Using time-adaptive probabilistic forecasts for grid management – challenges and opportunities
Raik Becker, Phd student, Chair for Management Science and Energy Economics, University Duisburg-Essen,
Phone: +492011832643, email:
Christoph Weber, Chairholder, Chair for Management Science and Energy Economics, University Duisburg-Essen,
Phone: +492011832966, email:
Overview
The literature on wind power forecasting has practically “exploded” in recent years [1]. Many methods to generate point forecasts as well as probabilistic forecasts have been developed and are in use. In addition, various publications focus on the characteristics of the wind power forecast error. However, many of these studies concentrate on single wind generators or wind parks. Unfortunately, transmission system operators (TSOs) seem to have adopted this approach and treat their control area as a single wind generator, namely by using just one forecast for the entire control zone. By doing this, they neglect not only spatio-temporal information, but also the spatial distribution of wind farms in their control area. It has been shown that there is a high cross-correlation between distinct wind sites in a control area due to the inertia of meteorological systems [2]. [2] use this information to improve very short-term point forecasts notably. Besides point predictions, probabilistic forecasts permit to describe the nature of wind power in-feeds completely and are, therefore, state-of-the-art in wind power prediction tools [1]. So far, the benefit from using spatio-temporal information to improve probabilistic forecasts has not been analysed except for a parametric approach. However, literature agrees that parametric approaches are not suitable for the description of wind power forecast errors due to its inherent restrictive assumptions [3].
It is the subject of our research to develop a method that uses spatio-temporal information in order to improve non-parametric probabilistic forecasts for a larger area. Thereby, the focus is on the applications for TSOs and it is assumed that they have point predictions for several wind farms, which are then adjusted and connected to each other by the presented method. The challenges to relate the forecasts of different wind parks to a respective grid node are discussed. Additionally, one objective is to obtain a probabilistic wind power forecast for each grid node. The potential benefits for TSOs are emphasized.
Methods
There exist three main approaches to generate probabilistic forecasts for wind power, namely quantile regression [4,5], adapted re-sampling with fuzzy inference [3,6] and kernel density estimation (KDE) [7,8]. Only the latter provides the forecast user with an entire probability density function (pdf). Moreover, KDE is capable of incorporating explanatory variables easily. This facilitates to account for the forecast errors at relevant neighbouring grid nodes. What makes a neighbouring grid node relevant depends on the prevailing wind direction in the area of interest.
Instead of deriving the probabilistic forecast from the wind power point prediction (direct approach), we focus on the distribution of the forecast error and add this one to the point prediction (prediction error approach). Thus, the approach is independent from the used forecast method, which is necessary since TSOs rather buy point predictions than generate their own.
Given the relevant explanatory variables X and its realisations x, the conditional pdf of the wind power forecast error f(y|X=x) can be estimated with KDE. Thereby, X should consist of the predicted wind power and foregone forecast errors of grid nodes that are upwind. The cross-correlation facilitates to choose the relevant grid nodes and most influencing time lag. This approach enables to make use of spatio-temporal information directly. For the problem of wind power prediction, y varies also with the look-ahead time k. Thus, f(y|X=x) becomes f(yt+k|X=xt|t), which leads to k different conditional pdfs.
Normally, the joint distribution function fxy(x,y) and the marginal pdf of X f(x) are required in order to compute f(y|X=x) [7,8]. Besides the estimation of the joint distribution function fxy(x,y), [8] present an approach that uses a time adaptive quantile-copula estimator to derive f(y|X=x). This only requires an estimation of the copula density and the unconditional pdf f(y). Although, [8] applied this approach directly to the wind power prediction instead to the forecast error, we adjust the estimation respectively.
Moreover, the two approaches will be compared in a case study. A proper kernel function will also be identified meanwhile the application of the methods. Thereby, more than two-third of Germany’s wind generation capacity is analysed. The wind power forecasts are derived directly from a numerical weather prediction (NWP) model using the physical approach to convert wind speed into wind power. Data from the NWP model is provided by the German meteorological service. All ENTSO-E grid nodes in Germany are within the scope of this work. Thereby, wind turbines are always assigned to the nearest grid node, because the feed in situation is unknown.
Furthermore, the data set has been separated into a training and test set.
The comparison and evaluation of the methods will be implemented according to [9].
Results
Currently, the case study data is compiled. Notably, a wind power curve has to be assigned to more than 8000 wind turbines. After the assignment, the actual and the predicted power output are computed with the data of the NWP model. After the completion of the case study data, the methods will be tested and evaluated.
Conclusions
So far, it became obvious that the particularities of KDE require “a look” at the results. Especially the selection of the bandwidth and the kernel function are hard to implement before a first estimation. However, at least the selecton of the bandwidth can be automated by applying cross-validation [10]. Another issue that will be addressed in the near future is the boundary correction of KDE to assure that the distribution of the predicted wind power does not include negative power production values.
References
[1] Giebel, G.; Brownsword, R.; Kariniotakis, G.; Denhard, M.; Draxl, C. (2011): The state-of-the-art in short-term prediction of wind power. ANEMOS-plus deliverable D-1.2
[2] Tastu, J.; Pinson, P.; Madsen, H. (2010): Multivariate conditional parametric models for a spatio-temporal analysis of short-term wind power forecast errors. In: Proceedings of the European Wind Energy Conference, EWEC 2010.
[3] Pinson, P. (2006): Estimation of the uncertainty in wind power forecasting. Ph.D. thesis, Ecole des Mines de Paris, Paris, France.
[4] Nielsen, H. A., Madsen, H., & Nielsen, T. S. (2006): Using quantile regression to extend an existing wind power forecasting system with probabilistic forecasts. Wind Energy, 9(1-2), pp. 95-108.
[5] Møller, J. K., Nielsen, H. A., & Madsen, H. (2008): Time-adaptive quantile regression. Computational Statistics & Data Analysis, 52(3), pp. 1292-1303.
[6] Pinson, P., & Kariniotakis, G. (2010): Conditional prediction intervals of wind power generation. Power Systems, IEEE Transactions on, 25(4), pp. 1845-1856.
[7] Juban, J., Siebert, N., & Kariniotakis, G. N. (2007): Probabilistic short-term wind power forecasting for the optimal management of wind generation. Power Tech, 2007 IEEE Lausanne, pp. 683-688.
[8] Bessa, R. J., Miranda, V., Botterud, A., Zhou, Z., & Wang, J. (2011): Time-adaptive quantile-copula for wind power probabilistic forecasting. Renewable Energy, 40(1), pp. 29-39.
[9] Pinson, P., Nielsen, H. A., Møller, J. K., Madsen, H., & Kariniotakis, G. N. (2007): Non-parametric probabilistic forecasts of wind power: Required properties and evaluation. Wind Energy, 10(6), pp. 497-516.
[10] Hall , Peter; Racine , Jeff; Li, Qi (2004): Cross-Validation and the Estimation of Conditional Probability Densities. Journal of the American Statistical Association, 99, pp. 1015-1026.