Novel Approach Towards Global Optimality of Optimal Power Flow Using Quadratic Convex Optimization

Optimal Power Flow (OPF) can be modeled as a nonconvex Quadratically Constrained Quadratic Program (QCQP). Our purpose is to solve OPF to global optimality. To this end, we specialize the Mixed-Integer Quadratic Convex Reformulation method (MIQCR) to (OPF). This is a method in two steps. First, a Se...

Full description

Saved in:
Bibliographic Details
Main Authors: Godard, Hadrien, Elloumi, Sourour, Lambert, Amelie, Maeght, Jean, Ruiz, Manuel
Format: Conference Proceeding
Language:English
Subjects:
Linear programming
Load flow
Mathematical model
Optimization
Production
Symmetric matrices
Upper bound
Citations: Items that cite this one
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Optimal Power Flow (OPF) can be modeled as a nonconvex Quadratically Constrained Quadratic Program (QCQP). Our purpose is to solve OPF to global optimality. To this end, we specialize the Mixed-Integer Quadratic Convex Reformulation method (MIQCR) to (OPF). This is a method in two steps. First, a Semi-Definite Programming (SDP) relaxation of (OPF) is solved. Then the optimal dual variables of this relaxation are used to reformulate OPF into an equivalent new quadratic program, where all the non-convexity is moved to one additional constraint. In the second step, this reformulation is solved within a branch-and-bound algorithm, where at each node a quadratic and convex relaxation of the reformulated problem, obtained by relaxing the non-convex added constraint, is solved. The key point of our approach is that the lower bound at the root node of the branch-and-bound tree is equal to the SDP relaxation value. We test this method on several OPF cases, from two-bus networks to more-than-a-thousand-buses networks from the MAT-POWER repository. Our first results are very encouraging.
ISSN:2576-3555
DOI:10.1109/CoDIT.2019.8820584