A Semi-Analytic Wind-State Predictability Benchmark for Single-Turbine Wind Power Forecasting

Abstract. Wind-power forecasting is commonly evaluated in relative terms, so a reported error is difficult to interpret without a reference for the uncertainty implied by the available information. We estimate a model-conditional wind-state predictability benchmark for single-turbine forecasting: the Bayes risk under squared loss implied by a Gaussian autoregressive description of future wind speed, propagated through an empirical turbine power curve and combined with scatter about that curve. The benchmark is conditional on the stated wind-only information set and fitted wind-dynamics model; it is not a universal lower bound for forecasters supplied with additional variables. We evaluate it deterministically by Gauss–Hermite quadrature over the conditional distribution of future wind speed and empirical averaging over contiguous observed AR(3) wind states. Low-order Taylor approximations overestimate the curve-variation component at long horizons by 22–61 %, depending on site and smoothing window. A variance decomposition separates the horizon-dependent contribution of wind uncertainty from residual scatter about the curve. Across two operational UK wind farms and nine horizons from one to forty-eight hours, every tested wind-only method has a point-estimate RMSE above its corresponding benchmark at all eighteen site–horizon combinations; point-estimate gaps range from 0.9 to 4.5 percentage points. The framework provides an interpretable reference for assessing forecast difficulty and for identifying where richer meteorological inputs may add value.