Optimal Capacity Planning for the Transition of Energy Systems: Mathematical Models, Methods and Solutions ; Eine optimale Kapazitätsplanung für die Energiewende: Mathematische Modelle, Methoden und Lösungen

Abstract

In this thesis, we present methods, which enable us to solve capacity expansion problems for the the transition of energy systems regarding long planning horizons. Based on the decisions of the German government concerning the energy transition (Energiewende) the energy supply system will be sustainably changed. As a result of the phase out plan for the German nuclear power plants until 2022 the goal is to further promote the increasing share of renewable energy feed-in. However, a large share of renewable energy sources within the energy mix also holds new challenges. Among others regional distinction between power production from renwable energy sources and locations of energy-intensive industry play an important role. The weather dependence and the resulting highly fluctuating feed-in of renewable en- ergy sources furthermore increases the need for additional storages as well as a progressive transition to a flexible conventional power supply system in order to meet demand re- quirements at all times. The aim is to find a cost minimal transition for the German energy system under certain frame conditions. The main focus of this work lies on the development of decomposition and adaptive re- laxation methods which enable us to reduce both, problem size and problem complexity. The basic idea is to decompose the general problem into a master/investment problem and a discrete control problem on the second stage. The discrete control problem is in Literature also known as unit commitment problem (UC). In order to solve the UC prob- lem we develop a primal-dual approach which exploits the special almost block diagonal structure of the underlying model. The combination of a Lagrange heuristic and an ex- act adaptive dis-/aggregation framework makes it possible to find a minimal ε-feasible description of the problem. That means we can find a minimal description of the model which fulfills all relaxed constraints and also achieves an a-priori defined solution quality ε > 0. Based on the aggregated Lagrangian ...