计及相关性的改进均值一阶鞍点估计概率潮流计算

Probabilistic Load Flow Calculation Based on Improved Mean Value First Order Saddle Point Approximation Considering Correlation

概率潮流是用于计算具有不确定性电力系统运行的重要工具。许多已知的算法都是假定给定的概率密度函数来模拟随机变量的不确定性,形成参数概率潮流工具。但是随机变量的不确定性可能不会落在标准的概率密度函数中,因此提出了非参数模型即均值一阶鞍点估计模型。均值一阶鞍点估计法要求输入变量相互独立,针对这种情况,提出利用Cholesky分解将相关的输入变量转化成不相关的变量,同时为了解决一些输入变量的累积量母函数不能用显函数表示的情况,提出采用Taylor级数展开。该方法在求解输出变量概率密度函数和累积分布函数时,不需要积分或者微分。最后,在改进的IEEE34节点系统上进行仿真,结果表明所提算法的有效性和实用性。

Probabilistic load flow is an important tool for solving uncertainty of power system operation. Many known algorithms assume a given probabilistic density function to simulate the uncertainty of a random variable to form a parametric probability load flow tool. However,the uncertainty of random variables to form a parametric probability density function,so a nonparametric model was presented,the mean first order saddle point estimation method,which requires that the input variables are independent of each other. In this case,the Cholesky decomposition was proposed to convert the relevant input variables into irrelevant variables. At the same time,Taylor series expansion was proposed to solve the problem that the cumulant generating function of some input variables can not be expressed by explicit function. The method does not need integration or differential when solving the probability density function and the cumulative distribution function of output variables. Finally,the modified IEEE 34-bus system was tested in the simulation calculation,the results show that the proposed algorithm is effective and practical.