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.

摘要

这项研究针对风速，太阳辐射和负荷的非线性关系提出了贝叶斯网络模型。基于贝叶斯网络模型的概率潮流计算可以考虑随机变量的相关性，有效地获得概率潮流解决方案的概率特征（如母线电压和支流的概率密度函数）。首先，通过核密度估计方法将风速，太阳辐射和负荷时间序列转换为随机变量，并获得随机变量的概率值。将随机变量的概率值用作贝叶斯网络的输入数据，通过基于蒙特卡洛马尔科夫链法的结构学习和基于最大似然估计法的参数学习建立相关模型。从贝叶斯网络中采样，获得离散概率值，然后通过插值将其转换为连续概率值。然后，通过对连续概率值进行累积概率分布逆变换来获得随机变量的相关样本。与C-vine copula方法和具有改进的交替投影的Latin超立方体采样相比，所提出的贝叶斯网络模型可以更好地展现风速，太阳辐射和负载之间的非线性相关性。最后，通过IEEE 69总线配电系统的概率潮流计算验证了该方法的有效性。