Application of Homotopy Methods to Power Systems (Journal of Computational Mathematics, 2004)
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.