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Mathematical Modeling and Problem Solving

Project 3: Is there a risk the UK will have an energy gap?

Assignment available from: 19 February 2024 Submission due: Either 1100 on Monday 4 March or 1100 on Wednesday 6 March 2024. A poster session will be held on Wednesday 6 March 2024 (1500 – 1630), to which you should bring a printed copy of your poster. You will receive your feedback for this assignment at this poster session and will have the opportunity to revise and resubmit it by 1700 on Friday 8 March 2024. You have approximately 10 working days to complete and submit this assessment in your groups and you may begin working on it immediately.
Sources of feedback:
Pre-submission	Post-submission
• Two workshop sessions (Weeks 6 & 7): discussion with module lecturer and PGTA. • Lecturer Office Hours: Tuesdays 1300- 1400. • Poster session in Week 8: pre- submission feedback from your PGTA and peers.	• Generic feedback (available Week 9). • Feedback review meeting with your PGTA in Week 10 workshop. • Lecturer Office Hour Drop-in: Tuesdays 1300- 1400.
Additional Resources	A range of useful resources, including grading criteria and samples of previous student work can be found in the ‘3. Project Guidance & Useful Resources Section’ of Canvas. You do not have to use LaTex for your poster, but if you wish to do so, LaTeX templates are available.
Generative AI	The use of generative AI is permitted within this assignment. Please ensure you read the guidance below and on Canvas.

Instructions

Working in your assigned groups you will spend the next two weeks (including the next two workshops) working on the problem below. For assessment each group must submit a poster on their solution. Your poster must be at least A3 size (but may be bigger), and concisely describe the problem and your solution. You don't need to give details of every step in your solution, but it needs to be clear how you have arrived at any final conclusions.

During Week 8 a poster presentation session will be organised outside of the 1MMPS group sessions. On this date you will display a printed version of your poster 1 and discuss your ideas and findings with other groups, staff members and students from the School of Mathematics, and other representatives from the University. All groups are expected to be represented and it is via this poster session that you will access your feedback for this assignment.

An electronic copy of your poster must also be uploaded to Canvas (as a PDF document) by either Either 1100 on 4 March (Monday Groups) or 1100 on 6 March 2024 (Wednesday Groups); late or non-submissions will be penalised with a 20 mark penalty. Following the poster session, where you will have the opportunity to receive feedback, you will have until 1700 on Friday 8 March 2024 to revise and resubmit your poster. It is this later submission that will be graded using the criteria available on the Project 3 page on Canvas.

Guidance on producing posters is available on Canvas. You may produce the posters in any format you wish, but a LaTeX template is available should you wish to use it.

Late submissions will be penalised as per University guidelines at a rate of 5% per 24-hour period. As well as your group submitting its report, you should also complete the individual reflective diary for this project which must be submitted on the same date as your project but before 2359. To complete and submit your individual diary, you should complete the ‘ Project 3: Reflective Project Diary’ within Canvas.

Before commencing your assignment you should read the guidance on the use of Generative Artificial Intelligence within 1MMPS. As part of your poster, you must also detail if, and how, generative AI has been used to develop your submission. For this assignment, this should be included within the 'Comments for this Attempt' box of the Canvas assignment submission page and with an appropriate statement on your poster itself. If you have not used generative AI tools within your work, you should clearly state so.

Problem Statement

Powering technological innovation requires energy, and in particular electricity. Increases in electric heating for homes, a move towards the electrification of vehicles, combined with an increase in population, means that our demand for electricity as a nation will only continue to rise.

In 2010, the House of Commons Library (Gore & Ares, 2010) noted in a briefing for the new Parliament that the “looming energy gap is on track to be filled but only if policy is implemented effectively and without delay”, but a January 2016 report from the Institution of Mechanical Engineers (IMechE, 216) was among the first to present evidence that the UK is facing an unprecedented ‘energy gap’ with demand for electricity likely to outstrip supply. Britain’s media outlets now carry many stories about an ‘energy gap’, often ahead of winter, and typically claimed to have arisen because the UK has failed to build enough power stations to meet demand. Talk of upcoming ‘blackouts’, with the UK unable to produce enough electricity to keep the lights on, is now commonplace, particular in light of changing energy prices (Guardian, 2023).

There is anever-increasing body of scientific evidence showing that human activity, especially the burning of fossil fuels such as coal and oil to generate electricity are altering the earth's climate through the production of CO2, the predominant gas that contributes to the so-called ‘greenhouse effect’. In addition, many of the UK’s current electricity generation plants are coming to the end of their working life and so additional investment in national infrastructure is now badly needed.

Based upon a mathematical modelling approach, you are tasked with advising the UK government on the future energy needs of the UK in 2040. The government wishes to know whether there is likely to bean ‘energy gap’ and if so, its extent. They are also keen to hear of suggestions for mitigating measures to address it.

Whilst you may use any data sources you wish to inform your models, there are several potentially helpful datasets available to help you online from the UK Department for Energy, Security and Net Zero and the Department for Business, Energy and Industrial Strategy:

1. Historical Electricity Data 1920 to 2022:https://www.gov.uk/government/statistical- data-sets/historical-electricity-data

2. Energy Consumption in the UK 2023:

https://www.gov.uk/government/statistics/energy-consumption-in-the-uk-2023

Some Suggestions

The following are merely suggestions of things you might wish to try or consider:

• This is again a very open and somewhat vague problem. It is suggested you spend time carefully considering the questions you will seek to answer (or the focus you will adopt) to address the brief. You may find you need to choose one or two specific aspects to explore.

• Whilst there are many aspects of this problem you may explore, you must not lose sight of the fact that this is a course in mathematical modelling. It is expected your underpinning mathematical models will be clearly evident in your final poster.

• You have been given two large datasets. However, not all information will be relevant to the problem and you may find you need (or would like) additional (reputable and reliable) data.

• Your developed model will need to extend further than a statistical analysis of the given data sets. You will need to combine information from different sources, make assumptions, and develop evidence-informed future predictions by exploring the impact of changes. These should again be evident within your poster.

• Whilst you may revise and resubmit your poster after the Poster Session after having received your feedback, you need to remember that by that time you will also be working on Project 4. You must ensure you build this into your planning.

Remember

This course is about thinking carefully and having ideas rather than producing a single identical ‘approved’ solution - this is a real problem and there is no ‘right answer’ .

This is a mathematics course, and so you will need to present reasoned mathematical arguments to justify your findings and conclusions. Each member of the group should spend between 6-8 hours per week outside of the workshop sessions working on this problem. The first workshop session is for you to get started on the problem and for the second you should come prepared with questions to ask the PGTAs. You won’t be able to ask them for help outside of the workshops so make sure you use your time wisely.

References

DESNZ (2023). Energy Consumption in the UK (ECUK) 1970 to 2022. September 2023. London,

UK: Department for Energy, Security & Net Zero. Available online

https://assets.publishing.service.gov.uk/media/651422e03d371800146d0c9e/Energy_Cons umption_in_the_UK_2023.pdf(accessed 16 February 2024).

Gore, D. & Ares, E. (2010). Balancing the UK energy supply. Key Issues for the New Parliament

2010. London, UK: House of Commons Research Library. Available online

https://www.parliament.uk/globalassets/documents/commons/lib/research/key_issues/ke y-issues-balancing-the-uk-energy-supply.pdf(accessed 16 February 2024).

Guardian (2023). National Grid says blackouts less likely this winter. (28 September 2023). Available online https://www.theguardian.com/business/2023/sep/28/national-grid- blackouts-this-winter-great-britain(accessed 16 February 2024).