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A novel technique for forecasting the optimal production of a wind generator installed at any geographical point located within a very large area


The need to integrate renewable energy sources into the energy mix is felt because of the many advantages they offer over fossil fuels, notably in terms of environmental protection and more uniformly distributed availability. The intermittent and stochastic ones, such as wind power, present many problems to network operators due to the volatile nature of their output power. This work presents a new technique for optimally forecasting the power output of a wind turbine installed at any geographic point located within a very large area. Once the study area is defined, it is gridded and optimally sampled in order to have a truly representative number of geographical points. The study area is then divided into sub-areas by grouping the samples by similarity of variation of meteorological parameters (wind speed and direction). For each sub-area, the optimal production periods are then identified and used for forecasting the power output. The forecasting technique used combines the LSTM model for forecasting meteorological parameters and the linear model for approximating the power curves of wind turbines. The technique was applied to the Beninese territory on which 90 sub-zones were formed. A 12 h forecasting of wind speed, wind direction and wind power were presented for one of the sub-areas. The clustering results gave a Silhouette score of at least 0.99. The wind speed and direction forecasting gave (0.34 m/s, 7.8 rad) and (93%, 70%) for RMSE and R2, respectively.


The announced depletion of conventional energy sources is the main reason for the interest in renewable energies in recent years. Indeed, for the resources identified in 54 years, 63 years, 112 years and 100 years, respectively, according to a report of 2021 of the International Energy Agency (IEA), oil, gas, coal and uranium are expected to run out contrary to the renewable ones which are supposed to be inexhaustible on a human scale [1, 2]. At the same time, the IEA estimates that by 2030, global energy demand is expected to grow by 45% due to the industrialization and development policies of various countries. In this context, countries with high production and high self-consumption will find themselves unable to meet all their energy needs with their energy mixes mainly made up of generators running on conventional resources. Countries with low production will consequently see their energy import costs increase and the quantity of imported energy decrease because of the difficulties that exporting countries would encounter. It should also be noted that these conventional resources are less evenly distributed than renewable energy sources and that climate change policies now require us to move toward green energy.

It seems quite obvious that new policies must be put in place, first of all for the exploitation of existing resources, but also for their production. Thus, two major solutions are emerging: energy efficiency and renewable energy sources as a means of energy production. Turning to this last solution, in terms of renewable energy production, Africa has an enormous potential with wind, solar photovoltaic (PV), hydroelectric, geothermal and biomass production of 978,066 TWh/year, 1,449,742 TWh/year, 1478 TWh/year, 105 TWh/year and 2374 TWh/year, respectively [3]. A potential that should allow the entire African population to have access to electricity. But unfortunately, according to a 2018 report by IRENA et al., 47% of the African population, i.e., more than 600 million people, 75% of whom live in rural areas, had no access to electricity [3]. Why this paradox? Looking closely, apart from the financial problems of exploitation of these renewable sources, they generally present problems of a natural and material nature. Indeed, the solar source is intermittent due to the natural movement of the earth around the sun and varies very randomly when it is available. This leads to a random variation of the output power of the PV generators. In the same way, the wind source (the wind) varies very randomly which leads to a random variation of the output power of the wind turbines but also an intermittence of this one due to a minimum of starting speed. In summary, these wind and PV generators have performances and powers that vary not only with time but also with the environment (space) in which they are installed.

In the literature, several solutions are proposed to the intermittence and random variability of these sources. For intermittency, it is possible to associate several generators with complementary productions: this would allow to have a production almost all the time without big interruption [4,5,6,7,8,9,10]. Another solution to intermittency is energy storage, but on a large scale, this is expensive from production to operation and recycling [11,12,13,14]. We can also think of international exchanges when the different countries are interconnected [15,16,17] or even the management of consumption by encouraging users to consume during periods of high production. For the random variability of the output power, the adequate solution encountered in the literature remains the forecasting thanks to the artificial intelligence techniques which allow to have an overview of the future evolution of these powers [18,19,20,21,22].

In a few years, it will be of great interest for everyone to be able to identify in his space any exploitable geographical point that can allow the development and exploitation of solar and wind resources mainly. It will also be necessary to be able to make an optimal and adapted forecast according to the type of system and the environment in order to be able to integrate well these fluctuating resources. In this paper, we propose a technique for forecasting and identifying the optimal production periods of a wind generator installed at any geographical point located within a very large area. The second part presents the material used and the methodology adopted, the third part the results obtained and the last part the conclusion.


Weather parameters influencing the variability of wind power

The random variation of the output power of the wind turbines is due to the randomness of the meteorological parameters. To control this variability, it is necessary to identify and control the evolution of these influencing parameters, as shown in the research flowchart in Fig. 1.

Fig. 1
figure 1

Research flowchart

As with photovoltaic modules, there are different models describing the behavior of a wind turbine [23,24,25,26]. The output power of the wind generator is most often obtained from its power curve, which represents the output power as a function of the wind speed. It is possible that the curve used corresponds to a real generator or is obtained from a model. The most commonly used model is the Pallabazzer model. It is also possible to use the mechanical power on the shaft of the wind turbine determined from the wind speed, the area swept by the blades and by the power coefficient.

From these different models, we can easily deduce the wind speed and direction as input weather parameters. Thus, these models generally take the wind speed as input to give the associated electrical power for a given wind turbine. The wind direction is used to orient the blades of the wind turbine in order to extract a maximum of energy. We therefore retain these two parameters for the following.

Study area definition, gridding and sampling

Once the meteorological influencing parameters have been identified, it is necessary to delimit the study area and to record these parameters on representative samples of the area, which constitute geographical points. For our study, we considered the entire Beninese territory, which covers 114,763 km2, as our study area.

The gridding and sampling technique is shown in Fig. 2. We define two types of samples: the green samples are the ones used for the work, and the red ones are the ones used for the results validation. We also define a grid spacing \(\Delta t\) which is the difference in latitude or longitude between two test or validation samples. We will see later on how the gridding step has been optimized.

Fig. 2
figure 2

Gridded and sampled map of Benin

Data and database used

As mentioned in the previous paragraph, the data used in this work are satellite data obtained from the NASA database. The main characteristics are presented below:

  • Database: POWER LARC NASA [27];

  • Data frequency: Hourly;

  • Data types:

    • V50M: Wind speed at 50 m from the ground;

    • D50M: Wind direction at 50 m from the ground;

  • Period: From January 1, 2012, to December 31, 2021.

Sample data pre-processing

Once the grid has been completed and the samples defined, meteorological data (wind speed and direction) must be collected on all samples. For this study, we use hourly satellite data taken from the NASA database at each geographical point (test and trial samples) from January 1, 2012, to December 31, 2021.

These data must be pre-processed so that we can derive the correct information that we desire. There are several processing steps for this purpose.

Identification and suppression of outliers

An anomaly or outlier is best described as an observation that differs so much from the rest of the record that it is suspected to have been generated by a different process (Hawkins, 1980). These outliers can be due to a variety of processes, such as measurement error or specific phenomena, such as the occurrence of a fire or weather event. In view of the large number of applied areas that make use of outlier detection, the existing literature offers a considerable number of approaches devoted to it. The easiest way to identify outliers in a dataset is to represent and observe them. This allows us to notice the values that are abnormally far from each other. Box plots, for example, allow us to visualize the distribution of a single variable. These graphs are based on the median, as well as the lower and upper quartiles. An outlier is any extreme value, greater or less than \(I\) times the interquartile range. Usually \(I\) is 1.5. We can also perform statistical calculations such as the calculation of the mean, the standard deviation, the maximum or the minimum. These statistics make it possible to quickly identify possible anomalies in the data set.

Check for data stationarity

Since our data are time series, it is important to ensure the conformity of some of their properties. An important property of the time series is its stationarity. If a process is stationary, it means that its statistical properties do not vary over time, namely its mean, its variance (homoscedasticity) or its covariance. This notion of stationarity represents a crucial point in the analysis of time series, where the estimation of non-stationary series leads to spurious or illusory regressions. A stationarity study of the data is therefore important to ensure that the structure of the process that generated these series does not change over time: this is a very important condition for the time series forecast. The augmented Dickey–Fuller test (ADF) is an appropriate statistical tool. The time series considered is stationary if the p value is low (according to the null hypothesis).

Adding new variables to the dataset

It is sometimes important to add new variables to the data set in order to facilitate the learning of the models. For time series such as meteorological data (wind speed, irradiation, temperature…), the notion of periodicity is important for their analysis and interpretation or forecast. In this work, the series undergo a fast Fourier transform in order to identify the highest frequencies. These frequencies are then used to add new variables by the formulas (1) and (2).

$$x_{{{\text{sin}}}} = {\text{sin}}\left( {t*\left( {\frac{{2*\pi }}{T}} \right)} \right)$$
$$x_{{{\text{cos}}}} = {\text{cos}}\left( {t*\left( {\frac{{2*\pi }}{T}} \right)} \right)$$

\(X_{{{\text{sin}}}}\) and \(X_{{{\text{cos}}}}\) are the new variables to be added for an identified important frequency \(f = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 T}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$T$}}\) and t is the time of data acquisition. It is also important in our case to make the models understand the concept of wind direction. Indeed, wind directions are angles and the models should understand for example that 0° and 360° are identical. Also, the wind direction is not very useful if the wind is weak. So, we associate these two variables (wind speed and direction) to create two new variables as shown in Eqs. (3) and (4).

$$W_{y} = W_{{\text{s}}} {\text{sin}}\left( {W_{{\text{d}}} } \right)$$
$${\text{W}}_{{\text{x}}} = W_{{\text{s}}} {\text{cos}}\left( {W_{{\text{d}}} } \right)$$

\({W}_{x}\) and \({W}_{y}\) are the two new variables, \(W_{{\text{s}}}\) and \(W_{{\text{d}}}\), respectively, the wind speed and direction at time t.

Data normalization or standardization

It is then essential, when one has in one's dataset variables of different orders of magnitude, to bring them to the same scale for training the models. For this purpose, two techniques are used: standardization and MinMax normalization. In this work we use the MinMax normalization presented by Eq. (5) which does not require the knowledge of data distribution.

$$x_{{{\text{norm}}}} = a + \frac{{\left( {x - {\text{min}}(x)} \right)\left( {b - a} \right)}}{{{\text{max}}\left( x \right) - {\text{min}}(x)}}$$

\(x_{{{\text{norm}}}}\) represents the normalized \(x\) variable, \(a\) and \(b\) are the bounds of the new scale.

Data set subdivision

The dataset is then subdivided into three parts: the trainset (70%) to train the models, the validation set (20%) to set the hyper parameters of the models and the test set (10%) to test them.

Study area subdivision

It should be remembered that the objective is to be able to say at any point of the study area how the power output of a wind turbine will evolve in the near future and in which periods of the year a good production could be obtained. For this purpose, we divide the study area into sub-areas (Fig. 3) in which the wind profiles over the study period are identical or nearly so.

Fig. 3
figure 3

Sub-area cutting technique

This is equivalent to grouping the samples (geographical points) whose meteorological parameters vary identically. For this study, a similarity threshold of at least 90% has been set. This technique will allow to reduce the number of study samples because we could take without risk a sample in each sub-area to represent the whole sub-area. In the literature, several time series clustering models have been identified [28,29,30,31,32,33,34,35].

Clustering is a statistical analysis method used to organize raw data into homogeneous silos. Within each cluster, data is grouped according to a common characteristic. The ordering tool is an algorithm that measures the proximity between each element based on defined criteria. In this study, we used the k-means algorithm for clustering wind speeds as time series. K-means is an unsupervised non-hierarchical clustering algorithm. It allows to group in \(K\) distinct clusters the observations of the data set. Thus, similar data will be found in the same cluster. Moreover, an observation can only be found in one cluster at a time (exclusivity of membership). The same observation cannot belong to two different clusters.

Choosing a number of clusters \(K\) is not necessarily intuitive especially when the dataset is large. A large number \(K\) can lead to a too fragmented partitioning of the data. This will prevent the discovery of interesting patterns in the data. On the other hand, a number of clusters that is too small will lead to having, potentially, too generalized clusters containing a lot of data. In this case, there will be no "fine" patterns to discover.

For the same dataset, there is not a single possible clustering. The difficulty will be to choose a number of clusters \(K\) that will allow to highlight interesting patterns between the data. The most common method to choose the number of clusters is to run K-means with different values of \(K\) and to calculate the variance of the different clusters. The variance is the sum of the distances between each centroid of a cluster and the different observations included in the same cluster. Thus, we try to find a number of clusters \(K\) such that the selected clusters minimize the distance between their centers (centroids) and the observations in the same cluster.

In our case, the number of clusters represents the different number of wind profiles that would have been identified in the whole study area. The search for a maximum number of clusters would allow us to optimize the grid spacing and thus the number of samples representative of the study area. Figure 4 shows the optimization principle that we have developed: we increase the number of samples until the number of clusters (wind profiles) does not increase anymore.

Fig. 4
figure 4

Grid pitch and cluster number optimization flow chart

Sub-area characterization

Once the sub-areas have been formed, it is now necessary to identify in which period(s) of the year one could optimally produce with a wind turbine. To do this, for each sub-zone, we must:

  • identify the periods where wind speeds are acceptable (medium high with low variance);

  • identify in which direction the wind turbine blades should be oriented.

We use the Weibull distribution to identify the most frequent wind speeds and the wind roses to identify the orientations.

Wind power forecasting

Forecasting technique options

Once the optimal production periods have been identified, the data on these periods are used to train wind power forecasting models, as it will be useless to pretend to make a forecast on periods when the wind turbine cannot be used. In the literature, several wind power forecasting techniques have been identified [20, 36,37,38,39,40,41,42,43,44,45,46]. The first technique is shown in Fig. 5.

Fig. 5
figure 5

Forecasting architecture 1

This first technique exploits a history of power readings on an existing wind turbine and forecasts a succession of future values of this power from a succession of past values using a time series forecasting model. It presents a simple architecture but the developed forecasting model is only usable for the installation on which the records have been made. Moreover, this configuration requires a long period of power measurement for the forecast to be effective.

A second technique (Fig. 6) we encountered combines a time series forecasting model and a regression model. The time series forecasting model predicts the meteorological influence parameters (wind speed in our case) and then the regression model associates the wind turbine power values to the predicted influence parameter values. For this purpose, historical data of the influence parameters and the wind power are required. The architecture is more complex and as for the previous one, the model is only usable for the system for which it is developed and, in the environment, where the system is located. Indeed, as the meteorological parameters are a function of the geographical locations, for the same system in two different environments the forecasting models will be different.

Fig. 6
figure 6

Forecasting architecture 2

The last technique (Fig. 7) always combines a time series forecasting model to estimate future values of the influencing parameters and a wind power estimation model (Pallabazzer model, linear model, Chang model) that typically takes wind turbine characteristics such as \({V}_{\mathrm{cut}-\mathrm{in}}\) the interlocking speed, \({V}_{\mathrm{cut}-\mathrm{off}}\) the trip speed, \({V}_{\mathrm{rated}}\) the speed for which rated power is obtained, \({P}_{\mathrm{rated}}\) the rated power. Thus, this technique can be easily retrofitted to another wind turbine by changing the characteristics of the wind turbine in the power estimation model. Only the influence parameter prediction model has to be repeated when the installation site changes. This technique has the advantage of being more flexible, easy to adapt and does not require the system to be existing. It is thus the technique retained for the continuation.

Fig. 7
figure 7

Forecasting architecture 3

Forecasting model’s selection

The forecasting technique chosen involves using a wind speed and direction forecasting model as a time series and then estimating future power from the predicted speed and direction from a wind turbine power curve approach model. In [36], Wang et al. give a fairly comprehensive summary of wind speed and wind power forecasting models. From this summary, we can retain as the most efficient basic wind speed forecasting models, the LSTM (Long short-term memory) and CNN (Convolutional neural network) models.

The convolution neural network is an improvement of the traditional neural network. It was originally designed for image processing and allows to encode the specific features of the image while reducing the number of parameters needed for the model configuration. Globally, CNNs apart from the input and output layers consist of three types of layers: convolutional layers, pooling layers and fully connected layers (Fig. 8).

Fig. 8
figure 8

CNN neural network architecture

The LSTM neural network is an improvement of the traditional recurrent neural network to overcome the vanish gradient problem. An LSTM unit is then composed of a cell, a dynamic memory C and three gates: Forget Gate, Input Gate, Output Gate. Indeed, the Forget Gate is an operation which leads the unit to forget or to decrease the weight of an information which was useful at the time t − 1 but which is not any more at the time t whereas the Input Gate allows the storage of new non-existent information or of very weak weight at the time t − 1. Finally, the output Gate controls the information which will be transmitted at time t + 1 according to the dynamic memory C and the activation function. The LSTM cell, thanks to this memory vector C, memorizes the values on arbitrary time intervals and the three gates regulate the flow of information entering and leaving the cell (Fig. 9).

Fig. 9
figure 9

LSTM unit architecture

These two models will be compared to select the most efficient one for each wind profile (wind speed variations in each sub-area).

To estimate the power produced by wind generators, we use the characteristic power curve. This curve allows to know the power produced from the wind speed. It is specific for each wind generator. There are two different approaches for modeling wind turbines, namely the application of a power curve model available in the literature on the one hand or the use of real curves to which an interpolation method is applied on the other hand. In the following, we present three power curve modeling methods, as well as different power curves of small and medium power machines available on the market. The characteristic parameters of each power curve are:

  • \({V}_{\mathrm{cut}-\mathrm{in}}\): speed at which the power is switched on;

  • \({V}_{\mathrm{rated}}\): speed at which the rated power is obtained;

  • \({V}_{\mathrm{cut}-\mathrm{off}}\): the speed at which the power is switched off;

  • \({P}_{\mathrm{rated}}\): rated power.

The linear model is the simplest and assumes that the power variation between \({V}_{\mathrm{cut}-\mathrm{in}}\) and \({V}_{\mathrm{rated}}\) is linear. Thus, the reduced power curve is expressed by three Eq. (6):

$$P=\left\{\begin{array}{c}0, \quad V\le {V}_{\mathrm{cut}-\mathrm{in}}\\ a+b*V, \quad {V}_{\mathrm{cut}-\mathrm{in}}<V<{V}_{\mathrm{rated}}\\ 1, \quad {V}_{\mathrm{rated}}<V<{V}_{\mathrm{cut}-\mathrm{off}}\end{array}\right.$$

where the coefficients \(a\) and \(b\) are obtained by (7):

$$\left\{\begin{array}{c}a=\frac{{V}_{\mathrm{cut}-\mathrm{in}}}{{V}_{\mathrm{rated}}-{V}_{\mathrm{cut}-\mathrm{in}}}\\ b=\frac{1}{{V}_{\mathrm{rated}}-{V}_{\mathrm{cut}-\mathrm{in}}}\end{array}\right.$$

Studies show an overestimation of the productivity of wind generators, but despite this, this model is often used in studies of hybrid systems.

We also have the Pallabazzer model [47, 48], which differs from the linear model by the nonlinear shape of the curve between the speed of engagement and that for which we obtain the nominal power. In this part, the reduced power is expressed by:


Some authors introduce a third degree polynomial in the central part of the curve [49]:


where \({a}_{1}\), \({a}_{2}\), \({a}_{3}\) et \({a}_{4}\) are calculated on the basis of the power curve of the wind generator.

The most commonly used model is the Pallabazzer model (Notton et al. 2001; Prasad and Nataeajan2006). It is also possible to use the mechanical power on the shaft of the wind turbine determined from the wind speed (V), the area swept by the blades (\({A}_{r})\) and by the power coefficient (\({C}_{\mathrm{p}}\)):

$${P}_{\mathrm{mec}}=\frac{1}{2}{C}_{\mathrm{p}}{A}_{r}{\rho }_{a}{V}^{3}$$

Subsequently, we selected the Pallabazzer model for wind power estimation.

Forecasting model hyperparameters optimization

It is important to find out for which parameters of a model one could obtain better performance. As mentioned above, we have selected the CNN and LSTM models as the meteorological parameter forecasting models. The hyperparameters of these two models are presented in Table 1 along with the ranges of values that these hyperparameters can take for optimization.

Table 1 CNN and LSTM parameters

We vary the input data sequence between 3 and 72 h, the sequence to forecast between 1 and 24 h. For the CNN network, the number of filters is varied between 50 and 300, the number of units between 100 and 1000. For the LSTM network the number of units is also varied between 100 and 1000. We use three different learning rates: 10–2, 10–3, 10–3. This optimization is done with the Keras Tuner library under Python [50].

Models training

To train the models, we use the meteorological data (wind speed and direction) of the identified optimal production periods as well as the optimal hyperparameters obtained. The trainings are performed under Python3 where the CNN and LSTM models are developed with the TensorFlow library [51].

Clustering and forecasting model’s performance evaluation

It is important to choose the right metric to evaluate a model, otherwise the assessment of its performance would be wrong. The following metrics are used to evaluate the models developed in this work.

The determination coefficient R2 is an indicator that allows to judge the quality of a linear regression, simple or multiple. With a value between 0 and 1, it measures the adequacy between the model and the observed data. In the case of a simple linear regression, it is the square of the correlation coefficient. The R2 is defined as the proportion of variance explained in relation to the total variance, i.e., [1 − (sum of squared residuals/total variance)]. This coefficient applies to both simple and multiple regression.

$${R}^{2}=1-\frac{\sum_{i=1}^{n}{\left({Y}_{i}-{\widehat{Y}}_{i}\right)}^{2}}{\sum_{i=1}^{n}{\left({Y}_{i}-\overline{Y }\right)}^{2}}$$

The mean square error (MSE) is defined as the average of the squares of the errors and allows to evaluate the quality of a prediction model. It penalizes the largest errors and outliers (outliers). Its expression is given by the following formula:


with \({Y}_{i}\) the actual value and \({\widehat{Y}}_{i}\) the predicted value and n the prediction size.

The root mean squared error (RMSE) is an extension of the MSE and allows to reduce the MSE to the same unit as the quantity evaluated. It is defined as the square root of the MSE:


The normalized root mean squared error (NRMSE) is an extension of the MSE and is the most commonly encountered metric in the literature for evaluating wind speed prediction models. It is defined as the quotient of the root mean squared error and the mean or range of the values in the series.

$$\mathrm{NRMSE}=\frac{\mathrm{RMSE}}{{Y}_{\mathrm{max}}-{Y}_{\mathrm{min}}}ou \mathrm{NRMSE}=\frac{\mathrm{RMSE}}{\overline{Y} }$$

The Silhouette score is the metric that indicates the quality of a clustering. It varies between − 1 and 1:

  • The classification is bad when we obtain a negative co-efficient;

  • The classified element is close to the decision boundary or is alone in the cluster when we obtain a coefficient equal to zero;

  • The classification is good when we obtain a positive coefficient.

Its expression is given by the formula (15):


where a and b represent, respectively, the average distance that separates the data point from its cluster and the neighboring cluster.

Results and discussion

Grid and sample results

Figure 10 recalls the principle of gridding and shows the range of variation of latitude (l) and longitude (L). It can be noted that the latitude of the samples was varied from 5.625° to 12.6° and the longitude from 0.7° to 4.075°. The optimal grid step ∆t obtained is 0.15°. We recall that the optimal grid spacing is the spacing for which the number of clusters does not vary anymore, i.e., the number of different profiles of the meteorological parameters (here the wind speed) does not vary anymore.

Fig. 10
figure 10

Benin map (study area) gridded

Thus, 0.15° separates in latitude or longitude two test samples or two validation samples and 0.075° separates in latitude or longitude a test sample and a validation sample. The test samples are those used for cluster formation and the validation samples are used to evaluate the quality of the formed clusters. We thus obtained 1080 test samples and 1080 validation samples.

Data presentation

Once the 1081 test samples were obtained, the wind speed and direction were downloaded for all of them for the study period (January 1, 2012 to December 31, 2021). Figure 11 shows the evolution of the mean, standard deviation and maximum for the wind speeds. We can see that there is no apparent anomaly. The averages vary between 3.35 and 5.26 m/s with maxima ranging from 7.97 to 15 m/s. These statistics allow us to continue the study over the entire study area because wind turbines generally need a minimum of 3 m/s as a starting speed. We also note a variation of standard deviations between 1.17 and 2.2 m/s. These variations in statistics also show a difference in the different samples.

Fig. 11
figure 11

Statistics evolution for all wind speed data

Clustering results

Once we are sure that the data are usable and that the study is useful for the entire study area, we proceed to clustering. In this step we group the samples whose wind speeds vary identically over the entire study area. In other words, each cluster represents a sub-area within which the wind speed varies identically at all points. We obtained a total of 90 clusters. Figure 12 shows the different Silhouette scores obtained for the 90 clusters. We can notice that for 89 clusters, the Silhouette score is close to 1 which means that the similarity within these clusters is perfect. For cluster 90, the Silhouette score is 0. This value comes from the fact that within this cluster there is only one sample.

Fig. 12
figure 12

Silhouette score of 90 clusters

Figures 13 and 14 show the evolution of wind speeds within clusters 56 and 90 for the month of August 2020. We can notice that the curves are perfectly stacked for the cluster 56. For cluster 90 we notice the presence of only one curve which confirms the value 0 of the Silhouette score obtained. For ease of interpretation, the wind speed profiles of the samples have been named as follows: Wind_Speed_Latitude_Longitude. Results for the other clusters are available at [52].

Fig. 13
figure 13

Wind speed evolution in August 2020 for Cluster 56

Fig. 14
figure 14

Wind speed evolution in August 2020 for Cluster 90

Once the clusters are set up, the validation samples are then used to verify the representation of the entire study area by the 90 clusters. Figure 15 shows the Silhouette score (quality of membership in one of the 90 trained clusters) for the 1080 validation samples.

Fig. 15
figure 15

Validation Silhouette score

We can notice that the silhouette scores are all above the threshold of 0.9 that we have set (vary between 0.96 and 1). We can therefore conclude that the wind speed variations in the whole study area can be represented by the 90 different profiles identified.

Characterization of each sub-area

After clustering we have 90 sub-zones. Now we have to characterize each sub-area by determining the predominant wind directions and by determining the periods of the year when a wind turbine installed there could optimally produce. Given the number of sub-zones obtained, the following results will only be presented for cluster 56, an arbitrary choice. Indeed, any sub-zone could be chosen.

Figure 16 shows the wind rose for sub-area 56. We can notice that in this zone, the wind blows mainly to the southwest. This allows us to identify a good orientation of the blades in this area. Figure 17 shows the Weibull distribution as well as the frequency histogram of the wind speeds. We can see that the most probable wind speed is 5.4 m/s. We can also notice that the most convincing wind speeds are between 3.2 and 6.4 m/s. This speed range allows the installation of a wind turbine in this area. But in which period(s) of the year would we obtain an optimal production?

Fig. 16
figure 16

Wind rose of sub-area 56

Fig. 17
figure 17

Weibull distribution of sub-area 56

Figure 18 shows the monthly wind speeds and standard deviations for sub-area 56, which range from (3.37 m/s and 6.3 m/s) to (1.56 m/s and 2.3 m/s), respectively. In order to determine the optimal production period, we calculate the differences between the monthly wind speeds and monthly standard deviations (Fig. 19).

Fig. 18
figure 18

Sub-area 56 monthly wind speeds and standard deviations

Fig. 19
figure 19

Optimal production period determination

Knowing that the wind turbines start with minimum speeds between 7.2 and 10 km/h [53], we obtain for this sub-area an optimal production period going from November to July.

Wind speed and direction forecasting

Once the optimal production periods have been determined for each sub-area, the meteorological data for these periods are used to train the models according to the structure shown in Fig. 7. To do this, the wind speed and direction data are transformed using Eqs. (3) and (4) and then the prevailing frequencies of the speeds are used to add new variables to the data set according to Eqs. (1) and (2). Figure 20 shows the results of the fast Fourier transform (FFT) of the wind speed of sub-area 56.

Fig. 20
figure 20

Sub-area wind speed FFT

We can notice the attendance of the annual, daily, half-day, third day and quarter day periods. Figure 21 shows the appearance of the dataset after adding the new columns.

Fig. 21
figure 21

Header of the data set after adding the new variables

Table 2 and 3 present the optimization results of the CNN and LSTM hyperparameters for wind speed and direction forecasts for sub-area 56. We can notice that for both models, the best forecast performances were obtained for a 12-h forecast from 18 h of past data. We therefore present here only the results for the 18_12 models.

Table 2 CNN and LSTM parameters and performance for \({W}_{x}\) forecasting
Table 3 CNN and LSTM parameters and performance for \({W}_{y}\) forecasting

Thus, it can be noticed that optimal (filters, units, learning rate) parameters of (70, 590, 10–3) and (50, 300, 10–3) were obtained for the \({{\varvec{W}}}_{{\varvec{x}}}\) and \({{\varvec{W}}}_{{\varvec{y}}}\) predictions for the CNN, respectively. For the LSTM, optimal (units, learning rate) parameters of (460, 10–3) and (160, 10–3) were obtained for the \({{\varvec{W}}}_{{\varvec{x}}}\) and \({{\varvec{W}}}_{{\varvec{y}}}\) forecasts, respectively.

For the prediction of \({{\varvec{W}}}_{{\varvec{x}}}\) and \({{\varvec{W}}}_{{\varvec{y}}}\), we can notice that the best performing model is the LSTM with coefficients of determination R2 and Root Mean Square Error RMSE of (86%, 0.47 m/s) and (91%, 0.33 m/s), respectively. The LSTM model is therefore retained for the forecast of wind speed and direction for this sub-area. Figures 22 and 23 show the forecast results of the parameters \({{\varvec{W}}}_{{\varvec{x}}}\) and \({{\varvec{W}}}_{{\varvec{y}}}\) for 12 h on three randomly selected parts of the test set.

Fig. 22
figure 22

\({{\varvec{W}}}_{{\varvec{x}}}\) forecast for 12 h on three portions of the test set

Fig. 23
figure 23

\({{\varvec{W}}}_{{\varvec{y}}}\) forecast for 12 h on three portions of the test set

We can notice from these forecast results that the forecast trend is often well predicted. Nevertheless, discrepancies can be noticed between the predicted and true \({{\varvec{W}}}_{{\varvec{x}}}\) and \({{\varvec{W}}}_{{\varvec{y}}}\) parameters. This is due to the very random variation of the wind speed which makes learning difficult.

From the forecast values of \({{\varvec{W}}}_{{\varvec{x}}}\) and \({{\varvec{W}}}_{{\varvec{y}}}\) we can then deduce the values of wind speed and direction from Eqs. (15) and (16). We thus obtain for the 12 h of forecast of \({{\varvec{W}}}_{{\varvec{x}}}\) and \({{\varvec{W}}}_{{\varvec{y}}}\), 12 h of forecast of wind speed and direction.

$$\left\{ {\begin{array}{*{20}c} {W_{y} = W_{{\text{s}}} \sin \left( {W_{{\text{d}}} } \right)} \\ {W_{x} = W_{{\text{s}}} \cos \left( {W_{{\text{d}}} } \right)} \\ \end{array} \Rightarrow \frac{{W_{y} }}{{W_{x} }} = \tan W_{{\text{d}}} } \right.$$

A validation of the forecasting performance of the models was performed on the data of 31 December 2020 and 1 January 2021. Figure 24 shows the 12 rows of input data and Fig. 25 the 12 rows of true values of the parameters \({{\varvec{W}}}_{{\varvec{x}}}\) and \({{\varvec{W}}}_{{\varvec{y}}}\) that the forecasts should give.

Fig. 24
figure 24

Validation input data

Fig. 25
figure 25

Validation output data

Figures 26 and 27 show the representative curves of target and predicted \({{\varvec{W}}}_{{\varvec{x}}}\) and target and predicted \({{\varvec{W}}}_{{\varvec{y}}}\), respectively. We can notice that the forecasting is quite good.

Fig. 26
figure 26

Validation target and forecasted \({{\varvec{W}}}_{{\varvec{x}}}\)

Fig. 27
figure 27

Validation target and forecasted \({{\varvec{W}}}_{{\varvec{y}}}\)

The forecasting performances are presented in Table 4.

Table 4 \({{\varvec{W}}}_{{\varvec{x}}}\) and \({{\varvec{W}}}_{{\varvec{y}}}\) forecasting performance

From the forecasting of \({{\varvec{W}}}_{{\varvec{x}}}\) and \({{\varvec{W}}}_{{\varvec{y}}}\) we deduce the values of wind speed and direction. Figure 28 shows the true (target) values of wind speed and direction that the forecasting should give.

Fig. 28
figure 28

Target values of wind speed and direction

Figures 29 and 30 show the representative curves of target and predicted wind speed and direction, respectively.

Fig. 29
figure 29

Validation target and forecasted wind speed

Fig. 30
figure 30

Validation target and forecasted wind direction

Table 5 presents the forecasting performances. We can note coefficients of determination of 93% and 70%, respectively, for the wind speed and direction with root mean square error of 0.34 m/s and 7.8 rad, respectively.

Table 5 Wind speed and wind direction forecasting performance

With these performances, we can qualify the LSTM model for medium term forecasting of wind speed and direction. In the literature, forecasting is mostly very short or short term with Root Mean Square Error above 0.7 m/s with deep learning networks [36, 54,55,56,57]. As an example, we list in Table 6 the results found in some recent articles. It must be said that the forecast horizons, the datasets and the computers used are rarely the same. This makes it difficult to compare performances in terms of accuracy and computation time. We can notice that for most of the proposed models for wind speed prediction, despite a horizon up to 12 h, our proposed LSTM model remains more efficient.

Table 6 Performance comparison

Power output estimation of a wind turbine installed in sub-area 56 from predicted speeds

From the predicted wind speed values and characteristics, we can now estimate future values of the power output using Eq. (6). As an example, we make this estimation on the 2 MW model of the manufacturer WindEnergy Lebanon whose characteristics are presented below:

  • Power (kW) 2000

  • Rated Power (kW) 2050

  • Diameter (m) 88

  • Cut-in speed (m/s) 3

  • Cut-out speed (m/s) 25

  • Rated speed (m/s) 12

  • Maximum Cp 0.41

  • Hub height (m) 80

Because the height of the wind turbine is 80 m and the data used for our prediction were taken at a height of 50 m, we extrapolated the velocities to a height of 80 with the logarithmic wind profile as defined below [63]:


The reference velocity v1 is measured at the reference height h1. v2 is the wind speed at height h2. z0 is the roughness length. We used a z0 value of 0.0024 m.

Figure 31 shows the power obtained for the 12 h forecasting with the three estimation models.

Fig. 31
figure 31

Estimated wind power


It is very important to be able to identify a favorable geographical site because of its characteristics when it comes to installing a wind generator. Also, when the generator is installed, it is necessary to have tools that can give an idea of how its output power will evolve given the stochastic character of the wind speed. The results of this work have shown that it is possible, based on artificial intelligence clustering techniques, to highlight the potential of wind power production at any point within a large geographical area and to delimit the periods of the year during which the production could be optimal. Moreover, these results led to the forecasting for 12 h of the wind speed and direction as well as of the output power of a wind generator by associating a time series forecasting model (LSTM) and an approximation model of the power curves of wind turbines. These results will be very useful for the identification of any potential site of installation of wind turbines for a country and the control in advance of the possible behavior of the wind turbine during all periods of the year.

Availability of data and materials

The references related to the downloaded data and materials used have been specified. The other data used in the current study are available from the corresponding author on reasonable request.



Artificial neural network


Root mean square error


Mean absolute percentage error


Mean square error


Long short-term memory


Evolutionary decomposition generalized normal distribution of bidirectional long-term memory model


Convolutional neural network


Improved hybrid time series decomposition strategy


Artificial neuro-fuzzy inference system


Stationary wavelet decomposition


Modified multi-objective dragonfly algorithm


Autoregressive integrated moving average


Gated recurrent unit


Improved complete ensemble empirical mode decomposition with adaptive noise


Renewable energy sources


Support vector machine

R2 :

Regression coefficient


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The first draft of the manuscript was written by AM. DA and AR performed the conceptualization of the research idea, participated in the interpretation of the results, and reviewed the edited manuscript. All authors have made a substantial contribution to the manuscript. All authors read and approved the final manuscript.

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Correspondence to Kossoko Babatoundé Audace Didavi.

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Agbomahena, B.M., Didavi, K.B.A. & Agbokpanzo, R.G. A novel technique for forecasting the optimal production of a wind generator installed at any geographical point located within a very large area. Journal of Electrical Systems and Inf Technol 10, 23 (2023).

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