# Stability of Synchrony against Local Intermittent Fluctuations in Tree-like Power Grids

## TL;DR

This paper investigates how the structure of tree-like power grids affects their stability against localized intermittent renewable energy fluctuations, highlighting the importance of network losses and node position.

## Contribution

It introduces a model of distributed resources as oscillators on lossy, tree-like power grids and reveals how network structure and node location influence stability against fluctuations.

## Key findings

- Losses in distribution grids are crucial for stability effects.
- Central nodes split the network into branches with different stability influences.
- Vulnerable regions can be predicted using an eigenvector-based measure.

## Abstract

80% of all Renewable Energy Power in Germany is installed in tree-like distribution grids. Intermittent power fluctuations from such sources introduce new dynamics into the lower grid layers. At the same time, distributed resources will have to contribute to stabilize the grid against these fluctuations in the future. In this paper, we model a system of distributed resources as oscillators on a tree-like, lossy power grid and its ability to withstand desynchronization from localized intermittent renewable infeed. We find a remarkable interplay of network structure and the position of the node at which the fluctuations are fed in. An important precondition for our findings is the presence of losses in distribution grids. Then, the most network central node splits the network into branches with different influence on network stability. Troublemakers, i.e. nodes at which fluctuations are especially exciting the grid, tend to be downstream branches with high net power outflow. For low coupling strength, we also find branches of nodes vulnerable to fluctuations anywhere in the network. These network regions can be predicted at high confidence using an eigenvector based network measure taking the turbulent nature of perturbations into account. While we focus here on tree-like networks, the observed effects also appear, albeit less pronounced, for weakly meshed grids. On the other hand the observed effects disappear for lossless power grids often studied in the complex systems literature.