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Conference Paper: Study of multisolution quadratic load flow problems and applied NewtonRaphson like methods
Title  Study of multisolution quadratic load flow problems and applied NewtonRaphson like methods 

Authors  
Issue Date  1995 
Citation  Proceedings  Ieee International Symposium On Circuits And Systems, 1995, v. 2, p. 15081511 How to Cite? 
Abstract  A 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 NewtonRaphson 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 colinear 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 Identifier  http://hdl.handle.net/10722/169776 
ISSN 
DC Field  Value  Language 

dc.contributor.author  Makarov, Yuri V  en_US 
dc.contributor.author  Hiskens, Ian a  en_US 
dc.contributor.author  Hill, David J  en_US 
dc.date.accessioned  20121025T04:55:34Z   
dc.date.available  20121025T04:55:34Z   
dc.date.issued  1995  en_US 
dc.identifier.citation  Proceedings  Ieee International Symposium On Circuits And Systems, 1995, v. 2, p. 15081511  en_US 
dc.identifier.issn  02714310  en_US 
dc.identifier.uri  http://hdl.handle.net/10722/169776   
dc.description.abstract  A 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 NewtonRaphson 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 colinear 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.language  eng  en_US 
dc.relation.ispartof  Proceedings  IEEE International Symposium on Circuits and Systems  en_US 
dc.title  Study of multisolution quadratic load flow problems and applied NewtonRaphson like methods  en_US 
dc.type  Conference_Paper  en_US 
dc.identifier.email  Hill, David J:  en_US 
dc.identifier.authority  Hill, David J=rp01669  en_US 
dc.description.nature  link_to_subscribed_fulltext  en_US 
dc.identifier.scopus  eid_2s2.00029192780  en_US 
dc.identifier.volume  2  en_US 
dc.identifier.spage  1508  en_US 
dc.identifier.epage  1511  en_US 
dc.identifier.scopusauthorid  Makarov, Yuri V=35461311800  en_US 
dc.identifier.scopusauthorid  Hiskens, Ian a=7006588301  en_US 
dc.identifier.scopusauthorid  Hill, David J=35398599500  en_US 