Estimating the Propagation of Interdependent Cascading Outages with Multi-Type Branching Processes

TL;DR

This paper applies multi-type branching processes to model and analyze the interdependent cascading outages in power systems, providing efficient estimation of outage propagation and joint distributions with limited data.

Contribution

It introduces a novel application of multi-type branching processes with EM estimation to quantify outage interdependencies and predict distributions efficiently.

Findings

The model accurately estimates joint outage distributions.

It predicts load shed and isolated bus outages effectively.

The approach requires fewer cascades for reliable estimates.

Abstract

In this paper, the multi-type branching process is applied to describe the statistics and interdependencies of line outages, the load shed, and isolated buses. The offspring mean matrix of the multi-type branching process is estimated by the Expectation Maximization (EM) algorithm and can quantify the extent of outage propagation. The joint distribution of two types of outages is estimated by the multi-type branching process via the Lagrange-Good inversion. The proposed model is tested with data generated by the AC OPA cascading simulations on the IEEE 118-bus system. The largest eigenvalues of the offspring mean matrix indicate that the system is closer to criticality when considering the interdependence of different types of outages. Compared with empirically estimating the joint distribution of the total outages, good estimate is obtained by using the multitype branching process with a much smaller number of cascades, thus greatly improving the efficiency. It is shown that the multitype branching process can effectively predict the distribution of the load shed and isolated buses and their conditional largest possible total outages even when there are no data of them.