Speaker
Description
The investigation of the dynamics of a network's stability is considered an important research area, whether it concerns neural networks, power supply networks, or communication and social networks. These networks are usually large graphs ranging from 10,000 (power grids) to 1 million (connectome) nodes. Solving the second-order Kuramoto equations that describe such systems optimally is usually done on GPUs making use of the power of parallelization.
In the case of power supply networks, and power grids, dynamic instabilities can lead to cascade failures, where a fault in one component or subsystem triggers a chain reaction of faults in other components or subsystems, resulting in widespread power outages or disruptions. Controlling these failures is crucial from economic, sustainability, and national security perspectives. Our study investigated high-voltage power grids from multiple perspectives. Firstly, the properties of cascade dynamics are examined: after the system thermalizes, we allow the overload of a single line, which leads to its disconnection, and we track subsequent overloads against threshold values. The probability distributions of cascade failures exhibit power-law tails near the synchronization point [1].
We also identify the weighted European power grids of 2016 and 2022, as well as their sensitive graph elements using two different methods: we determine bridges between connected communities and highlight "weak" nodes that show the smallest local synchronization of the "swing equation", and we strengthen them by creating structures that increase the graph's robustness. We compare the results with network variations where bridges are removed, similar to isolation, and with network variations where edges are randomly added or removed at random locations [2, 3] and we show that random augmentations of the network can lead to Braess paradox [4].
Lastly, we perform an analysis of the dynamics on the community level, where we discover chimera-like behavior. We try to explain the observed dynamics with spectral analysis and cycle detection.
[1] Ódor, G., Deng, S., Hartmann, B. & Kelling, J. Synchronization dynamics on power grids in europe and the united states.
Phys. Rev. E 106, 034311 (2022). URL https://link.aps.org/doi/10.1103/PhysRevE.106.034311.
[2] Hartmann, B. et al. Dynamical heterogeneity and universality of power-grids (2023). 2308.15326.
[3] Ódor, G., Papp, I., Benedek, K. & Hartmann, B. Improving power-grid systems via topological changes or how self-
organized criticality can help power grids. Phys. Rev. Res. 6, 013194 (2024). URL https://link.aps.org/doi/10.
1103/PhysRevResearch.6.013194.
[4] Braess, D., Nagurney, A. & Wakolbinger, T. On a paradox of traffic planning. Transportation science 39, 446–450 (2005).
