主元分析结合Cornish-Fisher展开的概率潮流三点估计法

A three-point estimate method for probabilistic load flow computation based on principal component analysis and Cornish-Fisher series

传统点估计概率潮流计算(Probabilistic Load Flow Calculation Based on Point Estimate Method, PLF-PEM)没有考虑输入随机变量相关系数矩阵非正定之情形。为克服上述不足,更准确地描述输出变量的统计特性,提出一种主元分析结合Cornish-Fisher级数展开的PLF-PEM算法。利用主元分析处理相关性输入随机变量,通过点估计方法得到输出变量的各阶矩。结合半不变量理论与Cornish-Fisher级数展开,利用输入变量的离散样本数据求得输出随机变量的数字特征和概率统计信息。算例表明所提算法能适应新能源发电高渗透电力系统的快速概率潮流计算。

The existing Probabilistic Load Flow Calculation based on Point Estimate Method(PLF-PEM)does not consider the case where the correlation matrix of random input variables is non-positive definite.To overcome the deficiency and describe the statistical characteristics of the outputs more accurately,a PLF-PEM computing method based on Principal Component Analysis(PCA)and Cornish-Fisher series expansion is suggested.The proposed method uses the PCA theory to deal with the correlated random inputs and applies the PEM to obtain the moments of the outputs.Then,based on the cumulant theory and the Cornish-Fisher expansion and by using the discrete sample data of the input variables,the digital characteristics and probability statistical properties of the outputs are obtained.Test examples show that the method is appropriate for fast PLF calculation of power systems with high penetrations of new energy power generations.