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Online Companion - Embedding Dependencies Within Distributionally Robust Optimization of Modern Power Systems

Authors: Arrigo, Adriano; Kazempour, Jalal; De Grève, Zacharie; Toubeau, Jean-François; Vallée, François;

Online Companion - Embedding Dependencies Within Distributionally Robust Optimization of Modern Power Systems

Abstract

The increasing share of renewables in the electricalenergy generation mix comes along with an increasing uncer-tainty in power supply. In the recent years, distributionallyrobust optimization has gained significant interest due to itsability to make informed decisions under uncertainty, which arerobust to misrepresentations of the distributional information(e.g., from probabilistic forecasts). This is achieved by introducingan ambiguity set that describes the uncertainty around anempirical distribution of all uncertain parameters. However, thisset typically overlooks the inherent dependencies of uncertainty,e.g., space-time dependencies of renewable energy sources. Thispaper goes beyond the state of the art by embedding suchdependencies within the definition of the ambiguity set. Inparticular, we propose a metric-based ambiguity set with anadditional constraint on dependence structure, using copulatheory. We develop a conic reformulation which is kept genericsuch that it can be applied to any decision-making problemunder uncertainty in power systems. As an example, we illustratethe performance of our proposed distributionally robust modelapplied to an energy and reserve dispatch problem in a powersystem with a high share of renewables.

Keywords

Distributionally robust optimization, copula, space-time dependencies, energy and reserve dispatch

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