optimal power flow

Tight-and-cheap conic relaxation for the AC optimal power flow problem

  • Miguel F. Anjos
  • Christian Bingane
  • Sébastien Le Digabel
    • Categories Applications - Science and Engineering, Nonlinear Optimization, Semi-definite Programming Tags , , ,

    The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, the computational efficiency for solving large-scale semidefinite … Read more

    Invex Optimization Revisited

  • Ksenia Bestuzheva
  • Hassan L. Hijazi
    • Categories Applications - Science and Engineering, Global Optimization Theory, Nonlinear Optimization Tags , , ,

    Given a non-convex optimization problem, we study conditions under which every Karush-Kuhn-Tucker (KKT) point is a global optimizer. This property is known as KT-invexity and allows to identify the subset of problems where an interior point method always converges to a global optimizer. In this work, we provide necessary conditions for KT-invexity in n-dimensions and … Read more

    Plea for a semidefinite optimization solver in complex numbers

  • Jean Charles Gilbert
  • Cedric Josz
    • Categories Semi-definite Programming Tags , , ,

    Numerical optimization in complex numbers has drawn much less attention than in real numbers. A widespread opinion is that, since a complex number is a pair of real numbers, the best strategy to solve a complex optimization problem is to transform it into real numbers and to solve the latter by a real number solver. … Read more

    Matrix Minor Reformulation and SOCP-based Spatial Branch-and-Cut Method for the AC Optimal Power Flow Problem

  • Santanu S. Dey
  • Burak Kocuk
  • Xu Andy Sun
    • Categories Applications - Science and Engineering, Global Optimization Applications Tags , , ,

    Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining near optimal primal solutions as well as high quality dual bounds for this non-convex program, presents a major … Read more

    Strong SOCP Relaxations for the Optimal Power Flow Problem

  • Santanu S. Dey
  • Burak Kocuk
  • Xu Andy Sun
    • Categories Applications - Science and Engineering, Global Optimization, Nonlinear Optimization Tags , , ,

    This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in … Read more

    Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow

  • Santanu S. Dey
  • Burak Kocuk
  • Xu Andy Sun
    • Categories Global Optimization Tags , , ,

    It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load over-satisfaction. In this paper, we investigate the situation where generation lower bounds are present. We show that even for a … Read more

    Application of the Moment-SOS Approach to Global Optimization of the OPF Problem

  • Jean Charles Gilbert
  • Cedric Josz
  • Jean Maeght
  • Patrick Panciatici
    • Categories Applications - Science and Engineering, Global Optimization Applications, Network Optimization Tags , , , ,

    Finding a global solution to the optimal power flow (OPF) problem is difficult due to its nonconvexity. A convex relaxation in the form of semidefinite programming (SDP) has attracted much attention lately as it yields a global solution in several practical cases. However, it does not in all cases, and such cases have been documented … Read more

    Convex Quadratic Relaxations for Mixed-Integer Nonlinear Programs in Power Systems

  • Carleton Coffrin
  • Hassan L. Hijazi
  • Pascal Van Hentenryck
    • Categories Basic Sciences Applications, Convex Optimization, Global Optimization Applications Tags , , , , ,

    This paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semi-definite … Read more

    New Versions of Interior Point Methods Applied to the Optimal Power Flow Problem

  • Jorge Mario Campagnolo
  • Edgardo Daniel Castronuovo
  • Roberto Salgado
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , , , ,

    Interior Point methods for Nonlinear Programming have been extensively used to solve the Optimal Power Flow problem. These optimization algorithms require the solution of a set of nonlinear equations to obtain the optimal solution of the power network equations. During the iterative process to solve these equations, the search for the optimum is based on … Read more