Abstract:  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.

Key words: average first-order saddle point approximation, probability power flow, probability density estimation