Probabilistic Load Flow Calculation Considering Correlation Based on Bayesian Network

Abstract

This study proposes a Bayesian network model for nonlinear dependence of wind speed, solar irradiation, and load. The probabilistic load flow calculation based on a Bayesian network model can effectively obtain the probability characteristics of probabilistic load flow solutions (such as the probability density function of the bus voltage and branch flow) considering the correlation of random variables. First, the wind speed, solar irradiation, and load time series are converted to random variables by the kernel density estimation method, and the probability values of random variables are obtained. Applying the probability value of a random variable as the input data of the Bayesian network, the correlation model is established through structure learning based on the Monte Carlo Markov chain method and parameter learning based on the maximum-likelihood estimation method. Sampling from the Bayesian network, discrete probability values are obtained, and they are transformed to continuous probability values by interpolation. Then, the correlation samples of random variables are obtained by cumulative probability distribution inverse transformation of continuous probability values. Compared to the C-vine copula method and Latin hypercube sampling with modified alternating projections, the proposed Bayesian network model can better present the nonlinear dependence among wind speed, solar irradiation, and load. Finally, the proposed method is verified by probabilistic load flow calculation of the IEEE 69-bus distribution system.