Port-Hamiltonian modeling of district heating networks
Abstract
This paper provides a first contribution to port-Hamiltonian modeling of district heating networks. By introducing a model hierarchy of flow equations on the network, this work aims at a thermodynamically consistent port-Hamiltonian embedding of the partial differential-algebraic systems. We show that a spatially discretized network model describing the advection of the internal energy density with respect to an underlying incompressible stationary Euler-type hydrodynamics can be considered as a parameter-dependent finite-dimensional port-Hamiltonian system. Moreover, we present an infinite-dimensional port-Hamiltonian formulation for a compressible instationary thermodynamic fluid flow in a pipe. Based on these first promising results, we raise open questions and point out research perspectives concerning structure-preserving discretization, model reduction, and optimization.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2019
- DOI:
- 10.48550/arXiv.1908.11226
- arXiv:
- arXiv:1908.11226
- Bibcode:
- 2019arXiv190811226H
- Keywords:
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- Mathematics - Optimization and Control;
- 93A30;
- 35Q31;
- 37D35;
- 76-XX