The convex hull of the AC power flow equations in rectangular coordinates

Qifeng Li; Vijay Vittal

doi:10.1109/PESGM.2016.7741777

The convex hull of the AC power flow equations in rectangular coordinates

Qifeng Li, Vijay Vittal

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

12 Scopus citations

Abstract

Obtaining the convex hull of the alternating current (AC) power flow equations is largely beneficial in the convexification of the optimization problems in power systems where the AC power flow constraints are taken into account. In this paper, the AC power flow formulation in rectangular coordinates which is a non-convex quadratic equality is equivalently decomposed into four quadratic inequalities whose coefficient matrices are positive semidefinite. Two of the quadratic inequalities are convex while the other two are not. The proposed decomposition facilitates the convexification of the power flow equations much. A convex hull formulation is proposed for the resulting non-convex quadratic inequalities. This formulation is applied to study the convex hull of the AC power flow.

Original language	English (US)
Title of host publication	2016 IEEE Power and Energy Society General Meeting, PESGM 2016
Publisher	IEEE Computer Society
Volume	2016-November
ISBN (Electronic)	9781509041688
DOIs	https://doi.org/10.1109/PESGM.2016.7741777
State	Published - Nov 10 2016
Event	2016 IEEE Power and Energy Society General Meeting, PESGM 2016 - Boston, United States Duration: Jul 17 2016 → Jul 21 2016

Other

Other	2016 IEEE Power and Energy Society General Meeting, PESGM 2016
Country/Territory	United States
City	Boston
Period	7/17/16 → 7/21/16

Keywords

AC power flow
Convex hull
Convex relaxation
Non-convex quadratic equality
Rectangular coordinates

ASJC Scopus subject areas

Energy Engineering and Power Technology
Nuclear Energy and Engineering
Renewable Energy, Sustainability and the Environment
Electrical and Electronic Engineering

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10.1109/PESGM.2016.7741777

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title = "The convex hull of the AC power flow equations in rectangular coordinates",

abstract = "Obtaining the convex hull of the alternating current (AC) power flow equations is largely beneficial in the convexification of the optimization problems in power systems where the AC power flow constraints are taken into account. In this paper, the AC power flow formulation in rectangular coordinates which is a non-convex quadratic equality is equivalently decomposed into four quadratic inequalities whose coefficient matrices are positive semidefinite. Two of the quadratic inequalities are convex while the other two are not. The proposed decomposition facilitates the convexification of the power flow equations much. A convex hull formulation is proposed for the resulting non-convex quadratic inequalities. This formulation is applied to study the convex hull of the AC power flow.",

keywords = "AC power flow, Convex hull, Convex relaxation, Non-convex quadratic equality, Rectangular coordinates",

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year = "2016",

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day = "10",

doi = "10.1109/PESGM.2016.7741777",

language = "English (US)",

volume = "2016-November",

booktitle = "2016 IEEE Power and Energy Society General Meeting, PESGM 2016",

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note = "2016 IEEE Power and Energy Society General Meeting, PESGM 2016 ; Conference date: 17-07-2016 Through 21-07-2016",

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T1 - The convex hull of the AC power flow equations in rectangular coordinates

AU - Li, Qifeng

AU - Vittal, Vijay

PY - 2016/11/10

Y1 - 2016/11/10

N2 - Obtaining the convex hull of the alternating current (AC) power flow equations is largely beneficial in the convexification of the optimization problems in power systems where the AC power flow constraints are taken into account. In this paper, the AC power flow formulation in rectangular coordinates which is a non-convex quadratic equality is equivalently decomposed into four quadratic inequalities whose coefficient matrices are positive semidefinite. Two of the quadratic inequalities are convex while the other two are not. The proposed decomposition facilitates the convexification of the power flow equations much. A convex hull formulation is proposed for the resulting non-convex quadratic inequalities. This formulation is applied to study the convex hull of the AC power flow.

AB - Obtaining the convex hull of the alternating current (AC) power flow equations is largely beneficial in the convexification of the optimization problems in power systems where the AC power flow constraints are taken into account. In this paper, the AC power flow formulation in rectangular coordinates which is a non-convex quadratic equality is equivalently decomposed into four quadratic inequalities whose coefficient matrices are positive semidefinite. Two of the quadratic inequalities are convex while the other two are not. The proposed decomposition facilitates the convexification of the power flow equations much. A convex hull formulation is proposed for the resulting non-convex quadratic inequalities. This formulation is applied to study the convex hull of the AC power flow.

KW - AC power flow

KW - Convex hull

KW - Convex relaxation

KW - Non-convex quadratic equality

KW - Rectangular coordinates

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U2 - 10.1109/PESGM.2016.7741777

DO - 10.1109/PESGM.2016.7741777

M3 - Conference contribution

AN - SCOPUS:85001958611

VL - 2016-November

BT - 2016 IEEE Power and Energy Society General Meeting, PESGM 2016

PB - IEEE Computer Society

T2 - 2016 IEEE Power and Energy Society General Meeting, PESGM 2016

Y2 - 17 July 2016 through 21 July 2016

ER -

The convex hull of the AC power flow equations in rectangular coordinates

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Keywords

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