基于多元高斯过程回归和空间聚类的复信号谐波源建模

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

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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

Received: 29 November 2024

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TM714

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	Chu Yulin
	Chen Hongkun
	Wang Jiaqi
	Wu Yanmei
	Lei Aoyu

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Chu Yulin,Chen Hongkun,Wang Jiaqi等. Complex Signal Modeling Method for Harmonic Source Based on Multivariate Gaussian Process Regression and DBSCAN Algorithm[J]. Transactions of China Electrotechnical Society, 2025, 40(23): 7621-7634.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.242151 OR https://dgjsxb.ces-transaction.com/EN/Y2025/V40/I23/7621

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