On the existence and uniqueness of steady state solutions of a class of dynamic hydraulic networks via actuator placement
Jeeninga, Mark LU
; Machado, Juan Eduardo
; Cucuzzella, Michele
; Como, Giacomo
LU
and Scherpen, Jacquelien
(2023)
2023 62nd IEEE Conference on Decision and Control (CDC)
p.3652-3657
- Abstract
- In this paper, using tools from graph theory we provide verifiable necessary and sufficient conditions for the existence of a unique hydraulic equilibrium in district heating systems of meshed topology and containing multiple heat sources. Even though numerous publications have addressed the design of efficient algorithms for numerically finding hydraulic equilibria in the general context of water distribution networks, this is not the case for the analysis of existence and uniqueness. Moreover, most of the existing work dealing with these aspects exploit the equivalence between the nonlinear algebraic equations describing the hydraulic equilibria and the KKT conditions of a suitably defined nonlinear convex optimization problem.... (More)
- In this paper, using tools from graph theory we provide verifiable necessary and sufficient conditions for the existence of a unique hydraulic equilibrium in district heating systems of meshed topology and containing multiple heat sources. Even though numerous publications have addressed the design of efficient algorithms for numerically finding hydraulic equilibria in the general context of water distribution networks, this is not the case for the analysis of existence and uniqueness. Moreover, most of the existing work dealing with these aspects exploit the equivalence between the nonlinear algebraic equations describing the hydraulic equilibria and the KKT conditions of a suitably defined nonlinear convex optimization problem. Differently, this paper proposes necessary and sufficient graph-theoretic conditions on the actuator placement for the existence and uniqueness of a hydraulic equilibrium, independent of the actuators’ control objective. An example based on a representative district heating network is considered to illustrate the key aspects of our contribution, and an explicit formulation of the steady state solution is given for the case in which pressure drops through pipes are linear with respect to the flow rate. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/33fc2cb7-7f9f-4cfc-9d91-8cce9a787bab
- author
- Jeeninga, Mark
LU
; Machado, Juan Eduardo
; Cucuzzella, Michele
; Como, Giacomo
LU
and Scherpen, Jacquelien
- organization
- publishing date
- 2023-12-13
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of the 2023 62nd IEEE Conference on Decision and Control
- pages
- 3652 - 3657
- conference name
- 2023 62nd IEEE Conference on Decision and Control (CDC)
- conference location
- Marina Bay Sands, Singapore
- conference dates
- 2023-12-13 - 2023-12-15
- external identifiers
-
- scopus:85184816162
- ISBN
- 979-8-3503-0123-6
- DOI
- 10.1109/CDC49753.2023.10384050
- language
- English
- LU publication?
- yes
- id
- 33fc2cb7-7f9f-4cfc-9d91-8cce9a787bab
- date added to LUP
- 2024-01-14 17:08:02
- date last changed
- 2024-02-27 15:01:42
@inproceedings{33fc2cb7-7f9f-4cfc-9d91-8cce9a787bab,
abstract = {{In this paper, using tools from graph theory we provide verifiable necessary and sufficient conditions for the existence of a unique hydraulic equilibrium in district heating systems of meshed topology and containing multiple heat sources. Even though numerous publications have addressed the design of efficient algorithms for numerically finding hydraulic equilibria in the general context of water distribution networks, this is not the case for the analysis of existence and uniqueness. Moreover, most of the existing work dealing with these aspects exploit the equivalence between the nonlinear algebraic equations describing the hydraulic equilibria and the KKT conditions of a suitably defined nonlinear convex optimization problem. Differently, this paper proposes necessary and sufficient graph-theoretic conditions on the actuator placement for the existence and uniqueness of a hydraulic equilibrium, independent of the actuators’ control objective. An example based on a representative district heating network is considered to illustrate the key aspects of our contribution, and an explicit formulation of the steady state solution is given for the case in which pressure drops through pipes are linear with respect to the flow rate.}},
author = {{Jeeninga, Mark and Machado, Juan Eduardo and Cucuzzella, Michele and Como, Giacomo and Scherpen, Jacquelien}},
booktitle = {{Proceedings of the 2023 62nd IEEE Conference on Decision and Control}},
isbn = {{979-8-3503-0123-6}},
language = {{eng}},
month = {{12}},
pages = {{3652--3657}},
title = {{On the existence and uniqueness of steady state solutions of a class of dynamic hydraulic networks via actuator placement}},
url = {{http://dx.doi.org/10.1109/CDC49753.2023.10384050}},
doi = {{10.1109/CDC49753.2023.10384050}},
year = {{2023}},
}