Dynamics of District Heating Networks : Modeling, Simulation and Optimization using Differential Algebraic Equations

Abstract

This thesis deals with the efficient numerical treatment of Differential-Algebraic Equations (DAEs) as constraints for an optimal control problem, with these DAEs representing district heating networks, which serve as the main motivation for the entire study. To establish a stable foundation for numerical treatment, the basic theory for DAEs is first addressed. Fundamental concepts are revisited, and various solution approaches are introduced. Strong solution theories impose overly restrictive conditions for optimization, thus weaker solution concepts are also introduced. Additionally, a new solution result for semi-explicit DAEs is presented. Equipped with robust theory, the modeling of district heating networks is pursued to simulate them under given input conditions. Attention is particularly paid to differences in index reduction, which, unlike in classical index reduction, are marginal. Therefore, further work can proceed with an index 1 system, simplifying the optimization process. To efficiently optimize the given networks, corresponding simplifications are introduced that do not alter the nature or physics of the problem. Numerical results demonstrate the applicability and feasibility of these methods for real-world applications, exemplified by a network located in Düsseldorf.