. CC and CT stand for combined cycle and combustion turbine, respectively. Please pay careful attention to units!

Generator	Fuel Type	Heat Rate (MMBtu/MWh)	Variable O&M ($/MWh)	Maximum Capacity (MW)	Fuel Price ($/MMBtu)	CO2 Emissions Rate (tons/MWh)
CC1	Natural gas	7	5	150	4	0.35
CC2	Natural gas	10	5	200	4	0.4
CT1	Natural gas	15	10	50	4	0.75
Coal1	Coal	12	10	500	3	1.2
Nuc1	Nuclear	10	5	200	1	0
Solar1	Solar	0	0	500	0	0

1. Gastopia is considering investing in a 100 MW/400 MWh lithium ion storage facility with a round trip efficiency of 90%. Please provide the new economic dispatch mathematical formulation that includes storage operations, using an equality for the supply and demand constraint. You may insert the formulation via equations in Word, via a picture of handwritten notes, or any other method you find easiest as long as it is legible. (10 pts)

2. Please add the above specified storage facility into the economic dispatch file. Include a screenshot of your model below. StorageUnit.csv contains the necessary storage parameterization. (10 pts)

3. Characterize the storage facility’s operations by displaying charging, discharging, and state of charge decisions as separate lines on a single plot. Include that plot below. Please briefly describe the operational profile of the storage facility. Does this profile align with your expectations? Why or why not? (15 pts)

4. Compare total system emissions (or emissions from all electricity generation) with and without storage. How did storage change system emissions? Why did this occur? (10 pts)

5. Although we learned how to add ramping constraints within a unit commitment and economic dispatch model, we can add ramping constraints to just an economic dispatch as follows:

where p = electricity generation (MWh) and RR = ramp rate per time step (MWh). (Remember to translate the absolute value to separate linear equations when including in your model.) Please add these constraints to your model that includes storage using parameters given in RampRate.csv. (If your generator fleet is imported into a pandas dataframe, you can add the ramp rate to the dataframe. with pd.concat, e.g. pd.concat([generatorDF,rampParametersDF], axis=1). Note the axis=1!)
How did they change your dispatch decisions relative to your results from question 3? Please explain why these changes occurred. (10 pts)

6. Now add 500 MW of wind power to your system. Use the provided WindCFs.csv for the wind capacity factors. Quantify how the storage unit specified in question 2 helps integrate wind and/or solar capacity by running your economic dispatch (with ramping constraints) with and without storage, then comparing curtailment of wind and/or solar. Please also quantify how storage affects total system emissions and consumer costs with the added wind plant. Give a brief explanation of your results. (20 pts)