Estimating the Wake Losses in Large Wind Farms: A machine learning approach Farah Japar
Sathyajith Mathew
Balakrishnan Narayanaswamy
Universiti Brunei Darussalam Gadong, Brunei Darussalam
Universiti Brunei Darussalam Gadong, Brunei Darussalam
IBM Research Bangalore, India
Chee Ming Lim
Jagabondhu Hazra
Universiti Brunei Darussalam Gadong, Brunei Darussalam
IBM Research Bangalore, India
Abstract—Estimating the wake losses in a wind farm is critical in the short term forecast of wind power, following the Numerical Weather Prediction (NWP) approach. Understanding the intensity of the wakes and the nature of its propagation within the wind farm still remains a challenge to scientist, engineers and utility operators. In this paper, five different machine learning methods are used to estimate the power deficit experienced by wind turbines due to the wake losses. Production data from the Horns Rev offshore wind farm, Denmark, have been used for the study. The methods used are linear regression, linear regression with feature engineering, nonlinear regression, Artificial Neural Networks (ANN) and Support Vector Regression (SVR). Power developed by individual turbines located at different positions within the farm were computed based on the above methods and compared with the actual power measurements. With the respective Variance Normalized Root Mean Square Error (VNRMSE) of 0.21 and 0.22, models based on ANN and SVR could estimate the wind farm wake effects at an acceptable accuracy level. The study shows that suitable machine learning methods can effectively be used in estimating the power deficits due to wake effects experienced in large wind farms. Index Terms-- Wind farms, Machine learning, Regression analysis, Artificial neural networks; Support vector machines.
I.
INTRODUCTION
With an average growth rate of 22% over the past 10 years, the global cumulative wind power capacity has reached up to 282.5GW by the end of 2012 [1]. As a result, the grid contribution of wind generated electricity has increased significantly in the recent years. This growth in the wind power sector is expected to continue and even in a moderate scenario, the global installations are projected to reach at 1,600 GW by 2030 [2]. This would enable wind power to contribute between 14.1 and 15.8% of the global electricity demand. Hence, wind energy would establish a significant presence in the power grids around the world in the near future. One major challenge in the grid integration of wind energy is the uncertainty in its availability. Being a stochastic phenomenon, the wind velocity and thus the available power vary significantly over time. Hence, for the smart management of wind integrated grids, an estimate of
the available wind energy, over different time scales, is essential. Such a forecast is critical for the utilities for ensuring the unit commitment, economizing the dispatch, formulating the tariff structures and assessing the dynamic security [3]. Technical and economical advantages of such forecasting in a dynamic electricity market are well established [4]-[7]. Physical models are widely being used for the short term wind power forecast. References [8]-[10] are some of the examples. In this approach, the free stream wind flow over the wind farm region is forecasted using the Numerical Weather Prediction (NWP) models. Effect of the wind turbines in the flow field is then incorporated in the forecast by computing the velocity deficit due to the wake effect. Thus, the actual wind velocities ‘felt’ by individual turbines in the farm are estimated, which is then used in conjunction with the power curve of the turbine to arrive at the power and energy expected from the turbines. Obviously, reliability of this forecasting approach greatly depends on the accuracy with which the wake effect within the wind farm is modeled. As the turbines interact with the wind stream and extract energy, wake is generated, which is propagated to the downstream side of the flow, resulting in a reduction in the velocity. As the flow proceeds downstream, these wakes gets diluted due to spreading and the flow would regain the free stream conditions after a certain distance. In a wind farm, where a number of turbines are clustered, the downstream turbines may come under this wake region and thus the velocity experienced by downstream turbines could be lesser than that received by the upstream turbine. This effect gets aggregated and the power losses due to the wake in large wind farms can be severe. This can cause up to 20% losses in the annual energy production [11]. Several models are being proposed to quantify the wake losses within the wind farms, which can be broadly classified into 2 groups: (i) kinematic models which basically apply the momentum equation to the flow field to model the velocity deficit behind the turbines (examples are Jensen Model [12], [13], Frandsen Model [14] and Larsen Model [15] and (ii) field models which analyzes the complete flow over the wind farm using Computational Fluid Dynamics (CFD) [16]. Though these models are extensively used with commercial
wind power forecast systems, quite often, their accuracy in predicting the wake losses are not impressive. The prediction error can vary significantly from case to case. For example, in some cases the Normalized Root Mean Square Error (NRMSE) can even be as high as 0.31 [17]. There are also methods using data mining algorithms such as neural networks and support vector machines as reported in [18], [19]. In this paper, it is proposed that the wake losses in wind farms can be better predicted using machine learning techniques. An offshore wind farm located in Horns Rev, Denmark, is considered for the analysis. The paper starts with the details of the wind farm data, which is followed by a brief discussion on the major factors influencing the wake deficit. Development of models based on five supervised machine learning techniques viz. linear regression, linear regression with feature engineering, nonlinear regression, Artificial Neural Networks and support vector regression are presented. Finally, the proposed models are validated with actual observations from the wind farm. II.
THE WIND FARM DATA
Performance data from the Horns Rev offshore wind farm, Denmark, is being used for the present analysis. It is an ideal site for such a study because (i) it is one of the well instrumented wind farms where the data are being logged following standard procedures (ii) It has similarities with a number of large wind farms being newly proposed [20]. The Horns Rev wind farm has 80 Vestas V80 turbines of 2MW rated capacity, arranged in 8 rows (north to south) and 10 columns (east to west). The vertical columns are aligned approximately at 7.2° West of North and the turbines are laid with the same row and column spacing of 560 m (7 times the rotor diameter) (Fig. 1). More specifications of the wind farm are available in [20].
Ten minutes averaged performance data were used for the study. To represent the wake free conditions, wind speeds and directions were also available from the nearby metrological masts. Three wind directions viz. 270°, 221° and 312o were considered as these directions defines the ‘worst’ cases, bringing maximum number of turbines under the wake field. In order to bring out the effect of wind speed on the wake losses, three different wind speeds of 6 m/s, 8 m/s and 10m/s were chosen. III.
FACTORS INFLUENCING THE WAKE
From the wind farm data, the major factors influencing the wake losses are identified. These are discussed in the following sections. Fig. 2, 3 and 4 demonstrate the wake losses at different turbines positions. A. The Incoming Wind Speed As it is evident from the figures, the wake losses are significantly influenced by the incoming free stream wind speed. For example, at 6 m/s speed and 270o flow direction (Fig. 2), the power produced by the downstream turbine was 35.5% lower in comparison with the extreme upstream turbine. However, when the wind speed increased to 8 m/s and 10 m/s, the corresponding wake losses were 38.5% and 42.9% respectively. Similar trends can be observed in the other two wind directions as in Fig. 3 and 4. B. Wind Direction The wake loss pattern changes with the changes in wind direction. Among the three directions considered, the wake losses are found to be higher when the wind blows at 270o. This is because, at this direction, the wake propagation distance between the consecutive turbines is at its minimum of 560 m (Fig. 1). Corresponding distances for 221o and 312o are approximately 752 m and 832 m respectively. Thus, in these cases, the wakes propagate over longer distances and regain a part of its lost velocity before it reaches and interacts with the immediate downwind turbine.
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Fig. 1. Layout of the Horns Rev wind farm indicating the wind directions considered.
Fig. 2. Power developed by the turbines at different wind velocities at 2700 wind direction
wind are represented by the changes in the wake propagation distances between the consecutive turbines as discussed above. Similarly, the column-wise position of a turbine is represented by its distance from the extreme upwind turbine. The data set was randomly divided into a training set of size two third of the total data points and the remaining was used for testing.
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A. Linear Regression The first algorithm tried was simple linear regression. In linear regression the function f() was approximated using a linear weight vector w, so that
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Zt w xt
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Fig. 3. Power developed by the turbines at different wind velocities at 2210 wind direction
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Zt i wi xit
Since the system is over-determined, a weight vector w was determined to minimize the mean squared error over the training data.
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where the product is understood as matrix multiplication. In other words
B. Linear Regression with Feature Engineering Based on the relationship of influencing parameters on wind power generation (for example, the cubic velocitypower relationship) more features are included in the linear regression under this method. Thus, a new feature vector Zt of length 9 was developed.
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Fig. 4. Power developed by the turbines at different wind velocities at 3120 wind direction C. Turbine position Column-wise position of the turbines (Fig. 1) in the wind farm is another factor influencing the wake losses. In general, a significant loss in power could be observed, when the flow passes through the first upstream turbine (turbine 1) and reaches its immediate downstream turbine (turbine 2). These losses are more significant at higher wind speeds. However, when the wakes continue to propagate further downstream, the velocity regains at a faster rate due to the influence of the surrounding undisturbed boundary flow. IV.
WAKE ESTIMATION METHODS
Based on the wind farm data, the wake losses are quantified by five different machine learning methods under the study. These are (i) linear regression (ii) linear regression with feature engineering (iii) nonlinear regression (iv) Artificial Neural Networks (ANN) and (v) support vector regression. Incoming free stream wind speed, wind direction and the turbine position are considered as the variables influencing the wake losses. The directional variations in
C. Nonlinear Regression The power developed by a turbine in the farm is directly proportional to the incoming wind speed and its distance from the immediate upwind turbine in the wake propagation path. Similarly, the power is inversely proportional to the turbines distance from the extreme upwind turbine. Keeping these in view, the regression function was developed as
V 3 D0.099 Pi in Ri 0.109
where Pi is the power developed by the turbine in the ith column, Vin is the incoming free stream wind velocity, D is the distance between successive turbines in the wake propagation path and Ri is the distance of the ith turbine from the extreme upwind turbine. The above three methods requires the knowledge of the power generation mechanism and leaves open the question ‘whether inclusion of other features could provide better results?’. Thus, more advanced statistical methods that work on the original features but are automatically able to capture the variance in output power, were explored as discussed below.
E. Support Vector Regression Support Vector Machines (SVMs) are machine learning methods that have recently become very popular in the machine learning community due to noise stability, lower training data requirements, good theoretical properties and relatively lower computational requirements. An SVM constructs a hyper-plane in a high dimensional feature space that separates or models the data. The model produced by SVMs for classification and SVR for regression depend only on the most critical subset of the training data (called the support vectors) because the cost function ignores any training data close to the model prediction (within a threshold). The choice of higher dimension is made through the choice of feature kernel. We chose among popular kernels and threshold values using the k-fold cross validation as described above.
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In cross validation, the training set itself is split into training and validation data, and the models learnt using the subset training data, for different parameter choices are evaluated on the validation set. The best performing training parameters are chosen and a model is trained using these parameters on the entire training set. This final model is evaluated on the test set, which is not used in any way for training or validation.
Fig. 5. Comparison of the measured power with the power estimates by the models at 6 m/s wind velocity.
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Fig. 6. Comparison of the measured power with the power estimates by the models at 8 m/s wind velocity. 1400 1200
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D. Artificial Neural Networks For Artificial Neural Networks (ANN), the transfer functions of the hidden layers and the number of hidden units and their interconnection pattern were parameterized. In order to select these parameters, k-fold cross validation [21] was performed on the training set, so that these do not need to be decided beforehand based again on expert knowledge.
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VALIDATION OF THE MODELS
The developed models are validated using the remaining field observations. For this, the actual power developed by a turbine at a given wind velocity is compared with the corresponding estimates from different models. The comparisons are shown Fig. 5, 6 and 7. 300
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Fig. 7. Comparison of the measured power with the power estimates by the models at 10 m/s wind velocity. It can be seen that models based on ANN and SVR could estimate the wake losses within the wind farm accurately for the wind speeds 6 m/s and 8 m/s (Fig. 5 and 6). However, the estimates by these models found deviating slightly from the measured values at 10 m/s. Although the linear regression with feature engineering could define the wake behavior reasonably at 6 m/s, its accuracy is not impressive at higher wind velocities. In contrast, the nonlinear regression model could improve its performance at higher wind velocities. In all the cases, the linear regression model failed to understand the wake losses within the wind farm.
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To quantify the differences in measured and estimated power variations due to wake effect, Root Mean Square Error (RMSE) and Variance Normalized Root Mean Square Error (VNRMSE) of the model outputs were computed using the expressions
i 1 Pi Pe n
RMSE
VII. ACKNOWLEDGMENT
2
n
and
VNRMSE
RMSE
P
where Pi is the power available at the ith turbine, Pe is the corresponding estimated power, n is the number of data points used in the validation and δP is the standard deviation of actual power. The results are shown in TABLE 1. The errors - both RMSE and VNRMSE - are lowest for ANN and SVR based models. As expected, error level was highest for the linear regression approach. This clearly indicates that among the models considered, ANN and SVR showed the best performance in characterizing the wake losses in the given wind farm. These methods, even with a few hand selected features, could understand the wake behavior well. This shows the power of statistical learning methods in wind farm wake estimation. It should be noted that, though the errors were slightly lower for ANN, SVR has the distinct advantages of smaller number of parameters and much faster training time.
The authors are thankful to DONG Energy and Vattenfall Group for making the wind farm data available for the study through the Wind Turbine Wake Virtual Laboratory Wakes Site. REFERENCES [1] [2] [3]
[4]
[5]
[6]
[7]
[8] TABLE I. COMPARISON OF VNRMSE AND RMSE FOR DIFFERENT MODELS. [9] Algorithm
RMSE
VNRMSE
Linear regression (LR)
148.86
0.54
65.07
0.24
87.34 57.17 59.40
0.32 0.21 0.22
Linear regression with feature engineering (LRFE) Nonlinear Regression (NLR) ANN SVR
[10] [11]
[12]
VI.
CONCLUSIONS
In this study, we explore the possibilities of using machine learning techniques in estimating the power losses due to wake in wind farms. The wind turbine performance data from the Horns Rev offshore wind farm was used for the study. Parameters influencing the wake intensity were identified which were further correlated with the power developed by the turbines at various positions in the wind farm using five different methods viz. linear regression, linear regression with feature engineering, nonlinear regression, Artificial Neural Networks (ANN) and Support Vector Regression (SVR). Among the methods compared, estimations based on ANN and SVR are found to be closely matching with the actual power measurements from the wind farm. The proposed models are further being combined with Numerical Weather Prediction (NWP) models to develop a wind power forecast system which could be an effective tool for the smart integration of wind energy with the power grids.
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