The Copula-NataF Point Estimate Method Based Probabilistic Power Flow Of Power System With Multiple Wind Farms

Power flow calculation is the basis for realizing power system state estimation,safe and stable operation,and power flow control.The basic principle of power flow calculation is to obtain the distribution of node voltage,active power and reactive power by solving nonlinear equations.Traditional power flow calculation is the process of using power flow calculation methods including Newton-Raphson method to solve the nonlinear equations with certain input states.In recent years,renewable energy represented by wind energy is being connected to the power system on a large scale.Because of the natural uncertainty of wind power,the traditional power flow calculation method must be improved to meet the requirements on accuracy and efficiency for power system power flow caculation.This paper works under the background of the power system with multiple wind farms,with the consideration of the uncertainty and correlation between wind farms.The aim is to employ two-dimensional Copula technology and NataF inverse transform technology to establish an improved new method to calculate the probabilistic power flow in power system.The main works in this paper are listed as follows.（1）Based on historical sampling data,Copula technology is employed to establish wind speed marginal probability density and joint probability density function.In this paper,the Non-parametric Kernel Density Estimate method（NKDE method）is used to estimate the marginal probability density of wind speed,which can not be restricted by the wind speed distribution function.When dealing with the correlation of multiple wind speeds,two-dimensional Copula technology is used as Copula module unit.This method of processing mudular can not only reflect the correlation between wind speeds of multiple wind farms,but also reflect the correlation between binary Copula alone,more flexible.Through the analysis of historical speed data from four wind farms in the central region of the United States,the accuracy of Copula’s randomness and correlation modeling method is verified.（2）A Considering uncertainty equivalent conversion strategy based on the Point Estimate Method（PEM）is proposed.This method converts the uncertain probabilistic power flow calculation into the deterministic one equivalently.Combining the point estimate method with the Newton-Raphson method,a probabilistic power flow calculation process for multiple wind farms connected to the power system is proposed.In the analysis of the calculation example,the two-point estimate method（2-PEM）was used to calculate the probabilistic power flow of the 10 wind farms connected grid,the analysis verified the validity of the method in the power flow calculation.（3）A probabilistic power flow calculation method which considers the wind speed correlation among multiple wind farms,the Copula-NataF point estimate method based probilistic power flow method is proposed.This method combines the inverse NataF transform technology with the point estimate method to establish an improved Copula-NataF point estimate method,and further establishes the power system probabilistic power flow calculation process considering the correlation of multiple wind farms.This method uses the two-dimensional Copula randomness modeling theory to obtain the marginal probability density of the wind farms and the Copula correlation coefficient matrix ρ_ij,uses the inverse NataF transformation to deal with the correlation between the wind farms,and combines it with the PEM to form a Copula-NataF based probabilistic power flow calculation method.This method not only considers the correlation of wind speed,but also transforms the uncertainty probabilistic power flow problem into a certainty one.The numerical simulation verified the correctness and validity of the proposed improved method.