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Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem

Michael Bynum (mlbynum***at***sandia.gov)
Anya Castillo (arcasti***at***sandia.gov)
Jean-Paul Watson (jwatson***at***sandia.gov)
Carl Laird (cdlaird***at***sandia.gov)

Abstract: We show that a strong upper bound on the objective of the alternating current optimal power flow (ACOPF) problem can significantly improve the effectiveness of optimization-based bounds tightening (OBBT) on a number of relaxations. We additionally compare the performance of relaxations of the ACOPF problem, including the rectangular form without reference bus constraints, the rectangular form with reference bus constraints, and the polar form. We find that relaxations of the rectangular form significantly strengthen existing relaxations if reference bus constraints are included. Overall, relaxations of the polar form perform the best. However, neither the rectangular nor the polar form dominates the other. Ultimately, with these strategies, we are able to reduce the optimality gap to less than 0.1% on all but 5 NESTA test cases with up to 300 buses by performing OBBT alone.

Keywords: ACOPF, bounds tightening, convex relaxation

Category 1: Global Optimization (Applications )

Citation: M. Bynum, A. Castillo, J. Watson and C. D. Laird, "Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem," in IEEE Transactions on Power Systems. doi: 10.1109/TPWRS.2018.2877099 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8500764&isnumber=4374138

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Entry Submitted: 04/10/2018
Entry Accepted: 04/10/2018
Entry Last Modified: 11/21/2018

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