基于多维高斯混合模型的电力系统不确定性建模方法

Power System Uncertainty Modeling Based on Multivariate Gaussian Mixture Model

在基于多维高斯混合模型的电力系统多变量概率建模中,针对期望最大化算法参数估计精度较低的问题,该文引入非参数核密度估计和密度保留的分层期望最大化算法,提出一种基于高斯成分数约简的建模方法。以非参数核密度估计结果作为基高斯混合模型,采用密度保留的分层期望最大化算法约简高斯成分数,能够建立任意高斯成分数的高斯混合模型,克服了期望最大化算法在高斯成分数较多时参数估计精度低的问题。为降低大样本下的建模计算负担,提出按时间尺度分层的建模方法。为解决相互独立的多个随机变量出现高斯成分数组合爆炸的问题,提出“组合–约简”分层建模方法。采用具有复杂分布特性的实测多维风速数据和负荷数据对所提方法作了测试,结果表明,所提方法的精度显著优于基于期望最大化算法的高斯混合模型和Copula函数法。

To overcome the low accuracy problem of the expectation-maximization(EM)algorithm in establishing multivariate probability models based on the Gaussian mixture model(GMM),this paper introduces kernel density estimation(KDE)and the density-preserving hierarchical expectation-maximization(DPHEM)algorithm,and proposes an improved KDE-DPHEM-based algorithm for establishing GMM.The proposed method first uses KDE to build a base GMM and then reduces its component number by DPHEM,which overcomes the problem that the EM algorithm fails to obtain an accurate GMM with large component numbers.Furthermore,to reduce the computational burden of dealing with big data,a hierarchical modeling method according to time scales is proposed;to overcome the combinatorial explosion problem on component numbers for modeling independent random variables,a combination-reduction hierarchical modeling method is also proposed.The proposed methods are tested based on actual wind speed and load data with complicated features.The results show that the proposed methods can obtain a highly accurate GMM,which is superior over the EM-based GMM and Copula functions.