An Adaptive Multi-Task Gaussian Process Regression Approach for Harmonic Modeling of Aggregated Loads in High-Voltage Substations

To address the challenges of complex harmonic characteristics, multi-source coupling, and strong time variability in aggregated loads downstream of high-voltage substations, this paper proposes an Adaptive Multi-Task Gaussian Process Regression (AMT-GPR) method for harmonic modeling. First, field measurements from the medium-voltage side of a 500 kV substation are denoised and analyzed using Fourier transform to reveal the dynamic patterns and interdependencies of harmonic current magnitudes. Then, a multi-task GPR framework is constructed, incorporating task correlation modeling and adaptive kernel functions to capture inter-task coupling and differences in feature scales. Finally, a probabilistic harmonic model is developed based on multiple sets of measured data, and the modeling performance of AMT-GPR is compared with single-task GPR, conventional MT-GPR, and mainstream machine learning approaches including RBF, LS-SVM, and LSTM. Simulation results demonstrate that traditional harmonic modeling methods are insufficient to capture the dynamic behavior and uncertainty of aggregated loads and AMT-GPR maintains strong robustness under small-sample conditions, significantly reduces prediction errors, and yields narrower uncertainty intervals, outperforming the baseline models. These findings validate the effectiveness of the proposed method in modeling harmonics of aggregated loads in high-voltage substations and provide theoretical support for subsequent harmonic assessment and mitigation strategies.