A SDP relaxation of an optimal power flow problem for distribution networks

被引:3
作者
Desveaux, Vivien [1 ]
Handa, Marouan [1 ,2 ]
机构
[1] Univ Picardie Jules Verne, LAMFA, UMR CNRS 7352, 33 Rue St Leu, F-80039 Amiens, France
[2] Inst Informat Theory & Automat, Prague 18208, Czech Republic
关键词
Electric power distribution network; Optimal power flow; Convex relaxation; Pareto-front; OPTIMIZATION; ALGORITHM;
D O I
10.1007/s11081-023-09801-3
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this work, we are interested in an optimal power flow problem with fixed voltage magnitudes in distribution networks. This optimization problem is known to be non-convex and thus difficult to solve. A well-known solution methodology consists in reformulating the objective function and the constraints of the original problem in terms of positive semi-definite matrix traces, to which we add a rank constraint. To convexify the problem, we remove this rank constraint. Our main focus is to provide a strong mathematical proof of the exactness of this convex relaxation technique. To this end, we explore the geometry of the feasible set of the problem via its Pareto-front. We prove that the feasible set of the original problem and the feasible set of its convexification share the same Pareto-front. From a numerical point of view, this exactness result allows to reduce the initial problem to a semi-definite program, which can be solved by more efficient algorithms.
引用
收藏
页码:2973 / 3002
页数:30
相关论文
共 20 条
[1]  
ApS MOSEK., 2019, MOSEK OPTIMIZATION T
[2]   Semidefinite programming for optimal power flow problems [J].
Bai, Xiaoqing ;
Wei, Hua ;
Fujisawa, Katsuki ;
Wang, Yong .
INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS, 2008, 30 (6-7) :383-392
[3]   Evaluating the Effects of Real Power Losses in Optimal Power Flow-Based Storage Integration [J].
Castillo, Anya ;
Gayme, Dennice F. .
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS, 2018, 5 (03) :1132-1145
[4]  
Conti S, 2003, 2003 IEEE BOL POW TE
[5]   Modified JAYA algorithm for optimal power flow incorporating renewable energy sources considering the cost, emission, power loss and voltage profile improvement [J].
Elattar, Ehab E. ;
ElSayed, Salah K. .
ENERGY, 2019, 178 :598-609
[6]  
Group DTFW, 2010, DISTR TEST FEED
[7]   A Congestive Heart Failure Detection System via Multi-input Deep Learning Networks [J].
Huang, Shan-Hsuan ;
Chuang, Bei-Lin ;
Lin, Yen-Hung ;
Hung, Chi-Sheng ;
Ma, Hsi-Pin .
2019 IEEE GLOBAL COMMUNICATIONS CONFERENCE (GLOBECOM), 2019,
[8]   RADIAL-DISTRIBUTION TEST FEEDERS [J].
KERSTING, WH .
IEEE TRANSACTIONS ON POWER SYSTEMS, 1991, 6 (03) :975-985
[9]  
Lam AYS, 2012, IEEE DECIS CONTR P, P430, DOI 10.1109/CDC.2012.6427082
[10]   Geometry of Power Flows and Optimization in Distribution Networks [J].
Lavaei, Javad ;
Tse, David ;
Zhang, Baosen .
IEEE TRANSACTIONS ON POWER SYSTEMS, 2014, 29 (02) :572-583