非线性原-对偶内点法无功优化中的修正方程降维方法

Dimension Reduction of Modified Equation for Reactive Power Optimization Based on Nonlinear Primal-dual Interior Point Algorithm

针对无功优化模型中含有离散变量的问题,采用非线性原–对偶内点法进行求解。根据卡罗需–卡恩–塔克条件下修正方程结构稀疏的特点,首先将松弛变量和不等式拉格朗日乘子的增量用决策变量的增量表示,再将其代入修正方程并从中消去变比和无功电源出力的增量,最终降维后方程仅含节点电压幅值及相角、等式拉格朗日乘子增量。在计及变比和无功补偿装置出力的离散性约束条件下,通过增加无功电源出力作为优化变量,保证了修正方程中变比的海森矩阵始终为对角矩阵,扩展了降维处理方法的适用范围。算例结果验证了该降维方法的有效性。

The nonlinear primal-dual interior point algorithm is used to solve the reactive power optimization model containing discrete variables. According to the feature that the structure of modified equation is sparse under Karush-Kuhn-Tucker （K-K-T） condition, firstly the increments of slack variables and those of Lagrangian multipliers of inequality is expressed by increments of decision variables; then the increments of decision variables are substituted into modified equation and from the modified equation the increments of transformation ratio and output of reactive power source are eliminated; finally the post-dimension-reduction modified equation only contains nodal voltage amplitude, phase angle and increments of Lagrangian multipliers of equality. Under the discrete constraint conditions in which the transformation ratio and output of reactive power compensation device are considered and by means of taking the output increase of reactive power source as optimization variable, it is ensured that the Hessian matrix of transformation ration is always diagonal matrix, thus＂ the applicability of dimension reducing processing method is expanded. The effectiveness of the proposed dimension-reduction method is verified by results of calculation example.