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Conference Paper: Study of multisolution quadratic load flow problems and applied Newton-Raphson like methods

TitleStudy of multisolution quadratic load flow problems and applied Newton-Raphson like methods
Authors
Issue Date1995
Citation
Proceedings - Ieee International Symposium On Circuits And Systems, 1995, v. 2, p. 1508-1511 How to Cite?
AbstractA number of facts about quadratic load flow problems y = f(x) = 0, x ε ∈ x n, y ε R y n is proved. The main results are the following [1]. If any point x belongs to a straight line connecting a pair of distinct solutions in the state space R x n, the Newton-Raphson iterative process goes along this line. If a loading process y(β) reaches a singular point of the problem, the corresponding trajectory of state variables x(β) in R x n tends to the right eigenvector nullifying the Jacobian matrix at the singular point. In any singular point of the quadratic problem. there are two solutions which merge at this point. The maximum number of solutions on any straight line in state the space R x n is two. Along a straight line through two distinct solutions of a quadratic problem, this problem can be reduced to a single scalar quadratic equation which locates these solutions. In addition, a number of other properties is reported. New proofs of them are given. There is a point of singularity in the middle of a straight line connecting a pair of distinct solutions in the state space R x n [2, 3, 4]. A vector co-linear to a straight line connecting a pair of distinct solutions in R x n nullifies the Jacobian matrix at the point of singularity in the middle of the line [2, 3].
Persistent Identifierhttp://hdl.handle.net/10722/169776
ISSN

 

DC FieldValueLanguage
dc.contributor.authorMakarov, Yuri Ven_US
dc.contributor.authorHiskens, Ian aen_US
dc.contributor.authorHill, David Jen_US
dc.date.accessioned2012-10-25T04:55:34Z-
dc.date.available2012-10-25T04:55:34Z-
dc.date.issued1995en_US
dc.identifier.citationProceedings - Ieee International Symposium On Circuits And Systems, 1995, v. 2, p. 1508-1511en_US
dc.identifier.issn0271-4310en_US
dc.identifier.urihttp://hdl.handle.net/10722/169776-
dc.description.abstractA number of facts about quadratic load flow problems y = f(x) = 0, x ε ∈ x n, y ε R y n is proved. The main results are the following [1]. If any point x belongs to a straight line connecting a pair of distinct solutions in the state space R x n, the Newton-Raphson iterative process goes along this line. If a loading process y(β) reaches a singular point of the problem, the corresponding trajectory of state variables x(β) in R x n tends to the right eigenvector nullifying the Jacobian matrix at the singular point. In any singular point of the quadratic problem. there are two solutions which merge at this point. The maximum number of solutions on any straight line in state the space R x n is two. Along a straight line through two distinct solutions of a quadratic problem, this problem can be reduced to a single scalar quadratic equation which locates these solutions. In addition, a number of other properties is reported. New proofs of them are given. There is a point of singularity in the middle of a straight line connecting a pair of distinct solutions in the state space R x n [2, 3, 4]. A vector co-linear to a straight line connecting a pair of distinct solutions in R x n nullifies the Jacobian matrix at the point of singularity in the middle of the line [2, 3].en_US
dc.languageengen_US
dc.relation.ispartofProceedings - IEEE International Symposium on Circuits and Systemsen_US
dc.titleStudy of multisolution quadratic load flow problems and applied Newton-Raphson like methodsen_US
dc.typeConference_Paperen_US
dc.identifier.emailHill, David J:en_US
dc.identifier.authorityHill, David J=rp01669en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0029192780en_US
dc.identifier.volume2en_US
dc.identifier.spage1508en_US
dc.identifier.epage1511en_US
dc.identifier.scopusauthoridMakarov, Yuri V=35461311800en_US
dc.identifier.scopusauthoridHiskens, Ian a=7006588301en_US
dc.identifier.scopusauthoridHill, David J=35398599500en_US

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