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Strengthening Convex Relaxations with Bound Tightening for Power Network Optimization

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9255)

Abstract

Convexification is a fundamental technique in (mixed-integer) nonlinear optimization and many convex relaxations are parametrized by variable bounds, i.e., the tighter the bounds, the stronger the relaxations. This paper studies how bound tightening can improve convex relaxations for power network optimization. It adapts traditional constraint-programming concepts (e.g., minimal network and bound consistency) to a relaxation framework and shows how bound tightening can dramatically improve power network optimization. In particular, the paper shows that the Quadratic Convex relaxation of power flows, enhanced by bound tightening, almost always outperforms the state-of-the-art Semi-Definite Programming relaxation on the optimal power flow problem.

Keywords

Continuous constraint networks Minimal network Bound consistency Convex relaxation AC power flow QC relaxation AC optimal power flow 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.NICTA - Optimisation Research GroupCanberraAustralia
  2. 2.College of Engineering and Computer ScienceAustralian National UniversityCanberraAustralia

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