Saatlik Ve Aylık Rüzgar Verisiyle Rüzgar Enerjisi Modellemesi

Abstract

Hava kütlelerinin hareketi olarak tanımlanan rüzgar, gelecekteki enerji ihtiyacımızın karşılanması bakımından ekonomik ve çevresel önem taşımaktadır. Büyük ölçekli hava hareketleri, temel olarak güneşin yeryüzeyini ve dolayısıyla atmosferi eşit miktarda ısıtmamasından kaynaklanan sıcaklık ve basınç farklılıklarından meydana gelmektedir. Rüzgar, yapısındaki türbülanslı çalkantılar nedeniyle analitik yöntemler yerine, daha çok istatistiksel teknikler kullanılarak, incelenebilmektedir. Bu çalışmada, sadece ortalama rüzgar şiddeti veya istatistiksel bir dağılım fonksiyonu yerine, hem ortalama rüzgar şiddetine hem de standart sapmaya bağlı olarak, V 'ün hesaplanmasında kullanılabilecek ampirik bir model oluşturulmaya çalışılmıştır. Bunun için ortalama rüzgar şiddeti ve standart sapmaya bağlı 10 parametreli bir ampirik model oluşturularak, çoklu regresyon tekniğiyle katsayılar çözülmüş ve V 'ün hesaplanmasında kullanılacak eşitlik elde edilmiştir. Daha sonra step-wise regresyon tekniği uygulanarak, eşitlikteki etkisiz terimler çıkartılmış ve modellerin daha basit bir şekle dönüştürülmesine çalışılmıştır. Çalışmada Türkiye, Avrupa ve Amerika'nın çeşitli istasyonlarında ölçülmüş saatlik rüzgar şiddeti değerleri kullanılmıştır. Çoklu regresyonla elde edilen saatlik model için regresyon katsayısı R2 = % 99.945, Standart Hata SH = 9.135 m Vs3, Step- Wise uygulanması sonucunda ise R2 = % 99.944 ve SH = 9.066 m'Vs3 olarak hesaplanmıştır. Çoklu regresyonla elde edilen aylık modelde ise R2 = % 98.604 ve SH = 46.088 m'Vs3; buna step-wise regresyon uygulanması sonucunda R2= % 98.566 ve SH = 45.871 mVs3 olarak hesaplanmıştır. Elde edilen saatlik modelin, VVeibull Dağılımı yöntemiyle karşılştırılması amacıyla yapılan değerlendirmeye göre bu çalışmadan elde edilen saatlik modelin daha iyi sonuç verdiği söylenebilir. Yapılan diğer bir karşılaştırmada ise küplerin yıllık ortalamasıyla yıllık ortalamanın küpünün oranının ( V JU ) sabit kabul edilemeyeceği konusu ortaya konmuştur. Modellerin, deneme amacıyla bağımsız örneklere uygulanması sonucunda saatlik modelin bağıl hatasının % 10'dan, aylık modelin bağıl hatasının ise % 20'den düşük olduğu hesaplanmıştır. Son olarak elde edilen aylık model, Türkiye'nin 114 meteoroloji istasyonunda gözlenmiş uzun dönem aylık rüzgar şiddeti ortalamalarına uygulanarak, rüzgar enerjisi potansiyeli daha yüksek olan istasyonlar belirlenmeye çalışılmıştır. Buna göre Bozcaada 682,35 mVs3, İskenderun 288.76 m'Vs3, Antakya 269.34 mVs3, Bandırma 245.31 mVs3, Çanakkale 211.78 m'Vs3 ile Türkiye'nin en yüksek rüzgar enerjisi potansiyeline sahip meteoroloji istasyonlarıdır.

Modeling Wind Energy Using Hourly And Monthly Wind Data Winds result from the fact that the equatorial regions of the Earth receive more solar energy than the polar regions, and this sets up large-scale convection currents in the atmosphere. The total energy in the atmosphere can be divided into potential and kinetic energy, the latter being only a small fraction of the potential energy. Winds are the results of the conversion of atmospheric potential energy into kinetic energy, mainly through the work of pressure gradients. One per cent of the daily wind energy input is equivalent to the present world daily energy consumption. On the other hand, on current estimates, fossil fuels will be depleted by the year 2250, and until that time their use will continue to pollute the atmosphere, land and sea. It has been said that renewable energy resources can and must meet all the future energy demands of the world. Therefore, work to promote renewable energy resources, and the development of new models, techniques and technologies related to them must be an essential part of any strategy for future energy policy. A number of models, and techniques have been developed to evaluate the wind energy potential and to determine locations having higher potentials for utilizing wind energy. The objective of this study is to develop a model to be used to evaluate the annual cube average (third moment) of hourly wind speed, assuming that only the mean and the standard deviation of the data are known. Models are attempted for two cases: 1. The statistical properties calculated using hourly data over a year, 2. The statistical properties calculated using monthly data over a year. Before going further into the constitution of the models, İt would be worthwhile to overview the nature of wind and the basic laws it obeys together with a review of the statistical principles related to wind speed measurement and prediction. Winds, in the macro-meteorological sense, are movements of air masses in the atmosphere. These large-scale movements are generated primarily by gradients in the temperature within the atmosphere which are due to non-uniform solar heating. As the energy per unit surface area received from the sun depends on geographical latitude, temperature differences and hence pressure gradients can arise between different geographical locations, which, together with the centripetal force and the Coriolis force associated with the rotation of the Earth, induce movements of the air masses known as gradient wind. If the effects of the centripetal forces are neglected then the phenomenon is called geostrophic wind. The lower region of the atmosphere, with a thickness that varies between 100 m and 2 km, is known as the planetary boundary layer. Movement of air in this region is retarded by frictional forces and large obstructions on the surface of the Earth, as well as by Reynolds stresses produced by the vertical exchange of momentum due to turbulence. Turbulence, which may be mechanical and/or thermal in origin, also causes rapid fluctuations in the wind velocity over a wide range of frequencies and amplitudes, commonly known as gusts. In the atmospheric surface layer which forms the lower 10 % of the atmospheric boundary layer, the wind profile for high wind speeds over a flat, homogeneous terrain cari be expressed by the logarithmic wind law. A., -,, where, w(z)is the wind speed at a height Z above ground, Z0 is the roughness length of the surface, k is the Von Karman constant and U* is the friction velocity The main characteristics of the flow in the region near the ground can be summarized as following: Wind speed increases with height; there are wind speed fluctuations, that is turbulence; the turbulence is spread over a broad range of frequencies; the turbulence at different heights is correlated, the correlation being stronger for small separations and at low frequencies. Turbulent fluctuations in wind speed are random in character and so cannot be analyzed using deterministic methods, but are best defined using statistical techniques. In order to separate the short period fluctuations of wind speed due to mixing from the long-term changes associated with macro-scale meteorological phenomena, the concept of mean wind speed is introduced. A spectral analysis of surface wind records by van der Hoven indicates that a good averaging period for defining mean wind speed lies between 20 min. and 1 hour. The direction free wind distribution can be expressed using the Rayleigh Distribution. However, in most cases the more flexible two parameter (A: scale, k: shape) Weibull distribution better represents the frequency distribution of wind. The probability density function for the Weibull distribution can be written as f^-Mî. fc-i exp u 7k) U> 0 where U is the wind speed. 147 Data sets consisting of hourly wind speed observations from Turkey, Europe and the USA have been used in this study. The flow chart given below expresses the methodology used for the preparation of input data for modeling, which are the annual cube average of hourly mean wind speeds ( V ), annual average of hourly wind speeds ( U ) and annual standard deviation of hourly ( SH ) and monthly ( SM ) mean wind speeds. /.ww/AwJw/y/AV>AW/wiw«/.' W.'sjj*MŞfffîWMJsSjjSSW&M&JM.j*ij*MwSJj&. % hourly wind speed data annual average 8760 ma S"H /7-I ii standard deviation (hourly)

i "go v- r " V 8760-1 in" " ' % ?M U H ^V.VAV»V'AV.V.VAV//AV.VdVJVkV,V^^/tV^/AW^,ViVV^iWA*AVA'''.'AW/A*J Pi monthly means 24»m !j VlH = 24"" S"H I standard deviation (monthly) third moment | 8760 8760 £,"" Evaluations show that the annual average of hourly mean wind speeds is equal to the annual averagi of monthly mean wind speeds, But, annual standard deviation of hourly mean wind speeds is not equal to the standard deviation of monthly mean wind speeds. It is clear that the annual standard deviations of hourly mean wind speeds are far larger than those calculated from monthly mean wind speeds. In this study, some well-known equations found in the literature which are used for wind energy evaluation are also overviewed. At a given time the power of wind incident on a surface of area A can be expressed by the following equation. P = \pAu3 where p is the air density. It is generally accepted that in order to perform a meaningful assessment of the wind climate of a particular site, data collected over a period at least 10 years is required. In order to evaluate the mean wind power density, it is necessary to know the annual cube average of hourly wind data (third moment). Its calculation is done by the statistical formula given by the following equation. i N where N is the number of observation. In this thesis, two empirical formulae are introduced to perform the calculation of V by using some statistical properties of wind data. These are the annual average of hourly wind speed, and standard deviation for the first case, and the annual average of monthly mean wind speed and standard deviation for the second case. In order to obtain a homogeneous model, that is one with dimensionless coefficients, the following equation is proposed, where all the terms in the equation have the dimension of ^ (m3/s3). U4 sx Vx3 = aQ + axU2 + a2U2 Sx + a2Usl + a4Sx + a5 U5 Sİ si ft/2V (slY + e Converting this to have the form of a linear multiple regression, the following equation is obtained. Y = a0 + axX{ + a2X2 + a3X3 + aAXA + a5X5 + cl^Xg + cijX7 + a.gX8 + a9X9 + al0Xl0 + 8 The subscript X refers to hourly (H) or monthly (M) data as appropriate and e represents errors arising from the regression process. It has to be noted that the annual average of hourly wind speeds and the annual average of monthly mean winds are equal. Therefore, a subscript has not been used for annual average of wind speeds in the equations. The equations represented by this model are solved using multiple linear regression by minimizing the error sum of squares, at the first stage. It is assumed that the errors are independent and have a normal distribution with mean zero and variance a2. At the second stage the method of step-wise regression is applied and is tried to reduce the number of independent variables, leaving only the most influential ones, whilst at the same time keeping the correlation coefficient high. In this thesis the step wise forward selection procedure is used. This method is a modified forward selection method in which f-value for each term in the model is calculated, compared to the corresponding tabular value of F, and rejected if it is not significant at the pre-set significance level. The next term is then added to the model and the process is repeated. In this study the pre-set F-ratio is selected to be 1 and the confidence level is selected to be 95%. The following empirical models are obtained from application of the above regression techniques to the available data sets:. Hourly Data - Multiple Regression V^=4.211323+%380.16953f/3-1.74*105f/2SH+2.05*I05[/s?/ -li8*105sL-3.37*104- + 6725.693379-^- + 76 157.06004^ H sH &H u - 2.1 *104^Ş- 586.438295 -- ? "^ -T00*1 °" U 2 VshJ +2514.794895 \Uj . Hourly Data - Step-wise Regression U5 si Vft = 4.109469 + 2.598748C/2 SH + 0.255322^- + 5.012789^4 -0.077133 rjj2\ 3 -2.554761 fç2 ^ wH/ uj S2H U' Monthly Data - Multiple Regression V&= 35.261001 -5864.538918LT3+50910.073779[/2Sm - 279603.71^ + 973300.İSİ, + 412.381274 U~ >M -16.065241-^4-- 2074215^- + 2459787-, U U2 5 M Sm rTTi\ + 0.264866 U 1239085 WAT/ V U j Monthly Data - Step-wise Regression V& = 32.772152 - 1.577858C/3 + 41.237016L/2 SM 145.15081 lUsh + 165.62231 5 sir + 5.38. 10 -4 rV2\ M \sm) As it can be seen from the equations, number of terms reduced from 1 0 to 5 by applying step-wise regression technique, whilst the R2 values remain almost the same. A summary of some statistical criteria used to check the quality of the models. As can be seen from the table, R2 values are high and all the F-ratios are bigger than the corresponding F-critic, indicating that the models are significant. Furthermore, residual averages are almost zero, as expected. In addition, calculated skewness coefficients for the hourly models indicate that the frequency distributions of residuals coming from the hourly models are normal. However, the frequency distributions of the residuals from monthly models are not normal. Calculated skewness coefficients are 1.96 and 2, which are both greater than 0.5 indicating that the distributions are right skewed. The relative errors, expressed as {(observation - model)* J 00 observation} vary between -10 % and +10 % for hourly models. In contrast, relative errors rise above 100 % for monthly models (at 3 stations). It has to be noted that relative errors calculated for 64 of the stations are below 10 % and for 104 stations they are below 20 %. As a conclusion, it can be said that hourly models are significant and can be applied with a high reliability. However, monthly models are not reliable as hourly models, despite the high R2 and F-value. It can also be added that the results obtained from the models for the stations having very low" mean wind speed (<2 m/s) are less reliable. 1 Here R: (adj.) is the R: adjusted for degrees of freedom, SE is Standard Error. MAE is Mean Absolute Error. F-critic is the table value according to degrees of freedom and significance level. Res is residual. >3SV is the number of standardized residual tliat is greater than.1 SE. In order to make a better assessment of the reliability of the models they are compared to some models available in the literature. Comparisons with the Weibull Model indicate that the new hourly models introduced in this study are more reliable. The average of the residuals due to the Weibull model is 1. 1 m3/s3 and the standard error is 21.1 nrVs3 which are greater than those from the new hourly models. Moreover, it is found that the number of stations with standardized residuals greater than 3Sy is 4 for the Weibull model, but only 3 for the new hourly model. Another investigation which is done here is to compare the ratio of annual cube average of hourly wind speeds with the cube of annual average of hourly wind speeds. Results show that the ratio is not constant and varies between 1.5 and 10. The models are also applied to 17 new hourly wind data sets and it is found that relative errors from the hourly model are less than 1 0 % and those from the monthly model are less then 20 %. Finally, the monthly model is applied to long term averaged monthly data from 1 14 meteorology stations in Turkey. According to the evaluations it is clear that the meteorology stations having higher wind energy potential are as follows: Bozcaada 682.35 mVs\ İskenderun 288.76 m3/s\ Antakya 269.34 nrVs3, Bandırma 245.31 mVs"\ Çanakkale 21 1.78 m"Vs"\ Gökçeada 163.32 m3/s? and Sinop 153.66 nrVs3. In conclusion, in situations* where a level of relative error around 10% and 20% for hourly and monthly data respectively, can be tolerated, these models can form viable alternatives to the existing techniques.