Mathematical Programming Computation, Volume 9, Issue 3, September 2017

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Convex quadratic relaxations for mixed-integer nonlinear programs in power systems

Hassan Hijazi, Carleton Coffrin, Pascal Van Hentenryck


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

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