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

Dynamical behaviour of modern distribution grids is increasingly shaped by power-electronic converters. This introduces novel instabilities that get expressed in the form of sub-synchronous oscillations from unwanted controller interactions. Corresponding studies requires computationally efficient and interpretable reduced-order models.
This thesis explores the dynamical interaction of controllers in grid-following converters. Using both a MatLab/Simulink model and an low-order model, the system’s response to grid voltage fluctuations 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 simulation frameworks, based on Matlab and Julia, are extended to support this analysis.
The research contributes to a deeper understanding of converter behavior under perturbations and informs the development of improved 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. Especially in weak grids, perturbations on the AC grid side can lead to loss of synchronisation of the converters, i.e., the converter enters a state where the voltage phase information can not be obtained, and subsequently converter tripping. This non-linear phenomenon has been observed in multiple contexts around the globe and several analytical have been developed, e.g. calculation of the converter's region of attraction, i.e., the set of perturbed states that evolve back to the operating point. Determining this region 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)