基于Nataf变换含相关性的扩展准蒙特卡洛随机潮流方法

随机潮流分析中,准蒙特卡洛方法在同样规模下不仅计算效率高于基于拉丁超立方的方法,且具有更好的扩展性质。因此提出一种基于Nataf变换的扩展准蒙特卡洛方法(NEQMC)并应用于概率潮流计算中。该方法利用Nataf变换重构输入变量的概率分布,而扩展技术可在随机潮流未收敛时保留已知的潮流计算结果,基于奇异值分解的相关系数控制技术不仅可保持扩展前后样本的相关性,且使得该方法也适用于相关系数矩阵非正定的情况。与基于Nataf变换的简单随机抽样、扩展拉丁超立方方法在IEEE 30和IEEE 118节点系统的比较分析证明了所提方法的高效性和准确性,仿真结果表明:相比于拉丁超立方和简单随机抽样,NEQMC的输出变量准确度更高,特别是标准差的准确度得到大幅改进,获得相同准确度的计算复杂度大大减小。

A Nataf Transformation Based on Extended Quasi Monte Carlo Simulation Method for Solving Probabilistic Load Flow Problems with Correlated Random Variables

For probabilistic load flow (PLF) analysis,quasi Monte Carlo (QMC) simulation method has higher efficiency than Latin Hypercube Sampling,and its extension is more flexible.Therefore,a Nataf transformation based extended QMC (NEQM) method is proposed to solve the PLF problems.During the process,the extended procedure enlarges the sample size with arbitrary step,and then the Nataf transformation is performed to reconstruct the probability distributions of input variables.With the increase of sample size,this method retains the load flow results already obtained.Furthermore,singular value decomposition method is employed to control the correlation matrix before and after the extension in place of Cholesky decomposition,which is able to handle the non-positive definite correlation matrixes,simultaneously.Through IEEE 30 and IEEE 118 bus systems,the proposed method shows its efficiency and accuracy in comparison with Simple Random Sampling and Nataf Transformation based Extended LHS.The simulation results suggest that,NEQM enhance the accuracy of obtained variables especially the standard deviations with shorter consuming time.