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Transient Gas Network Optimization

The problem of gas network optimization is as follows. The gas flows through the pipes and due to friction with the pipe walls gas pressure gets lost. This pressure loss has to be compensated. Therefore there are machines, the so called compressors. The gas flows through the compressor and the pressure of the gas is increased. Therefore the compressor needs some fraction of the gas flowing through it as fuel gas. Further on there are consumers that need a certain amount of gas at a specified quality and pressure, and sources where some gas is delivered with a certain pressure and volume. The goal of so called Transient Technical Optimization (TTO) is to operate the gas transmission in such a way that the consumer demands are satisfied and the compressors are set in cost-efficiently. This TTO problem leads to a complex mixed integer nonlinear optimization problem.

In a first step we treat the stationary case of gas network optimization where just one time step is considered. We develop techniques for a piece-wise linear approximation of the nonlinearities, where we generalize the so called SOS Type 2 constraints. This results in a large mixed integer linear program. We study sub-polyhedra linking these piece-wise linear approximations and show that the number of vertices is computationally tractable yielding exact separation algorithms. Suitable branching strategies complement the separation algorithms and guarantee the SOS conditions. Our computational results demonstrate the success of this approach.

In a next step we consider the time-dependent case which is also called transient case. At first we need an appropriate modelling of the gas dynamics in pipes. Again we approximate nonlinearities by piece-wise linear functions via SOS constraints. But further ideas are necessary to accelerate the algorithm. In the transient case we also get further conditions. For example we have min-up and min-down times and switching costs for compressors. Finally we need a feasible solution for an upper bound in our branch-and-cut algorithm. Therefore we develop a simulated annealing algorithm.

Mixed Integer Models for the Optimisation of Gas Networks
M. Möller
Schaltbedingungen bei der Optimierung von Gasnetzen: Polyedrische Untersuchungen und Schnittebenen
P. Marcinkowski
Der Simulated Annealing Algorithmus zur transienten Optimierung von Gasnetzen
D. Mahlke
Mixed integer models for the stationary case of gas network optimization
A. Martin, M. Möller and S. Moritz
A Simulated Annealing Algorithm for Transient Optimization in Gas Networks
D. Mahlke, A. Martin and S. Moritz

The first project phase was carried out together with University of Duisburg, Mathematical Programming and Algorithmic Discrete Mathematics, and with Zuse-Istitute Berlin.

The second project phase is carried out together with University of Erlangen-Nuremberg, Institute of Applied Mathematics, and with Research Group Numerical Analysis and Scientific Computing.

We are thankful to our industry partners from E.ON Ruhrgas AG and PSI AG.

We also kindly acknowledge the support of BMBF (German ministry of education and sciences) from 2001-2003 and of German Research Association DFG from 2006-2008.


For further details about this project please contact Björn Geißler

Last modified: Wed Nov 23 08:29:23 CET 2005