Abstract
Aiming for an efficient simulation of gas networks with active elements a structure-preserving model order reduction (MOR) approach is presented. Gas networks can be modeled by partial differential algebraic equations. We identify connected pipe subnetworks that we discretize in space and explore with index and decoupling concepts for differential algebraic equations. For the arising input-output system we derive explicit decoupled representations of the strictly proper part and the polynomial part, only depending on the topology. The proper part is characterized by a port-Hamiltonian form that allows for the development of reduced models that preserve passivity, stability and locally mass. The approach is exemplarily used for an open-loop MOR on a network with a nonlinear active element.
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Notes
- 1.
\(\textit {blkdiag}(\mathbf {A}_1, \mathbf {A}_2) = \begin {pmatrix} \mathbf {A}_1 & \mathbf {0} \\ \mathbf {0} & \mathbf {A}_2 \end {pmatrix}\).
- 2.
An enhanced Pade-approximation condition for the block-structure preserving reduction methods with the energy-conjugated output and \(s_0 \in \mathbb {R}\) can be shown with the help of [1], which justifies the use of possibly enlarged block bases.
References
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Acknowledgements
The funding by DFG CRC/Transregio 154, project C02 is acknowledged.
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Liljegren-Sailer, B., Marheineke, N. (2017). A Structure-Preserving Model Order Reduction Approach for Space-Discrete Gas Networks with Active Elements. In: Quintela, P., et al. Progress in Industrial Mathematics at ECMI 2016. ECMI 2016. Mathematics in Industry(), vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-63082-3_69
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DOI: https://doi.org/10.1007/978-3-319-63082-3_69
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