Embedding Dependencies Within Distributionally Robust Optimization of Modern Power Systems

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.