改进一阶鞍点近似的概率潮流

Probabilistic Power Flow Based on Improved Saddle Point Approximation

由于可再生能源和负荷的不确定性,电力系统潮流分析需要有效的工具。目前的多数研究都假设一组给定的概率密度函数(PDF:Probability Density Functions)建模不确定性,并开发参数概率潮流工具。为此,提出了一种非参数概率潮流分析方法确定潮流输出的偏微分方程。该方法基于平均值一阶鞍点近似。对于n个随机变量系统,利用潮流计算建立一阶Taylor级数展开,然后采用鞍点近似确定期望输出变量的概率特性。所提出的非参数估计器在需要合理的计算量的同时,能提供精确的结果。此外,在不使用积分或微分算子的情况下,直接建立了潮流输出的概率分布函数和累积分布函数。在IEEE 14总线和IEEE 118总线测试系统上进行了测试,所得结果与其他方法相比,MVFOSPA(Mean Value First Order Saddle Point Approximation)比MCS(Monte Carlo Simulation)算法运行时间减少了12%,验证了MVFOSPA方法的有效性。

Due to the uncertainty of renewable energy and load,power flow analysis of the power system needs effective tools. Many existing literatures assume a given set of PDF( Probability Density Functions) to model uncertainties and develop parametric probabilistic power flow tools. A nonparametric probabilistic power flow analysis method is proposed to determine the partial differential equation of power flow output. The method is based on the first order saddle point approximation of the mean value. For system with N random variables,the first order Taylor series expansion is established by power flow calculation,and then the probability characteristics of the expected output variables are determined by saddle point approximation. The proposed nonparametric estimator can provide accurate results while requiring reasonable computation. And the probability distribution function and cumulative distribution function of power flow output are directly established without using integral or differential operators. The test results on IEEE 14 bus and IEEE 118 bus test systems show that compared with other methods,mvfospa( Mean Value First Order Saddle Point Approximation) reduces the running time of MCS( Monte Carlo Simulation) algorithm by 12%. The effectiveness of MVFOSPA method is verified.