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 - <p style="text-align: justify;">&nbsp;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.</p>