Spectral Graph Analysis of the Geometry of Power Flows in Transmission Networks

Rétière, Nicolas; Ha, Dinh Truc; Caputo, Jean-Guy

doi:10.1109/jsyst.2019.2928852

Cited by 20 publications

(12 citation statements)

References 35 publications

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“…The GCNs show shorter computation time and higher accuracy than the conventional Monte-Carlo method. To decompose and solve the power flow equations of transmission networks, the spectralbased GCNs are presented to provide a geometric picture of the electrical variables in [89]. Similarly, to calculate the power flow in parallel and quickly, the GNNs are proposed to minimize the violation of Kirchhoff's law at each node during the training in [90].…”

Section: ) Power Flow Approximationmentioning

confidence: 99%

A Review of Graph Neural Networks and Their Applications in Power Systems

Liao

Bak‐Jensen

Pillai

et al. 2022

Journal of Modern Power Systems and Clean Energy

167

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Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks are typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as graph-structured data with high-dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many publications generalizing deep neural networks for graphstructured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNN structures, e. g., graph convolutional networks, are summarized. Key applications in power systems such as fault scenario application, time-series prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.

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Section: ) Power Flow Approximationmentioning

confidence: 99%

A Review of Graph Neural Networks and Their Applications in Power Systems

Liao

Bak‐Jensen

Pillai

et al. 2022

Journal of Modern Power Systems and Clean Energy

167

View full text Add to dashboard Cite

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“…Particularly relevant for our analysis is [114], which focuses on the efficient computation of the pseudo-inverse of the graph Laplacian and explores its intimate connection with effective resistances. Graph spectra-based methods have been extensively used in the context of power systems, in particular in the study of phase angles frequency dynamics [31,35,36,110,82,81], but also for power system restoration [113] and to analyze of the geometry of power flows [116,19]. A spectral characterization for the network bridges, which play a crucial role in our analysis, was already given in [20,128].…”

Section: Related Literaturementioning

confidence: 99%

A Spectral Representation of Power Systems with Applications to Adaptive Grid Partitioning and Cascading Failure Localization

Zocca¹,

Chen²,

Guo³

et al. 2021

Preprint

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Transmission line failures in power systems propagate and cascade non-locally. This well-known yet counter-intuitive feature makes it even more challenging to optimally and reliably operate these complex networks. In this work we present a comprehensive framework based on spectral graph theory that fully and rigorously captures how multiple simultaneous line failures propagate, distinguishing between non-cut and cut set outages. Using this spectral representation of power systems, we identify the crucial graph sub-structure that ensures line failure localization -the network bridge-block decomposition. Leveraging this theory, we propose an adaptive network topology reconfiguration paradigm that uses a two-stage algorithm where the first stage aims to identify optimal clusters using the notion of network modularity and the second stage refines the clusters by means of optimal line switching actions. Our proposed methodology is illustrated using extensive numerical examples on standard IEEE networks and we discussed several extensions and variants of the proposed algorithm.

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“…Concepts from graph theory and graphical models have been used in power systems for sensor placement [ 26 ], topology identification [ 27 , 28 , 29 ], state estimation [ 6 , 30 , 31 ], analysis [ 32 , 33 ], and optimal power flow calculation [ 34 , 35 ]. However, the graphical model methods assume a specific statistical structure, which does not necessarily apply in power systems, and often do not use the physical models, which may result in poor performance in practice.…”

Section: Introductionmentioning

confidence: 99%

State Estimation in Partially Observable Power Systems via Graph Signal Processing Tools

Dabush

Kroizer

Routtenberg

2023

Sensors

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This paper considers the problem of estimating the states in an unobservable power system, where the number of measurements is not sufficiently large for conventional state estimation. Existing methods are either based on pseudo-data that is inaccurate or depends on a large amount of data that is unavailable in current systems. This study proposes novel graph signal processing (GSP) methods to overcome the lack of information. To this end, first, the graph smoothness property of the states (i.e., voltages) is validated through empirical and theoretical analysis. Then, the regularized GSP weighted least squares (GSP-WLS) state estimator is developed by utilizing the state smoothness. In addition, a sensor placement strategy that aims to optimize the estimation performance of the GSP-WLS estimator is proposed. Simulation results on the IEEE 118-bus system show that the GSP methods reduce the estimation error magnitude by up to two orders of magnitude compared to existing methods, using only 70 sampled buses, and increase of up to 30% in the probability of bad data detection for the same probability of false alarms in unobservable systems The results conclude that the proposed methods enable an accurate state estimation, even when the system is unobservable, and significantly reduce the required measurement sensors.

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Spectral Graph Analysis of the Geometry of Power Flows in Transmission Networks

Cited by 20 publications

References 35 publications

A Review of Graph Neural Networks and Their Applications in Power Systems

A Review of Graph Neural Networks and Their Applications in Power Systems

A Spectral Representation of Power Systems with Applications to Adaptive Grid Partitioning and Cascading Failure Localization

State Estimation in Partially Observable Power Systems via Graph Signal Processing Tools

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