## Running theses and research assistant jobs

## Project seminar

**Student:** Benjamin Seeger

**Supervisor:** Julia Barbosa

**Time period:** 11/01/2023 - 02/01/2024

**Type:** Project Seminars Bachelor

Local electricity markets are a promising approach to foster the integration of renewable energy sources. These markets give priority to consuming electricity in close proximity to its generation, thereby alleviating the strain on the grid infrastructure. However, considering these local electricity markets as island systems is an unreasonable assumption. First, the presence of pre-existing transmission grid networks enhances energy security across all regions. Second, many supplier agents have assets in different regions and thus their strategies may not only be based on the outcome of a single market.

To understand how the coupling between local electricity markets affects the strategic behavior of supplier agents in such a market structure, this work shall propose a Nash-Cournot competition model that accounts for the transmission grid constraints.

## Bachelor theses

**Student:** Jan Niklas Witt

**Supervisor:** Sina Hajikazemi

**Time period:** 08/01/2023 - 02/01/2024

**Type:** Bachelor Thesis

Energy Planning Models (EPMs) are critical tools for simulating and guiding decisions about multimodal energy systems in specific regions or countries. These models provide strategies to meet future demands and environmental targets, which are often used by large energy companies to negotiate with the government and other investors. However, there is a concern that these profit-driven companies may manipulate the input data of EPMs to align with their interests.

This problem can be modeled as a bilevel linear programming problem, with linear lower and upper-level problems. Although bilevel programming problems are challenging in general, there are algorithms that can effectively solve them in the linear upper and lower-level form.

In this bachelor thesis, the student will develop interesting and interpretable examples of this problem for real-world EPMs that are relevant to current debates in energy policy. The goal is to show the potential impact of adversarial attacks on EPMs and to highlight the importance of developing robust models that are resistant to such attacks. The developed examples can be used as case studies to illustrate the impact of this problem on energy policy decisions and raise awareness among stakeholders in the energy sector. Requirements

• Proficiency in python programming

• Understanding of the fundamentals of mathematical programming

• Familiarity with energy planning models

• Experience with mathematical programming languages

**Student:** Helena Sax

**Supervisor:** Andreas Bott

**Time period:** 04/04/2022 - 08/01/2022

**Type:** Bachelor Thesis

District heating grid can help achieving CO2-reduction goals by providing renewable heat in densely populated areas. In combination with power-to-heat applications they can also help to balance the fluctuating power supply by wind and solar feed in, since heat can be stored easily and cheaply in large quantities.

The relative low speeds at which water flows through the network lead to a high inertia of the distribution system and to a significant delay between the time actions taken at the powerplant, e.g. changing the supply temperature, and these changes influencing the consumers. Utilizing the full flexibility of district heating networks therefore requires predictive operation strategies and simulations which are able to incorporate uncertainties such as changes in demand patterns.

Quasi-Steady-State (QSS) power flow calculations simplify the simulations by neglecting time delays for changes in pressures and mass flow rates, which are much lower than the delays implied by temperatures propagating through the networks.

For a given demand time series, these models can be solved by iterative algorithms, which comes at a high computational cost. For sampling-based applications, the simulations are solved repeatedly for randomly sampled demands. We can exploit this randomness for solving the QSS-system by sampling from a proxy-distribution. If the proxy-distribution is close enough to the true distribution, the results can be adjusted afterwards without losing much sampling efficiency.

For the QSS-system the mass flows at the consumers place should be such a close proxy-distribution which provides advantages for the QSS-calculations. Fixing the mass flows allows to separately solve the hydraulic equations, which were assumed to act instantiations and can therefore be solved for each time step independently. The time coupling thermal equations can then be solved in a second step, removing the need to iterate between the thermal and the hydraulic system.

The task of this thesis is to develop a representation of the QSS-equations which is best suited for the two steps solving approach outlined above as well as a corresponding solving algorithm for the QSS-system. The algorithms should be implemented in Python utilizing the Tensorflow package.

This thesis can also be started as Pro-Seminar or Project-Seminar

## Master theses

**Student:** Ruben Chacon

**Supervisor:** Tobias Gebhard

**Time period:** 05/22/2023 - 05/21/2024

**Type:** Master Thesis

The topology of underground electrical distribution infrastructure is often not publicly available because it may contain sensitive information. However, for researchers it is valuable to work with real (or realistic) grid models/data, e.g. to study new optimization algorithms or conduct power flow calculations. Therefore, there is a need for methods that are able to generate synthetic grids in an automated way. For this, publicly available data like GIS (geographic information system) data from OpenStreetMap (containing overhead power lines, street courses, building locations and types…) as well as statistical consumption data can be used.

**Student:** Kai Harder

**Supervisor:** Julia Barbosa

**Time period:** 01/15/2024 - 01/15/2025

**Type:** Master Thesis

The energy transition will require new approaches to energy contracting. Currently, energy contracting is an option to reduce the supply risk of utilities and the energy cost risk of large energy consumers, and mostly neglects the coupling between the demand for different energy commodities. With the electrification of heat supply through heat pumps, and the increased variability of electricity prices due to the integration of variable renewable energy, new designs of energy contracting and tariff structures are required to ensure fair pricing for consumers and utilities. The proposed Master's thesis will focus on the design and evaluation of energy contracting structures that consider the coupling between heat and electricity generation and demand, using the university energy system as a study case.

**Student:** Hans Stenglein

**Supervisor:** Florian Steinke

**Time period:** 05/01/2023 - 10/31/2023

**Type:** Master Thesis

The flow of power in electricity networks depends on various stochastic factors, e.g. renewable energy feed-ins or time-varying loads. Their importance is recently growing with the introduction of more wind and sun to our energy systems. At the same time, however, the range of options to counteract the fluctuations is also growing, since more and more in-feeds become controllable, in addition to the traditional conventional generators, e.g., electric vehicle chargers of power-to-heat converters.

Grid operators have to ensure that the grid remains feasible under variations, i.e., that line flows, voltages, and the system frequency remain in an acceptable range. To this end, they can measure the grid’s state at different locations to influence some of the controllable in-feeds accordingly. We ask:

**What is the minimal number of controllable in-feeds to influence and
the minimum number of measurement locations
such that the grid is guaranteed to remain in a feasible state with high probability?**

To attack this control challenge, we first linearize the power flow equations. We also assume that the grid operator uses a linear feedback controller for setting the values of the controlled in-feeds given the measurements. The resulting linear constrained system [1] with stochastic inputs can be analyzed and optimized based on the so-called polynomial chaos expansion (PCE) [2]. The key idea of PCE is to interpret the involved random variables as functions and to decompose them along different functional components.

The proposed thesis shall formulate these points formally and numerically compute controllers for different example settings. A code toolbox for various steps will be provided. The work will require the knowledge and understanding of some probability/measure theory as well as numerical convex optimization techniques.

The thesis is to be jointly supervised by Prof. Dr. Timm Faulwasser (TU Dortmund) and Prof. Dr. Florian Steinke (TU Darmstadt).

[1] Edwin Mora: Minimal Admissible Control of Constrained Static Linear Systems with Applications to Power Systems, PhD Thesis, 2022, https://doi.org/https://doi.org/10.26083/tuprints-00020805

[2] Mühlpfordt, Tillmann, Timm Faulwasser, and Veit Hagenmeyer. "A generalized framework for chance-constrained optimal power flow." Sustainable Energy, Grids and Networks 16 (2018): 231-242.

**Student:** Joao Kroeger

**Supervisor:** Allan Santos

**Time period:** 03/01/2023 - 08/31/2023

**Type:** Master Thesis

Smart grids are key components for enabling more flexible, cleaner and more robust energy systems. However, the real-time control of thousands of active elements such as distributed energy resources, batteries, and charging stations for electric vehicles is challenging. Grid operation relies on solving several optimization problems. One of them is the optimal power flow (OPF), whose goal is to find the operating point of all elements of the grid such that the power production cost is minimized while operation constraints are met. In legacy, static grids, OPF has to be solved every couple of minutes. On the other hand, the control of smart grids requires solving OPF problems with thousandfold more variables and on the order of seconds.

In this thesis, new methods for the speed-up of the OPF calculation are going to be investigated. Special focus will be given on using graph neural networks (GNN) for the development of surrogates. GNN is a special neural network architecture that is suited for learning on graph-like structures by leveraging non-Euclidian properties. This thesis also aims at developing zero-shot learning algorithms, i.e., methods that are able to solve the OPF with high accuracy not only for the grid from which training data was generated, but also on modified versions of it, e.g. the addition of new photovoltaic panels.