奇异值分解结合均匀设计采样的半不变量法概率潮流计算

在样本形成过程中半不变量法概率潮流(PLF-CM)计算可能遇到输入变量相关系数矩阵非正定的情况,此时常用的Cholesky分解不再适用。提出一种奇异值分解(SVD)结合均匀设计采样(UDS)的PLF-CM计算方法。通过SVD和UDS结合Nataf变换得到考虑相关性的随机变量样本,借助这些样本计算常规数值方法难以求解的部分输入变量的半不变量,利用SVD处理输入变量的协方差矩阵以准确计算输出变量的半不变量,采用Cornish-Fisher级数展开求得输出变量的概率分布。以改造后的IEEE 14节点测试系统为算例,验证了所提方法的快速性、有效性及对高渗透率新能源发电的适应性。

Probabilistic load flow calculation based on cumulant method combining singular value decomposition and uniform design sampling

In the process of sample formation, the PLF-CM(Probabilistic Load Flow based on Cumulant Method) calculation may encounter the condition that the correlation coefficient matrix of input variables is non-positive definite, where the commonly used Cholesky decomposition is no longer applicable. A PLF-CM calculation method with the combination of SVD(Singular Value Decomposition) and UDS(Uniform Design Sampling) is proposed. The random variable samples with the consideration of correlation are obtained by the combination of SVD, UDS and Nataf transformation, which are used to calculate the cumulants of some input variables that are hardly be solved by the conventional numerical methods. The SVD is adopted to deal with the covariance matrix of input variables to accurately calculate the cumulants of output variables, and the probability distribution of output variables is obtained through Cornish-Fisher series expansion. The modified IEEE 14-bus test system is taken as an example to verify the rapidity, effectiveness, and adaptability of the proposed method to high permeability new energy power generation.