Nonlinear Optimization of District Heating Networks

TL;DR

This paper presents a nonlinear optimization framework for district heating networks incorporating physical flow models, mixing constraints, and control strategies, demonstrating practical applicability through numerical experiments.

Contribution

It introduces a complementarity-constrained nonlinear optimization model with novel reformulations and control approaches for district heating networks.

Findings

Effective discretization and reformulation improve problem tractability.

The proposed methods successfully solve realistic network instances.

Numerical results validate the practical applicability of the approach.

Abstract

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.