求解最优潮流全局最优解的二阶半定规划方法  

Two-Degree SDP Method for Optimal Power Flow with Global Optimization

作　　者：柳影 田君杨 李佩杰[3] 黄超 LIU Ying;TIAN J unyang;LI Peijie;HUANG Chao(Department of Information and Electromechanical Engineering,Guangxi Vocational University of Agricultural Technical,Nanning 530005;Guangxi Power Grid Dispatching Control Cen ter,Nanni ng 530023;Guan gxi Key Laboratory of Power System Optimization and Energy Technology(Guangxi University),Nanning 530004,China)

机构地区：[1]广西农业职业技术大学信息与机电工程系,南宁530005 [2]广西电网电力调度控制中心,南宁530023 [3]广西电力系统最优化与节能技术重点实验室(广西大学),南宁530004

出　　处：《重庆师范大学学报（自然科学版）》2022年第2期22-30,共9页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.51407036);广西高校中青年教师基础能力提升项目(No.2021KY1566)。

摘　　要：【目的】半定规划凸松弛方法是求取电力系统最优潮流(Optimal power flow, OPF)问题全局最优解的有效技术手段,但解的秩为1的条件难以满足,导致应用具有一定的局限性。针对这一求解困境,提出了一种新的半定规划凸松弛方法。【方法】基于变量扩展,将原变量对应的二阶单项式扩展为新的变量,扩展后可构造一阶及二阶的半正定扩展矩阵,在此基础上将不等式约束转化为矩阵不等式约束,从而形成二阶半定规划凸松弛模型。【结果】为验证所提方法的有效性,求解了常规半定规划方法应用失败的一些反例,结果表明:二阶半定规划松弛模型能更可靠地求得秩为1的扩展矩阵,从而直接获得原OPF问题精确的全局最优解。【结论】二阶半定规划松弛方法为电力系统OPF问题提供了一种更可靠的全局最优算法,具有更好的应用前景。[Purposes]The convex relaxation method of semi-definite programming(SDP) is an important means to solve optimal power flow(OPF) problems with global optimums. But it is difficult to meet the rank-1 condition and it has certain limitations. A new convex relaxation approach is presented, called 2-degree SDP method, to facilitate the rank-1 condition satisfied for deterministic global optimal solution. [Methods] The method constructs 1-and 2-degree positive semi-definite expansion matrices based on variable expansion, and employs linear matrix inequalities to formulate the inequality constraints. Thus, the 2-degree SDP model is built for OPF problems. [Findings] This method is effectively applied to certain OPF’s examples of unsuccessful applications with conventional SDP method. Simulation results showed that the 2-degree SDP method can obtain rank-1 expansion matrices more reliably, then the global solutions can be gotten directly. [Conclusions] The 2-degree SDP relaxation is a more reliable algorithm with global optimality for OPF problems, it has a better application prospect.

关 键 词：最优潮流 半定规划 凸松弛 全局最优 

分 类 号：O224[理学—运筹学与控制论] TM73[理学—数学]