Weather Ensembles and the Day-Ahead Price

From Weather to Power

Hourly capacity factor (CF) comes from ERA5 10 m wind, a shear law and air density, run through a synthetic power curve (Ryberg et al., 2019) set by the capacity-weighted specific power of the onshore fleet in the German and Danish unit registers. A single speed correction (one slope and offset for all months), fitted on 2015-2016, is the only tuning. In 2018 and 2019 the modelled hourly CF of the fleet as built follows ENTSO-E realised onshore generation with a correlation of 0.94 to 0.97 and a mean bias under two percentage points of CF.

The Capture Rate

The capture rate is the CF-weighted mean day-ahead price divided by the time-mean price. Over 2015-2019 the 2019 onshore fleet captures of the baseload price in DE-LU and in DK1, a capture price of and respectively. Winter carries the deepest discount, with pooled December-February months at in DE-LU and in DK1. These are the prices that cleared with the fleet as built, so the rate is not what a 2019 fleet would have earned in 2015.

The Dunkelflaute Premium

Day-ahead prices inside a 48-hour low-wind spell, where the mean CF falls below the seasonal 10th percentile of 2000-2014, are higher than in comparable hours in DE-LU and in DK1, after month-of-sample and hour-of-week fixed effects. In DE-LU the premium is concentrated in winter, at EUR/MWh in December-February against in June-August. Spells are identified from realised wind, so the premium is an after-the-fact association with price.

Forecasting the Low Tail

Two post-processing routes turn the five-member reforecast into a probabilistic CF forecast, each refitted every year on earlier years and evaluated against ERA5-driven CF over 2005-2019 (5,478 forecasts per zone). The CF-direct route fits a censored-logistic EMOS to CF at each lead time. The wind-then-map route fits EMOS to wind at the fleet's nodes and runs every member through the power model above.

Across the bulk of the distribution the two routes are close, within of each other in CRPS skill at every lead. Both lift day 1-3 skill against climatology from the raw ensemble's 0.40-0.45 to 0.66-0.71, and their skill decays towards zero by day 11-16.

The low tail separates them. Below the seasonal 10th percentile of CF, the occurrence ratio (observed over forecast frequency, 1 when calibrated) stays between at every lead day out to day 16 for wind-then-map. The raw ensemble under-states low-wind hours (), and CF-direct over-states them (). Beyond day 7 much of that over-statement appears to come from the censored logistic itself, which piles probability onto exactly CF = 0 as its spread grows (44-76 % of the CF-direct tail probability at day 8-16), a value the ERA5-driven CF never takes. Post-processing the wind and mapping it through the power curve avoids that bound, and the low tail stays close to calibrated.

A Foundation Model in the Blend

Chronos-2, a pretrained time-series foundation model, receives the CF history with the reforecast mean and spread as known-future covariates. After full fine-tuning, a 50/50 quantile blend of Chronos-2 and the wind-then-map forecast improves on wind-then-map alone at day 4-10 in both zones over 2019, by in CRPS skill with every 95 % interval above zero.