论文信息 - An acceleration technique for the newton solution of quadratic equations

An acceleration technique for the newton solution of quadratic equations

Abstract The Newton method applied to certain quadratic operator equations on R n is considered. It is shown that there exists an invariant manifold corresponding to any pair of real or complex conjugate roots of the equation. These manifolds have significant application in finding neighboring solutions to the power flow problem in electric power systems.

[1] Y. Tamura,et al. A Load Flow Calculation Method for Ill-Conditioned Power Systems , 1981, IEEE Transactions on Power Apparatus and Systems.

[2] L. B. Rall. Convergence of the newton process to multiple solutions , 1966 .

[3] Y. Wallach,et al. Calculations and Programs for Power System Networks , 1986 .

[4] L. B. Rall. On the Uniqueness of Solutions of Quadratic Equations , 1969 .

[5] F.D. Galiana. Analytical Investigation of the Power Flow Equations , 1983, 1983 American Control Conference.

[6] K. Okuda,et al. Load Flow Convergence in the Vicinity of a Voltage Stability Limit , 1978, IEEE Transactions on Power Apparatus and Systems.

[7] L. B. Rall. Quadratic equations in Banach spaces , 1961 .

[8] K. Iba,et al. A method for finding a pair of multiple load flow solutions in bulk power systems , 1989, Conference Papers Power Industry Computer Application Conference.