Journal of Wind Engineering and Industrial Aerodynamics
Improvements in wind speed forecasts for wind power prediction purposes using Kalman filtering
Introduction
Limited-area models (LAMs) are widely applied for providing weather forecasts up to 3 days with their forecast skill ranging between 80% and 90%. The current requirements for long-term as well as accurate predictions have forced meteorologists to broaden the ability of Numerical Weather Prediction (NWP) models supplying reliable forecasts maintaining their skill for periods longer than 3 days.
It is well known that NWP models usually exhibit systematic errors in the forecasts of certain meteorological parameters, such as wind speed, especially near the surface. This drawback is a result not only of the shortcoming in the physical parameterization, but also of the inability of these models to successfully handle sub-grid phenomena. The model horizontal resolution associated with smoothing/averaging the orographic and landscape characteristics leads to weak representation of local effects on the airflow. For example, winds induced by the orography of a region are usually underestimated systematically.
A way of counteracting such a drawback is to increase the model resolution that may provide considerable improvement in the representation of smaller scale flow characteristics. Nevertheless, an open question remains as to whether the use of higher resolution LAMs improves the forecast skill considerably. Even in the case that this is true, it is still uncertain whether such improvement compensates the usage of computationally costly resources that are required for these applications (Mass et al., 2002).
An alternative way to reduce the limitation of the NWP models to accurately predict sub-grid phenomena is the use of post-processing approaches based on statistical methods. One of the most successful methods in this issue is the use of Kalman filters (Kalman, 1960; Kalman and Bucy, 1961; Persson, 1990; Dragulanescu, 1993; Galanis and Anadranistakis, 2002; Crochet, 2004; Kalnay, 2002). They consist of a set of mathematical equations that provides an efficient computational solution of the least square method with minor computational cost and easy adaptation to any alteration of the observations.
The aim of this paper is, on the one hand, to investigate the rate of improvement in wind speed predictions with the application of Kalman filtering and to study the effect of such a post-processing method on different horizontal resolution outputs. For this reason, an optimal polynomial Kalman filter is employed to two NWP models with different characteristics and horizontal resolution, and a detailed statistical analysis is performed. The discussion is focused on the capability of the filter to improve the direct model outputs even in cases of lower resolution taking also into account the requirements in CPU time.
On the other hand, the filtered wind speed predictions are used as input in wind power prediction models and the improvement in the final wind power forecasts is examined. Such forecasts are recognized today as useful tools for the management of power systems where wind penetration is important.
Section snippets
The modelling systems
In this section a general description of the models used is provided.
The Kalman filtering methodology
Kalman filters (Kalman, 1960; Kalman and Bucy, 1961; Kalnay, 2002; Persson, 1990; Dragulanescu, 1993; Galanis and Anadranistakis, 2002; Crochet, 2004) are the statistically optimal sequential estimation procedure for dynamic systems. Observations are recursively combined with recent forecasts with weights that minimize the corresponding biases.
The main advantage of this methodology is the easy adaptation to any alteration of the observations as well as the fact that it needs short series of
The case study
SKIRON NWP data of a time period statistically long for wind power purposes, i.e. 1 year, have been provided in the framework of E.U. ANEMOS project (http://anemos.cma.fr). In particular, SKIRON forecasts for wind speed and direction, air temperature and mean sea level pressure have been supplied for different locations in the Mediterranean Region where wind farms are operated. For the specific case study, SKIRON wind speed at 10 m above the ground for the area of Rokas in Crete, Greece (Lon:
Results
The results presented here are based on detailed statistical analysis of SKIRON and RAMS outputs, the Kalman filtered outcomes and the wind power prediction product presented as an application.
The statistical analysis was based on the calculation of the:
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Bias of direct model output in comparison with the corresponding bias of the improved, by the Kalman filter, forecasts: where obs(i) denotes the observed value at time i, for(i) the corresponding forecasted value
Conclusions
A new technique based on the implementation of non-linear polynomial functions (third order) in Kalman filter algorithms was applied to wind speed numerical predictions obtained at a particular wind farm in Crete, Greece. This method was applied to the outputs of two atmospheric numerical models with different capabilities in horizontal resolution. The methodology showed high performance for all cases leading to the elimination of any type of systematic errors. In particular, all error
Acknowledgements
The present work was carried out in the framework of the European Projects ANEMOS (development of a next generation wind resource forecasting system for the large-scale integration of onshore and offshore wind farms—Contract no. ENK5-CT-2002-00665) and POW’WOW (Prediction Of Waves, Wakes and Offshore Wind—Contract no. 019898(SES6), http://powwow.risoe.dk/).
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