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And also, its wind energy potential is at an acceptable level. ... EWRES - The European Workshop on Renewable Energy Systems, Antalya, TURKEY, 17-28 Sep ...
2012 - ANTALYA

STATISTICAL AND SPECTRAL ANALYSIS OF WIND SPEED IN KIRKLARELI AREA OF TURKEY Eleonora GUSEINOVIENE1, Audrius SENULIS1, Antanas Andrius BIELSKIS1, Valdas KUČINSKAS1, Tahir Cetin AKINCI2, Serhat SEKER2 [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] 1Klaipeda University, Department of Electrical Engineering, Klaipeda-Lithuania. 2Kirklareli University, Department of Electrical & Electronics Engineering, Kirklareli-Turkey Abstract This study is focused on the statistical and spectral properties of wind speed in Kirklareli city of Turkey. For this purpose, as results of this analysis, Weibull probability density function is determined for the wind speed from the annual data collected in Kirklareli. In this sense, the average wind speed is at around 3 m/sec. Also, spectral properties of the data are extracted by ShortTime Fourier Transform (STFT). Consequently, the data contains three different frequency levels and these are interpreted as reflections of the seasonal variations. The normalized frequency components were determined like 0.01 Hz (Fundamental frequency), 0.085 Hz for Spring-Summer time and 0.665 Hz for the Autumn-Winter.

Keywords: Wind Speed, Statistical parameters, Weibull distribution, Short Time Fourier Transform. 1. Introduction In this study, wind speed measurements are considered for Kirklareli region in Turkey. Kirklareli city takes place in Marmara region of Turkey. In this sense, it is a developing city in the west of Turkey. At the same time, it is a gate of the Turkey which opens to the Europe. And also, its wind energy potential is at an acceptable level. There is no important study for this area in terms of the wind energy [1]. A proper analysis of statistical wind data is a very important step when performing a wind resource assessment campaign which supports a wind energy feasibility initiative [2]. The researches aiming at determining wind energy potential in various regions of Turkey also make up another aspect of these studies. In diverse regions of the country such as Elazığ-Maden [4], Uğurlu and Aydıncık Parts of Gökçeada [5], and Alaçatı [6] which have important wind potential, potential analyses have been carried out with different methods. The measurements used in this study are collected by national meteorology station. This annual data is related to the measurements of 2008 year, from January 1, 2008 to December 31, 2008. There are two important aspects of the study. First one is related to calculation of the statistical parameters of raw data. As a second aspect of the study is the non-stationary data acceptance. Hence the Short Time-Fourier Transform (STFT) is used for the determination of the seasonal transitions under the normalized frequency concept. Consequently these results also show the seasonal effects of the raw data on the time-frequency plan. 2. Mathematical background These mathematical methods used in this study are Weibull distribution and Fourier transforms respectively. 2.1. Weibull Distribution The Weibull probability density function is given by Eq.1.

 k  v  f(v)      c  c 

k 1

  v k  exp     .  c    

(1)

EWRES - The European Workshop on Renewable Energy Systems, Antalya, TURKEY, 17-28 Sep. 2012

Where f(v) is the probability of the measured wind speed v, the coefficient k is the Weibull shape parameter and c is the Weibull scale parameter (m/s). The Weibull shape parameter k generally ranges from 1.5 to 3 for most wind conditions. The cumulative frequency distribution is the integral of the Weibull probability density function, and it is given by Eq.2. [2, 6, 7]:

 F(v)  1  exp    

v  c

k

 .  

(2)

By transforming into logarithmic form, Eq.2 can be expressed by Eq.3.

ln- ln1 - F(v)  k  ln(v)  k  ln(c) .

(3)

2.2 Short Time Fourier Transform and Spectrogram The Short Time Fourier Transform (STFT) introduced by Gabor 1946 is useful in presenting the time localization of frequency components of signals. The STFT spectrum is obtained by windowing the signal through a fixed dimension window. The signal may be considered approximately stationary in this window. The window dimension fixed both time and frequency resolutions. To define the STFT, let us consider a signal x(t) with assumption that it is stationary when it is windowed through a fixed dimension window g(t), centered at time location τ. The Fourier transform of the windowed signal yields the STFT [8].

STFTx(t)  X, f  



 x(t)g(t  τ)exp[- j 2ft]dt .

(4)



The equation maps the signal into a two-dimensional function in the time-frequency (t, f) plane. The analysis depends on the chosen window g(t). Once the window g(t) is chosen, the STFT resolution is fixed over the entire time-frequency plane. In discrete case, it becomes:

STFTx(n)  Xm, f  



 x(n)g(n  m) e- jwn .

(5)

n  

The magnitude squared of the STFT yields the “spectrogram” of the function.

Spectrogramx(t)  X, f  . 2

(6)

3. Application The wind speed variation for Kirklareli area in 2008 can be shown as follows (Figure 1). Annual Wind Energy 12

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EWRES - The European Workshop on Renewable Energy Systems, Antalya, TURKEY, 17-28 Sep. 2012

Probability density function of the wind data is presented by Weibull distribution as given in Section 2. In this sense, this statistical behavior can be shown by (Figure 2). Histogram for the wind speed measurements 3500

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(b) Figure 2. Histogram (a) and probability density function (b) of the Weibull distribution for the data As seen in (Figure 2), the average wind speed is 3.39 m/s and maximum likelihood wind speed is also at around 2.9 m/s.

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EWRES - The European Workshop on Renewable Energy Systems, Antalya, TURKEY, 17-28 Sep. 2012

Power Spectral Density for wind speed data

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(b) Figure 3. Power Spectral Density (a) and Short-Time Fourier Transform (b) of the wind speed variations in Kırklareli Due to the spectral analysis results, dominant frequency peaks are at around 0.1 Hz and 0.7 Hz as seen in (Figure 3 (a)). In terms of more detailed analysis results, (Figure 3 (b)) shows these normalized frequency components depending on the time.

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EWRES - The European Workshop on Renewable Energy Systems, Antalya, TURKEY, 17-28 Sep. 2012

4. Conclusion and discussions The statistical parameters of a distribution can be given by four parameters. These are mean value, standard deviation, skewness and kurtosis. Last two parameters are used to determine the non-Gaussian (or Gaussian) characteristics. Fort his study, the skewness (s) and kurtosis (ku) parameters are found as s>0 and ku >3 respectively. In this manner they indicate asymmetrical and non-Gaussian characteristics. Hence the wind speed distribution is defined by Weibull distribution and its probability density function is shown for shape parameter k=3 and average speed of the wind. Due to this density function most probable wind speed is easily calculated from its mode value. Statistical parameters were calculated of the wind speed data as below: Mean (m) = 1.72, Standard Deviation (s) = 1.01, Skewness (sk) = 1.82 and Kurtosis (ku) = 8.85. According to these results, the distribution is non-Gaussian. And also, as a result of the STFT, the normalized frequency components describing the seasonal variation of the wind speed and their numerical values are given as follows:  0.01 Hz (Fundamental Frequency) for all time;  0.085 Hz for Spring and Summer;  0.665 Hz Autumn and Winter. References [1]. Ersoz, S., Akinci, T. C., Nogay, H. S., Dogan, G., “Determination of wind energy potential in KirklareliTurkey”, International of Green Energy-Taylor & Franchis, Online. 9 March 2012, DOI:10.1080/ 15435075.2011.641702. [2]. Waewsak, J., Chancham, C., Landry, M., Gagnon, Y., “An analysis of wind speed distribution at Thasala, Nakhon si Thammarat, Thailand”, Journal of Sustainable Energy & Environment, 2, (2011), pp.51-55. [3]. Akpınar, E.K.; Akpınar, S.: “Determination of the Wind Energy Potential for Maden-Elazig, Turkey”, Energy Conversion and Management, Vol.45, (2004) 2901-2914. [4]. Eskin, N., Artar, H., Tolun, S., “Wind Energy Potential of Gokceada Island in Turkey”, Renewable and Sustainable Energy Reviews, Vol.12, (2008) 839-851. [5]. Mutlu, Ö. S., Akpınar, E., Balıkçı, A., “Power Quality Analysis of Wind Farm Connected to Alaçatı Substation in Turkey”, Renewable Energy, Vol.34, (2009) 1312-1318. [6]. Gupta, R., Biswas, A., “Wind data analysis of Silchar (Assam, India) by Rayleigh’s and Weibull methods”, Journal of Mechanical Engineering Research, Vol.2, No.1, (2010), pp.010-024. [7]. Lin, L., Hongxing, Y., “Wind Data Analysis and a Case Study of Wind Power Generation in Hong Kong”, Wind Engineering, Vol. 25, No. 2, 2001, pp 116-123. [8]. Seker, S., Akinci, T. C., Taskin, S., “Spectral and Statistical Analysis for Ferroresonance Phenomenon in Electric Power System”, Electrical Engineering-Springer, DOI: 10.1007/s00202-011-0224-4.

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