Master Thesis: Optimizing games for the future energy communities

Keywords: convex optimization, game theory, multi-agent systems, power systems, energy communities

Background

The ongoing electrification of the electric grid, as well as the introduction of unpredictable energy sources - such as wind and solar - has led to increased risks concerning power volatility. A possible answer comes from harvesting consumer’s local power production means, energy storage and demand flexibility, by coordinating consumers into energy communities which provide flexibility services to the distribution system operator [1].

However, consumers often have conflicting goals, namely, meeting their own power demands while minimizing their operating costs. In this context, they are unlikely to cooperate in order to to provide the regulation services required by the distribution grid. Instead, each consumer will pursue a “selfish-rational” and possibly highly suboptimal strategy, namely, a Nash Equilibrium. The role of the community coordinator is then to make a community-wide decision on the internal trade rates and the imported energy amount in a way which is beneficial to the distribution grid (thus, socially-rational) while considering the economic (selfish-rational) objectives of the consumers.

Mathematically, this translates to a bilevel optimization problem on the set of Nash equilibria.

Project scope

The aim of the project is to develop and test novel solution methods for optimization problems on the set of Nash equilibria, and to implement them on the day-ahead scheduling of an energy community. On the mathematical side, the problem was already partially solved [2], and we want to extend the results by leveraging recent results in computational game theory. On the implementation side, we aim at surveying and comparing various objectives that define a socially rational action, based on the current literature on power systems.

In conclusion, the project would involve a combination of a theoretical study in optimization and game theory, and code development for validation in a simulated power systems setting.

If the final results are promising, they can potentially be turned into a publication.

Your profile

We are looking for a motivated Master’s student with a strong interest in advanced theoretical topics and with the ability to apply them to a relevant engineering application.

Requirements:

•   Enrolled in a Master's course related to either Automation and control, (Applied) mathematics, or Electrical engineering
• Interest in control theory, convex optimization, game theory, or power systems (no specific knowledge required)
• Basic coding experience
• Proficiency in English

Nice to have (not strictly required):

• Background in convex optimization, game theory, or power systems
• Coding experience in Python or Julia
• Experience with Git and/or GitHub

What we offer

This project will be conducted at the Division of Decision and Control Systems under the supervision of Daniel Tihanyi, Dr. Emilio Benenati, and Prof. Giuseppe Belgioioso. Supervision will take place on a weekly basis. The selected candidate will be offered office space at DCS and will have the opportunity to participate in Prof. Belgioioso’s group meetings.

How to apply

Please send the following documents via email to Emilio Benenati ([email protected]) and Dániel Tihanyi ([email protected]).

•  Résumé/CV (including any relevant personal project/academic project/publication) (PDF)
•  Transcript of records (PDF)
• Brief introduction of yourself (in the email)

[1] “How can energy communities provide grid services? A dynamic pricing mechanism with budget balance, individual rationality, and fair allocation”. Crowley, Kazempour, Mitridati - Applied Energy, 2025

[2] “Optimal Selection and Tracking Of Generalized Nash Equilibria in Monotone Games”. Benenati, Ananduta, Grammatico - IEEE Transactions on Automatic Control, 2023