On Fragile Power Domination

TL;DR

This paper introduces a probabilistic model of power domination in power grids accounting for sensor failures, analyzes expected monitoring performance, and explores network modifications to control this behavior.

Contribution

It provides a new probabilistic framework for fragile power domination, characterizes when different networks behave similarly, and suggests methods to influence monitoring outcomes.

Findings

Expected number of observed nodes derived

Characterization of network equivalence under failure

Strategies for network structure to control monitoring

Abstract

Power domination is a graph theoretic model which captures how phasor measurement units (PMUs) can be used to monitor a power grid. Fragile power domination takes into account the fact that PMUs may break or otherwise fail. In this model, each sensor fails independently with probability $q\in [0,1]$ and the surviving sensors monitor the grid according to classical power domination. We study the expected number of observed nodes under the fragile power domination model. We give a characterization for when two networks and initial sensor placements will behave the same according to this expectation. We also show how to control the behavior of this expectation by adding structure to a network.