Search

This paper serves as an electronic companion to the paper "Affine and Exact Reformulations of Uncertainty-Aware Energy and Reserve Dispatch".Section 1 presents the nomenclature,Section2 introduces mathematical definitions of the different uncertainty-aware optimization models, and Section 3 presents further details of the case study.&nbsp

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 by embedding such dependencies within the definition of the 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 model 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. Both applications consider a high share of renewables.

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 by embedding such dependencies within the definition of the ambiguity set. In particular, we propose a copula-based ambiguity set which is tailored to capture any type of dependencies. 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 optimal power flow problem in a power system with a high share of renewables.&nbsp

The increasing share of natural gas-fired power plants in the electricity generation mix has tightened the existing link between power and gas systems. This may bring technical and economical risks, e.g., congestions and peak prices, which mainly stem from the non-coordinated operation of both systems and the failure to properly anticipate the multivariate and correlated demand uncertainty. In this paper, we propose a Wasserstein metric-based distributionally robust optimization framework for the joint power and gas dispatch to mitigate these risks. The distributionally robust decision-making approach strives to ensure risk-hedging dispatch solutions, by considering a set of potential distributions, the so-called ambiguity set. We go beyond the state of the art by considering a realistic dependence structure among the power and gas demands uncertainty. We show the benefits of the proposed approach via a numerical study based on the Belgian networks.