Interaction graph learning of line cascading failure in power networks and its statistical properties

Abstract

We consider line failure cascading in power networks where an initial random failure of a few lines leads to consecutive other line overloads and failures before the system settles in a steady state. Such cascades are rooted in non-obvious, long-range, and higher-order couplings among the lines’ flows induced by physical constraints on the network. Failure interaction graph encodes which and to what extent other lines in a networked system are affected after each line failure and can help to predict the final state after an initial disturbance. We perform data analytics on the final lines’ steady states of cascade trajectories to infer a specific line’s state given the states of others. We use a generative model to reconstruct possible steady states, and a predictive model aims to predict the probability of each line’s failures after the initial failure as a regression problem. The generative model uses regularized pseudolikelihood estimator to infer interaction weights by solving the inverse Ising problem and deploys Glauber dynamics to generate steady states. The discriminative model uses boosted trees to efficiently learn over training and predict over test data the state of each line as a target finding an appropriate subset of other lines’ states as explanatory variables. We analyze the degree distribution of the corresponding interaction graphs to study the number of other components affected by each line failure (out-degree) or the number of lines that affect the state of a given line (in-degree). Both models show that the in-degree follows a power-law distribution. Finally, we discuss the possible application of the interaction graph for early link removal to mitigate the failure-cascading consequences.