International Journal of Scientific & Engineering Research Volume 3, Issue 7, June-2012 1

ISSN 2229-5518

Wind Speed Behavioral Modeling for Economical

Energy Generation using Windmills

K. Aboul-Seoud, Alaa El-Din Sayed Hafez, Mohamed Abd El-latif, A. Abou-Raya

Abstract— the energy generation using windmills depends mainly on the wind speed which has a random behavior so; it is difficult to create statistical approaches with prior and deterministic parameters. Since wind speed is directly affected by some factors such as seasons, ye ars, solar activities and land breeze, the behavioral modeling can be achieved. Prediction of wind speed is essential in order to protect systems in-action from the effects of strong winds. In this paper, data represent wind speed in Alexandria, Egypt has been obtained over a time window of twenty ye ars. The frequency spec- trum of the wind speed data have been obtained using Fourier transform (FT). The spectrum is fitted by twelve Gaussian distributions wh ich are trans- formed back to the time domain. The central amplitudes are modified to accurately represent the actual time domain dat a using two different approac h- es. The proposed model is tested through the prediction of wind speed profile over the next two years following the available data window. The predicted data are compared with the actual ones. The constructed model showed a gr eat consistency and high accuracy in modeling the wind speed behavioral in the selected site.

Index TermsW ind speed prediction, W ind power generation, Power systems

—————————— ——————————

1 INTRODUCTION

he energy is a vital input for the social and economic de- velopment of any nation. With increasing agricultural and industrial activities in the country, the demand for energy
is also increasing. Formulation of an energy model will help in the proper allocation of widely available renewable energy sources as solar, wind, bioenergy and hydropower in meeting future energy needs. A study of the energy models helps ener- gy planning, research and policy making. The use of wind energy has been developed significantly throughout the world, in order to get an electric power without pollution. Wind speed is non-linear fluctuation. So; forecasting is very difficult in normal method. Many techniques can be used in solving a nonlinear problem such as the intelligent engineering represented by a neural network, a genetic algorithm, a chaos fractal. Literature reports provide different models for wind speed prediction [1-7]. Tore et al. used first order Markov chain models for synthetic generation of hourly wind speed time series in the Corsica region [8]. Youcef Ettoumi et al. have modeled wind speed and wind direction data by means of Markov chains [9].
Shamshad et al. have generated a wind speed model using
wind speed data measured from two different regions in Ma-
laysia [10]. Recently, Hocaoglu et al. also modeled the wind
speed data [11]. This paper proposes a wind speed model for
Alexandria, Egypt over a window of twenty years. This model
is used to evaluate the economy, size and specifications of
windmills to be installed. The predictive model is developed
and tested for the region of Alexandria on the northern coast of
Egypt.

2 PROPOSED MODEL FOR WIND SPEED PREDICTION

Data represents the wind speed at Alexandria area over twen- ty years window were obtained and stored as a data base. This data was used to construct the proposed model. Fourier trans- form is used to introduce the frequency spectrum and phase angle of the wind speed data at maximum amplitudes. Figure -

1 clarifies the frequency spectrum obtained where it forms a continuous function having twelve peaks in the frequency range between one hour to twenty years. The average wind speed is taken as a pole at zero frequency. The different peaks were fitted as Gaussian functions with complex amplitudes and real arguments given by the following equation,
where:

W(f) is the Fourier transform of the wind speed along a window of twenty years, (f) is the frequency, (fn) is the cen- tral frequency of the Gaussian function, ( n) is the standard deviation of the nth Gaussian function, (a0) is the average wind speed, and (an) is the maximum value of the nth Gaussian dis- tribution. Due to the above assumption the predictive wind speed function in time domain can be described as follows:

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K. Aboul-Seoud Alexandria University , Senior Member IEEE

Alaa El-Din Sayed Hafez , Alexandria University , Senior Member IEEE E-mail: Alaahafez @ieee.org

Mohamed Abd El-latif , Alexandria University, Member IEEE

E-mail: Turbocode_2000@yahoo.com

A. Abou-Raya, Alexandria University


where:
W(t) is the inverse Fourier transform of W(f), (b0) is the average wind speed, and (bn) is the coefficient in time domain corres- ponding to frequency domain coefficients. The real exponen-

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tial term decays to zero as time tends to infinity. This means that the predicted value will be vanished with time. To over- come this problem, a time series can be written in the form,

where:
W’(t) is the modified predicted wind speed function. (b0) is the average wind speed; (Cn) is a coefficient used in minimizing the difference between the proposed model and the actual da- ta. The coefficient Cn in the above equation can be obtained using two different approaches.

Fig.1. Frequency spectrum of wind speed data ranging between

1- Hour and twenty years in Alexandria- Egypt

2.1 Model Fitting


The cooefeicient Cn that is used to minimize the difference be- tween the prosed model and actual data can be calculated us- ing two approaches , the first one is a delta function where in time domain , the real part of Gaussian function is approx- imated by a delta function in the form :
The second approach to calculate the fitting parameter Cn is the time seires where in time domain both the frequencies of the cosine series and the phase angles corresponding to the peaks detected in the frequency spectrum is constructed. The cooefiecient are determined using a least root mean square (LMS) regression technique based on the available hourly data of the twenty years window.

3 SIMULATION RESULTS

The power spectrum plot of figure -1 can be represented by a set of Gaussian functions given in table-1. The two models can be constructed as explained before. The different values of the coefficient (Cn) are calculated.

TABLE- I

GAUSSIAN FUNCTIONS FITTING THE WIND SPEED SPECTRUM


The actual data for the wind speed in Alexandria- Egypt through the 21st and 22nd years were obtained and compared with the calculated predicted data using the above two mod- els, a high accuracy results have been obtained . To evaluate the proposed model performance, a cross correlation function at = 0 between the predicted and actual data in the 21th and
22th years have been calculated, the equation used can be writ- ten as follows:

where:

Wa(t) and Wp(t) are the actual and the predicted data of wind speed for Alexandria, Egypt respectively. The obtained re- sults are shown in tables (2-3).

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TABLE-2

NORMALIZED CROSS CORRELATION COEFFICIENTS BETWEEN THE ACTUAL AND PREDICTED W IND SPEED DATA FOR THE 21TH YEAR

0.94

0.92

0.9

0.88

0.86

0.84

0.82

0.8

0.78

0.76

Cross correlation using the proposed model with first approach

Cross correlation using the proposed model with second approach

0.74

0 2 4 6 8 10 12

Months of year

Fig.3 Comparison of wind speed cross correlation values of the proposed model using two different approaches for the 22th year

TABLE 3

NORMALIZED CROSS CORRELATION COEFFICIENTS BETW EEN THE ACTUAL AND PREDICTED W IND SPEED DATA FOR THE 22TH YEAR

It is clear that a better correlation have been obtained using
time series approach for the 21th and 22th years.

The proposed model using in wind speed prediction and windmills output is shown in figure – 4
Wind speed at Alexandria-Egypt area over twenty year's window
Proposed model using Fourier transform and time series ap-
Predicted wind speed
From the above tables, it is clear that the proposed model fit the actual data with very high accuracy. Comparison of wind speed cross correlation value of the proposed model using two different approaches is shown in figures (2-3).

0.94

0.92

0.9

0.88

0.86

0.84

Fig.4 W ind speed prediction and windmills output determination

0.82

0.8

0.78

Cross correlation using the proposed model with first approach

Cross correlation using the proposed model with second approach

4 CONCLUSION

In this paper, a predictive model for wind speed in Alex-

0.7 0 2 4 6 8 10 12

andria-Egypt is constructed. The model performance is

Months of year

Fig .2 Comparison of wind speed cross correlation values of the proposed model using two different approaches for the 21th year

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evaluated by cross correlating the predicted and the actual data for two years. It has been found that the predicted da- ta has a higher cross correlation values during day times
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rather than night times. It has also been found that smaller cross correlation is obtained in the winter months com- pared to those of summer months. This is due to the weather nature stability during the summer season. The proposed model which has been constructed using the time series method showed superiority over many pub- lished techniques. A very important advantage obtained using the suggested model is that, moving away from the data window has no effect on the predicted data.

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