Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On properties of hydraulic equilibria in district heating networks

Ask Hällström, Felix Agner, Richard Pates

TL;DR

This work develops a static hydraulic model for tree-structured district heating networks with valve-controlled leafs and a single root pump. It proves a monotone input-output property: under strictly increasing pipe-friction and valve-curve functions, increasing $p_0$ or valve positions $u_l$ raises the total leaf throughput $\\sum_{l} q_l$, with strict inequalities under certain conditions, and shows that opening some valves while keeping others fixed can reduce the flow through unopened valves. The results are validated numerically on a 2-consumer network and a larger 22-consumer network, illustrating both overall throughput gains and group-level effects. These insights support scalable, valve-based control strategies for optimal heat distribution in future smart energy systems.

Abstract

District heating networks are an integral part of the energy system in many countries. In future smart energy systems, they are expected to enhance energy flexibility and support the integration of renewable and waste energy sources. An important aspect of these networks is the control of flow rates, which dictates the heat delivered to consumers. This paper concerns the properties of flow rates in tree-structured district heating networks. We show that under mild assumptions of monotonicity in the hydraulic network components, statements regarding the stationary flow rate distribution can be made. In particular, when all consumers in a network incrementally open their valves, an increase in total flow rate throughput is guaranteed, while if one consumer does not open their valve when others do, they will receive a reduced flow rate. These properties are illustrated numerically on a small 2-consumer network as well as on a larger 22-consumer network. Previous works have shown that these properties allow the design and use of efficient control strategies for optimal heat distribution.

On properties of hydraulic equilibria in district heating networks

TL;DR

This work develops a static hydraulic model for tree-structured district heating networks with valve-controlled leafs and a single root pump. It proves a monotone input-output property: under strictly increasing pipe-friction and valve-curve functions, increasing or valve positions raises the total leaf throughput , with strict inequalities under certain conditions, and shows that opening some valves while keeping others fixed can reduce the flow through unopened valves. The results are validated numerically on a 2-consumer network and a larger 22-consumer network, illustrating both overall throughput gains and group-level effects. These insights support scalable, valve-based control strategies for optimal heat distribution in future smart energy systems.

Abstract

District heating networks are an integral part of the energy system in many countries. In future smart energy systems, they are expected to enhance energy flexibility and support the integration of renewable and waste energy sources. An important aspect of these networks is the control of flow rates, which dictates the heat delivered to consumers. This paper concerns the properties of flow rates in tree-structured district heating networks. We show that under mild assumptions of monotonicity in the hydraulic network components, statements regarding the stationary flow rate distribution can be made. In particular, when all consumers in a network incrementally open their valves, an increase in total flow rate throughput is guaranteed, while if one consumer does not open their valve when others do, they will receive a reduced flow rate. These properties are illustrated numerically on a small 2-consumer network as well as on a larger 22-consumer network. Previous works have shown that these properties allow the design and use of efficient control strategies for optimal heat distribution.

Paper Structure

This paper contains 12 sections, 1 theorem, 17 equations, 5 figures.

Table of Contents

  1. INTRODUCTION
  2. MATHEMATICAL MODELING OF DISTRICT HEATING NETWORKS
  3. Graph representation
  4. Hydraulic components
  5. Network properties
  6. Illustrative example
  7. MAIN RESULTS
  8. NUMERICAL EXPERIMENTS
  9. Two-consumer Network
  10. Large Network
  11. CONCLUSION
  12. Future Work

Key Result

Theorem 1

Consider the set of equations eq:theorem conditions defined by a given directed, rooted tree graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ where the functions $f_{ij}$ are strictly increasing and the functions $g_l$ are strictly increasing in the first argument and strictly decreasing in the second. with a strict inequality if $\overline{p}_0>\underline{p}_0$ or there exists an $l\in\mathcal{V}_L$

Figures (5)

  • Figure 1: Small two-consumer network with one pump and two valves.
  • Figure 2: Total flow rates ($q_1 + q_2$) in a 2-consumer network for varying valve positions $u_1$ and $u_2$.
  • Figure 3: The flow $q_2$, through the second consumer for varying valve positions $u_1$ and $u_2$.
  • Figure 4: Schematic of a district heating network with 22 consumers.
  • Figure 5: Flow rates through different parts of the system under various valve configurations. The red curve shows the total consumer flow when all valves in the network are opened simultaneously. The blue curves show the flow into each housing group (Flow 1, Flow 2, and Flow 3) when only the valves in the other two groups are opened. For example, Flow 1 represents the flow into Group 1 when only Groups 2 and 3 have open valves.

Theorems & Definitions (3)

  • Theorem 1
  • Remark 1
  • proof