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Interior‐point methods applied to the AC active‐reactive optimal power‐flow problem using cartesian coordinates
Author(s) -
Probst Roy,
Oliveira Aurelio,
Soares Secundino,
Thomaz Adriano
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700375
Subject(s) - hessian matrix , interior point method , cartesian coordinate system , polar coordinate system , dimension (graph theory) , mathematical optimization , representation (politics) , taylor series , karush–kuhn–tucker conditions , mathematics , ac power , flow (mathematics) , generalized coordinates , point (geometry) , computer science , power (physics) , mathematical analysis , geometry , physics , law , quantum mechanics , politics , political science , pure mathematics
The primal dual interior point methods are developed to the AC active and reactive optimal power flow problem. The representation of the tensions through cartesian coordinates is adopted, once the Hessian is constant and the Taylor expansion is accurate for the second order term. The advantage of working with polar coordinates, that easily model the tension magnitudes, lose importance due to the efficient treatment of inequalities proportionated by the interior point methods. Before the application of the method, the number of variables of the problem is reduced through the elimination of free dual variables. This elimination does not modify the sparse pattern of the problem. The linear system obtained can be further reduced to the dimension of twice the number of buses also with minor changes in the sparse structure of the matrices involved. Moreover, the final matrix is symmetric in structure. This feature can be exploited reducing the computational effort per iteration. Computational experiments for IEEE system problems are presented for several starting point strategies showing the advantages of the proposed approach. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)