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Related papers: The Power Domination Toolbox

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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

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 2023-05-24 Beth Bjorkman , Esther Conrad

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 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

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

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

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

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

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

Phasor Measurement Unit (PMU) technology is increasingly used for real-time monitoring applications, especially line outage detection and identification (D&I) in the power system. Current outage D&I schemes either assume a full PMU…

Systems and Control · Electrical Eng. & Systems 2020-09-08 Xiaozhou Yang , Nan Chen , Chao Zhai

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…

Power domination is a two-step observation process that is used to monitor power networks and can be viewed as a combination of domination and zero forcing. Given a graph $G$, a subset $S\subseteq V(G)$ that can observe all vertices of $G$…

Combinatorics · Mathematics 2022-09-09 Sarah E. Anderson , Kirsti Kuenzel , Houston Schuerger

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

Phasor measurement units (PMUs) provide accurate and high-fidelity measurements in order to monitor the state of the power grid and support various control and planning tasks. However, PMUs have a high installation cost prohibiting their…

Systems and Control · Electrical Eng. & Systems 2023-04-18 Saptarshi Ghosh , Murali Sankar Venkatraman , Shehab Ahmed , Charalambos Konstantinou

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

The power domination problem focuses on finding the optimal placement of phase measurement units (PMUs) to monitor an electrical power network. In the context of graphs, the power domination number of a graph $G$, denoted $\gamma_P(G)$, is…

Combinatorics · Mathematics 2022-09-09 Sarah E. Anderson , Kirsti Kuenzel

This paper presents an information-theoretic approach to address the phasor measurement unit (PMU) placement problem in electric power systems. Different from the conventional 'topological observability' based approaches, this paper…

Optimization and Control · Mathematics 2012-01-16 Qiao Li , Tao Cui , Yang Weng , Rohit Negi , Franz Franchetti , Marija D. Ilic

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

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 introduces an algorithm able to detect and localize the occurrance of a fault in an Active Distribution Network, using the measurements collected by Phasor Measurement Units (PMUs). First, a basic algorithm that works under the…

Systems and Control · Electrical Eng. & Systems 2022-04-13 Francesco Conte , Fabio D'Agostino , Bruno Gabriele , Giacomo-Piero Schiapparelli , Federico Silvestro
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