基于Levenberg-Marquardt算法的鞍结分岔点快速计算  

Fast Calculation of Saddle-node Bifurcation Point via Levenberg-Marquardt Algorithm

作　　者：林立亨 董树锋[1] 唐坤杰 毛航银[2] 宋永华[1,3] LIN Liheng;DONG Shufeng;TANG Kunjie;MAO Hangyin;SONG Yonghua(College of Electrical Engineering,Zhejiang University,Hangzhou 310027,Zhejiang Province,China;State Grid Zhejiang Electric Power Company,Hangzhou 310007,Zhejiang Province,China;State Key Laboratory of Internet of Things for Smart City(University of Macao),Macao SAR 999078,China)

机构地区：[1]浙江大学电气工程学院,浙江省杭州市310027 [2]国网浙江省电力公司,浙江省杭州市310007 [3]智慧城市物联网国家重点实验室(澳门大学),中国澳门特别行政区999078

出　　处：《电网技术》2021年第6期2352-2358,共7页Power System Technology

基　　金：国家电网公司科技项目:新能源电力系统随机稳定性分析研究(52110418000N)。

摘　　要：为了快速准确地计算静态电压稳定裕度,该文提出了2种鞍结分岔点快速求取算法,分别采用二分搜索和抛物线近似来进行计算。基于Levenberg-Marquardt算法在潮流方程的不可行域也能求得最小二乘解的特性,二分搜索算法利用解得的最小二乘值判断此算点是否处于潮流不可行域,通过二分搜索来快速逼近鞍结分岔点。抛物线近似算法对不可行域的最小二乘值-负荷裕度曲线进行抛物线近似,曲线的零点即为所求的鞍结分岔点。多个经典算例测试结果表明,相较于传统的连续潮流算法,二分搜索算法在保证计算准确地同时可以大幅度提升计算效率。而抛物线近似算法牺牲了一定的计算精度,在二分搜索算法的基础上进一步提升了效率。并且得益于Levenberg-Marquardt算法的强鲁棒性,2种算法即使在面对大型病态算例时也可以收敛,保证了计算的稳定性。In order to calculate static voltage stability margins quickly and accurately,this paper proposes two algorithms for searching saddle-node bifurcation points based on bisection search and parabolic approximation respectively.The Levenberg-Marquardt algorithm is applied to obtain the least-squares solution in the infeasible region of the power flow equations.The bisection search algorithm uses the least-squares solution to determine whether the current trial step is in the power flow infeasible region,and finally approaches the saddle-node bifurcation point.The parabolic approximation algorithm performs a parabolic approximation to‘the least-squares value’-‘load margin’curve in the infeasible region,and the zero point of the curve is corresponding to the required saddle-node bifurcation point.The numerical experiments on several classical cases show that compared with the traditional continuous power flow algorithm,the bisection search algorithm can significantly improve the computational efficiency while ensuring the accuracy.The parabolic approximation algorithm sacrifices some accuracy,but further improves the efficiency based on the bisection search algorithm.Also,thanks to the robustness of the Levenberg-Marquardt algorithm,these two algorithms in this paper can well converge under large ill-conditioned cases,ensuring the numerical stability of these two algorithms.

关 键 词：静态电压稳定裕度 LEVENBERG-MARQUARDT算法 鞍结分岔点 负荷裕度 二分搜索 抛物线近似 

分 类 号：TM721[电气工程—电力系统及自动化]