Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values
Autor(a) principal: | |
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Data de Publicação: | 2007 |
Outros Autores: | , |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1109/PCT.2007.4538299 http://hdl.handle.net/11449/70025 |
Resumo: | This paper presents an analyze of numeric conditioning of the Hessian matrix of Lagrangian of modified barrier function Lagrangian method (MBFL) and primal-dual logarithmic barrier method (PDLB), which are obtained in the process of solution of an optimal power flow problem (OPF). This analyze is done by a comparative study through the singular values decomposition (SVD) of those matrixes. In the MBLF method the inequality constraints are treated by the modified barrier and PDLB methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables and are perturbed by the barrier parameter. The first-order necessary conditions of the Lagrangian function are solved by Newton's method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. The electric systems IEEE 14, 162 and 300 buses were used in the comparative analysis. ©2007 IEEE. |
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Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular valuesModified barrier functionNewton's methodNonlinear programmingOptimal power flowMathematical modelsMatrix algebraNewton-Raphson methodPower electronicsInequality constraintsLagrange multipliersThis paper presents an analyze of numeric conditioning of the Hessian matrix of Lagrangian of modified barrier function Lagrangian method (MBFL) and primal-dual logarithmic barrier method (PDLB), which are obtained in the process of solution of an optimal power flow problem (OPF). This analyze is done by a comparative study through the singular values decomposition (SVD) of those matrixes. In the MBLF method the inequality constraints are treated by the modified barrier and PDLB methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables and are perturbed by the barrier parameter. The first-order necessary conditions of the Lagrangian function are solved by Newton's method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. The electric systems IEEE 14, 162 and 300 buses were used in the comparative analysis. ©2007 IEEE.IEEEElectrical Engineering Department Engineering School of São Carlos University of São PauloElectrical Engineering Department Engineering School of São Carlos University of São Paulo, São Carlos, SP 13566-590Department of Mathematics São Paulo State University (UNESP), BauruDepartment of Mathematics São Paulo State University (UNESP), BauruIEEEUniversidade de São Paulo (USP)Universidade Estadual Paulista (Unesp)De Sousa, V. A.Baptista, Edméa Cássia [UNESP]Da Costa, G. R M2014-05-27T11:22:39Z2014-05-27T11:22:39Z2007-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject98-102http://dx.doi.org/10.1109/PCT.2007.45382992007 IEEE Lausanne POWERTECH, Proceedings, p. 98-102.http://hdl.handle.net/11449/7002510.1109/PCT.2007.45382992-s2.0-5084909665784796874045269580000-0002-5642-8925Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPeng2007 IEEE Lausanne POWERTECH, Proceedingsinfo:eu-repo/semantics/openAccess2024-04-29T14:59:56Zoai:repositorio.unesp.br:11449/70025Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-04-29T14:59:56Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values |
title |
Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values |
spellingShingle |
Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values De Sousa, V. A. Modified barrier function Newton's method Nonlinear programming Optimal power flow Mathematical models Matrix algebra Newton-Raphson method Power electronics Inequality constraints Lagrange multipliers |
title_short |
Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values |
title_full |
Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values |
title_fullStr |
Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values |
title_full_unstemmed |
Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values |
title_sort |
Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values |
author |
De Sousa, V. A. |
author_facet |
De Sousa, V. A. Baptista, Edméa Cássia [UNESP] Da Costa, G. R M |
author_role |
author |
author2 |
Baptista, Edméa Cássia [UNESP] Da Costa, G. R M |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
IEEE Universidade de São Paulo (USP) Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
De Sousa, V. A. Baptista, Edméa Cássia [UNESP] Da Costa, G. R M |
dc.subject.por.fl_str_mv |
Modified barrier function Newton's method Nonlinear programming Optimal power flow Mathematical models Matrix algebra Newton-Raphson method Power electronics Inequality constraints Lagrange multipliers |
topic |
Modified barrier function Newton's method Nonlinear programming Optimal power flow Mathematical models Matrix algebra Newton-Raphson method Power electronics Inequality constraints Lagrange multipliers |
description |
This paper presents an analyze of numeric conditioning of the Hessian matrix of Lagrangian of modified barrier function Lagrangian method (MBFL) and primal-dual logarithmic barrier method (PDLB), which are obtained in the process of solution of an optimal power flow problem (OPF). This analyze is done by a comparative study through the singular values decomposition (SVD) of those matrixes. In the MBLF method the inequality constraints are treated by the modified barrier and PDLB methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables and are perturbed by the barrier parameter. The first-order necessary conditions of the Lagrangian function are solved by Newton's method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. The electric systems IEEE 14, 162 and 300 buses were used in the comparative analysis. ©2007 IEEE. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007-12-01 2014-05-27T11:22:39Z 2014-05-27T11:22:39Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1109/PCT.2007.4538299 2007 IEEE Lausanne POWERTECH, Proceedings, p. 98-102. http://hdl.handle.net/11449/70025 10.1109/PCT.2007.4538299 2-s2.0-50849096657 8479687404526958 0000-0002-5642-8925 |
url |
http://dx.doi.org/10.1109/PCT.2007.4538299 http://hdl.handle.net/11449/70025 |
identifier_str_mv |
2007 IEEE Lausanne POWERTECH, Proceedings, p. 98-102. 10.1109/PCT.2007.4538299 2-s2.0-50849096657 8479687404526958 0000-0002-5642-8925 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2007 IEEE Lausanne POWERTECH, Proceedings |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
98-102 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799964785031249920 |