基于阿基米德Copula和拉丁超立方采样的概率最优潮流计算

Probabilistic optimal power flow computation based on Archimedean Copula and Latin hypercube sampling

提出一种考虑随机变量相关性的概率最优潮流算法。选用广义lambda分布拟合最优潮流模型中的随机变量,建立逆累积分布函数;基于Clayton、Gumbel、Frank、Joe生成元,构筑4种部分嵌套式阿基米德Copula模型对随机变量的相关性结构建模;选取Kendall秩相关系数描述随机变量的相关性,采用相关系数匹配法求取Copula模型的参数;基于生成元的拉普拉斯逆变换,将阿基米德Copula与拉丁超立方采样相结合,生成相关的随机样本用于概率最优潮流计算。对某地区10个风电场风速样本的建模和分析,验证了广义lambda分布和部分嵌套式阿基米德Copula模型的有效性。基于IEEE 118节点系统对2种拉丁超立方采样法进行了对比。

A probabilistic optimal power flow algorithm is proposed.The generalized lambda distribution is employed to fit the random variables in optimal power flow model and build the inverse cumulative distribution functions.Based on Clayton,Gumbel,Frank and Joe generators,four partially nested Archimedean Copula models are constructed to model the dependence structure of random variables.Kendall rank correlation coefficient is adopted to describe the dependency among random variables,and a correlation coefficient matching method is used to obtain the parameters of Copula models.Based on the inverse Laplace transformation of generators,Archimedean Copula and Latin hypercube sampling are combined to generate correlated random samples for probabilistic optimal power flow computation.The modeling and analysis for wind speed samples of ten wind farms in a region verify the effectiveness of the generalized lambda distribution and partially nested Archimedean Copula models.Two Latin hypercube sampling methods are compared based on IEEE 118-bus system.