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Sensors called phasor measurement units (PMUs) are used to monitor the electric power network. The power domination problem seeks to minimize the number of PMUs needed to monitor the network. We extend the power domination problem and…

Combinatorics · Mathematics 2023-12-13 Beth Bjorkman , Esther Conrad , Mary Flagg

The power domination problem seeks to determine the minimum number of phasor measurement units (PMUs) needed to monitor an electric power network. We introduce random sensor failure before the power domination process occurs and call this…

Combinatorics · Mathematics 2023-12-20 Beth Bjorkman , Zachary Brennan , Mary Flagg , Johnathan Koch

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,…

Combinatorics · Mathematics 2025-07-22 Beth Bjorkman , Sean English , Johnathan Koch , Amanda Verga

Phasor Measurement Units (PMUs) are placed at strategic vertices in an electrical power network to monitor the flow of power. Determining the minimum number and optimal placement of PMUs is modeled by the graph theoretic process called…

Combinatorics · Mathematics 2026-05-27 Johnathan Koch , Beth Bjorkman

To monitor electrical activity throughout the power grid and mitigate outages, sensors known as phasor measurement units can installed. Due to implementation costs, it is desirable to minimize the number of sensors deployed while ensuring…

Data Structures and Algorithms · Computer Science 2020-06-08 Logan A. Smith , Illya V. Hicks

Power domination is a graph-theoretic model for the observance of a power grid using phasor measurement units (PMUs). There are many costs associated with the installation of a PMU, but also costs associated with not observing the entire…

Combinatorics · Mathematics 2026-02-19 Beth Bjorkman , Sean English , Johnathan Koch

The problem Power Dominating Set (PDS) is motivated by the placement of phasor measurement units to monitor electrical networks. It asks for a minimum set of vertices in a graph that observes all remaining vertices by exhaustively applying…

Data Structures and Algorithms · Computer Science 2023-06-19 Thomas Bläsius , Max Göttlicher

Power domination in graphs arises from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A power dominating set of a graph is a set of vertices that observes every vertex in…

Combinatorics · Mathematics 2017-11-15 Chassidy Bozeman , Boris Brimkov , Craig Erickson , Daniela Ferrero , Mary Flagg , Leslie Hogben

Power domination in graphs emerged from the problem of monitoring an electrical system by placing as few measurement devices in the system as possible. It corresponds to a variant of domination that includes the possibility of propagation.…

Discrete Mathematics · Computer Science 2019-12-12 Paul Dorbec , Antonio González , Claire Pennarun

Phasor measurement units (PMUs) provide a high-resolution view of the power system at the locations where they are placed. As such, it is desirable to place them in bulk in low voltage distribution circuits. However, the power consumption…

Phasor Measurement Units (PMUs) are being used extensively for electrical grid monitoring and control. However, their cost prohibits further adoption on the distribution grid and easy access for educational purposes. This paper proposes…

Systems and Control · Electrical Eng. & Systems 2023-05-30 Mislav Bui , Marko Jurčević

To provide real-time visibility of physics-based states, phasor measurement units (PMUs) are deployed throughout power networks. PMU data enable real-time grid monitoring and control -- and are essential in transitioning to smarter grids.…

Systems and Control · Electrical Eng. & Systems 2024-10-23 Mohamad H. Kazma , Ahmad F. Taha

The study of power domination in graphs arises from the problem of placing a minimum number of measurement devices in an electrical network while monitoring the entire network. A power dominating set of a graph is a set of vertices from…

Combinatorics · Mathematics 2017-12-08 Boris Brimkov , Derek Mikesell , Logan Smith

We consider a power transmission system monitored with Phasor Measurement Units (PMUs) placed at significant, but not all, nodes of the system. Assuming that a sufficient number of distinct single-line faults, specifically pre-fault state…

Machine Learning · Statistics 2021-04-08 Andrei Afonin , Michael Chertkov

The problem of effective use of Phasor Measurement Units (PMUs) to enhance power systems awareness and security is a topic of key interest. The central question to solve is how to use this new measurements to reconstruct the state of the…

Systems and Control · Electrical Eng. & Systems 2020-04-16 Alexey Bobtsov , Romeo Ortega , Nikolay Nikolaev , Johannes Schiffer , M. Nicolai L. Lorenz-Meyer

A significant portion of the literature on fault localization assumes (more or less explicitly) that there are sufficient reliable measurements to guarantee that the system is observable. While several heuristics exist to break the…

Systems and Control · Computer Science 2018-09-12 Mahdi Jamei , Anna Scaglione , Sean Peisert

Phasor Measurement Units (PMUs) are measurement devices long used in transmission systems and today even more essential for a proper monitoring of distribution grids. The expected massive penetration of distributed energy resources (DERs)…

Systems and Control · Electrical Eng. & Systems 2020-03-03 Carlo Guarnieri Calo\' Carducci , Gianluca Lipari , Nicola Giaquinto , Ferdinanda Ponci , Antonello Monti

Sensors such as phasor measurement units (PMUs) endowed with GPS receivers are ubiquitously installed providing real-time grid visibility. A number of PMUs can cooperatively enable state estimation routines. However, GPS spoofing attacks…

Systems and Control · Computer Science 2018-04-27 Paresh Risbud , Nikolaos Gatsis , Ahmad Taha

This paper proposes a procedure to solve combinatorial power network design problems such as phasor measurement unit (PMU) placement and protection assignment against cyber-physical attacks. The proposed approach tackles the design problems…

Optimization and Control · Mathematics 2016-02-19 Kin Cheong Sou

This paper addresses problems on the robust structural design of complex networks. More precisely, we address the problem of deploying the minimum number of dedicated sensors, i.e., those measuring a single state variable, that ensure the…

Optimization and Control · Mathematics 2016-06-13 Xiaofei Liu , Sergio Pequito , Soummya Kar , Bruno Sinopoli , A. Pedro Aguiar
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