Journal
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
Volume 70, Issue 1, Pages 267-294Publisher
SPRINGER
DOI: 10.1007/s10589-017-9970-1
Keywords
Mixed-integer optimal control; Instantaneous control; Partial differential equations on graphs; Gas networks; Mixed-integer linear optimization
Funding
- DFG [SFB/Transregio 154]
- Bavarian State Government
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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.
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