内点法有功优化调度的降阶方法

在采用基于直流潮流模型的内点法求解有功优化调度问题时,迭代过程中将面对一个大型稀疏线性方程组的反复求解,算法的计算速度及处理问题的规模主要取决于此方程组。针对这一问题,本文充分利用了问题本身的电网络的物理规律,将迭代过程中所要求解的大型稀疏线性方程组充分降阶。通过处理,使最初形成的线性系统求解的维数降至系统的节点数。根据对迭代过程中数值变化规律的分析,进一步利用Sherman-Morrison-Woodbury公式,使每次迭代中需要因子分解的矩阵的维数降至预参与调度机组数减一,从而减少了每次迭代求解的计算量。由此,在有功优化调度的解算速度和求解规模上有良好的适应性。

Method of Reduction of Dimension for Solving the Optimal Active Power Dispatch Problem with Interior Point Method

A large sparse linear system must be solved during its iteration when using interior point method for the optimal active power dispatch problem.The speed of the algorithm and the scale of the problem just depend on this linear system.This paper reduces the dimension of the linear system by using the electric network law.The original linear system dimension can be reduced to the number of buses after primary derivation.Moreover,by the analysis of the variable matrix element formed,the Sherman-Morrison- Woodbury equation is used to reduce more linear system dimension to the number of units participated.So,the speed of calculations is quickened obviously.Therefore,the method proposed in this paper has a good adaptation for the solution of speed and size to the optimal active power dispatch problem.