Context: Large scale problems exist for the electricity system both for short-term (e.g., the Unit Commitment problem) and long-term (system planning, e.g. ”Generation Expansion Planning”). In these problems concerning the modern and future electricity system, the question of the integration of energy consumption flexibility is crucial. This flexibility, consisting in “optimally” scheduling the power profile of particular electrical appliances (the most common and suitable ones for that purpose being Electric Vehicles (EV) and Water-Heaters (WH) for residential consumers), allows obtaining a supply-demand equilibrium with diminished total system cost, in comparison to the case where only production assets are controllable. Considering flexibilities related to “small” individual con- sumers (again, EV or WH), their very large number makes it inappropriate to model them individually in the typical electricity system optimization problems, for tractability reasons: it thus seems relevant to consider an aggregate model of consumption flexibilities. In turn, the question of the “right level” of aggregation modelling is of particular importance. Aggregation/disaggregation techniques are widely studied in the context of smart grids.
Objective: More precisely, the objective of this internship is to study, on a simple example, the impact of aggregation techniques and aggregation levels, and to solve an optimal energy scheduling problem considering such aggregated flexible load at a higher level. We will assume that flexible consumers are connected through a particular grid to be defined, and each of them have particular energy needs for a particular time horizon. Then an optimal scheduling considering nonflexible demand at each flexible consumer is determined following approaches based on water-filling concept. This result will be used as a benchmark. The second step is to consider an aggregation technique like the one based on ”electrical distance” on the grid (regional aggregate model). For example, flexible consumers which are close together into the grid can be seen as a mega-consumer. Then the same problem of determining opti- mal energy profile by considering mega-consumers with the overall demand and nonflexible loads will be tackled. Finally, the comparison between the lo- cal and aggregated solution will be deeply investigated in order to measure the impact of such aggregation technique on the performance of the flexibility proposed by many local EV/HV.
Profile of the Candidate and Supervision: We are looking for a highly motivated second year Master student, who would like to be involved in a 5 to 6 months internship. The internship can start as early as February but not later than June 2024. The intern will be hosted at Avignon Université, in France. Some collaborations are possible with EDF R&D Lab at Paris-Saclay and with Inria-Lille Nord Europe, both located in France. The candidate should have a very good background in mathematical optimization/game theory/operations research, interests for economics, and basic programming skills in Python. The internship student will be supervized by:
- Yezekael Hayel, LIA, Avignon Université
- Olivier Beaude & Paulin Jacquot, EDF R&D
Contact: Please send your application (short motivation letter+CV) by email to
URL: https://drive.google.com/file/d/1n8e5iiKaMmCulGLsDaJIQiPZrcQCv1k5/view?usp=sharing