Tight-and-Cheap Conic Relaxation for the Optimal Reactive Power Dispatch Problem

Christian Bingane, Miguel Anjos, Sebastien Le Digabel

Research output: Contribution to journalArticlepeer-review


The optimal reactive power dispatch (ORPD) problem
is an alternating current optimal power flow (ACOPF)
problem where discrete control devices for regulating the reactive
power, such as shunt elements and tap changers, are considered.
The ORPD problem is modelled as a mixed-integer nonlinear
optimization problem and its complexity is increased compared
to the ACOPF problem, which is highly nonconvex and generally
hard to solve. Recently, convex relaxations of the ACOPF problem
have attracted a significant interest since they can lead to global
optimality. We propose a tight conic relaxation of the ORPD
problem and show that a round-off technique applied with this
relaxation leads to near-global optimal solutions with very small
guaranteed optimality gaps, unlike with the nonconvex continuous
relaxation. We report computational results on selected
MATPOWER test cases with up to 3375 buses.
Original languageEnglish
Pages (from-to)4684-4693
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number6
Early online date23 Apr 2019
Publication statusPublished - 30 Nov 2019

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