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

Hongtao Wang,Bin Zou

doi:10.1109/access.2020.2977727

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.

Highlights

With the increasing permeability of distributed generation (DG) supplies, the influence of randomness and uncertainty of DG output on the safe and stable operation of a power grid should not be ignored [1]
Many researchers have applied copula theory to Probabilistic load flow (PLF) calculation, and the method has high precision. It is a typical method of correlation modeling, in which the copula function is used to connect the marginal distribution (MD) of input random variables (RVs), the joint probability distribution of input RVs is established, and the correlation of input RVs is described by a Kendall or Spearman rank correlation coefficient
From the results of 1000 instances of PLF calculation based on synthetic samples (Table 6), the Bayesian network (BN) method is better than C-vine copula and has high calculational accuracy

Summary

INTRODUCTION

With the increasing permeability of distributed generation (DG) supplies, the influence of randomness and uncertainty of DG output on the safe and stable operation of a power grid should not be ignored [1]. Many researchers have applied copula theory to PLF calculation, and the method has high precision It is a typical method of correlation modeling, in which the copula function is used to connect the marginal distribution (MD) of input RVs, the joint probability distribution of input RVs is established, and the correlation of input RVs is described by a Kendall or Spearman rank correlation coefficient. The BN model solves the problem of PLF calculation, whose input RVs are wind speed, solar irradiation, and load with complex nonlinear dependence. A Kendall or Spearman rank correlation coefficient is used to describe the correlation among RVs, but these can only describe some nonlinear dependence, so the C-vine copula method cannot completely describe the nonlinear dependence among RVs. We propose a BN method to obtain a joint probability distribution of RVs without Pearson, Kendall, and Spearman correlation coefficients.

BN MODEL

PROBABILISTIC LOAD FLOW CALCULATION BASED ON CORRELATION SAMPLES

CONCLUSION