Probabilistic Harmonic Power Flow Algorithm Based On Stochastic Analysis Methods

With a large number of non-linear components connected to the power system,harmonic pollution has become one of the most important power quality problems.Harmonics are propagated through the grid with randomness.Therefore,it is of great significance to study the propagation and distribution of harmonics in power system.The purpose of the probabilistic harmonic power flow calculation is to obtain the probability density function of the harmonics,which is helpful to evaluate the operational risk and the weak link of the power grid.The harmonic power flow calculation program based on C ++ language is prepared by using the harmonic power flow decoupling algorithm.The program can accurately build the computing network needed for the harmonic power flow.According to the harmonic impedance equivalent circuit and the grid topology,the harmonic admittance matrix is build.Use the sparse matrix technique to solve the harmonic power flow equation.The analysis of a simple power system is compared with the existing literature to prove the accuracy of the program calculation.A probabilistic harmonic power flow method based on cumulant,linear harmonic equation and maximum entropy model is proposed.Firstly,the numerical characteristic such as higher order moments and cumulant are obtained according to the samples of harmonic current.The harmonic power flow equation is constructed according to the basic data of the grid and linearized at the reference operating point.Calculate the harmonic current sensitivity matrix and the harmonic voltage numerical characteristic.Then use the maximum entropy model to fit the probability density function.The proposed method can avoid repeated operation and subjective error.The amount of calculation is small,and the results are objective and accurate.Finally,the probabilistic harmonic power flow is calculated on the IEEE 57-node power system with the harmonic samples in an actual grid.The results are compared with the Monte Carlo method to verify the effectiveness of the method.A probabilistic harmonic calculation method based on Pearson correlation coefficient matrix,Cholesky decomposition and linear transformation is proposed to consider the correlation of harmonic sources.Firstly,the correlation between the random harmonic currents is analyzed and described by the Pearson correlation coefficient matrix.Then decompose the correlation coefficient matrix to obtain the linear transformation matrix.The interrelated harmonic current is decoupled by linear transformation to get the independent harmonic current.At the same time,the harmonic current sensitivity matrix should be adjusted.Then use the proposed method to calculate the harmonic voltage probability density function.The proposed method is tested in the IEEE 57-node power system with a control experiment by Monte Carlo method.The results show the effectiveness of the proposed method.Further analysis shows that the correlation will cause some influence on the result of the calculation of the probability harmonic power flow.The standard deviation of the harmonic voltage may become larger,which has the guiding significance to the grid operation risk assessment.