基于多元高斯过程回归和DBSCAN算法的复信号谐波源建模方法

doi:10.19595/j.cnki.1000-6753.tces.242151

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摘要

数据驱动谐波源建模方法采用谐波电信号的幅值和相角数据训练模型,本质上是一种针对复信号的分析处理过程。传统数据驱动算法的设计与实现多在实数域上进行,在进行复信号回归时存在信息丢失的问题。对此本文首先提出一种基于矩阵变量高斯分布的多元高斯过程回归算法,借助行协方差矩阵刻画目标复信号实部虚部间的相关性信息,然后根据多类型谐波源的谐波发射影响因素选取特征变量建立复信号谐波源模型。针对当前数据驱动谐波源建模方法对全局样本学习效果差的问题,本文提出一种模型全局性提升方法,采用基于密度的空间聚类算法划分历史样本数据并建立相应的谐波源子模型,根据待回归样本的输入特征量选择最接近的子模型进行回归。算例表明本文所提算法的复信号回归效果优于高斯过程回归法和复线性最小二乘法,所选建模特征变量能够准确反映多类型谐波源的谐波发射特性,所述全局性提升方法能够提高模型对全局样本的回归精度并减少算法的训练时间。

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关键词 ：多元高斯过程回归, 谐波源建模, 谐波分析, 电能质量, 聚类

Abstract：

The data-driven harmonic source modeling method uses amplitude and phase angle data of harmonic electrical signals to train the model, which is essentially an analysis and processing process for complex signals. The design and implementation of traditional data-driven algorithms are mostly carried out in the real number field, and there is a problem of information loss when performing complex signal regression. In addition, the fitting effect of data-driven methods on harmonic source models is closely related to the learning samples. Due to limited data samples in certain scenarios, the current data-driven harmonic source model can only describe the local harmonic emission characteristics of harmonic source equipment under partial operating conditions, making it difficult to achieve global learning and regression.
To solve the problem of information loss in traditional data-driven algorithms for complex signal regression, this paper first proposed a Multivariate Gaussian Process Regression (MV-GPR) algorithm based on matrix variable Gaussian distribution. The MV-GPR algorithm uses the covariance matrix to characterize the correlation information between the real and imaginary parts of the target complex signal. the posterior distribution calculation and parameter estimation methods of multivariate Gaussian process were derived to achieve uncertainty regression of complex signals. Next, based on the influencing factors of harmonic emission characteristics of various types of harmonic sources, the modeling characteristic variables of complex signal harmonic sources under three-phase unbalance conditions were selected, and the principal component analysis method was used to reduce the dimensionality of the input characteristic variables to ensure the convergence of the algorithm.
To solve the problem of poor global learning performance in current data-driven harmonic source modeling methods, this paper proposed a model global improvement method according to the better performance of MV-GPR algorithm in small-scale sample regression. Firstly, the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm was used to divide historical sample data into sub sample sets representing different operating states of harmonic sources. Then, sub harmonic source models were established based on each sub sample set, and the closest sub model was selected for regression according to the distance between the sample to be regressed and the historical sub sample set, thereby improving the learning and regression effect of the harmonic source model on global samples.
Based on simulation data from multiple types of harmonic sources model and actual measurement data from a 500kV substation of Southern Power Grid, the MV-GPR algorithm, modeling feature selection results and model global improvement method proposed in this paper were compared and verified. The following conclusions can be drawn: (1) The MV-GPR algorithm has higher accuracy in complex signal regression than GPR and CLS algorithms, and can achieve high hit rate uncertainty regression with lower conservatism.(2) The selected MV-GPR complex signal harmonic source model input characteristic variables can accurately reflect the harmonic emission characteristics of multiple types of harmonic sources, and the equivalent fitting accuracy is significantly higher in harmonic source equipment group scenarios.(3) The DBSCAN algorithm can effectively divide historical sample sets under different operating states into multiple sub sample sets. The method of using sub sample set to train sub models can effectively improve the regression accuracy of the harmonic source model on global samples, and can significantly reduce the training time of the algorithm.

Key words： Multivariate gaussian process regression harmonic source modeling harmonic analysis power quality cluster

收稿日期: 2024-11-29

PACS:

TM714

基金资助:

中国南方电网有限责任公司科技项目资助（0000002023030101FK00007）

通讯作者: 陈红坤男,1967年生,教授,博士生导师,研究方向为电能质量分析、电力系统优化规划等。E-mail：chkinsz@163.com

作者简介: 褚昱麟男,2001年生,硕士研究生,研究方向为电能质量分析与评估。E-mail：1252002047@qq.com

引用本文:

褚昱麟, 陈红坤, 王嘉琦, 吴艳梅, 雷傲宇. 基于多元高斯过程回归和DBSCAN算法的复信号谐波源建模方法[J]. 电工技术学报, 0, (): 250433-. Chu Yulin, Chen Hongkun, Wang Jiaqi, Wu Yanmei, Lei Aoyu. Complex Signal Modeling Method for Harmonic Source Based on Multivariate Gaussian Process Regression and DBSCAN Algorithm. Transactions of China Electrotechnical Society, 0, (): 250433-.

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