### Abstract

In this report models for extreme negative wind power forecast errors are presented. The models can be applied to estimate levels below which the wind power rarely drops. Such levels could be call called ”certain-levels” or ”guaranteed levels” of wind power, well knowing that full guarantee never can be given. The estimated levels are obtained by modelling the error from already existing wind power forecasting software, this is accomplished by modelling the residuals with statistical extreme value techniques.

The forecasts can be used in the operation of power systems with significant amounts of wind power for example in the planning of ancillary power services, where the level of available wind power with a high degree of certainty is important to know.

The presented extreme value models are applied to negative forecast residuals from state-of-the-art wind power forecast software. This enables the estimation of return levels below which the extreme wind power forecast error events occur only at a specified rate, e.g. once a month or once every year. The techniques allows extrapolation beyond the available data period. In the study data from 1.5 years is used. It consists of hourly wind power production in the two regions of Denmark (DK1 and DK2) and corresponding wind power forecasts. The wind power forecasts are generated using the software WPPT and are based on the outcome of three numerical weather prediction models. They cover horizons from 1 to 42 hours ahead in time and are updated each hour.

In the report a range of extreme value models are suggested. They are of increasing complexity and a model selection is carried using statistical measures and test. A normal procedure when building forecasting models is to divide the data into a learning and a test set to cross-validate the results in order to avoid over-fitting the models. This is hardly ever possible for extreme value analysis, instead the model selection and evaluation sole rely on statistical techniques such as correlation measures, likelihood ratio-tests and information about uncertainty, for example in the form of confidence bands on parameter estimates and predictions.

The foundation to statistical extreme value theory was set by Fisher and Tippett in 1928 and later developed by Gumbel (1958). Since then it has been used for modelling extremes in a wide range of applications. Typical applications are for estimation of extreme weather induced phenomena, for example extreme water levels in a river, wind levels or at sea for design of dykes (de Haan and de Ronde, 1998). In insurance and finance the extreme value modelling is widespread (Embrechts et al., 1997). Extreme value statistics for energy and power applications is also widely used, for example for planning in wind power operation (Horvat et al., 2013) and peak wind prediction (Cook, 1982) and (Friederichs and Thorarinsdottir, 2012). Several books provide comprehensive introductions to extreme value theory, for example Coles (2001) and Beirlant et al. (2006). A really good overview of available extreme value analysis software is given by (Stephenson and Gilleland, 2005). In the present study the R R Core Team (2013) package extRemes Gilleland and Katz (2011) is used.

The forecasts can be used in the operation of power systems with significant amounts of wind power for example in the planning of ancillary power services, where the level of available wind power with a high degree of certainty is important to know.

The presented extreme value models are applied to negative forecast residuals from state-of-the-art wind power forecast software. This enables the estimation of return levels below which the extreme wind power forecast error events occur only at a specified rate, e.g. once a month or once every year. The techniques allows extrapolation beyond the available data period. In the study data from 1.5 years is used. It consists of hourly wind power production in the two regions of Denmark (DK1 and DK2) and corresponding wind power forecasts. The wind power forecasts are generated using the software WPPT and are based on the outcome of three numerical weather prediction models. They cover horizons from 1 to 42 hours ahead in time and are updated each hour.

In the report a range of extreme value models are suggested. They are of increasing complexity and a model selection is carried using statistical measures and test. A normal procedure when building forecasting models is to divide the data into a learning and a test set to cross-validate the results in order to avoid over-fitting the models. This is hardly ever possible for extreme value analysis, instead the model selection and evaluation sole rely on statistical techniques such as correlation measures, likelihood ratio-tests and information about uncertainty, for example in the form of confidence bands on parameter estimates and predictions.

The foundation to statistical extreme value theory was set by Fisher and Tippett in 1928 and later developed by Gumbel (1958). Since then it has been used for modelling extremes in a wide range of applications. Typical applications are for estimation of extreme weather induced phenomena, for example extreme water levels in a river, wind levels or at sea for design of dykes (de Haan and de Ronde, 1998). In insurance and finance the extreme value modelling is widespread (Embrechts et al., 1997). Extreme value statistics for energy and power applications is also widely used, for example for planning in wind power operation (Horvat et al., 2013) and peak wind prediction (Cook, 1982) and (Friederichs and Thorarinsdottir, 2012). Several books provide comprehensive introductions to extreme value theory, for example Coles (2001) and Beirlant et al. (2006). A really good overview of available extreme value analysis software is given by (Stephenson and Gilleland, 2005). In the present study the R R Core Team (2013) package extRemes Gilleland and Katz (2011) is used.

Original language | English |
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Place of Publication | Kgs. Lyngby |
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Publisher | Technical University of Denmark |

Number of pages | 73 |

Publication status | Published - 2015 |

Series | DTU Compute-Technical Report-2015 |
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Number | 01 |

ISSN | 1601-2321 |

### Cite this

Bacher, P., Madsen, H., Pinson, P., Mortensen, S. B., & Nielsen, H. A. (2015).

*Methodology and forecast products for the optimal offering of ancillary services from wind in a market environment*. Kgs. Lyngby: Technical University of Denmark. DTU Compute-Technical Report-2015, No. 01