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

Christian Bingane; Miguel Anjos; Sebastien Le Digabel

doi:10.1109/TPWRS.2019.2912889

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

Christian Bingane, Miguel Anjos, Sebastien Le Digabel

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	4684-4693
Number of pages	9
Journal	IEEE Transactions on Power Systems
Volume	34
Issue number	6
Early online date	23 Apr 2019
DOIs	https://doi.org/10.1109/TPWRS.2019.2912889
Publication status	Published - 30 Nov 2019

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title = "Tight-and-Cheap Conic Relaxation for the Optimal Reactive Power Dispatch Problem",

abstract = "The optimal reactive power dispatch (ORPD) problemis an alternating current optimal power flow (ACOPF)problem where discrete control devices for regulating the reactivepower, such as shunt elements and tap changers, are considered.The ORPD problem is modelled as a mixed-integer nonlinearoptimization problem and its complexity is increased comparedto the ACOPF problem, which is highly nonconvex and generallyhard to solve. Recently, convex relaxations of the ACOPF problemhave attracted a significant interest since they can lead to globaloptimality. We propose a tight conic relaxation of the ORPDproblem and show that a round-off technique applied with thisrelaxation leads to near-global optimal solutions with very smallguaranteed optimality gaps, unlike with the nonconvex continuousrelaxation. We report computational results on selectedMATPOWER test cases with up to 3375 buses.",

author = "Christian Bingane and Miguel Anjos and {Le Digabel}, Sebastien",

year = "2019",

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doi = "10.1109/TPWRS.2019.2912889",

language = "English",

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pages = "4684--4693",

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AU - Anjos, Miguel

AU - Le Digabel, Sebastien

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Y1 - 2019/11/30

N2 - The optimal reactive power dispatch (ORPD) problemis an alternating current optimal power flow (ACOPF)problem where discrete control devices for regulating the reactivepower, such as shunt elements and tap changers, are considered.The ORPD problem is modelled as a mixed-integer nonlinearoptimization problem and its complexity is increased comparedto the ACOPF problem, which is highly nonconvex and generallyhard to solve. Recently, convex relaxations of the ACOPF problemhave attracted a significant interest since they can lead to globaloptimality. We propose a tight conic relaxation of the ORPDproblem and show that a round-off technique applied with thisrelaxation leads to near-global optimal solutions with very smallguaranteed optimality gaps, unlike with the nonconvex continuousrelaxation. We report computational results on selectedMATPOWER test cases with up to 3375 buses.

AB - The optimal reactive power dispatch (ORPD) problemis an alternating current optimal power flow (ACOPF)problem where discrete control devices for regulating the reactivepower, such as shunt elements and tap changers, are considered.The ORPD problem is modelled as a mixed-integer nonlinearoptimization problem and its complexity is increased comparedto the ACOPF problem, which is highly nonconvex and generallyhard to solve. Recently, convex relaxations of the ACOPF problemhave attracted a significant interest since they can lead to globaloptimality. We propose a tight conic relaxation of the ORPDproblem and show that a round-off technique applied with thisrelaxation leads to near-global optimal solutions with very smallguaranteed optimality gaps, unlike with the nonconvex continuousrelaxation. We report computational results on selectedMATPOWER test cases with up to 3375 buses.

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DO - 10.1109/TPWRS.2019.2912889

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