Based on the discussion of the number of roots of univariate spline and the common zero points of two piecewise algebraic curves, a lower upbound of Bezout number of two piecewise algebraic curves on any given non-obt...Based on the discussion of the number of roots of univariate spline and the common zero points of two piecewise algebraic curves, a lower upbound of Bezout number of two piecewise algebraic curves on any given non-obtuse-angled triangulation is found. Bezout number of two piecewise algebraic curves on two different partitions is also discussed in this paper.展开更多
Load flow computations are the basis for voltage security assessments in power systems. All of the flow equation solutions must be computed to explore the mechanisms of voltage instability and voltage collapse. Conv...Load flow computations are the basis for voltage security assessments in power systems. All of the flow equation solutions must be computed to explore the mechanisms of voltage instability and voltage collapse. Conventional algorithms, such as Newton's methods and its variations, are not very desirable because they can not be easily used to find all of the solutions. This paper investigates homotopy methods which can be used for numerically computing the set of all isolated solutions of multivariate polynomial systems resulting from load flow computations. The results significantly reduce the number of paths being followed.展开更多
基金Supported by the Educational Commission of Hebei Province of China (Grant No. Z2010260)National Natural Science Foundation of China (Grant Nos. 11126213 and 61170317)
文摘Based on the discussion of the number of roots of univariate spline and the common zero points of two piecewise algebraic curves, a lower upbound of Bezout number of two piecewise algebraic curves on any given non-obtuse-angled triangulation is found. Bezout number of two piecewise algebraic curves on two different partitions is also discussed in this paper.
基金the National Key Basic Research SpecialFund (No. 19980 2 0 30 6 ) the National NaturalScience Foundation of China (No.198710 47)
文摘Load flow computations are the basis for voltage security assessments in power systems. All of the flow equation solutions must be computed to explore the mechanisms of voltage instability and voltage collapse. Conventional algorithms, such as Newton's methods and its variations, are not very desirable because they can not be easily used to find all of the solutions. This paper investigates homotopy methods which can be used for numerically computing the set of all isolated solutions of multivariate polynomial systems resulting from load flow computations. The results significantly reduce the number of paths being followed.
