Nonlinear Optimization of District Heating Networks

  • We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic 1d partial differential equations. In addition, a pooling-type mixing model is required at the nodes of the network to treat the mixing of different water temperatures. This mixing model can be recast using suitable complementarity constraints. The resulting problem is a mathematical program with complementarity constraints subject to nonlinear partial differential equations describing the physics. In order to obtain a tractable problem, we apply suitable discretizations in space and time, resulting in a finite-dimensional optimization problem with complementarity constraints for which we develop a suitable reformulation with improved constraint regularity. Moreover, we propose an instantaneous control approach for the discretized problem, discuss practically relevant penalty formulations, and present preprocessing techniques that are used to simplify the mixing model at the nodes of the network. Finally, we use all these techniques to solve realistic instances. Our numerical results show the applicability of our techniques in practice.

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Author:Richard Krug, Volker Mehrmann, Martin Schmidt
Parent Title (German):Optimization and Engineering
Document Type:Article
Language:English
Date of Publication (online):2019/10/04
Date of first Publication:2019/10/04
Release Date:2019/10/04
Tag:Complementarity constraints; Differential-algebraic equations; District heating networks; Euler equations; Nonlinear optimization
Issue:22(2)
Page Number:37
First Page:783
Last Page:819
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Technische Universität Berlin
Universität Trier
Subprojects:A05
B03
B08
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International
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