几种高阶收敛的Levenberg-Marquardt方法在潮流计算中的应用

发布时间：2018-06-22 05:02

本文选题：Levenberg-Marquardt法 + 高阶收敛　；参考：《电网技术》2017年04期

【摘要】：针对现代电力系统日益复杂的运行工况使得常规潮流算法面临不收敛的问题,在已有三阶和四阶收敛的改进Levenberg-Marquardt(LM)算法的基础上,通过不断引入LM近似迭代步,提出了2种高阶收敛的LM算法(五阶收敛的LM算法(LM5)、六阶收敛的LM算法(LM6))用于电力系统潮流计算。根据所提方法得到的最小二乘解,分析系统薄弱节点的相关信息,为电力运行部门潮流调整以及潮流收敛性的改善,提供有价值的参考信息。为了体现所提算法的收敛性和鲁棒性,将所提算法、牛顿法、二阶收敛LM法(LM2)、三阶收敛LM法(LM3)、四阶收敛LM法(LM4)分别在"良态"、"不同初始点位置"、"重负荷"、"小阻抗支路"、"线路或发电机故障"等工况下进行测试。算例表明:"良态"情况下,所提的高阶收敛LM算法具有迭代次数少、雅可比矩阵计算次数少的特点;"病态"情况下,在一定程度范围内,引入近似LM迭代步能够改善潮流收敛性,但超出该程度范围,不断引入近似LM迭代步对潮流收敛性的改善作用不明显。
[Abstract]:In view of the increasingly complex operating conditions of modern power system, the conventional power flow algorithm is not convergent. On the basis of the improved Levenberg-Marquardt (LM) algorithm, which has three order and four order convergence, through the continuous introduction of LM approximation, 2 high order convergent LM algorithms (five order convergent LM algorithm (LM5), and six order convergent L are proposed. M algorithm (LM6) is used in power system power flow calculation. According to the least square solution obtained by the proposed method, the relevant information of the weak nodes of the system is analyzed, and valuable reference information is provided for the power flow adjustment and the improvement of the convergence of the power flow. In order to reflect the convergence and robustness of the proposed algorithm, the proposed algorithm, Newton method, is presented. The two order convergent LM (LM2), the three order convergent LM (LM3) and the four order convergent LM method (LM4) are tested under the conditions of "good state", "different initial point position", "heavy load", "small impedance branch", "line or generator fault". The calculation example shows that the high order convergent LM algorithm has fewer iterations and the Jacobi matrix calculation times under the condition of "good state". In the case of "sick", the convergence of the power flow can be improved by introducing an approximate LM iterative step within a certain extent, but the effect of the approximate LM iteration on the improvement of the convergence of the power flow is not obvious beyond the extent of this degree.
【作者单位】：电力传输与功率变换控制教育部重点实验室(上海交通大学电气工程系);国家电网上海市电力公司市南供电公司;国家电网上海市电力公司电力科学研究院;
【基金】：国家自然科学基金项目(51377103) 国家电网公司科技项目(52094015001S)~~
【分类号】：TM744

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