利用混合块消去算法的电压稳定负荷裕度灵敏度计算

Loading Margin Sensitivity Computation With Mixed Block Elimination (BEM) Algorithm in Voltage Stability Analysis

电力系统中目前多采用潮流雅可比矩阵在鞍结分歧点(saddle-node bifurcation point,SNBP)零特征值对应的左特征向量计算负荷裕度对参数变化的灵敏度,存在零特征值左特征向量和负荷裕度高阶灵敏度不容易计算等难题。与传统方法不同,给出了一种直角坐标中通过递归求解系列线性方程组计算任意阶负荷裕度灵敏度的方法。线性方程组的右端向量通过双线性函数计算,采用W.Govaerts提出的数值向后稳定(backward stable)的混合块消去(mixed block elimination,BEM)算法求解线性方程组。在计算各阶灵敏度时,只需一次潮流雅可比矩阵三角分解。以实际电网为背景研究了网络参数、负荷变化、支路开断等对负荷裕度的影响。计算结果表明,当参数变化范围较大或系统非线性程度较强时,高阶灵敏度的计算精度要远高于1阶灵敏度,且不需要附加太多计算量。

In power systems analysis, the left singular vector of the power flow Jacobian at the saddle-node bifurcation point （SNBP） is used to compute the sensitivity of the loading margin with a changeable parameter. It is more difficult to compute the left singular vector of the power flow Jacobian. Moreover, the high-order sensitivities of the loading margin are not easily to be obtained. In this paper, a new method to compute any order sensitivities of the loading margin in rectangular coordinates by solving sequences of linear equations recursively was proposed. The backward stable mixed block elimination （BEM） algorithm proposed by W.Govaerts was used to solve the linear systems, with the right hand side vectors were computed through the bilinear maps, and only one LU-factorization of the power flow Jacobian is required for the computation of per-order sensitivity. Variations of the network parameters, load parameters and outage of branches to affect the loading margin were studied with a large scale power system. Numerical results show the accurate approximation of the higher-order sensitivity when large deviation of the parameter or strong nonlinearities occur, and no additional computational costs are required.