Port-Hamiltonian Modeling of District Heating Networks

  title={Port-Hamiltonian Modeling of District Heating Networks},
  author={Sarah-Alexa Hauschild and Nicole Marheineke and Volker Mehrmann and Jan Mohring and Arbi Moses Badlyan and Markus Rein and Martin Schmidt},
  journal={Progress in Differential-Algebraic Equations II},
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… 
On Port-Hamiltonian Approximation of a Nonlinear Flow Problem on Networks
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Modeling and Passivity Properties of District Heating Systems
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Adaptive Nonlinear Optimization of District Heating Networks Based on Model and Discretization Catalogs
An adaptive optimization algorithm for operating district heating networks in a stationary regime that adaptively controls where in the network which model is used and the granularity of the applied discretization is controlled in a similar adaptive manner.
Mixed-integer nonlinear optimization for district heating network expansion
A novel polynomial approximation is developed that is used in the optimization model for computing the optimal expansion of an existing tree-shaped district heating network given a number of potential new consumers.
Structure-Preserving Model Order Reduction for Index Two Port-Hamiltonian Descriptor Systems
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Local and global canonical forms for differential-algebraic equations with symmetries
Local and global canonical forms under congruence are presented and used to classify the geometric properties of the flow associated with the differential equation as symplectic or generalized orthogonal flow, applied to the analysis of dissipative Hamiltonian systems arising from circuit simulation and incompressible flow.
On non-Hermitian positive (semi)definite linear algebraic systems arising from dissipative Hamiltonian DAEs
Different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization are discussed and iterative methods based on efinite three-term recurrences are illustrated.
Decentralized temperature and storage volume control in multi-producer district heating
—Modern district heating technologies have a great potential to make the energy sector more flexible and sustainable due to their capabilities to use energy sources of varied nature and to efficiently


Model order reduction of hyperbolic systems at the example of district heating networks
In this article a framework for the generation of a computationally fast surrogate model for district heating networks is presented. An appropriate model results in an index-1 hyperbolic,
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The suggested reduced model decreases the computation time of the optimization significantly and the effectiveness of the presented approach is demonstrated for an existing, large‐scale heating network including changes of flux directions.
Distributed port-Hamiltonian modelling for irreversible processes
ABSTRACT Infinite-dimensional port-Hamiltonian representation of irreversible processes accounting for the thermal energy domain is presented. Two examples are studied: the transmission line and a
A Partitioned Finite Element Method for the Structure-Preserving Discretization of Damped Infinite-Dimensional Port-Hamiltonian Systems with Boundary Control
The Partitioned Finite Element Method, introduced in Cardoso-Ribeiro et al. (2018), is a structure preserving numerical method which defines an underlying Dirac structure, and constitutive relations in weak form, leading to finite-dimensional port-Hamiltonian Differential Algebraic systems (pHDAE).
A structured control model for the thermo-magneto-hydrodynamics of plasmas in tokamaks
ABSTRACT A thermo-magneto-hydrodynamics port-Hamiltonian model is derived for the plasmas in tokamaks. Electromagnetic field and material domain balance equations are expressed in covariant forms,
Structure-Preserving Model Reduction for Nonlinear Port-Hamiltonian Systems
A structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems that ensures the retention of port- Hamiltonian structure which assures the stability and passivity of the reduced model.