# Finding $K$ Contingency List in Power Networks using a New Model of Dependency

## TL;DR

This paper introduces the MIIR model to better understand power network dependencies and proposes a method to identify the most critical $K$ components whose failure could cause widespread outages, validated through simulations.

## Contribution

The paper presents the MIIR model for power network dependencies and formulates the $K$ Contingency List problem, offering both optimal and heuristic solutions for complex failure analysis.

## Key findings

- The heuristic provides near-optimal solutions significantly faster than the MIP.
- MIIR effectively models complex power network dependencies.
- Validation with 2011 Southwest blackout demonstrates model relevance.

## Abstract

Smart grid systems are composed of power and communication network components. The components in either network exhibit complex dependencies on components in its own as well as the other network to drive their functionality. Existing, models fail to capture these complex dependencies. In this paper, we restrict to the dependencies in the power network and propose the Multi-scale Implicative Interdependency Relation (MIIR) model that address the existing limitations. A formal description of the model along with its working dynamics and a brief validation with respect to the 2011 Southwest blackout are provided. Utilizing the MIIR model, the $K$ Contingency List problem is proposed. For a given time instant, the problem solves for a set of $K$ entities in a power network which when failed at that time instant would cause the maximum number of entities to fail eventually. Owing to the problem being NP-complete we devised a Mixed Integer Program (MIP) to obtain the optimal solution and a polynomial time sub-optimal heuristic. The efficacy of the heuristic with respect to the MIP is compared by using different bus system data. In general, the heuristic is shown to provide near optimal solution at a much faster time than the MIP.