MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems

Journal article
(Original article)


Publication Details

Author(s): Gugat M, Leugering G, Martin A, Schmidt M, Sirvent M, Wintergerst D
Journal: Computational Optimization and Applications
Publication year: 2018
Volume: 70
Journal issue: 1
Pages range: 267-294
ISSN: 0926-6003
Language: English


Abstract


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.



FAU Authors / FAU Editors

Gugat, Martin apl. Prof. Dr.
Lehrstuhl für Angewandte Mathematik
Martin, Alexander Prof. Dr.
Economics - Discrete Optimization - Mathematics (EDOM)
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen
Sirvent, Mathias
Economics - Discrete Optimization - Mathematics (EDOM)
Wintergerst, David
Lehrstuhl für Angewandte Mathematik


How to cite

APA:
Gugat, M., Leugering, G., Martin, A., Schmidt, M., Sirvent, M., & Wintergerst, D. (2018). MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems. Computational Optimization and Applications, 70(1), 267-294. https://dx.doi.org/10.1007/s10589-017-9970-1

MLA:
Gugat, Martin, et al. "MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems." Computational Optimization and Applications 70.1 (2018): 267-294.

BibTeX: 

Last updated on 2018-08-08 at 02:12