Usually, neural networks trained on historical feed-in time series of wind turbines deterministically predict power output over the next hours to days. Here, the training goal is to minimise a scalar cost function, often the root mean square error (RMSE) between network output and target values. Yet similar to the analog ensemble (AnEn) method, the training algorithm can also be adapted to analyse the uncertainty of the power output from the spread of possible targets found in the historical data for a certain meteorological situation. In this study, the uncertainty estimate is achieved by discretising the continuous time series of power targets into several bins (classes). For each forecast horizon, a neural network then predicts the probability of power output falling into each of the bins, resulting in an empirical probability distribution. Similiar to the AnEn method, the proposed method avoids the use of costly numerical weather prediction (NWP) ensemble runs, although a selection of several deterministic NWP forecasts as input is helpful. Using state-of-the-art deep learning technology, we applied our method to a large region and a single wind farm. MAE scores of the 50-percentile were on par with or better than comparable deterministic forecasts. The corresponding Continuous Ranked Probability Score (CRPS) was even lower. Future work will investigate the overdispersiveness sometimes observed, and extend the method to solar power forecasts.

The production of wind power predictions with artificial neural networks
(ANN) and other machine learning (ML) methods has become commonplace in
today's energy meteorology services. Recent advances in the field lead to the
development of Deep Neural Networks

While this is a very efficient and effective way to generate deterministic
forecasts, the growing demand for detailed error information in the forecast
poses new challenges. One popular option for providing probability
distribution functions (PDFs) instead of point forecasts is to use the
calibrated output from ensemble forecast models

There are alternatives, however: In the so-called Analog Ensemble (AnEn)
method

An empirical PDF can be implemented by splitting the continuous target values
into several classes representing probabilities. This is described in
Sect.

We demonstrate the new method on two different historical wind power data
sets (Table

The system uses different relevant fields from the GFS-4, IFS and HIRLAM NWP
models as predictors. In addition, live data from the wind farm as well as
aggregated wind power from EEX are ingested (Table

We aim to produce a forecast every hour. Therefore for each hour where all
input data are available, an input vector is compiled from the NWP forecasts
and the other data shown in Table

From each pattern data set, a test set is separated, which is only utilised for evaluation of the fully trained models. The rest of the data is used by the training framework described below.

In deterministic prediction schemes using ANN, the targets are simply
historical wind power observations for each forecast horizon, normalised to
installed capacity. In our method, the targets are instead discretised into
20 bins, leading to a 2-D target matrix for each training pattern
(Fig.

Historical wind power data used for the experiments. For the wind farm, 12 random months were held back as test data. The time ranges include start and end years, but contain periods of missing data. One training pattern per hour was generated for these experiments.

Input data for the DNN models, the setup of which was derived from
previous experiments with deterministic forecasts. We use several wind power
relevant fields from each NWP model, at nodes spread around the region of
interest.

Example forecasts with raw probabilistic output. The shading indicates probability per normalised power bin. The median of the distribution and a deterministic reference run are also shown.

Experiments have shown that DNN with two hidden layers are appropriate to
find a good solution for this kind of problem. We apply meta optimization to
find layer dimensions and the weight decay parameter, as well as automatic
feature selection to remove redundancies from the input vector

For each forecast horizon, the trained system produces an empirical power distribution learned from the variety of similar situations in the training data set.

Figure

As can be seen, the distribution median is systematically lower than the deterministic forecast. The latter minimizes the quadratic difference to the target, and thus rather represents a mean value. Hence, due to the underlying left-skewed distribution of the target values (not shown), the median ends up lower. In addition to the median, the PDFs can be processed into percentiles or other statistical quantities, just like the output from an ensemble forecast model.

A number of validation scores are computed on the test dataset, which, as
mentioned above, comprises only historical data that has been held back from
training. To compare the deterministic forecast with the PDFs, we calculate
the continuous ranked probability score (CRPS), which is equivalent to the
mean absolute error (MAE) in the case of a deterministic forecast

In both cases however, it can clearly be seen that the CRPS of the PDF
forecasts is significantly lower than the MAE. This shows that the PDF does
in fact contain additional information about the targets, which may be
exploited by the forecast's users. The PDF forecasts still leave room for
improvement, as shown in Fig.

Comparing CRPS scores of the full distribution with the equivalent
MAE of deterministic forecasts and the distribution median (50-percentile)
shows the additional information from the probabilistic output.

To validate the resulting error distributions over the forecast horizon, the fraction of observed test set target values below certain percentiles (blue labels on the right) are plotted. For example, at 48 h lead time, only about 5 % of the test data fall below the 10-percentile, which means that small power output values are generally underrepresented in the class histograms.

A prototype method to produce PDF wind power forecasts using only recent wind power measurements as well as deterministic historical forecasts from one or more NWP models was successfully demonstrated. It is conceptually similar to the AnEn method but based on Deep Neural Networks. It can be applied to wind power forecasts at all aggregation levels.

By means of this method, it is possible to deliver more detailed probability information about short term wind power to decision makers without the need for a comprehensive NWP model ensemble and the large computation time, storage and bandwidth requirements that come with it. However, the method depends on the availability and quality of historical data, hence it may not be applicable everywhere from the start.

From the discrete PDFs we can calculate percentiles and other statistical parameters. It has been found that when MAE is used as a quality criterion, the distribution median performs as well or better than a conventional, deterministic forecast using a DNN trained on the same data. The CRPS calculated on the PDF forecasts outperforms the deterministic forecast's MAE by a large margin.

Future work may include better tuning of the output distributions, adaptation to solar PV forecasts and operational implementation.

Data can be provided upon request, but are partially subject to non-disclosure agreements.

MF designed and carried out the experiments, using software contributions from KO. FS and LS provided input to DNN setup and training procedure. CJ delivered data and input regarding the AnEn method. AK oversaw the project. MF prepared the manuscript with input from all co-authors.

The authors declare that they have no conflict of interest.

This article is part of the special issue “European Geosciences Union General Assembly 2018, EGU Division Energy, Resources & Environment (ERE)”. It is a result of the EGU General Assembly 2018, Vienna, Austria, 8–13 April 2018.

This work was supported through grants 01DN15022 (BMBF) and 0325722A (BMWi) by the Government of Germany. Edited by: Michael Kühn Reviewed by: Johannes Schmidt and one anonymous referee