  The increasing share of renewables in the electrical energy generation mix
comes along with an increasing uncertainty in power supply. In the recent
years, distributionally robust optimization has gained significant interest due
to its ability to make informed decisions under uncertainty, which are robust
to misrepresentations of the distributional information (e.g., from
probabilistic forecasts). This is achieved by introducing an ambiguity set that
describes the uncertainty around an empirical distribution of all uncertain
parameters. However, this set typically overlooks the inherent dependencies of
uncertainty, e.g., space-time dependencies of renewable energy sources. This
paper goes beyond the state of the art by embedding such dependencies within
the definition of the ambiguity set. In particular, we propose a metric-based
ambiguity set with an additional constraint on dependence structure, using
copula theory. We develop a conic reformulation which is kept generic such that
it can be applied to any decision-making problem under uncertainty in power
systems. As an example, we illustrate the performance of our proposed
distributionally robust model applied to an energy and reserve dispatch problem
in a power system with a high share of renewables.
