基于非参数贝叶斯谐波阻抗估计的谐波责任区分Division of Harmonic Responsibility Based on Nonparametric Bayesian Harmonic Impedance Estimation
江友华,刘子瑜,张煜,杨兴武,吴卫民
JIANG Youhua,LIU Ziyu,ZHANG Yu,YANG Xingwu,WU Weimin
摘要(Abstract)：
线性回归法在背景谐波电压波动的情况下估计谐波阻抗有较大误差,其诸多改进方法又普遍具有局限性。为此,基于非参数贝叶斯估计提出一种普适性方法。将背景谐波电压视为隐变量,用GMM(高斯混合模型)建模,并指出GMM的参数在实际工程背景下的意义;将GMM参数、线性模型参数建模为狄利克雷过程混合模型,并推导出其后验分布;利用马尔科夫链-蒙特卡洛采样方法从后验分布中抽取样本,基于样本进行贝叶斯估计,求解谐波阻抗和背景谐波电压工况数,进而对谐波责任进行评估。将IEEE 14节点测试系统与实测案例结合进行仿真,通过非参数贝叶斯估计法与线性回归法仿真结果的对比,验证了非参数贝叶斯估计法的有效性。
Errors occur in harmonic impedance estimation by linear regression under the condition of background harmonic voltage fluctuations, but the improvements have their limitations. Therefore, a universal method based on non-parametric Bayesian estimation is proposed. The background harmonic voltage is regarded as a latent variable, and GMM(Gaussian mixture model) is used for modeling, and the significance of the parameters of the Gaussian mixture model in the actual engineering context is expounded. The Gaussian mixture model parameters and linear model parameters are modeled as Dirichlet process mixture models, and their posterior distributions are derived. The Markov chain monte Carlo sampling method is used to extract samples from the posterior distribution, and Bayesian estimation is performed based on the samples, the harmonic impedance and the number of background harmonic voltage conditions are solved, and then the harmonic responsibility is evaluated. The IEEE 14-nodes test system is combined with actual test cases for simulation, and the non-parametric Bayesian estimation method and linear regression method are compared to verify the effectiveness of the non-parametric Bayesian estimation method.
关键词(KeyWords)：
隐变量;高斯混合模型;狄利克雷过程混合模型;马尔科夫链-蒙特卡洛采样;背景谐波电压工况;谐波责任区分
latent variable;Gaussian mixture model;Dirichlet process mixture model;Markov chain Monte Carlo;background harmonic voltage conditions;harmonic responsibility division
基金项目(Foundation): 国家自然科学基金项目(51877130);; 上海市科技创新行动计划项目(19DZ1205402)
作者(Author):
江友华,刘子瑜,张煜,杨兴武,吴卫民
JIANG Youhua,LIU Ziyu,ZHANG Yu,YANG Xingwu,WU Weimin
DOI: 10.19585/j.zjdl.202103009
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