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MIP-Based Instantaneous Control of Mixed-Integer PDE-Constrained Gas Transport Problems

  • We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network.
Metadaten
Verfasserangaben:Martin Gugat, Günter Leugering, Alexander Martin, Martin Schmidt, Mathias Sirvent, David Wintergerst
DOI:https://doi.org/10.1007/s10589-017-9970-1
Titel des übergeordneten Werkes (Englisch):Computational Optimization and Applications
Dokumentart:Wissenschaftlicher Artikel
Sprache:Englisch
Datum der Veröffentlichung (online):11.04.2017
Datum der Erstveröffentlichung:11.04.2017
Datum der Freischaltung:11.04.2017
Freies Schlagwort / Tag:Gas networks; Instantaneous control; Mixed-integer linear optimization; Mixed-integer optimal control; Partial differential equations on graphs
Band:70
Ausgabe / Heft:1
Seitenzahl:28
Erste Seite:267
Letzte Seite:294
Institute:Friedrich-Alexander-Universität Erlangen-Nürnberg
Teilprojekte:A05
B07
C03
B08