Short-term wind forecasting using artificial neural ...€¦ · 3.1 Artificial neural networks and...

Short-term wind forecasting using artificial neural networks (ANNs)

Department of Engineering Innovation, Centro Ricerche Energia e Ambiente, University of Salento, Italy

Abstract

The integration of wind farms in power networks has become an important problem. As electricity cannot be preserved because of the highest cost of storage, electricity production must following market demand, necessarily. Short-long term wind forecasting over different time steps is becoming an important process for the management of wind farms. Time series modelling of wind speeds is based on the valid assumption that all the causative factors are implicitly accounted for in the sequence of occurrence of the process itself. Hence, time series modelling is equivalent to physical modelling. Artificial neural networks (ANNs), which perform a non-linear mapping between inputs and outputs, provide a robust approach for wind prediction. In this work, these models are developed for simulating wind speed and energy production of a wind farm with three wind turbines, comparing different prediction temporal periods. We applied artificial neural networks for short and long term load forecasting using real load data. Keywords: neural artificial networks (ANNs), forecasting wind, turbine, CFD.

1 Introduction

Electricity markets throughout the world are changing to allow the integration of alternative energy sources, in particular wind energy. The major criticality in the use of renewable energy, particularly of wind energy, concerns the management of wind farms. As electricity cannot be preserved because of the highest cost of storage, electricity production must follow the market demand, necessarily. In the state of the art there are two types of approach in the prediction of wind energy [1]: those based on physical

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modelling and those based on historical series analysis. The first is used in meteorology to reproduce the atmospheric state, but this is a very complex system since it requires big resources of hardware for the calculation. While, approaches based on historical series estimate the future values on the basis of past values after identification of a model that simulates the process analyzed. This methodology is based on the valid assumption that all the factors influence the process are taken into implicitly using the past values and so it is possible to make a probable prediction. A good prediction model in real time of wind energy must be able to guarantee reliability for the prediction as soon the time horizon is extended. In order to understand the different issues involved in wind energy forecasting it is useful to divide the problem into three difference time scales: very short-term (0-6 hrs), short-term (6-72 hours), and medium range (3-10 days). In the small terms, in particular when the time horizon swings from a few minutes to some hours, various studies, based on ARMA models [2,8] and ANNs model [3,5–7], obtained a good result in the prediction of wind energy. In [5] an ANN model is presented, based on a back-propagation method, it was evaluated with real data measured at two different locations and demonstrated a correct dynamic performance in all evaluation tests, so it can be concluded that the algorithm is valid for estimating average speed values. The initial point for the approach in [6] is mainly the fact that none of the forecasting approaches for hourly data, that can be found in the literature, based on time series analysis or meteorological models, gives significantly lower prediction error than the elementary persistent approach. This was combined with the characteristics of the wind speed data, which are determined by the power spectrum values, distinguished by the spectral gap in intervals between 20 minutes and 2 hours. The finally proposed methodology is based on the multi-step forecasting of 10 minutes averaged data and the subsequent averaging to generate mean hourly predictions. In [7] the ANNs models are found to perform better for the forecast length of one hour, as seen from the actual and simulated data. For the forecast length of one hour, artificial networks are found to perform better than other methods, but the study suggests that, for increased forecast lengths, modified methods need to be investigated. In [8] a linear, time-varying autoregressive (AR) process is used to model and forecast wind speed. This modelling approach takes into account the non-stationary nature of wind speed. The time-varying parameters of the AR model are modelled by smoothed, integrated random walk processes. A Kalman filter is used to estimate the time-varying parameters of the AR model. The algorithm is used to forecast wind speed from 1 h to a few hours ahead. Other studies, for example in [14], are focused on a real-world application, the long-term wind speed and power forecasting in a wind farm using locally recurrent multilayer networks as forecast models. To improve the performance of the models, considering the complexity of the process, a class of optimal on-line learning algorithms is employed for training the locally recurrent networks based on the recursive prediction error (RPE) algorithm. The experimental results demonstrate that the recurrent forecast models provide better multistep ahead forecasts compared to the persistent method, the atmospheric and time-series models. In [15] the wind speed prediction in wind

198 Energy and Sustainability II



farms has been performed by using local recurrent neural networks with internal dynamics, as advanced forecast models. The efficiency of the proposed approach is tested on a real-world wind farm problem, where multistep ahead wind speed estimates from 15 min to 3 h are sought. In [16] results are presented of a number of advanced prediction systems performed in the frame of the European project Anemos. The European project Anemos is focused on several topics related to wind power forecasting such as physical and statistical modeling, uncertainty estimation, upscaling and others. From the very first stage of the project it was recognized by both end-users and modelers the necessity to map the existing wind power forecasting technology both in terms of research approaches and also in terms of performance. In [17] a statistical forecasting system is implemented for short-term prediction (up to 48 h ahead) of the wind energy production of a wind farm: for a given wind farm, the input variables are the meteorological predictions of wind (velocity and direction) for the next 48 h and past values of output power. The forecasting system has then to supply, on an hourly basis, the predicted output power up to 48 h ahead. In this work, artificial neural networks have been applied for the prediction of wind energy when the time horizon swings from 1 to 24 hours, using historical series data wind only, for a wind farm. Preliminarily, the statistical analysis of the historical series was processed and the probable distribution of wind speed and direction of the three turbines were represented. Application of a neural network for the prediction of wind energy able to an acceptable error on the observation when the prediction length is under 6 hours. So, with the extension of a prediction time horizon, the reliability of a prediction based only on statistical methods reducing considerably, but the need of planning on medium-long terms of the wind productivity asks for approaches that are able to integrate knowledge from historical series with the outputs of numerical weather models.

2 Wind farm characteristics

There are a number of complex issues associated with the evaluation of wind energy forecasts. The most significant issue is which parameter(s) should be

Figure 1: Seasonal trend of wind

speed in year I of the wind park.

Figure 2: Wind speed and wind direction – Month of April (year I).




used as the metric(s) for forecast performance. One’s choice of metrics can have a significant impact on one’s impression of forecast performance. So the first step in the wind forecasting is the statistical analysis of the historical series data. Our data set contains wind speed observations for a period of four years (years I, II, III, IV). In fig. 1 the seasonal trend of average wind speed for the first year of dataset (year I) is represented: in general, the average daily wind speed is higher in the winter than the summer months. In Fig. 2, the peak of wind speed is at a consistent wind direction, this means that a consistent wind direction can be considered as a factor that explains the high wind speed.

3 ANNs models for wind speed and energy prediction

3.1 Artificial neural networks and architectures

Neural networks are composed of simple elements operating in parallel. These elements are inspired by biological nervous systems. As in nature, the network function is determined largely by the connections between elements. You can train a neural network to perform a particular function by adjusting the values of the connections (weights) between elements. A typical neural network used in the present study is the Multi Layer Feed Forward (MLFFN) network. In the Feed-Forward networks the data flow from input to output units is strictly feed-forward [13]. The data processing can extend over multiple (layers of) units, but no feedback connections are present, that is, connections extending from outputs of units to inputs of units in the same layer or previous layers. Each layer consists of units which receive their input from units from a layer directly below and send their output to units in a layer directly above the unit. There are no connections within a layer. The ANN learns through the set of examples supplied to it during the training process. Once the network weights and biases are initialized, the network is ready for training. During training the weights and biases of the network are iteratively adjusted to minimize the network performance. The default performance function for feed-forward networks is mean square error – MSE – the average squared error between the network outputs a and the target outputs t. Several algorithms for training use the gradient of the performance function to determine how to adjust the weights to minimize performance. The gradient is determined using a technique called back-propagation, which involves performing computations backward through the network. The goal of the algorithm is to minimise the global error E defined below,

2

1

1 ( ( ) ( ))2

n

kE t k o k

=

= −∑

(1)

where o(k) and t(k) are the outputs and target network for any k output node. The summation is carried out over all output nodes for every training pattern. A pair of input and output values constitutes a training pattern. The back-propagation




algorithm calculates the error E as per Eq. (1) and distributes it backward from the output to hidden and input neurons. This is done using the steepest gradient descent principle where the change in weight is directed towards negative of the error gradient. The incremental change in the weight may be expressed as,

1n nEw ww

α η−∂

∆ = ∆ −∂

(2)

where w is the weight between any two nodes ∆wn and ∆wn-1 are the changes in the weight at nth and n-1th iterations; α the momentum factor and η the learning rate. The learning rate governs the size of the weight change during each iteration. The momentum factor prevents the weight oscillations during training iterations and also accelerates the training on flat error surfaces [11]. The activation function used for the hidden neurons of the networks are generally the sigmoid function (‘tansig’). The output neurons can have linear activation function (‘purelin’). In the present study, fast algorithms, developed as modified versions to the standard back propagation algorithm are used, known as the Levenberg-Marquardt algorithm (‘trainlm’). Also, the learning function used are the gradient descent weight/bias learning function (‘learngd’).

3.2 Models

In the present work, ANN models are developed to obtain wind speed for forecast length of 1 hour and wind energy for forecast lengths of 3, 6, 12 and 24 hours. The available database concerns the wind farm is in the form of average wind speeds obtained through anemometric measurements and collected every 10 minutes. The wind speed data is divided into training dataset (years I, II, III) and test dataset (year IV). For each of the prediction lengths, results are obtained for Multi Layer Feed Forward Networks. The required functional relationship for the hourly average wind speeds observed for the site may be expressed as,

1 1 2 3( , , , ,...)t t t t tv f v v v v+ − − −= (3)

where vti is the hourly average wind speed of periods before t. The required functional relationship for the hourly wind energy observed for the site may be expressed as,

1, 2, 3( , ,...)t

i t t t ti t

P f v v v v∆

− − −=

=∑ (4)

where ∆t is the forecast length for the wind energy prediction (3, 6, 12 and 24 hours), Pi is the hourly wind energy and vti is the hourly average wind speed of periods before t. Energy wind is calculated by the mean power curve of turbines of park. There is no systematic approach for selection of the input variables which could be followed, but certain statistical parameters can be used to determine the relevant inputs. In this work an autocorrelation coefficient (ρ) was




Table 1: Statistical properties of wind speed for the site.

Wind speed Training set (years I,II,III) Test set (year IV) Minimum 0 0.34

Maximum 26.38 24.837

Mean 6.6 6.77

Standard deviation 4.1805 4.3148

Table 2: MSE for different number of inputs and prediction lengths (global training set).

Number of inputs 1 hour 3 hours 6 hours 12 hours 24 hours

7 0,0167 0,05 0,05 0,183 0,2

16 0,011 0,047 0,039 0,1 0,1

24 0,02 0,04539 0,01 0,0967 0,13

36 0,033 0,1 0,028 0,09 0,111

48 0,06 0,15 0,03 0,098 0,08

Table 3: Architecture network: Multi-layer feed forward networks. (1): (vt, vt-1, vt-2, …vt-16), (2): (vt, vt-1, vt-2, …vt-24), (3): (vt, vt-1, vt-2, …vt-24), (4): (vt, vt-1, vt-2, …vt-36), (5): (vt, vt-1, vt-2, …vt-48).

Parameters 1 hour 3 hours 6 hours Training function TRAINLM TRAINLM TRAINLM

Adapt learning function LEARNGD LEARNGD LEARNGD

Performance function MSE MSE MSE

Number layers 3 3 3

Neurons (layer 1) –inputs 16 (1) 24 (2) 24 (3)

Neurons (layer 2) 8 12 12

Neurons (layer 3) –output 1 (vt+1) 1 (Pt:t+3) 1(Pt:t+6)

Activation function hidden layer Tansig tansig tansig

Activation function output layer Purelin Purelin purelin

Epochs 150 300 100

Parameters 12 hours 24 hoursTraining function TRAINLM TRAINLM

Adapt learning function LEARNGD LEARNGD

Performance function MSE MSE

Number layers 3 3

Neurons (layer 1) –inputs 36 (4) 48 (5)

Neurons (layer 2) 18 24

Neurons (layer 3) –output 1(Pt:t+12) 1(Pt:t+24)

Activation function hidden layer Tansig tansig

Activation function output layer Purelin purelin

Epochs 200 200




used to obtain the required number of inputs for the models. The values of autocorrelation coefficient give an indication about the number of previous data values which are significant for forecasting the wind speed at a future time point. The database is partitioned into two disjoint subsets: training and test set. The motivation is to assess the network’s ability to generalize supplying a data set different from the one used for parameter estimation. Also, the target’s network for the prediction of 1 hour in advance is wind speed while for the prediction in the time horizon of 3-24 hours is the wind energy. The statistical properties of the wind speed data and for the various sets are given in table 1. Before training, inputs and targets are scaled so that they always fall within a specified range of [-1,1]. Post processing is done while simulating the network after the training process. For the selected network type and architecture, the parameters (weights and bias values) are assumed as random values. The parameters relevant in the training algorithm, error goal and number of epochs. Table 2 shows the observed MSE for different number of inputs and prediction lengths. Table 3 shows the principal parameters assumed for the networks.

4 Results and discussion

ANNs models are developed, simulated and tested for forecast lengths of 1 hour, 3, 6, 12 and 24 hours. So, in the following, results of network simulations were shown. In order to show the model accuracy, the results using the ANNs models, are compared with the observations. The MSE function, expressed as:

2

1

1 ( ( ) ( ))N

kMSE t k o k

N =

= −∑ (5)

measures the network’s performance according to the mean of squared errors. The correspondent values are shown in table 4. Results of network simulations are compared in terms of average percentage error on test data set. As shown in fig. 3, the approximation of the prediction of wind speed in the 1-hour ahead and for the two week of test set is good. During training of network the MSE stabilizes at value of 0.0115968 after 150 epoch.

Table 4: Values of performance function of ANNs – MSE.

ANNs 1 hour 3 hours 6 hours 12 hours 24 hours

MSE 0.0115968 0.04539 0.1 0.09769 0.08069

Forecast errors increase with increasing of prediction length. Fig. 4 shows the simulated of the network’s output for forecast energy for all time horizons in two weeks of test data. In the 3 hours ahead (a) the output of the network approximates the observed energy with an error greater than the error realized for forecasting the wind speed in the 1 hour ahead. The value of the MSE stabilizes at 0.05 after 300 epochs of learning. In the 6 hours ahead (b), the output of the




network approximates the observed energy with an error greater than the error realized obtained for forecasting the wind energy in the 1 and 3 hours ahead. The value of the MSE stabilizes at 0.1 after 100 epochs of learning. (c) shows the simulated of the network’s output for forecast energy in the 12 hours ahead, the value of the MSE stabilizes at 0.09769 after 200 epochs of learning. (d) shows the simulated of the network’s output for forecast energy in the 24 hours ahead, the value of the MSE stabilizes at 0.08069 after 200 epochs of learning.

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Figure 3: ANN for prediction of wind velocity (adimensionalized with respect to the maximum observed velocity in the period) – Prediction length of 1 hour.

The 24-hour forecast is the longest horizon forecast included in this study, and is well outside the acknowledged boundaries for statistical estimation of wind speed, as described in literature. The ANN method for prediction shows signs of reduced accuracy at this range. Fig. 5 shows the fraction of average errors on wind energy observed for the test set and for all prediction lengths. For prediction length of 1 hour the average percentage error on the power observed changes from a minimum of 1% (April) to a maximum of 2.6% (November). From April to August these figures show a lower error than winter months. This is correlated with the result of the statistical analysis in fact the wind speeds in winter months were higher than summer months: the neural network has major difficult to prediction the high wind speeds, so prediction errors in these months are greater. For prediction length of 3 hours the average percentage error on energy observed changes from a minimum of 7% (July) to a maximum of 12% (January). For prediction length of 6 hours the average percentage error changes from a minimum of 10% (December) to a maximum of 16% (August). For prediction length of 12 hours the average percentage error changes from a




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Figure 4: Forecast of wind energy (adimensionalized with respect to the

maximum observed value in the period) – different prediction length.

minimum of 13% (December) to a maximum of 18% (August-February). For prediction length of 24 hours the error on energy observed changes from a minimum of 16% (December) to a maximum of 25,5% (February).




So, with the extension of prediction time horizon, the reliability of a prediction based only the statistical methods reducing considerably. The maximum error rate is 25% with time horizon of 12 and 24 hours so we cannot consider acceptable these forecasts. Fig. 6 shows the fraction of standard deviation of prediction errors for all prediction lengths.

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Figure 5: Fraction of average errors on wind energy observed for the test set and for all prediction lengths.

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Figure 6: Fraction of standard deviation error on wind energy observed for the test set and for all prediction lengths.




5 Conclusions and perspectives

The present paper has developed artificial neural networks (ANN) models to forecast the wind power prediction of a wind farm for different time horizons. We have shown how wind power density forecasts, for lead times from one to 24 hours ahead, can be generated from wind speed observations. There is a clear difference in the ability of ANN forecast models applied to different time horizons. The results show that for a forecast horizon under 6 hours this method can be considered a valid instrument to support control by the management of a wind park. The study shows lower errors compared to those found in literature to forecast one hour in advance [7]. The reliability of a prediction based only the statistical methods reducing considerably, with the extension of prediction time horizon. The error rate is 20% with time horizon of 12 and 24 hours so we cannot consider these forecasts to be acceptable. For prediction with time horizons of 12 and 24 hours other methods should be investigated because forecasts with neural networks are not reliable. We believe that the errors obtained could be reduced with a neural network able of taking different atmospheric variables as inputs, such as wind direction (useful particularly for prediction of higher speeds), pressure, temperature, etc. Also, we think that an application, in future work, of mixed methods such as neuro-fuzzy networks, will be useful to obtain reliable wind forecasts.

Nomenclature

E= global error o(k)= network’s output t(k)= network’s target

ti iw= connection weight α = momentum factor η = learning rate ∆t =forecast length Pi=hourly wind energy MSE=mean square error

References

[1] Burton, N. J. & Bossanyi, Wind energy handbook, Wiley 2001. [2] Bossanyi, E.A. Short-term stochastic wind prediction and possible control

application, Proceedings of the Delphi Workshop on “Wind Energy Application” Greece (1985), pp. 137-142.

[3] Kariniotakis, N.E. & Stavrakakis, Advanced short-term forecasting of wind power production, Proceedings of the 1996 European Union Wind Energy Conference EUWEC’97 , Dublin, Ireland, 1997, pp. 751-754.




v = average wind speed t

[4] Dibike, P.C, Temporal neural networks for downscaling climate variability and extremes, Proceedings of the 2005 International Joint Conference on Neural Networks, Montreal, Canada, 2005.

[5] Flores, A. T. & G. Tapia, Application of a control algorithm for wind speed prediction and active power generation, Renewable Energy 30,p. 523-536, 2005.

[6] A. Sfetsos, A novel approach for the forecasting of mean hourly wind speed time series, Renewable Energy, 27 (2), pp. 163-174

[7] Jayaraj, K. P., E. S. & Arun, Wind speed and power prediction using artificial neural networks, European Wind Energy Conference 2004 (EWEC).

[8] Huang, Z.S., Chalabi, Use of time-series analysis to model and forecast wind speed, Journal of Wind Engineering and Industrial Aerodynamics, 56, pp. 311-322, 1995.

[9] Giebel, R. B, G. K., The state-of-the-art in short-term prediction of wind power. a literature overview. Wind Energy 6(3), pp.273-280, 2003.

[10] C. Mohrlen, Uncertainty in wind energy forecasting, 2004, PhD Thesis. [11] More, D.MC, Forecasting wind with neural networks, Marine Structures

2003, 16: 35-49. [12] Demuth, M. B., M.H, Neural network toolbox 5, User’s Guide, The

mathworks. [13] Krose & Van der Smagt, Mathematics, an introduction to neural networks.

Eighth edition, November 1996 [14] Barbounis, J.B. T, Locally recurrent neural networks for long-term wind

speed and power prediction, Neurocomputing, 69 (4), pp. 466-496, 2006 [15] Barbounis, J.B. T, Locally recurrent neural networks for wind speed

prediction using spatial correlation, Information Sciences, 177 (24), pp. 5775-5797, 2007

[16] Martí, G. K., Evaluation of advanced wind power forecasting models – results of the anemos project. http://anemos.cma.fr

[17] I. Sanchez, Short-term prediction of wind energy production. International Journal of Forecasting, 22 (1), pp.43-56, 2006.




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