Invited Session Thu.3.MA 550

Thursday, 15:15 - 16:45 h, Room: MA 550

Cluster 18: Optimization in energy systems [...]

Gas transport in networks


Chair: RĂ¼diger Schultz



Thursday, 15:15 - 15:40 h, Room: MA 550, Talk 1

Martin Schmidt
An extended interior point method for nonsmooth nonlinear optimization in gas networks

Coauthor: Marc C. Steinbach


Detailed physical and technical modeling of cost minimization in gas transport networks leads to nonsmooth nonlinear mixed-integer optimization models (NSMINLPs). After fixing prescribed discrete decisions given by an enclosing MIP framework we concentrate on the remaining nonsmooth nonlinear optimization problem (NSNLP). These problems cannot be seriously tackled by standard interior point methods due to the violation of C2-assumptions.
We present a modified interior point method using a special kind of
generalized gradients for the search direction computation and an extended
step length computation ensuring that the line-search subprocedure is only
applied to smooth regions of the nonsmooth problem functions.
The applicability of the proposed method is demonstrated by numerical
experiments on large-scale real world instances.



Thursday, 15:45 - 16:10 h, Room: MA 550, Talk 2

Imke Joormann
Analyzing infeasibility in natural gas networks


Infeasibilities in the mathematical description of natural gas networks in
real-world applications can arise for different reasons, including defective data, modeling issues and plain physical impracticability. In the considered case, we start with a mixed integer linear program (MILP) modeling the validation of nominations on the network, i.e., the task of deciding whether it is possible to transport a given flow amount with specific supply and demand nodes.
Our main purpose is to analyze this MILP and find physical reasons for the infeasibility of a given instance. To achieve this, we implemented and tested various approaches based on slack models. In addition, we investigated the explanatory power of irreducible infeasible subsystems; since it is possible to calculate them at least in a heuristic way, the remaining task is to transfer the gained information from the MILP back to the network. Complementing the modeling aspects we present computational results and derive cautious suggestions as to which model should be used, depending on the practical application.



Thursday, 16:15 - 16:40 h, Room: MA 550, Talk 3

Ralf Gollmer
Stationary gas transport - Structure of the problem and a solution approach

Coauthors: RĂ¼diger Schultz, Claudia Stangl


Detecting feasibility of transportation orders (nominations) in gas
networks is a problem of growing practical interest due to the regulatory
requirements in the course of unbundling gas trading and transport.
In the stationary flow case, already, this nonlinear non-convex
mixed-integer problem poses challenging mathematical questions. In
particular, we discuss some structural properties of the problem in
slightly simplified form. We sketch a heuristic solution approach choosing
switching decisions (the integer variables) from the solution of an
aggregated linear transshipment problem and referring to the so called
loop formulation when solving the resulting NLP. This approach is quite
successful when applied to real-world instances met in a meshed gas
network of a German utility.


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