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
Author:Martin Gugat, Günter Leugering, Alexander Martin, Martin Schmidt, Mathias Sirvent, David Wintergerst
DOI:https://doi.org/10.1007/s10589-017-9970-1
Parent Title (English):Computational Optimization and Applications
Document Type:Article
Language:English
Date of Publication (online):2017/04/11
Date of first Publication:2017/04/11
Release Date:2017/04/11
Tag:Gas networks; Instantaneous control; Mixed-integer linear optimization; Mixed-integer optimal control; Partial differential equations on graphs
Volume:70
Issue:1
Page Number:28
First Page:267
Last Page:294
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:A05
B07
C03
B08