Statistical method for on-line voltage collapse proximity estimation

This paper is aimed to propose a reliable method for estimating the voltage collapse proximity through a model obtained using statistical techniques. In the model building process a database is required, therefore the Voltage Collapse Proximity Index (VCPI) is used to obtain previous readings for di...

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Autores:: Posada, Johnny
Ramírez, Juan Manuel
Sanz, Fredy

Tipo de recurso:: Article of journal

Fecha de publicación:: 2016

Institución:: Universidad Autónoma de Occidente

Repositorio:: RED: Repositorio Educativo Digital UAO

Idioma:: eng

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dc.title.eng.fl_str_mv	Statistical method for on-line voltage collapse proximity estimation
title	Statistical method for on-line voltage collapse proximity estimation
spellingShingle	Statistical method for on-line voltage collapse proximity estimation Sistemas eléctricos Sistemas de energía eléctrica Centrales eléctricas Electrical systems Electric power systems Electric power systems Ingeniería eléctrica Electricidad Electricity Electric engineering Statistic Voltage stability Voltage collapse Estimation
title_short	Statistical method for on-line voltage collapse proximity estimation
title_full	Statistical method for on-line voltage collapse proximity estimation
title_fullStr	Statistical method for on-line voltage collapse proximity estimation
title_full_unstemmed	Statistical method for on-line voltage collapse proximity estimation
title_sort	Statistical method for on-line voltage collapse proximity estimation
dc.creator.fl_str_mv	Posada, Johnny Ramírez, Juan Manuel Sanz, Fredy
dc.contributor.author.none.fl_str_mv	Posada, Johnny Ramírez, Juan Manuel Sanz, Fredy
dc.subject.lemb.spa.fl_str_mv	Sistemas eléctricos Sistemas de energía eléctrica Centrales eléctricas
topic	Sistemas eléctricos Sistemas de energía eléctrica Centrales eléctricas Electrical systems Electric power systems Electric power systems Ingeniería eléctrica Electricidad Electricity Electric engineering Statistic Voltage stability Voltage collapse Estimation
dc.subject.lemb.eng.fl_str_mv	Electrical systems Electric power systems Electric power systems
dc.subject.armarc.spa.fl_str_mv	Ingeniería eléctrica Electricidad
dc.subject.armarc.eng.fl_str_mv	Electricity Electric engineering
dc.subject.proposal.eng.fl_str_mv	Statistic Voltage stability Voltage collapse Estimation
description	This paper is aimed to propose a reliable method for estimating the voltage collapse proximity through a model obtained using statistical techniques. In the model building process a database is required, therefore the Voltage Collapse Proximity Index (VCPI) is used to obtain previous readings for different contingencies and loading conditions. This analytical proposal could be combined with existing equipment in the power system control centers for future on-line applications. The proposed method is applied to the IEEE 14-bus test system and the 190-bus Mexican equivalent. Results indicate that the proposed strategy is a reliable choice
publishDate	2016
dc.date.issued.none.fl_str_mv	2016
dc.date.accessioned.none.fl_str_mv	2019-09-04T16:22:29Z
dc.date.available.none.fl_str_mv	2019-09-04T16:22:29Z
dc.type.spa.fl_str_mv	Artículo de revista
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dc.identifier.doi.spa.fl_str_mv	https://doi.org/10.1016/j.ijepes.2016.03.035
dc.identifier.instname.spa.fl_str_mv	Universidad Autónoma de Occidente
dc.identifier.reponame.spa.fl_str_mv	Repositorio Educativo Digital UAO
identifier_str_mv	1879-3517 (en línea) 0142-0615 (impresa) Universidad Autónoma de Occidente Repositorio Educativo Digital UAO
url	http://hdl.handle.net/10614/11046 https://doi.org/10.1016/j.ijepes.2016.03.035
dc.language.iso.eng.fl_str_mv	eng
language	eng
dc.relation.citationedition.spa.fl_str_mv	Volumen 82 (noviembre 2016)
dc.relation.citationendpage.none.fl_str_mv	399
dc.relation.citationissue.none.fl_str_mv	82
dc.relation.citationstartpage.none.fl_str_mv	392
dc.relation.cites.eng.fl_str_mv	Sanz, F. A., Ramirez, J. M., & Posada, J. (2016). Statistical method for on-line voltage collapse proximity estimation. International Journal of Electrical Power & Energy Systems, 82, p.392-399
dc.relation.ispartofjournal.eng.fl_str_mv	International journal of electrical power & energy systems
dc.relation.references.spa.fl_str_mv	J.-H. Teng, C.-Y. Chen, I. Martinez, C.-F. Chen Power system vulnerability assessment considering energy storage systems 2013 IEEE 10th international conference on Power Electronics and Drive Systems (PEDS) (2013), pp. 903-907 View Record in ScopusGoogle Scholar O.A. Mousavi, M. Bozorg, R. Cherkaoui Preventive reactive power management for improving voltage stability margin Electric Power Syst Res, 96 (2013), pp. 36-46 Google Scholar E. Zio, G. Sansavini Vulnerability of smart grids with variable generation and consumption: a system of systems perspective IEEE Trans Syst Man Cybern, 43 (3) (2013), pp. 477-487 CrossRefView Record in ScopusGoogle Scholar A. de Souza, J.C.S. De Souza, A. Leite da Silva On-line voltage stability monitoring IEEE Trans Power Syst, 15 (4) (2000), pp. 1300-1305 CrossRefGoogle Scholar V. Balamourougan, T.S. Sidhu, M.S. Sachdev Technique for online prediction of voltage collapse IEE Proc Gener Transm Distrib, 151 (4) (2004), pp. 453-460 View Record in ScopusGoogle Scholar A. Berizzi, C. Bovo, D. Cirio, M. Delfanti, M. Merlo, M. Pozzi Online fuzzy voltage collapse risk quantification Electric Power Syst Res, 79 (5) (2009), pp. 740-749 ArticleDownload PDFView Record in ScopusGoogle Scholar L. Sanchez, I. Couso, J.C. Viera Online SOC estimation of Li-FePO4 batteries through a new fuzzy rule-based recursive filter with feedback of the heat flow rate Vehicle Power and Propulsion Conference (VPPC), 2014 IEEE (2014), pp. 1-6 27–30 October CrossRefGoogle Scholar F.A. Althowibi, M. Mustafa On-line voltage collapse indicator for power systems 2010 IEEE international conference on power and energy (PECon) (2010), pp. 408-413 View Record in ScopusGoogle Scholar H.-D. Chiang, H. Li, J. Tong, P. Causgrove On-line voltage stability monitoring of large power systems 2011 IEEE power and energy society general meeting (2011), pp. 1-6 CrossRefGoogle Scholar D.T. Duong, K. Uhlen Online voltage stability monitoring based on PMU measurements and system topology 2013 3rd international conference on Electric Power and Energy Conversion Systems (EPECS) (2013), pp. 1-6 2–4 October CrossRefView Record in ScopusGoogle Scholar S.S. Biswas, C.B. Vellaithurai, A.K. Srivastava Development and real time implementation of a synchrophasor based fast voltage stability monitoring algorithm with consideration of load models Industry applications society annual meeting, 2013 IEEE (2013), pp. 1-9 6–11 October CrossRefView Record in ScopusGoogle Scholar Fengkai Hu, Kai Sun, A. Del Rosso, E. Farantatos, N. Bhatt An adaptive three-bus power system equivalent for estimating voltage stability margin from synchronized phasor measurements PES general meeting \| conference & exposition, 2014 IEEE (2014), pp. 1-5 27–31 July CrossRefView Record in ScopusGoogle Scholar S. Maslennikov, E. Litvinov, M. Vaiman, M. Vaiman Implementation of ROSE for on-line voltage stability analysis at ISO New England PES general meeting \| conference & exposition, 2014 IEEE (2014), pp. 1-5 27–31 July CrossRefGoogle Scholar S. Varshney, L. Srivastava, M. Pandit, M. Sharma Voltage stability based contingency ranking using distributed computing environment 2013 International Conference on Power, Energy and Control (ICPEC) (2013), pp. 208-212 View Record in ScopusGoogle Scholar S. DasGupta, M. Paramasivam, U. Vaidya, V. Ajjarapu, Real-time monitoring of short-term voltage stability using PMU data. IEEE Trans Power Syst. http://dx.doi.org/10.1109/TPWRS.2013.2258946. Google Scholar B. Leonardi, V. Ajjarapu An approach for real time voltage stability margin control via reactive power reserve sensitivities IEEE Trans Power Syst, 28 (2013), pp. 615-625 CrossRefView Record in ScopusGoogle Scholar W. Nakawiro Voltage stability assessment and control of power systems using computational intelligence Ph.D. thesis University of Duisburg-Essen (2011) Google Scholar Ben-Kilani K, Elleuch M. Structural analysis of voltage stability in power systems integrating wind power. IEEE Trans Power Syst. http://dx.doi.org/10.1109/TPWRS.2013.2258043. Google Scholar G.J. Correa, J.M. Yusta Grid vulnerability analysis based on scale-free graphs versus power flow models Electric Power Syst Res, 101 (2013), pp. 71-79 ArticleDownload PDFView Record in ScopusGoogle Scholar C. Bulac, I. Tristiu, A. Mandis, L. Toma On-line power systems voltage stability monitoring using artificial neural networks 2015 9th international symposium on Advanced Topics in Electrical Engineering (ATEE) (2015), pp. 622-625 7–9 May CrossRefView Record in ScopusGoogle Scholar P. Duraipandy, D. Devaraj On-line voltage stability assessment using least squares support vector machine with reduced input features 2014 International Conference on Control, Instrumentation, Communication and Computational Technologies (ICCICCT) (2014), pp. 1070-1074 10–11 July CrossRefView Record in ScopusGoogle Scholar Power system stability subcommittee special publication (Ed.), Voltage stability assessment: concepts, practices, and tools. Product number SP101PSS, IEEE Power Engenieering Society; 2002. ISBN: 0780378695. Google Scholar P.D.O.-D. Jesus, M. Alvarez, J. Yusta Distribution power flow method based on a real quasi-symmetric matrix Electric Power Syst Res, 95 (2013), pp. 148-159 Google Scholar P. Kessel, H. Glavitsch Estimating the voltage stability of a power system IEEE Power Deliv, 1 (3) (1986), pp. 346-354 CrossRefView Record in ScopusGoogle Scholar S. Perez Londono, L. Rodriguez Garcia, Y.U. Lopez Effects of doubly fed wind generators on voltage stability of power systems Proc. Sixth IEEE/PES Transmission and Distribution: Latin American Conf. and Exposition (T&D-LA) (2012), pp. 1-6 CrossRefGoogle Scholar E. Caro, R. Mınguez, A.J. Conejo Robust WLS estimator using reweighting techniques for electric energy systems Electric Power Syst Res, 104 (2013), pp. 9-17 ArticleDownload PDFView Record in ScopusGoogle Scholar N. Zhou, J. Pierre, D. Trudnowski A stepwise regression method for estimating dominant electromechanical modes IEEE Trans Power Syst, 27 (2) (2012), pp. 1051-1059 View Record in ScopusGoogle Scholar M.H. Kutner, C.J. Nachtsheim, J. Neter, W. Li Applied linear statistical models (5th ed.), McGraw-Hill (2005) Google Scholar N. Lahoud, J. Faucher, D. Malec, P. Maussion Electrical aging of the insulation of low-voltage machines: model definition and test with the design of experiments IEEE Trans Industr Electron, 60 (9) (2013), pp. 4147-4155 CrossRefView Record in ScopusGoogle Scholar L. Liu, X. Jin, G. Min, L. Xu Real-time diagnosis of network anomaly based on statistical traffic analysis 2012 IEEE 11th international conference on trust, security and privacy in computing and communications (TrustCom) (2012), pp. 264-270 CrossRefView Record in ScopusGoogle Scholar F. Dufrenois, J. Noyer Formulating robust linear regression estimation as a one-class LDA criterion: discriminative hat matrix IEEE Trans Neural Networks Learn Syst, 24 (2) (2013), pp. 262-273 CrossRefView Record in ScopusGoogle Scholar S. Yin, G. Wang A modified partial robust m-regression to improve prediction performance for data with outliers 2013 IEEE International Symposium on Industrial Electronics (ISIE) (2013), pp. 1-6
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spelling	Posada, Johnnyba0b927fb5d5b9e299f7bd413f450adeRamírez, Juan Manuel8fb8bf4d03c540070dfc234a5969f2eeSanz, Fredya3f0142a35a9dbae45f3406c905220fb2019-09-04T16:22:29Z2019-09-04T16:22:29Z20161879-3517 (en línea)0142-0615 (impresa)http://hdl.handle.net/10614/11046https://doi.org/10.1016/j.ijepes.2016.03.035Universidad Autónoma de OccidenteRepositorio Educativo Digital UAOThis paper is aimed to propose a reliable method for estimating the voltage collapse proximity through a model obtained using statistical techniques. In the model building process a database is required, therefore the Voltage Collapse Proximity Index (VCPI) is used to obtain previous readings for different contingencies and loading conditions. This analytical proposal could be combined with existing equipment in the power system control centers for future on-line applications. The proposed method is applied to the IEEE 14-bus test system and the 190-bus Mexican equivalent. Results indicate that the proposed strategy is a reliable choice7 páginasapplication/pdfengElsevier LtdDerechos Reservados Elsevierhttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2Statistical method for on-line voltage collapse proximity estimationArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTREFinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Sistemas eléctricosSistemas de energía eléctricaCentrales eléctricasElectrical systemsElectric power systemsElectric power systemsIngeniería eléctricaElectricidadElectricityElectric engineeringStatisticVoltage stabilityVoltage collapseEstimationVolumen 82 (noviembre 2016)39982392Sanz, F. A., Ramirez, J. M., & Posada, J. (2016). Statistical method for on-line voltage collapse proximity estimation. International Journal of Electrical Power & Energy Systems, 82, p.392-399International journal of electrical power & energy systemsJ.-H. Teng, C.-Y. Chen, I. Martinez, C.-F. Chen Power system vulnerability assessment considering energy storage systems 2013 IEEE 10th international conference on Power Electronics and Drive Systems (PEDS) (2013), pp. 903-907 View Record in ScopusGoogle ScholarO.A. Mousavi, M. Bozorg, R. Cherkaoui Preventive reactive power management for improving voltage stability margin Electric Power Syst Res, 96 (2013), pp. 36-46 Google ScholarE. Zio, G. Sansavini Vulnerability of smart grids with variable generation and consumption: a system of systems perspective IEEE Trans Syst Man Cybern, 43 (3) (2013), pp. 477-487 CrossRefView Record in ScopusGoogle ScholarA. de Souza, J.C.S. De Souza, A. Leite da Silva On-line voltage stability monitoring IEEE Trans Power Syst, 15 (4) (2000), pp. 1300-1305 CrossRefGoogle ScholarV. Balamourougan, T.S. Sidhu, M.S. Sachdev Technique for online prediction of voltage collapse IEE Proc Gener Transm Distrib, 151 (4) (2004), pp. 453-460 View Record in ScopusGoogle ScholarA. Berizzi, C. Bovo, D. Cirio, M. Delfanti, M. Merlo, M. Pozzi Online fuzzy voltage collapse risk quantification Electric Power Syst Res, 79 (5) (2009), pp. 740-749 ArticleDownload PDFView Record in ScopusGoogle ScholarL. Sanchez, I. Couso, J.C. Viera Online SOC estimation of Li-FePO4 batteries through a new fuzzy rule-based recursive filter with feedback of the heat flow rate Vehicle Power and Propulsion Conference (VPPC), 2014 IEEE (2014), pp. 1-6 27–30 October CrossRefGoogle ScholarF.A. Althowibi, M. Mustafa On-line voltage collapse indicator for power systems 2010 IEEE international conference on power and energy (PECon) (2010), pp. 408-413 View Record in ScopusGoogle ScholarH.-D. Chiang, H. Li, J. Tong, P. Causgrove On-line voltage stability monitoring of large power systems 2011 IEEE power and energy society general meeting (2011), pp. 1-6 CrossRefGoogle ScholarD.T. Duong, K. Uhlen Online voltage stability monitoring based on PMU measurements and system topology 2013 3rd international conference on Electric Power and Energy Conversion Systems (EPECS) (2013), pp. 1-6 2–4 October CrossRefView Record in ScopusGoogle ScholarS.S. Biswas, C.B. Vellaithurai, A.K. Srivastava Development and real time implementation of a synchrophasor based fast voltage stability monitoring algorithm with consideration of load models Industry applications society annual meeting, 2013 IEEE (2013), pp. 1-9 6–11 October CrossRefView Record in ScopusGoogle ScholarFengkai Hu, Kai Sun, A. Del Rosso, E. Farantatos, N. Bhatt An adaptive three-bus power system equivalent for estimating voltage stability margin from synchronized phasor measurements PES general meeting \| conference & exposition, 2014 IEEE (2014), pp. 1-5 27–31 July CrossRefView Record in ScopusGoogle ScholarS. Maslennikov, E. Litvinov, M. Vaiman, M. Vaiman Implementation of ROSE for on-line voltage stability analysis at ISO New England PES general meeting \| conference & exposition, 2014 IEEE (2014), pp. 1-5 27–31 July CrossRefGoogle ScholarS. Varshney, L. Srivastava, M. Pandit, M. Sharma Voltage stability based contingency ranking using distributed computing environment 2013 International Conference on Power, Energy and Control (ICPEC) (2013), pp. 208-212 View Record in ScopusGoogle ScholarS. DasGupta, M. Paramasivam, U. Vaidya, V. Ajjarapu, Real-time monitoring of short-term voltage stability using PMU data. IEEE Trans Power Syst. http://dx.doi.org/10.1109/TPWRS.2013.2258946. Google ScholarB. Leonardi, V. Ajjarapu An approach for real time voltage stability margin control via reactive power reserve sensitivities IEEE Trans Power Syst, 28 (2013), pp. 615-625 CrossRefView Record in ScopusGoogle ScholarW. Nakawiro Voltage stability assessment and control of power systems using computational intelligence Ph.D. thesis University of Duisburg-Essen (2011) Google ScholarBen-Kilani K, Elleuch M. Structural analysis of voltage stability in power systems integrating wind power. IEEE Trans Power Syst. http://dx.doi.org/10.1109/TPWRS.2013.2258043. Google ScholarG.J. Correa, J.M. Yusta Grid vulnerability analysis based on scale-free graphs versus power flow models Electric Power Syst Res, 101 (2013), pp. 71-79 ArticleDownload PDFView Record in ScopusGoogle ScholarC. Bulac, I. Tristiu, A. Mandis, L. Toma On-line power systems voltage stability monitoring using artificial neural networks 2015 9th international symposium on Advanced Topics in Electrical Engineering (ATEE) (2015), pp. 622-625 7–9 May CrossRefView Record in ScopusGoogle ScholarP. Duraipandy, D. Devaraj On-line voltage stability assessment using least squares support vector machine with reduced input features 2014 International Conference on Control, Instrumentation, Communication and Computational Technologies (ICCICCT) (2014), pp. 1070-1074 10–11 July CrossRefView Record in ScopusGoogle ScholarPower system stability subcommittee special publication (Ed.), Voltage stability assessment: concepts, practices, and tools. Product number SP101PSS, IEEE Power Engenieering Society; 2002. ISBN: 0780378695. Google ScholarP.D.O.-D. Jesus, M. Alvarez, J. Yusta Distribution power flow method based on a real quasi-symmetric matrix Electric Power Syst Res, 95 (2013), pp. 148-159 Google ScholarP. Kessel, H. Glavitsch Estimating the voltage stability of a power system IEEE Power Deliv, 1 (3) (1986), pp. 346-354 CrossRefView Record in ScopusGoogle ScholarS. Perez Londono, L. Rodriguez Garcia, Y.U. Lopez Effects of doubly fed wind generators on voltage stability of power systems Proc. Sixth IEEE/PES Transmission and Distribution: Latin American Conf. and Exposition (T&D-LA) (2012), pp. 1-6 CrossRefGoogle ScholarE. Caro, R. Mınguez, A.J. Conejo Robust WLS estimator using reweighting techniques for electric energy systems Electric Power Syst Res, 104 (2013), pp. 9-17 ArticleDownload PDFView Record in ScopusGoogle ScholarN. Zhou, J. Pierre, D. Trudnowski A stepwise regression method for estimating dominant electromechanical modes IEEE Trans Power Syst, 27 (2) (2012), pp. 1051-1059 View Record in ScopusGoogle ScholarM.H. Kutner, C.J. Nachtsheim, J. Neter, W. Li Applied linear statistical models (5th ed.), McGraw-Hill (2005) Google ScholarN. Lahoud, J. Faucher, D. Malec, P. Maussion Electrical aging of the insulation of low-voltage machines: model definition and test with the design of experiments IEEE Trans Industr Electron, 60 (9) (2013), pp. 4147-4155 CrossRefView Record in ScopusGoogle ScholarL. Liu, X. Jin, G. Min, L. Xu Real-time diagnosis of network anomaly based on statistical traffic analysis 2012 IEEE 11th international conference on trust, security and privacy in computing and communications (TrustCom) (2012), pp. 264-270 CrossRefView Record in ScopusGoogle ScholarF. Dufrenois, J. Noyer Formulating robust linear regression estimation as a one-class LDA criterion: discriminative hat matrix IEEE Trans Neural Networks Learn Syst, 24 (2) (2013), pp. 262-273 CrossRefView Record in ScopusGoogle ScholarS. Yin, G. Wang A modified partial robust m-regression to improve prediction performance for data with outliers 2013 IEEE International Symposium on Industrial Electronics (ISIE) (2013), pp. 1-6PublicationCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/f9f20997-31f9-4674-88f9-ad065b55a1b4/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/c07170ae-b469-492b-b9d4-94ae76c7617e/download20b5ba22b1117f71589c7318baa2c560MD5310614/11046oai:red.uao.edu.co:10614/110462024-05-10 09:48:44.123https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos Reservados Elseviermetadata.onlyhttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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

Statistical method for on-line voltage collapse proximity estimation

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