基于预测-校正原对偶内点法的无功优化新模型

在有载可调变压器模型中引入虚拟节点，并通过该节点的电压来表示理想变压器对功率、电压的转换关系，由此在直角坐标系中建立了无功优化问题的二阶新模型。该新模型的海森矩阵是精确的常系数矩阵，在内点法迭代过程中只需要计算一次，从而缩短了每次迭代的计算时间。利用AMD算法对内点法修正方程的系数矩阵进行节点优化编号，减少了其LU分解所产生的注入元。通过存储海森矩阵的非零元素值、其行、列号及对应的拉格朗日乘子编号，提出了一种新的非零元素存储方式，极大地减少了海森矩阵与乘子线性组合的计算量。基于节点数从14到1338的7个测试系统进行了仿真计算，结果验证了所建模型与方法的正确性与有效性。这种建立模型的思想还可以应用到需要计算海森矩阵的动态无功优化、最优潮流以及状态估计等问题的算法中，以提高其计算速度。

A NEW MODEL OF REACTIVE OPTIMIZATION BASED ON PREDICTOR CORRECTOR PRIMAL DUAL INTERIOR POINT METHOD

A second-order nonlinear model is established by adding the voltage of the dummy nodes in the on-load tap changer transformer model to express the power and voltage relations. The Hessian matrix of every function in this model is constant, so it will be calculated once in the entire optimal process based on interior point method, which speeds up each iteration. AMD algorithm is used to order the coefficient matrix of the correction equation in the interior point method, which reduces fill-in elements compared with the conventional data structure. To cut down the computation in the linear combination of the Hessian matrices and their Lagrangian multipliers, a new nonzero element storing structure is proposed, which stores the values and row numbers of the nonzero elements and the numbers of the Lagrangian multipliers corresponding to the nonzero elements. The numerical results of seven test systems that rang in size from 14 to 1338 buses indicate that the proposed model and methods are accurate and have faster speed. This proposed modeling idea can also be applied to dynamic reactive optimization, optimal power flow and state estimation for a faster calculation.