Data-Driven Probabilistic Forecasting of Voltage Quality in Distribution Transformers Using Gaussian Processes

A probabilistic data-driven framework for voltage quality forecasting in distribution transformers based on Gaussian process regression and high-resolution field measurements is presented. Voltage time series acquired under real operating conditions were modeled using composite covariance functions designed to capture long-term trends and stochastic multi-scale fluctuations. The proposed approach enables simultaneous prediction and uncertainty quantification, allowing direct compliance assessment with voltage quality standards. The additive Gaussian process models achieved coefficients of determination above 0.75 and produced statistically uncorrelated residuals, indicating an adequate representation of the intrinsic temporal structure. However, the predictive intervals exhibit a certain level of undercoverage, indicating that, while uncertainty is effectively quantified, there is still room for improvement in calibration. The selected kernel structures revealed distinct physical regimes in the voltage dynamics, including smooth steady operation, moderately irregular behavior associated with localized disturbances, and multi-scale stochastic variability. For benchmarking purposes, results were compared with those obtained from a stochastic damped harmonic oscillator with restoring force, a naive model, a seasonal naive model and an Autoregressive Integrated Moving Average model. The oscillator model, the naive model, the seasonal naive model, and the Autoregressive Integrated Moving Average model generated strongly autocorrelated residuals, whereas the Gaussian process models yielded consistent white-noise residuals that outperformed all the other models. These findings demonstrate that probabilistic Gaussian process modeling provides an interpretable, scalable, and uncertainty-aware alternative for predictive voltage quality assessment in modern distribution systems.