Modelling and Simulation of District Heating Networks

TL;DR

This paper develops a detailed mathematical model for district heating networks using differential-algebraic equations, demonstrating its accuracy through numerical experiments and simplifying assumptions about water velocity.

Contribution

It introduces a high-dimensional DAE model for district heating networks with a simplified approach to water velocity effects.

Findings

Model accurately describes real district heating networks

DAEs have index one under certain assumptions

Numerical experiments validate the model's effectiveness

Abstract

In the present paper a detailed mathematical model is derived for district heating networks. After semidiscretization of the convective heat equation and introducing coupling conditions at the nodes of the network one gets a high-dimensional system of differential-algebraic equations (DAEs). Neglecting temporal changes of the water velocity in the pipes, the numerical solutions do not change significantly and the DAEs have index one. Numerical experiments illustrate that the model describes the real situation very well.