具有三阶收敛速度的潮流算法

Power flow algorithm with cubic convergence

首次系统地推导了几个具有三阶收敛速度的牛顿类迭代法的多变量矩阵求解格式,并将它们应用于电力系统潮流计算。文中对IEEE14-300节点测试系统和一个实际系统共7个算例进行了仿真测试,结果表明,这些算法具有良好的收敛特性,并且在达到同样精度要求的情况下,它们较之经典牛顿法需要较少的迭代次数。尤其是,算法1和算法5由于在每步迭代中充分利用了Jacobian矩阵三角分解的因子表,提高了潮流计算的速度。最后指出,这些算法在潮流计算中的应用是对潮流计算方法的拓展,本文的研究为这些算法在电力系统中的进一步应用开辟了道路。

In this paper, multivariate matrix calculation formulations of several Newton-like iterative methods with cubic convergence are systematically derived for the first time, then applied them into power flow calculation in electric power systems. Extensive numerical simulations on the test systems that range in size from IEEE14 to 300 buses and a practical life system show that these algorithms have the excellent convergence characteristics, and more, in the same convergence tolerance, these algorithms need less iterative numbers than classical Newton iterative method. Especially, algorithm No.1 and algorithm No.5 make the most of the factorization tables of the Jacobian matrix in each iterative step, so, the speeds of power flow calculation are obviously improved. Lastly, this paper draws a conclusion that these algorithms are the extension to classical Newton iterative method, and the study of this paper makes a routine for applying them into electric power systems.