Conditional Prediction Intervals of Wind Power Generation

A generic method for the providing of prediction intervals of wind power generation is described. Prediction intervals complement the more common wind power point forecasts, by giving a range of potential outcomes for a given probability, their so-called nominal coverage rate. Ideally they inform of the situation-specific uncertainty of point forecasts. In order to avoid a restrictive assumption on the shape of forecast error distributions, focus is given to an empirical and nonparametric approach named adapted resampling. This approach employs a fuzzy inference model that permits to integrate expertise on the characteristics of prediction errors for providing conditional interval forecasts. By simultaneously generating prediction intervals with various nominal coverage rates, one obtains full predictive distributions of wind generation. Adapted resampling is applied here to the case of an onshore Danish wind farm, for which three point forecasting methods are considered as input. The probabilistic forecasts generated are evaluated based on their reliability and sharpness, while compared to forecasts based on quantile regression and the climatology benchmark. The operational application of adapted resampling to the case of a large number of wind farms in Europe and Australia among others is finally discussed.

Nomenclature

Nominal proportion of quantile forecasts.

,

Nominal proportions of the lower and upper bounds of prediction intervals.

Fuzzy set.

Nominal coverage of interval forecasts.

Number of bootstrap replications.

Forecast condition.

Set of forecast conditions.

Support of a fuzzy set.

Forecast error.

Indicator variable for quantile forecasts.

,

Probability density function, density forecast.

,

Cumulative distribution function (cdf), estimated/predictive cdf.

Fuzzy inference model.

, , ,

Common indices.

Interval forecast.

Forecast horizon.

Size of the error sample .

Size of dataset used for evaluating probabilistic forecasts.

Function permitting to identify the subsets of forecast conditions.

Set of forecast errors.

Pn

Wind farm nominal capacity.

,

Quantile, quantile forecast.

Sample of forecast errors.

Sc

Scoring rule for probabilistic forecast evaluation.

SSc

Skill score for probabilistic forecast evaluation.

Time index.

Membership function of a fuzzy set.

Wind speed forecast.

Influential variable.

Set of values for an influential variable.

Weight in the combination of probability density functions.

,

Wind power measurement, forecast.

Number of hits when evaluating the quantile forecasts with nominal proportion .