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Article: A method for direct calculation of quadratic turning points
Title  A method for direct calculation of quadratic turning points 

Authors  
Issue Date  2004 
Publisher  The Institution of Engineering and Technology. The Journal's web site is located at http://www.ietdl.org/IPGTD 
Citation  IET Generation, Transmission and Distribution, 2004, v. 151 n. 1, p. 8389 How to Cite? 
Abstract  For a given oneparameter nonlinear system, the simplest bifurcation is the quadratic turning bifurcation where the Jacobian matrix becomes singular due to rank deficiency 1. To overcome the difficulty in solving the quadratic turning point caused by the singularity of the Jacobian matrix, the conventional Newton method can be applied to the socalled MooreSpence determination system to solve for the quadratic turning point. However, the MooreSpence system has much higher dimensions and causes much more complexity in factorisation of the extended Jacobian matrix. In the paper, by introducing an auxiliary variable and an auxiliary linear equation into Newton iterations in solving the MooreSpence determination system, a matrix reduction technique can be worked out to solve the MooreSpence extended equations much more efficiently. The high dimensions of the matrix can thus be reduced and the complexity involved in matrix factorisation can be reduced noticeably. The technique is proposed for general nonlinear systems. Formulation is derived for applying this technique to solving quadratic turning points, or say nose points, on loadflow solution curves of power systems. Computer tests on the IEEE 30busbar system and a 2416busbar East China power system are reported to show the effectiveness of the suggested technique. 
Persistent Identifier  http://hdl.handle.net/10722/73586 
ISSN  2015 Impact Factor: 1.576 2015 SCImago Journal Rankings: 1.332 
DC Field  Value  Language 

dc.contributor.author  Yan, Z   
dc.contributor.author  Liu, Y   
dc.contributor.author  Wu, F   
dc.contributor.author  Ni, Y   
dc.date.accessioned  20100906T06:52:48Z   
dc.date.available  20100906T06:52:48Z   
dc.date.issued  2004   
dc.identifier.citation  IET Generation, Transmission and Distribution, 2004, v. 151 n. 1, p. 8389   
dc.identifier.issn  17518687   
dc.identifier.uri  http://hdl.handle.net/10722/73586   
dc.description.abstract  For a given oneparameter nonlinear system, the simplest bifurcation is the quadratic turning bifurcation where the Jacobian matrix becomes singular due to rank deficiency 1. To overcome the difficulty in solving the quadratic turning point caused by the singularity of the Jacobian matrix, the conventional Newton method can be applied to the socalled MooreSpence determination system to solve for the quadratic turning point. However, the MooreSpence system has much higher dimensions and causes much more complexity in factorisation of the extended Jacobian matrix. In the paper, by introducing an auxiliary variable and an auxiliary linear equation into Newton iterations in solving the MooreSpence determination system, a matrix reduction technique can be worked out to solve the MooreSpence extended equations much more efficiently. The high dimensions of the matrix can thus be reduced and the complexity involved in matrix factorisation can be reduced noticeably. The technique is proposed for general nonlinear systems. Formulation is derived for applying this technique to solving quadratic turning points, or say nose points, on loadflow solution curves of power systems. Computer tests on the IEEE 30busbar system and a 2416busbar East China power system are reported to show the effectiveness of the suggested technique.   
dc.language  eng   
dc.publisher  The Institution of Engineering and Technology. The Journal's web site is located at http://www.ietdl.org/IPGTD   
dc.relation.ispartof  IET Generation, Transmission and Distribution   
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.title  A method for direct calculation of quadratic turning points   
dc.type  Article   
dc.identifier.email  Yan, Z: zhengyan_cu@yahoo.com   
dc.identifier.email  Wu, F: ffwu@eee.hku.hk   
dc.identifier.email  Ni, Y: yxni@eee.hku.hk   
dc.identifier.authority  Ni, Y=rp00161   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.1049/ipgtd:20030940   
dc.identifier.hkuros  89811   
dc.identifier.volume  151   
dc.identifier.issue  1   
dc.identifier.spage  83   
dc.identifier.epage  89   
dc.publisher.place  United Kingdom   