电网可靠性评估中相关性变量的非参数R藤Copula模型

A Nonparametric Regular Vine Copula Model for Multidimensional Dependent Variables in Power System Reliability Assessment

Copula函数可将多维随机变量的边缘分布和相关性结构分开表达,在计及相关性的电网风险分析中日益得到重视。在二维相关性建模上Copula函数精度较好,而高维情况则面临模型参数估计的复杂性和准确性问题。据此,该文提出非参数R藤Copula模型,基于高维模型分解思路将高维Copula函数分解成多个二维Copula函数的乘积,并基于数据驱动方式实现二维Copula函数的非参数估计,此外为避免非参数估计中随机变量分布范围超出实际可行域的问题,进一步提出概率空间变换的思路。该文方法可实现高维随机变量相关性模型的灵活准确构建,最后,通过相关算例分析验证方法的正确性和有效性。

Copula function has merit in formulating the marginal distribution and dependence structure of multidimensional random variables separately,and gains increasing attention in the probabilistic risk analysis of power system.Although Copula function does well in dependence modeling for two-dimensional case,it encounters problem of computational complexity and modeling accuracy for high dimensional scenarios.This paper proposed a nonparametric regular vine copula model,which converts the highdimensional Copula function into the product of some bivariate Copulas functions.Moreover,the parameters of these bivariate Copulas were estimated based on data-driven nonparametric method.Furthermore,in order to avoid the problem in nonparametric estimation that the distribution range of the estimated Copula exceeds its feasible domain,a probability distribution transformation method was also presented.The dependence model of multivariate can be modeled flexibly and accurately by the proposed method,and its validity was verified by case studies.