Application of sliding window technique for prediction of wind velocity time series
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Abstract
The uncertainty caused by the discontinuous nature of wind energy affects the power grid. Hence, forecasting the behavior of this renewable resource is important for energy managers and electricity traders to overcome the risk of unpredictability and to provide reliability for the grid. The objective of this paper is to employ and compare the potential of various artificial neural network structures of multi-layer perceptron (MLP) and radial basis function for prediction of the wind velocity time series in Tehran, Iran. Structure analysis and performance evaluations of the established networks indicate that the MLP network with a 4-7-13-1 architecture is superior to others. The best networks were deployed to unseen data and were capable of predicting the velocity time series via using the sliding window technique successfully. Applying the statistical indices with the predicted and the actual test data resulted in acceptable RMSE, MSE and R^{2} values with 1.19, 1.43 and 0.85, respectively, for the best network.
Keywords
Wind energy ANN Time series prediction Sliding window Multi-layer perceptron Radial basis function TehranIntroduction
To cover the uncertainty caused by the discontinuous nature of wind resources, a reliable energy system is required [6, 7]. Hence, forecasting the behavior of the wind resource can be a crucial role for energy managers, policy makers and electricity traders, to overcome the risk of unpredictability, and to provide energy security, for energy planning and handling energy storage policies including economic dispatch. Furthermore, such forecasting gives perspectives regarding time of operation, repair and replacement of wind generators and conversion lines and could help to shift towards optimum electrical networks.
Various approaches to forecast wind velocity and power have been reported. Examples include autoregressive integrated moving average (ARIMA) [8, 9, 10], nearest neighbor search, polynomial regression, Bayesian structural break [11], support vector machines (SVM) [12], Taylor Kriging [9], fuzzy logic and artificial neural network (ANN) [13, 14], ARIMA–Kalman [15], ARIMA–ANN [16] and wavelet derivatives such as wavelet-GP, wavelet-ANFIS, wavelet-ANN and wavelet packet [17, 18, 19, 20]. These approaches are among the most utilized methods to predict wind resource components. The ANNs have resulted in acceptable performance compared to conventional methods due to their robustness and capability to address unpredictable complexities.
Sliding window technique, artificial neural networks
Network structures
Effective parameters considered in training of MLPs in preferred order
Effective parameter | Values/types |
---|---|
No. of input neurons | 1–10 |
No. of hidden layers | 1–2 |
No. of neurons in hidden layer | 1–13 |
Transfer functions | Tansigmoid, Logsigmoid |
Comparison function | MSE |
Also, the same data are provided to various radial basis function neural networks (RBFNNs) [27] for comparing their best outcome to the best performance yielded from the MLP networks trained by the LM algorithm. Regarding structure of the trained RBFNNs, a greater range of neuron numbers in the hidden layer is tested and compared to the MLP networks. To identify the best structure of the RBFNN, 0–25 neurons are examined in the hidden layer and the performances calculated for each structure are determined and compared in the results section.
Statistical indices for performance evaluation
Statistical indices and their related expressions
Statistical index | Expression |
---|---|
RMSE | $\sqrt{\frac{1}{n}\sum _{i=1}^{n}{({v}_{i,\text{m}}-{v}_{i,\text{f}})}^{2}}$ |
R ^{2} | $\frac{{\sum}_{i=1}^{n}({v}_{i,\text{m}}-{v}_{\text{m,avg}})\times ({v}_{i,\text{f}}-{v}_{\text{f},\text{avg}})}{\sqrt{\left[{\sum}_{i=1}^{n}{({v}_{i,\text{m}}-{v}_{i,\text{m}})}^{2}\right]\times \left[{\sum}_{i=1}^{n}{({v}_{{}_{i,\text{f}}}-{v}_{\text{f,avg}})}^{2}\right]}}$ |
MBE | $\frac{1}{n}\sum _{i=1}^{n}({v}_{i,\text{m}}-{v}_{i,\text{f}})$ |
Results and discussion
The results of training various networks with different structures are presented in this section.
Performance summary of trained structures with all (train, validation and test) data using MLP
Transfer function | No. of neurons in hidden layers | MSE | RMSE | R ^{2} |
---|---|---|---|---|
Logsig | 4 | 1.5303 | 1.2371 | 0.8397 |
Logsig | 5 | 1.4863 | 1.2191 | 0.8421 |
Logsig | 7 | 1.4689 | 1.2120 | 0.8442 |
Logsig | 10 | 1.4890 | 1.2203 | 0.8426 |
Logsig | 13 | 1.4854 | 1.2188 | 0.8427 |
Tansig | 4 | 1.4896 | 1.2206 | 0.8418 |
Tansig | 5 | 1.4758 | 1.2148 | 0.8433 |
Tansig | 7 | 1.4770 | 1.2153 | 0.8438 |
Tansig | 10 | 1.4749 | 1.2145 | 0.8435 |
Tansig | 13 | 1.4796 | 1.2164 | 0.8434 |
Tansig–Logsig | 7–7 | 1.4742 | 1.2142 | 0.8436 |
Tansig–Logsig | 7–13 | 1.4430 | 1.2012 | 0.8472 |
Tansig–Logsig | 10–7 | 1.4586 | 1.2077 | 0.8454 |
Tansig–Logsig | 10–13 | 1.4697 | 1.2123 | 0.8442 |
Logsig–Tansig | 13–7 | 1.4544 | 1.206 | 0.8458 |
Logsig–Tansig | 7–13 | 1.6862 | 1.2985 | 0.8221 |
According to the results, a network with 4-7-13-1 structure is chosen as the best MLP network of this study. This network utilizes 4 input data in the input layer with 7 and 13 neurons in its first and second hidden layers to predict the output. The activation functions of the first and the second relevant hidden layers of this network are Tansigmoid and Logsigmoid, respectively. The network utilizes a linear function in its output layer to transfer the data to the output.
Performance comparison of the best MLP and RBF trained structures
Network | Best structure | R ^{2} | RMSE | MSE |
---|---|---|---|---|
MLP | 4-7-13-1 | 0.85 | 1.19 | 1.43 |
RBF | 4-25-1 | 0.83 | 1.36 | 1.84 |
Conclusions
Forecasting the behavior of the wind resource can provide valuable information for energy managers, energy policy makers and electricity traders, as well as times of operation, repair and replacement of wind generators and conversion lines. However, reliable power generation and effective integration of wind energy systems into the power distribution grid are affected by the intermittent and nonlinear nature of the wind resource. Accurate forecasting of wind velocities not only can address the challenges such as adverse shocks in conventional power units caused by excessive wind speed but also can provide useful information regarding voltage and frequency instabilities resulting from variation in wind power. ANNs are robust tools with advantageous capabilities for addressing the unpredictable complexities of nonlinear phenomena such as the stochastic behavior of the wind resource, which cannot be handled by conventional methods accurately. In this paper, wind velocity data for 1 year at 1-h intervals are utilized to train various artificial neural network (ANN) architectures for prediction of wind velocity data of Tehran, Iran. Structure analysis and performance evaluations of the established networks determine that the MLP network with a 4-7-13-1 architecture is superior to others. The best network was deployed to the unseen data and found to be capable of predicting velocity data via the sliding window technique successfully. Applying the statistical evaluation indices with the predicted and the actual test data results in acceptable RMSE, MSE and R^{2} values of 1.19, 1.43 and 0.85, respectively. Predictions of wind power density or wind energy density, which are related to wind velocity, as well as comparing the performance of the ANN with other forecasting approaches, merit further investigation as an extension of the present study.
Notes
Conflict of interest
The authors declare that they have no competing interests
Authors’ contributions
MV, OR, and PA have participated in implementation of the methods, computation process, validation of the results, and giving the study ideas. MV has also drafted the manuscript. As supervisor Profs., MR and FF have checked the study procedure and commented for qualification of the manuscript structure. All authors read and approved the final manuscript.
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