arXiv subjects

Elizabeth Wong

Publications and source records attributed to Elizabeth Wong.

4 recordsLinked to original sources

arXiv2022

Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition

The optimal power flow problem is central to many tasks in the design and operation of electric power grids. This problem seeks the minimum cost operating point for an electric power grid while satisfying both engineering requirements and physical laws describing how power flows through the electric network. By additionally considering the possibility of component failures and using an accurate AC power flow model of the electric network, the security-constrained AC optimal power flow (SC-AC-OPF) problem is of paramount practical relevance. To assess recent progress in solution algorithms for SC-AC-OPF problems and spur new innovations, the U.S. Department of Energy's Advanced Research Projects Agency--Energy (ARPA-E) organized Challenge 1 of the Grid Optimization (GO) competition. This paper describes the SC-AC-OPF problem formulation used in the competition, overviews historical developments and the state of the art in SC-AC-OPF algorithms, discusses the competition, and summarizes the algorithms used by the top three teams in Challenge 1 of the GO Competition (Teams gollnlp, GO-SNIP, and GMI-GO).

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arXiv2021

Projected-Search Methods for Bound-Constrained Optimization

Projected-search methods for bound-constrained optimization are based on performing a search along a piecewise-linear continuous path obtained by projecting a search direction onto the feasible region. A benefit of these methods is that many changes to the active set can be made at the cost of computing a single search direction. As the objective function is not differentiable along the search path, it is not possible to use a projected-search method with a step that satisfies the Wolfe conditions, which require the directional derivative of the objective function at a point on the path. Thus, methods based on a simple backtracking procedure must be used to give a step that satisfies an "Armijo-like" sufficient decrease condition. As a consequence, conventional projected-search methods are unable to exploit sophisticated safeguarded polynomial interpolation techniques that have been shown to be effective for the unconstrained case. This paper concerns the formulation and analysis of projected-search methods based on a new quasi-Wolfe line search that is appropriate for piecewise differentiable functions. The behavior of the line search is similar to conventional Wolfe line search, except that a step is accepted under a wider range of conditions. These conditions take into consideration steps at which the restriction of the objective function on the search path is not differentiable. Two new classes of method are proposed that may be broadly categorized as active-set and interior-point methods. Computational results are given for two specific methods from these general classes: a projected-search active-set method that uses a limited-memory quasi-Newton approximation of the Hessian; and a projected-search primal-dual interior-point method. The results show that in these contexts, a quasi-Wolfe line search is substantially more efficient and reliable than an Armijo line search.

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arXiv2021

A Decomposition Algorithm for Large-Scale Security-Constrained AC Optimal Power Flow

A decomposition algorithm for solving large-scale security-constrained AC optimal power flow problems is presented. The formulation considered is the one used in the ARPA-E Grid Optimization (GO) Competition, Challenge 1, held from November 2018 through October 2019. The techniques found to be most effective in terms of performance in the challenge are presented, including strategies for contingency selection, fast contingency evaluation, handling complementarity constraints, avoiding issues related to degeneracy, and exploiting parallelism. The results of numerical experiments are provided to demonstrate the effectiveness of the proposed techniques as compared to alternative strategies.

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arXiv2015

Primal and dual active-set methods for convex quadratic programming

Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables. In the first part of the paper, two methods are proposed, one primal and one dual. These methods generate a sequence of iterates that are feasible with respect to the equality constraints associated with the optimality conditions of the primal-dual form. The primal method maintains feasibility of the primal inequalities while driving the infeasibilities of the dual inequalities to zero. The dual method maintains feasibility of the dual inequalities while moving to satisfy the primal inequalities. In each of these methods, the search directions satisfy a KKT system of equations formed from Hessian and constraint components associated with an appropriate column basis. The composition of the basis is specified by an active-set strategy that guarantees the nonsingularity of each set of KKT equations. Each of the proposed methods is a conventional active-set method in the sense that an initial primal- or dual-feasible point is required. In the second part of the paper, it is shown how the quadratic program may be solved as a coupled pair of primal and dual quadratic programs created from the original by simultaneously shifting the simple-bound constraints and adding a penalty term to the objective function. Any conventional column basis may be made optimal for such a primal-dual pair of shifted-penalized problems. The shifts are then updated using the solution of either the primal or the dual shifted problem. An obvious application of this approach is to solve a shifted dual QP to define an initial feasible point for the primal (or vice versa). The computational performance of each of the proposed methods is evaluated on a set of convex problems.

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