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

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 relaxa...

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Bibliographic Details
Published in:Mathematical programming computation Vol. 9; no. 3; pp. 321 - 367
Main Authors: Hijazi, Hassan, Coffrin, Carleton, Hentenryck, Pascal Van
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2017
Springer Nature B.V
Subjects:
Computational efficiency
Computing time
Full Length Paper
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear systems
Operations Research/Decision Theory
Optimization
Power flow
Semidefinite programming
Switching
Theory of Computation
Global optimization
90C30
Mixed-integer nonlinear programming
Optimal power flow
90C25
90C11
Convex relaxation
Capacitor placement
90C90
90C26
Optimal transmission switching
ISSN:1867-2949, 1867-2957
Online Access:Get full text
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Summary: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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ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-016-0112-z