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
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
Mixed Integer Models for the Optimisation of Gas Networks
Schaltbedingungen bei der Optimierung von Gasnetzen: Polyedrische
Untersuchungen und Schnittebenen
Der Simulated Annealing Algorithmus zur transienten Optimierung von
Mixed integer models for the stationary case of gas network
A. Martin, M. Möller and S. Moritz
A Simulated Annealing Algorithm for Transient Optimization in Gas
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
The second project phase is carried out together with University of
Erlangen-Nuremberg, Institute of Applied Mathematics, and with Research
Numerical Analysis and Scientific Computing.
We are thankful to our industry partners from E.ON Ruhrgas AG and
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
Last modified: Wed Nov 23 08:29:23 CET 2005