Nonlinear optimization of district heating networks

• Published in: Optimization and engineering Vol. 22; no. 2; pp. 783 - 819
• Main Authors: Krug, Richard, Mehrmann, Volker, Schmidt, Martin
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2021; Springer Nature B.V
• Subjects: Constraints; Control; District heating; Engineering; Environmental Management; Financial Engineering; Formulations; Heat transmission; Mathematical models; Mathematics; Mathematics and Statistics; Networks; Nodes; Nonlinear differential equations; Operations Research/Decision Theory; Optimization; Partial differential equations; Research Article; Systems Theory; Time dependence; Water temperature; Mixing; 90C30; Complementarity constraints; 90C35; 90Cxx; District heating networks; Nonlinear optimization; 90C90; Euler equations; Differential-algebraic equations; 90-XX
• ISSN: 1389-4420; 1573-2924
• DOI: 10.1007/s11081-020-09549-0

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.