283 2019 2021 eng 783 819 37 22(2) article 1 2019-10-04 2019-10-04 -- 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. Optimization and Engineering 2 Creative Commons - CC BY - Namensnennung 4.0 International Richard Krug Volker Mehrmann Martin Schmidt eng uncontrolled District heating networks eng uncontrolled Nonlinear optimization eng uncontrolled Euler equations eng uncontrolled Differential-algebraic equations eng uncontrolled Complementarity constraints Friedrich-Alexander-Universität Erlangen-Nürnberg Technische Universität Berlin A05 B03 B08 Universität Trier https://opus4.kobv.de/opus4-trr154/files/283/dhn-nl-opt_preprint.pdf