Abstract

This
talk starts off with a brief introduction to hierarchical optimisation and
equilibrium problems, and continues with a broad overview of different
applications of these types of problems within the electricity system (such
as transmission and generation expansion planning, strategic bidding in
markets and many more). We then establish the status quo of the existing
models and analyse: what level of technical detail existing models cover;
what are corresponding CPU times, model size and complexity; what are the
current methods available to solve the arising problems, and, raise the
discussion of what gets lost in translation. With the former analysis in
mind, we outline the existing lack in the literature, or better yet the
existing need to represent complex technical realities in our models. Complex
realities such as: the AC optimal power flow, or unit commitment constraints.
We then try to establish the link between the technical nature, and the
corresponding arising mathematical difficulties in the hierarchical models,
discussing issues such as non-convexities and non-existence of solutions. The
talk concludes by pointing out some of the most recent methodological
advances in these directions, and what still remains to be done.