A Study on the Strong Duality of Second-Order Conic Relaxation of AC Optimal Power Flow in Radial Networks

被引：44

作者：

Cao, Xiaoyu ^{[1
,2
]}

Wang, Jianxue ^{[3
,4
]}

Zeng, Bo ^{[5
,6
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Automat Sci & Engn, Xian 710049, Shaanxi, Peoples R China

[2] Xi An Jiao Tong Univ, Minist Educ Key Lab Intelligent Networks & Networ, Xian 710049, Shaanxi, Peoples R China

[3] Xi An Jiao Tong Univ, Sch Elect Engn, Xian 710049, Shaanxi, Peoples R China

[4] Xi An Jiao Tong Univ, Shaanxi Key Lab Smart Grid, Xian 710049, Shaanxi, Peoples R China

[5] Univ Pittsburgh, Dept Ind Engn, Pittsburgh, PA 15106 USA

[6] Univ Pittsburgh, Dept Elect & Comp Engn, Pittsburgh, PA 15106 USA

来源：

IEEE TRANSACTIONS ON POWER SYSTEMS | 2022年 / 37卷 / 01期

基金：

国家重点研发计划; 美国国家科学基金会; 中国博士后科学基金;

关键词：

Reactive power; Planning; Optimization; Numerical models; Distribution networks; Computational modeling; Topology; AC optimal power flow; strong duality; second-order conic program; radial network; REACTIVE POWER; DISTRIBUTED GENERATION; MICROGRIDS; TRANSMISSION; OPTIMIZATION; RESILIENCE; MODEL;

D O I：

10.1109/TPWRS.2021.3087639

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

For the popular second-order conic program (SOCP) formulation of AC optimal power flow (OPF) in a radial network, this paper first shows that it does not have the strong duality property in general. Then, through a series of restrictive reformulations, we derive a set of closed-form sufficient conditions on network parameters that ensure its strong duality. Numerical studies on IEEE 33-bus, 69-bus test networks and two real-world distribution systems confirm that non-negligible duality gaps do exist in this SOCP formulation, and also demonstrate the validity of the proposed sufficient conditions on closing the duality gap. Our results provide an analytical tool to ensure the strong duality of the SOCP power flow formulation and to support algorithm developments for its complex extensions.

引用

页码：443 / 455

页数：13

共 40 条

[1] Notes on duality in second order and p-order cone optimization [J].