Probabilistic Wind Power Modelling via Heteroscedastic Non-Stationary Gaussian Processes

TL;DR

The paper tackles probabilistic wind-power forecasting from SCADA data by addressing two core challenges: non-stationarity in the wind–power relationship and input-dependent noise. It introduces a heteroscedastic non-stationary Gaussian process built on the generalized spectral mixture kernel, with kernel parameters and noise variance learned as smooth input functions via MAP. Empirical results on 10-minute SCADA records show that jointly modeling non-stationarity and heteroscedasticity yields superior calibrated predictive distributions (lower NLPD, CRPS, and Winkler scores) and sharper uncertainty intervals compared to stationary GP, non-stationary GP, and non-GP baselines. The approach offers an interpretable, data-efficient framework for uncertainty quantification in wind farm operations and suggests scalable extensions (e.g., sparse/variational GP, higher-dimensional features).

Abstract

Accurate probabilistic prediction of wind power is crucial for maintaining grid stability and facilitating the efficient integration of renewable energy sources. Gaussian process (GP) models offer a principled framework for quantifying uncertainty; however, conventional approaches typically rely on stationary kernels and homoscedastic noise assumptions, which are inadequate for modelling the inherently non-stationary and heteroscedastic nature of wind speed and power output. We propose a heteroscedastic non-stationary GP framework based on the generalised spectral mixture kernel, enabling the model to capture input-dependent correlations as well as input-dependent variability in wind speed-power data. We evaluate the proposed model on 10-minute supervisory control and data acquisition (SCADA) measurements and compare it against GP variants with stationary and non-stationary kernels, as well as commonly used non-GP probabilistic baselines. The results highlight the necessity of modelling both non-stationarity and heteroscedasticity in wind power prediction and demonstrate the practical value of flexible non-stationary GP models in operational SCADA settings.

Figures (3)

• Figure 1: Filtered SCADA dataset and data subsets used for model development and evaluation. The left panel shows the active power (kW) versus wind speed (m/s) after removing non-operational and faulted records. The middle and right panels display the training and test subsets, respectively, derived from temporally disjoint periods between 2017-2019 (training) and mid-2019 (testing).
• Figure 2: Comparison of point-predictive and probabilistic performance across all models. The first column reports point-error metrics (RMSE, MAE, NMAPE), and the second column presents probabilistic scores (NLPD, CRPS, MACE). The middle panel shows Winkler scores at nominal levels of $80$%, $90$%, and $95$%. The fourth column displays quantile losses at $\tau = \{0.1, 0.5, 0.9\}$, while the last column shows empirical coverage at nominal levels of $80$%, $90$%, and $95$%. Lower values indicate better performance across all metrics, whereas coverage closer to the nominal target (dashed dark grey line) reflects improved calibration. Abbreviations: CRPS -- continuous ranked probability score, GP -- Gaussian process, GSM -- generalised spectral mixture, MAE -- mean absolute error, MACE -- mean absolute coverage error, NMAPE -- normalized mean absolute percentage error, NLPD -- negative log predictive density, Prob. -- probabilistic, RBF -- radial basis function, RMSE -- root mean square error, SM -- spectral mixture.
• Figure 3: Predictive mean and 95% predictive intervals (PI) for all models. The shaded regions indicate the 95% confidence intervals, and the percentage of test observations falling outside each interval is reported within each subplot. Abbreviations: GP -- Gaussian process, GSM -- generalised spectral mixture, Prob. -- probabilistic, RBF -- radial basis function, SM -- spectral mixture.