Port-Hamiltonian modeling of district heating networks

TL;DR

This paper introduces a port-Hamiltonian modeling framework for district heating networks, emphasizing thermodynamic consistency and providing both finite- and infinite-dimensional formulations for energy flow systems.

Contribution

It presents the first port-Hamiltonian models for district heating networks, including a discretized network model and an infinite-dimensional formulation for thermodynamic fluid flow.

Findings

Finite-dimensional port-Hamiltonian network model derived from energy advection.

Infinite-dimensional port-Hamiltonian formulation for thermodynamic pipe flow.

Open questions on discretization, reduction, and optimization of the models.

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.