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A Correlation Analysis Method for Power Systems Based on Random Matrix Theory
The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems. In this situation, the model-based methods need to be revisited. A data-driven method, as the novel alternative on the other hand, is proposed in...
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Published in: | IEEE transactions on smart grid 2017-07, Vol.8 (4), p.1811-1820 |
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container_title | IEEE transactions on smart grid |
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creator | Xinyi Xu Xing He Qian Ai Qiu, Robert Caiming |
description | The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems. In this situation, the model-based methods need to be revisited. A data-driven method, as the novel alternative on the other hand, is proposed in this paper. It reveals the correlations between the factors and the system status through statistical properties of data. An augmented matrix as the data source is the key trick for this method and is formulated by two parts: (1) status data as the basic part; and (2) factor data as the augmented part. The random matrix theory is applied as the mathematical framework. The linear eigenvalue statistics, such as the mean spectral radius, are defined to study data correlations through large random matrices. Compared with model-based methods, the proposed method is inspired by a pure statistical approach without a prior knowledge of operation and interaction mechanism models for power systems and factors. In general, this method is direct in analysis, robust against bad data, universal to various factors, and applicable for real-time analysis. A case study based on the standard IEEE 118-bus system validates the proposed method. |
doi_str_mv | 10.1109/TSG.2015.2508506 |
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(IEEE) 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c361t-966c27fa47fd11a9bc3f8c445271fde772192596366fe8a07f551bee70fe384e3</citedby><cites>FETCH-LOGICAL-c361t-966c27fa47fd11a9bc3f8c445271fde772192596366fe8a07f551bee70fe384e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/7368184$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,778,782,27911,27912,54783</link.rule.ids></links><search><creatorcontrib>Xinyi Xu</creatorcontrib><creatorcontrib>Xing He</creatorcontrib><creatorcontrib>Qian Ai</creatorcontrib><creatorcontrib>Qiu, Robert Caiming</creatorcontrib><title>A Correlation Analysis Method for Power Systems Based on Random Matrix Theory</title><title>IEEE transactions on smart grid</title><addtitle>TSG</addtitle><description>The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems. In this situation, the model-based methods need to be revisited. A data-driven method, as the novel alternative on the other hand, is proposed in this paper. It reveals the correlations between the factors and the system status through statistical properties of data. An augmented matrix as the data source is the key trick for this method and is formulated by two parts: (1) status data as the basic part; and (2) factor data as the augmented part. The random matrix theory is applied as the mathematical framework. The linear eigenvalue statistics, such as the mean spectral radius, are defined to study data correlations through large random matrices. Compared with model-based methods, the proposed method is inspired by a pure statistical approach without a prior knowledge of operation and interaction mechanism models for power systems and factors. In general, this method is direct in analysis, robust against bad data, universal to various factors, and applicable for real-time analysis. A case study based on the standard IEEE 118-bus system validates the proposed method.</description><subject>augmented matrix</subject><subject>Big data</subject><subject>big data analytics</subject><subject>Buses (vehicles)</subject><subject>Complexity</subject><subject>Correlation</subject><subject>Correlation analysis</subject><subject>Covariance matrices</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Line spectra</subject><subject>linear eigenvalue statistics</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Matrices (mathematics)</subject><subject>Matrix methods</subject><subject>Matrix theory</subject><subject>Power system stability</subject><subject>power systems</subject><subject>random matrix theory</subject><subject>Real time</subject><subject>Robustness (mathematics)</subject><issn>1949-3053</issn><issn>1949-3061</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNo9kEFPAjEQRhujiQS5m3hp4nmx027b7RGJoglEI3huyu40LAGK7RLdf-8SCHP55vC-yeQRcg9sCMDM02I-GXIGcsglKyRTV6QHJjeZYAquL7sUt2SQ0pp1I4RQ3PTIbETHIUbcuKYOOzrauU2b6kRn2KxCRX2I9DP8YqTzNjW4TfTZJaxoh365XRW2dOaaWP_RxQpDbO_IjXebhINz9sn368ti_JZNPybv49E0K4WCJjNKlVx7l2tfATizLIUvyjyXXIOvUGsOhkujhFIeC8e0lxKWiJp5FEWOok8eT3f3MfwcMDV2HQ6x-z1ZMMC1NIUSHcVOVBlDShG93cd662JrgdmjN9t5s0dv9uytqzycKjUiXnAtVAFFLv4BB25ntg</recordid><startdate>20170701</startdate><enddate>20170701</enddate><creator>Xinyi Xu</creator><creator>Xing He</creator><creator>Qian Ai</creator><creator>Qiu, Robert Caiming</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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In this situation, the model-based methods need to be revisited. A data-driven method, as the novel alternative on the other hand, is proposed in this paper. It reveals the correlations between the factors and the system status through statistical properties of data. An augmented matrix as the data source is the key trick for this method and is formulated by two parts: (1) status data as the basic part; and (2) factor data as the augmented part. The random matrix theory is applied as the mathematical framework. The linear eigenvalue statistics, such as the mean spectral radius, are defined to study data correlations through large random matrices. Compared with model-based methods, the proposed method is inspired by a pure statistical approach without a prior knowledge of operation and interaction mechanism models for power systems and factors. In general, this method is direct in analysis, robust against bad data, universal to various factors, and applicable for real-time analysis. 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subjects | augmented matrix Big data big data analytics Buses (vehicles) Complexity Correlation Correlation analysis Covariance matrices Eigenvalues and eigenfunctions Line spectra linear eigenvalue statistics Mathematical analysis Mathematical models Matrices (mathematics) Matrix methods Matrix theory Power system stability power systems random matrix theory Real time Robustness (mathematics) |
title | A Correlation Analysis Method for Power Systems Based on Random Matrix Theory |
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