A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks

Shaojun Huang; Qiuwei Wu; Jianhui Wang; Haoran Zhao

doi:10.1109/TPWRS.2016.2574805

A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks

Shaojun Huang
, Qiuwei Wu
, Jianhui Wang
, Haoran Zhao

The University of Chicago

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks.

Original language	English
Journal	IEEE Transactions on Power Systems
Volume	32
Issue number	2
Pages (from-to)	1359 - 1368
ISSN	0885-8950
DOIs	https://doi.org/10.1109/TPWRS.2016.2574805
Publication status	Published - 2016

Bibliographical note

(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

Keywords

AC optimal power flow (AC OPF)
Convex relaxation, convexity
Electric vehicle (EV)
Power distribution network
Second order cone program (SOCP)

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10.1109/TPWRS.2016.2574805

Convex relaxation of Optimal Power Flow in Distribution networks finalAccepted author manuscript, 266 KB

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title = "A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks",

abstract = "This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks. ",

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note = "(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.",

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AU - Huang, Shaojun

AU - Wu, Qiuwei

AU - Wang, Jianhui

AU - Zhao, Haoran

N1 - (c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

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N2 - This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks.

AB - This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks.

KW - AC optimal power flow (AC OPF)

KW - Convex relaxation, convexity

KW - Electric vehicle (EV)

KW - Power distribution network

KW - Second order cone program (SOCP)

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DO - 10.1109/TPWRS.2016.2574805

M3 - Journal article

SN - 0885-8950

VL - 32

SP - 1359

EP - 1368

JO - IEEE Transactions on Power Systems

JF - IEEE Transactions on Power Systems

IS - 2

ER -

A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks

Abstract

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