# Small vulnerable sets determine large network cascades in power grids

arXiv: https://arxiv.org/abs/1804.06432 · HTML: https://mlsanity.com/paper/1804.06432/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2018.

## Built on by (most cited first, 8 of 8)

- [Machine learning dismantling and early-warning signals of disintegration in complex systems](https://mlsanity.com/paper/2101.02453/) (2021)
- [Power-grid stability predictions using transferable machine learning](https://mlsanity.com/paper/2105.07562/) (2021)
- [Predicting Dynamic Stability from Static Features in Power Grid Models using Machine Learning](https://mlsanity.com/paper/2210.09266/) (2022)
- [Inferring Attracting Basins of Power System with Machine Learning](https://mlsanity.com/paper/2305.14374/) (2023)
- [A Criminology of Machines](https://mlsanity.com/paper/2511.02895/) (2025)
- [Questions of science: chatting with ChatGPT about complex systems](https://mlsanity.com/paper/2303.16870/) (2023)
- [Reinforcement Learning for Public Safety Power Shutoffs Under Decision-Dependent Uncertainty and Nonlinear Wildfire Ignition Models](https://mlsanity.com/paper/2604.26150/) (2026)
- [PowerZooJax: A JAX-based Power System Benchmark for Reinforcement Learning](https://mlsanity.com/paper/2609.36052/) (2026)

## Abstract (arXiv)

The understanding of cascading failures in complex systems has been hindered by the lack of realistic large-scale modeling and analysis that can account for variable system conditions. Here, using the North American power grid, we identify, quantify, and analyze the set of network components that are vulnerable to cascading failures under any out of multiple conditions. We show that the vulnerable set consists of a small but topologically central portion of the network and that large cascades are disproportionately more likely to be triggered by initial failures close to this set. These results elucidate aspects of the origins and causes of cascading failures relevant for grid design and operation, and demonstrate vulnerability analysis methods that are applicable to a wider class of cascade-prone networks.