Journal ArticleDOI
A locally parameterized continuation process
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The design of a package of continuation procedures called PITCON to handle the following tasks is described: follow numerically any a priori specified curve on an equilibrium manifold determine the exact location of target points where a given variable has a specified value.Abstract:
The design of a package of continuation procedures called PITCON to handle the following tasks is described' (1) follow numerically any a priori specified curve on an equilibrium manifold; (2) on such a curve determine the exact location of target points where a given variable has a specified value; and (3) on such a curve identify and compute exactly the (simple) limit points where stability may be lost. The process is based on the local parametenzatmn wh]ch uses an estimate of the curvature to control the chome of parameter varmble. Categorms and Subject Descriptors. G 1.5 [Numerical Analysis]Roots of Nonlinear Equations-tteratwe methods, systems of equattons General Terms" Algorithms, Design Addltmnalread more
Citations
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Journal ArticleDOI
The continuation power flow: a tool for steady state voltage stability analysis
TL;DR: In this paper, the authors present a method of finding a continuum of power flow solutions starting at some base load and leading to the steady-state voltage stability limit (critical point) of the system.
Journal ArticleDOI
Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space
Ulrich Maas,Stephen B. Pope +1 more
TL;DR: In this article, a general procedure for simplifying chemical kinetics is developed, based on the dynamical systems approach, in contrast to conventional reduced mechanisms no information is required concerning which reactions are to be assumed to be in partial equilibrium nor which species are assumed to remain in steady state.
Journal ArticleDOI
Exact coherent structures in pipe flow: travelling wave solutions
Håkan Wedin,Richard R Kerswell +1 more
TL;DR: In this paper, three-dimensional travelling wave solutions for pressure-driven fluid flow through a circular pipe are found for wall-bounded shear flows using a constructive continuation procedure based on key physical mechanisms.
Journal ArticleDOI
Available transfer capability calculations
TL;DR: In this article, a program for available (transmission) transfer capability (ATC) calculations based on full AC power flow solution to incorporate the effects of reactive power flows, voltage limits and voltage collapse as well as the traditional line flow (thermal loading) effects is presented.
Journal ArticleDOI
Continuation and path following
Eugene L. Allgower,Kurt Georg +1 more
TL;DR: The main ideas of path following by predictor–corrector and piecewise-linear methods, and their application in the direction of homotopy methods and nonlinear eigenvalue problems are reviewed.
References
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Book
Algorithms for Minimization Without Derivatives
TL;DR: In this paper, a monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions, and some of these methods can be used to find approximate minima as well.
Journal ArticleDOI
An incremental approach to the solution of snapping and buckling problems
TL;DR: In this paper, an incremental approach to the solution of buckling and snapping problems is explored, where the authors use the length of the equilibrium path as a control parameter, together with the second order iteration method of Newton.
Journal ArticleDOI
A fast incremental/iterative solution procedure that handles "snap-through"
TL;DR: In this article, a modified version of the Newton-Raphson method is proposed to overcome limit points in the finite element method with a fixed load level and a constraint equation.