基于Copula理论和高斯混合近似的半不变量研究

Research on Semi-Invariants Based on Copula Theory and Gaussian Mixture Approximation

随着光伏可再生能源越来越多地并入电力系统,传统的确定性潮流无法准确描述电力系统的实际运行状态。为此,提出了一种将半不变量法、Copula理论和高斯混合逼近法相结合的概率潮流分析方法。该方法克服了现有的级数展开法无法逼近多峰概率分布的缺点,考虑了输入总线功率的高斯型、非高斯型和离散型概率分布的混合,在不使用任何级数展开方法的情况下,精确地得到了与这些相关输入的多模母线电压和线路功率流的概率分布。同时,考虑了多输入相关性,在IEEE14和IEEE57节点系统中验证了该方法的性能。实验结果表明,该方法精确地建立了期望随机变量的多模态分布,与Gram-Charlier法相比,运行时间降低了76%。

With more and more photovoltaic renewable energy integrated into the power system,the traditional deterministic power flow can not accurately describe the actual operation state of the power system.We present a probabilistic power flow analysis method which combines semi invariant method,Copula theory and Gaussian mixture approximation method.This method overcomes the shortcoming that the existing series expansion method can not approximate the multimodal probability distribution.The mixture of Gaussian,non Gaussian and discrete probability distributions of input bus power is considered.Without using any series expansion method,the probability distributions of multi-mode bus voltage and line power flow with these correlated inputs are obtained accurately.Multi input correlation is considered.The performance of this method is verified in IEEE14 and IEEE57 bus system.Experimental results show that the multi-modal distribution of the expected random variables is accurately established,and the running time of the proposed method is reduced by 76%compared to the Gram-Charlier method.