  The increasing share of renewables in the electricity 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
potential deviations from an empirical distribution of all uncertain
parameters. However, this set typically overlooks the inherent dependencies of
uncertainty, e.g., spatial dependencies of weather-dependent energy sources.
This paper goes beyond the state-of-the-art models by embedding such
dependencies within the definition of ambiguity set. In particular, we propose
a new copula-based ambiguity set which is tailored to capture any type of
dependencies. The resulting problem is reformulated as a conic program which is
kept generic such that it can be applied to any decision-making problem under
uncertainty in power systems. Given the Optimal Power Flow (OPF) problem as one
of the main potential applications, we illustrate the performance of our
proposed distributionally robust model applied to i) a DC-OPF problem for a
meshed transmission system and ii) an AC-OPF problem using LinDistFlow
approximation for a radial distribution system.
