Supervisor: Benedikt Grüger
Earliest start: immediately
Type: Master Thesis

Since modern power systems increasingly depend on power electronic converters accurate dynamical stability studies of distribution grids become more necessary. Reduced-order models are expected to contribute to velocity and scalability of simulation frameworks. Order reduction i soften based on time-scale separation arguments: Fast inner control loops and slower outer dynamics uncouple. However, this assumption may break down during transient events caused by large perturbations leading to erroneous conclusions on stability.
This thesis explores the dynamical interaction of controllers in grid-following converters. Using both a full-order Simulink model and reduced-order models, the system’s response to disturbances—such as voltage fluctuations at the point of common coupling—is analyzed. With this, we explore which type of perturbations lead to instability. Particular attention is given to the validity of time-scale separation and how different control layers influence one another during transients. The existing code base, developed in Matlab and Julia, is extended to support this analysis.
The research contributes to a deeper understanding of converter behavior under severe perturbations and informs the development of more accurate and reliable modelling approaches.
The following papers are considered a good starting point:

• Synchronization stability and multi-timescale analysis of renewable-dominated power systems (Ma et al. 2023)
• Voltage Dynamics of Current Control Time-Scale in a VSC-Connected Weak Grid (Zhao et al. 2016)
• Understanding Small-Signal Stability of Low-Inertia Systems (Markovic et al. 2021)

Supervisor: Benedikt Grüger
Earliest start: immediately
Type: Master Thesis

With the ongoing large-scale integration of renewable energy sources, distribution grids are increasingly dominated by grid-following converters. Since converter control operates on significantly shorter time scales, evaluating their dynamic stability under varying grid conditions becomes crucial. In the presence of large disturbances, the non-linear behavior of converter dynamics becomes particularly important. In such cases, stability analysis can be based on the concept of the region of attraction—the set of initial states from which the system returns to its desired operating point without external intervention. Determining this region, however, is computationally demanding, especially for higher-order systems. To address this, several numerical methods have been developed to approximate the boundary of the region of attraction, such as the unstable manifold method and the interval stability method. This thesis investigates different numerical techniques for approximating the region of attraction boundary for a grid-following converter. In particular, these methods are compared against the standard Monte Carlo approach. Their practical applicability is demonstrated using two lower-order models of grid-following converters. Overall, this work contributes to ongoing efforts in converter modeling and provides insights into the impact of non-linear dynamics on the stability of future power systems.

• Stability threshold approach for complex dynamical systems (Klinshov, Nekorki, and Kurths 2015)
• Interval stability for complex systems (Klinshov et al. 2018)
• Domain of Attraction’s Estimation for Grid Connected Converters With Phase-Locked Loop (Zhang et al. 2022)
• Dominant Transient Equations of Grid-Following and Grid-Forming Converters by Controlling-Unstable- Equilibrium-Point-Based Participation Factor Analysis (Ma et al. 2024)