You are here: Home PIK Members Dr. Frank Hellmann COEN Projects for Students

Topics for Bachelor's or Master's Theses

We offer a wide range of possible Bachelor and Masterthesis projects as well as Praktika. If you are interested in any of these topics, or something in the direction of the below, please contact me. (hellmann@pik-potsdam.de).

Further topics are offered in cooperation with our partners at TU Berlin.


Power Grid Topics

Delays in Networks (BA/MA)

A central problem in the dynamics of future power systems is the delayed reaction of electronics that control the system. When many such elements are combined in a large system it is hard to understand the emergent behavior and guarantee stability. Modeling and understanding delayed systems and their network properties is an open field with several potential thesis topics. There is scope for both, numerical and analytical work on this topic.

Machine Learning for vulnerability predictors (BA/MA)

From numerical experiments it is known that particular network structures can be highly vulnerable to perturbations. This vulnerability is a deeply non-linear property of a highly complex system that is not analytically accessible. As such it is an interesting problem to ask whether machine learning techniques can accurately find and predict such vulnerabilities. This is mostly a numerical investigation, though good analytic understanding is required for successfully applying ML techniques in novel contexts.

Develop and implement intermediate complexity models (BA/MA)

The methods developed for the analysis of networked systems are in principle applicable to arbitrary models. In order to investigate actual power grids it is necessary to implement intermediate level complexity models of real and realistic power grids in a way that is amenable to sampling based methods. This will be done in the context of PowerDynamics.jl in the programming language Julia. This involves both, numerical and analytical work to find appropriate simplifications of detailed engineering models.

Further numerical work (BA/MA/Praktikum)

While a set of tools for numerical investigations of complex systems already exists, there is still a great need for further developing the software ecosystem and implementing well written libraries for these investigations, particularly in the rather young Julia ecosystem.

Optimizing nonlinear properties of power grids (BA/MA)

By using semi-analytic approximations of non-linear stability measures, we will investigate the performance of standard optimization algorithms for optimizing the non-linear behavior of high dimensional power grids. A more far reaching project (MA only) is to investigate the use of sensitivity analysis to develop novel gradient descent algorithms for optimizing sampling based non-linear properties directly.

General Network Topics

Evolutionary Algorithms (and other advanced sampling methods) for investigating non-linear emergent network properties (BA/MA)

While naive sampling approaches can reveal the dominant behavior of a complex system, they do not allow us to efficiently understand rare events. This project will develop and test advanced optimization and sampling methods that purposefully drive the system towards rare failure modes. Such methods will allow us to efficiently investigate and model complicated emergent phenomena such as cascading failures in power grids and other networks.

Network of Network models for infrastructure (BA/MA)

In order to investigate the behavior of networked systems in the intermediate regime between case studies and general analytic results, it is necessary to have stochastic descriptions of the networks under investigation. Building on existing models for single layer infrastructure models, this thesis will build multi-layered Network of Network models for accurately describing networks with several hierarchical layers (highway system vs local roads, voltage layers in power grids, etc...)

Theory Topics

Clustering trajectories in dynamical systems, space-time manifold learning (MA)

In order to understand the behavior of high dimensional systems under parameter change, their bifurcation structure, we need novel methods. By adapting manifold learning techniques, that extract non-linear structures from data, we will develop algorithms and software tools that allow us to extract mathematically accurate information about system behavior from sampling data.

Approximation theory for networked systems (MA)

The complex non-linear behavior of networked systems can not be understood analytically in general. Control theory provides an interesting set of approximation techniques though, that can be adapted to this context. A successful flow-based approximation theory along these lines would bring the behavior of such systems into the realm of analytic treatment.

Stochastic control for colored noise (MA)

General stochastic control methods deal with Gaussian noise only. This project investigates the use of linear filters to generalize these methods to arbitrary spectra. It is known from various empirical and analytical results that these spectra are particularly important in a networked context.

Loop base control (BA/MA)

Loops or cycles play a fundamental role in the behavior of networked systems. A basis of the possible flow states in a networked system is given by a basis of cycles. This project will investigate the potential of controlling a networks dynamical behaviors through the cycle flows.

Further Topics

Intelligent sampling methods for probabilistic stability measures (BA/MA)

Probabilistic stability measures are being used extensively to study dynamical systems. In this thesis we will introduce importance sampling for some of these measures, that has the potential to improve their performance considerably.

Sprouts Model (BA/MA)

For many phenomena observed in high dimensional systems we can find simplified low dimensional models. We will explore the behavior of some of these models analytically and semi-analytically and develop new ones.



Last updated on 11.12.2018.

Document Actions