# Robustification of Physical Parameters in Gas Networks

## Robustification of Physical Parameters in Gas Networks

### Description

The goal of research project B06 within the CRC 154 is the development of tractable robust counterparts for global optimization problems, with a focus on gas networks. The motivation stems from the fact that for many real-life problems some parameters can only be estimated roughly. A well-known example in gas network optimization is the roughness value of the pipe that influences the friction of the gas and thereby effects the pressure loss between the endpoints of the pipe. However, the roughness depends on the contamination of the pipe and can only be measured with great effort. Another example is the real gas factor which depends on the gas mixture. Since gases with different chemical composition are mixed within the network, usually the exact gas mixture is unknown, and the real gas factor has to be estimated. Moreover, different formulas are used that describe the function for determining the friction from the pipe roughness. Finally, there are methodological uncertainties from the approximation of nonlinear functions in the context of mixed-integer linear optimization problems (MIPs). Similar situations are found in a wide range of applications. Therefore, results of this research project may be used for other optimizations problems under uncertainty, e.g. for water-network optimzation. In our robust optimization setting, continuous state variables are categorized as adjustable (“wait-and-see”), whereas binary decision variables are modeled as static or “here-and-now” variables. The robustification of the mentioned problem leads to mixed-integer linear, conic quadratic or positive semidefinite optimization problems, depending on the given uncertainty set and the occurance of the uncertain data. These different modeling options are adapted for gas-network optimization. A major goal will be the development of exact methods that use positive semidefinite subproblems. Initially, only the stationary case is considered. However, an extension to straight-forward transient models is a mid-term goal.

### People involved

Denis Aßmann

Frauke Liers

Michael Stingl

### Contact

For further details about this project please contact Denis Aßmann (denis.assmann [at] fau.de)

### Supported by

Deutsche Forschungsgemeinschaft, CRC/Transregio 154