Probabilistic Computational Model for Correlated Wind Speed, Solar Irradiation, and Load Using Bayesian Network

Abstract

This paper proposes a Bayesian network (BN) that can construct the nonlinear dependence among wind speed, solar irradiation, and load. The correlations of random variables (RVs) are analyzed using the Pearson correlation coefficient, Kendall rank correlation coefficient, and Spearman rank correlation coefficient. According to Bayesian theory, the Bayesian information criterion (BIC) and maximum likelihood estimation (MLE) methods are employed to determine the structure and parameters of a BN. Then the BN model of RVs is established. The constructed model is the joint probability distribution of RVs that can present the nonlinear dependence and marginal distribution (MD) of RVs without limitation. The testing samples of wind speed, solar irradiation, and load are generated using the autoregressive integrated moving average (ARMA) model. Then these samples are utilized to construct the probability model of a BN and C-vine copula, whose modeling accuracy and efficiency are compared, and the quality of their output synthetic samples are analyzed. In the modified IEEE 118-bus test system, two kinds of synthetic samples are used to calculate the probabilistic load flow (PLF), whose accuracy and efficiency based on the BN are tested. The validity of the BN model is verified.

Keywords

• Bayesian network
• C-vine copula
• nonlinear dependence
• joint probability distribution
• uncertainty
• probabilistic load flow