ISBN 978-3-8439-4971-2

978-3-8439-4971-2, Reihe Mathematik

Kristina Goschin
Optimal Design of an Energy Network Involving Renewable Energies for a Settlement

269 Seiten, Dissertation Technische Universität Darmstadt (2021), Softcover, B5

Zusammenfassung / Abstract

The ongoing trend towards sustainable energy supply and the corresponding impact of environmental aspects lead to significant energy sector changes. Energy networks have a central infrastructure that needs to be changed and adjusted by decentralized elements. New complex models for network design and optimal distribution of coupled energy sources have to be created to meet this difficulty. We develop an optimization problem that minimizes the overall costs of an energy network with central elements and decentralized acquisition technologies. To meet the consumers' heat and power demand within a settlement setting, we investigate the energy network design of multiple energy carrier systems, concentrating on electricity, natural gas, and district heating and their coupling through energy conversion plants. In addition to conventional energy sources, we consider geothermal, solar, and wind energy sources.

Due to different technology sizes and diameter sizes for distribution lines, binary decision variables occur. Along with nonlinear equations for modeling the energy generation and the flow dynamics given by partial differentiable equations (PDEs), this results in a mixed-integer non-convex optimization problem (MINLP) with PDE constraints.

In the first part of this work, we model a decentralized energy network and solve the developed quasi-stationary MINLP by the spatial branch-and-bound algorithm.

In the second part, we handle the system's dynamics by including the PDE constraints, which significantly increase the complexity. We focus on the gas subnetwork and present our treatment of the isothermal semi-linear Euler equations for the gas flow distribution in the Branch-and-Bound framework. Therefore, we show several methods to compute accurate upper and lower bounds for the PDE-solution by appropriate numerical schemes.