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Volume 22, Issue 1
Application of Homotopy Methods to Power Systems

Dayong Cai & Yurong Chen

J. Comp. Math., 22 (2004), pp. 61-68.

Published online: 2004-02

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  • Abstract

 In this paper, the application of homotopy methods to the load flow multi-solution problems of power systems is introduced. By the generalized Bernshtein theorem, the combinatorial number $C_{2n}^n$ is shown to be the BKK bound of the number of isolated solutions of the polynomial system transformed from load flow equations with generically chosen coefficients. As a result of the general Bezout number, the number of paths being followed is reduced significantly in the practical load flow computation. Finally, the complete P-V cures are obtained by tracking the load flow with homotopy methods.

  • Keywords

Homotopy methods, Bezout number, Bernshtein-Khoranski-Kushnirenko (BKK), bound, Load flow computations.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-61, author = {Cai , Dayong and Chen , Yurong}, title = {Application of Homotopy Methods to Power Systems}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {1}, pages = {61--68}, abstract = {

 In this paper, the application of homotopy methods to the load flow multi-solution problems of power systems is introduced. By the generalized Bernshtein theorem, the combinatorial number $C_{2n}^n$ is shown to be the BKK bound of the number of isolated solutions of the polynomial system transformed from load flow equations with generically chosen coefficients. As a result of the general Bezout number, the number of paths being followed is reduced significantly in the practical load flow computation. Finally, the complete P-V cures are obtained by tracking the load flow with homotopy methods.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10334.html} }
TY - JOUR T1 - Application of Homotopy Methods to Power Systems AU - Cai , Dayong AU - Chen , Yurong JO - Journal of Computational Mathematics VL - 1 SP - 61 EP - 68 PY - 2004 DA - 2004/02 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10334.html KW - Homotopy methods, Bezout number, Bernshtein-Khoranski-Kushnirenko (BKK), bound, Load flow computations. AB -

 In this paper, the application of homotopy methods to the load flow multi-solution problems of power systems is introduced. By the generalized Bernshtein theorem, the combinatorial number $C_{2n}^n$ is shown to be the BKK bound of the number of isolated solutions of the polynomial system transformed from load flow equations with generically chosen coefficients. As a result of the general Bezout number, the number of paths being followed is reduced significantly in the practical load flow computation. Finally, the complete P-V cures are obtained by tracking the load flow with homotopy methods.

Cai , Dayong and Chen , Yurong. (2004). Application of Homotopy Methods to Power Systems. Journal of Computational Mathematics. 22 (1). 61-68. doi:
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