1994), which argues that if errors are present in the regressors the use of the true system for prediction will not result in optimal predictions.
4.2 What are the options?
The purpose of this section is to identify the most important variables in developing prediction models for wind power, and outline ideas for how statistics and physics can be combined. Based on the description of the meteorological theory in the previous chapter, the variables which can be assumed to be most important in the description of the wind speed and consequently the power production at a given location are: the wind speed and direction from some model level from the numerical weather prediction model and the turbulence intensity. The energy content in the air flow is related to the density of the air, this variable is therefore also of importance when wind power is considered. As no measure of this variable has been available, this dependency has not been considered.
4.2.1 Direct use of statistics in HIRLAM
The numerical weather prediction model, HIRLAM, has not been the subject of development in this study. All developed models and methods start from the variables which have been delivered by HIRLAM.
This does not mean, though, that statistical models could not be used in the numerical weather prediction model. One way to include a sta-tistical modelling approach would be to use stochastic differential equa-tions directly in HIRLAM. Such an approach could for instance be ap-plied to the HIRLAM soil model described in Section A.4. Stochas-tic versions of ordinary differential equations are easily derived, see e.g.
(Melgaard 1994), while it is more difficult to work with stochastic ver-sions of partial differential equations. Partial differential equations are usually transformed into ordinary differential equations using the same approach as in HIRLAM for the soil temperature prognostic equations, where the soil is divided into three layers. These equations could there-fore easily be replaced by stochastic versions, and statistical estimation
methods could be used to estimate the parameters in these equations.
The potential advantage of integrating this approach in the numerical weather prediction model is that the drag imposed on the flow in the atmosphere is directly related to the turbulence intensity as described in AppendixA, and the surface temperature and wetness are necessary in the calculation of the turbulence intensity.
Stochastic versions of the soil model equations could also be used outside the numerical weather prediction model. This approach could be used to predict e.g. the surface temperature locally at the wind farms. The temperature could then be used in calculation of the surfaces fluxes of the sensible and latent heat fluxes, which in turn could be used in the stability dependent wind speed profile. This approach has not been tested in this thesis, the main reason is that some of the necessary variables were not available, and that the three hour time resolution which the available data is given in, would not be sufficient for this approach.
Another area for potential improvement of the numerical weather predic-tions, is to consider the data assimilation procedure. The 3-dimensional data assimilation procedure is briefly described in (Sass et al. 1999) and in more detail in (Lorenc 1981, Lonnberg & Shaw 1987). The current as-similation procedure used in HIRLAM consists of several steps. Bilinear interpolation is used in the vertical, tension spline interpolation is used in the vertical, subsequent averaging is applied followed by a covariance dependent weighting between predicted values and corresponding obser-vations. Nevertheless, in the description of the assimilation procedure, there does not seem to be any feedback from the prediction errors to the assimilation procedure. The introduction of the feedback concept in the assimilation procedure is beyond the scope of this thesis, but is definitely worth pointing out as an area of potential improvement.
4.2.2 Intermediate models
Potentially statistical models possess the ability to outperform any phys-ical model in performance, but it should be noted that the development of statistical models is based on finite data samples, and it is possible that some relations exist which are not visible in such a sample. Generally,
4.2 What are the options? 41 as the number of explanatory variables increases, the noise in the data might severely contaminate the relations which are found by statistical methods. In local regression this problem has be dubbed the ”curse of dimensionality”, and in this context the problem is particularly difficult to cope with, because very weak assumptions are imposed on the rela-tion between the explanatory variables and the response. In practice this means that one needs to select the explanatory variables which provide the highest degree of explanation.
Therefore, it might be advantageous to incorporate known statistical re-lations in statistical models, such rere-lations can be viewed as intermediate models, linking one or more explanatory variables to one single variable which can be used as input to a subsequent relation. This approach can therefore effectively reduce the dimension of the problem. The parame-ters of a known relation might be estimated using statistical estimation methods, or only a subset of the parameters could be estimated. Known relations could also be used directly to model some parts of the relation between the explanatory variables and the response. Physical systems are often described by differential equations, and, from the description in the previous section it is clear that such relations can also be combined with statistics.
4.2.3 The Risø model
From the considerations in the previous section it is clear, that one way to combine physics and statistics in short-term prediction models, is e.g.
to use the relations in the Risø system to calculate the wind speed at the wind turbine hub-height.
In Section2.3.5it was shown that the wind speedωh at the wind turbine hub height calculated by the Risø system could be written as
ωh =a(θs)G (4.1)
where G is the geostrophic wind speed and θs is the surface wind di-rection. It is seen that this corresponds to a conditionally parametric model if an error term is added. In Paper E models of this type have been examined. In this paper it is not pointed out, that in a statisti-cal model we need to make a choice with regard to the wind direction.
In Section 2.3.5 it was shown that the surface wind direction depends non-linearly on the geostrophic wind speed and direction, and therefore the surface wind direction should be calculated by the geostrophic drag law. It turned out that it made no difference in the performance results whether the geostrophic wind direction was used directly instead of the calculated surface wind direction. Furthermore, the results in Paper E indicate that the physical wind direction dependency used in the Risø system is not optimal.
When a conditionally parametric model where the parameters are consid-ered to be functions of the wind direction is used, it should be noted that the wind direction dependency does not necessarily correspond to the de-pendency found by the WAsP application. In (Troen & Petersen 1989b) wind roses for a large number of locations in Denmark are shown, and from these wind roses it can be verified that the average wind speed de-pends on the wind direction, e.g. the wind speed is usually higher when coming from South-East compared to North or West. Therefore, this must be a feature of the overall atmospheric flow not local conditions.
As long as the predictions from the numerical weather prediction model are not perfect, this dependency is automatically included in the con-ditionally parametric model. This means also, that if a WAsP analysis finds that local effects prescribe a correction of the wind which is not in accordance with average wind direction dependency, then the WAsP corrected wind might lead to worse performance than the uncorrected wind.
The reason for considering the non-linear model in PaperEis also based on the considerations in the previous sections. The non-linearity is in-troduced at the final stage in the Risø system, where the wind speed in transformed into power. The results from this model were also rather disappointing, as a simple linear model, where the power curve was ap-proximated by a polynomial in the wind speed, performed just as well.
The final conclusion of these findings is therefore that the physical rela-tions used in the Risø system are of little use when there is data available, and statistical models can be used. It should be noted though, that if no data is available, then the physical relations can be used, also, the statistical models need one to three months of data before the parameter estimates are fully reliable, therefore the physical relations can be used until the statistical models are fully reliable.
4.2 What are the options? 43 4.2.4 Turbulence intensity
From the description in the previous chapter it is clear that the relation between the wind speed at two different heights above the ground de-pends on the turbulence intensity. If the numerical weather prediction model handles this dependency properly, then the model level which is closest to the wind turbine hub-height can be selected. The approach taken here has been, first of all to find which model level gives the best performance, the results from this examination are described in PaperI.
Secondly a closer look is taken at the winds at different model levels in HIRLAM, and how these winds depend on the Buoyancy flux, which is a measure of turbulence intensity. The results from this examination are described in PaperI. The purpose of the analysis is to find out if it is nec-essary to include the turbulence intensity dependency in the statistical models.
Chapter
5
The implementation – Zephyr
The aim of this chapter is to describe the software application Zephyr.
Zephyr is implemented in the JavaT M programming language, and it is assumed that the reader has some basic knowledge of object oriented programming and terms used in object oriented design. A comprehensive description of the Java programming language and the Java Application Programming Interface (API) is available atwww.java.sun.com
The first version of Zephyr is planned to go into operation in May 2000.
This beta version will be evaluated by the two Danish utilities Elkraft and Elsam.
The reason for choosing the Java programming language, is that pro-grams written in this language are not limited to run on one computer platform. Java programs can run on all platforms, which have a Java Virtual Machine (JVM) available. The list of platforms for which the JVM is available is long, and includes Windows95/98/NT, Linux, OS/2 and Sun.
The level of detail in this description of the Zephyr system is rather low, as a complete description of all objects and object methods would be
far too comprehensive. The objective of the description is to provide an overview of the system and outline the system architecture. A description of some of the object patterns used in the implementation of Zephyr can be found in (Reese 1997) and a more genereal description of design patterns can be found in (Gamma, Helm, Johnson & Vlissides 1994).
The description of the server part of the Zephyr system focuses on the software architecture and some level of detail in the implementation.
The aim of the description of the client is to illustrate the graphical user interface; no implementation details are provided on this part of the system.
5.1 Requirements to the application
The requirements to the Zephyr application are based on experience gained by the Danish utilities Elkraft, Eltra and Elsam, by the use of the Risø and the WPPT on-line systems. These two systems are described briefly in PaperH.
There has been no formal requirement specification to the system, al-though, as a minimum, all the tools which are available in the applica-tions mentioned above, need to be available in the new system. Zephyr has been developed in a process, where project meetings with partici-pants from the utilities has been the forum where the requirements to the system have been formulated. The following description summarizes the requirements obtained from this process:
• Any prediction application, which is to be a useful tool in the daily dispatch and control in the utility control room, requires that the application is highly automated and easily customizable.
• In general there are three sources of data to the system, numerical weather predictions from a national weather service, measurements of meteorological variables and power production from the wind farm sites. The system needs to maintain a database of this data, validate the data and update the prediction models and calculate predictions as soon as new data becomes available.