Probabilistic Operating-Error Forecasting for 10 kV Instrument Transformers Using Intrinsic Variation–Trend Decomposition and Multi-Kernel Deep Gaussian Processes

Accurate forecasting of ratio and phase errors of 10 kV current transformers (CTs) is difficult under distorted and time-varying conditions due to mixed harmonics, ambient-driven drifts, and limited reference-grade field data. This paper proposes a reference-free probabilistic framework for CT operating-error forecasting. First, three-phase secondary waveforms from multiple CTs on the same electrical branch are converted into synchronized phasors, and relative ratio and phase errors are estimated under the common primary current assumption. Then, intrinsic variation–trend decomposition (IVD) separates each error sequence into high-frequency disturbances, medium-frequency operating components, and low-frequency trends, forming an interpretable multiscale representation. Finally, modal features and meteorological variables are fused and fed into a kernel deep Gaussian process (KDGP) model to capture nonlinear, periodic, and trend-related error patterns and generate probabilistic forecasts with adaptive confidence intervals. Experiments on real 10 kV field data show that the proposed IVD–KDGP achieves lower root mean square error (RMSE) and mean absolute error (MAE) than representative deep learning, decomposition-based, and Gaussian process baselines for three-phase ratio- and phase-error forecasting. It also provides well-calibrated prediction intervals and low continuous ranked probability scores (CRPS), showing its effectiveness in both point forecasting and uncertainty quantification. The proposed method offers a practical tool for online error tracking, prioritized calibration, and long-term power quality management of CTs.