Probabilistic Spatiotemporal Modeling of Day-Ahead Wind Power Generation with Input-Warped Gaussian Processes

TL;DR

This work introduces a probabilistic spatiotemporal Gaussian Process framework with input warping to model day-ahead wind-power forecast errors across hundreds of wind farms. The model employs a separable kernel in warped spatial and temporal inputs, incorporating both spatial 2D and temporal 1D warping via flexible RBF layers, and a temporal kernel that combines a Matérn component with a daily periodic term. Through synthetic validation and an ERCOT case study, the authors demonstrate that joint, warped GP modeling improves calibration and sharpness of probabilistic forecasts and enables realistic scenario generation for grid operations. The approach yields actionable uncertainty quantification for asset-level and zonal planning, supporting more robust risk-aware unit commitment and dispatch strategies. The work also offers practical guidance on kernel selection, warp configuration, and model selection via a modified BIC, with potential extensions to multi-output GPs and continuous-time temporal modeling.

Abstract

We design a Gaussian Process (GP) spatiotemporal model to capture features of day-ahead wind power forecasts. We work with hourly-scale day-ahead forecasts across hundreds of wind farm locations, with the main aim of constructing a fully probabilistic joint model across space and hours of the day. To this end, we design a separable space-time kernel, implementing both temporal and spatial input warping to capture the non-stationarity in the covariance of wind power. We conduct synthetic experiments to validate our choice of the spatial kernel and to demonstrate the effectiveness of warping in addressing nonstationarity. The second half of the paper is devoted to a detailed case study using a realistic, fully calibrated dataset representing wind farms in the ERCOT region of Texas.

Figures (13)

• Figure 1: Locations $\mathbf{s}_m$ of the $m=1,\ldots,181$ wind power facilities in a longitude-latitude coordinate map, colored by the 8 ERCOT zones. Most wind farms are in the Northern and Western areas of Texas.
• Figure 2: Power ratios at Ajax Wind Farm for every hour in May 2018 (336 hours total). a): Actual $\Tilde{p}^{A}$ and forecasted $\Tilde{p}^{F}$ wind power ratios. b) Forecast errors $y$. $\Tilde{p}^A_{\cdot}$ is systematically higher than $\Tilde{p}^F_{\cdot}$ during this period. The forecast error $y_{\cdot}$ is symmetrically distributed around zero.
• Figure 3: The autocorrelation of forecast errors at different hour lags within a single day. The regional ACF is calculated as the mean of ACFs of each location within that region. The grey region is the bootstrapped 95% confidence interval of ACF.
• Figure 4: Variograms of the forecast error data. The pairs $(d, v)$ are visualized with the x-axis representing the distance and the y-axis representing the estimated variance.
• Figure 5: Illustration of input warping with RBF units $g_{\text{rbf}}$. We visualize how a uniform $(0,1)\times(0,1)$ grid is transformed by one and two RBF warping units with indicated hyperparameters.