Predicting Cascading Failures with a Hyperparametric Diffusion Model

TL;DR

This work addresses cascading failures in power grids by casting propagation as a diffusion process and adapting the Independent Cascades framework to grid-specific physics features. It introduces a hyperparametric IC model where edge probabilities are logistic functions of endpoint features and a global hyperparameter, enabling learning from cascades and generalization to unseen grid configurations via maximum likelihood and PAC analysis. The approach yields a diffusion probability matrix that, when used in Monte Carlo simulations, accurately models propagation, supports mitigation decisions, and demonstrates superior generalization compared to baselines across demand and topology changes. The study also derives sample complexity bounds, provides a GPU-enabled learning pipeline, and validates the method on IEEE300 and Polish grid variants, highlighting practical implications for grid strengthening and resilience.

Abstract

In this paper, we study cascading failures in power grids through the lens of information diffusion models. Similar to the spread of rumors or influence in an online social network, it has been observed that failures (outages) in a power grid can spread contagiously, driven by viral spread mechanisms. We employ a stochastic diffusion model that is Markovian (memoryless) and local (the activation of one node, i.e., transmission line, can only be caused by its neighbors). Our model integrates viral diffusion principles with physics-based concepts, by correlating the diffusion weights (contagion probabilities between transmission lines) with the hyperparametric Information Cascades (IC) model. We show that this diffusion model can be learned from traces of cascading failures, enabling accurate modeling and prediction of failure propagation. This approach facilitates actionable information through well-understood and efficient graph analysis methods and graph diffusion simulations. Furthermore, by leveraging the hyperparametric model, we can predict diffusion and mitigate the risks of cascading failures even in unseen grid configurations, whereas existing methods falter due to a lack of training data. Extensive experiments based on a benchmark power grid and simulations therein show that our approach effectively captures the failure diffusion phenomena and guides decisions to strengthen the grid, reducing the risk of large-scale cascading failures. Additionally, we characterize our model's sample complexity, improving upon the existing bound.

Figures (7)

• Figure 1: Probability distribution of cascades and failure occurrence rate (excluding initial failures) for IEEE300.
• Figure 2: Mean relative error for line failure distribution and diffusion probability matrix (IEEE300 dataset).
• Figure 3: Training the model with CF data from one grid, testing on the others (IEEE300 dataset).
• Figure 4: Physical graph of power grid, and the diffusion graph learned from the hyperparametric model, filtered with the probability value $p_{uv}\geqslant 0.01$. Cascade failures before and after increasing the capacities of ten most critical branches (IEEE300 dataset).
• Figure 5: Mean absolute error for line failure distribution and diffusion probability matrix (IEEE300 dataset).

Theorems & Definitions (7)

• definition 1: Agnostic PAC learnability valiant1984theoryshalev2014understanding
• lemma 1
• lemma 2
• lemma 3: Covering Number
• lemma 4: Rademacher Bound
• lemma 5: Sample Complexity
• lemma 6