Motivation
The spread of distributed energy resources turns passive consumers into prosumers that both draw from and inject into the distribution grid, and recent legislation lets them organise into *Local Energy Markets* (LEMs): coalitions that trade energy internally and coordinate towards collective self-consumption. How a grid is partitioned into such coalitions is not a neutral choice.
It sets how much power crosses coalition boundaries: small coalitions shorten power flows and lower the risk of voltage violations, while larger ones pool complementary generation and demand for more efficient dispatch.
Prior work formulated the search for an optimal stable partition and reformulated it as a Mixed-Integer Quadratic Program (MIQP) solvable to global optimality.
It established a working exact solver, while also exposing two structural limitations that this project is designed to address.
Goal and Directions
The goal of this project is to develop a cost model in which coalition structure carries economic benefit, and to characterise systematically how the optimal partition responds to the model’s parameters.
The project sits on the optimisation and modelling side and builds directly on the existing MIQP solver.
The following directions will be explored.
A peak-shaving cost reformulation. Introduce a coalition level peak (demand-charge) term on the exchange of each LEM with the grid.
This would change the time coupling in the MIQP and significantly influence the shape of the optimal partition for a given grid.
Joint analysis of investment and operation. The existing framework analyzes grid partitioning to minimize operating costs under pre-installed distributed energy resources. The goal of the project would be to extend the current formulation to additionally include investments for installing new energy resources. This will allow us to build on existing literature on joint investment and operation [5,6], by incorporating grid partitioning under power flow constraints and load and generation uncertainty.
The candidate will extend the existing exact solver, work with a realistic distribution grid model, and produce a characterisation of when and why partitioning into Local Energy Markets pays off.
Requirements
We are seeking candidates with a strong background in mathematics, optimisation (mixed-integer and convex programming), and power systems. Familiarity with bilevel or parametric optimisation, and with graph theory, is a plus. Good programming skills in Python are required; experience with a mathematical-programming solver (e.g. Gurobi) is desirable.
Contact
Interested candidates may send their transcripts and resume to [[email protected]](mailto:[email protected]) and [[email protected]](mailto:[email protected]).
References
1. S. D. Vaishampayan and M. Kamgarpour, “Optimal stable partitioning of distribution networks into local energy markets,” *IEEE Transactions on Smart Grid*, 2025.
2. M. E. Baran and F. F. Wu, “Network reconfiguration in distribution systems for loss reduction and load balancing,” *IEEE Trans. Power Delivery*, vol. 4, no. 2, pp. 1401–1407, 1989.
3. S. H. Low, “Convex relaxation of optimal power flow – Part I: Formulations and equivalence,” *IEEE Trans. Control of Network Systems*, vol. 1, no. 1, pp. 15–27, 2014.
4. B. Herold, P. Bauer, J. Buchmeier, S. Wilker and T. Sauter, “The Building as Energy Storage: Sector Coupling for Peak Shaving in Active Energy Communities,” *2025 IEEE Kiel PowerTech*, Kiel, Germany, 2025, pp. 1-7.
5. H. Wang and J. Huang, “Joint Investment and Operation of Microgrid” *IEEE Transactions on Smart Grid*, vol. 8, no. 2, pp. 883-845, 2017.
6. T. Weckesser, D. F. Dominković, E. M. V. Blomgren, A. Schledorn, and H. Madsen, “Renewable Energy Communities: Optimal sizing and distribution grid impact of photo-voltaics and battery storage”, *Applied Energy*, vol. 301, 2021.