Data-driven conditional flexibility index

Computers & Chemical Engineering, vol. 211, pp. 109647

Abstract

With the increasing flexibilization of processes, determining robust scheduling decisions has become an important goal. Traditionally, the flexibility index has been used to identify safe operating schedules by approximating the admissible uncertainty region using simple admissible uncertainty sets, such as hypercubes. Presently, available contextual information, such as forecasts, has not been considered to define the admissible uncertainty set when determining the flexibility index. We propose the conditional flexibility index (CFI), which extends the traditional flexibility index in two ways: by learning the parametrized admissible uncertainty set from historical data and by using contextual information to make the admissible uncertainty set conditional. This is achieved using a normalizing flow that learns a bijective mapping from a Gaussian base distribution to the data distribution. The admissible latent uncertainty set is constructed as a hypersphere in the latent space and mapped to the data space. By incorporating contextual information, the CFI provides a more informative estimate of flexibility by defining admissible uncertainty sets in regions that are more likely to be relevant under given conditions. Using an illustrative example, we show that no general statement can be made about data-driven admissible uncertainty sets outperforming simple sets, or conditional sets outperforming unconditional ones. However, both data-driven and conditional admissible uncertainty sets ensure that only regions of the uncertain parameter space containing realizations are considered. We apply the CFI to a security-constrained unit commitment example and demonstrate that the CFI can improve scheduling quality by incorporating temporal information.

Authors 4

1. Moritz Wedemeyer Aachen

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Institute of Climate and Energy Systems, Energy Systems Engineering (ICE-1), Forschungszentrum Jülich GmbH, Jülich 52425, Germany

   RWTH Aachen University, Aachen 52062, Germany

2. Eike Cramer Aachen

   RWTH Aachen University · University College London

   Affiliation as printed

   Department of Chemical Engineering, Sargent Centre for Process Systems Engineering, University College London (UCL), London, WC1E 7JE, United Kingdom

   RWTH Aachen University, Process Systems Engineering (AVT.SVT), Aachen 52074, Germany

3. Alexander Mitsos Aachen

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   Institute of Climate and Energy Systems, Energy Systems Engineering (ICE-1), Forschungszentrum Jülich GmbH, Jülich 52425, Germany

   JARA-ENERGY, Jülich 52425, Germany

   RWTH Aachen University, Process Systems Engineering (AVT.SVT), Aachen 52074, Germany

4. Manuel Dahmen corresponding

   Forschungszentrum Jülich

   Affiliation as printed

   Institute of Climate and Energy Systems, Energy Systems Engineering (ICE-1), Forschungszentrum Jülich GmbH, Jülich 52425, Germany