My industrial secondment took place over two months (July and August) in Paris at the optimization firm Artelys. I really enjoyed spending the summer in Paris, which contrasted Konstanz, the small city where I was living just beforehand. I worked with fellow TENORS students Yassine Koubaa and Luca Wellmeier.
At Artelys, I worked on AC power flow problems, specifically focused on finding infeasibility certificates for given electrical networks. Our project involved proving that a grid with certain parameters does not admit any physically valid operating configuration. To accomplish this, we employed polynomial optimization techniques and the moment-SOS (Sum of Squares) hierarchy.
This approach differs significantly from current industrial practices, which rely on the use of local solvers. These solvers provide upper bounds on the objective function value. In contrast, polynomial optimization methods deliver global minima and thus lower bounds on the objective function value. A certified lower bound can prove the infeasibility of a network.
The project was challenging, particularly because we worked with preexisting software (PowSyBl) that uses a model not based on polynomials. This provides a meaningful proof-of-concept for applying polynomial optimization techniques in practical grid settings.
Through this experience, I learn a great deal about power systems, and mathematical modelling. I also came to appreciate how hard it is to accurately model the diversity of equipment found in operational electrical grids. While we had access to industrial data, the networks we studied did not encompass all possible equipment categories.
The office culture is different from the academic vibe I was accustomed to, though not as much as I anticipated. I still found people who were curious and eager to discuss ideas. The main different is that the meetings were rapid fire half-hour sessions rather than the relaxed two-hour discussion over a coffee.
Even though my secondment is over, the project will continue with other TENORS students building off of the work done. Our hope is to publish our results before the end of the year.
Artelys office building in Paris