Abstract
Wind turbine blades have been constantly increasing since wind energy becomes a popular renewable energy source to generate electricity. Therefore, the wind sector requires a more efficient and representative characterization of vertical wind speed profiles to assess the potential for a wind power plant site. This paper proposes an alternative characterization of vertical wind speed profiles based on Ward’s agglomerative clustering algorithm, including both wind speed module and direction data. This approach gives a more accurate incoming wind speed variation around the rotor swept area, and subsequently, provides a more realistic and complete wind speed vector characterization for vertical profiles. Real wind data-base collected for 2018 in the Forschungsplattformen in Nord-und Ostsee (FINO) research platform is used to assess the methodology. A preliminary pre-processing stage is proposed to select the appropriated number of heights and remove missing or incomplete data. Finally, two locations and four heights are selected, and 561588 wind data are characterized. Results and discussion are also included in this paper. The methodology can be applied to other wind database and locations to characterize vertical wind speed profiles and identify the most likely wind data vector patterns.
DURING the last decade, larger grid-connected wind energy solutions have been getting more attention and being more economically feasible [
In terms of remaining useful lifetime (RUL) estimation of wind turbines and corrective/preventive maintenance, wind speed intervenes significantly in the maintenance schedule and influences notably on the RUL determination. Indeed, aerodynamic load on the horizontal axis wind turbine (HAWT) blade is different in the top and bottom positions because the wind speed along the length of the blades is significantly different. The blade operates in different torques and transfers the pulsing vibrations to the hub, which may cause damage and other failures [
From the specific literature, more accurate and subsequently more complex characterization of vertical wind speed profile is required by a variety of topics—maintenance, wind energy resource estimation, collected data in field characterization, etc. These alternative solutions should focus on accounting for wind climate realism and open for further improvement. Moreover, [
1) An alternative vertical wind speed profile based on module and direction data is proposed and tested against real data corresponding to the Forschungsplattformen in Nord-und Ostsee Nos. 1, 2, 3 (FINO research platforms in the North Sea and Baltic Sea [
2) A clustering considering both wind speed module and wind direction data trajectories is proposed by using Ward’s agglomerative clustering algorithm.
3) The most representative vertical wind speed trajectories are identified for subsequent wind resource evaluation.
The proposed solution can be applied to offshore and onshore wind data evaluations. The rest of this paper is structured as follows. Section II describes the methodology. The case study is given in Section III. Results corresponding to the FINO research platform case study are conducted in Section VI. Finally, Section V provides the conclusions.
In line with the specific literature, the clustering is widely used as one of the important steps in the exploratory data analysis. Indeed, clustering algorithms are used to find the useful and unidentified classes of patterns and divide data into groups of similar objects. Depending upon the chosen metric, a data object may belong to a single cluster or more than one cluster. Actually, the choice of selecting the clustering algorithm is a critical step of the process [
Clustering, classification, and association rule mining are thus crucial to current data mining. Recent contributions analyzed the challenges associated with the clustering algorithms for two- and high-dimensional databases, and identified such key parametric attributes to evaluate the most appropriate clustering algorithm to be implemented [
In this case, the agglomerative clustering algorithm is selected. Indeed, it is considered one of the earliest and the most widely used clustering strategies. According to [

Fig. 1 Bi-dimensional v.s. uni-dimensional data configuration. (a) Bi-directional. (b) Uni-directional.
The Euclidean distance matrix is firstly defined to determine the distance between each pair of points and , given as vectors in a 2n-dimensional space, for .
(1) |
where is the vector of wind speed module and direction values for different heights at the sample time. From a data set of points, the Euclidean distance among all these points is determined and the corresponding Euclidean distance matrix is constructed. The clustering procedure output gives a list of triples (, , , ), which encodes a step-wise dendrogram. The triple contains the information of which nodes are joined into a new node in the step, and what is the cluster dissimilarity between and . This information is enough to provide the common graphical representation of the dendrogram as a rooted tree, where each leaf represents the initial nodes, and a branching point at a given height represents the joining of nodes and with mutual similarity measure . At each iteration, pairs of clusters that were not previously joined are inspected, and the pair of clusters having the minimum value is joined to form a new cluster [
Linkage method | Dissimilarity measure between clusters and |
---|---|
Single linkage | |
Complete linkage | |
Average linkage | |
Ward’s linkage | |
Centroid linkage | |
Median linkage |
Note that is the centroid of cluster and is the point defined iteratively and depending on the clustering step order. is determined as assuming that the cluster L is formed by joining I and J. Among the different criteria to determine the distance of the data groups, Ward’s linkage method is selected for this case study, as will discussed in Section IV. The Ward’s linkage method is a well-known clustering method based on minimizing the loss associated with each partition (), with . With this aim, such loss is represented in an interpretable and quantifiable form. In Ward’s clustering method, each potential merge of clusters must be analyzed, and those two possible clusters are then combined together, whose merger results in the minimum increase in information loss. To define information loss, Ward used sum of square ESS, which is a mathematical technique to find the function which varies least or fits best from the data.
(2) |
This criterion can also be defined as the variance as it measures the deviation of the particular data point from the mean . An extending Ward’s minimum variance method can be found in [
The FINO research platforms, which belong to the Federal Government of Germany, are used as case study. There are three different platforms (FINO1, FINO2, and FINO3), and their main aim is to determine the environmental conditions for offshore wind power generation in such areas, as well as find potential impacts of the offshore wind power plants on the marine habitat.

Fig. 2 Location of FINO platforms.
FINO1 was brought into service in 2003. Data are available since January 2004, including meteorological and oceanographic data, with a total amount of 88 parameters. It is located around 45 km north of the Borkum island. This platform is settled close to wind power plants under operation or under construction: Alpha Ventus, Borkum Riffgrund I, Trianel Borkum, Borkum Riffgrund II, and Merkur. The measured data are sent and transmitted to the Borkum island through a 32 Mb/s directional radio link. Data are fed into the landline system, and transmitted to the German research network. Once the German research network receives such data, they can be processed by the agents of measuring institutes. Most of these results are published in the FINO database, being available to the public. Nowadays, the collected meteorological variables comprise wind speed, wind direction, air temperature, atmospheric pressure, humidity and density, among others. These meteorological variables are measured with a wind measuring mast of 80 m height, being capable of measuring a maximum height of 103 m. The used sensors are balanced to the mast and are located at several heights of the platform [
With regard to FINO2, it was completed in 2007 and has been operated by DNV GL since 2010. Data have been available since August 2007. It is around 40 km north-west of the Rügen island, in the border triangle Germany-Denmark-Sweden. In contrast to FINO1, the database of FINO2 only includes meteorological data, considering 32 parameters in total. Such meteorological variables include wind speed, wind direction, temperature, global radiation, humidity and intensity of the precipitations, among others. These variables are measured at different heights and with several sensors (i.e., wind speed is measured with a cup anemometer and an ultrasonic anemometer, depending on the height) [
Finally, FINO3 has published meteorological and oceanographic data since September 2009, involving a total of 71 parameters. It is 80 km west of Sylt, surrounded by three German operating offshore wind power plants (Butendiek, DanTysk, and Sandbank). The meteorology data include wind speed and direction, temperature, humidity, pressure, and precipitation. These data are collected at different heights, by using a 100 m wind measurement mast [
From the three different platforms described in Section III, FINO1 and FINO2 are considered for analysis. Indeed, FINO3 is close to FINO1 and thus, the results would be really similar between both platforms. From the available database of FINO1 and FINO2 platforms, the corresponding data characterization is carried out for year 2018, which provides a more complete information for the whole year. An initial collected data of 717851 and 1362240 for FINO1 and FINO2, respectively, are considered with 10-min sample time. Before applying the clustering method described in Section II, data are pre-processed to remove missing and incomplete data. Subsequently, relevant heights for both wind speed module and wind direction collected data are identified. More specifically, 34, 51, 71, and 91 m heights are selected for FINO1 data vector including wind speed and direction consistent data, with a total of 141764 values to be analyzed. Regarding FINO2, the 31, 51, 71, and 91 m heights are identified after such pre-processing stage, accounting for 419824 data to be finally analyzed. As a graphical example of the selected data,

Fig. 3 Evolution of wind speed module and direction for a month. (a) Hour 5. (b) Hour 11. (c) Hour 17. (d) Hour 23.
In line with
Hour | Hierarchical agglomerative clustering coefficients | |||
---|---|---|---|---|
Average | Complete | Single | Ward’s | |
0 | 0.9660 | 0.9811 | 0.9505 | 0.9964 |
1 | 0.9686 | 0.9831 | 0.9556 | 0.9969 |
2 | 0.9677 | 0.9820 | 0.9531 | 0.9961 |
3 | 0.9699 | 0.9831 | 0.9548 | 0.9966 |
4 | 0.9594 | 0.9823 | 0.9483 | 0.9960 |
5 | 0.9675 | 0.9832 | 0.9354 | 0.9967 |
6 | 0.9661 | 0.9814 | 0.9464 | 0.9962 |
7 | 0.9664 | 0.9836 | 0.9485 | 0.9964 |
8 | 0.9686 | 0.9835 | 0.9469 | 0.9963 |
9 | 0.9697 | 0.9839 | 0.9245 | 0.9967 |
10 | 0.9706 | 0.9835 | 0.9557 | 0.9964 |
11 | 0.9715 | 0.9838 | 0.9437 | 0.9963 |
12 | 0.9704 | 0.9846 | 0.9157 | 0.9965 |
13 | 0.9648 | 0.9839 | 0.9429 | 0.9964 |
14 | 0.9587 | 0.9823 | 0.9296 | 0.9960 |
15 | 0.9709 | 0.9833 | 0.9305 | 0.9966 |
16 | 0.9689 | 0.9828 | 0.9435 | 0.9967 |
17 | 0.9729 | 0.9836 | 0.9543 | 0.9970 |
18 | 0.9745 | 0.9851 | 0.9407 | 0.9973 |
19 | 0.9703 | 0.9838 | 0.9467 | 0.9969 |
20 | 0.9703 | 0.9827 | 0.9487 | 0.9969 |
21 | 0.9715 | 0.9820 | 0.9463 | 0.9968 |
22 | 0.9650 | 0.9789 | 0.9444 | 0.9964 |
23 | 0.9659 | 0.9798 | 0.9441 | 0.9965 |
The identification of the “knee” of the agglomerative clustering coefficient indicates the largest magnitude difference between two adjacent points. The Ward’s linkage method was the clustering routines applied. The final number of clusters to be included in the solution was determined by the agglomerative clustering coefficient with the use of the stopping rule. The stopping rule evaluates the changes in the coefficient at each stage of the hierarchical process. The number of clustering groups was deemed appropriate when a continued increase in the number of clusters resulted in a large percentage change in the agglomerative clustering coefficient [
Hour | Wind data clustering distribution (%) | ||||
---|---|---|---|---|---|
Cluster 1 | Cluster 2 | Cluster 3 | Cluster 4 | Cluster 5 | |
0 | 42.31 | 26.04 | 13.20 | 12.12 | 6.33 |
1 | 28.99 | 26.27 | 21.74 | 16.85 | 6.16 |
2 | 35.69 | 28.26 | 16.67 | 12.86 | 6.52 |
3 | 32.07 | 27.72 | 17.57 | 16.49 | 6.16 |
4 | 26.45 | 26.09 | 19.75 | 14.31 | 13.41 |
5 | 28.26 | 24.64 | 21.74 | 14.49 | 10.87 |
6 | 28.62 | 25.91 | 24.46 | 12.86 | 8.15 |
7 | 46.38 | 18.12 | 16.30 | 11.23 | 7.97 |
8 | 40.40 | 18.84 | 15.58 | 15.04 | 10.14 |
9 | 30.07 | 24.09 | 23.37 | 12.68 | 9.78 |
10 | 28.62 | 25.91 | 23.01 | 16.67 | 5.80 |
11 | 33.70 | 27.90 | 23.01 | 9.96 | 5.43 |
12 | 42.75 | 15.94 | 15.22 | 14.67 | 11.41 |
13 | 42.93 | 20.11 | 15.22 | 14.49 | 7.25 |
14 | 39.13 | 18.66 | 18.48 | 16.12 | 7.61 |
15 | 40.04 | 17.75 | 15.94 | 15.22 | 11.05 |
16 | 26.27 | 23.73 | 19.20 | 16.67 | 14.13 |
17 | 26.63 | 26.45 | 18.84 | 14.31 | 13.77 |
18 | 36.23 | 23.19 | 17.21 | 15.40 | 7.97 |
19 | 32.25 | 27.36 | 17.21 | 16.30 | 6.88 |
20 | 29.53 | 28.80 | 27.72 | 10.69 | 3.26 |
21 | 37.50 | 22.64 | 20.83 | 15.76 | 3.26 |
22 | 32.25 | 22.28 | 19.75 | 18.48 | 7.25 |
23 | 41.12 | 20.65 | 16.67 | 15.04 | 6.52 |
A total of five differentiated clustering groups (clusters 1-5) are finally identified. Differences between choosing five or eight clustering groups are not significant; and the most representative clustering (about 30% of the trajectories) remains in both distribution, whether five or eight groups are identified. Therefore, five groups simplify the representation of results and optimize the number of such groups. Additionally, the corresponding dendrograms for such bi-dimensional data are determined by applying the hierarchical grouping based on the Ward’s linkage method and using the Euclidean distance. Dendrogram allows a visual representation by means of different branches to show the order and relationship in terms of similarity or dissimilarity among trajectories [

Fig. 4 Dendrograms of hierarchical agglomerative clustering for selected hours. (a) Hour 5. (b) Hour 11. (c) Hour 17. (d) Hour 23.

Fig. 5 3D graphical representation of wind speed and wind direction data for identified cluster patterns. (a) Hour 5. (b) Hour 11. (c) Hour 17. (d) Hour 23.

Fig. 6 3D graphical representation of wind speed and wind direction data for identified clusters. (a) Hour 5. (b) Hour 11. (c) Hour 17. (d) Hour 23.
As an addition result, Figs.

Fig. 7 Wind data clustering distribution and pattern identification (hour 5). (a) Wind data clustering distribution. (b) Wind data clustering pattern.

Fig. 8 Wind data clustering distribution and pattern identification (hour 11). (a) Wind data clustering distribution. (b) Wind data clustering pattern.

Fig. 9 Wind data clustering distribution and pattern identification (hour 17). (a) Wind data clustering distribution. (b) Wind data clustering pattern.

Fig. 10 Wind data clustering distribution and pattern identification (hour 23). (a) Wind data clustering distribution. (b) Wind data clustering pattern.
A methodology to characterize vertical wind speed patterns from bi-dimensional wind data (wind speed and direction) is described and assessed. The proposed solution is based on Ward’s agglomerative clustering algorithm applied to bi-dimensional data. A 3D representative wind data patterns are then provided for each hour of the day, considering both wind speed module and direction evolution with the height. This characterization allows us a more accurate wind data analysis, and subsequently gives a robust information to determine the potential wind power available for large swept areas. Real wind data-base collected in the FINO research platform is used to assess the methodology. A preliminary pre-processing stage is proposed to select the appropriated number of heights and reduce the amount of data. In this case, two locations are selected and around 20800000 wind data are finally analyzed. From both locations, five clustering groups are identified and their corresponding patterns provide the most likely wind speed and direction values according to the height for each hour of the day. The most likely wind speed and direction vector pattern involves more than 26% of the total bi-dimensional trajectories for the averaged daily wind data, including some hours over 40% of such data. The proposed solution can be applied to other wind data bases, both on-shore and off-shore. In fact, this methodology can be extended to analyze potential wind power plant locations, providing the most likely wind vector data patterns for different sample times.
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