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

Hassan L. Hijazi (hassan.hijazi***at***anu.edu.au)
Carleton Coffrin (cjc***at***lanl.gov)
Pascal Van Hentenryck (pvanhent***at***umich.edu)

Abstract: 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 programming relaxations. Three case studies in optimal power flow, optimal transmission switching and capacitor placement demonstrate the benefits of the new relaxations.

Keywords: Nonlinear Programming, Mixed-Integer Nonlinear Programming, Convex Relaxations, Optimal Power Flow, Line-Switching Optimal Power Flow, Capacitor Placement

Category 1: Applications -- Science and Engineering (Basic Sciences Applications )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Global Optimization (Applications )

Citation: H. L. Hijazi and C. Coffrin and P. Van Hentenryck "Convex Quadratic Relaxations of Mixed-Integer Nonlinear Programs in Power Systems" Mathematical Programming Computation 2016

Download: [PDF]

Entry Submitted: 09/30/2013
Entry Accepted: 09/30/2013
Entry Last Modified: 10/02/2016

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