Modeling and Analysis of District Heating Networks with Applications in Optimal Control

This thesis deals with modeling and simulation of district heating networks (DHN) and the mathematical analysis of the proposed DHN model. We provide a detailed derivation of the complete system of governing equations, starting from a brief exposition of the physical quantities of interest, continued with the components to set up a graph based network model accounting for fluxes and coupling conditions, the transport equations for water and thermal energy in pipelines, and the terms representing consumers and producers. On this basis, we perform an analysis of the solvability of the model equations, starting from the scalar advection problem in a single–consumer single–producer network, to a generalized problem suitable to model simple networks without loops. We also derive an abstract formulation of the problem, which serves as a rigorous mathematical model that can be utilized for optimization problems. The theoretical results can be utilized to perform tran- sient simulations of real world DHN and optimize their performance by optimal control, as indicated in a case study