EXPERIMENTS IN SHORT-TERM WIND POWER PREDICTION

USING VARIABLE SELECTION

Javier Lorenzo

Institute SIANI, Univ. de Las Palmas de Gran Canaria, Campus Taﬁra, 35017 Las Palmas, Spain

Juan M´endez

Dept. of Inform´atica y Sistemas, Univ. de Las Palmas de Gran Canaria, Campus Taﬁra, 35017 Las Palmas, Spain

Daniel Hern´andez, Modesto Castrill´on

Institute SIANI, Univ. de Las Palmas de Gran Canaria, Campus Taﬁra, 35017 Las Palmas, Spain

Keywords:

Machine learning, Neural networks, k-NN, Short-term wind farm power prediction.

Abstract:

In this paper some experiments have been realized to test how the introduction of variable selection has an

effect on the predictor performance in short-term wind farm power prediction. Variable selection based on

Kraskov estimation of the mutual information will be used due to its capability to deal with sets of continuous

random variables. A Multilayer Percetron and a k-NN estimator will be the predictor based models with

different topologies and number of neighbors. Experiments will be carried out with actual data of wind speed

and power of an experimental wind farm. We also compute the output of an ideal wind turbine to enrich the

dataset and estimate the effect of variable selection on one isolated turbine. This will allow us to deﬁne four

different settings for the experiments which vary in the nature of the inputs to the model, wind speed, wind

farm or isolated wind turbine power, and the predicted variable, wind farm or isolated wind turbine power.

1 INTRODUCTION

Society is very worried about the impact of the human

activities on the environment being pollution a result

of those human activities. Electricity production con-

sumes a big amount of fossilfuel, which producescar-

bon dioxide, so the use of renewable energy sources

will reduce the emission of it. Among the renewable

energy sources, wind is a promising alternative with a

increasing installed power capacity.

However, the wind is not constant and it can be

considered as a chaotic system whose predictability

is limited. This fact along with the increase in in-

stalled power capacity have made that in many coun-

tries research groups have been granted to develop

forecasting systems (Landberg, 2001; Focken et al.,

2002; S´anchez, 2006).

Depending on the forecast horizon, models can

be divided into very short-term, short-term and long-

term models. In each country, the Transmission Sys-

tem Operator have to deal with the management of the

electric system in the different control and planning

levels and also with the power production schedules

in power plants. So the very short-term and short-

term forecasting of wind power production is essen-

tial (Costa et al., 2008).

The statistical models such as ARMA, ARX and

Box-Jenkins methods have been used historically for

very short-term wind forecasting up to few hours

ahead (Costa et al., 2008). Artiﬁcial neural networks

(ANN) have been also used for wind or power fore-

cast due to their ability of dealing with non linear-

ities unlike AR models. Mohandes et al. (Mohan-

des et al., 1998) present a comparison between AR

model and neural networks for wind speed prediction

and obtain that the ANN model outperforms the AR

model in both one day and some days horizon. An-

other comparison between regression and ANN mod-

els was presented by Li et al. (Li et al., 2001) using as

input the speed and direction of the wind in two me-

teorological towers. They found that Multilayer Per-

ceptron ANN model outperforms the best regression

model, which is a 3rd degree polynomial. More re-

cent works have also conﬁrmed the validity of ANN

370

Lorenzo J., Méndez J., Hernández D. and Castrillón M..

EXPERIMENTS IN SHORT-TERM WIND POWER PREDICTION USING VARIABLE SELECTION.

DOI: 10.5220/0003182703700375

In Proceedings of the 3rd International Conference on Agents and Artiﬁcial Intelligence (ICAART-2011), pages 370-375

ISBN: 978-989-8425-40-9

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

v(t)

v(t-1)

v(t-n+1)

p(t+h)

FeatureSelection

Predictor

Figure 1: Wind power prediction based on previous wind

speed with variable (feature) selection.

models for power forecasting (M´endez et al., 2009;

Kusiak et al., 2009).

The selection or extraction of features has demon-

strated that can improve the performance of the in-

duced model in classiﬁcation tasks. In prediction of

time series, feature selection has also been investi-

gated. Kusiak et al. (Kusiak et al., 2009) propose

both feature selection and extraction in short-term and

long-term prediction based on NWP data provided

in 16 locations. Feature selection is used to select

the locations that have more inﬂuence on the predic-

tion. Feature extraction is carried out with PCA to

reduce the high dimensionality of the data provided

by the models, 10 and 12 respectively for each lo-

cation. Interactive Neural Filter (INF) (Crone and

Kourentzes, 2010) is a method that remove the sea-

sonality, trends and noise of a time series that do

not explain it thus removing any bias to the predict-

ing model. In (Yoon et al., 2005) a method called

CLeVer based on PCA and descriptive common prin-

cipal components (DCPC) is presented to select fea-

tures in multivariate time series.

In this paper, we study the effect of feature se-

lection in very-short term wind power forecast using

mutual information. The prediction for different fore-

cast horizons is computed both from wind speed as

previous power generated using Multilayer Percep-

tron (MLP) and k-NN interpolation. The experiments

have been carried out from real wind and power data

of a wind farm. The period of time considered has

been of six months which gives a better understand-

ing of the variable selection incidence. To evaluate the

results, the reference measure described in (Nielsen

et al., 1998) is used.

The paper is organizedas follows: in section 2, the

methodology is presented. Experiments are shown

in section 3 and in section 4 conclusions and further

works are presented.

2 METHODOLOGY

In this work, the inputs to predict the wind farm

power at a horizon h, ˆp(t + h), are wind speeds from

p(t)

p(t-1)

p(t-n+1)

p(t+h)

FeatureSelection

Predictor

Figure 2: Wind power prediction based on previous power

of the wind farm with variable (feature) selection.

SCADA,

ˆp(t + h) = f(v(t), . . . , v(t − n+ 1) (1)

or alternatively, previouspowergenerated by the wind

farm,

ˆp(t + h) = f(p(t), . . . , p(t − n+ 1) (2)

Usually n is estimated with the aid of the autocorrel-

ogram.

In these models, the assumption that all the n

previous measures have the same relevance is done.

However as in many other applications of forecast-

ing, the ranking of the variables according to a rel-

evance measure can improve the performance of the

predictor. As relevance measure Mutual Information

has been chosen because it has proved good results in

feature selection (Chow and Huang, 2005). In time

series, Ji et al. (Ji et al., 2005) propose the use of

the mutual information to rank variables in time se-

ries prediction. Guillen et al. (Guill´en et al., 2010)

also make use of mutual information to prototype and

variable selection in a decremental approach, where

variables are removed while the mutual information is

above a threshold. Here the estimation of mutual in-

formation proposed by Kraskov et al. (Kraskov et al.,

2004), which is based on k-nearest neighbor statistics,

is used. MILCA is a implementation of this method

that can be downloaded from (MILCA, 2010).

A ﬁlter feature selection approach with a sequen-

tial forward selection strategy is going to be imple-

mented (Figures 1 and 2), where a feature selection

stage comes before the forecast module. To assess if

any improvement (Imp

RMSE

) is achieved, a compar-

ison with a reference model (Nielsen et al., 1998) is

carried out using,

Imp

RMSE

reference

− RMSE

model

RMSE

reference

100% (3)

As reference model it is used the one proposed by

Nielsen (Nielsen et al., 1998) which is an improve-

ment over the pure persistence model because it also

includes long-term information using the linear ex-

pression, ˆy(t + k) = b+ ay(t).

EXPERIMENTS IN SHORT-TERM WIND POWER PREDICTION USING VARIABLE SELECTION

371

Table 1: Imp

RMSE

for MLP model (8 neurons in the hidden layer) with different topologies and horizons (in hours) for the

four settings.

Prediction horizon Setting A Setting B Setting C Setting D

h = 1 −313.32± 2.89 −185.20± 3.32 50.10± 16.86 −0.59± 1.15

h = 2 −176.02± 2.25 −110.72± 1.75 63.62± 11.92 3.76± 0.40

h = 3 −122.67± 2.37 −82.11 ± 1.60 71.19± 11.34 6.74 ± 0.23

h = 4 −91.52 ± 1.67 −67.05 ± 1.22 56.24± 9.89 8.03± 0.33

h = 5 −70.08 ± 1.57 −55.53 ± 1.49 47.24± 6.90 9.24± 0.20

h = 6 −54.93 ± 1.36 −48.08 ± 1.78 45.34± 9.72 10.24± 0.33

Table 2: Imp

RMSE

for k-NN (k = 8) for six prediction horizons (in hours) in the four settings.

Prediction horizon Setting A Setting B Setting C Setting d

h = 1 −101.78 −10.20 95.98 −5.73

h = 2 −50.62 −5.02 95.70 0.43

h = 3 −32.94 −4.97 95.57 2.38

h = 4 −22.14 −4.46 95.82 4.88

h = 5 −14.25 −4.32 95.32 5.95

h = 6 −8.91 −4.36 94.98 6.93

3 EXPERIMENTS

Experiments were made with actual wind speeds and

wind farm power obtained from the website of So-

tavento Galicia project. The wind speed series com-

prises from August 5th, 2009 until February 4th, 2010

with time steps of 10 minutes. Data were prepro-

cessed to obtain mean hourly wind speed which yield

a total of 4416 values. The data set was split in two

subset, the train (2/3) and test (1/3). Two models

to predict the very-short term wind power are con-

sidered: Multilayer Perceptron (MLP) and K-Nearest

Neighbor (kNN). Due to the random initialization of

the MLP weigths, we provide the mean and the stan-

dard deviation obtained from 25 training trials as:

µ± σ, in order to reduce the uncertainty of the results.

As it is not possible to access to the power pro-

duced by only one turbine, the output of an ideal wind

turbine (p

vesta

(t)) whose transfer function has 5 and

12.5 m/sec cut-off values is included in the experi-

ments. So, four different settings are going to be con-

sidered in the experiments depending on the predicted

variable and the inputs that feed the models:

Setting A. The predicted variable is the wind farm

power computed from the wind speeds, ˆp(t+h) =

f(v(t), v(t − 1), v(t − 2), . . . ))

Setting B. The predicted variable is the ideal turbine

output computed from the wind speeds, ˆp

vesta

(t +

h) = f (v(t), v(t − 1), v(t − 2), . . . ))

Setting C. The predicted variable is the wind farm

power computed from previous wind farm power

values, ˆp(t + h) = f (p(t), p(t − 1), p(t − 2), . . . ))

Setting D. The predicted variable is the ideal tur-

bine output computed from previous ideal tur-

bine outputs, ˆp

vesta

(t + h) = f(p

vesta

(t), p

vesta

(t −

1), p

vesta

(t − 2), . . . ))

Variables in the previous settings are the wind speed,

wind farm power or ideal turbine output. Coefﬁcients

of the enhanced persistence model (3) for wind farm

power are: A

= 0.9487 and B = 37.5692; and for

ideal turbine output: A

= 0.8947 and B = 0.0281.

3.1 Results without Variable Selection

To allow an analysis of the effect of variable selec-

tion in the problem addressed in this paper, at ﬁrst the

improvement over the reference model (eq. 3) with-

out variable selection is carried out. The number of

variables used for the model induction is set to four

because we have auto correlated the power with itself

and cross correlated it with the wind speed and con-

cluded that the highest values are for offsets until the

range of 4-6 hours back.

In the experiments three different topologies for

the MLP were tested: 4, 6 and 8 neurons in the hidden

layer, however results for the 8 neurons in the hidden

layer are shown in Table 1 due to space constraints. In

Setting A the MLP model performance is lower than

the reference model and this behavior does not de-

pend on the number of neurons in the hidden layer.

Results are a bit better as the horizon is far away al-

though they are still worse than the reference model.

In Setting B the MLP exhibits a better performance

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

372

Table 3: Imp

RMSE

for MLP model (8 neurons in the hidden layer) with different topologies and horizons (in hours) for the

four settings using variable selection.

Prediction horizon Setting A Setting B Setting C Setting d

h = 1 −314.34± 3.00 −185.80± 3.32 46.97± 14.49 0.23± 0.79

h = 2 −177.31± 1.41 −112.11± 1.76 68.81± 9.82 4.00± 0.29

h = 3 −126.23± 2.54 −85.20± 1.34 71.70± 9.29 5.77± 0.33

h = 4 −95.29± 1.78 −70.33 ± 2.04 67.34± 7.33 6.97± 0.29

h = 5 −75.33± 2.19 −59.68 ± 2.61 56.29± 17.40 7.87± 0.43

h = 6 −59.26± 2.35 −52.13 ± 2.85 50.39± 20.27 8.92± 0.26

Table 4: Imp

RMSE

for k-NN (k = 8) for six prediction horizons (in hours) in the four settings using variable selection.

Prediction horizon Setting A Setting B Setting C Setting d

h = 1 −90.16 −10.41 93.91 −6.74

h = 2 −40.98 −6.74 95.74 −1.38

h = 3 −26.62 −5.02 96.63 2.05

h = 4 −19.41 −5.06 94.61 2.59

h = 5 −12.62 −5.92 94.37 3.72

h = 6 −7.65 −7.01 95.73 4.48

but it is still worse than the reference model. No in-

ﬂuence of the number of neurons in the hidden layer is

observed and the farther the horizon is, the better the

results are. When in Setting C the wind farm power is

used as input variable, MLP model clearly surpasses

the reference model with a maximum improvement of

71.19% for a horizon of 3 hours. Unlike previous set-

tings, here the number of neurons in the hidden layer

has inﬂuence over the results but there is no clear pat-

tern because it also depends on the prediction horizon.

In the latter setting, the MLP model achieves better

performance than the reference model although not

so high as in Setting C due to the absence of external

interferences. Only for 1 hour horizon the reference

model is slightly better than the MLP model which is

explained to the high inertia of the atmosphere that is

gathered in the ideal turbine output.

For the data used in this set of experiments it can

be concluded that short-term wind power prediction

based on a MLP model only improves a reference

model based on persistence when the inputs are also

power measures and not wind speeds.

The other model under study is the k-NN interpo-

lation. In this model there is no random initialization

of parameters so one run for each experiment is car-

ried out. As the number of neighbors k used in the ap-

proximation can produce different outcomes, the re-

sults were obtained for values of k from 1 to 10. Due

to space requirements only results for 8 neighbors is

shown in Table 2.

The same four settings are used and the results

achieved with the k-NN model (Table 2) display the

same behavior than the results achieved with the MLP

model. For Setting A, the k-NN model has a worse

performance than the reference model but unlike in

MLP in this model as the number of neighbors in-

creases the result also improves although it never sur-

passes the reference model. In Setting B, k-NN nei-

ther improves the performance of the reference model

although the results are better than in Setting A. Here

the model also yields better results as the number

of neighbor increases as in previous setting. k-NN

model exhibits better improvement in Setting C than

in the other settings. Here the improvements over the

reference model are normally around the 95%. Un-

like the Setting A and Setting B, in this case results do

not always got better as the number of neighbors in-

creases. Finally for Setting D, the results are better as

the horizon and number of neighbors increase.

Comparing the performance of the k-NN with

MLP without variable selection, both models im-

prove the reference model in the same settings but k-

NN model gives better performance than MLP model

when both surpass the reference model. This can be

explained due to fact that k-NN is a non parametric

model and exhibits the ability of modeling any dis-

tribution if the noise level is low. The noise effect is

played down as the number of neighbors is larger.

3.2 Results with Variable Selection

In this section, we repeat the experiments presented in

the previous section using as inputs to the models the

variables selected with Mutual Information (Figures

1 and 2). A time window of twelve hours before to

the prediction time is considered and the subset of the

four variables with highest mutual information is used

to feed the two models. Tables 5, 6, 7 and 8 show the

EXPERIMENTS IN SHORT-TERM WIND POWER PREDICTION USING VARIABLE SELECTION

373

Table 5: Selected variables for the Setting A.

Selected Variables

ˆp(t + 1) v(t), v(t − 1), v(t − 4), v(t − 9)

ˆp(t + 2) v(t), v(t − 5), v(t − 9), v(t − 11)

ˆp(t + 3) v(t), v(t − 4), v(t − 9), v(t − 11)

ˆp(t + 4) v(t), v(t − 3), v(t − 7), v(t − 9)

ˆp(t + 5) v(t), v(t − 4), v(t − 8), v(t − 11)

ˆp(t + 6) v(t), v(t − 5), v(t − 9), v(t − 11)

Table 6: Selected variables for the Setting B.

Selected Variables

ˆp

vesta

(t + 1) v(t), v(t − 1), v(t − 6), v(t − 8)

ˆp

vesta

(t + 2) v(t), v(t − 4), v(t − 10), v(t − 11)

ˆp

vesta

(t + 3) v(t), v(t − 3), v(t − 8), v(t − 11)

ˆp

vesta

(t + 4) v(t, v(t − 2), v(t − 5), v(t − 10)

ˆp

vesta

(t + 5) v(t), v(t − 1), v(t − 5), v(t − 11)

ˆp

vesta

(t + 6) v(t), v(t − 5), v(t − 9), v(t − 10)

selected variables for each setting. As expected, in

all settings the closest value to the prediction instant

(v(t), p(t), p

vesta

(t)) is always selected owing to the

inertia of the atmosphere.

For Setting A, predicting wind farm power from

wind speed (Table 5), it can be observed that selected

variables, except the ﬁrst one, are around v(t − 4),

v(t − 9) and v(t − 11). In Setting B (Table 6) there

is no clear pattern in selected variables and for each

horizon the selected variables differ each others. The

most clear pattern in selected variables appears in Set-

ting C where variables around p(t − 1),p(t − 2) and

p(t − 8) are always selected for the different hori-

zons(Table 7). Finally in Table 8 there is no clear

pattern in the selected variables.

To assess if variable selection has an effect in the

performance of the MLP model we have to compare

Table 1 with Table 3. For Setting A, it can be ob-

served that the introduction of variable selection has

no effect in the performance of the MLP. For the sec-

ond setting, the introduction of variable selection is

not relevant for horizons of 1 and 2 hours and even

worse for far away horizons, where the performance

of the MLP without variable selection is better for all

the topologies. In Setting C, selection increases the

performance of the MLP (Tables 1 and 3), observing

that for horizons from 2 to 6 hours, the improvement

of the MLP over reference model is higher with vari-

able selection but at the expense of a high variance.

Finally in Setting D, the introduction of variable se-

lection does not improve the MLP performance over

reference model because a slight decrease in improve-

ment values is observed for high horizons. After this

analysis we can consider that variable selection has

only a positive effect in Setting C where the wind farm

Table 7: Selected variables for the Setting C.

Selected Variables

ˆp(t + 1) p(t), p(t − 3), p(t − 7), p(t − 9)

ˆp(t + 2) p(t), p(t − 1), p(t − 2), p(t − 8)

ˆp(t + 3) p(t), p(t − 1), p(t − 2), p(t − 7)

ˆp(t + 4) p(t), p(t − 1), p(t − 2), p(t − 8)

ˆp(t + 5) p(t), p(t − 1), p(t − 2), p(t − 7)

ˆp(t + 6) p(t), p(t − 1), p(t − 3), p(t − 8)

Table 8: Selected variables for the Setting D.

Selected Variables

ˆp

vesta

(t + 1) p

vesta

(t), p

vesta

(t − 1), p

vesta

(t − 4),

vesta

(t − 7)

ˆp

vesta

(t + 2) p

vesta

(t), p

vesta

(t − 2), p

vesta

(t − 8),

vesta

(t − 11)

ˆp

vesta

(t + 3) p

vesta

(t), p

vesta

(t − 2), p

vesta

(t − 10),

vesta

(t − 11)

ˆp

vesta

(t + 4) p

vesta

(t), p

vesta

(t − 4), p

vesta

(t − 9),

vesta

(t − 10)

ˆp

vesta

(t + 5) p

vesta

(t), p

vesta

(t − 4), p

vesta

(t − 10),

vesta

(t − 11)

ˆp

vesta

(t + 6) p

vesta

(t), p

vesta

(t − 4), p

vesta

(t − 9),

vesta

(t − 10)

power is predicted from previous measures of gener-

ated power.

Once the effect of the variable selection has been

analyzed for the MLP model, we repeat the same

analysis for the k-NN model. In this case two com-

parisons can be done: one with MLP with variable

selection and another with k-NN without variable se-

lection. The comparison of k-NN model and the MLP

model, both with variable selection, yields the same

results as the comparison of both models without vari-

able selection. k-NN model increase in improvement

is higher when both surpass the reference model and

the explanation is the same that it was given above

(Sec. 3.1).

When comparing k-NN model with and without

variable selection is found that in general there is not

a remarkable effect of the variable selection. For Set-

ting A (Tables 2 and 4) and Setting B the improve-

ments of the k-NN model are lower than the reference

model and it increases as the horizon and the number

of neighbors raise. In Setting C and Setting D, the

effect of the variable selection in the results of the k-

NN model is negligible because they are almost the

same. On sight of the results it can be thought that

k-NN is less affected by the variables because the non

parametric nature of the model which adapts better to

the underlying distribution of the values than the MLP

model.

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

374

4 CONCLUSIONS

In this work we have presented a comparative study

of the use of variable selection in short-term wind

farm power prediction. The variable selection is done

with the Mutual Information that is estimated with the

method proposed by Kraskov. Two models are con-

sidered to study the effect of the variable selection.

One is a Multilayer Perceptron with different topolo-

gies and the other is the k-NN model for different val-

ues of the number of neighbors k.

Four different set of experiments were proposed

with different input and predicted variables. To assess

the quality of the results instead of the RMSE value,

the improvement of the RMSE over an improved per-

sistence model is used.

From the obtained results it can be concluded that

the k-NN model performs better than MLP model for

the different considered horizons and this is more em-

phasized as the number of neighbors increase. An in-

teresting conclusion is that the wind farm power pre-

diction is better done when power is used as predict-

ing variables instead of wind speed. Another fact that

the experiments has brought up and that it is in con-

sonance with the nature of the persistence model, it

is that as the horizon goes farther the MLP and k-NN

models yield better performance.

With respect to the introduction of a previous

stage of variable selection, in the experiments carried

out there is no evidence of a remarkable effect in the

results. In the MLP this effect is a bit noticeable when

predicting the wind farm power from previous mea-

sures of generated power and negligible in the k-NN

model.

ACKNOWLEDGEMENTS

This work has been partially supported by the Ca-

nary Islands government throught the project Sol-

SubC200801000137 and by the Spanish government

and FEDER through the project TIN2008-06068.

REFERENCES

Chow, T. W. S. and Huang, D. (2005). Estimating opti-

mal feature subsets using efﬁcient estimation of high-

dimensional mutual information. IEEE Transactions

on Neural Networks, 16(1):213–224.

Costa, A., Crespo, A., Navarro, J., Lizcano, G., Madsen, H.,

and Feitosa, E. (2008). A review on the young history

of the wind power short-term prediction. Renewable

and Sustainable Energy Reviews, 12(6):1725–1744.

Crone, S. F. and Kourentzes, N. (2010). Feature selection

for time series predictiona combined ﬁlter and wrap-

per approach for neural networks. Neurocomputing,

73:1923–1936.

Focken, U., Lange, M., Monnich, K., Waldl, H., Beyer, H.,

and Luig, A. (2002). Short-term prediction of the

aggregated power output of wind farms - a statisti-

cal analysis of the reduction of the prediction error by

spatial smoothing. Journal of Wind Engineering and

Industrial Aerodynamics, 90:231–246.

Guill´en, A., Herrera, L., Rubio, G., Pomares, H., Lendasse,

A., and Rojas, I. (2010). New method for instance or

prototype selection using mutual information in time

seriesprediction. Neurocomputing, 73:2030–2038.

Ji, Y., Reyhani, N., and Lendasse, A. (2005). Direct

and recursive prediction of time series using mu-

tual information selection. In Computational Intelli-

gence and Bioinspired Systems (IWANN 2005), vol-

ume 3512/2005 of Lecture Notes in Computer Sci-

ence, pages 1010–1017.

Kraskov, A., Stgbauer, H., and Grassberger, P. (2004). Es-

timating mutual information. PHYSICAL REVIEW E,

69(6):066138.

Kusiak, A., Zheng, H., and Song, Z. (2009). Wind farm

power prediction: A data-mining approach. Wind En-

ergy, 12:275–293.

Landberg, L. (2001). Short-term prediction of local wind

conditions. Journal of Wind Engineering and Indus-

trial Aerodynamics, 89:235245.

Li, S., Wunsch, D. C., Ohair, E. A., and Giesselmann, M. G.

(2001). Using neural networks to estimate wind tur-

bine power generation. IEEE Transactions on Energy

Conversion, 16(3):276–282.

M´endez, J., Lorenzo, J., and Hern´andez, M. (2009). Ex-

periments and reference models in training neural net-

works for short-term wind power forecasting in elec-

tricity markets. In Bio-Inspired Systems: Computa-

tional and Ambient Intelligence, volume 5517/2009

of Lecture Notes in Computer Science, pages 1288–

1295.

MILCA (2010). Mutual information least-dependent com-

ponent analysis library. http://www.klab.caltech.edu/

∼kraskov/MILCA/. Last visited july, 2010.

Mohandes, M. A., Rehman, S., and Halawani, T. O. (1998).

A neural networks approach for wind speed predic-

tion. Renewable Energy, 13(3):345 – 354.

Nielsen, T. S., Joensen, A., Madsen, H., Landberg, L., and

Giebel, G. (1998). A new reference for wind power

forecasting. Wind Energy, 1(1):29–34.

S´anchez, I. (2006). Short-term prediction of wind en-

ergy production. International Journal of Forecasting,

22:43–56.

Yoon, H., Yang, K., and Shahabi, C. (2005). Feature sub-

set selection and feature ranking for multivariate time

series. IEEE Transactions on Knowledge and Data

Engineering, 17(9):1186–1198.

EXPERIMENTS IN SHORT-TERM WIND POWER PREDICTION USING VARIABLE SELECTION

375